P ima y and Seconda y Relaxa ions
in Nea and Bina y Glass Fo me s
S udied by Means o
Dielec ic Spec oscopy
Von de Uni e si ¨a Bay eu h zu
E langung des G ades eines Dok o s
de Na u wissenscha en (D . e . na .)
genehmig e Abhandlung
on
Robe Kahlau
gebo en am 3. Juni 1982 in Cobu g
E s e Gu ach e : P o . D . E ns R¨oßle
Zwei e Gu ach e : P o . D . Roland B¨ohme
Tag de Ein eichung: 10. Janua 2014
Tag des Kolloquiums: 12. M¨a z 2014
Falls Go die Wel gescha en ha , wa seine
Haup so ge siche nich , sie so zu machen,
dass wi sie e s ehen k¨onnen.
Albe Eins ein
Con en s
1 Abs ac 5
2 Ku zda s ellung 9
3 Ex ended Abs ac 13
3.1 In oduc ion.............................. 13
3.2 P ope ies o Liquids, Supe cooled Liquids and Glasses . . . . . . 15
3.3 Molecula Dynamics o a Liquid . . . . . . . . . . . . . . . . . . . 17
3.4 Dynamic He e ogenei ies . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Dielec ic Spec oscopy . . . . . . . . . . . . . . . . . . . . . . . . 21
3.5.1 Dipole Fluc ua ions and Mac oscopic Pola iza ion . . . . . 21
3.5.2 S a ic Elec ic Fields . . . . . . . . . . . . . . . . . . . . . 23
3.5.3 Dynamic Response . . . . . . . . . . . . . . . . . . . . . . 25
3.5.4 Measu emen Se up . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Con empo a y B oadband Dielec ic Spec oscopy . . . . . . . . . 32
3.7 Exis ing App oaches o Desc ibe Gene ic Relaxa ion Phenomena,
Open Ques ions, and Majo Resul s . . . . . . . . . . . . . . . . . 35
4 Publica ions 53
4.1 Gene aliza ion o he Cole–Da idson and Kohl ausch Func ions o
Desc ibe he P ima y Response o Glass-Fo ming Sys ems . . . . 59
4.2 E olu ion o Excess Wing and β-P ocess in Simple Glass Fo me s 67
4.3 Quinaldine: Accessing Two C ys alline Polymo phs ia he Supe -
cooledLiquid ............................. 79
4.4 Seconda y Relaxa ions in a Se ies o O ganic Phospha e Glasses
Re ealed by Dielec ic Spec oscopy . . . . . . . . . . . . . . . . . 91
4.5 On he Coope a i e Na u e o he β-P ocess in Nea and Bina y
Glasses: A Dielec ic and Nuclea Magne ic Resonance Spec osco-
pyS udy................................ 101
4.6 Dynamics o Asymme ic Bina y Glass Fo me s. I. A Dielec ic and
Nuclea Magne ic Resonance Spec oscopy S udy . . . . . . . . . 115
Bibliog aphy 129
Danksagung 137

1 Abs ac
The subjec o his hesis is he in es iga ion o nea and bina y molecula glass
o me s s udied wi h he help o dielec ic spec oscopy (DS). One o wo main
in e es s ollowed by his hesis is o e ine he gene ic pic u e o he dynamic
suscep ibili y, including he empe a u e e olu ion o p ima y and seconda y e-
laxa ion phenomena. The o he objec i e is o gain insigh in o he mic oscopic
o igin o he β-p ocess (a seconda y elaxa ion obse ed o T.Tg) in nea and
bina y sys ems, as well as he p ima y elaxa ion phenomena in bina y sys ems.
The esul s o all in es iga ions a e collec ed in six pa ially in e ela ed publica-
ions.
Th ee classes o glass o ming sys ems a e analyzed: ype-A sys ems showing no
disce nible β-p ocess, bu in mos cases he so-called excess wing (EW) appea ing
as a powe law ε00(ν)∝ν−γin he suscep ibili y a equencies beyond he α-peak
posi ion (ννmax); ype-B sys ems which ha e a β-p ocess clea ly esol ed as a
suscep ibili y peak; and bina y sys ems which a e ep esen ed by mix u es o he
ype-A sys em polys y ene (PS, Mw≈2 kg/mol) and he ype-B sys em ip opyl
phospha e (TPP) in his hesis.
The analysis o ype-A sys ems as p esen ed in Pape s 1 & 2 is based on he
applica ion o a speci ically in oduced h ee-pa ame e i unc ion, which in-
e pola es con inuously be ween Kohl ausch and Cole–Da idson spec al shapes.
Wi h he help o his unc ion small empe a u e-a ec ed spec al changes o he
α-peak can be assigned ully o a a ia ion o i s low- equency beha io . In he
amewo k o his ansa z he me hod o spec al analysis, which has become usual
o be applied o ype-A sys ems by ou g oup, can be ad anced.
The in es iga ion o he ype-A glass o me quinaldine (2-me hyl quinoline)
leads o he disco e y o a amily o subs ances which ha e me as able dielec i-
cally ac i e c ys alline polymo phs. Dielec ic spec a o all obse ed phases a e
p esen ed in Pape 3. The phase ansi ions, occu ing in he deeply supe cooled
s a e, show empe a u e-dependen ans o ma ion kine ics, which a e acked
and quan i ied by pe o ming long- e m DS expe imen s. As a consequence o he
empe a u e dependence o he ans o ma ion kine ics, he me as able phases
(including he supe cooled liquid) can be kine ically s abilized by lowe ing em-
pe a u e. In addi ion o DS expe imen s X- ay di ac ion (XRD) and di e en ial
scanning calo ime y (DSC) measu emen s a e pe o med, which help o cha ac-
e ize he quinaldine phases and o ack hei phase ansi ions.
Fu he , a amily o nea , chemically ela ed ype-B glass o me s, i.e. symme ic
phospho ic es e s, a e in es iga ed in Pape 4 in o de o ind a possible co ela ion
be ween hei molecula s uc u es and he co esponding molecula dynamics, in
5
1 Abs ac
pa icula conce ning he β-p ocesses. In wo aspec s a uni e sal beha io o hei
β-p ocesses is obse ed. Fi s ly, empe a u e-independen dis ibu ions o ac i a-
ion ene gies g(E), which con ol he spec al e olu ion o he β-p ocesses, a e
ound o all sys ems o empe a u es well below he glass ansi ion empe a u e
(T < 0.9Tg). Secondly, he elaxa ion s eng h ∆εβ(T) is nea ly cons an o
T < 0.9Tg. When Tgis app oached (T > 0.9Tg), a dis inc inc ease o he mean
ac i a ion ene gy as well as a s ong inc ease o he elaxa ion s eng h is obse ed.
Bo h men ioned p ope ies a e in e p e ed o be sensi i e o he so ening o he
glassy sample nea Tg, poin ing, in u n, owa ds he coope a i e na u e o he
β-p ocesses. Since he beha io o ∆εβ(T) is known o s uc u al as well as o
o ien a ional glasses made up by igid molecules, and since no s ong co ela ion
be ween g(E) and he numbe o in e nal deg ees o eedom o he phospho ic
es e s is ound, all ypes o β-p ocesses appea o be mainly de e mined by in e -
molecula in e ac ions and a e no o me ely local na u e. Ra he hey may be
conside ed as a gene ic ea u e o he glass ansi ion.
The sys em TPP/PS, a so-called asymme ic bina y glass o me wi h a Tg
con as o ∆Tg= 201 K, is in es iga ed in he o m o a join s udy by DS and
31P/2H NMR, suppo ed by depola ized ligh sca e ing (DLS) as well as DSC ex-
pe imen s. The esul s a e collec ed in Pape s 5 & 6. T ip opyl phospha e (TPP),
which is also subjec o he jus summa ized s udy on phospho ic es e s, ac s
now as low-Tgcomponen wi h a well- esol ed β-p ocess. The high-Tgcomponen
polys y ene (PS) has a ela i ely low molecula mass and shows no indica ion o
aβ- elaxa ion. The β-p ocess ound in nea TPP is also obse ed in he mix-
u es (Pape 5), and o high TPP concen a ions (cT P P ) i s p ope ies a e nea ly
concen a ion-independen . Selec i e NMR expe imen s p o e he coope a i e na-
u e o he β-p ocess: he β- elaxa ion, which is induced by he TPP molecules, is
imposed on he PS monome s in he mix u e. NMR expe imen s show ha , when
cT P P is educed con inuously, he e exis inc easing ac ions o TPP molecules as
well as PS monome s no being in ol ed in he β-p ocess.
Due o he high Tgcon as o he componen s in TPP/PS, wo p ima y e-
laxa ions (α1and α2) and, co espondingly, wo calo ime ic glass ansi ion em-
pe a u es (Tg1and Tg2) a e esol ed (Pape 6). Selec i e NMR expe imen s allow
o a gene al assignmen o he α1- elaxa ion o ma ix dynamics and o he α2-
elaxa ion o addi i e dynamics. On he o he hand, i is shown ha a ac ion o
TPP molecules is in ol ed in he ma ix dynamics, i.e. he molecules elax on he
long ime scale o he PS monome s. The analysis o he DS spec a shows ha
his ac ion is empe a u e-dependen and anishes abo e a empe a u e Tc. As a
u he esul , he α2-p ocess is ound o change i s appea ance wi h a ying TPP
concen a ion: a high cT P P i s empe a u e-dependen peak shape esembles he
α-peak o a liquid in con inemen , while i s ime cons an s ollow a non-A henian
empe a u e dependence. While, on he one hand, NMR expe imen s p o e ha
he α2-p ocess is also iso opic a low cT P P , i de elops, on he o he hand, in o
a he mally ac i a ed p ocess wi h a empe a u e-independen dis ibu ion o ac-
i a ion ene gies g(E) when cT P P is dec eased. In addi ion, a u he educ ion
6
o cT P P leads o a dec ease o he mean ac i a ion ene gy o he α2-p ocess. As
a consequence, he glass ansi ion empe a u e ela ed o he α2- elaxa ion (Tg2)
exhibi s a maximum a in e media e TPP concen a ions.
7
3 Ex ended Abs ac
Figu e 3.1: (a) Ske ch o he dynamic anges o se e al expe imen al me hods; igu e aken
om [14]. (b) Ske ch o he dynamic anges o he dielec ic me hods applied
by P. Lunkenheime and co-wo ke s in Augsbu g; igu e aken om [15]. Red
ma ks indica e he dynamic ange o he DS se up used o his hesis.
he o he hand, co e ing 14 decades o mo e o a physical p ope y is na u ally an
expe imen al challenge, oo. Figu e 3.1 (a) gi es an o e iew o he accessible co -
ela ion ime anges o se e al expe imen al me hods p obing molecula dynamics
o liquids [14]. Neu on sca e ing (NS), op ical Ke e ec (OKE) and depola -
ized ligh sca e ing (DLS) consis ing o pho on co ela ion spec oscopy (PCS)
and he applica ion o a double monoch oma o in combina ion wi h a andem
Fab y–P´e o in e e ome e (DM/FPI) a e aken in o accoun , besides dielec ic
spec oscopy (DS), solid s a e NMR me hods (2D NMR, s imula ed echo) and
as ield cycling (FC) elaxome y. Ob iously, DS co e s he wides dynamical
ange wi hou any gaps, which is again demons a ed in Fig. 3.1 (b), whe e he
equency anges o he dielec ic me hods used by A. Loidl, P. Lunkenheime and
co-wo ke s in Augsbu g a e compiled [15]. The dynamical ange co e ed in his
hesis is ma ked ed in bo h pa s o Fig. 3.1. Dielec ic spec oscopy has he
u he ad an age o a uniquely la ge esolu ion, i.e. dielec ic losses o 10−4a e
s ill measu ed wi h high accu acy wi h up- o-da e ins umen s. Due o his high
esolu ion, e en iny seconda y elaxa ion ea u es o small a ia ions o he main
elaxa ion peak a e disco e ed wi h he help o dielec ic spec oscopy. O en i
is di icul o judge i he obse ed phenomena a e quali a i ely gene ic ea u es
o he glass ansi ion o a he indi idual p ope ies o he analyzed subs ance.
Consequen ly, he es ablishmen o a cohe en pic u e o he empe a u e e olu-
ion o he dynamic suscep ibili y o supe cooled liquids and glasses cons i u es a
g ea challenge and is one impo an issue deal wi h in his hesis.
Since DS is, compa ed o NMR me hods, basically no selec i e o di e en
ypes o molecules wi hin he sample, NMR expe imen s a e indispensable in his
hesis o he in es iga ion o he complex dynamics o a bina y sys em. Also o
14

3.2 P ope ies o Liquids, Supe cooled Liquids and Glasses
gaining new in o ma ion on he mic oscopic o igin o seconda y (β-) elaxa ions
he combina ion o DS and NMR is a success ul ecipe.
3.2 P ope ies o Liquids, Supe cooled Liquids and
Glasses
A liquid is a o m o condensed ma e , i.e. an ensemble o pa icles (e.g. a oms,
molecules, monome ic uni s o polyme chains, pa icles o colloidal suspensions)
wi h in e -pa icle dis ances o he o de o he pa icle size [11]. The s uc u e o
a liquid shows sho ange o de , bu no long ange o de . This is demons a ed
in Fig. 3.2 ( aken om [16]), whe e he adial dis ibu ion unc ion g( ) o liquid
a gon is plo ed, clea ly showing b oad pe iodic peaks which lose in ensi y a
highe . Liquids show a low comp essibili y and a high densi y, jus like c ys als.
Figu e 3.2: Radial dis ibu ion unc ion g( )o liquid A gon a T= 85 K [16].
Unlike c ys als, liquids show a ini e iscosi y being s ill highe han he iscosi y
o gases wi h much la ge in e -pa icle dis ances.
The eason o he luid cha ac e o liquids lies in he mobili y o hei pa icles,
which ha e o ea ange pe manen ly when he liquid lows. In his con ex he
S okes-Eins ein equa ion
D=kT
6πηR (3.1)
is usually ci ed, which connec s he di usion coe icien Dwi h he iscosi y η, a
mac oscopic p ope y. Toge he wi h
h 2i= 6D , (3.2)
which is alid o di usional p ocesses in h ee-dimensional space on long ime
scales, i ollows ha he mean squa ed displacemen o a pa icle o he liquid
pe uni ime inc eases wi h dec easing iscosi y [11,17].
15
3 Ex ended Abs ac
Cooling a liquid and, a he same ime, a oiding any phase ansi ions like he
c ys alliza ion below Tm, esul s in smoo h a ia ions o all mac oscopic p ope -
ies. Va iables like he he modynamic po en ials, hea capaci y o speci ic olume
unde go only small changes, while he iscosi y ηinc eases o e 14 decades [18].
Simila o he inc ease o η, he s uc u al elaxa ion ime τo he liquid unde -
goes a emendous inc ease un il any labo a o y ime scale is exceeded. Then no
ea angemen o he mic oscopic pa icles in he sample is possible any mo e. In
he simples case he sample has become a s uc u al glass wi h he mechanical
p ope ies o a solid (η→ ∞) and he s uc u e o a liquid (c . g( ) in Fig. 3.2).
Figu e 3.3 shows he empe a u e dependence o he en opy S(T) o o- e phenyl.
The black line ollows he he modynamically s able beha io o he sample: a
he mel ing poin Tm he i s o de phase ansi ion be ween liquid and c ys al
mani es s i sel as a s ep in S(T). I a liquid sample is supe cooled below Tm he
en opy e olu ion o he liquid is con inued (blue solid line). He e, al hough he
liquid phase is no he he modynamically s able s a e, he sample may be con-
side ed as being in he mal equilib ium (i.e. he equilib ium o he liquid phase)
as long as any expe imen is pe o med a e wai ing a leas o he s uc u al
elaxa ion ime τ(τobs ≥τ). When empe a u e alls u he , τexceeds labo a-
o y ime scales (τobs τ). A his poin , any measu emen will in es iga e a
non-e godic sample which is s uc u ally a es ed o , espec i ely, a sample s ill
app oaching equilib ium (compa e so-called aging expe imen s [19, 20]). The en-
opy e olu ion (now ep esen a i e o any he modynamic a iable) bends o e
and uns nea ly pa allel o (o mimics) S(T) o he c ys al ( ed solid line in Fig.
3.3). In his empe a u e egime he sample is conside ed o be in he glassy
s a e. The glass empe a u e Tgis only a bi a ily de inable since no phase ansi-
ion is obse able be ween liquid and glass. Con en ionally, he calo ime ic Tgis
de ined as he onse o he “glass-s ep” in he DSC (di e en ial scanning calo ime-
y) signal eco ded a he hea ing a e Q= 10 K/min, de ec ing he empe a u e
whe e he s uc u al elaxa ion ime is on he o de o τ≈100 s (see, e.g., [21]).
An o en p e e ed, mo e p ecise de ini ion ollows he ule τα(Tg) = 102s, i.e.
he co ela ion ime o molecula eo ien a ion, which is accessed amongs o he
me hods by dielec ic spec oscopy, assumes 100 s a he glass empe a u e. Fu -
he , independen o he applied de ini ion, Tgdepends s ongly on he cooling
a e [17,22].
In Fig. 3.3 he so-called Kauzmann pa adox [23] is ske ched, which is no ob-
se ed in eal expe imen s bu which is o heo e ical ele ance: i he supe cooled
liquid was u he cooled e y slowly in o de o allow o ull elaxa ion, he en-
opy e olu ion o he liquid is assumed o be con inued unin e up edly (dashed
line in Fig. 3.3). As a consequence, S(T) o he supe cooled liquid would, i s ly,
in e sec he en opy cu e o he c ys al a he Kauzmann empe a u e TKand,
secondly, inally anish a ini e empe a u es. Di e en heo e ical scena ios a e
possible in o de o esol e his pa adox, e.g. a phase ansi ion o an ideal glassy
s a e [24, 25]. Ye an answe canno be ound expe iman ally since τinc eases
abo e expe imen ally accessible ime scales al eady abo e TK.
16
3.3 Molecula Dynamics o a Liquid
Figu e 3.3: En opy S(T)o o- e phenyl, aken om [26].
The pic u e o he dynamic glass ansi ion gi en abo e may be gene alized o
any supe coolable phase, e.g. plas ic c ys als and o o phases [1–9, 27] o ming
o ien a ional glasses, o colloidal suspensions [28, 29]. Fu he , a glass ansi ion
can be induced by pa ially emo ing he sol en o a solu ion [10].
3.3 Molecula Dynamics o a Liquid
In he ollowing sec ion a close look on he pa icle dynamics o supe cooled
liquids shall be aken by in oducing he incohe en in e media e sca e ing unc-
ion Fs(q, ), which e lec s he (q-dependen ) au oco ela ion o he posi ion o a
agged pa icle.
In Fig. 3.4 (a) Fs(q, ) o a Lenna d-Jones mix u e, as ob ained by a molecula
dynamics simula ion [30,31], is shown o di e en simula ion empe a u es Tand
a cons an q=qmax = 7.25, he la e de ining he maximum posi ion o he s uc-
u e ac o S(q). Choosing q- alues in he icini y o qmax assu es ha dynamics
on mic oscopic leng h scales (compa able o in e -pa icle dis ances) on co e-
spondingly sho ime scales a e p obed, which u he allows o a compa ison
wi h o he expe imen al me hods, e.g. p obing molecula eo ien a ion [32–35].
Co ela ion imes (now and in he ollowing called τ) ob ained o such leng h
scales a e hus compa able wi h he s uc u al elaxa ion ime in oduced abo e.
Inspec ing now Fig. 3.4 (a), a single-s ep co ela ion decay a high empe a u es
is obse ed, which app oxima ely has he shape o a simple exponen ial decay.
When Tis dec eased, he cu e shi s o longe imes and, simul aneously, de-
elops in o a wo-s ep decay. Fig. 3.4 (b) displays he same da a as pa (a),
now scaled o he co ela ion ime τ, he e de ined as he poin o ime when
Fs(q, ) has eached he alue e−1. F om his ep esen a ion one can in e ha
he long- ime pa s o he wo-s ep decays collapse o a common mas e cu e.
Addi ionally, hey a e mo e s e ched han he single-s ep decays co esponding
o highes empe a u es. The empe a u e independence o he cu e shapes is
17
3 Ex ended Abs ac
Figu e 3.4: Incohe en in e media e sca e ing unc ion o one componen o a bina y
Lenna d-Jones liquid (solid lines). Figu es adap ed om [31]. Simula ion em-
pe a u es Tindica ed. (a) Raw simula ion da a. (b) Da a scaled o co ela ion
ime τ. Dashed lines: guides o he eye.
a phenomenon usually e e ed o as ime- empe a u e supe posi ion (TTS) o ,
in equency domain, equency- empe a u e supe posi ion (FTS). The wo-s ep
cha ac e o he co ela ion unc ions as well as he alidi y o TTS/FTS and
he non-exponen iali y (s e ching) o he long ime beha io a e cha ac e is ic
o “glassy dynamics”, i.e. he molecula dynamics o liquids appea ing below he
boiling poin , ye well abo e he mel ing poin (Tm< T < Tb) [36].
Figu e 3.5 shows he mean squa ed displacemen h 2( )io one componen o
he bina y Lenna d-Jones liquid jus discussed. He e, ano he ypical signa u e
o glassy dynamics is seen: looking a i s o high empe a u e cu es in Fig. 3.5
(a), a c osso e om h 2( )i ∝ 2a sho imes o ∝ 1a long imes is obse ed.
When Tis dec eased, he whole cu e shi s o longe imes, and he 1- egime
becomes mo e and mo e sepa a ed om he h 2( )i ∝ 2- egime by a pla eau (∝ 0)
eme ging a in e media e imes. The 2- egime is called ballis ic egime. He e he
Figu e 3.5: Mean squa ed displacemen o one componen o a bina y Lenna d-Jones liq-
uid. Figu es aken om [30]. Simula ion empe a u es Tindica ed. (a) Raw
simula ion da a. (b) Da a scaled o long ime beha io (see abscissa).
18
3.3 Molecula Dynamics o a Liquid
pa icle simply mo es a a cons an eloci y. On longe ime scales he pa icle
ine i ably in e ac s wi h i s neighbo s. Thus, he mechanism o ansla ion mus
ans o m in o a di usi e p ocess a long imes, mani es ing i sel as a 1-law
(di usi e egime). When empe a u e is lowe ed, he di usi e p ocess is slowed
down mo e s ongly han he ballis ic one, leading o a sepa a ion o bo h egimes.
In be ween a pla eau eme ges, because a in e media e imes he pa icle is apped
by i s neighbo s o a ce ain pe iod. This is usually e e ed o as he “cage
e ec ” [11]. A longe imes he pa icle escapes again om i s cage ia he
delayed di usional p ocess. Figu e 3.5 (b) shows he same da a as pa (a) a e
scaling he abscissa wi h he empe a u e-dependen di usion coe icien D(T).
Simila o he scaling beha io demons a ed o Fs(q, ) in Fig. 3.4 (b) he long
ime pa s o he h 2( )icollapse.
In many cases he mic oscopic pa icles o a liquid a e no highly symme ic
objec s like he pa icles in he simula ion jus conside ed; he la e in e ac ia
sphe ically symme ic po en ials. Molecula liquids, o example, consis o gen-
e ally asymme ic molecules. The spa ial ea angemen o he molecules, leading
inally o he ull decay o Fs(q, ), in ol es also hei eo ien a ion. P obing
molecula eo ien a ions o supe cooled liquids wi h he help o di e en me hods,
hus, cons i u es a a ie y o expe imen al ways o in es iga e he glass an-
si ion. The expe imen al me hod o depola ized ligh sca e ing (DLS) p obes
collec i e molecula eo ien a ions by measu ing he collec i e eo ien a ional au-
oco ela ion unc ion C(2)( ) o he aniso opic pa o he molecula pola izabili y
enso [36,37]. Figu e 3.6 shows he ime domain ep esen a ion o DLS da a o
m- ic esylphospha e (m-TCP). Fo all empe a u es a mono onic decay o C(2)( )
om 1 o 0 is obse ed. When Tis dec eased, he cu e shi s o longe imes and,
abo e all, de elops in o a wo-s ep decay. This eme gence o a wo-s ep co ela ion
unc ion upon cooling is compa able o he empe a u e e olu ion o he Fs(q, )-
cu es in Fig. 3.4 as well as he h 2( )i-da a in Fig. 3.5, and is conside ed again
as he signa u e o glassy dynamics. The e minal elaxa ion in Fig. 3.6 will la e
be a ibu ed o he s uc u al elaxa ion o α-p ocess o he liquid. On cooling
close o Tg, he e minal loss o co ela ion shi s o long imes. The co esponding
co ela ion imes inc ease abou wel e o de s o magni ude om τ≈10−11 s o
τ≈101s, which is again he mani es a ion o he glass ansi ion desc ibed abo e.
F om Fig. 3.6 one also in e s ha TTS is ul illed o e he comple e empe a u e
ange. This is demons a ed o he T= 290 K ≈Tmcu e, which ma ches exac ly
he shape o he T= 207 K ≈Tgcu e (blue dashed line). Lowe ing empe a u e
below Tgwould esul in he e minal decay shi ing ou o he accessible ime
ange. The sample would all ou o equilib ium, since he expe imen akes place
on a sho e ime scale han he s uc u al elaxa ion o he sample. Then, he
sample may be conside ed as a glass.
As will become clea below, dielec ic spec oscopy (DS) expe imen s e eal a
mul i ude o dynamical p ocesses, which appea on ime scales be ween he sho
ime limi and he e minal s ep o he co ela ion unc ion. The analysis o he
19

3 Ex ended Abs ac
Figu e 3.6: Time domain ep esen a ion o DM/TFPI as well as pho on co ela ion spec-
oscopy da a o m- ic esyl phospha e ( ed solid lines), aken om [36]. Dashed
blue line: da a om T= 290 K shi ed on op o he T= 207 K cu e.
mani es a ion o hese p ocesses as spec al ea u es in he dielec ic suscep ibili y
is he ac ual scope o his wo k.
3.4 Dynamic He e ogenei ies
Al hough he o igin o he phenomenon is no cla i ied, i is a commonly accep ed
iew ha supe cooled liquids show dynamic he e ogenei y [26,38–41]. This means
ha di e en subensembles o molecules in he liquid show di e en mobili ies,
which causes a dis ibu ion o co ela ion imes. Figu e 3.7 shows esul s o a
molecula dynamics simula ion o a bina y Lenna d-Jones liquid. He e, each a ow
indica es he displacemen o a pa icle a e some wai ing ime on he o de o
he s uc u al elaxa ion ime. As can be seen clea ly, spa ially con iguous egions
o qui e di e en mobili ies a e ound, demons a ing s ong spa ial co ela ions.
The e a e also expe imen al a emp s o explo e dynamic he e ogenei ies. Rus-
sel e al. de ec ed he luc ua ions o dielec ic p ope ies o a poly enyl-ace a e
ilm on nm-scale wi h he help o a piezo-can ile e o an a omic o ce mic o-
scope [42, 43]. The au ho s ound domains o common dynamical p ope ies on
he leng h scale o abou 10 nm, su i ing on he ime scale o he s uc u al e-
laxa ion. Ano he expe imen al possibili y o moni o ing dynamic he e ogenei ies
a e, e.g., non- esonan dielec ic hole bu ning expe imen s [39,44,45]. I a sample
shows dynamic he e ogenei y, his me hod leads o a selec i e hea ing o dynam-
ically ela ed subensembles o molecules, which leads o a de o ma ion o he
dis ibu ion o co ela ion imes G(ln τ). Blochowicz e al. [45] ound pa icula ly
s ong e ec s in bina y mix u es. Bina y sys ems analyzed wi hin his hesis by
DS and NMR show, likewise, b oad dis ibu ions o co ela ion imes, which a e
a ibu ed o s ong dynamic he e ogenei ies.
20
3.5 Dielec ic Spec oscopy
Figu e 3.7: MD simula ion esul s o a bina y Lenna d-Jones mix u e in wo dimensions.
A ows o di e en leng hs indica e single pa icle displacemen s a e a pe iod
o he o de o he s uc u al elaxa ion ime. Figu e aken om [41].
Dynamic he e ogenei y is a possible explana ion o he decoupling o di usi i y
and iscosi y close o Tg[38,46], which is subjec o many expe imen al app oaches.
Fo example Edige e al. [47] analyze c ys alliza ion kine ics o se e al o ganic and
ino ganic sys ems in o de o ind a dependence D∝η−ξwi h ξ < 1 ( ac ional
S okes-Eins ein ela ion, compa e Eq. 3.1). Mapes e al. [48] ind a iola ion o Eq.
3.1 by pe o ming acuum deso p ion expe imen s wi h p o ona ed/deu e a ed
o- e phenyl bilaye ilms, and Ehlich e al. [49] use o ced Rayleigh sca e ing a
holog aphic g a ings made o se e al glass o me s. Impo an o men ion a e also
he con ibu ions by S ickel e al. [50,51], whe e he decoupling o he s uc u al
elaxa ion ime om he ionic conduc i i y con ibu ion o he dielec ic loss (see
below) is in e p e ed as a decoupling o iscosi y om di usi i y.
3.5 Dielec ic Spec oscopy
3.5.1 Dipole Fluc ua ions and Mac oscopic Pola iza ion
Reo ien a ions o pola pa icles (i.e. pola molecules o molecula liquids o pola
monome ic uni s in polyme mel s) cause luc ua ions o he mac oscopic pola -
iza ion
~
Po ( ) = 1
VX
i
~µi( ) (3.3)
o he sample, whe e Vis he sample olume and ~µia e he pe manen dipole
momen s o he molecules. No e ha he ime a e age o ~
Po anishes when no
21
3 Ex ended Abs ac
ex e nal ield is p esen . When he liquid unde in es iga ion is placed in o a
capaci o , hese luc ua ions can be measu ed. The ac ual quan i y o in e es ,
wi h a clea a omis ic meaning, is he dipole au oco ela ion unc ion
Cµ( ) = 1
µ2h~µ(0)~µ( )i,(3.4)
wi h h·i deno ing he ensemble a e age [44,52,53]. Cµ( ) is a single pa icle au o-
co ela ion unc ion and has o be connec ed wi h he (collec i e) au oco ela ion
unc ion o he mac oscopic pola iza ion CP( ):
CP( ) = h~
Po (0)~
Po ( )i
h~
Po (0)~
Po (0)i=
N
P
i,j=1
h~µi(0)~µj( )i
N
P
i,j=1
h~µi(0)~µj(0)i
=
N
P
i=1
h~µi(0)~µi( )i+
N
P
i,j=1
i6=j
h~µi(0)~µj( )i
Nµ2+
N
P
i,j=1
i6=j
h~µi(0)~µj(0)i
.(3.5)
He e he sum e ms wi h iden ical indices (i=j) a e au oco ela ion con ibu ions,
while exp essions wi h i6=j ep esen so-called c oss-co ela ion con ibu ions. I
he la e anish due o some app oxima ion, he exp ession
CP( ) = 1
Nµ2
N
X
i=1
h~µi(0)~µi( )i=1
µ2h~µ(0)~µ( )i=Cµ( ) (3.6)
ollows. One could a gue ha his app oxima ion ne e holds in pola liquids.
Howe e , i is usually assumed ha he c oss-co ela ion con ibu ions beha e
simila ly o he au oco ela ion e ms [54] and, hus, do no play a signi ican ole.
As a u he app oxima ion, he equi alence o ensemble and ime a e age, ac ually
only alid in e godic sys ems [55], is ex ended o empe a u es below Tg, i.e. o
he modynamic si ua ions whe e he liquid has allen ou o equilib ium. Thus,
he au oco ela ion unc ion o he mac oscopic pola iza ion may be gene ally
de ined as
CP( ) = h~
Po (0)~
Po ( )i= lim
T→∞ 
1
T
T
Z
0
~
Po (τ)~
Po (τ+ ) dτ
.(3.7)
22
3.5 Dielec ic Spec oscopy
Acco ding o he Wiene -Khin chine heo em [56,57], he spec al densi y o dipole
luc ua ions can be o mula ed like [58]
SP(ω) = 1
2
∞
Z
−∞
CP( ) exp [iω ] d =
∞
Z
0
CP( ) cos(ω ) d . (3.8)
The las equali y in Eq. 3.8 is due o he ac ha CP( ) is an e en unc ion.
Dielec ic spec al densi ies o glyce ol and PVC ha e been measu ed abo e and
below Tgby Is aelo e al. [59,60]. As will become clea below, molecula dynamics
may be in es iga ed al e na i ely by measu ing he eac ion o he sample o an
ex e nal ield. In o de o adap his s a emen o dielec ic spec oscopy, he
ques ion o how elec ic ields in e ac wi h pola samples has o be add essed a
i s .
3.5.2 S a ic Elec ic Fields
I a s a ic ex e nal elec ic ield is p esen , a non- anishing ime a e age o he
mac oscopic pola iza ion ~
Pis ound. I he ex e nal ield is su icien ly low, he
linea dependence ~
P=ε0χ
:
~
E(3.9)
wi h he gene ally enso ial suscep ibili y χ
:
is a good app oxima ion. The mac o-
scopic pola iza ion consis s o he o ien a ional pa ~
Po (c . p e ious sec ion) and
a con ibu ion ~
Pind due o a de o ma ion o he molecula cha ge densi y dis i-
bu ion:
~
P=~
Po +~
Pind and (3.10)
χ
:
=χ
:
o
+χ
:
ind
.(3.11)
When he dynamic esponse is discussed (see nex sec ion), his has o be kep in
mind. The dielec ic displacemen is hen calcula ed o
~
D=ε0~
E+~
P
=ε0
1
:+χ
:~
E
=ε0ε
:
~
E(3.12)
23
3 Ex ended Abs ac
and he sapphi e disk secu e a spacing o abou 60 µm be ween bo h elec odes,
whe e he liquid sample unde in es iga ion is placed. No addi ional space ma-
e ial like, e.g., ibe glass is equi ed o his se up. The diame e o he uppe
elec ode is abou 18 mm, which leads o an emp y capaci y C0≈38 pF. As can
be in e ed om Fig. 3.9, he e is enough space abo e he uppe elec ode o col-
lec excess sample ma e ial no i ing in he gap be ween he elec odes. When
bina y liquids we e measu ed, he O- ing in he lowe elec ode was used o p e-
en e apo a ion o he ola ile componen and, hus, o keep he concen a ion
o he mix u e cons an .
The sample capaci o was connec ed o he “Alpha-A Analyze ” by No ocon-
ol, which ope a es in he equency ange ν= 10−3–107Hz. Since measu ing
below ν= 10−2Hz is e y ime consuming, he lowe bound o he equency
ange was limi ed o ν= 10−2Hz o mos measu emen s. Since measu emen a -
i ac s a ound ν= 106Hz end o in luence he esul s, da a acqui ed in he ange
ν= 105–107Hz a e pa ially omi ed in he igu es. Fo he equency-dependen
measu emen a ha monic ol age
ˆ
U(ω, ) = U0exp(iω ) (3.36)
is applied o he sample. The phase-sensi i e de ec ion o he cu en ˆ
I(ω, ) allows
o he measu emen o he impedance
ˆ
Z=ˆ
U
ˆ
I.(3.37)
Fo a capaci o I=˙
Q=C˙
Uholds, which can be adap ed o he complex p ope -
ies like ˆ
I(ω, ) = ˆ
C(ω)·iω ˆ
U(ω, ) (3.38)
inally leading o
ˆε(ω) = 1
iωC0ˆ
Z(ω).(3.39)
No e ha any DC conduc i i y σo he sample (now hough o as ohmic esis o ),
which appea s solely in he eal pa o he impedance ( ˆ
Z(ω) = R), will con ibu e
exclusi ely o he imagina y pa o he dielec ic unc ion ˆε(ω). In oducing he
esis i i y
ρ=RA
d=RC0
ε0
=1
σ(3.40)
leads o
ˆεcond(ω) = 1
iωC0R=σ
iωε0
(imagina y) (3.41)
and
ε00
cond(ω) = σ
ε0ω.(3.42)
30

3.5 Dielec ic Spec oscopy
The conduc i i y con ibu ion o he dielec ic suscep ibili y gi en in Eq. 3.42
appea s in he o m o a powe law ε00(ω)∝ω−1.
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
-1
10
0
10
1
∼ω
+1
∼ω
-1
ε
''(
ω
)
ω
/ ad s
-1
∼ω
-1
ω
p
=1/
τ
0
5
10
15
ε
∞
ε
'(
ω
)
ε
∞
+
∆ε
Debye unc ion
wi h conduc i i y
τ
=10
-3
s
σ
=
ε
0
∆ε
=10
ε
∞
=1.5
Figu e 3.10: Sum o a Debye unc ion and a ypical DC conduc i i y con ibu ion. Uppe
panel: eal pa ε0(ω)acco ding o Eq. 3.45; lowe panel: imagina y pa ε00(ω)
acco ding o Eq. 3.46.
The simples case o a s ep esponse unc ion is a single exponen ial decay
ΦP( ) = exp −
τ.(3.43)
Acco ding o Eq. 3.31, he co esponding dielec ic unc ion is gi en by
ˆε(ω) = ∆ε
∞
Z
0
−d
d exp −
τexp(−iω ) d +ε∞
= ∆ε·1
1 + iωτ +ε∞(3.44)
(c . also Eq. 3.14) and called Debye unc ion. The co esponding eal and imagi-
na y pa s a e
ε0(ω) = ∆ε·1
1 + ω2τ2+ε∞and
ε00(ω) = ∆ε·ωτ
1 + ω2τ2.(3.45)
Adding a conduc i i y con ibu ion (Eq. 3.42) o he imagina y pa is in acco d
wi h a common app oach, assuming an ohmic esis o connec ed in pa allel o he
31
3 Ex ended Abs ac
sample capaci o , and yields
ε00(ω) = ∆ε·ωτ
1 + ω2τ2+σ
ε0ω.(3.46)
Figu e 3.10 displays eal and imagina y pa o a Debye unc ion including a DC
conduc i i y con ibu ion. The co esponding pa ame e s a e gi en in he igu e.
In he uppe panel he eal pa ε0(ω) acco ding o Eq. 3.45 is shown, decaying
mono onically om ε∞+∆ε o ε∞. The s ep (maximum slope) is si ua ed a ound
ω= 1/τ. The lowe panel o Fig. 3.10 displays he imagina y pa ε00(ω) showing
a peak a ωp= 1/τ. Due o he double loga i hmic ep esen a ion he lanks o
he peak, powe laws ∝ω1and ∝ω−1, appea as s aigh lines. Some equency
decades below ωpa minimum is obse ed; le o he minimum he DC conduc i i y
con ibu ion is ound. The conduc i i y con ibu ion also appea s as a s aigh
line on he low equency side o he peak (powe law ∝ω−1; acco ding o Eqs.
3.42 and 3.46).
When he iso opic molecula eo ien a ion in supe cooled liquids is p obed,
he obse ed suscep ibili y peak, he α-p ocess, is b oadened asymme ically on
he high- equency side in compa ison wi h he Debye peak. This b oadening is
usually in e p e ed as a signa u e o he coope a i e na u e o he α-p ocess. A
dis ibu ion o co ela ion imes due o dynamic he e ogenei ies also co esponds
o a b oadened suscep ibili y peak. Se e al phenomenological i unc ions quan i-
ying he b aodening, such as he Kohl ausch- o he Cole–Da idson- unc ion [52],
o modeled dis ibu ions o co ela ion imes [44, 65] exis ; a new unc ion is dis-
cussed in Pape 1. Ne e heless, he special case o he exponen ial co ela ion
decay and he co esponding Debye line shape o ε00(ω) is expe imen ally obse ed,
oo [66, 67]. A elaxa ion p ocess ound in monoalcohols like n-bu anol [68], 2-
e hyl-1-hexanol [69], e hanol [4] o wa e [68, 70], he mechanism o which is no
ully elucida ed ye , causes a ypical Debye line shape o ε00(ω), and is hus usually
e e ed o as he Debye p ocess.
3.6 Con empo a y B oadband Dielec ic
Spec oscopy
His o ical dielec ic expe imen s, which we e limi ed o he de e mina ion o he
empe a u e-dependen s a ic dielec ic cons an o he measu emen o he di-
elec ic unc ion ˆε(ν=cons ., T) a single equencies, ha e been eplaced by
b oadband echniques wi h a wide equency ange. P esen ing da a o iso he mal
measu emen s co e ing eigh equency decades has become he scien i ic s anda d.
Combining se e al b oadband se ups (including ime-domain se up, mic owa e
e lec ome y and Fou ie - ans om in a ed spec oscopy), as done o example
in he dielec ic labo a o y a he Uni e si y o Augsbu g un by A. Loidl and
P. Lunkenheime [19], makes i possible o measu e he dielec ic suscep ibili y
32
3.6 Con empo a y B oadband Dielec ic Spec oscopy
o e he ange o 16 equency decades, which may be conside ed as he expe -
imen al s a e o he a (c . also Fig. 3.1 (b)). Impo an o men ion is also
he applica ion o high p ecision capaci ance b idges as done, o example, by
C. Gaina u e al. in o de o ob ain highly accu a e suscep ibili y da a e en a
lowes empe a u es [53, 71]. The b idge used by Gaina u e al. has a na owe
equency ange, bu a highe accu acy, o sensi i i y o low signals, han he
b oadband spec ome e applied wi hin he p esen wo k.
Figu e 3.11: (a) Dielec ic suscep ibili y o supe -cooled glyce ol, measu ed by he Augs-
bu g g oup a ound P. Lunkenheime . Figu e aken om Re . [72]. Inse :
empe a u e dependence o he suscep ibili y peak posi ions. (b) The same
da a as in (a), escaled o he suscep ibili y minimum acco ding o he axes
i ling [73]. C osses: da a acqui ed in he empe a u e ange T= 184–273 K.
Ci cles: empe a u e ange T= 289–413 K. (c) Selec ion o he da a shown
in (a), now scaled o he maxima [53].
In Figu e 3.11 (a) dielec ic suscep ibili y da a o glyce ol as published by he
Lunkenheime g oup [72] a e shown, co e ing he equency ange ν≈10−5–
1012 Hz. The signal ampli udes each om ε00 ≈0.01–20, hence a wide dynamic
ange is accessed and e en iny spec al ea u es can be esol ed. Fo all iso he ms
shown in Fig. 3.11 (a) a p ominen peak is obse ed, which shi s om νP= 1010 Hz
33
3 Ex ended Abs ac
a T≈400 K o νP= 10−4Hz a T= 184 K. The empe a u e dependence o he
peak posi ion νPis displayed in he inse o Fig. 3.11 and shows a s ong cu a-
u e, i.e. a supe -A henius beha io o he ime cons an τP= 1/(2πνP) ypical
o glassy dynamics [18,26, 36, 74] is obse ed. No e ha only in he case o he
Debye peak τ=τmax holds exac ly. In mos cases he e is ye no signi ican di e -
ence be ween he empe a u e dependences o τmax(T), co esponding o he peak
posi ions, and he mean co ela ion imes τ(T) as de ined by Eq. 3.21. Ob iously
an inc ease o he co ela ion ime beyond any labo a o y ime scale is expec able
when Tis lowe ed u he (c . Sec. 3.3).
When he DS da a a e escaled o he suscep ibili y minimum be ween α- e-
laxa ion and he so-called boson peak a highes equencies (Fig. 3.11 (b)), he
da a o he empe a u e ange T= 289–413 K (ci cles) ha e a common en elope
[73]. Da a o empe a u es below T= 289 K (c osses) de ia e om he common
en elope due o seconda y elaxa ion ea u es eme ging be ween α- and boson
peak in he o m o excess suscep ibili y. Fo example, inspec ing he ε00(ν) cu e
o T= 184 K in Fig. 3.11 (a), he high equency side o he main elaxa ion
peak has he shape o a powe law in he ange ν= 10−3–10−1Hz. A highe
equencies (ν= 100–102Hz) a dis inc posi i e cu a u e is obse ed, ma king a
c osso e o ano he powe law shape in he ange (ν= 102–107Hz). The la e
ea u e is usually e e ed o as excess wing (EW); glass o me s showing an EW
ins ead o seconda y elaxa ion peaks a e called ype-A sys ems, acco ding o he
classi ica ion by Kudlik e al. [75].
All peaks shown in Fig. 3.11 (a) ha e nea ly he same spec al shape, as demon-
s a ed in Fig. 3.11 (c), whe e he da a a e scaled o he suscep ibili y maxima [53].
Thus, FTS ( equency domain equi alen o TTS, c . Sec. 3.3) is obeyed in good
app oxima ion by he main elaxa ion peak. (As will be discussed in Pape 2
a sligh sha pening o he peaks wi h inc easing empe a u e can be quan i ied
anyway.) TTS is also obse ed o he long- ime decay o he co ela ion unc-
ions acqui ed by b oadband DLS shown in Fig. 3.6 in Sec. 3.3. Rema kably, he
da a collapse shown in he mas e cu e in Fig. 3.11 (c) also in ol es he EW
con ibu ion.
Besides he EW, as obse ed in he glyce ol da a (Fig. 3.11) and many o he
ype-A glass o me s (see Pape s 2 & 3), explici seconda y elaxa ion (o β-) peaks
a e ound in he suscep ibili y o ype-B sys ems [75] (see Pape s 4 & 5). In con-
as o he α- elaxa ions, he ime cons an s o which show non-A henius beha -
io , he β-p ocesses show he mally ac i a ed dynamics, i.e. hei ime cons an s
ollow A henius laws [53,75,76]. Kudlik e al. [75] ind mean ac i a ion ene gies
o hEi ≈ 24 Tg o mos cases and a emp imes in he ange τ0= 10−18–10−15 s.
The elaxa ion s eng hs o he β-p ocesses ∆εβin ela ion o he espec i e α-
elaxa ion s eng hs di e s ikingly when se e al glass o me s a e compa ed [44].
Below Tg he ∆εβ(T) a e nea ly cons an , while hey show a s ong inc ease when
empe a u e is inc eased abo e Tg[65,77]. In Fig. 3.12 [44] DS da a o he ype-B
sys ems (a) oluene (TOL) and (b) 3- lou o aniline (o m- luo o aniline; m-FAN)
a e collec ed, showing explici β-peaks in addi ion o he α- elaxa ion peaks, ap-
34
3.7 Exis ing App oaches, Open Ques ions, and Majo Resul s
pea ing a clea ly highe maximum equencies han he la e s. Fo TOL (Fig.
3.12 (a)) an immedia e c osso e om α- o β-peak is obse ed. In he case o
m-FAN (Fig. 3.12 (b)) indica ions o an addi ional EW, appea ing as a powe law
be ween α- and β-peak, a e ound.
Figu e 3.12: Dielec ic suscep ibili y o ype-B sys ems; igu es aken om [44]. (a) Toluene
(Tg= 117 K). (b) 3- lou o aniline (Tg= 172 K).
The in es iga ion o seconda y elaxa ions in supe cooled liquids has become an
impo an ask wi hin he “glass communi y”, as well i is a signi ican issue o he
p esen wo k. In Pape 4 an ensemble o chemically ela ed sys ems consis ing o
six ype-B glass o me s a e in es iga ed. Since hese sys ems con ain phospho us,
hey a e e y in e es ing sys ems o being also analyzed wi h he help o 31P NMR
as done by ou g oup. In he Pape s 5 & 6 bina y mix u es o one o hese sys ems
( ip opyl phospha e; TPP) and polys y ene a e in es iga ed wi h DS as well as
31P and 2H NMR. A majo s eng h o dielec ic spec oscopy compa ed o o he
me hods is he abili y o esol e hese seconda y p ocesses wi h high accu acy
despi e o hei usually low signal compa ed o he p ima y elaxa ion. Due o he
high sensi i i y o he me hod, e en sub le a ia ions o he line shapes o p ima y
as well as seconda y elaxa ion ea u es a e de ec able and quan i yable wi h he
help o DS. Each publica ion included in his hesis h i es on his ac (Pape s
1–6).
3.7 Exis ing App oaches o Desc ibe Gene ic
Relaxa ion Phenomena, Open Ques ions, and
Majo Resul s
Con empo a y b oadband DS on supe cooled o ganic glass o me s deals wi h he
challenge o unde s anding he empe a u e e olu ion o he dynamic suscep ibil-
i y, i.e. o phenomenologically comp ehend he glass ansi ion. An impo an s ep
owa ds his unde s anding, which has been ollowed since long, is o es ablish an
ex ensi e da a collec ion o di e en glass o ming sys ems co e ing equencies
35

3 Ex ended Abs ac
om 0–1 THz. In his con ex , i is no less impo an o lea n how o dis inguish
be ween sys em speci ic and gene ic phenomena by inding a conclusi e way o
disen angling he indi idual elaxa ion ea u es. Today, se e al app oaches a e
ollowed by di e en wo king g oups, leading o di e en pe cep ions o EW, α-
and β- elaxa ion. In he ollowing sec ion he mos impo an in e p e a ions a e
summa ized.
α- elaxa ion The main p ocess o molecula ea angemen in a liquid causes he
so-called α- elaxa ion in he case o an ex e nal dis u bance. This α- elaxa ion
is esponsible o he s uc u al elaxa ion o he sample, which is accompanied
by an iso opic and coope a i e eo ien a ion o he molecules (o , espec i ely,
monome uni s in polyme s). This molecula eo ien a ion mani es s i sel as he
α-peak in he dynamic suscep ibili y. O ien a ional elaxa ion in plas ic c ys als
shows a simila phenomenology [2–9].
One o he main expe imen al con o e sy conce ning he α- elaxa ion is he
ques ion whe he equency- empe a u e supe posi ion (FTS) holds o he α-
elaxa ion a all empe a u es T≥Tg. O cou se, any eme ging seconda y
p ocesses appea ing close o Tgha e o be sepa a ed adequa ely om he α-
peak when his ques ion is add essed. Schneide e al. [72] e alua ed he da a
shown in Fig. 3.11 (a) by i ing exclusi ely he α-peaks and ound a sys ema i-
cally empe a u e-dependen peak wid h, which is con a y o he esul s o he
scaling analysis men ioned abo e (Fig. 3.11 (c)) p esen ed en yea s la e [53] and
ac ually e lec ing he in e p e a ion ollowed by he Bay eu h g oup since hen.
The e a e also ea lie publica ions by his g oup explici ly showing sys ema ic
empe a u e dependences o he wid h pa ame e o he α-peak, yielded by i ing
analyses [4,58,65,73,75,78,79]. These esul s we e la e pu in o pe spec i e wi h
he p oblem o a limi ed a ailable i ing ange (see below). Fu he mo e, in he
con ex o a scaling analysis used by S. R. Nagel (Uni e si y o Chicago) and co-
wo ke s [80–82], which applies wi hin a ce ain app oxima ion [83,84], a ailu e o
FTS is epo ed.
On he o he hand, Olsen e al. [85] showed, o he sys em iphenyl phosphi e,
ha FTS holds o he main elaxa ion peak e en down o he glass ansi ion em-
pe a u e, as long as seconda y p ocesses a e absen (EW) o a leas well-sepa a ed
(β- elaxa ion) om he α-peak. Based on his idea, Gaina u e al. in oduced he
app oach o unde s anding he dielec ic suscep ibili y as being composed addi-
i ely o α- elaxa ion, excess wing (EW) and, i necessa y, a β- elaxa ion [53,76]
(in his hesis o en e e ed o as he Gaina u app oach). Wi hin his ansa z, be-
sides a empe a u e-in a ian line shape o he α-peak a empe a u e-independen
exponen o he EW is assumed. Only ταand he ampli udes o α-peak and EW
a e empe a u e-dependen . This app oach gi es a much simple pic u e o he
e olu ion o he dynamic suscep ibili y han he s aigh o wa d i ing p oce-
du es p esen ed by Blochowicz e al. [65,79]. Fu he mo e, B odin e al. showed
ha he ypical empe a u e dependence o he line shape pa ame e s o se e al
36
3.7 Exis ing App oaches, Open Ques ions, and Majo Resul s
sys ems p esen ed he e may be me ely an a i ac due o he pa icula i ing
s a egy and he limi ed equency ange o he da a [86]. The au ho s showed
wi h he help o simple scaling ep esen a ions, ha ac ually FTS holds in good
app oxima ion o he α- elaxa ion peak, and e en he compa ison o α-peaks o
di e en sys ems do no show signi ican di e ences. This new pic u e gi es new
inpu o , e.g., he ad ancemen o heo ies like MCT. In addi ion o ha , p oce-
du es o any analysis o da a wi h a limi ed equency ange, e.g. he e alua ion
o as ield cycling NMR da a, is based on FTS.
The ollowing open ques ions conce ning he α- elaxa ion a e ( e-)add essed
in he p esen wo k:
•To which ex en does FTS hold o he α- elaxa ion close o Tg? (→Pape s
1 & 2.)
•Can appa en a ia ions o he b oadening o he α-peak be explained by a
empe a u e-dependen excess wing ampli ude? (→Pape 2.)
•How can suscep ibili y spec a be in e pola ed adequa ely on he basis o
he e ined pic u e o he α- elaxa ion? (→Pape s 1 & 2.)
•How does he main elaxa ion peak o a plas ic c ys alline phase o med in
he supe cooled egime di e om he α-peak o he co esponding liquid?
(→Pape 3.)
The majo esul s o he p esen wo k conce ning he α- elaxa ion shall be
summa ized in he ollowing. The i s pa o Pape 2 ocuses on he empe a u e
dependence o he dielec ic suscep ibili y o glass o me s wi h no esol ed β-peak
( ype-A sys ems), i.e. he e olu ion o α-peak and EW unde a ying empe a u e.
Plo ing he no malized spec a e sus ωταleads o a collapse o he da a on he
low- equency side o he α-peak (low- equency scaling). While he line shape
o he α-peak was conside ed o be essen ially empe a u e-independen in he
con ex o Gaina u’s app oach [53,76,86], a sub le bu sys ema ic a ia ion in he
high- equency egion o he mas e cu es becomes ob ious he e. When he da a
se s a e escaled as demons a ed o PG in Fig. 3.13 (a), an almos pe ec collapse
on he high- equency pa o he da a is obse ed, including he high- equency
lank o he α-peak as well as he EW. This high- equency scaling sugges s ha
empe a u e-a ec ed changes o he line shape, which canno be explained solely
by he a ying EW ampli ude, conce n me ely he o e all peak wid h ins ead o
he high- equency exponen o he α-peak. The sub le iola ion o FTS can hus
be p ojec ed comple ely o he low- equency egion o he α- elaxa ion. This
esul is o high impo ance o he Gaina u app oach i sel since o his ansa z
a empe a u e-independen high- equency exponen o he α-peak is a necessa y
implica ion.
In o de o quan i y hese indings, a phenomenological h ee pa ame e i unc-
ion o he no malized α- elaxa ion peak in oduced in Pape 1 is applied. The
37
3 Ex ended Abs ac
Figu e 3.13: (a) No malized suscep ibili y o p opylene glycol (PG) plo ed e sus a educed
equency (high- equency scaling; igu e aken om Pape 2). (b) Fi unc ion
in oduced in Pape 1 o se e al alues o he shape pa ame e α, no malized
and plo ed e sus ωτα.
unc ion is de ined as s ep- esponse unc ion Φg( ) and has wo shape pa ame-
e s αand βbesides he ime cons an τg. While he Cole-Da idson (CD) and
Kohl ausch (K) unc ions ha e only one s e ching pa ame e , which a ec s he
b oadening o he peak by de e mining he exponen o i s high- equency powe
law, he new unc ion has a u he shape pa ame e , which changes he shape o
he ip o he elaxa ion peak wi hou a ec ing he high- equency exponen . The
special y o he new unc ion is ha he well-es ablished K and CD unc ions a e
ep oduced in he limi ing cases α→βand α→1, espec i ely. In o he wo ds,
he unc ion Φg( ) in e pola es con inuously be ween K and CD peak shape (Fig.
3.13 (b)). Con a y o he Ha iliak-Negami (HN) unc ion, Φg( ) has a well-
de ined mean elaxa ion ime ταdue o he physically alid low- equency limi
ε00(ν)∝ν1o i s suscep ibili y ep esen a ion. Finally i is shown in Pape 1 ha
Φg( ) has a non-nega i e dis ibu ion o co ela ion imes G(ln τ), which is he
p econdi ion o a physically alid elaxa ion unc ion.
In Pape 2 dielec ic suscep ibili ies o PC, PG, m-TCP, GLY and 4-TBP a e
i ed wi h his unc ion, which is now ex ended o accoun also o he EW con i-
bu ion. The esul s a e displayed in Fig. 3.14. Fo basically all conside ed sys ems
he shape pa ame e γo he EW as well as he high- equency pa ame e βo he
α-peak a e, in he spi i o he Gaina u app oach, kep cons an o all empe -
a u es. The esul ing pa ame e s α(addi ional shape pa ame e o he α-peak)
and C( ela i e elaxa ion s eng h o he EW) a e ound o be empe a u e-
dependen : wi h inc easing T α inc eases om α < 1 o α= 1, e lec ing he
peak assuming a Cole-Da idson (CD) shape abo e a ce ain empe a u e. A he
same ime C > 0 is nea ly cons an o e a ce ain empe a u e ange, be o e i
dec eases quickly o 0 when αassumes uni y. The sys em 4- e -bu ylpy idine
(4-TBP), which is also discussed in Pape 2, canno be analyzed in he same way.
As can be in e ed om Fig. 3.13 (inse ), he shape pa ame e βis signi ican ly
38
3.7 Exis ing App oaches, Open Ques ions, and Majo Resul s
empe a u e-dependen (inse ), u he he empe a u e dependence o i s shape
pa ame e αdi e s om he beha io o he o he analyzed sys ems. I u ns ou
ha his i egula i y is caused by he p esence o a weak β-p ocess in he spec a
o 4-TBP, which is hidden by he EW (see below).
Figu e 3.14: Fi pa ame e s αand Cas p esen ed in Pape 2.
Quinaldine (2-me hyl quinoline) is an exempla y ype-A glass o me [87]. In
Pape 3 he h ee-pa ame e i unc ion in oduced in Pape 1 is ex ended o
accoun o EW and conduc i i y con ibu ion and is now used o quan i y he
e olu ion o he dynamic suscep ibili y o quinaldine. Again, he high- equency
shape pa ame e βo he α-peak as well as he powe law exponen γdesc ibing
he EW a e ound o be empe a u e-independen , while αand Cshow a weak
a ia ion wi h T. Fu he , he low- equency scaling o he suscep ibili y cu es
e eals a empe a u e dependence o he line shape, which is limi ed o he EW
egion. The α- elaxa ion peak i sel appea s o obey FTS almos pe ec ly.
A empe a u es well abo e Tg= 180 K (200 K < T < Tm) wo subsequen
phase ansi ions o liquid quinaldine (2mq1) in o wo dielec ically ac i e phases
(2mq2 and 2mq3) a e obse ed. Pape 3 is unded h ough he p ojec “Schwe -
punk p og amm (SPP) 1415: K is alline Nich gleichgewich sphasen - P ¨apa a-
ion, Cha ak e isie ung und in-si u-Un e suchung de Bildungsmechanismen” by
Deu sche Fo schungsgemeinscha (DFG). Pa icula in e es o he SPP lies in
he mechanism o o ma ion o he me as able c ys alline phase. Thus, he anal-
ysis o he phase ansi ions and he phases i sel is he ac ual main conce n o
Pape 3.
Figu e 3.15 (a) displays esul s o a DS long- e m measu emen acking he
phase ansi ion om he liquid phase 2mq1 o he dielec ically ac i e c ys alline
phase 2mq2. A quan i a i e analysis o he ime dependence o his phase an-
si ion e eals s e ched exponen ial decays (A ami laws, c . Fig. 3.15 (b)) wi h
empe a u e-dependen ans o ma ion ime cons an s and exponen s, he e alu-
a ion o which s ongly sugges s ha he c ys alliza ion p ocess is con olled by
39
3 Ex ended Abs ac
ha he ac ions o PS monome s as well as TPP molecules pa icipa ing in he
β-p ocess dec ease wi h dec easing TPP concen a ion. This is in e p e ed as he
eme gence o “islands o igidi y”, as also obse ed o oluene/a oclo mix u es
by ou g oup [96]. Al hough he concep o “islands o mobili y” [89,98] has been
ejec ed o nea glass o me s [93,97], hese esul s sugges i s e-in oduc ion o
bina y sys ems.
excess wing (EW) As can be in e ed om Fig. 3.11 (Sec. 3.6), he high- e-
quency lank o he α- elaxa ion peak bends o e o show a lowe dispe sion a
high equencies. This high equency ea u e, which can be desc ibed by a powe
law ε00(ν)∝ν−γ(wi h γbeing smalle han he high- equency exponen o he
α-peak) is called excess wing (EW), and i he e is no a β- elaxa ion domina ing
he spec a, i.e. i a ype-A glass o me [75,78] is conce ned, i is usually ound
in he dynamic suscep ibili y o supe cooled liquids and glasses. The e a e h ee
possible in e p e a ions:
1. The excess wing is pa o he α-p ocess.
2. The excess wing is an indi idual elaxa ion p ocess and has o be dis in-
guished om α- and β-p ocess.
3. The excess wing is a subme ged β- elaxa ion peak.
The i s in e p e a ion is ound p ima ily in he con ex o he scaling p ocedu e
applied by Nagel e al. [80–82]. In Re . [107] i is s a ed explici ly ha he EW
exponen γis s ic ly ela ed o he exponen o he high equency lank o he
α- elaxa ion peak, and ha FTS is no obeyed.
The second in e p e a ion is ollowed in he amewo k o he analysis by Gaina u
and co-wo ke s [53, 76, 86]. He e, he shape pa ame e s o α-peak and EW a e
ound o be cons an in he whole empe a u e ange down o Tg, which is in con-
as o he indings by Blochowicz e al. [65,79], and which implies ha FTS is
obeyed by he α-peak. Solely he ela i e ampli ude o he EW in ela ion o he
α- elaxa ion changes sligh ly wi h empe a u e, causing an appa en a ia ion o
he high equency exponen o he α-peak. The assump ion ha β-p ocess and
EW a e sepa a e p ocesses is suppo ed by he ac ha he EW is esol ed in
DLS expe imen s, whe e he β- elaxa ion is in isible [36,108, 109]. Mo eo e , i
is demons a ed in [110] ha he EW obscu es he g(E)-scaling o he he mally
ac i a ed β-p ocess desc ibed abo e (Fig. 3.17 (b) and 3.18 (b)), which again
poin s in o he di ec ion ha EW and β-p ocess ha e o be dis inguished. Fu -
he , con a y o he empe a u e-dependen peak shape o β-p ocesses, he EW
exponen γshows no signi ican empe a u e dependence. Thus, by means o he
Gaina u app oach aging expe imen s pe o med by Schneide e al. [19,111] can be
ein e p e ed by assuming he high- equency suscep ibili y con ibu ion as being
composed addi i ely o EW and β-p ocess ( he au ho s hemsel es p e e he hi d
46

3.7 Exis ing App oaches, Open Ques ions, and Majo Resul s
in e p e a ion; see below). Simila aging expe imen s on 4- e -bu ylpy idine (4-
TBP) a e shown in Pape 2 (see below), whe e hey a e also in e p e ed acco ding
o his in e p e a ion.
The hi d in e p e a ion is suppo ed by he esul s o dielec ic aging expe -
imen s pe o med by Schneide e al. [19, 111]. He e, he sample is cooled o
empe a u es ew Kel in below Tgand, hence, pushed ou o he mal equilib ium,
which is eached only on ime scales o 106s. While wai ing he α- elaxa ion peak
(no obse ed di ec ly below Tg) becomes mo e sepa a ed om he EW. The la -
e s a s o show a dis inc cu a u e and de elops con inuously in o a elaxa ion
peak. The au ho s conclude ha his peak is he “ eal ace” o he EW, which,
hus, is no hing else han a β- elaxa ion, usually subme ged below he α-peak.
This is suppo ed by Casalini e al. [112], pe o ming p essu e-dependen DS ex-
pe imen s on a ype-B glass o me . Wi h inc easing p essu e an ini ially abscen
EW eme ges and, inally, de elops in o a u he well- esol ed peak.
No e ha up o now he o igin o EW as well as β-p ocess a e s ill o be cla i ied.
NMR measu emen s on ype-A glass o me s below Tgdo no e eal indica ions
o es ic ed molecula mo ion like in he case o ype-B sys ems [36]. Howe e ,
sligh ly abo e Tg he spec a s a o esemble hose o ype-B glass o me s [36,
113], which makes a clea dis inc ion be ween he wo p ocesses again appea
di icul . Lea ning abou commonali ies, simila i ies and di e ences be ween bo h
p ocesses, and inding he answe o he ques ion i he e a e wo di e en kinds
o seconda y p ocesses a all, a e issues o cu en and u u e esea ch.
In he p esen wo k he second in e p e a ion in he spi i o he Gaina u ap-
p oach is a o ed. Conce ning he EW, he ollowing open ques ions a e ad-
d essed in he publica ions:
•How can he EW be desc ibed wi hin he Gaina u app oach e ined acco ding
o he sub le line shape a ia ions o he α-peak? (→Pape 2.)
•A e he e u he examples o ype-A sys ems which ha e a β- elaxa ion
co e ed by he EW? (→Pape 2.)
•Which commonali ies among ype-A sys ems may indica e ha he EW has
a mic oscopic o igin di e en om ha o β-p ocesses? (→Pape 2.)
•How does he EW ound o he liquid phase o quinaldine beha e, and is i
also obse ed o he o he dielec ically ac i e phases? (→Pape 3.)
I was al eady s a ed in he con ex o he α-p ocess ha he EW is no obse ed
in he usual way in he c ys alline phases o quinaldine, all he same i is poin ed
ou abo e how dielec ic spec a o ype-A sys ems can gene ally be quan i ied
by accoun ing o he EW con ibu ion. In he ollowing, he majo esul s
p esen ed in he second pa o Pape 2 conce ning he EW shall be summa ized
a his poin .
Aging expe imen s on supe cooled 4-TBP a empe a u es closely below Tg
moni o he suscep ibili y app oaching he mal equilib ium wi hin a numbe o
47
3 Ex ended Abs ac
Figu e 3.19: (a) Equilib ium spec um o 4-TBP a T= 161 K (ci cles). C osses: he same
da a a e sub ac ion o a powe law ∝ν−0.2(dashed line). Inse : DS da a o
glyce ol ( ull ci cles; T= 179 K) and p opylene ca bona e (PC, ull diamonds;
T= 153 K. Open symbols: da a se s a e sub ac ion o a powe law ∝
ν−0.2. (b) Tempe a u e dependence o he no malized dielec ic suscep ibili y
o se e al ype-A (open symbols) and ype-B sys ems ( ull symbols) a ixed
equency ν= 1 kHz, plo ed e sus educed empe a u e. (c) Time cons an s
o αand β-p ocesses o se e al glass o me s.
days. Since he analysis o ype-A sys ems has shown (high- equency scaling;
EW ampli ude C≈cons . nea Tg, see Fig. 3.14) ha he EW con ibu ion is
s ongly coupled o he α- elaxa ion peak, he suscep ibili y a ia ion o 4-TBP
du ing aging ( o de ails see Pape 2) is in e p e ed, consequen ly wi hin he ideas
o he Gaina u app oach, as a anishing o he spec al con ibu ion o he EW.
The la e wi hd aws oge he wi h he α-peak, which shi s slowly o longe ime
scales. The cu a u e in ε00(ν) o 4-TBP, which is al eady p esen in he non-
equilib ium spec a, bu ge s mo e p onounced upon aging, is in e p e ed as he
signa u e o a hidden β- elaxa ion. Finally, he β-peak is comple ely e ealed by
sub ac ing he EW con ibu ion in he o m o a powe law ε00(ν)∝ν−γwi h
γ≈0.2. The esul ing β-peak is symme ic, and i s ime cons an s show ypical
A henius beha io wi h he ac i a ion ene gy hEi= 24 Tgas o en ound o β-
48
3.7 Exis ing App oaches, Open Ques ions, and Majo Resul s
p ocesses (c . Fig. 3.19 (c)). Figu e 3.19 (a) illus a es his p ocedu e o spec al
decomposi ion, displaying he suscep ibili y o 4-TBP a T= 161 K be o e and
a e he sub ac ion o he EW con ibu ion.
Dielec ic measu emen s on se e al molecula glass o me s ( ype-A and -B)
down o lowes empe a u es o T≈2 K ha e been pe o med in he amewo k o
Pape 2. In Fig. 3.19 (b) a compa ison o esul ing ε00(T) da a a ixed equency
ν= 1 kHz, no malized by he elaxa ion s eng h o he α- elaxa ion nea Tg, is
displayed. Fo all sys ems he signa u e o he α-peak is ound nea Tg. A lowes
empe a u es (0 < T/Tg<0.3) low- empe a u e anomalies in e p e able as he -
mally ac i a ed dynamics in asymme ic double well po en ials (ADWP) [71] ap-
pea as peaks. In he in e media e empe a u e ange suscep ibili y con ibu ions
o excess wings as well as β- elaxa ions o , espec i ely, hei low- empe a u e sig-
na u es, a e obse ed. He e, almos iden ical ampli udes wi hin di e en ype-A
sys ems a e ound, sugges ing ha α- elaxa ion and EW ha e s ongly co ela ed
molecula o igins. On he o he hand, highe and s ongly a ying loss ampli-
udes a e ound o ype-B glass o me s, sugges ing ha he β- elaxa ion has
a mic oscopic o igin di e en om ha o he EW phenomenon. This inding
also jus i ies he Gaina u app oach used o he spec al decomposi ion o 4-TBP:
any β-p ocess con ibu ion in Fig. 3.19 (b) appea s as addi ional con ibu ion o
a gene ic, “basic” suscep ibili y. This esul suppo s s ongly he Gaina u ap-
p oach, i.e. he o e all suscep ibili y may, hus, be in e p e ed as a supe posi ion
o α-p ocess, β-p ocess, and EW.
A compila ion o ime cons an s desc ibing β-p ocesses o a a ie y o glass
o me s, including also 4-TBP and o he ype-A sys ems whe e he β-p ocess was
e ealed by sub ac ing he EW con ibu ion, is shown in Fig. 3.19 (c). Thei
ac i a ion ene gies a y wi hin hEi= 11 Tg–26 Tg. Thus, he hEi= 24 Tg ule
in oduced by Kudlik e al. [75,78] seems obsole e (c . also Fig. 3.17 (a) and (b),
as well as Pape 4).
elaxa ion p ocesses in bina y sys ems Two-componen mix u es o o ganic
glass o me s a e called bina y sys ems in his hesis. P o iding a comp ehen-
si e desc ip ion o he phenomenology o he p ima y elaxa ions in bina y sys-
ems may become qui e challenging, as documen ed by se e al con ibu ions on
polyme -plas icize sys ems [114–118] and mix u es o low molecula weigh glass
o me s [119–121]. Only in he case o asymme ic bina y sys ems, i.e. mix u es
o componen s wi h a high Tgcon as [35,122], wo p ima y elaxa ions a e well
esol ed and a ibu ed o he molecula dynamics o each componen . P inci-
pally, FTS does no hold in bina y sys ems since b oad empe a u e-dependen
dis ibu ions o co ela ion imes caused by s ong dynamic he e ogenei y unde lie
he p ima y elaxa ions [38, 45]. Mo eo e , in he ecen wo k by Blochowicz e
al. [35, 122] a empe a u e-dependen ac ion o plas icize molecules a ibu ed
o he ma ix dynamics is iden i ied. Howe e , he e ec o a low-Tgcomponen
on he s uc u al elaxa ion o he high-Tgcomponen (plas icize e ec ) as well
49
3 Ex ended Abs ac
as he e ec o he high-Tgcomponen on he p ima y elaxa ion o he low-Tg
componen (an i-plas icize e ec ) a e well known, e.g. om di e en ial scanning
calo ime y (DSC) expe imen s showing wo glass ansi ion empe a u es o bi-
na y mix u es [123–128] (c . also Fig. 3.20).
Besides a complex phenomenology conce ning he p ima y elaxa ion ea u es
o he componen s “in he mix u e”, and he exis ence o wo concen a ion de-
penden Tg, bina y sys ems o e ano he iewpoin on seconda y elaxa ions. I a
β- elaxa ion is p esen , i may be ound o almos all in es iga ed mixing p opo -
ions [96,122,129]. In some cases, a high concen a ions o he low Tgcomponen
(c→1), α- and β-peak app oach each o he and he β- elaxa ion e en subme ges
below he α-peak, i.e. he β-peak de elops con inuously in o an EW [44,119,122].
The in es iga ion o bina y glass o ming sys ems is a qui e new, wide ield o
esea ch. Since many combina ions o componen s a e possible and each combi-
na ion has o be analyzed o se e al concen a ions, much e o is equi ed o
he comple e cha ac iza ion o a bina y sys em, and, hence, compa ably li le
knowledge on he molecula dynamics o bina y sys ems has been accumula ed.
In he con ex o he analysis o a highly asymme ic bina y sys em wi hin he
p esen wo k, he ollowing open ques ions a e add essed:
•How a e he p ima y elaxa ions o each componen a ec ed by he p esence
o he o he componen in he mix u e? (→Pape 6.)
•A e he e addi ional dynamics in he mix u e, which we e no obse ed in
he nea componen s? (→Pape 6.)
•Do he mic oscopic mechanisms (iso opic s. spa ially hinde ed) o he p i-
ma y elaxa ions o hei appea ance ( he mally ac i a ed s. non-A henian
τ(T); FTS) a y wi h concen a ion? (→Pape 6.)
•How do he Tgdepend on concen a ion? (→Pape 6.)
•How can he geome y o molecula mo ion be cha ac e ized o bo h com-
ponen s? (→Pape s 5 & 6.)
The majo esul s conce ning he p ima y elaxa ion phenomena o he asym-
me ic bina y sys em TPP/PS ( ip opyl phospha e, Tg= 134 K; polys y ene,
Mw= 2250 g/mol, Tg= 335 K) shall be summa ized he e. As al eady poin ed ou
abo e, he molecules o he wo componen s possess highly di e ing pe manen
dipole momen s. As a consequence, DS moni o s solely he dynamics o TPP.
The esul s o TPP/PS mix u es o 13 concen a ions a e p esen ed in de ail in
Pape 6, which is a join s udy by dielec ic spec oscopy (DS), 31P and 2H nuclea
magne ic esonance spec oscopy (NMR) and, ac ually, also di e en ial scanning
calo ime y (DSC) and depola ized ligh sca e ing (DLS) expe imen s.
Due o he high Tgcon as o he componen s, wo dis inc glass s eps a e
obse ed in he DSC aces o he mix u es, si ua ed a he wo concen a ion-
dependen glass ansi ion empe a u es Tg1(cT P P ) and Tg2(cT P P ). 2H NMR ex-
pe imen s on he PS monome s and, equi alen ly, 31P NMR measu emen s on he
50
3.7 Exis ing App oaches, Open Ques ions, and Majo Resul s
Figu e 3.20: (a) Time cons an s om DS ( ull iangles: α1; ull ci cles: α2), NMR (open
iangles: α1; open ci cles: α2), DSC (open diamonds: α1; c ossed diamonds:
α2) and DLS (le pen agons: α1; igh pen agons: α2) o all in es iga ed
concen a ions (c . colo code). Lines a e guides o he eye. Fo de ails see
Pape 6. (b) Glass ansi ion empe a u es Tgas yielded by DSC, NMR and
DS o all in es iga ed mix u es. Dashed lines: guides o he eye.
TPP molecules assign Tg1 o PS (“ma ix”) dynamics, and Tg2 o TPP dynamics
occu ing on sho e ime scales. DLS expe imen s demons a e, ha he ime
scales o he TPP and PS dynamics a e sepa a ed up o highes concen a ions
and empe a u es. DS measu emen s p obing, as said abo e, solely dynamics o
he pola TPP molecules e eal wo p ima y TPP elaxa ions on di e en ime
scales. The ime cons an s τ2o he as e elaxa ion (α2-p ocess) co espond wi h
he TPP dynamics obse ed by NMR and iden i ied as Tg2in he DSC aces o
51

3 Ex ended Abs ac
he espec i e concen a ions. The τ1o he slow α1- elaxa ion ag ee wi h he
ime cons an s o PS dynamics obse ed by NMR, as well as he Tg1o he DSC
expe imen s. We conclude ha wo sub-ensembles o TPP molecules exis , one o
which is dynamically “ apped” by (o a ibu ed o) he PS ma ix. The o he
TPP sub-ensemble pe o ms “ ee” TPP dynamics, ye unde he concen a ion
dependen an i-plas icizing e ec o he PS ma ix.
A quan i a i e analysis o he dielec ic elaxa ion s eng hs ∆ε1and ∆ε2o
he α1- and α2-p ocess, espec i ely, e eals ha he ac ion o TPP molecules
associa ed wi h he high-Tgcomponen (i.e. he ma ix componen ) dec eases
wi h inc easing Tand, inally, anishes a a empe a u e Tc. This phenomenon
was also obse ed by Blochowicz e al. [35], who in e p e ed i as he signa u e o
a so-called ype-A glass ansi ion as p edic ed by MCT.
The combina ion o me hods yields ime cons an s o bo h elaxa ions in a
wide empe a u e and concen a ion ange and, he e o e, gi es an unp eceden ed
o e iew o e he qui e complex dynamics o he bina y sys em (Fig. 3.20 (a)).
The ime cons an s τ2(T) o he α2-p ocess a e ound o de elop om VFT beha -
io a high TPP concen a ions o an A henian empe a u e dependence a low
concen a ions, i.e. a ansi ion om agile o s ong beha io unde dec easing
concen a ion is obse ed. This leads, by applying he de ini ion τ2(Tg2) = 100 s,
o a maximum in Tg2(cT P P ), which is con i med by he DSC esul s, bu has, up
o ou knowledge, no been obse ed be o e (Fig. 3.20 (b)).
The α2-peak has a ypical α-peak shape a high TPP concen a ions. He e,
he ailu e o FTS is es ic ed o he low- equency side o he peak. When
cT P P is lowe ed, he α2-peak assumes a b oad shape inc easing i s wid h wi h
dec easing empe a u e, which eminds o he beha io o a he mally ac i a ed
β-p ocess. Indeed, he scaling p ocedu e also used in Pape s 4 and 5 wo ks, and
p o es ha he α2-p ocess is he mally ac i a ed a low addi i e concen a ions,
yielding empe a u e independen dis ibu ions o ac i a ion ene gies g(E). How-
e e , 31P NMR spec a o he cT P P = 20% mix u e iden i y he α2- elaxa ion as
a p ocess o iso opic, liquid-like molecula eo ien a ion, e en in he case o low
TPP concen a ions.
52
4 Publica ions
Lis o publica ions o ming his hesis:
Pape 1 Gene aliza ion o he Cole–Da idson and Kohl ausch Func ions
o Desc ibe he P ima y Response o Glass-Fo ming Sys ems.
R. Kahlau, D. K uk, T. Blochowicz, V. N. No iko ,
and E. A. R¨
ossle ,
Jou nal o Physics: Condensed Ma e 22, 365101 (2010).
Pape 2 E olu ion o Excess Wing and β-P ocess in Simple Glass Fo me s
C. Gaina u, R. Kahlau, E. A. R¨
ossle , and R. B¨
ohme ,
The Jou nal o Chemical Physics 131, 184510 (2009).
Pape 3 Quinaldine: Accessing Two C ys alline Polymo phs ia he
Supe cooled Liquid
R. Kahlau, T. Gnu zmann, F. Emme ling,
K. Rademann, and E. A. R¨
ossle ,
The Jou nal o Chemical Physics 137, 054505 (2012).
Pape 4 Seconda y Relaxa ions in a Se ies o O ganic Phospha e Glasses
Re ealed by Dielec ic Spec oscopy
R. Kahalu, T. D¨
o le , and E. A. R¨
ossle ,
The Jou nal o Chemical Physics 139, 134504 (2013).
Pape 5 On he Coope a i e Na u e o he β-P ocess in Nea and Bina y
Glasses: A Dielec ic and Nuclea Magne ic Resonance Spec-
oscopy S udy
D. Bock, R. Kahlau, B. Micko, B. P¨
o zschne ,
G. J. Schneide , and E. A. R¨
ossle ,
The Jou nal o Chemical Physics 139, 064508 (2013).
Pape 6 Dynamics o Asymme ic Bina y Glass Fo me s. I. A Dielec ic
and Nuclea Magne ic Resonance Spec oscopy S udy
R. Kahlau, D. Bock, B. Schmid ke, and E. A. R¨
ossle ,
The Jou nal o Chemical Physics 140, 044509 (2014).
53
4 Publica ions
Indi idual con ibu ion o each publica ion:
Pape 1 I had he idea o applying he in oduced modi ica ions o he
s ep- esponse ep esen a ion o he Cole–Da idson unc ion. The
p ope ies o he esul ing i unc ion we e analyzed by me,
and I calcula ed he mean co ela ion ime. I showed ha he
Kohl ausch unc ion is he second limi ing case o he unc ion
(besides he Cole–Da idson unc ion). Following he ad ice gi en
by T. Blochowicz, I applied Be ns ein’s heo em o show ha he
new unc ion is a physically alid elaxa ion unc ion, and p o ed
i s comple e mono onici y. The dis ibu ion o co ela ion imes
was calcula ed and nume ically e alua ed by D. K uk.
Pape 2 I eanalyzed p e iously published DS spec a o molecula glass
o me s by applying he low- equency and he high- equency
scaling, as demons a ed in Fig. 2. Fo his pu pose, I no malized
he da a by he elaxa ion s eng h, which is demons a ed in
Fig. 3. I inally i ed he da a o p opylene ca bona e (PC),
p opylene glycol (PG), m- ic esyl phospha e (m-TCP), 4- e -
bu ylpy idine (4-TBP), and glyce ol wi h he unc ion in oduced
in Pape 1. The esul s o his analysis a e collec ed in Fig. 4,
co esponding da a in e pola ions a e shown in Fig. 3. The second
pa o Pape 2 is basically he wo k by C. Gaina u. Da a o
decahyd oisoquinoline (DHIQ) we e measu ed by me, bu al eady
shown in my Diploma hesis. Besides some modi ica ions, Fig. 8 as
well as ela ed measu emen s a e also pa o my Diploma hesis.
Pape 3 I execu ed DS measu emen s on liquid quinaldine and liquid 3-
me hyl quinoline, which inally led o he disco e y o he di-
elec ically ac i e phases 2mq2 and 2mq3, as well as 3mq2 and
3mq3. I conduc ed all u he expe imen s, including equency
esol ed dielec ic spec oscopy on he dielec ically ac i e phases
o 2-me hyl quinoline and 3-me hyl quinoline, ime esol ed DS
expe imen s moni o ing he ime dependen phase ans o ma-
ions, ime esol ed X- ay di ac ion (XRD) expe imen s ( o-
ge he wi h T. Gnu zmann in he labo a o y o Bundesans al ¨u
Ma e ial o schung und -p ¨u ung in Be lin) and di e en ial scan-
ning calo ime y (DSC) expe imen s. All analyses shown in his
pape , excep he p ocessing o XRD da a (T. Gnu zmann), we e
execu ed by me.
54
Pape 4 I measu ed ie hyl phospha e (TEP), ip opyl phospha e (TPP)
and ibu yl phospha e (TBP). Da a o TEP and TPP a e pa -
ially published in [104], da a o TPP a e u he used in Pape s 5
& 6. The sys ems is(2-bu oxye hyl) phospha e (T2BOEP) and
is(2-e hylhexyl) phospha e (T2EHP) we e measu ed, unde my
guidance, by T. D¨o le in he amewo k o his Bachelo hesis.
All analyses shown in his pape we e done by me.
Pape 5 I execu ed all DS measu emen s o his publica ion. Da a we e
also used in Pape 6, da a o nea TPP we e also shown in Pape
4 and in [104]. I u he did all analyses o dielec ic da a. All
NMR expe imen s and ela ed analyses on TPP, PS, and TPP/PS
mix u es we e done by D. Bock.
Pape 6 I pe o med all DS measu emen s o his publica ion. Da a we e
also used in Pape 5, da a o nea TPP we e also shown in Pape
4 and in [104]. I u he did all analyses o dielec ic da a. All
NMR and DSC expe imen s as well as ela ed analyses on TPP,
PS, and TPP/PS mix u es we e done by D. Bock.
55
J. Phys.: Condens. Ma e 22 (2010) 365101 RKahlaue al
Figu e 1. Compa ison o Debye, Cole–Da idson (CD) and
Kohl ausch (K) suscep ibili y as a unc ion o educed equency; he
co esponding s e ching pa ame e s a e se o 0.6.
spec al shape o he αp ocess e en in simple glass o me s,
a esul al eady an icipa ed by Olsen e al [15]aswellas
by Blochowicz e al [14]. Mo eo e , hey obse ed ha
an in e pola ion by he CD unc ion wo ks well a high
empe a u es, whe eas usually he Kohl ausch unc ion gi es
a be e desc ip ion a low empe a u es. Thus, looking
o a suscep ibili y unc ion which con ains bo h CD and K
unc ions as special cases is a s a ing poin o an imp o ed
desc ip ion o he measu ed suscep ibili ies.
In he p esen con ibu ion we shall in oduce a h ee-
pa ame e s ep- esponse unc ion encompassing he CD and K
unc ions, which allows o a s aigh o wa d in e pola ion o
he expe imen al α- elaxa ion peak (excluding any seconda y
elaxa ion p ocesses). As will be demons a ed, he unc ion
is su icien ly lexible o p o ide almos pe ec i s o bo h
simple as well as bina y glass o me s.
The mos widely applied h ee-pa ame e suscep ibili y is
gi en by he Ha iliak–Negami (HN) unc ion [7]. Howe e ,
he HN unc ion exhibi s an unphysical low- equency (ωτ 
1) beha io , i.e. i s ime cons an (o he i s momen o he
co esponding dis ibu ion o elaxa ion imes) di e ges. Thus,
he unc ion is no adequa e o desc ibe he main elaxa ion in
liquids, and he e is a need o a physically well-beha ed (and
simply implemen ed) h ee-pa ame e suscep ibili y unc ion.
As discussed in a p elimina y s udy [16], applying his
suscep ibili y unc ion o simple liquids e eals a c osso e
om a CD suscep ibili y a high empe a u e o a K
suscep ibili y a low empe a u es while he high- equency
pa ame e βmay be kep empe a u e-independen .
2. Gene aliza ion o he Cole–Da idson and
Kohl ausch s ep esponses
Be o e in oducing a gene aliza ion o CD and K suscep ibili y
unc ions we b ie ly ecall he de ini ions o bo h. The CD
suscep ibili y is gi en by
χCD(ω) =1
(1+iωτCD)β0<β⩽1(1)
wi h βdesc ibing he imagina y pa χ
CD(ω) o he complex
suscep ibili y. The co esponding pulse esponse unc ion is
gi enby[7]
ϕCD( )=−dφCD( )
d =1
τCD(β) 
τCD β−1
exp −
τCD 
(2)
and he s ep- esponse unc ion by
φCD( )=1
(β) ∞
τCD
xβ−1exp(−x)dx=β,
τCD 
(β) (3)
wi h
(β) =∞
0
xβ−1exp(−x)dx(4)
deno ing he Gamma unc ion and
(β, y)=∞
y
xβ−1exp(−x)dx(5)
being he uppe incomple e Gamma unc ion [18].
The K unc ion ep esen s a s ep esponse:
φK( )=exp −
τKα(6)
wi h he co esponding s e ching pa ame e α. Bo h he K as
well as he CD unc ions con e ge o a Debye suscep ibili y
when he co esponding s e ching pa ame e eaches 1.
Figu e 1shows he CD and K unc ions, he la e
a e (nume ically calcula ed) Fou ie ans o ma ion in o he
equency domain, wi h he same elaxa ion ime ταand
s e ching pa ame e α=β. Gene ally, o a gi en s e ching
pa ame e he Kohl ausch elaxa ion peak is b oade han
he Cole–Da idson peak. Fo he ealis ic alue o α=
β=0.6 his di e ence is expec ed o be esol able in
expe imen s (c below). Mos expe imen al wo ks analyzing,
o example, dielec ic spec a o glass- o ming sys ems
use he CD o K unc ions, and some de iciencies o he
in e pola ion a e accep ed when a la ge empe a u e ange is
co e ed. As men ioned in sec ion 1, indica ions ha e been
ound ha ac ually wo lineshape pa ame e s a e needed o
ully ep oduce he p ima y elaxa ion peak [14,15]. This
is once again demons a ed in igu es 2(a) and (b) whe e he
no malized dielec ic spec a o p opylene ca bona e (PC) [5]
and p opylene glycol (PG) [14] a e escaled o ag ee a he
high- equency lank o he elaxa ion peak. Figu e 2(a)
shows he ull spec al ange o which he dielec ic da a
ha e been measu ed. In igu e 2(b) we ocus on he
da a a ound he elaxa ion maximum, as he unc ion o be
in oduced desc ibes he elaxa ion peak only. Indeed, he da a
coincide o e a subs an ial equency ange a high equencies,
indica ing ha he high- equency pa ame e does no change
signi ican ly wi h empe a u e. We no e ha a he highes
equencies ( igu e 2(a)) indica ions o he so-called excess
wing a e ecognized which may change i s ampli ude upon
cooling [5,6,17]. A he low- equency lank and a ound
he peak ( igu e 2(b)) no ag eemen is ound. He e, he
peak appea s o b oaden when lowe ing empe a u e. The
o e all change o he wid h is also e lec ed in a dec easing
heigh o he peak. Mo eo e , as demons a ed by he i s in
2

J. Phys.: Condens. Ma e 22 (2010) 365101 RKahlaue al
Figu e 2. (a) P opylene ca bona e (PC, le axis) and p opylene glycol (PG, igh axis) suscep ibili y da a no malized by he elaxa ion
s eng h and plo ed e sus a educed equency o allow o a o e lapping o he da a a high equencies (PG da a: [14]; PC da a: [5]).
(b) The same plo s shown o he equency ange o he main elaxa ion peak only. In addi ion Cole–Da idson and Kohl ausch in e pola ions,
espec i ely, a e shown o he indica ed empe a u es.
Figu e 3. (a) In e pola ion o he main elaxa ion o p opylene glycol (c osses) wi h a Kohl ausch suscep ibili y unc ion ( ed lines, i
weigh ed, da a om [14]); no e de ia ions a ound peak a high empe a u e. (b) Main elaxa ion o glyce ol (c osses) in e pola ed wi h he
Cole–Da idson (CD) unc ion ( ed lines) wi hou weigh ing. Blue do ed line: CD i (weigh ed i , da a om [1]); sys ema ic de ia ions occu
a low empe a u es.
igu e 2(b) a c osso e om a CD spec al shape owa ds a K
shape is sugges ed, i.e. a CD unc ion wo ks be e a high
empe a u e whe eas a K unc ion is be e a low empe a u e.
Consequen ly, a i o e a la ge empe a u e ange by he CD
o K unc ions yields sys ema ic de ia ions independen o he
applied i ing s a egy. This is demons a ed in igu e 3.Once
again we ocus only on he da a a ound he elaxa ion peak.
Nex , we p esen a unc ion φg( )which may be called
a gene aliza ion o K and CD unc ions; i includes he CD
and K unc ions as special cases. The unc ion φg( )can be
in oduced by modi ying φCD( )in equa ion (3):
φg( )=∞
τg
xβ−1exp(−xα)dx
∞
0xβ−1exp(−xα)dx(7)
by adding a s e ching pa ame e α o he exponen ial
exp ession, i.e. changing he exponen ial e m in equa ion (3)
o a Kohl ausch exp ession (c equa ion (6)). An al e na i e
de ini ion o φg( )which is mo e sui able o a nume ical
implemen a ion o he model unc ion is gi en by
φg( )=1
β
α∞

τgαyβ
α−1exp(−y)dy=
β
α,
τgα
β
α.(8)
This o mula has been ob ained by subs i u ing y=xαin
equa ion (7).
I is ob ious ha φg( )=φCD( )i α=1andβ=βCD
(c equa ion (3)), and one can easily p o e ha he condi ion
α=βgi es again he K unc ion:
φg( )=1
(1)∞

τgαexp(−y)dy=exp −
τgα=φK( )
=exp −
τKα o α=β. (9)
By in eg a ing φg( )(equa ion (8)) one ge s he mean
co ela ion ime (c he appendix):
τα=τg
1+β
α
β
α.(10)
Again, he limi s o CD and K suscep ibili y [7,19]a e
eco e ed:
τα,CD =lim
α→1τα=τg
(1+β)
(β) =τgβ(11)
τα,K=lim
α→βτα=τg
1+α
α
(1)=τg1
α+1=τg
α1
α.
(12)
3
J. Phys.: Condens. Ma e 22 (2010) 365101 RKahlaue al
(a) (b)
Figu e 4. (a) G aphs o he suscep ibili y unc ion χ
g(ωτα)(c equa ion (8)) o α=0.6,0.7,0.8,0.9,1.0andβ=0.6. Dashed ed line:
powe law p opo ional o (ωτα)−0.6. (b) Co esponding dis ibu ion o co ela ion imes G(ln τ); solid line: α=β=0.5 (Kohl ausch
dis ibu ion); dashed line: α=0.4,β =0.5; do ed line: α=0.6,β =0.5; dashed–do ed line: Cole–Da idson dis ibu ion o β=0.5.
Figu e 4(a) shows he suscep ibili y χ
g(ω) calcula ed
om equa ion (8) ia Fou ie ans o ma ion o he pa ame e
β=0.6andse e alα alues anging be ween 0.6 (α=β)
and 1.0. A con inuous c osso e o he spec al shape om
CD o K ype is illus a ed. The pa ame e βde e mines
he high- equency slope o he peak, in analogy o he CD
s e ching pa ame e , and αis esponsible o i s la ening. The
co esponding dis ibu ion G(lnτ) is displayed in igu e 4(b)
(c he appendix). Wi h espec o he CD dis ibu ion wi h i s
clea cu o a long co ela ion imes he new unc ion allows
us o a y i s long- ime lank con inuously.
Any alid elaxa ion unc ion φ( )o a sys em in
he modynamic equilib ium can be exp essed in e ms o a
non-nega i e dis ibu ion o elaxa ion imes ep esen ing φas
a sum o single exponen ial decays [7,20]. This is equi alen
o φbeing comple ely mono onic, which in u n, by i ue o
Be ns ein’s heo em, is he equi alen o [21–23]
(−1)nφ(n)( )⩾0 o 0⩽ <∞(13)
wi h φ(n)( )=dnφ( )
d nbeing he n h de i a i e o φ( ).In he
case o φg( ), i is easily seen ha
φ(0)
g( )>0 o 0⩽ <∞(14)
(equa ions (7)and(8)). Using he p ope ies o he egula ized
incomple e Gamma unc ion [18] he i s de i a i e can be
calcula ed:
φ(1)
g( )=d
d 1−1
β
α
τgα
0
xβ
α−1exp(−x)dx
=−
α
τg
β
α
τgβ−1
exp−
τgα⩽0 (15)
o α, β, τg>0and0⩽ <∞.
F om Be ns ein’s heo em i ollows ha he highe -o de
de i a i es (n⩾2) o φ(n)
g( )will be o opposi e signs i and
only i he exp ession

τgβ−1
exp −
τgα(16)
Figu e 5. Suscep ibili y da a o p opylene glycol (c osses)
in e pola ed by he χ
g(ω) unc ion ( ed lines, β ixed o 0.72). Inse :
empe a u e dependence o he pa ame e α(boxes); s aigh line:
guide o he eye.
is comple ely mono onic in . Since i is well known [21,22]
ha he p oduc o wo comple ely mono onic unc ions is
again comple ely mono onic, and o he ac o s exp[−(
τg)α]
as well as (
τg)β−1equa ion (13) is ob iously ul illed o τg>
0andα, β ⩽1, he comple e mono onici y o φgis p o en.
The e o e φg( )is a physically alid elaxa ion unc ion o
α, β, τg>0andα, β ⩽1.
3. Applica ions
In igu e 5we show dielec ic spec a o p opylene glycol
(PG) [14] in e pola ed by he new unc ion φg( )gi en as a
Fou ie ans o m χ
g(ω). A pe ec in e pola ion is p o ided
and he de iciencies o he CD unc ion a e emo ed. O
cou se, his is o no su p ise as a second shape pa ame e
has been in oduced. Howe e , he in e pola ions shown a e
achie ed by keeping he high- equency pa ame e β=0.72
empe a u e-independen and changing only he pa ame e α.
In o he wo ds, as sugges ed by he high- equency scaling in
igu e 2 he suscep ibili y keeps i s high- equency lank while
i b oadens on he low- equency side. When inspec ing he
4
J. Phys.: Condens. Ma e 22 (2010) 365101 RKahlaue al
Figu e 6. α- elaxa ion peaks o 2-picoline (5%) in i-s y ene
(c osses) compa ed o p opylene glycol (PG) a 176 K (blue iangles,
shi ed a bi a ily). In e pola ions by he model unc ion φg( )( ed
lines, c equa ion (8)): o compa ison in e pola ion by Kohl ausch
unc ion (dashed blue line) showing sys ema ic de ia ions.
empe a u e e olu ion o he pa ame e α(c inse o igu e 5),
i dec eases s a ing om 0.89 a he highes empe a u e o
0.72 a he lowes empe a u e, i.e. a end owa ds he K
unc ion (α=β) is ecognized while cooling.
In o de o demons a e he lexibili y o he in oduced
unc ion φg( )we y o in e pola e b oad αpeaksas heya e
ypically obse ed in bina y glass o me s [8,9]. Figu e 6
shows he dielec ic spec a o he bina y sys em 2-picoline
(5%) in i-s y ene in compa ison o he spec a o he simple
liquid PG. Clea ly, he elaxa ion peak in he bina y sys em
is much b oade han in he simple liquid PG. Again, he
in e pola ion by φg( )is supe io o a i by, o example, a
K unc ion. In con as o nea glass o me s he pa ame e α
s ays i ually cons an wi h α=0.57 while βd ops om 0.3
o 0.18 wi h inc easing empe a u e.
4. Discussion and conclusions
The in oduced h ee-pa ame e s ep- esponse unc ion φg( )
p o ides a highly lexible desc ip ion which allows o
‘in e pola ing’ be ween he CD- ype and K- ype spec al
shapes o he suscep ibili y in nea as well as bina y
glass o me s. Th ee-pa ame e desc ip ions o he main
elaxa ion ha e al eady been in oduced, such as he gamma
dis ibu ion [14,24] o he HN suscep ibili y[7]. Rega ding he
HN suscep ibili y, o en applied o in e pola ing, o example,
he spec a o polyme s, as al eady men ioned in sec ion 1, he
unc ion does no show he physically co ec low- equency
limi , i.e. i s ime cons an is no de ined. Thus i is no
expec ed ha he HN unc ion p o ides a co ec in e pola ion
o any main elaxa ion in complex liquids. In he case o he
gamma dis ibu ion he suscep ibili y has o be calcula ed ia
a Laplace ans o m o he dis ibu ion o co ela ion imes
whe eas he p esen ly in oduced unc ion applies di ec ly o
he s ep- esponse unc ion.
As sugges ed by he high- equency scaling o he expe -
imen al suscep ibili y in nea glass o me s (c igu e 2(b)),
he unc ion enables one o keep he high- equency pa ame e
β empe a u e-independen while a ying he pa ame e α o
accoun o he expe imen ally documen ed changes o he
linewid h. Thus, i appea s ha he ailu e o FTS in nea glass
o me s migh also be e lec ed by a low- equency b oadening.
Gene alizing he esul s, he in a iance o he high- equency
lank o he main elaxa ion peak migh be a gene ic p ope y o
nea glass- o ming liquids, and could become an essen ial inpu
o a ull lineshape analysis including main and seconda y
elaxa ion. Independen o such conclusions he p esen ed
unc ion o e s a new ool o in e pola ing elaxa ion peaks
in complex luids.
Appendix
A.1. Mean co ela ion ime
S a ing om he de ini ion o φg( ):
φg( )=1
β
α∞

τgαyβ
α−1exp(−y)dy=
β
α,
τgα
β
α(A.1)
one can calcula e he mean co ela ion ime o φg( )by
changing he a iable z=(
τg)α:
τα=∞
0
φg( )d =1
β
α∞
0
β
α,
τgαd
=1
β
α∞
0∞

τgαyβ
α−1exp(−y)dyd
=
τg
α
β
α∞
0
z1
α−1β
α,zdz.(A.2)
This exp ession can be con e ed [18] o
τα=τg
1+β
α
β
α.(A.3)
A.2. Dis ibu ion o co ela ion imes
A s ep- esponse unc ion φ( )can be explici ly ew i en as
φ( ,˜τ) wi h (˜τ=τCD,τ
KKW,τ
g) and ela ed o a dis ibu ion
unc ion G(τ, ˜τ)de ined as
φ( ,˜τ) =∞
0
G(τ, ˜τ)exp −
τdτ(A.4)
and connec ed wi h he o en-used o m G(lnτ) ia
G(lnτ, ˜τ) =τG(τ, ˜τ).
Subs i u ing s=τ−1one can w i e equa ion (A.4)in he
o m
φ( ,˜τ) =∞
0
G(s,˜τ)
s2exp(−s )ds
=∞
0
k(s,˜τ)exp(−s )ds.(A.5)
This implies ha he dis ibu ion unc ion G(τ, ˜τ) =
s2k(s,˜τ) =k(τ−1,˜τ)
τ2can be ob ained by aking he in e se
Laplace ans o m o he s ep- esponse unc ion φ( ,˜τ):
L−1
s[φ( ,˜τ)]=k(s,˜τ). De ailed calcula ions show ha i
is con enien o exp ess he dis ibu ion unc ion in e ms o
u=τ
˜τ:G(u)=s2k(s,˜τ). The dis ibu ion unc ion GCD(u)
5
J. Phys.: Condens. Ma e 22 (2010) 365101 RKahlaue al
associa ed wi h he Cole–Da idson s ep- esponse unc ion,
φCD( ,τ
CD)≡φCD(u), is gi en as [7]
GCD(u)=sin(πβ)
π
1
uu
1−uβ
(A.6)
while he dis ibu ion unc ion GK(u)co esponding o he
Kohl ausch s ep- esponse unc ion φK( ,τ
K)≡φK(u)is gi en
by he o mula [19]
GK(u)=−1
π
∞

k=0
(−1)k
k!sin(πkα)(αk+1)uαk−1.(A.7)
The φg( ,τ
g)≡φg(u)is ela ed o a dis ibu ion unc ion
Gg(u)which can be ob ained in a ‘semi-analy ical’ o m by
aking he ollowing s eps:
Gg(u)=τgs2kg(s,τ
g)=τgs2L−1
s[φ( ,τ
g)]
=−τgsL−1
sd
d φ( ,τ
g)
=τgs
β
αL−1
sd
d 
τgα
0
xβ
α−1exp(−x)dx
=τgsα
β
αL−1
s
τgβ−1
exp−
τgα.(A.8)
Since he dis ibu ion unc ion anyway depends on u=τ
τg,i
is con enien a his s age o se τg=1. The in e se Laplace
ans o m can be ob ained by applying he ule o a Laplace
ans o m o a p oduc o wo unc ions, which yields
L−1
s{ β−1exp(− α)}=s
0
g(s−σ)h(σ) dσ(A.9a)
whe e
g(s−σ) =(s−σ)−β
(1−β) (A.9b)
is he in e se Laplace ans o m o β−1, while h(σ) is gi en by
equa ion (A.4) wi h σ=u−1. Finally, he dis ibu ion unc ion
Gg(s) akes he o m
Gg(s)=sα
β
α(1−β)−1
π∞

k=0
(−1)k
k!sin (παk)
×(αk+1)s
0
(s−σ)−βσ−(αk+1)dσ. (A.10)
Fo he special case o α=0.5 he dis ibu ion unc ion is
gi en by a simple exp ession:
Gg(s)=s
4√π(2β)(1−β)
×s
0
(s−σ)−βσ−3/2exp−1
4σdσ. (A.11)
Examples o he co esponding G(lnτ) dis ibu ion a e
plo ed in igu e 4.
Re e ences
[1] Lunkenheime P, Schneide U, B and R and Loidl A 2000
Con emp. Phys. 41 15
[2] Edige M D 2002 Annu. Re . Phys. Chem. 51 99
[3] Blochowicz T, B odin A and R¨ossle E A 2006 Ad . Chem.
Phys. A133 127
[4] Joha i G P and Golds ein M 1970 J. Chem. Phys. 53 2372
[5] Kudlik A, Benkho S, Blochowicz T, Tschi wi z C and
R¨ossle E 1999 J. Mol. S uc . 479 201
[6] Ngai K L and Paluch M 2004 J. Chem. Phys. 120 857
[7] B¨o che C J and Bo dewijk P 1978 Theo y o Elec ic
Pola iza ion ol 2 (Ams e dam: Else ie )
[8] Blochowicz T and R¨ossle E A 2004 Phys. Re . Le .
92 225701
[9] Capaccioli S, Kessai i K, P e os o D, Lucchesi M and
Ngai K L 2006 J. Non-C ys . Solids 352 4643
[10] B¨ohme R, Ngai K L, Angell C A and Plazek D J 1993
J. Chem. Phys. 99 4201
[11] B odin A, Gaina u C, Po okhonskyy V and R¨ossle E A 2007
J. Phys.: Condens. Ma e 19 205104
[12] Nielsen A I, Pawlus S, Paluch M and Dy e J C 2008 Phil. Mag.
88 4101
[13] G¨o ze W and Sj¨og en L 1992 Rep. P og. Phys. 55 241
[14] Blochowicz T, Gaina u C, Medick P, Tschi wi z C and
R¨ossle E A 2006 J. Chem. Phys. 124 134503
[15] Olsen N B, Ch is ensen T and Dy e J C 2001 Phys. Re . Le .
86 1271
[16] Gaina u C, Kahlau R, R¨ossle E A and B¨ohme R 2009
J. Chem. Phys. 131 184510
[17] Ho mann A, K eme F, Fische E W and Sch¨onhals A 1994
Diso de E ec s on Relaxa ional P ocesses (Be lin:
Sp inge ) chap e 10
[18] Ab amowi z M and S egun I A 1972 Handbook o
Ma hema ical Func ions (New Yo k: Do e )
[19] Lindsey C P and Pa e son G D 1980 J. Chem. Phys. 73 3348
[20] Wagne K W 1913 Ann. Phys. (Leipzig) 40 817
[21] Alze H and Be g C 2002 Ann. Acad. Sci. Fenn. Ma h. 27 445
[22] Alze H and Be g C 2006 Ramanujan J. 11 225
[23] Widde D V 1972 The Laplace T ans o m (P ince on:
P ince on Uni e si y P ess)
[24] Nicolai T, Gimel J C and Johnsen R 1996 J. Physique 6695
6
Pape 2
E olu ion o Excess Wing and β-P ocess in Simple Glass
Fo me s
C. Gaina u, R. Kahlau, E. A. R¨
ossle , and R. B¨
ohme ,
The Jou nal o Chemical Physics 131, 184510 (2009).
c
2009 Ame ican Ins i u e o Physics
doi:10.1063/1.3258430
67

68
E olu ion o excess wing and
␤
-p ocess in simple glass o me s
Ca alin Gaina u,1,2,a兲Robe Kahlau,1E ns A. Rössle ,1and Roland Böhme 2
1Physikalisches Ins i u , Uni e si ä Bay eu h, Bay eu h 95440, Ge many
2Fakul ä ü Physik, Technische Uni e si ä Do mund, Do mund 44221, Ge many
共Recei ed 1 Augus 2009; accep ed 12 Oc obe 2009; published online 13 No embe 2009兲
Dielec ic loss spec a o glass o ming liquids a e analyzed, wi h emphasis on sys ems o which a
peak due o a seconda y elaxa ion is no immedia ely ob ious. Thus, glass o me s a e conside ed
o which he high- equency lank o he
␣
- elaxa ion peak appea s o be domina ed by a so-called
wing con ibu ion. I is shown ha e en o such supe cooled liquids he shape o he
␣
-peak has o
be cha ac e ized by wo pa ame e s. By pe o ming a se ies o aging expe imen s i is demons a ed
ha he high- equency lank o he
␣
- elaxa ion, assumed o ollow a powe -law beha io , is
supe imposed by con ibu ions om an excess wing and om a
␤
- elaxa ion peak. In pa icula , he
excess wing, p e iously associa ed wi h ei he he
␣
-o he
␤
- elaxa ion, is iden i ied as a ea u e
ha e ol es in i s own igh . I is a gued ha excess wing and
␤
- elaxa ion a e always p esen albei
wi h ela i e s eng hs ha may as ly di e om glass o me o glass o me .
©2009 Ame ican Ins i u e o Physics.关doi:10.1063/1.3258430兴
I. INTRODUCTION
When cooling o comp essing glass o ming liquids hei
dynamic suscep ibili ies e ol e in a complica ed ashion.
The s uc u al o p ima y
␣
- elaxa ion slows down om pi-
coseconds a TⰇTg o abou 100 s nea he glass ansi ion
empe a u e Tg. This elaxa ion is ma kedly nonexponen ial,
i.e., s e ched in ime, and de ines he ul ima e long- ime de-
cay o s uc u al luc ua ions in small-molecule glass o m-
e s. A sho es imes mic oscopic dynamics a e obse ed as
an oscilla ion dephasing wi h ypical equencies in he e a-
he z ange a all empe a u es. In he eno mous ange o
mo e han 14 decades in ime o equency which sepa a e
he ime scale o he
␣
- elaxa ion nea Tg om ha o he
mic oscopic dynamics a a ie y o o he elaxa ion p ocesses
eme ges. In dielec ic loss spec a hese ea u es mani es
hemsel es as so-called excess wing 共EW兲and mo e o en as
seconda y elaxa ion peaks. The las we e i s s udied sys-
ema ically by Joha i and Golds ein.1,2P ima y and second-
a y elaxa ions can o en, bu no always, be dis inguished
om each o he on he basis o hei di e en spec al, aging,
p essu e, and empe a u e e olu ions. Whe he he excess
wing is a ea u e sepa a e om hose elaxa ions is
deba ed,3,4because a gene ally accep ed p ocedu e allowing
one o disen angle he wing con ibu ions om hose o he
p ima y and/o o he seconda y elaxa ions is cu en ly no
a ailable.5–11
Cla i ying he ole o he seconda y peak and/o o he
wing con ibu ions is impo an since any assump ion ega d-
ing hei spec al shapes may a ec he esul o ha o he
p ima y elaxa ion. Fo example, aking esul s om
neu on12 o om ligh sca e ing measu emen s13 as well as
om o he expe imen al14 o compu a ional wo k,15,16 e-
quency empe a u e supe posi ion 共FTS兲has been epo ed o
be obeyed by he
␣
-p ocess o glass o me s a high empe a-
u es o which nei he seconda y peaks no wing elaxa ions
signi ican ly in e e e. While FTS is assumed o be an essen-
ial ea u e o glassy dynamics by ce ain heo ies,17 a em-
pe a u es close o Tgi was o en ound ha he spec al
shape p obed, e.g., by dielec ic spec oscopy is empe a u e
dependen .3,18,19 Some s udies emphasize ha ia app op ia e
spec al analyses FTS can be eco e ed, a leas
asymp o ically,14,20,21 h oughou he supe cooled egime.
Recen ly, based on high-p essu e expe imen s as well as on
heo e ical wo k i was a gued ha he spec al shape should
emain in a ian nei he along a line o cons an empe a u e
no unde cons an -p essu e condi ions, bu me ely along an
isoch onal line in he empe a u e- olume plane.22–24 How-
e e , di e en phenomenological app oaches o disen an-
gling he con ibu ion o he
␣
-peak om he o he elaxa ion
p ocesses we e p oposed,18,19,25–28 wi hou leading o an
o e all consensus ega ding he si ua ion.
Dis ega ding seconda y p ocesses o he momen , i
may be asked whe he a single pa ame e is su icien o
desc ibe he shape o he dielec ic
␣
- elaxa ion close o i s
peak equency a a gi en empe a u e. Such a one-pa ame e
desc ip ion was assumed in s udies inqui ing in o co ela-
ions be ween he supe -A henius wi h he non-Debye cha -
ac e o he
␣
-p ocess.29 In he mean ime he e a e some
indica ions ha mo e han one shape pa ame e may be nec-
essa y o desc ibe he spec al p o ile o he
␣
- elaxa ion
e en in ela i ely simple low molecula weigh glass
o me s.14,18,27 Such a case ob iously complica es he sea ch
o s aigh o wa d co ela ions among a ious pa ame e s
and could a ionalize epo s sugges ing sho comings o
simple co ela ions.21,30 To cla i y he na u e o
␤
-p ocesses
hemsel es, an unambiguous sepa a ion o hem om he
p ima y elaxa ion is some imes conside ed desi able, oo. In
iew o he connec i i y be ween he
␣
- and
␤
-p ocess31,32 i
is no clea , howe e , o which ex en such a sepa a ion can
a兲Elec onic mail: [email p o ec ed].
THE JOURNAL OF CHEMICAL PHYSICS 131, 184510 共2009兲
0021-9606/2009/131共18兲/184510/10/$25.00 © 2009 Ame ican Ins i u e o Physics131, 184510-1
Au ho complimen a y copy. Redis ibu ion subjec o AIP license o copy igh , see h p://jcp.aip.o g/jcp/copy igh .jsp
be achie ed no only phenomenologically, bu unde which
ci cums ances a sepa a e conside a ion is pe missible in p in-
ciple.
The empe a u e a which seconda y elaxa ion peaks o
excess wing i s appea upon cooling is some imes aken o
signal a c osso e in he dynamics o supe cooled liquids.9,33
Ye , i s clea -cu mani es a ion in suscep ibili y spec a well
abo e Tg emains a ma e o deba e.
In o de o disen angle he a ious p ocesses, dielec ic
s udies moni o ing p essu e22,34 and aging dependences28,35
u ned ou o be pa icula ly use ul. In aging expe imen s
Schneide e al.35 ound sub le spec al changes in he high-
equency wing o he
␣
-peak o glyce ol and p opylene
ca bona e 共PC兲. These esul s we e in e p e ed as a ising
om an eme ging seconda y elaxa ion peak and led hose
au ho s o sugges ha he excess wing is a elaxa ion p o-
cess o he JG ype.2,35 The ci ed aging s udy was impo an
in poin ing ou ha
␤
- elaxa ions may exis in glass o me s
in which hei p esence is no ob ious, a i s glance. How-
e e , as al eady sugges ed on he basis o high-p essu e ex-
pe imen s we will a gue “ ha he excess wing and he
␤
elaxa ion canno be ea ed on he same oo ing.”22
To pu hese esul s in a b oade pe spec i e and o ad-
d ess he ques ion whe he seconda y elaxa ions may be
uni e sally p esen in glass o me s, in Fig. 1we compile
dielec ic loss spec a o se e al supe cooled liquids o scal-
ing empe a u es Ts⬇Tg. The da a a e no malized o hei
maximum loss, see Table I o ␧max
⬙,Ts, and e e ences o he
o iginal wo ks. Fo some subs ances such as oluene o dim-
e hylph hala e 共DMP兲,a
␤
- elaxa ion peak is clea ly disce n-
ible a abou 5 decades abo e he
␣
-peak equency. These
liquids a e hus ypical examples o ype B sys ems.11 Fo
glass o me s like diglycyl e he o bisphenol A 共DGEBA兲o
ime hylphospha e 共TMP兲only he low- equency lank o a
seconda y peak is ecognized in Fig. 1. He e he sepa a ion
om he
␣
-peak is la ge han 8 decades and we will show
below ha in ac all deg ees o sepa a ion a e obse ed. Fo
me hyl- e ahyd o u an 共MTHF兲a
␤
-p ocess is ba ely
esol ed.36 Fo o he supe cooled liquids he
␤
- elaxa ion
ampli ude is e en smalle and a
␤
-peak seemingly absen .
Glass o me s in his limi ha e been called ype A sys ems11
wi h glyce ol, p opylene glycol 共PG兲, and p opylene
ca bona e37 usually conside ed as classical examples.38 We
poin ou ha o sys ems such as m- lou oaniline 共m-FAN兲,
TMP, and DGEBA bo h a well esol ed EW and a
␤
-peak
a e obse ed, sugges ing ha he wo p ocesses a e indepen-
den elaxa ion phenomena. As e ealed in Fig. 1, sligh ly
s onge high- equency con ibu ions a e exhibi ed by
2-picoline 共2-PIC兲and 4 e -bu yl py idine 共4-TBP兲.Inall
ype A sys ems collec ed in Fig. 1 he high- equency loss
asymp o ically a ies as ␧⬙⬀
␯
−
␥
wi h
␥
⬇0.2. Al hough
2-PIC and 4-TBP appea ela i ely simila in his plo , in
Sec. IV we will poin ou ha he beha io s o hese glass
o me s a e in ac o be dis inguished. He e, we men ion ha
he excess wing is equi alen 39 o wha has been e med he
in e media e powe -law on he basis o op ical Ke e ec
s udies.21,40,47 The e, again a e y simila exponen close o
␥
⬇0.2 has been epo ed.
The main poin o he p esen a icle is ha nea Tg he
EW and he
␤
- elaxa ion a e o be conside ed as uni e sally
p esen bu dis inguishable ea u es o a ying ela i e
s eng hs. Thus, we do no iew he EW as a special 共sub-
me ged兲
␤
-p ocess. Me ely, he high- equency wing in mos
ype A glass o me will be in e p e ed o in ol e an EW and
a e y weak
␤
-p ocess. As will be demons a ed his in e -
p e a ion also allows one o desc ibe he aging expe imen s
p esen ed in Re s. 35 and 51, and in Sec. III, below.
Be o e discussing ou aging esul s, we i s p esen a
  





m



mA
EBA


C
B

C

mC
ν

εε
ν
−
=
FIG. 1. Dielec ic loss spec a o a ious glass o me s eco ded o com-
pa able peak equencies and scaled o he same peak heigh . The spec a
exhibi a succession o dec easing high- equency con ibu ions hus illus-
a ing a con inuous ansi ion om ype B o ype A p o iles. This ep esen-
a ion is compa ible wi h
␤
-p ocess and excess wing always being simul a-
neously p esen , albei wi h di e en ela i e in ensi ies. The spec al shape
o his glass o me is hus in e media e be ween so-called ype A and o he
ype B sys ems. Re e ences and in o ma ion ega ding he measu emen
empe a u es and ␧max
⬙a e p o ided in Table I.
TABLE I. The scaling pa ame e s ␧max
⬙and Tsused o Fig. 1a e summa ized. Typically, Tsis sligh ly highe han Tgas de ined by Tg=T共
␶
␣
=100 s兲. The line
shape pa ame e s
␤
and
␥
om he i s a e epo ed he e, i hey we e kep cons an , while he empe a u e dependence o he ee pa ame e s is p esen ed in
Fig. 4.The
␥
exponen s o m-TCP and TMP a e hose gi en in Fig. 9.
Glyce ol PC 2-PIC PG 4-TBP m-TCP TMP DHIQ Toluene m-FAN MTHF DGEBA DMP
␧max
⬙22.5 30.3 4.5 26.5 4 2 16.6 0.063 0.06 7 6.3 2.7 0.15
Ts共K兲196 163 133 173 168 213 140 183 119 177 94 256 198
Tg共K兲189 158 130 168 166 205 136 179.5 117 172 92 251 195
␤
0.66 0.78 0.6 0.74 ¯0.6 ¯¯ ¯0.52 ¯¯¯
␥
0.23 0.23 0.2 0.23 0.2 0.19 0.17 ¯¯0.23 ¯¯¯
Re e ences 10,11 11 11 27 27 27 68 共This wo k兲11 28,11 54 69 70
184510-2 Gaina u e al. J. Chem. Phys. 131, 184510 共2009兲
Au ho complimen a y copy. Redis ibu ion subjec o AIP license o copy igh , see h p://jcp.aip.o g/jcp/copy igh .jsp
scaling analysis 共Sec. II A兲which implies ha a one-
pa ame e desc ip ion is some imes insu icien o desc ibe
he shape o he
␣
-p ocess. This is e en he case in he egion
whe e we may dis ega d he con ibu ions om he excess
wing and om he
␤
-p ocess. Then, in Sec. II B we quan i y
hese indica ions using a phenomenological i ing app oach
which suppo s he no ion ha
␣
- elaxa ion and excess wing
a e go e ned by di e en beha io s. In Sec. III hese indica-
ions a e u he con i med by in es iga ing he aging-
induced change o he spec al shape o 4-TBP, PC, and glyc-
e ol, glass o me s ha we e al eady well s udied unde
equilib ium condi ions.27,41 Finally, in Secs. IV and V we
discuss and summa ize ou main indings.
II. SHAPE OF THE RELAXATION PEAK T>Tg
A. Scaling ea u es
Line shape pa ame e s ha change wi h empe a u e a e
o en used o desc ibe he e olu ion o he main elaxa ion
o e a b oad equency ange.2Howe e , i no seconda y
elaxa ion peak in e e es, empe a u e independen line
shape pa ame e s we e ex ac ed om some spec al
analyses.14,21 The de e mina ion o hese pa ame e s depends
on he ex en o which con ibu ions om he
␣
-peak egion
and om he EW we e included in he analysis. This ambi-
gui y demons a es he di icul y encoun e ed when using
di e en i ing s a egies, a p oblem ha is pa icula ly acu e
a high empe a u es. He e, he spec al ange in which sec-
onda y elaxa ion ea u es a e obse able becomes smalle
and smalle so ha he powe laws o igina ing om he
␣
-peak may become indis inguishable om hose o he EW.
This si ua ion may ad e sely a ec he ou come o “ ee i s”
in he sense ha i is likely ha a i icial empe a u e depen-
dences a e in oduced. To ci cum en such p oblems, le us
eso o s udying he scaling p ope ies o dielec ic suscep-
ibili y da a om a wide empe a u e ange in a model inde-
penden way.
In o de o de ec possible changes o he loss shape we
conside no malized suscep ibili y spec a,
␹
⬙共
␯
兲=␧⬙共
␯
兲/⌬␧.
He e he elaxa ion s eng h ⌬␧ was ex ac ed om he co -
esponding ␧⬘共
␯
兲da a by aking hei low- and high-
equency limi s ␧sand ␧⬁in o accoun . ␧⬁was conside ed
cons an in he en i e empe a u e ange T⬎Tg. A empe a-
u es close o Tg he pla eau associa ed wi h ␧sis no longe
ully eached. To ob ain he pla eau alue in hose cases he
␧⬘共
␯
兲cu es we e ex apola ed o lowe equencies, acco d-
ing o hei beha io a highe empe a u es. The in eg al o
such no malized spec a yielded
␲
/2⫾0.05 o all he da a
we will p esen below. In a nex s ep we plo ed hem as a
unc ion o educed equency
␻
␶
␣
wi h
␶
␣
deno ing he ime
cons an o he
␣
- elaxa ion.
␶
␣
was de e mined in a model-
ee way as ollows: I is an in insic p ope y o he no mal-
ized spec al densi y J共
␻
兲o simple liquids ha
冏d
␹
⬙共
␻
兲
d
␻
冏
␻
␶
␣
→0
=J共0兲=
␶
␣
,共1兲
and hence
␹
⬙共
␻
␶
␣
兲兩
␻
␶
␣
→0=
␻
␶
␣
.共2兲
The e o e, as a unc ion o empe a u e, he low- equency
lank o he no malized suscep ibili y should collapse when
plo ing
␹
⬙ e sus
␻
␶
␣
. This low- equency scaling is dem-
ons a ed in Fig. 2共a兲 o a a ie y o sys ems. Le us ocus
i s on glass o me s ha we e p e iously ca ego ized as
being o ype A such as PG, glyce ol, 2-PIC, 4-TBP, and PC.
Fo se e al o hese sys ems he peak sys ema ically becomes
na owe and, since he a ea unde he peak is conse ed, he
peak ampli ude becomes highe wi h inc easing empe a u e.
To quan i y he wid h changes we no e ha , e.g., o PC a
hal he peak alue o ␧⬙ he ho izon al shi o he loss
cu es is abou 0.2 decades, while o he o he sys ems, like
2-PIC, such e ec s a e less p onounced. All cu es in Fig.
2共a兲in e sec a a equency sligh ly highe han ha co e-
sponding o he peak maximum. Fu he mo e, he high-
 





 



ε∆ε ε∆ε ()
ωτα
D
A
B


C

C

 
    
 
ω/ω




FIG. 2. 共a兲No malized dielec ic suscep ibili y spec a plo ed s educed
equency o glass o me s p e iously ca ego ized as ype B 共DHIQ and
m-FAN兲o ype A sys ems 共all o he s兲. The da a we e aken om he e e -
ences quo ed in Table I. A e scaling by ⌬␧ he da a se o each glass
o me was shi ed e ically o cla i y. The ed and he black lines e e o
he highes and o he lowes empe a u es, espec i ely, o each se o da a.
While in ame 共a兲a “low- equency scaling” p ocedu e was implemen ed,
ame 共b兲in ol es “high- equency scaling” o he example o PG.
184510-3 E olu ion o excess wing and
␤
-p ocess J. Chem. Phys. 131, 184510 共2009兲
Au ho complimen a y copy. Redis ibu ion subjec o AIP license o copy igh , see h p://jcp.aip.o g/jcp/copy igh .jsp
15 W. Kob and H. C. Ande sen, T ansp. Theo y S a . Phys. 24, 1179 共1995兲.
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19 K. L. Ngai, P. Lunkenheime , C. León, U. Schneide , R. B and, and A.
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20 A. I. Nielsen, T. Ch is ensen, B. Jakobsen, K. Niss, N. B. Olsen, R.
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28 C. Gaina u, A. B odin, V. N. No iko , and E. A. Rössle , a Xi :cond-
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32 K. Kessai i, S. Capaccioli, D. P e os o, M. Lucchesi, S. Sha i i, and P. A.
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33 V. N. No iko and A. P. Sokolo , Phys. Re . E 67, 031507 共2003兲.
34 R. Casalini and C. M. Roland, Phys. Re . Le . 91, 015702 共2003兲.
35 U. Schneide , R. B and, P. Lunkenheime , and A. Loidl, Phys. Re . Le .
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36 F. Qi, T. El Go esy, R. Böhme , A. Döß, G. Diezemann, G. Hinze, H.
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37 This does no necessa ily imply ha local 共in e nal兲mo ions a e absen .
F om NMR and calo ime y a CH3 o a ion was iden i ied o PC, see F.
Qi, R. Böhme , and H. Sillescu, Phys. Chem. Chem. Phys. 3, 4022
共2001兲.
38 A pa e n simila o ha shown in Fig. 1is also obse ed o a se ies o
polyalcohols, see A. Döß, M. Paluch, H. Sillescu, and G. Hinze, Phys.
Re . Le . 88, 095701 共2002兲; A. Döß, M. Paluch, H. Sillescu, and G.
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39 A. B odin and E. A. Rössle , J. Chem. Phys. 125, 114502 共2006兲;126,
244508 共2007兲.
40 M. Ricci, P. Ba olini, and R. To e, Philos. Mag. B 82, 541 共2002兲.
41 K. Kessai i, S. Capaccioli, D. P e os o, M. Lucchesi, and P. A. Rolla, J.
Chem. Phys. 127, 174502 共2007兲.
42 R. Kahlau e al. 共unpublished兲.
43 Handbook o Ma hema ical Func ions, edi ed by M. Ab amowi z and I.
A. S egun 共Na ional Bu eau o S anda ds, Washing on, D.C., 1964兲,
Chap. 26.
44 C. J. F. Bö che and P. Bo dewijk, Theo y o Elec ic Pola iza ion: Di-
elec ics in Time-Dependen Fields 共Else ie , Ams e dam, 1978兲, Vol. 2.
45 No e ha his connec ion o
␣
-p ocess and EW does no imply ha hese
p ocesses a e iden ical. Recen s udies show ha while he
␣
-p ocess is
iso opic, he excess wing o igina es om a spa ially highly es ic ed
mo ion, see M. Vogel, C. Tschi wi z, S. Schneide , C. Koplin, P. Medick,
and E. Rössle , J. Non-C ys . Solids 307–310, 326 共2002兲; C. Gaina u,
O. Lips, A. T oshagina, R. Kahlau, A. B odin, F. Fuja a, and E. A.
Rössle , J. Chem. Phys. 128, 174505 共2008兲.
46 The Fou ie ans o ma ion was ca ied ou nume ically using a p og am
w i en by D . A. B odin whom we hank o making his p og am a ail-
able o us.
47 The eme gence o he EW a high empe a u es is bes ecognized in
op ical Ke e ec as well as in ligh sca e ing expe imen s, see Re . 21
and H. Cang, V. N. No iko , and M. D. Faye , J. Chem. Phys. 118,2800
共2003兲.
48 No e ha o polyme ic glass o me s wo pa ame e s a e in gene al e-
qui ed o a desc ip ion o he main elaxa ion, albei he e o a di e en
eason, see A. Schönhals, F. K eme , and E. Schlosse , Phys. Re . Le .
67, 999 共1991兲.
49 The condi ions 共i兲 h ough 共iii兲can be ul illed wi h
␤
=0.63 and
␥
=0.21 o glyce ol and wi h
␤
=0.78 and
␥
=0.23 o PC. He e he
␤
-pa ame e s a e hose esul ing om p e ious scaling analyses o glyc-
e ol 共Re . 68兲and o PC 共Re . 27兲, espec i ely.
50 A ecen s udy on glyce ol a ul ahigh p essu e also epo s mo e “no -
mal”
␤
ime cons an s below he
␣
-
␤
me ging egion, see A. A. P onin,
M. V. Kond in, A. G. Lyapin, V. V. B azhkin, A. A. Volko , P. Lunken-
heime , and A. Loidl 共unpublished兲.
51 Fo xyli ol ex ended aging led o a esol ed
␤
-peak, see R. Wehn, P.
Lunkenheime , and A. Loidl, J. Non-C ys . Solids 353, 3862 共2007兲.
52 I is clea ha a he lowes empe a u es he high- equency pa o he
␣
-p ocess is i ele an o de e mining
␶
␤
.
53 G. P. Joha i, Ann. N. Y. Acad. Sci. 279,117共1976兲.
54 Fo MTHF he E/Tg a io was epo ed o be 1650/91=18.1, see Re . 36.
Since in ha a icle a di e en me hod o analysis was employed he da a
a e no included in Fig. 7.
55 T. Blochowicz and E. A. Rössle , Phys. Re . Le . 92, 225701 共2004兲.
56 R. B and, P. Lunkenheime , U. Schneide , and A. Loidl, Phys. Re . B 62,
8878 共2000兲共and e e ences ci ed he ein兲.
57 See, e.g., T. El Go esy and R. Böhme , J. Phys.: Condens. Ma e 19,
205134 共2007兲and e e ences ci ed he ein.
58 K. L. Ngai, Phys. Re . E 57, 7346 共1998兲.
59 D. Pisignano, S. Capaccioli, R. Casalini, M. Lucchesi, P. A. Rolla, A.
Jus l, and E. A. Rössle , J. Phys.: Condens. Ma e 13, 4405 共2001兲.
60 The same alue o he exponen
␥
was used by U. Buchenau, J. Chem.
Phys. 131, 074501 共2009兲; see also R. Casalini and C. M. Roland, Phys.
Re . B 69, 094202 共2004兲.
61 The beha io o TPP was a ionalized in Re . 21.
62 A. Ri e a-Calzada, 共p i a e communica ion兲, see also Fig. 3in A. Ri e a-
Calzada, K. Kaminski, C. Léon, and M. Paluch, J. Phys.: Condens. Ma -
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63 C. Gaina u, A. Ri e a, S. Pu selyk, G. Eska, and E. A. Rössle , Phys.
Re . B 72, 174203 共2005兲.
64 Apa om he da a o Re s. 63 and 65 we included da a on 3,3,4,4-
benzophenone e aca boxylic dianhyd ide 共2PC兲 om Re . 2and da a on
DHIQ om his wo k.
65 C. Gaina u, Disse a ion, Uni e si ä Bay eu h, 2007.
66 The peaks obse ed o T⬍0.3Tgin Fig. 8a e due o he elaxa ion in
asymme ic double well po en ials, see he discussion in Re . 63.
67 A. Kudlik, C. Tschi wi z, T. Blochowicz, S. Benkho , and E. Rössle , J.
Non-C ys . Solids 235-237, 406 共1998兲.
68 S. Adich che , T. Blochowicz, C. Gaina u, V. N. No iko , E. A. Rössle ,
and C. Tschi wi z, J. Phys.: Condens. Ma e 15, S835 共2003兲.
69 C. Gaina u e al. 共unpublished兲.
70 A. B odin, R. Be gman, J. Ma sson, and E. A. Rössle , Eu . Phys. J. B
36, 349 共2003兲.
184510-10 Gaina u e al. J. Chem. Phys. 131, 184510 共2009兲
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Pape 3
Quinaldine: Accessing Two C ys alline Polymo phs ia he
Supe cooled Liquid
R. Kahlau, T. Gnu zmann, F. Emme ling, K. Rademann, and
E. A. R¨
ossle ,
The Jou nal o Chemical Physics 137, 054505 (2012).
c
2012 Ame ican Ins i u e o Physics
doi:10.1063/1.4738583
79
80
THE JOURNAL OF CHEMICAL PHYSICS 137, 054505 (2012)
Quinaldine: Accessing wo c ys alline polymo phs ia
he supe cooled liquid
Robe Kahlau,1Tanja Gnu zmann,2,3 F anziska Emme ling,2Klaus Rademann,3
and E ns A. Rössle 1
1Physikalisches Ins i u , Uni e si ä Bay eu h, Bay eu h 95440, Ge many
2BAM Fede al Ins i u e o Ma e ials Resea ch and Tes ing, Be lin 12489, Ge many
3Depa men o Chemis y, Humbold -Uni e si ä , Be lin 12489, Ge many
(Recei ed 6 Ma ch 2012; accep ed 6 July 2012; published online 3 Augus 2012)
Quinaldine (2-me hyl quinoline) is a liquid a oom empe a u e, which can be supe cooled o each
inally he glassy s a e. By hea ing he glass abo e he glass ansi ion empe a u e Tg=180 K he
sample pe o ms wo subsequen ansi ions in o, likewise, dielec ically ac i e phases. Thus, he e-
o ien a ional elaxa ions o hese phases as well as he kine ics o he phase ansi ions can be acked
in a highly esol ed way by dielec ic spec oscopy. X- ay di ac ion analysis clea ly shows wo
s uc u ally di e en c ys alline phases in addi ion o he supe cooled liquid. Calo ime ic measu e-
men s suppo he no ion o i s o de phase ansi ions, occu ing i e e sibly in he supe cooled
egime, and sugges ha he in e media e c ys alline phase is me as able, oo. Analyzing he qui e
dis inc dielec ic elaxa ion s eng hs, we discuss he possible na u e o he wo c ys alline phases.
Addi ionally, a e y simila beha io o quinaldine is obse ed o 3-me hyl quinoline, indica ing a
b oad ield o polymo phism among he quinoline de i a i es. © 2012 Ame ican Ins i u e o Physics.
[h p://dx.doi.o g/10.1063/1.4738583]
I. INTRODUCTION
O ganic compounds a e commonly known o showing
he phenomenon o polymo phism,1–8i.e., hey may exis in
s uc u ally di e en c ys alline phases. Fo example, in he
case o he compound ROY, a leas se en polymo phs ha e
been iden i ied.2Unde he gi en condi ions, only a single
phase can be he modynamically s able whe eas he o he s
a e all me as able. Finding he ou es o ob ain and cap u e
such me as able phases has hus become an impo an issue in
ma e ials science.
Many liquids can be supe cooled leading o a s ong in-
c ease o hei anspo coe icien s like iscosi y o di u-
sion coe icien . A empe a u es a ound he glass ansi ion
empe a u e Tg, he c ys alliza ion p ocess o he deeply su-
pe cooled liquid is ypically di usion con olled and he e-
o e a oided on labo a o y ime scales.1Then he liquid is in
a me as able s a e. Conside ing he chemical po en ial μl(T)
o he highly supe cooled liquid as a unc ion o empe a-
u e, usually a la ge gap opens wi h espec o he po en-
ial μc(T) o he he modynamically s able c ys alline phase
(c . Fig. 1). A me as able c ys alline phase wi h i s po en ial
μm(T), i p esen , will appea wi hin his gap. In o he wo ds,
by inc easing he empe a u e o he highly iscous liquid and
hus again acili a ing di usion he usually occu ing phase
ansi ion does no necessa ily ha e o end up wi h he he mo-
dynamic equilib ium phase bu may yield me as able phases.
Thus, s ongly supe cooling a liquid opens he possibili y o
sea ching unknown me as able phases o molecula sys ems.
A p ominen example is liquid e hanol,9,10 which ans-
o ms in o a me as able c ys al i i is kep close o Tg=97 K,
i.e., well below he mel ing poin Tm=159 K. Rega ding i s
o ien a ional deg ees o eedom, his c ys al exhibi s “glassy”
dynamics, i.e., highly coope a i e molecula o a ion abo e
he co esponding Tg. Upon hea ing, he glassy c ys al phase
o e hanol ans o ms in o he o ien a ionally o de ed and
he modynamically s able phase, which mel s a Tm.
S udying he egime o a supe cooled liquid o e en he
glass (T<Tg) wi h espec o possible phase ansi ions is also
an impo an issue in unde s anding how o s abilize glasses
agains c ys alliza ion. Fo some applica ions, o example,
pha maceu icals, he glassy s a e is ad an ageous o e he
c ys alline s a e, and i is impo an o a oid c ys alliza ion o
a leas o minimize he a e o c ys al g ow h. In a ecen ap-
plica ion, Edige and co-wo ke s11 ha e in es iga ed he di -
usion coe icien Do he supe cooled liquid indome hacin
(Tg=315 K). The au ho s ha e ound ha he empe a u e de-
pendence o he di usion is signi ican ly weake han ha o
iscosi y, and ha i is indeed D(T), which con ols he ans-
o ma ion in o he h ee iden i ied12,13 c ys alline polymo phs
o indome hacin.
In he p esen con ibu ion, he polymo phism o he
compound quinaldine (2-me hyl quinoline, 2mq, see Fig. 3)is
examined. Quinaldine is a liquid a oom empe a u e, which
can easily be supe cooled below i s mel ing empe a u e
Tm≈264–270 K as demons a ed by Capaccioli e al.14
Like in o he glass- o ming liquids, he s uc u al elax-
a ion becomes e y slow upon cooling, i.e., he eo ien-
a ional co ela ion ime o a molecule ises om τ=
10−12 s a he mel ing poin o τ=100 s a he glass
empe a u e Tg. Since he quinaldine molecule is pola ,
his beha io is well e i iable by means o dielec ic
spec oscopy,15 and we ha e de e mined he glass ansi-
ion empe a u e o be Tg≈180 K. We demons a e ha
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054505-2 Kahlau
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J. Chem. Phys. 137, 054505 (2012)
μ
m
(T)
μ
c
(T)
T
m
μ
(T)
T
T
g
liquid
s able solid phase
me as able solid phase
μ
l
(T)
FIG. 1. Sea ching o me as able phases: chemical po en ial o s able and
me as able solid phases oge he wi h ha o he (supe cooled) liquid phase;
mel ing (Tm) and glass ansi ion empe a u es (Tg) a e indica ed.
wo phase ansi ions can be moni o ed wi h he help o
dielec ic spec oscopy, x- ay di ac ome y (XRD) and di -
e en ial scanning calo ime y (DSC) upon hea ing he highly
supe cooled liquid. He e, we bene i om he ac ha all he
h ee phases o quinaldine a e dielec ically ac i e and hus al-
low o p obe he dynamics in each phase as well as bo h phase
ansi ions. Mo eo e , as quinaldine is a igid molecule o low
symme y, any dynamics has o in ol e he o al molecule.
This is likely o esul in some kind o coope a i e dynamics
in he c ys alline s a e, he na u e o which we a e in e es ed
in. Finally, we show ha simila polymo phs a e iden i ied o
3-me hyl quinoline.
II. EXPERIMENTAL
A. Chemicals
2-me hyl quinoline (“quinaldine,” CAS 91-63-4, 97+%)
was pu chased om Al a Aesa , 3-me hyl quinoline (CAS
612-58-8, 99%) was deli e ed by Sigma-Ald ich. Bo h sub-
s ances we e used as ecei ed wi hou any u he ea men .
B. Dielec ic spec oscopy
Dielec ic measu emen s we e ca ied ou wi h he
Alpha-A analyze by No ocon ol, which allows o e-
quency esol ed measu emen s o he dielec ic suscep ibili y
in he ange o ν=10−2–106Hz. Du ing a equency scan, he
sample empe a u e was kep cons an wi hin ±0.2 K wi h he
help o a Qua o-H empe a u e con olle by No ocon ol.
In o de o in e pola e he main elaxa ion peak in he
dielec ic spec a o he (supe cooled) liquid phase (2mq1),
we used a s ep esponse unc ion, which gene alizes he
Kohl ausch and he Cole-Da idson spec al shape and has
u ned ou o be a e sa ile esponse unc ion o supe cooled
liquids.16 Explici ly,
φg( )=1
β
α∞

τgαyβ
α−1exp(−y)dy =
β
α,
τgα
β
α(1)
was used o he s uc u al elaxa ion o α-peak. He e (...)
deno es he gamma unc ion and (...,...) heuppe incom-
ple e gamma unc ion as de ined by Eq. (1), espec i ely. This
(no malized) s ep esponse unc ion is connec ed wi h he sus-
cep ibili y spec a in he equency domain by he one-sided
Fou ie ans o m F(...)
ε (ω)=εχ (ω)=εωRe {F[φ( )]}(2)
wi h ε being he dielec ic elaxa ion s eng h. The in eg al
o φg( )(Eq.(1)) yields he mean elaxa ion ime
τα=τ0
β+1
α
β
α.(3)
The in e pola ion o he so-called excess wing (EW), ap-
pea ing on he high- equency lank o he α- elaxa ion peak
as a kind o powe -law, was ob ained by including he s ep
esponse o he Cole-Da idson unc ion (CD unc ion)
φCD ( )=γ,
τCD 
(γ)(4)
oge he wi h he Williams-Wa s app oach17
φ( )=[CφCD ( )+(1−C)]φg( )(5)
wi h Cbeing a measu e o he ampli ude o he EW. The
ime cons an s o bo h con ibu ions a e se equal (τg=τCD)
so ha only he high- equency powe -law wi h he exponen
γo he Cole-Da idson con ibu ion emains isible.18
The second obse ed quinaldine phase (2mq2) exhibi s
a elaxa ion peak, which has again he spec al shape o a
s uc u al elaxa ion peak a he han he shape o a seconda y
p ocess. Since i s low- equency lank, howe e , has an expo-
nen sligh ly smalle han 1 we used he no malized Ha iliak-
Negami suscep ibili y unc ion as i unc ion,
ˆχHN (ω)=1
[1 +(iωτ)α]β.(6)
The hi d phase (2mq3) shows a b oad elaxa ion peak,
which is bes in e pola ed by he dis ibu ion o co ela ion
imes usually applied o seconda y elaxa ions in glasses.19
Explici ly,
Gβ(ln τ)=Nβ(a,b)1
bτ
τβa+τ
τβ−ab (7)
wi h he no maliza ion ac o
Nβ(a,b)=a(1+b)
πbb
1+bsin πb
1+b.(8)
The pa ame e acauses a symme ic b oadening o he
dis ibu ion while bonly a ec s i s sho ime lank. The e o e
bcan also be called “asymme y pa ame e .” A e Laplace
ans o ming Gβ(ln τ) in o equency domain, he esul ing
suscep ibili y peak is b oadened symme ically by a, which
is also he exponen o he powe -law app oached asymp o i-
cally by he peak’s low equency lank. The exponen o he
powe -law asymp o e o he high- equency lank is gi en by
he p oduc ab.
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054505-3 Kahlau
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J. Chem. Phys. 137, 054505 (2012)
Fo all phases, a powe -law accoun s addi i ely o he dc
conduc i i y con ibu ion
χ
DC (ω)=Aω−1.2···−0.8.(9)
C. Di e en ial scanning calo ime y
Fo he DSC measu emen s, we used a Ne zsch DSC
200. I s empe a u e scale was calib a ed wi hin he ange
o in e es wi h he help o he i s o de phase ansi ions
o six e e ence samples (cyclohexane, chlo o o m, me cu y,
ca bon e achlo ide, wa e , benzene). The DSC-signal in en-
si y was no calib a ed; ye , any conclusions can be d awn
in a quali a i e way. Th oughou he DSC s udies wi hin his
wo k, empe a u e has ei he been kep cons an (iso he mal
measu emen ) o hea ing/cooling a es o 20 K/min ( amp ex-
pe imen s) we e applied. Any empe a u e scan shown below
was compiled o a cooling s age om oom empe a u e o
120 K, an iso he mal s age las ing 10 min and a hea ing un
back o oom empe a u e. I addi ional s ages we e applied
in o de o induce phase ansi ions, i will be explained
explici ly.
D. X- ay s uc u e analysis
The x- ay di ac ion (XRD) expe imen s we e ca ied
ou using Cu-Kα1 adia ion and a cu ed posi ion sensi i e
de ec o (INEL CPS120) and a u nace (MRI) as sample en-
i onmen . The sample was kep on a empe a e s age in a
he mally isola ing acuum. Using his se up, i was possible
o gain di ac og ams on sho ime scales in o de o ob ain
se e al snapsho s o he phase ansi ion p ocesses in he sam-
ple. In o de o gain highe signal quali ies o cha ac e izing
he nea c ys alline phases, he da a accumula ion ime could
be inc eased and adap ed o he expe imen al si ua ion.
III. RESULTS
A. Dielec ic spec a
1. Supe cooled liquid (2mq1)
Typical dielec ic suscep ibili y spec a o he supe -
cooled quinaldine’s liquid phase (2mq1, T>Tg)a eshown
in Fig. 2. In addi ion o a main (α-) elaxa ion peak, an EW is
obse ed on he high- equency lank o he elaxa ion peak.
Since no seconda y β- elaxa ion peak can be esol ed, he
sys em can be ca ego ized as ype-A glass o me .15 Bo h
spec al ea u es shi o lowe equencies wi h dec easing
empe a u e wi hou any signi ican spec al changes.
In o de o i he ull spec a, including he EW, he e-
laxa ion unc ion is made up o a con olu ion o he gene al-
ized Kohl ausch/Cole-Da idson unc ion (α-p ocess, Eq. (1))
wi h a CD unc ion wi h wid h pa ame e γ(Eq. (4)) applying
he Williams-Wa s ansa z (Eq. (5)); he CD unc ion accoun s
o he EW, which ollows a powe -law beha io (εEW(ν)
∝ν−γ). The decomposi ion o he spec a is indica ed in
Fig. 2. The high- equency shape pa ame e o he α-peak is
ound o be empe a u e independen wi h β=0.71, and also
10-2 10-1 100101102103104105106107
10-3
10-2
10-1
100
101
~
ν−β
185K 192K
ε''(ν)
ν / Hz
β=0.71
γ
=0.30
liquid phase (2mq1)
186K 190K 195K 200K 210K 215K
~
ν−γ
FIG. 2. Dielec ic spec a o supe cooled liquid quinaldine (2mq1, open
symbols: his wo k, connec ed do s: da a aken om Re . 14). Con inuous
lines: i s including elaxa ion peak and EW (Eqs. (1)–(5)). Dashed lines: de-
composed i o he spec um a 185 K. The shape pa ame e s βand γha e
been kep ixed o all empe a u es (numbe s); he shape pa ame e αand
he EW ampli ude C a y weakly (inse in Fig. 3).
he exponen o he EW γ=0.30 can be kep cons an a
all measu ed empe a u es. The pa ame e s α(low- equency
shape pa ame e ) and C(ampli ude o he EW) a y weakly
wi h empe a u e (c . inse Fig. 3). In o he wo ds, equency-
empe a u e supe posi ion (FTS) holds in good app oxima-
ion o he ull spec a. This is e i ied once again wi h he
help o he co esponding mas e cu e shown in Fig. 3whe e
he no malized suscep ibili y is plo ed e sus ωτα.Nosig-
ni ican changes in he spec al shape o bo h main elaxa ion
and EW a e obse ed. The spec al shape is in almos pe ec
ag eemen wi h ha epo ed by Capaccioli e al.14 as demon-
s a ed in Fig. 2. A small disc epancy in ampli ude ( ac o 1.1)
and equency posi ion ( ac o 1.4) exis s, which is ba ely ec-
ognized on loga i hmic scale and p obably due o a iny mis-
ma ch in empe a u e calib a ion.
The ex ac ed elaxa ion imes τα(c . Eq. (3)) a e shown
in Fig. 4(a) (squa es). Thei non-A henius empe a u e
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
-5
10
-4
10
-3
10
-2
10
-1
180 190 200 210
0.0
0.2
0.4
0.6
0.8
1.0
ε''/Δε
ωτ
α
2mq1
2mq2
liquid phase (2mq1)
scaled by
ωτ
α
T / K
α
C
FIG. 3. Suscep ibili y spec a (182 K– 215 K) o supe cooled liquid quinal-
dine no malized by he elaxa ion s eng h ε and plo ed e sus ωτα(con-
inuous lines). Fo compa ison: main elaxa ion o he second phase 2mq2 (a
215 K, dashed line). Inse : empe a u e dependence o he i pa ame e s α
and C(c . Eqs. (1),(4),and(5)).
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054505-4 Kahlau
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J. Chem. Phys. 137, 054505 (2012)
4.44.85.25.6
10-6
10-3
100
103
2mq1
2mq2
2mq3
τ / s
1000K / T
Tg1=(180±0.5)K
Tg3=(180±2)K
Tg2=(193±1)K
(a)
quinaldine
ime cons an s
180 190 200 210 220
101
102
103
104
2mq3
2mq2
TΔε
T / K
2mq1
quinaldine
elaxa ion s eng hs (b)
FIG. 4. (a) Time cons an s τo he h ee dielec ically ac i e phases o quinaldine; τo 2mq1 (liquid, squa es) a e in e pola ed by a VFT law (Eq. (10)); τ
o 2mq2 ( iangles) and 2mq3 (c osses) a e i ed by A henius laws. The co esponding alues o Tg(de ined by τ(Tg)=100 s) a e indica ed. La ge open
symbols: ime cons an s as ob ained by DSC. (b) Tes ing he Cu ie law: p oduc Tε e sus empe a u e o each phase.
dependence being ypical o supe cooled liquids, indica ing
coope a i e molecula dynamics, can be in e pola ed by a
Vogel-Fulche -Tammann (VFT) law, explici ly
τ=τ0exp B
T−T0.(10)
We de ine he glass ansi ion empe a u e as Tg=T(τα
=100 s), which is de e mined as Tg1=180 K (c . Fig. 4(a)).
In o de o compa e he e ec i e dipole momen s μe pa ic-
ipa ing in he elaxa ion p ocesses o he di e en quinaldine
phases, we analyze he elaxa ion s eng hs (see also Eq. (2))
ia he Cu ie law
ε =Nμ2
e
3kBT(11)
wi h Nbeing he numbe densi y o dipoles. In Fig. 4(b), he
p oduc Tε o phase 2mq1 is plo ed e sus empe a u e
and compa ed o ha o he o he phases (c . below). In ag ee-
men wi h Eq. (11), a cons an alue is ob ained all o e he
analyzed empe a u e ange.
2. Second phase (2mq2)
When he supe cooled liquid o quinaldine is kep a
empe a u es abo e, say, 200 K, he dielec ic spec a be-
come ime dependen , c . Fig. 5. He e he sample was kep
a T=210 K. The ime in e al be ween wo shown da a
sweeps was abou 35 min. Wi h ad ancing ime, he am-
pli ude o he α- elaxa ion o he liquid dec eases mono-
onically, while he dc-conduc i i y con ibu ion a low
equencies is lowe ed simila ly. A in e media e equencies
a second, weake elaxa ion peak is e ealed. I s ampli ude
inc eases mono onically wi h ime (a ows in Fig. 5(a)). Fi-
nally, he dielec ic esponse becomes again empe a u e in-
dependen , and he ans o ma ion was comple ed a e 6 h.
Since he ampli ude o he elaxa ion peak in he dielec ic
suscep ibili y is p opo ional o he densi y o o a ionally mo-
bile dipoles (c . Eq. (11)), he s ong dec ease o he signal in
he equency ange o he main elaxa ion o he liquid indi-
ca es he disappea ance o he liquid phase. We conclude ha
he sample is pe o ming a phase ansi ion o ano he phase
(2mq2) wi h di e en o a ional deg ees o eedom, which
esul s in a new elaxa ion peak a lowe equencies.
100101102103104105106
10-2
10-1
100
101
ε''(ν)
ν / Hz
2mq2
elaxa ion
dc conduc i i y 2mq1
elaxa ion
2mq1 o 2mq2
T=210K
=0...6h
(a)
4.50 4.75 5.00 5.25 5.50 5.75
10-20
10-16
10-12
10-8
10-4
100
104
108
103104105
0
600
1200
1800
τ
τα
ime / s
1000K / T
(b)
TΔε(2mq1)
/ s
200K
210K
215K
FIG. 5. (a) Moni o ing dielec ic spec a (symbols) a T=210 K o e 6 h demons a ing he phase ansi ion om he liquid (2mq1) o a second phase (2mq2);
a ows: p og ess o ime. Lines: i s made up o he sum o he con ibu ions o 2mq1 elaxa ion (Eqs. (1),(4) and (5)), o 2mq2 elaxa ion (Eq. (6))and
o conduc i i y con ibu ion (Eq. (9)). (b) T ansi ion imes τ (open diamonds) compa ed o he s uc u al elaxa ion imes ταo 2mq1 ( ull squa es). Inse :
dec ease o he p ope y Tε( ) o he liquid phase 2mq1 du ing ansi ion o phase 2mq2 e sus ime a di e en empe a u es (squa es). Lines: i s acco ding
o he A ami law (Eq. (12)).
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054505-5 Kahlau
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J. Chem. Phys. 137, 054505 (2012)
In Fig. 5(a), he o e all suscep ibili y cu es a di e en
imes a e compa ed and in e pola ed by he sum o h ee spec-
al con ibu ions: he 2mq1 elaxa ion desc ibed by Eqs. (1),
(4), and (5), he 2mq2 elaxa ion (Ha iliak-Negami, Eq. (6)),
and he conduc i i y con ibu ion gi en by Eq. (9). Du ing i -
ing, all ime cons an s and spec al shape pa ame e s we e
kep cons an . Only he elaxa ion s eng h pa ame e ε o
bo h phases and he conduc i i y pa ame e s we e adjus ed.
Fo he sake o cla i y, only e e y six h suscep ibili y scan is
shown in Fig. 5(a). In o de o access he phase ansi ion ki-
ne ics, he ime dependence o he elaxa ion s eng h o he
liquid’s spec al con ibu ion shall be quan i ied. In he inse
o Fig. 5(b) he ob ained decay cu es Tε( ) a e in e pola ed
wi h he A ami law
Tε( )=Tε( =0)exp −
τ n,(12)
which is o en used o desc ibe c ys alliza ion kine ics.20 Any
induc ion pe iod is neglec ed since he p epa a ion ime o
each expe imen is sho compa ed o he ans o ma ion p o-
cess, which i sel se in al eady du ing he i s equency
scans. He e Tε( ) is assumed o be p opo ional o he ac-
ion o un ans o med liquid. The esul ing exponen s nshow
some a ia ion: n(200 K) =2.2, n(210 K) =2.6 and n(215
K) =2.9. Dan ulu i e al.21 ha e ound alues o he same
ange o he c ys alliza ion kine ics o supe cooled celecoxib.
In Fig. 5(b), he ob ained ans o ma ion imes τ (open di-
amonds) a e compa ed o he s uc u al elaxa ion imes τα
( ull squa es) o he liquid phase 2mq1 (c . Fig. 4(a)). Ob-
iously, τ shows a empe a u e dependence di e en om
ha o he s uc u al elaxa ion, ollowing he ela ion τ ∝
τα0.44. Acco ding o Re . 22, he A ami ansi ion ime τ is
connec ed wi h he linea c ys alliza ion eloci y u ia
u∝τ−n
n−1
∝τ0.44
α−n
n−1=τ−0.72
α,(13)
assuming a ime and clus e -size independen a e o he mal
nuclea ion a cons an empe a u e. The las equali y was ob-
ained a e inse ing he a e age exponen o he h ee A ami
in e pola ions n=2.57 (see ex abo e). Since a decoupling
o he di usion coe icien D om iscosi y η,explici ly
D∝η−ξ∝τ−ξ
αwi h ξ≤1,(14)
is well es ablished,23 di usion con olled c ys al g ow h is ex-
pec ed o lead o u∝D∝τα−ξ. This has been con i med by
Sun e al.2 o he c ys alliza ion o di e en (supe cooled)
liquids (ξ=0.7–0.8). As we ind a simila exponen , we as-
sume ha he phase ansi ion om 2mq1 o 2mq2 is con-
olled by di usion, oo.
The dielec ic spec a o he phase 2mq2 a di e en
empe a u es can be moni o ed as demons a ed in Fig. 6.
In o de o accoun o he low- equency exponen o he
elaxa ion peak, which is smalle han one, in e pola ions
ha e been done by applying he Ha iliak-Negami unc ion
(Eq. (6)). The dc conduc i i y con ibu ion has been included
in he i ing p ocedu e by adding a powe law acco ding
o Eq. (9). A low empe a u es, he suscep ibili y de ia es
om he Ha iliak-Negami shape due o an eme ging high-
equency con ibu ion eminding o an EW. Since his ea-
u e is no esol ed well in he whole empe a u e ange,
10-1 101103105
10-3
10-2
10-1
205 210 215 220
0.3
0.6
0.9
ε''(ν)
ν / Hz
206K 209K 212K 215K 218K
2mq2
α
αα
αβ
ββ
β
β
ββ
β
T / K
α
αα
α
FIG. 6. Dielec ic suscep ibili y spec a o he second phase o quinaldine
2mq2 a indica ed empe a u es; in e pola ion (solid lines) by Ha iliak-
Negami unc ion (Eq. (6)) including a dc-conduc i i y con ibu ion (Eq. (9)).
Inse : empe a u e dependence o he co esponding shape pa ame e s α( i-
angles; exponen o he low equency peak lank) and β(do s). The p oduc
αβ (squa es) ep esen s he high- equency lank’s exponen .
i has been excluded om he i s. A highe empe a u es,
he conduc i i y con ibu ion de ia es om a simple powe -
law beha io . He e he i ing ange was limi ed o equen-
cies one decade below he minimum posi ion. As shown in
Fig. 6, a small inc ease o he low- equency exponen β
o he elaxa ion peak is obse ed. This is e lec ed once
again by he inc ease o α(low equency exponen ) wi h
a cons an p oduc αβ (high- equency exponen , c . inse
o Fig. 6). The esul ing ime cons an s τHN a e included in
Fig. 4(a). In con as o he supe cooled liquid, τHN o 2mq2
seems o show an A henius empe a u e beha io yielding
an ac i a ion ene gy Ea/kB=24 100 K. Conside ing he ex-
ponen ial p e ac o τ0=7.10 ×10−53 s o he A henius
i , which is no a physically easonable alue o a single
pa icle a emp ime, we expec he τ(T) cu e o la en a
highe empe a u es. Since he pe mi i i y cu es a e p e-
sen ed on loga i hmic scale, i shall be poin ed ou ha he sec-
ond phase’s elaxa ion s eng h is s ikingly smalle han he
one o he liquid. In Fig. 4(b) he p oduc Tε is plo ed in o -
de o be compa ed wi h he indings o he liquid (2mq1). We
ind again a empe a u e independen alue wi h Tε(2mq2)
≈0.06 Tε(2mq1).
3. Thi d phase (2mq3)
Simila o he abo e desc ibed ans o ma ion o he su-
pe cooled liquid, he dielec ic spec a o 2mq2 become ime
dependen a high empe a u es, say, T=210 K– 230 K. The
phase ans o ma ion e ol es on a slowe ime scale compa ed
o ha om phase 2mq1 o 2mq2, he e o e, sligh ly highe
empe a u es a e conside ed. The ans o ma ion leading o
he hi d phase (2mq3) a T=218 K is displayed in Fig. 7.
The ime in e al be ween wo shown spec a is now abou
158 min. The comple e ans o ma ion ook 130 h. In con as
o he ans o ma ion shown in Fig. 5, he appea ing elaxa ion
peak o phase 2mq3 is si ua ed a sligh ly highe equencies,
compa ed o he diminishing peak o phase 2mq2.
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054505-6 Kahlau
e al.
J. Chem. Phys. 137, 054505 (2012)
10
2
10
3
10
4
10
5
10
6
10
-2
10
-1
ε
''(
ν
)
ν
/ Hz
2mq2 o 2mq3
T=218K
=0...129h
FIG. 7. Time e olu ion o he dielec ic spec a documen ing he phase an-
si ion om phase 2mq2 o 2mq3 a T=218 K; (a ow) p og ess o ime.
The spec a o phase 2mq3 a di e en empe a u es a e
shown in Fig. 8. He e he bes in e pola ions o he qui e b oad
peaks can be ob ained wi h he help o a dis ibu ion o co -
ela ion imes Gβ(ln τ)(Eq.(7); cons an b=0.36), ypi-
cally applied o in e pola e a seconda y elaxa ion p ocess in
molecula glasses.19 The esul ing ime cons an s τβshow ap-
p oxima e A henius beha io wi h a mean ac i a ion ene gy
o Ea/kB=19 100 K (c . Fig. 4(a)). Fo a he mally ac i a ed
p ocess go e ned by a dis ibu ion o ac i a ion ene gies, he
wid h o he elaxa ion peak is expec ed o diminish un il he
peak assumes Debye shape a in ini e empe a u e, since he e
he empe a u e dependen Gβ(ln τ) becomes a δ-dis ibu ion.
The ime cons an hen app oaches he a emp ime τ0o he
A henius law. As shown in he inse o Fig. 8, he ecip ocal
wid h pa ame e 1/adoes no anish a in ini e bu a he a
a ini e empe a u e. This may be explained15 by w i ing he
Ey ing exp ession o each co ela ion ime o he dis ibu ion
τ=τ00 exp −Sa
kBexp Ea
kBT(15)
10
-2
10
0
10
2
10
4
10
6
10
-3
10
-2
0
1
2
-10
-8
-6
-4
-2
4.00 4.25 4.50 4.75 5.00
ε
''(
ν
)
ν
/ Hz
τ00
=10-9s
1000K / T
log(
τ
β/s)
1/a
216K
196K
212K
206K
2mq3
T
δ
=235K
1/a
b=0.36
τβ
FIG. 8. Relaxa ion peaks o he hi d quinaldine phase 2mq3 a empe a u es
as indica ed (2K-inc emen , open symbols). Dashed lines: In e pola ions wi h
a dis ibu ion o co ela ion imes Gβ(ln τ)(Eqs.(7) and (8)) and a dc con-
duc i i y con ibu ion (Eq. (9)). Inse : Tempe a u e dependence o he ime
cons an τβ(squa es) and he wid h pa ame e 1/a ( iangles). The asymme-
y pa ame e could be kep ixed o b=0.36.
wi h Eabeing he ac i a ion en halpy and Sa he ac i a ion
en opy. In oducing now he so-called Meye -Neldel ule,24
which assumes a linea ela ionship be ween en opy and en-
halpy, explici ly
Sa=Ea
Tδ
,(16)
leads o he exp ession
τ=τ00 exp Ea
kB1
T−1
Tδ,(17)
which explains he limi τβ(T)=τ00 o be eached a T=Tδ.
The wid h o he elaxa ion peak, and hus he p ope y 1/a,
ollows he empe a u e dependence19
1
a∝1
T−1
Tδ
(18)
and consequen ly anishes when Tδis eached. We ind o
2mq3 Tδ=235 K, being ac ually qui e a low alue, and τβ(T
=Tδ)=τ00 =10−9s, which is a leas somewha close o
a physically easonable alue o a single molecule a emp
ime (c . inse o Fig. 8).
B. Di e en ial scanning calo ime y
The ansi ions obse ed by dielec ic spec oscopy we e
in es iga ed u he wi h DSC. DSC hea ing scans applying
a hea ing a e Q=20 K/min o he supe cooled quinaldine
(2mq1) in he empe a u e ange om 120 K o oom em-
pe a u e e ealed an endo he mal s ep wi h an onse a 183
K (“glass s ep,” see Fig. 9, opmos line). Addi ionally, an
exo he mal peak was obse ed a 235 K ollowed by an en-
do he mal peak a 255 K. Finally, a 266 K he endo he -
mal mel ing peak is ound in acco dance wi h he li e a u e
(Tm≈264–270 K). Ten a i ely, we a ibu e he wo peaks
obse ed in he DSC scan below he egula mel ing poin o
phase ansi ions o he phases 2mq2 and 2mq3, espec i ely.
The elaxa ion imes p obed by DSC can be compa ed
wi h hose om dielec ic spec oscopy a e calcula ing he
120 140 160 180 200 220 240 260 280 300
185 195 205
185 195 205
2mq3
2mq2
T
g
=(183±0.5)K
DSC signal (a b. uni s)
T / K
quinaldine
2mq1
Tg=(195±2)K
Tg=(191±2)K
FIG. 9. DSC scans o he quinaldine phases 2mq1 ( opmos line), 2mq2 (cen-
al line), and 2mq3 (lowe mos line)—see ex . S aigh do ed lines: Guides
o he eye, indica ing he onse s o he endo he mal s eps.
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054505-7 Kahlau
e al.
J. Chem. Phys. 137, 054505 (2012)
10 15 20 25 30 35 40 45 50
In ensi y (a. u.)
2θ / °
2mq1
200 K, = 17 h
205 K, = 2 h
205 K, = 1 h
200 K, = 0
2mq2
(a)
10 20 30 40 50
2mq2, 200K
In ensi y (a. u.)
2θ / °
(b)
2mq3, 200K
FIG. 10. (a) XRD da a o quinaldine moni o ed du ing he phase ansi ion om 2mq1 o 2mq2 (e olu ion imes and eco ding empe a u es as indica ed).
(b) Compa ison o he long- ime di ac og ams (15 h accumula ion ime) o bo h c ys alline quinaldine phases 2mq2 and 2mq3 a e p esumably comple e
ans o ma ion.
calo ime ic ime cons an ia25,26
τcal =kBT2
g
He Q.(19)
He deno es he ac i a ion en halpy aken om he dielec-
ic da a a he calo ime ic Tg. Thus,
He =kB
∂ln τ
∂1
T
1
Tg
=kBB
1−T0
Tg2(20)
holds in he case o a VFT empe a u e dependence (Eq. (10)),
and He =Ea=cons . o he case o an A henius empe -
a u e dependence. The ex ac ed DSC ime cons an s o all
h ee phases (see below) a e plo ed in Fig. 4(a) as open sym-
bols and show ai acco dance wi h he dielec ic ime con-
s an s.
In o de o u he cla i y he na u e o he phase an-
si ion, in he nex s ep he hea ing scan s a ing below Tg
is in e up ed a , e.g., T=218 K. Now he phase ansi ion
om 2mq1 o 2mq2 s a s and will be comple ed in less han
30 min. A e wa ds, a cooling o 120 K, 10 min o wai ing,
and ehea ing o oom empe a u e esul s in he cen al ace
in Fig. 9. As expec ed, he exo he mal peak is missing now,
only a e y weak s ep in he same empe a u e egion emains.
The endo he mal peaks a highe Ta e ound a he same posi-
ions as in he o me measu emen . This p o es ha he cen-
al cu e in Fig. 9 esul s om p obing he 2mq2 phase o
quinaldine. A T=195 K, a weak s ep is ound in he DSC
signal (c . inse ) which we in e p e , simila o he glass ansi-
ion o he liquid, as an indica ion o a “ eezing” o mo ional
deg ees o eedom wi hin phase 2mq2. Calcula ing he co -
esponding calo ime ic ime cons an acco ding o Eq. (19)
leads o he esul included in Fig. 4(a).
The expe imen can be epea ed wi h 2mq2 by in oduc-
ing an addi ional iso he mal s age a , o ins ance, T=255 K.
A e subsequen cooling, wai ing, and hea ing again o oom
empe a u e, he lowe mos line in Fig. 9is ob ained. The
missing o he i s endo he mal peak is p oo o he second
phase ansi ion om QN2 o QN3 o ha e al eady p oceeded
du ing he iso he mal s age. We now ind a weak DSC-s ep a
T=191 K (c . inse ), which is si ua ed abou 4 K below he
s ep in 2mq2 and in acco dance wi h he dielec ic indings
(c . Fig. 4(a)).
C. X- ay di ac ion
XRD expe imen s p o ide a s aigh o wa d way o iden-
i y he obse ed quinaldine phases. The expe imen is s a ed
wi h cooling he liquid below Tg=180 K. A e wa ds, he
sample empe a u e was inc eased in 5 K s eps. A e each
inc emen , XRD da a we e accumula ed iso he mally o ca.
15–20 minu es. In Fig. 10(a), he amo phous “halo” o he
supe cooled liquid (2mq1) is shown (“ =0”). A e inc eas-
ing he empe a u e up o 205 K, he sample was kep o 1 h
while se e al di ac og ams we e eco ded. The las one is
shown in Fig. 10(a) (“ =1 h”). As can clea ly be seen,
B agg e lexes om some c ys alline phase, mos p obably
2mq2, ha e eme ged on op o he di ac og am o he liquid.
A e 2 h, he amo phous con ibu ion has dec eased u he
(“ =2 h”). Since his las signal did no seem o e ol e any-
mo e e en a e u he empe a u e inc emen s up o 215 K,
he sample was cooled again o 200 K in o de o conse e
he p esen phase o he sample. He e ano he di ac og am
was accumula ed o 15 h (Fig. 10(a),“ =17 h”). The e is no
ecognizable change bu an imp o ed S/N a io due o longe
accumula ion ime.
Subsequen ly, he same s a egy as desc ibed abo e was
epea ed wi h he p esen c ys alline sample a highe empe -
a u es. A 220 K– 225 K, he signal becomes ime dependen
again: new peaks appea and old peaks s a o sh ink o e en
anish, espec i ely. This is in e p e ed as he phase ansi ion
om 2mq2 o 2mq3. A e keeping he sample a 225 K o
ca. 6 h and a 230 K o ano he hou , no mo e change in he
signal could be obse ed. The sample was hen cooled again
o 200 K, whe e ano he di ac og am was accumula ed o
15 h. Figu e 10(b) shows he compa ison o he measu emen s
wi h long accumula ion imes o bo h, signi ican ly di e en ,
c ys alline phases o quinaldine.
Due o he isola ion acuum in he chambe whe e he
sample is si ua ed du ing he measu emen , i was no pos-
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134504-2 Kahlau, Dö le , and Rössle J. Chem. Phys. 139, 134504 (2013)
seconda y p ocess. O ganic phospha e glass o me s a e also
well sui ed o be in es iga ed by 31PNMR.
15,19 Due o hei
high molecula dipole momen hese sys ems show a s ong
dielec ic esponse, oo. The spec al analysis will ocus on
scaling he da a in an app op ia e way o allow o ex ac ing
he dis ibu ion o ac i a ion ene gies g(E)aswellas he e-
laxa ion s eng h unde lying he dynamics o he β-p ocesses
in a a he model independen way, i.e., wi hou applying any
pa icula i ing p ocedu e. We will demons a e ha a s ong
inc ease o he elaxa ion s eng hs o all β-p ocesses abo e
Tgis obse ed, which again signals he “non-local” cha ac e
o seconda y p ocesses in glasses. In addi ion, compa ing he
di e en glasses con aining es e g oups wi h inc easing num-
be o in e nal deg ees o eedom, we do no see sys ema ic
changes in he spec al e olu ion, i.e., in he dis ibu ion g(E);
in some cases e en iden ical dis ibu ions g(E) a e ound.
II. EXPERIMENTAL DETAILS
T ie hyl phospha e (TEP),19 ip opyl phospha e
(TPP),15,19 ibu yl phospha e (TBP), is(2-bu oxye hyl)
phospha e (T2BOEP), and is(2-e hylhexyl) phospha e
(T2EHP) we e pu chased om Sigma-Ald ich and used
wi hou u he ea men (c . Table I). Da a o ime hyl
phospha e (TMP) is aken om Re . 20. Fo he dielec ic
measu emen s pe o med wi hin his wo k an Alpha-A ana-
lyze by No ocon ol was used in combina ion wi h a sample
cell design desc ibed in Re . 21. Absolu e empe a u e was
assumed o be accu a e wi hin ±1 K and was kep cons an
wi hin ±0.2 K by using a Qua o-H empe a u e con olle
by No ocon ol in combina ion wi h an Ox o d c yos a ,
cooled wi h liquid Ni ogen. Dielec ic measu emen s on
TMP20 we e pe o med wi h a SI1260 spec al analyze by
Schlumbe ge wi h a simila empe a u e con olling and
sample cell se up.
III. RESULTS
A. Measu emen s
The dielec ic suscep ibili y da a o TBP, TPP, T2EHP,
and TEP (c . Table I) a e compiled in Fig. 1. In all ou cases
he α- elaxa ion peak is obse able as he mos p ominen e-
laxa ion ea u e abo e Tg, while below Tgaβ- elaxa ion is
ecognized. The maximum alue ε
max o he α-peak is abou
2 o T2EHP, while in he o he cases alues a ound 10 a e
ound. When empe a u e is inc eased, he α- elaxa ion shi s
o highe equencies wi hou essen ially changing i s spec al
shape. A he same ime a loss con ibu ion caused by ionic
conduc i i y ( o mos da ase s in Fig. 1omi ed o he sake
o cla i y) mo es in o he equency window and shows he
same empe a u e dependence as he α-peak. A leas as long
as i is obse able i s onse is si ua ed 1-2 equency decades
below he equency o he α-peak in he cases TBP, TPP, and
TEP. T2EHP shows an excep ionally low conduc i i y con-
ibu ion a equencies h ee decades below he α- elaxa ion
peak equency.
A high empe a u es, when he α- elaxa ion eaches
peak equencies in he kHz egime, TBP, TPP, as well as TEP
s a o c ys allize, and no mo e pe mi i i y da a o he supe -
cooled liquid can be acqui ed. Again T2EHP is excep ional
TABLE I. Mola masses and s uc u al o mulae o he in es iga ed glass
o me s.
Sys em M(10−3kg/mol) Tg(K) S uc u e
TMP 140 137
P
O
CH
3
OCH
3
O
CH
3
O
TEP 182 137
P
O
CH
2
CH
3
OCH
2
CH
3
O
CH
2
CH
3
O
TPP 224 134
P
O
CH
2
CH
2
CH
3
OCH
2
CH
2
CH
3
O
CH
2
CH
2
CH
3
O
TBP 266 140
P
O
CH
2
CH
2
CH
2
CH
3
OCH
2
CH
2
CH
2
CH
3
O
CH
2
CH
2
CH
2
CH
3
O
T2EHP 435 159
P
O
O
OO
T2BOEP 398 167
P
O
O
O
O
O
O
O
since no c ys alliza ion endency is obse ed up o highes
peak equencies.
Clea ly, all sys ems in Fig. 1show a seconda y (β-) e-
laxa ion peak on he high- equency side o he α-peak, which
su i es below Tgdown o lowes measu ed empe a u es
(abou 80 K). Thus, all sys ems o Fig. 1may be called ype-B
sys ems. Sligh ly abo e Tg, when he α-peak is si ua ed close
o he edge o he accessible equency ange, his β-peak is
si ua ed abou 3-4 equency decades abo e he α-peak e-
quency o TBP, TPP, and T2EHP; in he case o TEP bo h
peaks a e spec ally mo e dis an .
Figu e 2shows he dielec ic da a o TMP and T2BOEP
(c . Table I). The empe a u e e olu ion o he α- elaxa ion o
hese sys ems is again simila o he o he s discussed abo e.
The maximum alue ε
max is abou 10 o TMP and 5 o
T2BOEP. TMP s a s o c ys allize when he α-peak is si -
ua ed in he kHz egime, while T2BOEP shows no c ys al-
liza ion endency. In con as o he sys ems shown in Fig. 1
TMP and T2BOEP show a mo e complex seconda y elax-
a ion pa e n. In he suscep ibili y da a o TMP an EW is
clea ly obse able in addi ion o a β- elaxa ion, i.e., on he
high- equency side o he α-peak (abou 2 equency decades
igh o he peak posi ion) ε(ν) ollows a powe law wi h
an exponen o , as ypical o he excess wing phenomenon,
−γ∼
=−0.2 (c . Fig. 2(a)). A e en highe equencies his
EW is ollowed by a β- elaxa ion peak simila o he one o
TEP (c . Fig. 1(d)). T2BOEP e en shows wo seconda y e-
laxa ion peaks, which a e well esol ed a empe a u es be-
low Tg(c . Fig. 2(d)), so TMP as well as T2BOEP, and hence
all measu ed sys ems, may be called ype-B sys ems. I shall
be men ioned ha all p esen ed sys ems may ha e an excess
wing con ibu ion which is obscu ed by he explici ly obse -
able β-peaks. Since his canno be cla i ied wi hou a model
dependen quan i a i e analysis, we ocus on he elaxa ion
peaks o α- and β- elaxa ion. We assume u he ha he di-
elec ic spec a below Tga e domina ed by he con ibu ion o
he β- elaxa ion.
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134504-3 Kahlau, Dö le , and Rössle J. Chem. Phys. 139, 134504 (2013)
10
-2
10
0
10
2
10
4
10
6
10
-2
10
0
138K
132K
110K
120K
100K
90K
80K
142K144K 148K152K156K
ε''(ν)
ν / Hz
TBP
162K
(a)
10
-2
10
0
10
2
10
4
10
6
10
-3
10
-1
10
1
114K
130K
122K
104K
94K
82K
154K
150K
144K
140K
ε''(ν)
ν
/ Hz
136K
TPP
(b)
10
-2
10
0
10
2
10
4
10
6
10
-2
10
0
220K
210K
200K
190K180K
170K
165K
135K
105K
ε
''(
ν
)
ν
/ Hz
T2EHP 95K (c)
10
-2
10
0
10
2
10
4
10
6
10
-2
10
0
74K
92K 116K
128K
134K
138K 140K 144K 148K
ε''(ν)
ν / Hz
TEP
152K
(d)
FIG. 1. Dielec ic loss da a o (a) TBP (Tg=140 K), (b) TPP (Tg=134 K), (c) T2EHP (Tg=159 K), and (d) TEP (Tg=137 K) a indica ed empe a u es.
See Table I o chemical s uc u es.
Time cons an s o all α- and β- elaxa ion peaks om
Figs. 1and 2as gi en by τmax =1/(2πνmax) a e compiled
in Fig. 3. Due o simila glass empe a u es he α- elaxa ion
imes ταo TMP, TEP, TPP, and TBP almos coincide. A sim-
ila s a emen can be made o ταo T2EHP and T2BOEP,
ye hei Tgdi e s conside ably in compa ison wi h he o he
sys ems. The ime cons an s τβ ollow A henius empe a u e
dependences a empe a u es well below Tg(s aigh lines in
Fig. 3, c . Sec. III B). The co esponding ac i a ion ene gies
(gi en in K) a y om E≈2100 – 4200 K, while he a -
emp imes a e se led a ν0=10−13 –10
15 s−1(c . Table II).
No e ha a ep esen a ion on Tg/T scale does no lead o a
collapse o he da a and does no yield u he in o ma ion.
When Tgis app oached he empe a u e dependence o τβ
10
-2
10
0
10
2
10
4
10
6
10
-2
10
-1
10
0
10
1
138K
135K
131K
120K
101K
141K 144K 147K
ε''(ν)
ν / Hz
150K
TMP
~
ν-0.17
(a)
10
-2
10
0
10
2
10
4
10
6
10
-2
10
-1
131K
66K
71K 81K 91K 101K
120K
ε''(ν)
ν / Hz
135K
TMP
(b)
10
-2
10
0
10
2
10
4
10
6
10
-1
10
0
10
1
ε
''(
ν
)
ν
/ Hz
230K
220K
210K
200K
190K
180K175K
170K
T2BOEP
(c)
10
-2
10
0
10
2
10
4
10
6
0.02
0.04
0.06
ε
''(
ν
)
ν
/ Hz
160K
150K
140K
130K
120K
110K
100K
T2BOEP
(d)
FIG. 2. Dielec ic loss da a o TMP ((a) and (b), Tg=137 K) and T2BOEP ((c) and (d), Tg=167 K) a indica ed empe a u es (c . Table I o chemical
s uc u es). Dashed lines in (a) ep esen powe laws ∼ν−γwi h γ=0.17 a ibu ed o he excess wing.
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134504-4 Kahlau, Dö le , and Rössle J. Chem. Phys. 139, 134504 (2013)
4812
10
-7
10
-5
10
-3
10
-1
10
1
TMP
TEP
TPP
TBP
T2EHP
T2BOEP
τ
max / s
1000K / T
FIG. 3. Time cons an s o αand β-p ocess de e mined om he elaxa ion
peak posi ions o all in es iga ed sys ems (c . symbol map). Small symbols:
α- elaxa ions. He e, cu ed lines a e guides o he eye. La ge symbols: β-
elaxa ions. He e, s aigh lines a e calcula ed om he dis ibu ions o ac i-
a ion ene gies g(E) in oduced in Sec. III B. No e he change o he τβ(T)
a ound Tg.
becomes weake (ac ually a kink is obse ed nea Tg, bes ec-
ognized o TBP), which is caused by an appa en inc ease o
he mean ac i a ion ene gy nea Tg(see Sec. III B,c .also
Re s. 22 and 23). In e es ingly, he ime cons an s τβ(T)o
TMP and TEP as well as TPP and TBP coincide, which may
sugges ha he mean ac i a ion ene gy as well as he a emp
ime τ0a e de e mined a he by in e molecula in e ac ions
han by in amolecula in e ac ions dependen on he di e -
en ( lexible24,25) es e g oups. As we will demons a e in
Sec. III B, he spec a o he β-p ocess can be scaled ac-
co ding o he assump ion ha i is go e ned by a b oad dis-
ibu ion o ac i a ion ene gies, i.e., he β- elaxa ion is go -
e ned by a mul i ude o he mally ac i a ed p ocesses well
below Tg.
B. Scaling analysis o he β-p ocess spec a
In his sec ion a scaling p ocedu e o he mally ac i-
a ed p ocesses will be applied o he β- elaxa ions ound
in he in es iga ed sys ems.26–28 I a empe a u e indepen-
den dis ibu ion o ac i a ion ene gies g(E) o ms he basis
o a elaxa ion p ocess, i.e., o a gi en “si e” in he glass
wi h ac i a ion ene gy E(gi en in K) a simple A henius law
TABLE II. Scaling pa ame e s (maximum ac i a ion ene gy Emand a emp
equency ν0) and i pa ame e s (Em,c,andbacco ding o Eqs. (5) and (6))
o he in es iga ed β- elaxa ions.
Scaling gβ(E) i s
Sys em Tg(K) Em(K) ν0(s−1)Em(K) cb
TMP 137 2113 1014 2074 0.00411 0.5067
TEP 137 2143 2 ×1014 2127 0.0043 0.45646
TPP 134 3350 1015 3333 0.00417 0.5318
TBP 140 3251 7 ×1014 3250 0.00356 0.5908
T2EHP 159 3458 1013 3472 0.00277 0.49246
T2BOEP 1 167 2541 4 ×1013 2526 0.00176 1.32432
T2BOEP 2 167 4284 3 ×1014 4267 0.0015 1.05335
τ=τ0exp E
Tholds, he co esponding dis ibu ion o co -
ela ion imes can be calcula ed ia
G(ln τ)d(ln τ)=g(E)d(E),(1)
G(ln τ)=T·g(E).(2)
The co esponding suscep ibili y measu ed by dielec ic spec-
oscopy is hen calcula ed o
ε(ν)=ε
∞

−∞
G(ln τ)2πντ
1+(2πντ)2d(ln τ)∼
=Tεπ
2·g(E).
(3)
He e, he app oxima ion in he las pa o he equa ion can
be made in he case o a b oad dis ibu ion G(ln τ) (leading
o a b oad g(E)), which is usually obse ed o β-p ocesses
in molecula glass o me s.5A e subs i u ing he a iable E
wi h he A henius exp ession τ=τ0exp( E
T), he dis ibu ion
o ac i a ion ene gies can be exp essed like28
g(E)=g(Tln(ν0/ν)) =2
π
ε(ν)
Tε.(4)
In o he wo ds, plo ing he igh hand side exp ession o
Eq. (4) e sus Tln(ν0/ν) e eals a mas e cu e which yields
he dis ibu ion o ac i a ion ene gies g(E). He e, he a emp
equency ν0is assumed o be cons an o all E. Since he de-
pendence o g(E)onν0is loga i hmic, any dependence o ν0
on Eas, e.g., assumed o a kind o Meye -Neldel ela ion,5,29
can be neglec ed in he scaling p ocedu e. In he ollowing
his scaling is applied o he dielec ic loss spec a o all β-
peaks o he in es iga ed sys ems in o de o cla i y i indeed
a empe a u e independen dis ibu ion o ac i a ion ene gies
is p esen .
Figu e 4displays he suscep ibili y o TBP a e he scal-
ing along Eq. (4). Ins ead o di iding he suscep ibili y ε(ν)
by Tand εβ, he la e o which would ha e had o be de-
e mined in ad ance independen ly, he da a was no malized
only by Tas a i s s ep. A e wa ds, he ε(ν)/T cu es we e
plo ed s. Tln(ν0/ν), and emaining sys ema ic de ia ions in
2000 3000 4000 5000
0.0
0.2
0.4
0.6
0.8
1.0
E=3480K
72-134K
136-148K
1000*g(E) ~
ε
''/(T
Δε
)
E = T ln(
ν
0
/
ν
) [K]
TBP
ν0=7*1014s-1
E=3251K
FIG. 4. Suscep ibili y da a o TBP (72-134 K; Tg=140 K) scaled acco ding
o Eq. (4) (black lines); suscep ibili y da a o T =136-148 K (dashed lines).
A ows indica e maximum posi ions, he co esponding alues a e gi en. A -
emp equency ν0indica ed.
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134504-5 Kahlau, Dö le , and Rössle J. Chem. Phys. 139, 134504 (2013)
2000 3000 4000 5000
ν
0
=4*10
13
s
-1
ν
0
=3*10
14
s
-1
ν
0
=10
15
s
-1
ν
0
=7*10
14
s
-1
ν
0
=10
13
s
-1
ν
0
=2*10
14
s
-1
g(E)
[
a. u.
]
E=T ln(
ν0
/
ν
) [K]
TMP
TEP
T2BOEP
T2EHP
TBP
TPP
T2BOEP
ν
0
=10
14
s
-1
FIG. 5. Dis ibu ion o ac i a ion ene gies g(E) o he indica ed sys ems.
Red lines: in e pola ions se ing as guides o he eye. No e ha T2BOEP
exhibi s wo seconda y elaxa ions.
heigh we e co ec ed by di iding he cu es by hei maxi-
mum alues. The la e a e p opo ional o εβ(T) and will
be discussed below. Ac ually, his allows o de e mine he
ela i e empe a u e e olu ion o εβ(T) no assuming any
pa icula spec al shape o he β- elaxa ion. As a hi d s ep,
he mas e cu e was no malized by i s a ea. As can be in-
e ed om Fig. 4, a e y good collapse o he da a o
T=72–134 K is obse ed o an a emp equency ν0=7
×1014 s−1. The scaling wo ks e y well o he spec a below
Tg o all in es iga ed sys ems, e en in he cases o T2BOEP,
o which wo β-p ocesses a e iden i ied. All mas e cu es
a e compa ed in Fig. 5. In o de o c oss check he alidi y o
he scaling p ocedu e, o all β- elaxa ions he mean loga i h-
mic τβ(T) we e calcula ed along he A henius law using τ0
=1/(2πν0) and he mos p obable E alues aken om g(E)
displayed in Fig. 5. They a e included in Fig. 3, and good
coincidence is ound o all da ase s well below Tg, i.e., all
s aigh lines in e pola e he measu ed poin s.
Abo e 134 K, 6 K below Tg, he scaling (Fig. 4)s a s o
ail and he elaxa ion peaks shi o highe Ewi h inc easing
empe a u e, which may co espond o a dis inc inc ease o
he mean ac i a ion ene gy nea Tg. Al e na i ely, a dec ease
o ν0nea Tgmigh also be a possible eason o he bend
in τβ(T)inFig.3(c . Sec. IV). The change o g(E)isalso
obse ed o TPP, T2EHP, and T2BOEP, when empe a u e
ge s close o Tg.
Figu e 5compiles he dis ibu ions g(E) o all in es-
iga ed β-p ocesses as ob ained by applying he discussed
scaling p ocedu e. He e, only he da ase s well below Tga e
0 1000 2000 3000 4000 5000 6000 7000
0.0
0.2
0.4
0.6
0.8
1.0
TMP
TEP
TPP
TBP
T2EHP
T2BOEP (2x)
g
β
(E)
1000*g(E) no malized
E=T ln(
ν
0/
ν
) [K]
FIG. 6. gβ(E) unc ion (dashed lines) i ed o he expe imen ally ob ained
g(E) dis ibu ions. Solid lines aken om Fig. 5; c . symbol map). No e: he
glass T2BOEP exhibi s wo β-p ocesses.
shown. In all cases, clea ly asymme ic dis ibu ions g(E)a e
e ealed. Mos p obable ene gies Em=2100–4200 K a e
ound, while ν0 a ies om 1013 s−1 o 1015 s−1. Again, s ik-
ing coincidence in peak posi ion and shape o g(E) be ween
TMP and TEP, as well as be ween TBP and TPP, espec-
i ely, is obse ed (c . also Figs. 3and 6). We no e ha a
u he plo o all g(E) e sus a educed ene gy scale E/Tg
does no yield addi ional in o ma ion. Ins ead, he coinci-
dence be ween TMP/TEP and TPP/TBP is co up ed. The dis-
ibu ion g(E) o T2EHP shows some excess con ibu ion a
E≈2000 K, po en ially indica ing ano he β- elaxa ion
(c . Figs. 5and 6).
In he ollowing he dis ibu ions o ac i a ion ene gies
shall be analyzed in a mo e quan i a i e way. Since he dis-
ibu ions o ac i a ion ene gies a e ound o be asymme ic,
he model unc ion o g(E) in oduced in Re . 30 ( he e also
applied o in e pola e seconda y elaxa ion spec a)
gβ(E)=Nβ(c, b)1
bexp[c(E−Em)] +exp[−cb(E−Em)]
(5)
wi h he no maliza ion ac o
Nβ(c, b)=c(1 +b)
πbb
1+bsin πb
1+b(6)
is adequa e and shall be i ed o he no malized g(E)o Fig.5.
No e ha a suscep ibili y unc ion such as Ha iliak-Negami
is no sui able o desc ibing a elaxa ion p ocess de e mined
by he mally ac i a ed dynamics.30,31 The esul s a e dis-
played in Fig. 6and allow a di ec compa ison o he g(E)o
he sys ems in es iga ed. All in all, good i s wi h ew mino
de ia ions a e ob ained. The s onges de ia ions a e ound o
TMP, TEP, and, due o he excess ampli ude a E=2000 K,
o T2EHP. Table II summa izes all pa ame e s cha ac e izing
he β-p ocess. Ob iously he pa ame e c, which e lec s he
in e se o e all wid h o he dis ibu ions, is lowes o bo h
elaxa ion p ocesses o T2BOEP and he p ocess o T2EHP.
The pa ame e bis a measu e o he asymme y o he dis-
ibu ion. Values a ound b =0.5 a e ound o TMP, TEP,
TPP, TBP, and T2EHP, e lec ing he high ene gy slope being
s eepe han he low ene gy slope. The elaxa ion o T2BOEP
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134504-6 Kahlau, Dö le , and Rössle J. Chem. Phys. 139, 134504 (2013)
1.0 1.5 2.0 2.5
1
2
3
Δεβ(T) / Δεβ(0.9 T
g
)
T
g
/ T
TMP (ex ap.)
TEP
TPP
TBP
T2BOEP 1
T2BOEP 2
T2EHP 1
FIG. 7. Relaxa ion s eng hs εβ(T) o he in es iga ed β- elaxa ions
(c . Table I) no malized wi h εβ(0.9 Tg) and plo ed e sus he educed
empe a u e scale Tg/T. As he TMP alues a e nea ly cons an , εβ(T)was
ex apola ed linea ly o T=0.9 Tg.
wi h Em=2500 K has a b>1, which e lec s a con e se il
o he peak. The o he T2BOEP peak is a he symme ic and
hus has a b=1.
As explained abo e, he empe a u e dependence o a
quan i y which is p opo ional o he elaxa ion s eng hs
εβ(T) is ob ained by p oducing he mas e cu es o
Fig. 5.InFig.7 he εβ(T)o allβ- elaxa ions a e compiled,
no malized o he espec i e alue εβ(T=0.9Tg), and plo -
ed e sus a educed empe a u e scale Tg/T.BelowTg he al-
ues a e ei he cons an (TMP and TEP) o dec ease sligh ly
wi h dec easing empe a u e. The only excep ion is he e-
laxa ion p ocess o T2BOEP wi h Em=4300 K (“T2BOEP
2”, c . Table II), he εβ(T) o which inc eases sligh ly
wi h dec easing T. S ikingly, all εβ(T) da a accessible a
highe empe a u es inc ease s ongly when Tgis app oached.
This inc ease se s in al eady 13–16 K below he con en ion-
ally de ined glass ansi ion empe a u e, which is gi en by
Tg=T(τα=100 s). As discussed in he In oduc ion, we ake
he s ong inc ease o εβabo e Tgas an indica ion o all β-
p ocesses o be coupled o he α-p ocess, in he sense ha g(E)
changes abo e Tgwhen he glass “so ens.” Acco ding o he
in e p e a ion sugges ed by he 2H NMR s udies10,11,13,18 he
inc ease o εβ e lec s he inc easing angula displacemen
o he molecules in ol ed in he β-p ocess.
IV. SUMMARY AND DISCUSSION
Dielec ic loss spec a o six phospha e glass o me s
wi h di e en es e g oups ha e been analyzed. A model inde-
penden scaling p ocedu e e eals a empe a u e independen
dis ibu ion o ac i a ion ene gies g(E) o all in es iga ed β-
elaxa ions well below Tg. We no e ha he scaling p ocedu e
yielding g(E) has al eady been applied success ully o se e al
molecula glass o me s.15,26–28 In pa icula , a e sion o he
scaling has been used o iden i y he low empe a u e dielec-
ic and mechanical losses assumed o o igina e om de ec s
leading o he unneling sys ems a e y low empe a u es (so-
called Gil oy-Phillips app oach).32
The dis ibu ions g(E) o di e en β- elaxa ions a y
in maximum posi ion, wid h, and asymme y and a e ca -
ego ized quan i a i ely wi h an adequa e model dis ibu ion
gβ(E). Ye , o wo pai s o sys ems iden ical dis ibu ions a e
ound, al hough di e en es e g oups a e in ol ed. Al eady
somewha below he glass empe a u e (T≈0.9 Tg) heg(E)
appea s o change. He e, an appa en inc ease o he mean ac-
i a ion ene gy (a cons an a emp equency ν0) can be in-
e ed om he sys ema ic shi o he scaled da a peaks. This
is o mally in acco d wi h a educed empe a u e dependence
o he ime cons an s τβ, a phenomenon well obse ed in he
da a and which has also been epo ed in, e.g., Re s. 22 and
23. The e ec can al e na i ely be in e p e ed as a educ ion o
he a emp equency o he A henius law (a cons an ac i a-
ion ene gy E), which may be explained by a so ening o he
po en ial landscape caused by he he mally induced inc ease
o molecula mobili y nea Tg. One may hink o b oadened
po en ial wells, leading o lowe oscilla ion equencies in a
ha monic app oxima ion.
This appa en change o g(E) is accompanied by a d as-
ic inc ease o he elaxa ion s eng hs εβ(T), which has
also been obse ed o many s uc u al glasses as well as
glassy c ys als.17 Thus, he appea ance o he change o ν0
o mean Eand he s ong inc ease o εβ(T) may be con-
side ed as a gene ic beha io o β-p ocesses obse ed in
molecula glasses. The idea o he su ounding glassy ma ix
go e ning he elaxing cen e has al eady been p esen ed by
Joha i and Golds ein.14 He e, he au ho s s a e ha in e -
molecula in e ac ions make up he po en ial ba ie land-
scape, no ma e i he elaxing g oups o molecules ha e
in e nal deg ees o eedom o mo e igidly. The phospha e
sys ems in es iga ed in his wo k a e known o ha e di e -
en con o ma ional s a es, depending on he leng h o he side
chains,24,25 which implies he p esence o in e nal mo ional
deg ees o eedom. One could expec each (chemical) p o-
longa ion o he alkyl side chain, leading o an inc ease o
in e nal deg ees o eedom, o cause a change o he ac i a-
ion ene gy dis ibu ion o he β- elaxa ion, i he la e is sig-
ni ican ly de e mined by in amolecula po en ials. Ins ead,
he g(E) is some imes a ec ed (Emax(TPP) >Emax(TEP))
and some imes no (Emax(TMP) =Emax(TEP); Emax(TPP)
=Emax(TBP)). Hence, he in e p e a ions gi en abo e con-
ce ning he empe a u e independen g(E) and he in luence o
he so ening glassy ma ix on he elaxa ion p ocess appea
o be una ec ed by he cha ac e o he in amolecula de-
g ees o eedom being p esen . Clea ly, since he elaxa ion
s eng h changes abo e Tg, heβ-p ocess is no go e ned by
a simple he mally ac i a ed p ocess as i is pa adigma ically
ound in c ys alline o o phases (e.g., solid benzene). He e,
he mo ional mechanism is caused by he (high) symme y o
he molecule, hus he quali y o he mo ion does no change
abo e and below Tg.33 We hink ha in he dense ma ix o he
glass as well as he supe -cooled liquid a signi ican , ye hin-
de ed mo ion is only possible i some ex en o coope a i i y
is p esen as in he case o he α-p ocess. This is signaled by
he gene ic change o εβ(T) abo e Tg.
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100
Pape 5
On he Coope a i e Na u e o he β-P ocess in Nea and
Bina y Glasses: A Dielec ic and Nuclea Magne ic Resonance
Spec oscopy S udy
D. Bock, R. Kahlau, B. Micko, B. P¨
o zschne , G. J. Schneide , and
E. A. R¨
ossle ,
The Jou nal o Chemical Physics 139, 064508 (2013).
c
2013 AIP Publishing LLC
doi:10.1063/1.4816374
101
102
THE JOURNAL OF CHEMICAL PHYSICS 139, 064508 (2013)
On he coope a i e na u e o he β-p ocess in nea and bina y glasses: A
dielec ic and nuclea magne ic esonance spec oscopy s udy
D. Bock,1R. Kahlau,1B. Micko,1B. Pö zschne ,1G. J. Schneide ,2and E. A. Rössle 1
1Expe imen alphysik II, Uni e si ä Bay eu h, 95440 Bay eu h, Ge many
2Jülich Cen e o Neu on Science JCNS, Ou s a ion a FRM2, Fo schungszen um Jülich GmbH,
85747 Ga ching, Ge many
(Recei ed 28 May 2013; accep ed 9 July 2013; published online 14 Augus 2013)
By means o dielec ic as well as 2H and 31P nuclea magne ic esonance spec oscopy (NMR)
he componen dynamics o he bina y glass ip opyl phospha e (TPP)/polys y ene (PS/PS-d3)is
selec i ely in es iga ed o concen a ions dis ibu ed o e he ull ange. We s udy he seconda y
(β-) elaxa ion below Tg, which is ound in all in es iga ed samples con aining TPP, bu no in nea
polys y ene. The dielec ic spec um o he β-p ocess is desc ibed by an asymme ic dis ibu ion o
ac i a ion ene gies, essen ially no changing in he en i e concen a ion egime; i s mos p obable
alue is E/k∼
=24 Tg. Pe sis ence o he β-p ocess is con i med by 31P NMR Hahn-echo and spin-
la ice elaxa ion expe imen s on TPP, which iden i y he na u e o he β-p ocess as being highly
spa ially hinde ed as ound o o he (nea ) glasses s udied p e iously, o e-in es iga ed wi hin his
wo k. The co esponding 2H NMR expe imen s on PS-d3con i m he absence o a β-p ocess in nea
PS-d3, bu e eal a clea signa u e o a β-p ocess in he mix u e, i.e., polys y ene monome s pe o m
essen ially he same ype o seconda y elaxa ion as he TPP molecules. Ye , he e a e indica ions ha
some ac ions o PS-d3as well as TPP molecules become immobilized in he mix u e in con as o
he case o nea glasses. We conclude ha in a bina y glass he β-p ocess in oduced by one compo-
nen induces a highly simila mo ion in he second componen , and his may be aken as an indica ion
o i s coope a i e na u e. © 2013 AIP Publishing LLC.[h p://dx.doi.o g/10.1063/1.4816374]
I. INTRODUCTION
Since he wo ks o Joha i and Golds ein (JG)1a second
(o β-) elaxa ion peak is a well documen ed elaxa ion ea-
u e obse ed in many liquids a equencies highe han hose
o he p ima y α– elaxa ion upon (supe -) cooling.2–7In some
cases, o ype-A glass o me s8(in con as o ype-B sys-
ems wi h a well esol ed seconda y p ocess), such a β-peak
is missing and only an “excess wing” appea s on he high-
equency lank o he α-peak. E en wo esol ed seconda y
elaxa ion peaks may be ound.9,10 Pho on co ela ion spec-
oscopy (PCS) s udies o ype-B glass o me s ha e iden i-
ied only an excess wing, which is masked by a s ong β-peak
in he dielec ic spec um.10–12 Why PCS does no p obe he
β-p ocess while i is clea ly de ec ed in dielec ic and me-
chanical elaxa ion as well as in nuclea magne ic esonance
(NMR) expe imen s emains a challenge o be unde s ood.
Thus, he si ua ion is qui e puzzling since he e exis s no inal
conclusion conce ning he na u e o hese p ocesses and hei
ele ance wi h ega d o he glass ansi ion phenomenon.
As a β-p ocess is also obse ed o molecules wi hou in-
e nal deg ees o eedom, i is assumed o be gene ic o he
glassy s a e. In con as o he α-p ocess he β-p ocess is o -
en loosely called a “local” p ocess. This classi ica ion may
sugges ha he ex en o coope a i i y o he dynamics yp-
ical o he α-p ocess is no ound o seconda y elaxa ions.
Ac ually, howe e , all co ela ion leng hs discussed o he α-
p ocess a e, i a all p esen , on he o de o a ew nanome e s
which s ill is a he local. A p ominen ea u e which migh
poin o a local cha ac e o he dynamics is he ac ha be-
low Tg he mos p obable elaxa ion ime τβo he β-p ocess
ollows an A henius empe a u e dependence, he peak wid h
inc eases wi h ecip ocal empe a u e as expec ed o a em-
pe a u e independen dis ibu ion o ac i a ion ene gies, and
he elaxa ion s eng h changes only weakly.8,13 Ye , he
mean ac i a ion ene gies a e qui e high, usually in he ange
E/k ∼
=11–26 Tg.5,7I s gene ic na u e is also signaled by
he ac ha he elaxa ion s eng h s ongly inc eases abo e
Tg, i.e., he β-p ocess p obes he “so ening” o he glass
abo e Tg. Impo an o no e is ha a β-p ocess is also ob-
se ed in supe -cooled plas ic c ys als (glassy c ys als) wi h
ac i a ion ene gies almos no al e ed wi h espec o ha o
he co esponding s uc u al glass.13,14
Sys ema ic 2H NMR solid-echo s udies on s uc u al
glass o me s such as oluene, decalin, and polybu adiene15–18
as well as on glassy c ys als like e hanol19 o cyano
cyclohexane20,21 ha e been ca ied ou in he pas . Due o
i s high sensi i i y on small-angle eo ien a ions, he solid-
echo echnique yields a clea pic u e o he na u e o he β-
p ocess in e ms o i s single-pa icle dynamics.22,23 Spa ially
highly es ic ed eo ien a ion o essen ially all molecules p e-
ails in he glassy s a e o nea sys ems. As sugges ed by
andom walk simula ions,22,24 he β-p ocess is a mul i-s ep
p ocess (like he α-p ocess), so ha he o e all loss o co e-
la ion is no achie ed be o e a numbe o elemen a y s eps
wi h a jump ime τJτβa e pe o med. The wobbling-
on-a-cone model allows o ep oduce he salien ea u es o
he NMR spec a as well as o quan i y he ex en o spa ial
0021-9606/2013/139(6)/064508/12/$30.00 © 2013 AIP Publishing LLC139, 064508-1
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064508-8 Bock
e al.
J. Chem. Phys. 139, 064508 (2013)
1000 2000 3000 4000 5000 6000
10
-5
10
-3
2546 ν
0
=5×10
13
Hz
10%
E / k = T ln(ν
0
/ν)
10
-5
10
-3
2582ν
0
=5×10
13
Hz
20%
10
-5
10
-3
3030 ν
0
=4×10
14
Hz
30%
10
-5
10
-3
3090
ν
0
=4×10
14
Hz
45%
10
-5
10
-3
3198
ν
0
=6×10
14
Hz
60%
g(E) ~
ε
'' / (T
Δε
β
)
10
-5
10
-3
3319
80%
10
-5
10
-3
3404
ν
0
=9×10
14
Hz
ν
0
=2×10
15
Hz
90%
10
-5
10
-3
3367 ν
0
=10
15
Hz
95%
10
-5
10
-3
100% ν
0
=10
15
Hz
E
max
/k=3367K
α (TPP)
FIG. 9. Dis ibu ion o ac i a ion ene gies g(E) ob ained om scaling he
suscep ibili y (c . ex ) o he sub-Tgmeasu emen s o all in es iga ed mix-
u es (concen a ions, a emp a es, and mos p obable ac i a ion ene gies
indica ed). Dashed lines: Guides o he eye. No e: A high E/k de ia ions a e
obse ed due o he α-p ocess o TPP.
go e ned by asymme ic bu empe a u e independen dis i-
bu ions o ac i a ion ene gies g(E). As a consequence, all ime
cons an s τβ ollow A henius laws. All suscep ibili y da a
can be collapsed in o de o e eal g(E), making a de ailed
discussion o shape pa ame e s, as ob ainable by da a i ing,
needless in he con ex o his wo k.
D. Cha ac e izing he β-p ocess in he TPP/PS-d3
mix u es by NMR expe imen s
As documen ed by he dielec ic spec a, he β-p ocess
in he TPP/PS mix u es is well sepa a ed om he α-p ocess.
This is an impo an p e equisi e o p obing i by NMR, in
pa icula , by applying a Hahn-echo (31P) o a solid-echo (2H)
wo-pulse sequence. The concen a ion selec ion o TPP/PS-
d3mix u es in es iga ed wi h hese echniques can be in e ed
om Table I. Figu e 10(a) shows he Hahn-echo spec a o
TPP o he c=20% mix u e. A se ies o spec a, again no -
malized o hei maximum alues, is collec ed a h ee se-
lec ed empe a u es wi h a pulse delay p=40 μs, 80 μs, and
200 μs. While a high as well as low empe a u e no spec al
changes a e ecognized, a weak bu well disce nible dec ease
o in ensi y a ound ν=−δCSA/4 is ecognized a he in e -
media e empe a u e T=121.0 K. Again, he cha ac e is ic
spec al changes associa ed wi h a β-p ocess a e well iden i-
ied. In he case o he c=50% sample a simila e olu ion o
he 31P spec a is obse ed (c . Fig. 10(b)), he e, e en longe
p alues ha e been applied a T=120.3 K (solid lines) and
he in ensi y a ound ν=−δCSA/4 almos anishes a longes
ime pas in he case o nea TPP (c . Figs. 4(b) and 5(b)).
As be o e o he nea componen s he spec al e ec can
be quan i ied by measu ing he in ensi y close o he cen e
o he spec um wi h espec o he singula i y, i.e., he quan-
-15 0 15 -15 0 15 -15 0 15
121.0K
101.5K
20% TPP / PS-d
3
31P
(a)
ν
/ kHz
166.0K
-15 0 15
-15 0 15-15 0 15
148.5K
ν
/ kHz
120.3K
50% TPP / PS-d3
31P
(b)
96.2K
FIG. 10. 31P Hahn-echo spec a o TPP/PS-d3glass a indica ed empe -
a u es, (a) c=20%, each se wi h p=40 μs, 80 μs, and 200 μs
(b) c=50%, 20 μs and 200 μs each, a T=120.3 K e y long in e -
pulse delays we e applied addi ionally (solid lines, p=400 μs, 800 μs, and
1600 μs) and he in ensi y a ν=−δCSA/4 almos anishes. Fo sho es pa
i by a CSA powde spec um is included (solid line).
i y R( p) (c . Eq. (2)). In Fig. 11(a) he R alues o long p
(200 μs) (solid symbols) measu ed o h ee TPP concen a-
ions (c=10%, 20%, 50%, and o compa ison 100%) a e
plo ed e sus empe a u e. Excep o c=100% (as dis-
cussed be o e) a dis inc minimum, essen ially no shi ing,
is displayed. This signals immedia ely ha he ime cons an
o he p ocess does no signi ican ly change in he mix u es, a
esul al eady known om ou DS s udy (c . Fig. 2). In con-
as o he c=100% sample he minimum in R( p)iswell
esol ed due o he la ge sepa a ion o α- and β-p ocess in
he mix u es. Also he dep h o he minimum is e y simila ,
a lowes concen a ion c=10% i is somewha less deep.
The decays o R( p) o he di e en TPP concen a ions
a e y simila empe a u es a e displayed in Fig. 11(c) and
compa ed o he da a o nea TPP. While o he c=50%
sample he decay o R( p) is simila o ha o c=100%, he
si ua ion o c=20% is di e en . The R( p) appea s no o
elax comple ely down o ze o, indica ing ha a low TPP
concen a ions only a ac ion o TPP molecules pa icipa es
in he β-p ocess, i.e., some molecules ha e become immobi-
lized. Ye , in all cases he decay is desc ibed by a Kohl ausch
unc ion (c . Eq. (3), below) wi h β=0.95, and he appa en
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064508-9 Bock
e al.
J. Chem. Phys. 139, 064508 (2013)
0.2
0.3
0.4
100 150 200 250 300
0.0
0.2
0.4
2
H
(a)
R
10%
20%
50%
100%
p
=200
μ
s
31
P
T / K
R
0%
10%
20%
50%
80%
90%
TPP / PS-d
3
(b)
0 500 1000 1500 2000
0.00
0.25
0.50
0.75
1.00
0.0 0.5 1.0
250
500
750
R / R(
p
=0)
p
/
μ
s
20%, 121.0K
50%, 120.3K
100%, 123.0K
31
P NMR
(c)
τ
[
μ
s]
c
FIG. 11. Tempe a u e dependence o line-shape pa ame e Ra p=200 μs o (a) TPP and (b) PS-d3; mass ac ions as indica ed. Lines se e as guides o
he eye. (c) Dependence o R( p), no malized o sho p alues,on he in e -pulse delay pas e ealed by 31P Hahn-echo; mass ac ions, and empe a u es as
indica ed; inse : ime cons an as a unc ion o concen a ion, dashed lines: a possible in e p e a ion.
ime cons an (Fig. 11(b), inse ) becomes somewha sho e as
also obse ed in he dielec ic spec a (c . Fig. 2).
Nea PS is a ype-A glass o me no showing any spec-
ally esol ed β-p ocess in he DS spec a. This is also con-
i med by 2H spin-la ice elaxa ion measu emen s, which dis-
play only a weak empe a u e dependence in he glassy s a e
as discussed be o e (c . Fig. 3). He e, he ques ion a ises
whe he polys y ene in he mix u e exhibi s a β-p ocess. Due
o he selec i i y o 2H NMR p obing solely he dynamics o
he PS-d3molecules 2H solid-echo spec a can gi e a clea -
cu answe . Figu e 12 shows a se ies o solid-echo spec a o
TPP/PS-d3wi h c=50% aken a di e en p alues o h ee
empe a u es. A p onounced spec al change is obse ed a
in e media e empe a u e T=121.5 K. Simila esul s a e ob-
se ed o he c=20% sample, in pa icula , he la ges spec-
al change is again obse ed a 123.0 K. Mo eo e , he e ec
is ound a simila empe a u es as in he case o TPP s udied
by 31P NMR. I seems ha PS in he mix u e shows some sec-
onda y elaxa ion, oo, which passes h ough he solid-echo
ime window well below Tga simila empe a u es as in he
case o TPP. The co esponding R(T) alues (a long in e -
pulse delay p=200 μs) a e included in Fig. 11(b). While
no dis inc empe a u e dependence is obse ed in nea PS-d3
(c=0%), a minimum eme ges when TPP molecules a e
added. Up o c=50% he minimum dep h inc eases
mono onously. Rema kably, he minima do no shi wi h con-
cen a ion and hey a e posi ioned oughly a he same empe -
a u e as he minima esul ing om he 31P Hahn-echo expe -
imen on TPP (Fig. 11(a)). Ac ually, he minimum o R(T)is
sligh ly shi ed o highe empe a u es in he case o he 2H
spec a o PS-d3, which is expec ed due o he highe cou-
pling cons an δQ. Taking δQ=122.4 kHz om an analy-
sis o he low- empe a u e 2H solid-s a e spec a o PS-d3,
he ex ac ed ime cons an τβag ees well wi h hose de e -
mined by DS as well as by 31P Hahn-echo expe imen (c .
Fig. 2). These indings s ongly sugges ha in he mix u es
polys y ene monome s pa icipa e in he highly hinde ed e-
o ien a ion o he β-p ocess in oduced by he TPP molecules.
In o he wo ds, he β-p ocess is no solely an in amolecula
p ocess. I appea s ha he TPP molecules cause he monome
uni s o polys y ene o wobble in a a he simila way and on
he same ime scale as he TPP molecules do.
In o de o u he in es iga e he pdependence o he
2H solid-echo spec a, Fig. 13(a) shows he solid-echo spec-
a a e y simila empe a u es o he di e en in es iga ed
-
200 0 200 -150 0 150 -150 0 150-150 0 150
87.6 K
50% TPP / PS-d3
ν
/ kHz
121.5 K 156.2 K
102.2 K
(a)
2
H NMR
-150 0 150 -150 0 150 -150 0 150 -150 0 150
ν
/ kHz
80.0K 98.8K123.0K 173.0K
20% TPP / PS-d
3
(b)
2
H NMR
FIG. 12. 2H NMR spec a o TPP/PS-d3, no malized o maxima, a indica ed
empe a u es. (a) c =50%; each se wi h p=20 μs, 200 μs (solid lines),
40 μs and 80 μs (dashed lines), (b) c=20%, p=20 μs and 200 μs. Fo
lowes empe a u es i s wi h Pake spec al shape a e included (solid ed line,
δQ=122.4 kHz).
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064508-10 Bock
e al.
J. Chem. Phys. 139, 064508 (2013)
-150 0 150
-150 0 150 -150 0 150
-150 0 150 -150 0 150
121.5K
50%
TPP / PS-d
3
ν
/ kHz
121.6K
0%
(a)
123.0K
20%
2
H
NMR
121.5K
10%
123.0K
90%
0 200 400
0.00
0.25
0.50
0.75
1.00
R / R(
p
=0)
p
/
μ
s
0%, 121.6K
10%, 121.5K
20%, 123.0K
50%, 121.5K
80%, 122.0K
90%, 123K
TPP / PS-d
3
2
H NMR
(b)
FIG. 13. (a) 2H NMR spec a o TPP/PS-d3 o a ious concen a ions o TPP a indica ed empe a u es; each se wi h p=20 μs, 40 μs, 80 μs, and 200 μs.
(b) R alues as a unc ion o in e -pulse delay, no malized o sho p alue. Lines a e i s acco ding o Eq. (3).
concen a ions. Fo nea PS-d3one ecognizes only weak
spec al changes, which is ac ually due o some o he elax-
a ion mechanism, while he spec al changes induced by la ge
p alues signi ican ly g ow wi h inc easing TPP concen a-
ion. Explici ly, a p=200 μs he spec al in ensi y a ze o
equency is he lowe , he highe cis. I seems as i he ac-
ion o PS molecules pa icipa ing in he β-p ocess g ows
wi h he ac ion o TPP molecules p esen in he mix u e.
Figu e 13(b) displays he co esponding e olu ion o R( p).
Fo all concen a ions c >0R( p) decays on simila p ime
scale (τ=(170 ±20) ms and β=1.28), while o c=0 (nea
PS-d3) a quali a i ely di e en , slowe decay is obse ed. The
la e inding is in acco dance wi h he ac ha ac ually nea
PS does no exhibi a β-p ocess and ano he elaxa ion p o-
cess may be ac i e. Fo c=90% and c=80% R( p) de-
cays down o e y low alues a long delay imes, while o
c≤50% R( p) appea s o le el o a di e en pla eaus a
longes p. In pa icula , a sys ema ic end o he inal pla eau
o inc ease wi h dec easing concen a ion is ecognized.
To access quan i a i ely he decay R( p) and in pa icu-
la he pla eau a longes imes pwe desc ibe he no malized
decay by he ollowing exp ession25
Rn( p,c)= β(c)·exp − p
τβ+(1 − β(c)),(3)
whe e β(c) is in e p e ed as a ac ion o molecules which
con ibu es o he β-p ocess, and τand βa e pa ame e s de-
sc ibing he e ec i e ime e olu ion o he echo spec a. We
no e ha he la e ime cons an is no iden ical wi h τβas
de e mined om he DS spec a. In he case o TPP, a ee
i by Eq. (3) o R( p)(c .Fig.11) p o ides simila elaxa ion
imes τ(and simila β=0.95 ±0.05) wi h a small end o
become somewha sho e a low c=20%. Since a co ela ion
be ween τand τβis expec able, his is in acco dance wi h he
DS esul whe e a weak end o sho e τβis e ealed o
c<60% (c . Fig. 3). The long- ime alue 1 – βis no any
longe ze o bu inc eases wi h dec easing TPP concen a ion.
The co esponding alue β(c) e lec ing he ac ion o TPP
molecules pa icipa ing in he β-p ocess is ound in Fig. 14.
The highe is he TPP concen a ion, he highe is he ac-
ion o TPP molecules pa icipa ing in he β-p ocess. We no e
ha in he case o e hanol, cyano cyclohexane, and oluene
(Fig. 5(a)) we ind a pla eau alue 1 – β=0.0 ±0.04 while
in he case o nea TPP we ind β=0.93, i.e., 1 – β=0.07
±0.04 pu ing ou abo e gi en s a emen on a quan i a i e
basis: in nea glasses essen ially all molecules ake pa in he
β-p ocess while his is no longe he case in a bina y sys em.
In he case o PS-d3a co esponding analysis o R( p)
along Eq. (3) (solid lines in Fig. 13(b)) p o ides essen ially
he same ime cons an s, bu , ne e heless, a ying ac ions
o PS molecules pa icipa ing in he β-p ocess. The esul is
included in Fig. 14. Wi h inc easing TPP concen a ion also
he ac ion o PS molecules pa icipa ing in he β-p ocess
g ows quickly. I e en appea s ha he ac ion βo PS is
highe han ha o TPP. This excess ac ion becomes mos
conspicuous a c=0, whe e a pla eu alue o β(c=0) =0.25
is ound. This is somewha un easonable, since, due o he ab-
sence o TPP molecules, no con ibu ion o he β- elaxa ion
is expec ed a all. One can a gue ha , due o some u he
0.0 0.2 0.4 0.6 0.81.0
0.00
0.25
0.50
0.75
1.00
( )
31
P NMR
2
H NMR, no m. o
p
→ 0
2
H NMR, no m. o c=0,
p
→∞
TPP / PS-d
3
β
c
( )
FIG. 14. F ac ion o molecules o TPP (c osses) and PS-d3( ull squa es:
no malized o beha io o nea PS-d3; open squa es: no malized o sho p
alue) pa icipa ing in he β-p ocess as es ima ed by he Hahn-echo and solid-
echo expe imen s. Dashed s aigh lines: A possible in e p e a ion.
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064508-11 Bock
e al.
J. Chem. Phys. 139, 064508 (2013)
elaxa ion p ocess in nea PS, R( p) decays o some pla eau
which has o be aken in o accoun also in he mix u e. Thus
eno malizing 1 – βby 1 – β(nea PS), he ac ion βde-
c eases and becomes simila o ha o TPP. Thus he ac ions
o TPP and PS molecules pa icipa ing in he β-p ocess coin-
cide o each concen a ion.
As discussed abo e, he dynamics o nea PS-d3and TPP
ha e also been cha ac e ized by he spin-la ice elaxa ion
moni o ed as a unc ion o empe a u e (c . Fig. 3(a)). No
indica ion o a β-p ocess shows up o PS-d3while below
Tgin TPP he 31P elaxa ion is clea ly con olled by he β-
p ocess. The indings o he TPP/PS mix u e wi h c=50%
a e shown in Fig. 3(b). Wi h espec o he nea componen s,
he esul s a e now qui e di e en . Below Tg he empe a-
u e dependences T1(T) o TPP and PS-d3 un pa allel, i.e.,
he same s ong empe a u e dependence is obse ed in bo h
me hods. Abo e Tga minimum is ound o TPP which e-
lec s he iso opic eo ien a ion o he TPP molecules in he
mix u e. A simila minimum occu ing ye a highe empe -
a u es is ound o PS-d3. This di e ence di ec ly e lec s he
decoupling o he p ima y (iso opic) dynamics o he com-
ponen s: in he mix u e PS eo ien s much slowe han TPP,
a ac well known om esul s on asymme ic bina y glass
o me s.42,43 The e is a u he ea u e he de ailed discus-
sion o which is pos poned o a o hcoming publica ion: A
empe a u es o which he T1minimum o TPP occu s, pa -
icula i ies a e also obse ed in he 2H elaxa ion o PS-d3.
This shows ha he as iso opic dynamics o TPP a ec s he
polys y ene monome s leading o a highly hinde ed (i.e., non-
iso opic) dynamics, howe e , occu ing a simila ime scale
as he TPP molecules. These indings demons a e ha a plas-
icize molecule does no only change he Tgbu also induces
addi ional dynamics on he polyme .
As in he case o nea TPP he empe a u e dependence
o he spin-la ice elaxa ion can be unde s ood on a quan i a-
i e le el by aking he dielec ic esul s in o accoun . These
p o ide he dynamic suscep ibili y de e mined by a empe -
a u e independen dis ibu ion o ac i a ion ene gies, which
ac ually does no change signi ican ly in he mix u e. Analo-
gously o he case o 31P dielec ic suscep ibili y da a can be
compa ed o T1(T)o 2H NMR a e ex apola ing i o highe
equencies. As can be seen in Fig. 3(b) (dashed line) he slope
o T1(T) o TPP as well as PS-d3is ep oduced.
IV. DISCUSSION AND CONCLUSION
We ha e s udied he seconda y (β-) elaxa ion p ocess in
he bina y glass mix u e TPP/PS by dielec ic spec oscopy as
well as TPP/PS-d3by 31P and 2H NMR. While nea TPP ex-
hibi s a β-p ocess ( ype-B glass o me ) and nea polys y ene
shows none ( ype-A), in he mix u e also PS-d3molecules
clea ly pa icipa e in he β- elaxa ion. He e, o bo h TPP
and PS-d3, NMR spec a e eal a spa ially highly es ic ed
mo ion as iden i ied by NMR in o he ype-B sys ems, like
oluene16,22 o e hanol.17,23 Up o ou knowledge a Hahn-
echo sequence (he e o 31P) has been applied o he i s
ime o moni o he sub le spec al changes deep in he glass
cha ac e is ic o he β-p ocess. The dielec ic spec a e lec
a dis ibu ion o ac i a ion ene gies which is empe a u e in-
dependen ; ye , i s asymme ic shape is a he unusual o
β-p ocesses and does no change wi h concen a ion, a phe-
nomenon obse ed also in o he bina y glass o me s.25,43,44
E en a a TPP concen a ion o c=10% he mean ac i a-
ion ene gy is s ill simila o ha o nea TPP. The β-p ocess
in oduced by he ype-B componen su i es in he mix-
u e and induces he ype-A molecule o pa icipa e in he
elaxa ion p ocess. Ye , in con as o nea sys ems no all
molecules pa icipa e in he β-p ocess; islands o igidi y o
immobili y appea . The highe he concen a ion o he ype-
B componen he highe is he ac ion o bo h componen s
which pa icipa e. We emphasize, as we do no ind any in-
dica ion o he mixed glasses o decompose, he immobi-
lized molecules a e no pa o c ys alline egions. Ins ead he
mix u es become glasses wi h inhomogeneously dis ibu ed
dynamics. In a ecen 2H NMR s udy o ano he bina y sys-
em ( oluene/a oclo ) an indica ion o a h eshold concen a-
ion has been ound below which immobile ype-B molecules
appea .25 Al hough no su icien NMR da a a a ious con-
cen a ions has been collec ed in he p esen s udy a simila
beha io can be an icipa ed also o TPP/PS-d3. Only below,
say, c=60% some ele an ac ion o TPP o PS-d3appea
o become immobilized. This co esponds wi h he (sligh )
change o he mean ac i a ion ene gy below 60% (c . Figs. 7
and 9).
All oge he he p esen ed expe imen al indings poin
in o he di ec ion ha also he β-p ocess exhibi s some co-
ope a i e na u e. When mixed wi h ype-B molecules, ype-A
molecules do eac o he highly hinde ed mo ion in oduced
by he β-p ocess, ac ually a beha io expec ed in (dense) con-
densed ma e . A simila phenomenon is obse ed o he de-
coupled iso opic eo ien a ion o he TPP molecules in he
i i ied ma ix o polys y ene. Whe he he ex en o spa ial
hind ance is he same o he wo molecules is ye o be in es-
iga ed. In any case bo h componen s show dynamics on he
same ime scale.
ACKNOWLEDGMENTS
The au ho s acknowledge inancial suppo by Deu sche
Fo schungsgemeinscha (DFG) unde G an No. RO 907/10.
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Pape 6
Dynamics o Asymme ic Bina y Glass Fo me s. I. A Dielec ic
and Nuclea Magne ic Resonance Spec oscopy S udy
R. Kahlau, D. Bock, B. Schmid ke, and E. A. R¨
ossle ,
The Jou nal o Chemical Physics 140, 044509 (2014).
c
2014 AIP Publishing LLC
doi:10.1063/1.4861428
115

116
THE JOURNAL OF CHEMICAL PHYSICS 140, 044509 (2014)
Dynamics o asymme ic bina y glass o me s. I. A dielec ic and nuclea
magne ic esonance spec oscopy s udy
R. Kahlau, D. Bock, B. Schmid ke, and E. A. Rössle a)
Expe imen alphysik II, Uni e si ä Bay eu h, 95440 Bay eu h, Ge many
(Recei ed 30 Oc obe 2013; accep ed 20 Decembe 2013; published online 29 Janua y 2014)
Dielec ic spec oscopy as well as 2H and 31P nuclea magne ic esonance spec oscopy (NMR)
a e applied o p obe he componen dynamics o he bina y glass o me ip opyl phospha e
(TPP)/polys y ene (PS/PS-d3) in he ull concen a ion (cTPP) ange. In addi ion, depola ized ligh
sca e ing and di e en ial scanning calo ime y expe imen s a e pe o med. Two glass ansi ion
empe a u es a e ound: Tg1(cTPP) e lec s PS dynamics and shows a mono onic plas icize e ec ,
while he lowe Tg2(cTPP) exhibi s a maximum and is a ibu ed o ( as e ) TPP dynamics, occu ing
in a slowly mo ing o immobilized PS ma ix. Dielec ic spec oscopy p obing solely TPP iden i ies
wo di e en ime scales, which a e a ibu ed o wo sub-ensembles. One o hem, again, shows as
TPP dynamics (α2-p ocess), he o he (α1-p ocess) displays ime cons an s iden ical wi h hose o
he slow PS ma ix. Upon hea ing he α1- ac ion o TPP dec eases un il abo e some empe a u e Tc
only a single α2-popula ion exis s. In e sely, below Tca ac ion o he TPP molecules is apped by
hePSma ix.A lowcTPP he α2- elaxa ion does no ollow equency- empe a u e supe posi ion
(FTS), ins ead i is go e ned by a empe a u e independen dis ibu ion o ac i a ion ene gies leading
o co ela ion imes which ollow A henius laws, i.e., he α2- elaxa ion esembles a seconda y p o-
cess. Ye , 31P NMR demons a es ha i in ol es iso opic eo ien a ions o TPP molecules wi hin a
slowly mo ing o igid ma ix o PS. A high cTPP he supe -A henius empe a u e dependence o
τ2(T), as well as FTS a e eco e ed, known as ypical o he glass ansi ion in nea sys ems. © 2014
AIP Publishing LLC.[h p://dx.doi.o g/10.1063/1.4861428]
I. INTRODUCTION
The e olu ion o he dynamic suscep ibili y in nea glass
o me s is well documen ed s a ing a empe a u es close o
he boiling poin and eaching he glass ansi ion empe a-
u e Tg,whe e he liquid becomes an amo phous solid.1–7In
pa icula , ligh sca e ing, dielec ic, and NMR spec oscopy
ha e p o ided a weal h o in o ma ion. In con as , bina y
glass o me s a e less s udied, and no b oadly accep ed pic-
u e o he a he complex dynamics has es ablished so a .
O special in e es a e so-called asymme ic glass o me s,
which a e cha ac e ized by a la ge di e ence o he Tg al-
ues o he componen s. They a e mos con enien ly p e-
pa ed by blending a polyme wi h a low-molecula mass
addi i e,8–13 ye also pu ely low-molecula weigh mix u es
ha e been s udied.14–18 I is well es ablished ha such sys-
ems exhibi wo glass ansi ion empe a u es albei hey a e
ully miscible.19–25 In o he wo ds, such bina y liquids display
p onounced dynamic he e ogenei ies,5,26,27 which a e in pa -
icula well documen ed by NMR.28–30 Fo example, in insic
con inemen e ec s a e expec ed when he mobile (low-Tg)
componen s ill elaxes in a ma ix o an a es ed (high-Tg)
componen . Indeed, he NMR phenomenology is simila o
ha o nea glass o me s embedded in po ous sys ems.31–34
Bina y sys ems consis ing o so o ha d sphe es ha e
also been in es iga ed by simula ions35–37 as well as by mode
a)Au ho o whom co espondence should be add essed. Elec onic mail:
[email p o ec ed].
coupling heo y (MCT).38–41 In con as o nea sys ems, o
which a ype-B glass ansi ion scena io is expec ed by MCT,
which is igge ed by cage o ma ion and cha ac e ized by a
discon inuous change o he non-e godici y pa ame e om
ze o o >0 a a c i ical empe a u e Tc, he mobile molecules
in bina y liquids a e expec ed o exhibi a ype-A ansi ion,
and should inc ease con inuously om ze o upon cooling
below Tc. He e, he mobile (small) pa icles unde go a local-
iza ion ansi ion, while he less mobile (la ge) ones a e s ill
a es ed due o he cage e ec . In a ecen pape by Blochow-
icz e al.13 expe imen al hin s ha e been gi en ha indeed
such ype-A ansi ions migh be obse ed in mixed molecu-
la liquids. We no e ha such dynamic he e ogenei ies ha e
also been explained ei he by concen a ion luc ua ions42,43
o so-called sel -concen a ion e ec s.44 I is he aim o he
p esen con ibu ion o dwell on his issue by applying se -
e al expe imen al me hods o s udy selec i ely he dynamics
o each componen on a (sho -chain) polyme -addi e
sys em.
The bina y glass ip opyl phospha e (TPP)/(deu e a ed)
polys y ene (PS/PS-d3,Mw≈2×103g/mol) is cha ac e -
ized by means o dielec ic spec oscopy (DS), 2H and 31P
NMR as well as by dynamic depola ized ligh sca e ing
(DLS) and di e en ial scanning calo ime y (DSC). Thi -
een concen a ions equally sp ead o e he ull concen a-
ion ange a e in es iga ed. The sys em is cha ac e ized by a
la ge Tgcon as o he pu e componen s (Tg∼
=200 K).45,46
Due o he choice o his sys em he applica ion o 31P and
2H NMR allows o p obing selec i ely he dynamics o TPP
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044509-2 Kahlau
e al.
J. Chem. Phys. 140, 044509 (2014)
TABLE I. TPP mass concen a ions cTPP o mix u es s udied by he di e en me hods, including he assumed e o s (see ex ). NMR da a o 80% will be
discussed in Pape II.47
cTPP [%] nom. 0 10 20 30 36 45 50 60 70 80 90 95 100
DS 0 8 ±318±329±2 ... 45±1 ... 60±1 ... 80±190±195±1 100
DSC 0 10 ±120±1 ... 36±145±1 ... 60±170±183±190±1 ... 100
DLS ... ... ... ... ... ... ... ... ... 80±190±1 ... 100
2HNMR 0 10±120±1 ... ... ... 50±1 ... ... 80±1 (Pape II)47 90 ±1 ... ...
31PNMR ... 10±120±1 ... ... ... 50±1 ... ... 80±1 (Pape II)47 90 ±1 . . . 100
and PS-d3, while dielec ic spec oscopy p o ides essen ially
in o ma ion on he dynamics o he mobile componen TPP,
since i s molecula dipole momen is signi ican ly highe han
ha o PS. Rega ding he p onounced β-p ocess p esen in he
mixed sys em, i has been s udied ho oughly by ou g oup.45
I s ime cons an shows he ypical A henius beha io wi h
an ac i a ion ene gy E/k∼
=24 Tg, which i ually does no
a y due o mixing, and which is associa ed wi h a spa ially
highly hinde ed dynamics as ound in o he glasses. Ac ually,
h oughou his wo k, only a spa ially highly es ic ed p o-
cess shall be unde s ood as a β-p ocess. Al hough in oduced
by TPP, in he mix u e bo h componen s pa icipa e in he β-
p ocess. This has been aken as an indica ion o i s coope a i e
na u e.
In he p esen con ibu ion we ocus on he dynamics o
bo h componen s abo e Tg, mo e p ecisely abo e Tg2o he
mobile componen . By pe o ming DSC expe imen s we can
iden i y wo glass ansi ion empe a u es. We will demon-
s a e ha he high-Tgcomponen PS shows liquid dynam-
ics simila o ha o nea sys ems while TPP displays a he
complex he e ogeneous dynamics. Fo example, he empe a-
u e dependence o he co ela ion ime changes om supe -
A henius a high cTPP o A henius beha io a low concen-
a ions. Thus, he addi i e p ocess may be con used wi h a
β-p ocess, and i is up o NMR o p oo whe he he p ocess
is s ill liquid-like (iso opic) o β-p ocess-like.
This con ibu ion consis s o wo pa s, he p esen one
essen ially deals wi h he esul s collec ed by dielec ic spec-
oscopy, complemen ed by ime cons an s p o ided by NMR
and DLS as well as DSC. In Pape II47 con inua i e NMR ex-
pe imen s a e epo ed and analyzed in acco dance wi h he
dielec ic esul s.
II. EXPERIMENTAL DETAILS AND DATA ANALYSIS
A. Sys ems
A polys y ene sample wi h he molecula mass
Mw=2250 g/mol (PS), and ano he polys y ene sam-
ple, pa ially deu e a ed a he backbone, wi h e y simila
mass Mw=2440 g/mol (PS-d3) we e pu chased om Poly-
me S anda ds Se ice (Mainz, Ge many) and used wi hou
u he ea men . Fo he DS expe imen s PS was used o
he p epa a ion o he mix u es, while PS-d3was used o he
NMR measu emen s. T ip opyl phospha e (TPP, 99%) was
bough om Sigma Ald ich and used as ecei ed, oo. We do
no ind any indica ion ha phase sepa a ion o c ys alliza ion
occu s in he mix u es. Among o he es s, ligh sca e ing
expe imen s show a homogeneous sample. NMR and DLS
samples we e p epa ed in he measu emen ubes and cells,
while he DSC and DS samples had o be p epa ed in sepa a e
es ubes (exac concen a ions alid o di e en me hods
a e lis ed in Table I). Gene ally a concen a ion e o o ±1%
is assumed o he sample p epa a ion. A e he p epa a ion
all sample essels we e le a ele a ed empe a u es o one
o wo days in o de o gua an ee a maximum possible spa ial
homogenei y. In he case o DSC and DS he sample had
o be ans e ed a e wa ds om he p epa a ion essel o
he measu emen cell. In he case o DS he samples o low
concen a ions had o be hea ed ca e ully du ing he ans e ,
because hey a e highly iscous a oom empe a u e. Since
some ac ion o he TPP con en may ha e e apo a ed
du ing his p ocess, he assumed ac ual e o o he cTPP
=10%–30% samples is somewha highe (Table I). In con-
as , he DSC samples could be ans e ed o he measu e-
men cells wi hou hea ing. Fo he sake o cla i y he nominal
(nom.) concen a ions a e discussed h oughou he pape .
B. Dielec ic spec oscopy
Dielec ic measu emen s we e ca ied ou wi h he
Alpha-A Analyze by No ocon ol while empe a u e was
kep cons an wi hin ±0.2 K by using he Qua o-H empe a-
u e con olle by No ocon ol. The absolu e accu acy is as-
sumed o be be e han ±1 K. The sample cell has he de-
sign desc ibed by Wagne and Riche and assu es a cons an
sample olume.48 In o de o ex ac ime cons an s om he
dielec ic suscep ibili y da a, unless desc ibed di e en ly in
he ex a Kohl ausch s e ched exponen ial was used o i he
α1- elaxa ion peaks (on he imescale o PS dynamics), and
he mean elaxa ion ime τ=(1/βK)τ0/βKis discussed.
Fo he α2-peaks ( e lec ing as e TPP dynamics) a Ha iliak-
Negami (HN) unc ion had o be used due o s e ching pa am-
e e s signi ican ly less han uni y on he low- equency side o
he peak. In hese cases he maximum co ela ion imes gi en
by τmax =1/(2πνmax) a e discussed.
C. Depola ized ligh sca e ing
Depola ized dynamic ligh sca e ing measu emen s we e
pe o med wi h a e ically pola ized Cohe en Ve di-V2 lase
a a wa eleng h o 532 nm and 200 mW op ical powe in
combina ion wi h a andem Fab y-Pé o in e e ome e (TFPI;
JRS Scien i ic, iple-pass- andem E alon) wo king pa allel
wi h a double monoch oma o (DM; Jobin Y on, U1000).
The TFPI was ope a ed a ho izon al pola iza ion in almos
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150 200 250 300 350 400
0.05
0.10
0.15
0.20
= dq/d [W/g]
T / K
0%
10%
20%
36%
45%
60%
70%
80%
90%
100%
Q = 10K/min
(a)
140 160 180 200 220 240 260
0.00
0.01
36%
45%
d /dT [W/(gK)]
(shi ed)
T / K
70%
Q = 30K/min
(b)
FIG. 1. (a) DSC aces (hea low pe sample mass =dq/d ) o mix u es and nea sys ems (cTPP =0%–100%) a he hea ing a e Q=10 K/min.
(b) Tempe a u e de i a i e o DSC aces d /dT a hea ing a e Q=30 K/min o indica ed concen a ions.
backsca e ing geome y, whe eas he DM was ope a ed a
o hogonal geome y ( o de ails, see Re s. 49 and 50). The
TFPI measu emen s we e done wi h h ee di e en ee spec-
al anges, and he DM measu emen s wi h wo combina ions
o sli s and equency in e als. The spec al pa s a e hen
adjus ed in ampli ude o ma ch oge he and o m a smoo h
spec um.
D. DSC
DSC expe imen s we e pe o med wi h a Q1000 ana-
lyze by TA Ins umen s. By using a liquid ni ogen cool-
ing sys em he empe a u e ange T=120–400 K was co -
e ed. Expe imen s p esen ed we e un a hea ing a es Q
=10–40 K/min. Figu e 1(a) displays DSC aces o nea PS
and TPP as well as mix u es wi h cTPP =10%–90% TPP in PS
(nominal concen a ions, see Table I), eco ded wi h a hea ing
a e o Q=10 K/min. Fo bo h o he nea samples a dis inc
glass s ep is ound. Fo he mix u es a compa ably b oad glass
ansi ion empe a u e ange is obse ed, consis ing o wo in-
di idual, mo e o less sepa a ed s eps. This is bes seen in
Fig. 1(a) o in e media e concen a ions. In o de o achie e a
be e esolu ion o bo h con ibu ions he empe a u e de i a-
i e o he DSC aces13 a e conside ed (Fig. 1(b)). The bes
esul s we e ob ained he e by choosing a hea ing a e o
Q=30 K/min o all samples. Glass empe a u es as yielded
by DSC expe imen s we e de ined as he peak empe a u es
o he empe a u e de i a i es jus desc ibed (c . Fig. 10).
In o de o calcula e calo ime ic ime cons an s he
o mula,
τcal ≈RT 2
g
He
·1
Q,(1)
was used.17,51 I u ns ou ha o all sys ems a cons an p e -
ac o RT 2
g
He ≈1.7 could be used in good app oxima ion, lead-
ing oane o inτDSC smalle han a ac o o wo. The
ex ac ed ime cons an s a e included in Fig. 9.
E. NMR
Rega ding he NMR analysis we e e o Pape II.47 In
he p esen pape we only epo some o he NMR esul s
conce ning co ela ion imes.
III. RESULTS
A. Nea componen s – dielec ic spec a
The suscep ibili y spec a o PS (Tg=335 K) a e shown
in Fig. 2and i well in o he collec ion o dielec ic da a on
polys y ene samples o di e en molecula weigh s gi en in
Re . 52. Abo e Tga p onounced peak is isible, which is iden-
i ied as s uc u al o α- elaxa ion shi ing o high equencies
wi h inc easing empe a u e. The low ampli ude e lec s he
a he non-pola na u e o he PS monome . Close o Tg, he
high- equency side o he α-peak is made up o a c osso e
om one powe -law beha io o ano he one, he la e o en
being called excess wing.1,7,53 When he sample is cooled be-
low Tg he α-peak mo es ou o he equency window and he
signal, now consis ing only o he excess wing con ibu ion,
d ops close o he esolu ion limi o he spec ome e . No in-
dica ions o a seconda y (β) elaxa ion peak a e obse ed o
PS (c . Re . 45).
The dielec ic spec a o nea TPP (Tg=135 K) a e also
displayed in Fig. 2. As in he case o PS, abo e Tgan α-
elaxa ion peak can be iden i ied, he ampli ude o which ex-
ceeds he one o PS by a ac o o 1000, i.e., he TPP molecule
ca ies a high dipole momen . A equencies se e al decades
abo e he maximum posi ion o he α-peak a seconda y elax-
a ion is well esol ed ( ype-B glass o me ). This seconda y
(β-) peak su i es a empe a u es below Tgwhen he α-peak
has al eady le he equency window. When empe a u e is
inc eased abo e, say, T=150 K, bo h peaks app oach each
10
-3
10
-1
10
1
10
3
10
5
10
7
10
-4
10
-3
10
-2
10
-1
10
0
10
1
142K
138K
345K
148K
290K
375K
365K
355K
156K
330K
335K
ε
''(ν)
ν/ Hz
395K
PS
152K
144K
140K
136K
TPP
FIG. 2. Suscep ibili y spec a o nea TPP ( op, ci cles; empe a u es indi-
ca ed). Dielec ic spec a o nea PS; T=290 K and T=330–355 K in 5 K
s eps, T=365–395 K in 10 K s eps (bo om, iangles; some empe a u es
indica ed).
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10-2 100102104106
0.00
0.02
0.04
270K
169K
330K
310K
ε
''(
ν
)
ν
/ Hz
298K
20% TPP / PS
FIG. 13. Da a om Fig. 4(b); iangles: α1- elaxa ion o T=290–330 K,
ci cles: α2- elaxa ion o T=169–280 K. Dashed lines: α2-con ibu ions
calcula ed om he g(E) scaling esul shown in Fig. 12(a) along Eq. (2).
Solid lines: i s (c . ex ).
equencies. In his empe a u e ange, each spec um was
i ed wi h he sum o a Kohl ausch unc ion wi h βK(T)
=0.28–0.38 and he co esponding ( ixed) α2-con ibu ion
calcula ed om he empe a u e independen g(E). The e-
sul s (solid ed lines in Fig. 13) ag ee wi h he da a. Resul ing
ime cons an s τ1,as well as τ2,calc =(1/2πν0)exp(Emax/T)
calcula ed wi h Emax =6000 K and ν0=2.3 ×1015 s−1
(Fig. 12(a)), a e included in Fig. 5(c osses). Good co e-
spondence wi h he expe imen al τ2,as well as, espec i ely,
he τ1yielded by he di ec i ing analysis o he α1-peak
(Secs. II B and III B), is obse ed. The esul ing elaxa ion
s eng hs ε1(T) a e included in Fig. 6(open iangles).
APPENDIX B: REVEALING THE α1-PROCESS
AT INTERMEDIATE CONCENTRATIONS
Figu e 14 shows dielec ic da a o he (a) 30% and (b)
45% TPP/PS mix u es. In con as o he 10% and 20% da a
(Fig. 4) only one elaxa ion peak is explici ly obse able.
No e ha be ween 30% and 100% TPP only a single peak
is obse ed in he suscep ibili y (besides he β-p ocess; c .
Appendix C), and wi h highe concen a ions his peak in-
c eases u he in ampli ude and de elops con inuously in o
he α-p ocess o nea TPP. In he case o he 30% and 45%
mix u es s ill aces o he α1- elaxa ions can be iden i ied.
10
-2
10
0
10
2
10
4
10
6
10
-3
10
-2
10
-1
10
0
10
1
β
K
=0.23
308K
298K
288K
278K
268K
258K
248K
ε''(ν)
ν / Hz
∼ν
-1
238K
30% TPP / PS
FIG. 15. Suscep ibili y o he cTPP =30% sample (squa es). Red lines: con-
duc i i y con ibu ion. Blue lines: suscep ibili y a e sub ac ing conduc i i y
con ibu ion. Dashed lines: Kohl ausch unc ions wi h βK=0.23.
By plo ing he da a on linea scale, one can in e om
Fig. 14(a) ha a e y b oad minimum is loca ed be ween con-
duc i i y and α2-peak. When empe a u e is inc eased beyond
abou 272 K up o 346 K he ini ially b oad minimum be-
comes na owe and dec eases i s ampli ude. A simila , ye
weake e ec is obse ed o cTPP =45% be ween T=230 K
and 250 K (Fig. 14(b)). Since in he case o he 10% and 20%
mix u es a dec ease o ε1(T) wi h inc easing Tis obse ed,
we specula e ha he dec easing minimum e lec s a hidden
α1- elaxa ion peak.
In o de o e eal he α1- elaxa ion peak, he conduc i i y
con ibu ion has o be sub ac ed. This allows o es ima ing
elaxa ion ime and s eng h. In Fig. 15 his is demons a ed
exempla ily o he suscep ibili y da a o he 30% sample; o
he 45% da a a simila p ocedu e was applied. The esul ing
τ1(T) co espond well wi h he NMR indings (Fig. 5).
APPENDIX C: FURTHER SUSCEPTIBILITY DATA
Fig. 16 shows u he spec a o he mix u es wi h he
TPP concen a ions cTPP =60%, 80%, 95%. A hese high
concen a ions no easonable es ima ion o he dielec ic ime
cons an τ1o he α1- elaxa ion is possible any mo e.
FIG. 14. Dynamic suscep ibili y da a o TPP/PS mix u es. (a) 30% TPP in PS, T=190–260 K in 10 K s eps and T=262–346 K in 2 K s eps. (b) 45% TPP in
PS, T=200–230 K in 10 K s eps and T=232–250 K in 2 K s eps.
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044509-11 Kahlau
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J. Chem. Phys. 140, 044509 (2014)
10
-3
10
-1
10
1
10
3
10
5
10
7
10
-1
10
0
β
60% TPP / PS
250K
210K200K
190K
180K170K
ε
''(
ν
)
ν
/ Hz
160K
α
2
(a)
10
-3
10
-1
10
1
10
3
10
5
10
7
10
-1
10
0
β
80% TPP / PS
ε
''(
ν
)
ν
/ Hz
146K 152K 158K 164K
170K
176K
182K
188K
194K
200K
α
2
(b)
10
-3
10
-1
10
1
10
3
10
5
10
7
10
-1
10
0
10
1
β
95% TPP / PS
154K 162K
220K
210K
198K
170K
166K
158K
150K
146K
142K
ε
''(
ν
)
ν
/ Hz
138K
α
2
(c)
FIG. 16. Suscep ibili y spec a o mix u es wi h a TPP concen a ion o
(a) cTPP =60%, (b) cTPP =80%, and (c) cTPP =95%.
APPENDIX D: LINE SHAPE PARAMETERS
OF THE α2-PROCESS AT HIGH CONCENTRATIONS
As is demons a ed in Fig. 11(b), a high TPP concen a-
ions he main empe a u e e ec ega ding he shape o he
spec a is a b oadening on he low- equency lank o he α2-
130 140 150 160 170 180 190 200
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
c
TPP
= 80%
c
TPP
= 90%
c
TPP
= 95%
a(T)
T / K
α2
- elaxa ion peak
low eq. pa ame e
c
TPP
= 100%
FIG. 17. Ha iliak-Negami i pa ame e a(T), ep esen ing he low
equency exponen o he α2- elaxa ion peak, o se e al concen a ions.
Lines: guides o he eye.
elaxa ion upon cooling. This is also e lec ed in he shape pa-
ame e s o he α2-peak as ob ained by i s wi h he Ha iliak-
Negami unc ion. In Fig. 17 he empe a u e dependence o
he HN pa ame e ais displayed o se e al concen a ions.
In all cases he s ong empe a u e dependence obse ed a
low empe a u es seems o disappea a high empe a u es,
al hough a Cole-Da idson beha io wi h low- equency ex-
ponen 1 canno be in e ed. Ye , one may specula e ha he
spec al shape does no change any longe a high empe a-
u es, i.e., he e FTS applies also o he α2-p ocess.
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