Assessment and applications of magnetoelastic resonators as platforms for remote real-time mass detection

D O C T O R A L T H E S I S
Assessmen and applica ions o
magne oelas ic esona o s as pla o ms
o emo e eal- ime mass de ec ion
Bea iz Sisniega So iano
Supe iso s:
P o . Al edo Ga cía A ibas
P o . Jon Gu ié ez E xeba ia
2025
(cc) 2025 Bea iz Sisniega So iano (cc by-nc-sa 4.0)
Ag adecimien os
Las p ime as pe sonas a las que quie o da las g acias son mis di-
ec o es, Al edo y Jon. En p ime luga , po habe me apad inado du-
an e es os años, po odo lo que gene osamen e me habéis enseñado, po
habe me iniciado en el mundo de la ciencia y enseña me a desen ol e me
en él, animándome a publica y dándome la opo unidad de pa icipa
en con e encias. También po habe con iado en mí y habe me dado
libe ad pa a oma decisiones y abaja au ónomamen e; c eo que he
ap endido mucho de eso. Quie o ag adece a Jon su labo como in e -
media io acili ándome ecu sos, ges iones y con ac os (consegui ma e-
iales, co a mues as, isi a o os labo a o ios...), y su ayuda con el
papeleo de la esis. Y a Al edo, su disposición y su ce canía, g acias po
da me siemp e los mejo es consejos cien í icos, p o esionales y ambién
pe sonales; alo o mucho u opinión, u gus o po las cosas bien hechas
y u buen ojo.
Po supues o, ambién quie o da las g acias a Robe o Fe nández
de Luis po su g an ayuda con una pa e de es a esis. Pa a mí has sido
un ejemplo de gene osidad y de abajo. G acias po u paciencia, po
enseña me an as cosas sob e MOFs, po pone a mi disposición odos
los equipos, po ayuda me siemp e que e lo he pedido y po mos a me
una o ma de abaja que me oy a lle a conmigo.
O a pe sona a la que quie o ag adece su ayuda es Manu Ba an-
dia an, po lo amable que ha sido siemp e y po que siemp e que se ha
implicado mucho más de lo que e a azonable espe a cuando le hemos
pedido ayuda. G acias po compa i conmigo u sabe y u in uición.
También quie o da le las g acias a Jo ge Feuch wange , que sabe de
odo y que me ha ayudado genuinamen e con odo ipo de cosas, con el
alle , con el diseño y la imp esión de piezas, con el mon aje de equipos,
con dudas cien í icas, in o má icas, o de la ida. Casi cada ez que me
lo encuen o, me ayuda con algo. Muchas g acias po u p edisposición
a ayuda siemp e.
I would also like o hank P o esso Ong o his wa m welcome o his
g oup in he Knigh Campus. Thank you o gi ing me he oppo uni y
o wo k wi h you and sha ing wi h me you knowledge and expe ise, i
has been a pleasu e. I also wan o men ion Will and Je , who spen
he days eaching me how o wo k wi h he cells, and we e e y kind
o me om he e y i s day. Those mon hs in O egon we e a e y
good expe ience bo h p o essionally and pe sonally, which I hink I will
always keep in my mind, hank you guys!
También engo que menciona a las pe sonas (amigos) que han an-
dado po es e camino conmigo, los demás es udian es de doc o ado y
compañe os que han pasado po el depa amen o, Danny, Guille, Ne ea,
Jon Ande , Ca men, Alain, Ande , Mikel, Andoni, Asie , Eide , Ma ín,
Alba..., y a los doc o andos de a iba ( ísica). G acias po habe he-
cho es os años mucho más di e idos. A los que habeis acabado, en-
ho abuena! Y a los que aún os queda, mucho ánimo!
G acias a mi amilia, y a Da id, que son siemp e el mejo apoyo.
Po úl imo, g acias al Gobie no Vasco po concede me la beca del
P og ama P edoc o al de Fo mación que me ha pe mi ido ealiza es a
esis. A la gen e del depa amen o de Elec icidad y Elec ónica y del
G upo de Magne ismo y Ma e iales Magné icos po acoge me. También
quie o da las g acias a la gen e de BCMa e ials po deja me usa sus
ins alaciones, y a los se icios gene ales de la uni e sidad.
Abs ac
Magne oelas ic Resonance senso s (MER senso s) ha e a ac ed he
a en ion o he senso communi y o e he pas decades as hey ha e,
besides hei sensi i i y, e sa ili y and low cos , he po en ial o ope -
a e emo ely hanks o hei magne ic exci a ion and de ec ion. MER
senso s a e based on he mechanical esonance phenomenon ha can
be exci ed in e omagne ic ma e ials ( ypically amo phous) ia hei
exposi ion o al e na ing magne ic ields. This is possible due o he
magne os ic ion, which is a p ope y o hese ma e ials ha couples
mechanical de o ma ion wi h magne iza ion, and allows o exci e mag-
ne oelas ic wa es wi hin hem. Speci ic equencies o ha exci a ion
(ma ching he dimensions o he ma e ial) gi e ise o he magne oe-
las ic esonance beha io , which can be magne ically de ec ed. MER
senso s de eloped in ecen yea s a e based on he changes o his es-
onance beha io (and mo e speci ically, o i s esonance equency) e-
la ed o changes on di e en ex e nal ac o s a ec ing he ma e ial (as
empe a u e, iscosi y, p essu e, magne ic ield, mass loads…), and hei
po en ial is s ill being explo ed o ind new applica ions. In pa icula ,
hei use as mass senso s ( esponse o changes on hei mass) is one o
hei mos e sa ile uses, as he unc ionaliza ion o hei su ace wi h
di e en ac i e ma e ials p o ides hem wi h adso p ion capaci ies o
di e en na u e (which ans o ms he in e ac ion wi h he a ge in o a
mass change). Magne oelas ic esona o s ha e been used as mass senso s
o de ec nanopa icles, di e en gases, bac e ia, pH changes...,e c.
The p esen Thesis, ocuses on he s udy o he pe o mance and ap-
plicabili y o hese magne oelas ic senso s ope a ing as emo e eal- ime
mass senso s. Di e en s a egies o imp o e he de ec ion o hese sen-
so s and he e alua ion o some limi a ions ha e been s udied. Then, he
subsequen applica ion o di e en eal- ime mass de ec ion expe imen s
ha e been pe o med.
Fi s , in o de o cha ac e ize he MER senso s and pe o m a eal-

ime acking o he esonance cu es, a measu emen sys em based on
impedance measu emen s was de eloped and con olled wi h LabVIEW.
Then, he nume ical i ing o he esonance cu es o he senso o an-
aly ical exp essions has been e alua ed as a pos -p ocessing s a egy o
imp o e he de ec ion. I was ound ha he i ing imp o es signi i-
can ly he esolu ion o he senso s, by imp o ing he accu acy in he
de e mina ion o he main esonance pa ame e s (especially he eso-
nance equency).
On he o he hand, he in luence ha he magne ic elaxa ion su -
e ed by hese ma e ials has on he sensing pe o mance has been in es i-
ga ed. I was ound ha unde he e ec o he bias magne ic ield, mag-
ne oelas ic ma e ials expe ience a elaxa ion phenomenon ha g ea ly
a ec s he senso pe o mance and limi s i s accu acy, as i causes a
ime d i o i s esonance signal (and esonance equency). This e -
ec and di e en app oaches o a oid i s nega i e impac (selec ing he
condi ions o he expe imen and pos -p ocessing he sensing da a) ha e
been s udied. I was ound ha he ampli ude o he exci a ion ield
has a g ea in luence on his elaxa ion beha io and can signi ican ly
educe i s e ec s. Besides ha , i was ound ha he ime-d i o he
esonance equency associa ed wi h his phenomenon can be co ec ed
by modeling he elaxa ion beha io and sub ac ing i s e ec .
Rega ding he applica ion o hese MER senso s, i s hey ha e been
applied o moni o he p og ess o he p ecipi a ion eac ion o calcium
oxala e c ys als (one o he mos common mine als ha o ms calci ica-
ions on he u ina y ac ). A ibbon o a co osion esis an amo phous
e omagne ic alloy (Fe73C 5Si10B12) was selec ed as he esona o ma-
e ial. This magne oelas ic pla o m was success ully used o moni o in
eal- ime he o ma ion o hese sal c ys als, allowing o s udy he quan-
i y o calcium oxala e o med in di e en condi ions and he dynamics
o he eac ion. In o de o ob ain a alid mass sensi i i y calib a ion
o he senso , a de ailed s udy o i s sensi i i y in he expe imen al con-
di ions was pe o med. The e ec o he su ounding medium and he
elas ic p ope ies o he coa ing ma e ial (analy e) on he mass sensi i -
i y was analyzed. I was ound ha he medium, al hough a ec s he
esonance, does no a ec he mass sensi i i y. Ins ead, he coa ing ma-
e ial’s p ope ies ha e a signi ican impac on he mass sensi i i y, and
should be aken in o accoun when calib a ing he senso s. The nume -
ical i ing o he esonance cu es and he co ec ion o he elaxa ion
beha io we e pe o med in hese p ecipi a ion eac ion expe imen s o
imp o e he esolu ion o he senso and lowe i s limi o de ec ion.
Finally, he Thesis explo es he unc ionaliza ion o he magne oe-
las ic pla o ms wi h MOF (Me al O ganic F amewo k) ac i e laye s, in
o de o de elop wi eless humidi y senso s. Me al o ganic amewo ks
a e highly po ous ma e ials, buil by me allic ions linked by o ganic
molecules. They hold high adso p ion capaci y alues (adso p ion pe
g am o ma e ial) and can be designed o abso b speci ic molecules, so
hey esul in a e y p omising ac i e ma e ial o combine wi h mag-
ne oelas ic de ec ion. Di e en wa e -adso ben MOF ma e ials we e
syn hesized, cha ac e ized and in eg a ed on o he MER pla o ms. The
senso s de eloped wi h hese ac i e laye s p esen good sensi i i y, se-
lec i i y and compe i i e esponse imes, esul ing in e y p omising
gas senso s based on magne oelas ic de ec ion o moni o in eal- ime
he ela i e humidi y. Besides, MER senso s ha e p o en o be a ool
wi h g ea po en ial o cha ac e ize he dynamic adso p ion capaci y o
MOFs, and in ex ension, po ous ma e ials.
Con en s
1 In oduc ion 1
1.1 Senso s based on magne oelas ic esonance . . . . . . . . 2
1.1.1 Magne oelas ici y . . . . . . . . . . . . . . . . . . . 2
1.1.2 Magne oelas ic esonance . . . . . . . . . . . . . . 4
1.1.3 E ec o mass loading . . . . . . . . . . . . . . . . 8
1.1.4 Quali y o he esonance signal . . . . . . . . . . . 11
1.1.5 The ∆Ee ec . . . . . . . . . . . . . . . . . . . . 12
1.1.6 Magne os ic i e ma e ial . . . . . . . . . . . . . . 15
1.2 Ou line o he Thesis . . . . . . . . . . . . . . . . . . . . . 16
Bibliog aphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 MER de ec ion ins umen a ion and da a p ocessing 25
2.1 Magne oelas ic esonance de ec ion sys em . . . . . . . . 27
2.1.1 Induc ion-based measu emen sys em . . . . . . . 28
2.1.2 Impedance-based measu emen sys em . . . . . . . 30
2.2 LabVIEW con ol . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.1 DC ield con ol . . . . . . . . . . . . . . . . . . . 35
2.2.2 ∆Ee ec measu emen s . . . . . . . . . . . . . . . 37
2.2.3 Time-e olu ion measu emen s o he esonance . . 38
2.3 Nume ical i ing o he esonance cu es o imp o e he
de ec ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
i
This chap e gi es a b ie in oduc ion abou a p ope y o e o-
magne ic ma e ials, magne os ic ion, and how we can use i o de elop
e y e sa ile magne ic senso s based on hese ma e ials. The basis
o his phenomenon and he subsequen phenomenon o magne oelas ic
esonance will be desc ibed and analyzed ocusing on he applica ion o
hese ma e ials as mass de ec ion pla o ms. Th oughou he chap e ,
he mos impo an pa ame e s o magne oelas ic esonance-based sen-
so s will be poin ed ou , as well as some applica ions and de ails abou
he ma e ial used. The e sa ili y, sensi i i y and especially, he e-
mo e ope a ion o hese senso s make hem pa icula ly in e es ing o
be applied o a wide ange o de ec ion ields.

T ansduce s a e de ices ha con e one o m o ene gy in o an-
o he [1]. In his con ex , senso s (which a e a o m o ansduce s),
con e an inpu physical quan i y in o a measu able o p ocessable
ou pu quan i y (usually in o an elec ical signal), as hei pu pose is o
de ec and measu e ha physical quan i y. The o he o m o ansduce
is he ac ua o , which ecei es an inpu (usually an elec ical signal), and
con e s i in o some physical ou pu (usually mechanical), as hey a e
in ended o ans o m ene gy. So ansduce s enable a ious sys ems o
in e ac wi h he physical wo ld by ei he sensing changes o gene a ing
esponses based on inpu s (Figu e 1.1).
En i onmen
Senso Ac ua o
Con olle
Measu e/Gene a ion
o elec ical signal
Physical
s imulus
Physical
ac ion
Ou pu Inpu
Figu e 1.1: Scheme o ope a ion o ansduce s (senso s/ac ua o s).
T ansduce s, and pa icula ly senso s, a e undamen al o ou so-
cie y as hey a e key in many echnologies [2]: om he senso s ha
con ol ou ehicles (ca s, planes...), o he biosenso s able o de ec
in ec ious diseases, passing h ough wa e o ai quali y con ol, diag-
nos ic ins umen a ion in hospi als, he elec ical-based echnology, he
In e ne o Things (IoT) de ices, e c. The g ea a ie y o senso s ha
exis and he di e se ields o whe e hey a e applied, make i difficul o
es ablish a unique way o classi y hem. Senso s a e di e en ia ed om
di e en pe spec i es: he basis o hei ope a ion (chemical, magne ic,
op ical...), he con e sion p inciple hey use (piezoelec ic, magne o e-
sis i e...), he physical quan i y hey measu e ( iscosi y, empe a u e...)
o hei applica ion (biosenso s, posi ion senso s, en i onmen al sen-
so s...) [1]. In pa icula , he amily o magne ic senso s ha e enabled us
1
Chap e 1. In oduc ion
o con ol and de elop housands o unc ions o cen u ies. F om he
in en ion o he magne ic compass o de ec he geomagne ic ield o
na iga ion pu poses, o he magne ic memo ies o compu e s [3, 4]. Di -
e en magne ic senso s ha e been de eloped based on di e en physical
phenomena: elec omagne ic induc ion, Hall e ec , unnel magne o esis-
ance (TMR), gian magne o esis ance (GMR), aniso opic magne o e-
sis ance (AMR) o gian magne oimpedance (GMI). This Thesis ocuses
on he s udy and applica ion o a kind o magne ic senso s which a e
based on he magne oelas ic esonance (MER) phenomenon. These sen-
so s a e made o magne os ic i e ma e ials, which can con e be ween
magne ic and elas ic ene gy.
1.1. Senso s based on magne oelas ic esonance
1.1.1. Magne oelas ici y
In 1842, J. P. Joule [5] obse ed ha he leng h o a e omagne ic
specimen changes as a esul o magne iza ion, he ca aloged his phe-
nomenon as a new class o magne ic o ce and ound a ela i e change
o leng h o 1.4×10−6on a ba o i on upon magne iza ion. This phe-
nomenon is nowadays known as magne os ic ion, and i is a magne o-
mechanical p ope y ha e omagne ic ma e ials ha e.
Figu e 1.2: Pages o he James Joule publica ion on magne os ic ion
e ec .
In 1865, E. Villa i [6] desc ibed he e e se o his e ec , known
2
1.1. Senso s based on magne oelas ic esonance
as Villa i e ec o in e se magne os ic i e e ec , which desc ibes he
change in he magne ic p ope ies o he ma e ial due o he applica ion
o mechanical s ess.
The undamen al o igin o magne os ic ion is ela ed o he spin-
o bi coupling [7, 8], ha ansmi s he spin o ien a ion o he elec onic
o bi als causing a physical de o ma ion; bu i s mechanism a a mac o-
scopic le el may be unde s ood by he magne iza ion p ocess ha akes
place in he ma e ial in he p esence o an ex e nal magne ic ield. In ab-
sence o a magne ic ield, he magne os ic i e ma e ial has a magne ic
domain dis ibu ion which minimizes i s magne ic ene gy (wi h ze o ne
magne iza ion). When he ma e ial is exposed o a magne ic ield, he
magne ic domains a e eo ien ed (minimizing i s ene gy again) by bo h
he mig a ion o domain walls and he o a ion o he domains [7]. This
p ocess allows he ma e ial o ea ange he domains, which in u n
causes a dimensional change acco ding o i s magne os ic ion (ma e-
ials wi h posi i e magne os ic ion elonga e, ma e ials wi h nega i e
magne os ic ion sh ink). This mechanism is ep esen ed in Figu e 1.3.
Since he de o ma ion is isocho ic ( he olume emains cons an ) he e
is an opposi e dimensional change in he o hogonal di ec ion.
L
DL
L
DL
Joule magne os ic ion Villa i e ec
H=0 s=0
H
Hs
s
Figu e 1.3: Rep esen a ion o he mechanism o magne oelas ic e ec s
on a magne os ic i e ma e ial wi h posi i e magne os ic ion.
This e ec is quan i ied wi h he ac ional change in leng h (deno ed
as λ) exhibi ed by he ma e ial when i is exposed o a magne ic ield
3
Chap e 1. In oduc ion
and i is gi en by:
λ=∆L
L,(1.1)
whe e Lis he ini ial leng h o he ma e ial in he di ec ion o he applied
ield and ∆Li s de o ma ion. This mechanical de o ma ion is ela ed
o he magne iza ion p ocess, so i depends on he applied bias ield, as
i can be obse ed in Figu e 1.4 [7]. The maximum de o ma ion o sa -
u a ion magne os ic ion (λs), co esponds o he magne ic sa u a ion
s a e (sa u a ion magne iza ion (Ms)), and i is cha ac e is ic o each
ma e ial. I s magni ude is gene ally small, o he o de o some pa s
pe million.
M
Msls
l
HH
Figu e 1.4: Va ia ion o magne iza ion (M) and magne os ic ion (λ)
wi h he applied bias ield (H) o a ma e ial wi h posi i e magne os ic ion.
1.1.2. Magne oelas ic esonance
The dynamic beha io o his p ocess, when we apply an al e na ing
magne ic ield o he magne os ic i e ma e ial, esul s in magne oelas ic
wa es p opaga ing along i . Thanks o he s ong coupling be ween he
elas ic and magne ic p ope ies o hese ma e ials, he magne oelas ic
wa es can be gene a ed (and de ec ed) ei he mechanically o magne i-
cally. When hese wa es a e exci ed in a ma e ial o a gi en leng h ( o
example, in a ibbon o magne oelas ic ma e ial o leng h L), s anding
wa es can be achie ed i he wa eleng h o he induced magne oelas ic
wa es ma ches he dimensions o he ibbon ( ul illing he ela ionship
L=n(λ/2), whe e nis an in ege ), causing a magne oelas ic esonance.
4
1.1. Senso s based on magne oelas ic esonance
A his esonan condi ion, he s ains, he changes o magne iza ion and
he suscep ibili y o he ma e ial each a maximum. This magne oelas ic
esonance phenomenon is he basis o he use o magne os ic i e ma e-
ials as senso pla o ms, as his esonance condi ion can be measu ed
(as will be desc ibed in Chap e 2) and is highly sensi i e o se e al
ex e nal ac o s (as will be explained in he ollowing).
Fo a ee-s anding ec angula -shaped magne os ic i e ibbon (which
is he shape usually used o senso applica ions), he induced longi u-
dinal wa e along he leng h di ec ion (he e aken as he x-axis, Figu e
1.5) can be desc ibed by he ollowing equa ion o mo ion [9]:
∂2u(x, )
∂ 2=E
ρ(1 −ν2)
∂2u(x, )
∂x2,(1.2)
whe e Eis he Young’s modulus, ρis he densi y, and νis he Poisson’s
coefficien o he magne oelas ic ma e ial, and u(x, )is he displacemen
unc ion o he longi udinal elas ic wa e.
x=0
x
u(x)
L
Figu e 1.5: Scheme o he ee s anding magne os ic i e ibbon.
This equa ion can be sol ed by using ha monic solu ions [10]:
u(x, ) = u0cos nπ
Lxei2π n ,(1.3)
whe e u0is a cons an and nis he esonance equency o he n- h
ha monic mode. The e m u0cos nπ
Lx ep esen s he oscilla ion ampli-
ude. Tha is, all poin s in he senso oscilla e a he same equency,
bu wi h di e en ampli udes.
The solu ion o his equa ion gi es he exp ession o he longi udinal
esonance equency, which depends on he dimensions and he elas ic
p ope ies o he ibbon:
5

Chap e 1. In oduc ion
n
=n
2LsE
ρ(1 −ν2).(1.4)
So, selec ing he equency o he al e na ing magne ic ield wi h
which we exci e he ma e ial o ma ch he esonance condi ion, we can
exci e a magne oelas ic esonan beha io in i . The di e en esonance
equencies ha can be exci ed in he ibbon a e desc ibed by equa ion
1.4. In mos senso applica ions only he undamen al mode (n= 1)
is conside ed because i p esen s he highe signal ampli ude (as can
be seen in Figu e 1.6a), al hough some s udies ha e also used highe
ha monics o imp o e he sensi i i y [11].
F equency
Ampli ude
n=1
n=2
n=3
n=4 n=5
1 2 3 4 5
(a)
Maximum
ampli iude
Resonance
F equency
An i-Resonance
F equency a
(b)
Figu e 1.6: (a) Magne oelas ic esonance modes o a ee magne oelas-
ic ibbon showing he undamen al esonance (n= 1) and he subsequen
ha monics. (b) De ail o a esonance cu e and he main esonance pa-
ame e s.
Figu e 1.6b shows an example o a esonance cu e and i s main
pa ame e s: he maximum ampli ude and he co esponding equency,
which is he esonance equency. This esonance equency is he pa-
ame e which is mainly used o senso applica ions since, as i will be
shown below, i is highly sensi i e o changes o se e al ex e nal ac o s
a ec ing he ma e ial such as magne ic ield, empe a u e, mass load-
ing, p essu e, e c. The cu e also shows he an i- esonance equency,
which co esponds o he minimum ampli ude (due o he ou -o -phase
coupling be ween he s ain and he magne iza ion).
6
1.1. Senso s based on magne oelas ic esonance
Figu e 1.7 shows he displacemen s ha ake place in di e en modes
o oscilla ion ( ed colo indica es he maximum displacemen and da k
blue he null displacemen ).
n=1
=109.61 kHz
n=2
=218.91 kHz
n=3
=327.53 kHz
Displacemen
max
Figu e 1.7: Fini e elemen me hod simula ions o he i s esonan modes
o oscilla ion (n= 1,2,3) o a magne os ic i e s ip o dimensions 20 ×2
mm and co esponding esonance equencies. Red colo indica es maxi-
mum displacemen and da k blue indica es no displacemen . The igh side
shows he no malized displacemen along he leng h o he ibbon ( aken as
he x-axis).
As i can be obse ed, o he n- h ha monic mode he e a e nnodes
whe e he displacemen is null (shown in blue in he igu e). These nodes
a e loca ed a x=L/2n(2m−1) (whe e mis a posi i e in ege om
1 o n), and do no con ibu e o he sensi i i y o he magne oelas ic
senso . As i has been s udied, he mos sensi i e pa s o he ibbon a e
7
Chap e 1. In oduc ion
hose ha su e he g ea es displacemen (in he undamen al mode o
a ec angula ibbon, hose zones a e he ips) [11].
1.1.3. E ec o mass loading
As we ha e commen ed on he p e ious sec ion, he magne oelas ic
esonan beha io is highly sensi i e o di e en ex e nal pa ame e s,
which is he phenomenon ha has led o he use o hese ma e ials in a
wide a ie y o sensing sys ems.
The e ec ha he mass loading on he esona o su ace (a change
on i s o al mass) has on i s esonance equency, is he mos widely used
mechanism o de eloping di e en senso s. A wide a ie y o analy es
can be ela ed o changes on he senso mass and mo eo e , he es-
ona o s may be unc ionalized wi h di e en ma e ials on hei su ace
in o de o p o ide hem wi h speci ic adso p ion capaci ies, making he
mass de ec ion a e y e sa ile ea u e. Some examples o mass de ec ion
wi h hese senso s can be ound on Table 1.1.
Analy e Func ionaliza ion Re e ence
CO2Amide- unc ionalized polyme [12]
Ammonia Poly(ac ylic acid-co-isooc ylac yla e) polyme [13]
Humidi y Honeycombed hin ilm ce amic TiO2[14]
Fe3O4nanopa icles - [15]
Cell g ow h Pa ylene-C [16, 17]
pH Poly(ac ylic acid) [18]
Glucose pH- esponsi e polyme + glucose oxidase (GOx) [19, 20]
Toluene UiO-66-NH2Me al O ganic F amewo k [21]
Swine e e i us An igen an i-CSFV IgG [22]
Hea y me al ions Bo ine se um albumin [23]
Salmonella yphimu ium Polyclonal an ibody o Salmonella [24]
Bacillus An h acis Filamen ous phage [25]
An i-Sa s-Co -2 an ibody N an ige N-nucleocapsid phosphop o ein o SARS-CoV-2 [26]
Pb2+ - [27]
Esche ichia coli Gold+an i-E. coli O157:H7 an ibodies [28]
Table 1.1: Di e en applica ions o magne oelas ic senso s ope a ing as
mass senso s.
To analyze he e ec ha a uni o m mass inc emen (∆m) o he
8
1.1. Senso s based on magne oelas ic esonance
esona o mass (m0) has on i s esonance equency ( ), we can assume
he mass change as a change on he esona o densi y (ρ) as:
ρ′=m0+ ∆m
A·d,(1.5)
whe e Ais he su ace a ea o he senso and di s hickness (as desc ibed
in Figu e 1.8).
m0d
Dm
A
m0
Dm
D
Figu e 1.8: E ec o he mass loading on he esona o ’s esonance.
Sol ing he equa ion o mo ion (equa ion 1.2) wi h his modi ied
densi y (ρ′), we can ob ain a new undamen al esonance equency:
′
=1
2LsE
ρ′(1 −ν2)=1
2Ls1
1 + ∆m/m0
A·d
m0
E
(1 −ν2).(1.6)
No e ha in his exp ession, i is assumed ha he coa ing does no
change he elas ic p ope ies o he esona o ( he elas ic modulus o he
sys em esona o + coa ing is conside ed he same as he esona o ’s
Young’s modulus, E). When he e ec o he coa ing elas ic cons an s
is aken in o accoun , he beha io is di e en [29], as will be explained in
de ail in Chap e 4. The new esonance equency ( ′
) can be exp essed
in e ms o he ini ial esonance equency ( ) as:
′
= s1
1 + ∆m/m0
,(1.7)
since he ini ial densi y is ρ=m0/A ·d. Fo small mass loads ela i e
9
Chap e 1. In oduc ion
he diso de ed s a e o he liquid phase ( ha is why hey a e also called
me allic glasses). Usually, hey a e Fe- ich and pa ially alloyed wi h
nickel o cobal , as well as doped wi h o he me als in smalle p opo -
ions (bo on, molybdenum, silicon...), in o de o s abilize hem o gi e
hem pa icula p ope ies [48].
When i comes o senso applica ions, he mos widely employed
e omagne ic amo phous alloy is he comme cially a ailable Me glas
2826MB (a e age composi ion Fe40Ni38Mo4B18 [52]), as i p esen s ex-
cellen magne ic and magne oelas ic p ope ies. Bu in his wo k an-
o he composi ion was selec ed as he senso ma e ial: an amo phous
alloy o composi ion Fe73C 5Si10B12 which was p o ided by Ana Ca a-
ina Lopes and manu ac u ed in Vacuumschmelze GmbH & Co., KG,
Ge many [53].
This composi ion con ains a small amoun o ch omium (5 % a omic)
ha allows he o ma ion o a passi izing laye on he su ace o he ma-
e ial when i is in con ac wi h he ai (consis ing o oxidized ch omium)
[54]. This laye a o s he co osion- esis ance beha io o he ma e ial
wi hou he need o a p e ea men ( o example, wi h laye s o gold,
ch omium o polyme s [55, 56]). In addi ion, his alloy p esen s excellen
magne oelas ic p ope ies, which a e collec ed and compa ed wi h Me -
glas 2826MB p ope ies in Table 1.2. Fo he applica ions de eloped in
his Thesis (desc ibed in he ollowing chap e s), whe e he senso would
be ope a ing unde wa e exposu e, his co osion esis an composi ion
was selec ed as he magne os ic i e ma e ial.
Table 1.2: Magne ic, magne oelas ic and elec ochemical cha ac e iza ion
o Fe73C 5Si10B12 and Me glas 2826MB samples. Da a aken om [53],
∆Eand k alues compa ed o 30 mm ×3 mm samples.
Composi ion µ0Ms
(T)
λs
(ppm)
∆E
(%) kCo osion a e
(µm/yea )
ρ
(g/cm3)
Fe73C 5Si10B12 1.12 14 17 0.41 0.035 7.207
Fe40Ni38Mo4B18
Me glas 2826MB 0.88 12 2.5 0.16 23.4 7.900
1.2. Ou line o he Thesis
The objec i es o his Thesis mainly di ide in wo di ec ions. The
i s one, is he analysis o limi a ions and imp o emen o he pe o -
mance o MER senso s when hey a e used o emo e eal- ime mass
16

1.2. Ou line o he Thesis
de ec ion, and he second one, is hei applica ion o di e en mass-
de ec ion expe imen s, whe e we aim o ake ad an age o hei wi eless
ope a ion.
Magne oelas ic de ec ion, especially when he e is a g ea damp-
ing in luence o he measu emen s ake place in aqueous media, may
equi e some s a egies o imp o e he esolu ion. And eal- ime de ec-
ion speci ically, as we will see, may ha e some hings o deal wi h, as
signal ime-ins abili ies. So, he i s pa o he Thesis will be ocused
on analyze his d awbacks and ind s a egies o o e come hem.
Chap e 2 is dedica ed in he i s place, o he home-made expe i-
men al measu emen sys em de eloped o s udy he magne oelas ic sen-
so s and he di e en de ec ion applica ions. In addi ion, he pe o -
mance o nume ical i ings o he esonance cu es o he senso s will
be explo ed as a pos -p ocessing ool o imp o ing he de ec ion eso-
lu ion. Di e en i ing exp essions will be es ed bo h whi heo e ical
and expe imen al da a, and hei pe o mance in ob aining he main
esonance pa ame e s (and especially he esonance equency) will be
compa ed wi h ha o di ec me hods.
Chap e 3 add esses a limi a ion we ha e ound on he pe o mance
o hese senso s when ope a ing in eal- ime de ec ion: he in luence
o he magne ic elaxa ion su e ed by hese ma e ials on hei sensing
pe o mance. I was ound ha unde he e ec o he bias magne ic
ield, magne oelas ic ma e ials expe ience a magne ic elaxa ion ha
a ec s nega i ely he senso pe o mance and limi s he accu acy o he
de ec ion, as i causes a ime-d i o i s esonance signal (and esonance
equency). This e ec and di e en app oaches o a oid i s nega i e
impac (selec ing he condi ions o he expe imen o pos -p ocessing
he sensing da a) ha e been s udied.
The second pa o his Thesis is ocused on he applica ion o hese
senso s o wo di e en moni o ing expe imen s. Chap e 4 p esen s he
use o a co osion esis an MER senso o eal- ime acking a chemical
p ecipi a ion eac ion: he o ma ion eac ion o calcium oxala e c ys-
als (one o he mos common mine als ha o ms calci ica ions on he
u ina y ac ). These magne oelas ic pla o ms we e success ully used
o moni o he o ma ion o he sal c ys als as he eac ion p og esses,
allowing he s udy o he dynamics o he eac ion and he ac o s in lu-
encing i . To de elop his applica ion, an e alua ion o he mass sensi-
i i y o hese senso s will be pe o med in e ms o he e ec ha he
17
Chap e 1. In oduc ion
ope a ion media and he elas ic p ope ies o he coa ing ma e ial ha e
on i . In addi ion, in hese de ec ion expe imen s, bo h he imp o e-
men o he de ec ion by using he nume ical i ings o he esonance
cu es (Chap e 2), and he e alua ion and co ec ion o he magne ic
elaxa ion e ec (Chap e 3) we e ca ied ou in o de o imp o e he
sensing pe o mance.
Finally, Chap e 5 will explo e he unc ionaliza ion o he magne oe-
las ic pla o ms wi h MOF (Me al O ganic F amewo k) ac i e laye s in
o de o de elop a wi eless humidi y senso . MOF ma e ials a e highly
po ous ma e ials ha can be designed o abso b speci ic molecules wi hin
hei po es, hus when used as ac i e laye s in MER senso s hey can
ac as adso ben laye s which can ans o m he p esence o he ana-
ly e o a change on he senso mass. Di e en wa e -adso ben MOF
ma e ials we e selec ed and syn hesized in o de o unc ionalize he
magne oelas ic senso s o achie e high sensi i i y humidi y senso s wi h
ailo ed selec i i y. The quali y o he MOF ma e ials will be analyzed,
and hei adso p ion capaci y will be ca e ully s udied. Wi h his, hei
o e all pe o mance when in eg a ed as ac i e laye s in MER senso s
will be analyzed in e ms o adso p ion capaci y, esponse ime, s abil-
i y, epea abili y and selec i i y.
In Chap e 6, he gene al conclusions and open pe spec i es de i ed
om his wo k will be poin ed ou .
18
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[52] D. Kouzoudis and D. E. Mouzakis, “A 2826 mb me glas ibbon as
a s ain senso o emo e and dynamic mechanical measu emen s,”
Senso s and Ac ua o s A: Physical, ol. 127, no. 2, pp. 355–359,
2006.
[53] A. Sagas i, V. Paloma es, J. M. Po o, I. O úe, M. B. Sánchez-
Ilá duya, A. C. Lopes, and J. Gu ié ez, “Magne ic, magne oelas ic
23
Chap e 1. In oduc ion
and co osion esis an p ope ies o ( e–ni)-based me allic glasses
o s uc u al heal h moni o ing applica ions,” Ma e ials, ol. 13,
no. 1, p. 57, 2019.
[54] M. F. López, M. Escude o, E. Vida, and A. Pie na, “Co osion
beha iou o amo phous e� c � ni�(si, p) alloys,” Elec ochimica ac a,
ol. 42, no. 4, pp. 659–665, 1997.
[55] S. Huang, J. Hu, J. Wan, M. Johnson, H. Shu, and B. Chin, “The e -
ec o annealing and gold deposi ion on he pe o mance o magne-
oelas ic biosenso s,” Ma e ials Science and Enginee ing: C, ol. 28,
no. 3, pp. 380–386, 2008.
[56] N. Bou opoulos, D. Kouzoudis, and C. G imes, “The eal- ime,
in si u moni o ing o calcium oxala e and b ushi e p ecipi a ion
using magne oelas ic senso s,” Senso s and Ac ua o s B: Chemical,
ol. 109, no. 2, pp. 227–232, 2005.
24
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
se and a ailable in he labo a o y (loca ed a BC Ma e ials).
An example o a esonance cu e o a magne oelas ic ibbon mea-
su ed in his sys em is shown in Figu e 2.4.
DC Powe Supply
Digi al mul ime e
Spec um analyze
Figu e 2.3: Scheme o he induc ion-based measu emen se -up.
Figu e 2.4: Resonance cu e o a ibbon o composi ion Fe73C 5Si10B12
and dimensions 20 mm ×2 mm a Hbias = 14 Oe measu ed in he
induc ion-based measu emen sys em.
2.1.2. Impedance-based measu emen sys em
In his Thesis, ano he expe imen al se -up based on impedance mea-
su emen s was design and de eloped (Figu e 2.5). This sys em was he
p incipal se -up used du ing his wo k (wi h some modi ica ions o addi-
ional elemen s depending on each applica ion case). The main ad an-
age o his se -up compa ed o he induc ion-based one is i s simplici y.
Unlike he o he sys em, his one only equi es a single coil o he
30

2.1. Magne oelas ic esonance de ec ion sys em
exci a ion o he esonance and de ec ion o he induced signal. This
me hod is based on he e ec ha he magne oelas ic ma e ial has on
he impedance o he pick-up coil. Tha impedance is gi en by:
Z(ω) = R+jωL(ω),(2.5)
being ω he equency, R he esis ance o he coil and Li s induc ance.
The induc ance o a coil is di ec ly p opo ional o he pe meabili y (µ)
o he ma e ial inside i (in ou case, he pe meabili y o he magne oe-
las ic ma e ial when he ibbon is placed inside he pick-up coil):
L(ω) = N2A
lµ(ω),(2.6)
being N he numbe o u ns o he coil, Ai s c oss sec ion and li s
leng h. Since he pe meabili y o he magne oelas ic ma e ial inc eases
signi ican ly a esonance [5], a sha p peak occu s in he coil’s impedance
spec um a ha esonance equency, and so ha he esonance beha -
io o he senso can be obse ed h ough he impedance spec um o
he coil.
DC Powe Supply
Digi al mul ime e
Impedance analyze
Se ing Up he OSA
Se ing Up he OSA
book.book Page 3 Monday, Janua y 31, 2000 10:34 AM
Se ing Up he OSA
Se ing Up he OSA
book.book Page 3 Monday, Janua y 31, 2000 10:34 AM
Figu e 2.5: Scheme o he impedance-based measu emen sys em.
In he expe imen al sys em, he DC magne ic bias ield is p oduced
by a Helmhol z pai (16.2 Oe/A (1.289 kAm-1/A)) which is ed by a
powe supply (KIKUSUI PBZ40-10). A digi al mul ime e (Agilen
34401A) was used o measu e he applied bias ield ( h ough he ol age
d op on a esis ance connec ed in se ies o he Helmhol z coil). The
31
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
impedance o he pick-up coil was measu ed wi h an impedance ana-
lyze (Keysig h E4990A, 20 Hz - 10 MHz, see de ails in Appendix A.1).
The sel - esonance equency o he pick-up coil ( = 637.5 kHz), is
abo e he ope a ion equencies o he magne oelas ic senso s used in
his Thesis (a ound 100 kHz).
A pic u e o he expe imen al se -up can be ound in Figu e 2.6.
Figu e 2.6: Impedance-based measu emen sys em.
In his case, he e is no compensa ion coil, as he e will be no pa -
asi ic ead signal om he AC ield ( he exci a ion coil is he pick-up
coil i sel ), in e u n, he magne oelas ic signal appea s supe imposed o
he sel -induc ion o he coil (Figu e 2.8a). The backg ound signal co e-
sponding o he coil impedance can be obse ed in Figu e 2.7. Mo eo e ,
he pe meabili y o he senso i sel (jus by placing i inside he pick-up
coil) will con ibu e o inc ease he induc ance (and impedance) o he
coil and he e o e, o u he inc ease he backg ound (see Figu e 2.7).
In o de o ob ain he senso esonance signal wi h a la baseline, he
backg ound co esponding o he pick-up coil wi h he senso inside i
(wi hou any bias ield applied) was measu ed be o e each measu emen
and sub ac ed om he esonance da a.
Since he esonance cu es measu ed wi h his sys em we e acqui ed
in magni ude (module o he impedance), he backg ound co ec ion was
pe o med di ec ly by sub ac ing he backg ound impedance magni-
ude. Mo e p ecise backg ound co ec ion could be done by sub ac ing
32
2.1. Magne oelas ic esonance de ec ion sys em
Figu e 2.7: Backg ound impedance o he pick-up coil (pink), and he
pick-up coil wi h a senso inside i (g een).
he complex impedance ( eal and imagina y pa s), bu ha would e-
qui e measu ing and p ocessing he complex senso esonance ( eal and
imagina y pa s), and ha , in e u n, will inc ease he measu emen
ime.
Figu e 2.8 shows an example o a esonance cu e o a magne oelas ic
ibbon measu ed wi h his sys em.
(a) (b)
Figu e 2.8: Resonance cu e o a ibbon o composi ion Fe73C 5Si10B12
and dimensions 20 mm ×2 mm a Hbias = 14 Oe measu ed in he
impedance-based measu emen sys em (a) wi hou backg ound co ec ion
and (b) wi h backg ound co ec ion.
Figu e 2.8a shows he aw esonance cu e, wi h a backg ound slope
33
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
co esponding o he induc ance o he pick-up coil, and Figu e 2.8b
shows he same cu e a e he backg ound sub ac ion. As can be
obse ed, as he impedance module is being measu ed di ec ly wi h his
me hod, bo h and aa e p ecisely ob ained.
The senso is placed in a sample holde ha loca es he sample in he
cen e o he pick-up coil and he coil sys em. All measu emen s we e
pe o med wi h his con igu a ion, as he posi ion o he ibbon wi h
espec o he pick-up coil a ec s he ampli ude o he signal, which
dec eases as he ibbon is mo ed om he cen e (see Figu e 2.9).
0 mm 5 mm 10 mm
10 mm
0 mm
5 mm
0 mm 5 mm 10 mm
Z
Figu e 2.9: E ec o he posi ion o he senso wi h espec o he cen e
o he pick-up coil (and he e o e also wi h espec o he cen e o he coil
sys em) on he esonance equency and ampli ude o he signal.
As can be obse ed, he posi ion o he ibbon also a ec s he alue o
he esonance equency, which inc eases as he ibbon is displaced om
he cen e . This is p obably due o he sligh ly di e en exci a ion ields
o which he senso is exposed in each posi ion. The equal placemen
o he sample in he cen e o he sys em (0 mm in Figu e 2.9) ensu es
ha any a ia ion o his equency is no due o i s posi ion, bu o he
analy e being de ec ed.
34
2.2. LabVIEW con ol
2.2. LabVIEW con ol
Se e al LabVIEW-based p og ams we e de eloped h oughou he
Thesis in o de o con ol he measu emen sys em and au oma e and
synch onize all measu emen s. The di e en measu emen p og ams
we e de eloped using VISA (Vi ual Ins umen So wa e A chi ec u e)
communica ion in o de o communica e wi h he di e en ins umen s
( ia GPIB (Gene al-Pu pose Ins umen a ion Bus)).
Lab iew so wa e de eloped by he ins umen manu ac u e s as well
as cus om-made so wa e was in eg a ed in he p og ams. The basic
p og ams used o measu e he magne oelas ic esonance a e de ailed in
he ollowing.
2.2.1. DC ield con ol
As he magne oelas ic senso is sensi i e o he s a ic magne ic ield
(as illus a ed wi h he ∆Ee ec ), o ensu e a eliable esponse o
he senso o mass changes, he bias ield mus emain s able du ing
measu emen s. Compa ed o he induc ion-based measu emen sys em,
which had no con ol o e he bias ield, a bias ield con ol ea u e
has been added o he impedance de ec ion sys em, which imp o es he
de ec ion accu acy.
In his sys em, as we ha e seen, he Helmhol z coils a e ed by a
ol age-d i en powe supply. The sel -hea ing o he coils can p oduce
an inc emen o hei esis ance which aduces in less cu en passing
h ough he coils ( o a gi en ol age inpu om he powe supply) and
he e o e less gene a ed bias ield. To compensa e o his e ec and
main ain he bias ield alue cons an , a PID (p opo ional–in eg al–
de i a i e) con olle [6] was de eloped o con ol he ol age ha he
powe supply p o ides o he Helmhol z pai (see de ails o he PID
con olle in he Appendix A.2).
The PID con olle ies o minimize he di e ence (e( )) be ween
he desi ed bias ield (se poin ) and he ac ual bias ield by applying
a co ec ion wi h p opo ional (Kp), in eg al (Ti) and de i a i e (Td)
e ms:
u( ) = Kpe( ) + 1
TiZ
0
e( )d +Td
de( )
d .(2.7)
35

Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
The ac ual bias ield p oduced by he Helmhol z coils is measu ed
by a mul ime e h ough he ol age d op in a se ies esis ance (10 Ω)
connec ed o he Helmhol z pai (which p o ides he cu en passing
h ough he sys em ha can be hen con e ed o magne ic ield using
he calib a ion cons an o he coils). This alue o he bias ield is
cons an ly gi en o he PID con olle as he eedback (see Figu e 2.10).
DC Powe Supply
Digi al
mul ime e
Helmhol z pai
Inpu
(H se poin ) PID
Feedback
Ou pu
(Vol age)
10
non-induc i e esis ance
Figu e 2.10: Scheme o ope a ion o he PID con olle .
The con olle ou pu is con inuously passed o he powe supply as
he desi ed ou pu ol age o eed he Helmhol z coils. The esolu ion
o he digi al mul ime e is 0.1 mV, which when using a esis ance o 10
Ω ansla es o a con ol o bias ield di e ences o he o de o 0.1 mOe.
The PID con olle was de eloped in LabVIEW en i onmen (Figu e
2.11). The p og am communica es wi h he mul ime e , o con inuously
ead he ac ual bias ield, and wi h he powe supply, o con ol i s
ou pu ol age. The applica ion has he op ion o se he alues o Kp,
Tiand Td o adjus he con ol beha io . In ou case, a e s udy he
beha io o he con olle wi h se e al gains, Tdwas se o 0 (PI con ol),
as he de i a i e e m did no imp o e he con ol.
36
2.2. LabVIEW con ol
Figu e 2.11: LabVIEW on panel o he PID con olle .
2.2.2. ∆Ee ec measu emen s
One impo an measu emen ha allows us o cha ac e ize he mag-
ne oelas ic ibbons and ind he bes poin o ope a ion o he senso s, is
he measu emen o he ∆Ee ec . Such measu emen can be ob ained
by obse ing he esonance beha io (and speci ically i s esonance e-
quency) as a unc ion o he applied bias ield, as we ha e seen in he
in oduc ion chap e . A LabVIEW p og am was de eloped in o de o
measu e he ∆Ee ec o he MER senso s. The p og am con ols he
applied bias ield, pe o ming a sweep o i s alue, and collec s he co -
esponding esonance signal o he senso .
The p og am con igu es he impedance analyze pa ame e s ( ype o
measu emen , ange o equency sweep, numbe o sweep poin s, mea-
su emen speed...), and he bias magne ic ield ange: ini ial, inal and
s ep alues. Then i sa es he backg ound ace (impedance magni ude
o he pick-up coil wi h he MER senso inside) be o e he measu emen
37
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
Figu e 2.12: F on panel o he LabVIEW p og am de eloped o measu e
he ∆Ee ec .
s a s and be o e he bias ield is applied. The p og am sub ac s he
eco ded backg ound om he subsequen measu ed esonance signals
using he buil -in unc ions o he analyze . Fo each bias ield s ep (in-
c emen ), he p og am wai s o he ield alue o s abilize ( his p og am
uns simul aneously wi h he PID ield con olle ) and hen collec s and
sa es he co esponding magni ude (module o he impedance) o he es-
onance cu e (Figu e 2.12). F om he cu es, he esonance equency
is ob ained as he equency a which he ampli ude is maximum using
he buil -in analysis p ocedu es o he analyze . Bo h he maximum
impedance and he co esponding equency ( esonance equency) a e
sa ed in da a iles as a unc ion o he bias ield.
2.2.3. Time-e olu ion measu emen s o he esonance
The p incipal measu emen needed in he Thesis was a eal- ime
eco ding o he esonance signal, since he objec i e o he Thesis was
o s udy he ope a ion and applica ions o hese ma e ials as pla o ms
o eal- ime mass de ec ion.
38
2.2. LabVIEW con ol
Figu e 2.13: F on panel o he LabVIEW p og am de eloped o measu e
he e olu ion o he esonance o e ime.
The implemen ed LabVIEW p og am ( ime-measu emen p og am,
Figu e 2.13) ini ializes he impedance analyze (selec ing he ope a ional
pa ame e s), eco ds he backg ound (impedance magni ude o he pick-
up coil wi h he senso inside i ( aken wi hou H ield)) and pe o ms
sweeps o he exci a ion equency o e he selec ed equency ange.
The p og am asks o a alue o he bias ield, which is main ained
cons an du ing he measu emen by he PID ield con olle (which
uns simul aneously wi h he ime-measu emen p og am). The ace
(impedance magni ude o he esonance cu e wi h backg ound sub-
ac ion), and he co esponding esonance equency and maximum
impedance a e ob ained using he buil -in analysis p ocedu es o he
analyze , ansmi ed o he con ol compu e and sa ed as a unc ion
o ime. The alues o he empe a u e (using a he mocouple) and he
bias ield a e also eco ded h oughou he en i e measu emen .
These a e he main magne oelas ic measu emen p og ams used in
his Thesis. Howe e , o he de ec ion applica ion explained in Chap e
5, some modi ica ions o bo h he measu emen sys em and he Lab-
VIEW con ol will be needed in o de o inco po a e some addi ional
elemen s (since, o example, a low con ol uni was added o he main
de ec ion sys em). The measu emen se up and modi ica ions pe o med
39
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
Figu e 2.16).
Table 2.1 shows an example o he alues o he main esonance
pa ame e s ob ained om he i ings compa ed o hose ob ained by
di ec me hods.
Table 2.1: Compa ison be ween he pa ame e s used o gene a e he heo-
e ical cu es, hose e ie ed h ough he nume ical i , and hose calcula ed
om di ec me hods when he signal has a le el o noise co esponding o
a SNR = 20.
Theo e ical Di ec me hod Fi ed
(kHz) 40.00 37.90 40.02
Q5.00 4.35 4.95
k20.70 0.84 0.69
In o de o e alua e quan i a i ely he accu acy o each me hod, he
e o ela i e o he heo e ical alue (%) was analyzed (Table 2.2). The
ela i e e o (ε , in %) was calcula ed as:
ε =|X heo e ical −Xob ained |
X heo e ical ×100,(2.16)
whe e X heo e ical is he heo e ical alue o each esonance pa ame e ,
and Xob ained is he co esponding pa ame e ob ained ( h ough he i -
ings o di ec calcula ions).
Analyzing he e o alues, i was clea ha he accu acy o he
pa ame e s was imp o ed in all cases when nume ical i ings we e used
compa ed o he esul s calcula ed by di ec me hods. Specially when
he e is noise o he peak is damped and has less quali y, since di ec
me hods a e qui e sensi i e o noise, while nume ical i ing o he whole
cu e educes i s e ec signi ican ly. Fo example, he de e mina ion o
Qwi h di ec me hods leads o e o s up o 20%, as al eady epo ed
in o he wo ks [11], whe eas nume ical i ings signi ican ly educe hese
e o s. The imp o emen in accu acy is also, in gene al, mo e no iceable
as he coupling pa ame e akes smalle alues.
Thus, nume ical i ings will be use ul o imp o e he esolu ion on
he de e mina ion o he esonance equency (and o he esonance pa-
ame e s) when he senso has noise o i is damped ( o example, when
wo king in liquid media, o when a as measu emen is needed and he
46

2.3. Nume ical i ing o he esonance cu es o imp o e he de ec ion
equency de e mina ion could no be e y ine).
ε (Q)(%) ε (k2)(%) ε ( )(%)
SNR Di ec Fi Di ec Fi Di ec Fi
Q=5
k2= 0.5
= 40 kHz
10 26.54 6.93 46.06 2.64 4.50 0.12
30 20.42 0.16 22.35 0.13 4.50 0.05
50 17.87 0.03 26.96 0.04 3.50 0.00
Q=5
k2= 0.9
= 40 kHz
10 8.33 1.27 5.30 2.39 2.50 0.42
30 3.46 0.29 11.60 0.13 2.25 0.04
50 4.15 0.01 5.12 0.01 1.75 0.00
Q=20
k2= 0.5
= 40 kHz
10 10.55 2.70 10.69 3.01 0.50 0.05
30 5.00 0.09 2.03 0.03 0.25 0.01
50 5.00 0.02 3.13 0.00 0.25 0.00
Q=20
k2= 0.9
= 40 kHz
10 10.55 0.94 1.39 1.11 0.50 0.03
30 5.00 0.09 1.48 0.06 0.25 0.01
50 5.26 0.01 0.49 0.01 0.00 0.00
Table 2.2: Compa ison o he ela i e e o in he de e mina ion o he
pa ame e s (Q,k2and ) h ough bo h me hods: calcula ed by he di ec
o mulas and e ie ed om nume ical i ings. Resul s a e shown o
di e en alues o he pa ame e s and SNR.
2.3.2.2. Fi ing o expe imen al cu es
In o de o es he beha io o he i ings wi h some expe imen al
esonance da a, se e al expe imen al cu es wi h di e en alues o he
ampli ude, esonance equency and damping we e used (Figu e 2.17).
The igu e also shows he nume ical i ing o he cu es o exp ession
2.10 (dashed-lines). The backg ound e m (aω +b) was added o he
i ing exp essions since i was ound ha i imp o ed he i ing pe o -
mance.
In Figu e 2.18, i can be seen ha he i ings o exp ession 2.10 be-
ha e sligh ly be e , wi h lowe alue o he esidual (lowe e o be ween
he expe imen al da a and he alues ob ained h ough he model). This
is p obably due o he ac ha exp ession 2.10 has one mo e deg ee o
eedom (7 i ing pa ame e s) han exp ession 2.8 (6 pa ame e s). Ne -
e heless, bo h models i he expe imen al da a easonably well.
47
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
Figu e 2.17: Expe imen al magne oelas ic esonance cu e signals
(cu es 1-5), and co esponding nume ical i ings o exp ession 2.10.
(a) (b)
Figu e 2.18: Example o he nume ical i ings o a expe imen al cu e
(Cu e 3) o (a) equa ion 2.10 and (b) equa ion 2.8, and he co esponding
e o s ( esiduals).
I we compa e he esonance pa ame e s ob ained h ough he i -
ings o he expe imen al cu e shown in Figu e 2.18, we ound ha ,
e ec i ely, hey a e simila (Tables 2.3 and 2.4).
48
2.3. Nume ical i ing o he esonance cu es o imp o e he de ec ion
χ0a b Qk2δ δa
0.0750 -0.0004 0.0414 109.91 36.482 0.10340 0.013706 0.014319
Table 2.3: Resonance pa ame e s ob ained wi h he i ing o Cu e 3 da a
o equa ion 2.8. δ and δawe e ob ained wi h he equi alence exp essions
2.13 and 2.14.
A a b aδ δa
0.0714 -0.0004 0.0433 109.89 115.04 0.013500 0.011300
Table 2.4: Resonance pa ame e s ob ained wi h he i ing o Cu e 3
da a o equa ion 2.10.
Analysis o he i ed esonance equency
An impo an cha ac e is ic o he i ing p ocedu e is ha he ob-
ained alues o he pa ame e do no co espond o he posi ion
o he maximum ampli ude o he esonance cu es (he e called max).
I we ake a look a he cu es and he pa ame e s, especially in he
cases wi h mo e damping, we obse e ha max is sys ema ically lowe
han he esonance equency ob ained wi h he i ings ( ) (see Figu e
2.19a).
(a) (b)
Figu e 2.19: (a) Obse ed disc epancy be ween he esonance equency
aken as he equency o maximum ampli ude ( max) and he one ob ained
wi h he i ings ( ). (b) Di e ence be ween he expe imen al esonance
equency ( max) and he esonance equency ob ained h ough he i ing
o Equa ion 2.10 ( ) as a unc ion o he damping (δ ).
This ells us ha wha we usually ake as he esonance equency
49
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
( equency o he maximum o he esonance cu e), is no ac ually he
na u al esonance equency o he senso , , which can be ob ained
om he i ing o he analy ical exp essions. Ins ead, max is a ec ed
by he damping o he cu e, which shi s i owa d lowe alues (i is
an e ec i e esonance equency). A simila e ec applies o he e-
quency o an i- esonance (minimum o he cu e), which, when a ec ed
by damping (due o he mass deposi ion o example), inc eases wi h e-
spec o he alue which is ob ained om he i s, a(see Figu e 2.19a).
In ac , his di e ence be ween and max depends linea ly on he
damping o he cu e, as can be seen on Figu e 2.19b, ge ing g ea e
o highe damping alues.
To be e unde s and his, we can di ide he equency esponse o
a magne oelas ic esona o as di e en ans e unc ions ep esen ing
sys ems o : a pu e esonance (G1), a pu e an i- esonance (G2), and
he combina ion o bo h (G3), which ep esen s he obse ed esonance-
an i esonance beha io :
G1(s) = ω2
s2+ 2δ ω s+ω2
(2.17)
G2(s) = s2+ 2δaωas+ω2
a
ω2
a
(2.18)
G3(s) = G1·G2=ω2
ω2
a·s2+ 2δaωas+ω2
a
s2+ 2δ ω s+ω2
(2.19)
Figu e 2.20 illus a es his disc epancy, showing he equency e-
sponse o he sys em, o ideal esonance (G1, in blue) and an i- esonance
(G2, pu ple) sepa a ely, and o he en i e cu e a ec ed by damping
(sum o esonance and an i- esonance, G3, o ange).
The equency alues ob ained o he esonance (maximum) and
an i- esonance (minimum) o he espec i e cu es (blue and pu ple),
coincide wi h hose ob ained in he i ings ( Fi and aFi in Fig-
u e 2.20). In he combined cu e (o ange), howe e , he maximum and
minimum a e shi ed wi h espec o hese alues, esul ing in he al-
ues o he esonance and an i- esonance equencies ( Damped and a
Damped in Figu e 2.20), which ma ch he expe imen al da a.
50
2.3. Nume ical i ing o he esonance cu es o imp o e he de ec ion
Figu e 2.20: (a) F equency esponse o he sys em o esonance and
an i- esonance beha io , and he o al esponse a ec ed by he damping.
When using nume ical i ings o imp o e he de e mina ion o he
esonance equency in a de ec ion expe imen , he i ed pa ame e
could be used, bu i is also possible o use he alue o he equency
which co esponds o he maximum o he i ing cu e, which will be
mo e compa able o he one we ob ain expe imen ally. In his Thesis,
when using he nume ical i ings o imp o e he senso esolu ion, he
equency o he maxima o he i ing cu es will be used.
Ope a ion o he nume ical i ings unde educed equency
ange
Finally, he beha io o he i ings when he equency ange o
he da a is educed has been s udied in o de o es i hey can s ill
p o ide, unde hese condi ions, a alid pe o mance. As an example o
his, Figu e 2.21 shows he i ing o he esonance cu e in a educed
equency ange (pu ple). I was ound ha he i ings s ill i well
he expe imen al da a and gi e accu a e alues o he pa ame e s when
he equency ange is conside ably smalle . The e o e, when using he
nume ical i ings o he cu es, he equency ange can be educed on
behal o a quick measu emen .
As an example, he Q alue ob ained wi h his educed equency
i ing, Q= 17.4, is p ac ically he same as he one ob ained wi h he
comple e cu e, Q= 17.5. This is specially in e es ing since he analysis
51

Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
o Q alue by di ec me hods (using he FWHM) is no e en applicable
in his educed equency case.
Figu e 2.21: Magne oelas ic esonance cu e and co esponding i ing
o Equa ion 2.10 (in dashed black line) o a educed ange o equencies
(in pu ple).
2.4. Conclusions
In his chap e , he ins umen a ion de eloped o cha ac e ize he
magne oelas ic esona o s and de ec hei esonance signal has been
de ailed, as well as he so wa e de eloped o pe o m all he magne-
oelas ic measu emen s done h ough his Thesis. The measu emen
sys ems consis o an induc ion-based and an impedance-based se -ups.
The measu emen p og ams allow us o cha ac e ize he magne oelas ic
ma e ials (∆Ee ec p og am) and o moni o he esonance signal in
eal ime ( ime-e olu ion measu emen p og am). Special emphasis has
been gi en o he con ol o he bias ield, whose s abili y is essen ial o
eal- ime de ec ion (since i s a ia ions can cause changes in he signal).
As a da a p ocessing s a egy o enhance he de ec ion o hese sen-
so s, he nume ical i ing o he esonance cu es ha e been explo ed
as a ool o e ie e he go e ning esonance pa ame e s. The s udy has
demons a ed ha he i ings a e mo e accu a e in ob aining he es-
onance equency (and o he pa ame e s desc ibing he esonance, such
as he coupling pa ame e o he quali y ac o ) han he classical di ec
me hods, in pa icula when signals ha e conside able noise o a e highly
damped. The e o e, hey can be e y use ul when using hese senso s in
52
2.4. Conclusions
liquid media o when a apid measu emen (less quali y) is needed, as
we will see in he ollowing chap e s.
The pe o mance o wo di e en i ing exp essions was analyzed,
and analy ical ela ionships be ween he di e en pa ame e s ha e been
es ablished . Bo h exp essions pe o med well (wi h a e y low esidual
in ela ion o he expe imen al da a) and ha e p o en o be sui able o
imp o ing he de ec ion esolu ion. I was ound ha he equency a
which he esonance cu e is maximum ( max), does no coincide wi h
he na u al esonance equency o he sys em, , as included in he
analy ical exp essions used o he i ings. The di e ence is p oduced
because he damping displaces he maximum o he esonance owa ds
lowe equencies. Th ough his Thesis, when using hese nume ical
i ings, he esonance equency ob ained will be he equency co e-
sponding o he maximum ampli ude o he i ing cu e (which will
be mo e compa able o he expe imen ally ob ained one, and ye i s
esolu ion will be imp o ed).
Du ing his Thesis, he nume ical i ings we e pe o med as a pos -
p ocessing o he measu emen s once hey we e made. As u u e wo k,
he nume ical i ings could be in eg a ed in o he gene al measu emen
p og ams using he LabVIEW en i onmen , so ha he i ings would
be pe o med simul aneously wi h he expe imen al measu emen s.
53
Chap e 2. MER de ec ion ins umen a ion and da a p ocessing
Bibliog aphy
[1] C. A. G imes, S. C. Roy, S. Rani, and Q. Cai, “Theo y, ins u-
men a ion and applica ions o magne oelas ic esonance senso s: a
e iew,” Senso s, ol. 11, no. 3, pp. 2809–2844, 2011.
[2] K. Zeng, K. G. Ong, C. Mungle, and C. A. G imes, “Time domain
cha ac e iza ion o oscilla ing senso s: Applica ion o equency
coun ing o esonance equency de e mina ion,” Re iew o Scien-
i ic Ins umen s, ol. 73, no. 12, pp. 4375–4380, 2002.
[3] Y. Le B as and J.-M. G eneche, “Magne o-elas ic esonance: P in-
ciples, modeling and applica ions,” Resonance, ol. 2, pp. 13–34,
2017.
[4] N. Ida and N. Ida, “Fa aday’s law and induc ion,” Enginee ing
Elec omagne ics, pp. 515–563, 2015.
[5] C. A. G imes, C. S. Mungle, K. Zeng, M. K. Jain, W. R. D eschel,
M. Paulose, and K. G. Ong, “Wi eless magne oelas ic esonance
senso s: A c i ical e iew,” Senso s, ol. 2, no. 7, pp. 294–313,
2002.
[6] A. Visioli, P ac ical PID con ol. Sp inge Science & Business Me-
dia, 2006.
[7] A. C. Lopes, A. Sagas i, A. Lashe as, V. Mu o, J. Gu ié ez,
D. Kouzoudis, and J. M. Ba andia án, “Accu a e de e mina ion
o he q quali y ac o in magne oelas ic esonan pla o ms o ad-
anced biological de ec ion,” Senso s, ol. 18, no. 3, p. 887, 2018.
[8] P. J. Pe e san and S. M. Anlage, “Measu emen o esonan e-
quency and quali y ac o o mic owa e esona o s: Compa ison o
me hods,” Jou nal o applied physics, ol. 84, no. 6, pp. 3392–3402,
1998.
[9] H. Sa age and R. Abbundi, “Pe pendicula suscep ibili y, magne-
omechanical coupling and shea modulus in b. 27 dy. 73 e 2,”
IEEE T ansac ions on Magne ics, ol. 14, no. 5, pp. 545–547, 1978.
[10] A. Ga cía-A ibas, J. Gu ié ez, G. V. Ku lyandskaya, J. M. Ba an-
dia án, A. S alo , E. Fe nández, A. Lashe as, D. De Cos, and
I. B a o-Imaz, “Senso applica ions o so magne ic ma e ials based
54
Bibliog aphy
on magne o-impedance, magne o-elas ic esonance and magne o-
elec ici y,” Senso s, ol. 14, no. 5, pp. 7602–7624, 2014.
[11] Z. Kaczkowski, “Piezomagne ic pa ame e s o he magne os ic i e
ma e ials,” A chi es o Acous ics, ol. 23, no. 2, pp. 307–29, 2014.
55
Chap e 3. In luence o magne ic elaxa ion on MER de ec ion
(χ) do no each hei inal alues immedia ely a e he ield is applied,
bu some ime is needed o he ma e ial o elax in o an equilib ium
s a e ( h ough a complex in e play be ween he in e nal s uc u e, mag-
ne ic domains, and he mal luc ua ions).
This elaxa ion has been explained by some au ho s o ha e i s o igin
in an o de ing mechanism o s uc u al de ec s (in insic o he amo -
phous s a e (shea s esses, ee olume o densi y luc ua ions) [6]) in-
e ac ing wi h he local magne iza ion ec o ia he magne os ic i e
coupling [3, 7–11]. This beha io a ises a e a sudden ea angemen
o he magne ic domain s uc u e (as i happens when a magne ic ield
is suddenly applied o supp essed). When he ma e ial is exposed o
he bias ield, he di ec ion o he magne iza ion ec o su e s a sud-
den change, p oducing small sho - ange a omic e-a angemen s in he
ma e ial (which a e e e sible). Tha in e ac ion leads o a p og essi e
hinde ing o domain-wall mo ion [12], which leads o a ime-dependen
magne iza ion (cha ac e ized by a long- e m beha io , wi h conside ably
la ge elaxa ion imes).
Usually he cha ac e iza ion o his magne ic elaxa ion is pe o med
by ollowing magni udes such as M,χo µa e demagne iza ion [13–
15], bu any o he magne ic- ela ed p ope y o hese ma e ials will
also su e his elaxa ion beha io . This e ec was soon ecognized
as a d awback in applica ions o hese ma e ials ha equi e s able
p ope ies o ensu e p ope pe o mance. Fo example, he in luence
o he elaxa ion o amo phous magne ic alloys has been de ec ed in
some pa ame e s used in sensing applica ions, such as he magne o-
impedance [9, 10, 16].
Howe e , li le in o ma ion abou his issue can be ound in MER
senso applica ions, whe e, usually, magne ic elaxa ion is no aken
in o accoun . Ne e heless, as we will see, his magne ic elaxa ion can
be no iced in he mos impo an pa ame e when using amo phous
ma e ials as MER senso s, hei esonance equency. As he esonance
equency is ela ed o he magne ic s a e o he ma e ial ( h ough he
∆Ee ec ), he ime-e olu ion o Mwill be aduced o a ime-e olu ion
o he esonance equency ( ).
The e o e, a de ailed s udy o his phenomenon is basic o assess
he MER senso pe o mance and o a oid i s nega i e e ec s on he
de ec ion capabili y o hese ma e ials. Such s udy will be desc ibed in
he ollowing sec ions.
62

3.2. Measu emen me hodology
3.2. Measu emen me hodology
Senso ma e ial
The ma e ial used in he in es iga ion was an as-quenched magne oe-
las ic ibbon wi h composi ion Fe73C 5Si10B12, lase cu wi h dimensions
20 mm × 2 mm × 25 µm and a o al weigh o abou 8 mg.
The magne iza ion cu e o he ibbon is shown in Figu e 3.4 oge he
wi h he dependence o i s esonance equency on he applied bias ield
H(o ∆Ee ec ). As desc ibed in he in oduc ion chap e , he ield a
which he esonance equency is minimum, abou 7.8 Oe, is conside ed
he e ec i e alue o he aniso opy ield o he ibbon [17–19].
Magne ic elaxa ion expe imen s we e pe o med a di e en alues
o he bias ield (H), ep esen ed wi h ed do s in Figu e 3.4: 4, 7.8 and
10 Oe.
Figu e 3.4: Hys e esis loop o he ma e ial (solid line) measu ed in an
induc i e loop ace , and dependence o he esonance equency on he
applied bias ield (dashed line). Do s indica e he bias ield alues (H) se-
lec ed o he elaxa ion measu emen s. Blue lines a e depic ed o illus a e
he es ima ion o he aniso opy ield om he M(H)cu e.
Measu emen se -up
Relaxa ion measu emen s we e ca ied ou by con inuously moni o -
ing he esonance signal (and in pa icula , he alue o he esonance
equency) o a magne oelas ic senso du ing a ime in e al o 2000 s
63
Chap e 3. In luence o magne ic elaxa ion on MER de ec ion
while he measu emen condi ions and pa ame e s (DC-bias ield, exci-
a ion ield, empe a u e, and, in gene al, all he measu emen sys em
con igu a ion) emained s able, so ha he changes obse ed in he sen-
so signal could no be a ibu ed o a ia ions in hose pa ame e s.
The expe imen al se up used o ca y ou he magne oelas ic mea-
su emen s (Figu e 3.5), was he impedance-based measu emen sys em
desc ibed in Chap e 2. I consis s o a pai o Helmhol z coils p oducing
a cons an ield longi udinal o he ibbon axis which biases he ma e-
ial, and an in e oga ion coil ha p oduces he al e na ing magne ic
ield ( o magne os ic i ely exci e he sample) and, in u n, de ec s he
magne iza ion oscilla ions induced in he ma e ial.
Se ing Up he OSA
Se ing Up he OSA
10:34 AM
Se ing Up he OSA
Se ing Up he OSA
00 10:34 AM
Impedance Analyze
Powe supply
PID con olle
The mocouple
Gaussme e
Figu e 3.5: Scheme o he expe imen al se up used o measu e he elax-
a ion on magne oelas ic esonance.
The exci a ion magne ic ield (h), is p oduced by an al e na ing cu -
en passing h ough he in e oga ion coil, which is ed by a ol age
gi en by he impedance analyze (which can be uned by selec ing i s
ampli ude, OSC le el in mV). In o de o know he ampli ude o he ex-
ci a ion ield (h) ha is gene a ed by a gi en OSC le el in he analyze ,
he cu en lowing h ough he in e oga ion coil was measu ed wi h
an induc i e cu en p obe (Tek CT-2) ( he ou pu o he cu en p obe
was collec ed using an oscilloscope). The measu ed cu en was hen
con e ed in o magne ic ield ampli ude using he calib a ion cons an
o he coil (84.6 Oe/A (6.732 kAm−1/A)). The elaxa ion expe imen s
64
3.2. Measu emen me hodology
we e pe o med o di e en ampli udes o he exci a ion ield h: 20,
42, 100 and 180 mOe. All he measu emen s we e ca ied ou a oom
empe a u e, which was moni o ed by a he mocouple (NI USB-TC01,
ype K) inside he measu emen sys em ( empe a u e a ia ions du ing
he measu emen s we e below 0.1 ◦C). The cons an bias ield Hwas
con olled wi h he PID con olle and con inuously moni o ed wi h a
gaussme e (Lakesho e, 475 DSP Gaussme e ).
Nume ical i ing o he esonance cu es
In o de o imp o e he accu acy in he de e mina ion o du ing
he elaxa ion measu emen s, he esonance cu es we e nume ically i -
ed o he analy ical exp ession 2.8, as explained in Chap e 2. Figu e
3.6 shows he imp o emen in he de e mina ion o he esonance e-
quency and he educ ion o noise when nume ical i ings a e used in
an example o a elaxa ion expe imen .
Figu e 3.6: Compa ison o he esonance equency ob ained di ec ly
as he maximum o he expe imen al cu es (black) and he esonance e-
quency ob ained as he maximum o he nume ically i ed esonance cu es
( ed).
He e he i ing exp ession is shown again in o de o ha e i a hand:
Z( ) = Z0"1−8k2
π21− 2
2+jQ−1
−1#+a +b, (3.1)
whe e Zis he impedance (ampli ude) o he signal, and he i ing
65
Chap e 3. In luence o magne ic elaxa ion on MER de ec ion
pa ame e s a e: ( esonance equency), Z0(ampli ude o he signal
a low equency), k(magne oelas ic coupling coefficien ), Q(quali y
ac o ), and aand b(backg ound pa ame e s). As explained in Chap e
2, he alues o ob ained by he i ing we e aken as he equencies
co esponding o he maximum o he i ed cu es, so ha hey a e
compa able o he expe imen al esonance equencies.
3.3. Relaxa ion measu emen s
An example o he ime e olu ion o he esonance signal o he mag-
ne oelas ic senso unde cons an bias ield is depic ed in Figu e 3.7a.
A = 0 s, he bias ield is se o i s desi ed alue (H= 10 Oe in his
case). A e ha , due o he elaxa ion o he magne iza ion owa ds
he equilib ium alue, he esonance cu e expe iences a equency shi
owa ds highe alues in bo h, esonance (maximum) and an i- esonance
(minimum) equencies. The ime e olu ion o and ais ep esen ed
in Figu e 3.7b.
(a) (b)
Figu e 3.7: (a) Changes p oduced in he esonance signal o he senso
due o magne ic elaxa ion du ing he measu emen unde a cons an bias
ield o 10 Oe and exci a ion ampli ude o 20 mOe (each cu e co esponds
o a di e en ime, om = 0 s (when he bias ield is se ), up o 2000
s). (b) Tempo al e olu ion o he esonance and an i- esonance a
equencies du ing elaxa ion co esponding o he cu es shown in (a),
ob ained om he nume ical i ing o he cu es o equa ion 3.1.
Apa om he e ec on and a, he magne ic elaxa ion can
also be no iced in he impedance (ampli ude o he signal), which also
inc eases wi h ime.
66
3.3. Relaxa ion measu emen s
3.3.1. Relaxa ion phenomenon unde di e en biasing and
exci a ion ields
Figu e 3.8 shows he elaxa ion measu emen s pe o med wi h di -
e en condi ions o he bias ield (H) and he exci a ion ield (h).
(a)
(b)
(c)
Figu e 3.8: Inc emen o he esonance equency o he senso (colo ed
lines) and co esponding nume ical i ing o exp ession (3.2) (dashed lines)
o di e en exci a ion ampli udes (h= 20, 42, 100, 180 mOe) due o
magne ic elaxa ion unde he applica ion o a cons an bias ield o (a) 4
Oe; (b) 7.8 Oe (e ec i e aniso opy ield); (c) 10 Oe.
67

Chap e 3. In luence o magne ic elaxa ion on MER de ec ion
In he igu e, he inc emen (change wi h espec o i s ini ial alue)
o he esonance equency ( ) o he senso du ing he measu emen
ime (2000 s) is shown o he di e en alues o hand H. Colo ed-lines
co espond o he expe imen al esonance equencies (ob ained om he
nume ical i ing o he da a such as he ones shown in Figu e 3.6) and
dashed-lines o he i ing o he elaxa ion beha io model (which will
be desc ibed in he ollowing sec ion). As i can be obse ed, inc eases
wi h ime in all cases, up o 0.24 % o i s ini ial alue in he case o a
bias ield o H= 4 Oe and an exci a ion ampli ude o h= 20 mOe. In a
eal- ime de ec ion de ice, his change o abou 270 Hz in he esonance
equency would appea as a ime-d i o he ou pu , ep esen ing a
conside able sou ce o e o ha would a ec he pe o mance o he
senso , educing conside ably i s limi o de ec ion.
The endency obse ed is ha he change in he esonance equency
due o he elaxa ion is g ea e in he cases in which he exci a ion ampli-
ude is weake . In addi ion, he phenomenon is mo e no iceable a lowe
bias ields (as also epo ed by o he au ho s [20]), below he aniso opy
ield alue, when magne iza ion occu s mainly due o domain-wall mo-
ion, he slope o he hys e esis loop is g ea e , and small changes o
he applied ield lead o g ea changes in magne iza ion (see Figu e 3.4).
Fo highe applied ields, whe e he magne iza ion p ocess is go e ned
by domain o a ion, he elaxa ion e ec dec eases. This sensi i i y o
he elaxa ion ampli ude wi h he ype o magne iza ion p ocess has
al eady been obse ed in amo phous alloys, being he elaxa ion in-
ensi y educed when magne iza ion e e sal occu s mainly by o a ion
p ocesses [21, 22].
3.3.2. Modeliza ion o he elaxa ion beha io
In o de o s udy in de ail he pa ame e s ha cha ac e ize he e-
laxa ion in hese ma e ials, he empo al e olu ion o he esonance e-
quency was i ed o he ollowing exp ession, which desc ibes he elax-
a ion beha io and is de i ed om he o malism o s ongly co ela ed
sys ems [15, 23]:
( ) = 0+I[1 −e−( /τ)1−n],(3.2)
whe e 0is he esonance equency o he magne oelas ic senso a he
ini ial ime, Iaccoun s o he ampli ude (o in ensi y) o he elaxa ion,
τis he elaxa ion ime, and nis called he coupling pa ame e and
68
3.3. Relaxa ion measu emen s
accoun s o he co ela ion o he sys em. This unc ion is also known in
he li e a u e as he s e ched exponen ial, which was i s in oduced o
desc ibe elaxa ion p ocesses in dielec ic ma e ials [24]. The nume ical
i ings o his exp ession we e pe o med using a non-linea leas squa es
i ing in MATLAB, and he esul s a e in good acco dance wi h he
expe imen al da a (as shown in Figu e 3.8, dashed black lines). The
e olu ion o he pa ame e s i ed o equa ion 3.2 was hen analyzed as
a unc ion o he exci a ion ampli ude (Figu e 3.9).
(a)
(b)
(c)
Figu e 3.9: E olu ion o he i ed pa ame e s as a unc ion o he am-
pli ude o he exci a ion ield h o di e en alues o he applied DC-bias
ield (H = 4, 7.8 and 10 Oe): (a) elaxa ion ampli ude I, (b) elaxa ion
ime τ, and (c) coupling pa ame e n.
69
Chap e 3. In luence o magne ic elaxa ion on MER de ec ion
The endencies obse ed ma ch he beha io p e iously obse ed in
he expe imen al da a (Figu e 3.8). I was ound ha he elaxa ion
ampli ude pa ame e Iand he elaxa ion ime τ, bo h dec ease wi h
he inc ease o he exci a ion ampli ude h. The elaxa ion ime dec eases
om alues o up o 2300 s o alues o o e 300 s. This educ ion o
he elaxa ion imes sugges s ha he ene gy supplied by he exci a ion
(Table 3.1), compe es wi h he he mal ene gy (κBT= 4.14×10−21J o
Tamb=300 K), and helps he sys em o elax as e . As he empe a u e
(and he e o e he he mal ene gy) is he same in all he expe imen s,
he ene gy p o ided by he bias and exci a ion magne ic ields d i es
he changes in he elaxa ion kine ics.
h=20 mOe h=42 mOe h=100 mOe h=180 mOe
H=4 Oe 3.26 ×10−10J6.89 ×10−10J1.66 ×10−9J3.04 ×10−9J
H=7.8 Oe 5.51 ×10−10J1.16 ×10−9J2.78 ×10−9J5.04 ×10−9J
H=10 Oe 6.44 ×10−10J1.36 ×10−9J3.24 ×10−9J5.85 ×10−9J
Table 3.1: Magne ic ene gy (Emag) p o ided o he ma e ial by he bias
and exci a ion ields (es ima ed as Emag =1
2RHTBdV , whe e Vis he
olume o he ibbon and HTis he sum o Hand hampli udes).
In a simila manne , he elaxa ion ampli ude Idec eases om a
alue o abou 420 Hz o abou 30 Hz when he exci a ion is inc eased
( o he case o H= 4 Oe). This dec ease o he a e -e ec in ensi y
wi h highe ampli udes o he d i ing ield has al eady been poin ed ou
by o he au ho s [25, 26]. The coupling pa ame e n, ollows a simila
end, decaying as he exci a ion ampli ude is inc eased.
The cha ac e iza ion o his elaxa ion beha io , is undamen al o
op imize he ope a ional pa ame e s o hese senso s in o de o enhance
hei eal- ime pe o mance. Fo example, a p ope selec ion o he
exci a ion ield ampli ude (h) can signi ican ly educe he e ec o he
magne ic elaxa ion on he esonance equency (in e ms o i s in ensi y
and elaxa ion imes). This op imiza ion will be gene ally used in he
ollowing chap e s o his Thesis. Apa om ha , i he expe imen
allows i , a wai ing ime wi h he senso unde he H ield can be se
be o e he measu emen s o le mos o he elaxa ion o ake place.
Tha wai ing ime would be de e mined by he elaxa ion ime ob ained
h ough he elaxa ion beha io s udy. This s a egy was ollowed in
he applica ion shown in Chap e 5.
In he cases whe e he expe imen al p ocedu e o he na u e o he
70
3.4. In luence o he exci a ion ampli ude on he esonance signal
de ec ion expe imen do no allow o wai o he ma e ial o elax, he
elaxa ion model (equa ion 3.2) can be used o co ec he equency
d i in he measu emen s caused by he elaxa ion. I a con ol un
is measu ed o collec he elaxa ion beha io o he senso (change in
i s esonance equency), i can be i ed o exp ession 3.2 o ob ain
he main elaxa ion pa ame e s. Knowing hese pa ame e s, he senso
measu emen s o he analy e can be co ec ed by sub ac ing he
elaxa ion om he senso signal. This p ocedu e was ollowed in he
applica ion shown in Chap e 4 and will be explained in de ail in ha
chap e .
3.4. In luence o he exci a ion ampli ude on he
esonance signal
As we ha e seen, he exci a ion ampli ude (h) has an e iden in-
luence on he elaxa ion beha io and can be selec ed o minimize i .
Howe e , i also has a di ec e ec on he in insic alue o he esonance
equency and he ampli ude o he signal. As he exci a ion ampli ude
inc eases, bo h and he esonance ampli ude dec ease. Figu e 3.10
shows he alue o bo h pa ame e s as a unc ion o he bias ield H o
di e en exci a ion ampli udes (h= 20, 42, 100, 180 mOe).
Figu e 3.10: In luence o he exci a ion ield (h) on he esonance e-
quency (solid lines) and maximum ampli ude (Z, dashed lines) o he es-
onance cu es o di e en bias ields (H). Do s co espond o he elaxed
alues o he esonance equency (calcula ed h ough he pa ame e s i ed
o equa ion 3.2 o he di e en exci a ion and bias ield alues).
71
Chap e 3. In luence o magne ic elaxa ion on MER de ec ion
[11] P. Allia, G. Soa do, and F. Vinai, “Magne ic pe meabili y a e -
e ec and s uc u al de ec s o amo phous e omagne ic alloys,”
Jou nal o Magne ism and Magne ic Ma e ials, ol. 31, pp. 1527–
1532, 1983.
[12] P. Allia and F. Vinai, “Kine ic aspec s o magne ic elaxa ion in
amo phous e omagne ic alloys,” in Relaxa ion in Complex Sys ems
and Rela ed Topics, pp. 51–59, Sp inge , 1990.
[13] J. Ri as, M. López-Quin ela, D. Ma ínez, F. Walz, and H. K o-
nmülle , “Magne ic elaxa ion in amo phous me als,” Jou nal o
Non-C ys alline Solids, ol. 131-133, pp. 1235–1239, 1991. P o-
ceedings o he In e na ional Discussion Mee ings on Relaxa ions
in Complex Sys ems.
[14] P. Kwapuliński and G. J. Haneczok, “Magne ic elaxa ion in i on
based mel spun ibbons,” Ac a Physica Polonica A, ol. 136, no. 5,
2019.
[15] P. Kwapuliński and G. Haneczok, “Fo ma ion o he elaxed amo -
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elaxa ion echniques,” IEEE T ansac ions on Magne ics, ol. 58,
no. 4, pp. 1–7, 2020.
[16] P. Allia, C. Bea ice, M. Knobel, P. Tibe o, and F. Vinai,
“Relaxa ion o magne o esis ance and magne iza ion in g anula
cu90co10 ob ained om apidly quenched ibbons,” Jou nal o Ap-
plied Physics, ol. 76, no. 10, pp. 6817–6819, 1994.
[17] A. Lashe as, J. Gu ié ez, A. Balza, J. Ba andia án, and A. R.
Pie na, “Radio equency magne oelas ic esona o s o magne o-
elec ic applica ions,” Jou nal o Physics D: Applied Physics,
ol. 47, no. 31, p. 315003, 2014.
[18] A. Lashe as, J. Gu ié ez, and J. Ba andia án, “Quan i ica ion o
size e ec s in he magne oelec ic esponse o me allic glass/p d
lamina es,” Applied Physics Le e s, ol. 108, no. 22, 2016.
[19] A. Sagas i, J. Gu ié ez, A. Lashe as, and J. M. Ba andia án, “Size
dependence o he magne oelas ic p ope ies o me allic glasses o
ac ua ion applica ions,” Senso s, ol. 19, no. 19, 2019.
[20] Y. Wang, C. Li, Y. Li, X. Zhou, W. Wu, R. Yu, J. Zhao, C. Yin,
Y. Shi, C. Jin, J. Luo, L. Zhao, T. Xiang, G. Liu, and X. J. Zhou,
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“Long- ime magne ic elaxa ion in an i e omagne ic opological
ma e ial eucd2as2,” Chinese Physics Le e s, ol. 38, p. 077201,
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[21] P. Allia, C. Bea ice, F. Vinai, M. Knobel, and R. S. Tu elli, “Sup-
p ession o he magne ic‐pe meabili y elaxa ion in nanoc ys alline
e73.5cu1nb3si13.5b9,” Applied Physics Le e s, ol. 59, pp. 2454–
2456, 11 1991.
[22] S. C uz Filho, M. Knobel, J. Sinnecke , R. S. Tu elli, and
M. Vázquez, “Disaccommoda ion measu emen s in amo phous
wi es,” Jou nal o Magne ism and Magne ic Ma e ials, ol. 104,
pp. 105–106, 1992.
[23] G. Haneczok and J. Rasek, “F ee olume di usion and op imisa ion
o so magne ic p ope ies in amo phous alloys based on i on,” in
De ec and Di usion Fo um, ol. 224, pp. 13–26, T ans Tech Publ,
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[24] G. Williams and D. C. Wa s, “Non-symme ical dielec ic elax-
a ion beha iou a ising om a simple empi ical decay unc ion,”
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[25] P. Allia, C. Bea ice, and F. Vinai, “The ole o magne oelas ic
coupling on magne ic disaccomoda ion o amo phous and nanoc ys-
alline alloys. in magne oelas ic e ec s and applica ions,” Fi s In .
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[26] A. Rezende, R. Tu elli, and F. Missell, “Magne ic pe meabili y
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[27] A. Ga cıa-A ibas, J. Ba andia an, J. Gu ié ez, and
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[28] A. Hube and R. Schä e , Magne ic domains: he analysis o mag-
ne ic mic os uc u es. Sp inge Science & Business Media, 1998.
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[29] A. Lashe as, J. J. Saiz Ga i aonandia, I. Quin ana, J. L. Vilas-
Vilela, and A. C. Lopes, “Sel -bias magne oelas ic esonance sen-
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nanoc ys alliza ion induc ion by annealing,” A ailable a SSRN
4824115.
[30] A. Lashe as, J. Ga i aonandia, I. Quin ana, J. Vilas, and A. C.
Lopes, “De elopmen o nanoc ys allized magne oelas ic senso s
wi h sel -biased e ec and imp o ed mass sensi i i y,” Senso s and
Ac ua o s Repo s, p. 100251, 2024.
80
CHAPTER 4
Moni o ing o p ecipi a ion
eac ions

In his chap e , a magne oelas ic esonance senso is used o moni o
he p ecipi a ion eac ion o calcium oxala e (CaC2O4) c ys als in eal-
ime, by measu ing he shi o he esonance equency caused by he
mass inc ease on i s su ace as he eac ion p og esses. Calcium oxala e
is one o he mos common mine als which o m he calci ica ions on
he u ina y ac , so he s udy o he eac ion dynamics, igge s and in-
hibi o s could be o special in e es . In his sense, magne oelas ic senso s
could be highly use ul o he ask as hey exhibi a emo e ope a ion,
which allows hem o moni o he eac ion while i is aking place. The
de ec ion o he p ecipi a ed mass was pe o med when oxalic acid and
calcium chlo ide we e mixed in di e en concen a ions ( om 1mM o
100 mM). The alidi y o he mass calib a ion o he senso s was ca e-
ully analyzed, as he senso s we e designed o ope a e in liquid media.
In addi ion, nume ical i ings o he esonance cu es we e pe o med
in o de o imp o e he de ec ion esolu ion in low concen a ion p e-
cipi a ion eac ions. Also a co ec ion o he magne ic elaxa ion was
implemen ed o imp o e he de ec ion limi . The esul s show ha he
senso is capable o acking he p ecipi a ion eac ion o solu ions o
concen a ion as low as 1 mM, wi h he senso being able o esol e a
mass o p ecipi a e o 2 µg.
The wo k p esen ed in his chap e has esul ed in he ollowing publica-
ions:
• Sisniega, B., Sagas i Sedano, A., Gu ié ez, J. and Ga cía-A ibas, A.
“Real ime moni o ing o calcium oxala e p ecipi a ion eac ion
by using co osion esis an magne oelas ic esonance senso s”.
Senso s, 20(10), 2802 (2020).
• Sisniega, B., Gu ié ez, J. and Ga cía-A ibas, A. “Magne oelas ic
esonance de ec ion o calcium oxala e p ecipi a ion in low con-
cen a ion solu ions”.IEEE T ansac ions on Magne ics, 58(2), 1-5
(2021).
4.1. In oduc ion
4.1. In oduc ion
As we ha e seen, he sensi i i y o magne oelas ic senso s o mass
changes, oge he wi h hei abili y o que y and de ec emo ely, make
hese de ices especially in e es ing o sensing biological and chemical
agen s (see Table 1.1).
In pa icula , he emo e moni o ing o p ecipi a ion eac ion p o-
cesses wi h hese senso s is especially in e es ing, as hey can p o ide
eal- ime acking o he e olu ion o he eac ion when hey a e placed
inside he eac o whe e he p ocess occu s. This moni o ing can p o-
ide in o ma ion abou he eac ion kine ics o he ac o s ha in lu-
ence i , o example he e ec o some inhibi o s o ca alys s. Among
he p ecipi a ion eac ions, some o hem a e o special impo ance in
biomedicine as hey a e ela ed o biochemical p ocesses ha a ec he
human heal h. In he human body, he e a e essen ial ino ganic sal s
o di e se me abolic ac i i ies, which a e dissocia ed in solu ion in o
ions (o elec oly es). I some o hese ions a e no p ope ly abso bed
wi hin he body, hey will end o c ys allize and e en ually, o o m
s ones. One o hese p ecipi a ion p ocesses is he o ma ion o calcium
oxala e (CaC2O4) c ys als, one o he mos common mine als ha o m
calci ica ions in he u ina y ac (so-called kidney o bladde s ones,
Figu e 4.1) [1]. Kidney s ones, also known as enal calculi, a e mos ly
calcium based [2], and in pa icula calcium oxala e is he mos common
componen (app oxima ely 70% o s ones a e calcium oxala e-based [3]).
Figu e 4.1: Calcium oxala e u oli h.
Unde no mal condi ions, u ine has a ema kable abili y o inhibi
calcium oxala e c ys alliza ion, which p e en s mos o he popula ion
om con inuously o ming such s ones. Bu some diso de s, such as
83
Chap e 4. Moni o ing o p ecipi a ion eac ions
hype calciu ia o hype oxalu ia (u ine supe sa u a ed wi h calcium o
oxala e), can con ibu e o inc easing he isk o su e ing his pa hology.
In a u ine sample collec ed o e 24 h om an a e age adul , a quan i y o
100–250 mg o calcium is usually ound. In condi ions o hype calciu ia
he u ine calcium exc e ion can be g ea e han 275–300 mg/day [4, 5],
which can be es ima ed as 5 mM concen a ion o calcium ( aken a
24-hou s anda d u ine olume o 1.5 L). Hype oxalu ia, on he o he
hand, is an inc eased exc e ion o oxala e in u ine, and i is also ela ed
o he o ma ion o s ones in he u ina y ac [6]. The no mal alues o
oxala e exc e ion in u ine a e unde 40 mg/day [7], which co esponds
o app oxima ely a concen a ion o 0.3 mM.
The use o magne oelas ic senso s o emo ely moni o hese ypes o
eac ions can p o ide undamen al in o ma ion abou he p ecipi a ion
p ocesses in biological luids. I can inc ease ou unde s anding o hese
complex p ocesses o bio-mine aliza ion, since his echnique allows, o
example, o s udy p ecipi a ion sys ems unde he in luence o di e -
en ac o s (such as pH, o concen a ion and chemical composi ion o
he u ine [8]), in o de o know which ac o s o subs ances a o o in-
hibi he o ma ion o c ys als in he u ina y ac [9–11]. In o ma ion
abou he p ecipi a e mass in eal- ime can complemen he in o ma ion
(usually ob ained by moni o ing changes in pH o concen a ion [12]) o
s udies in a i icial sys ems ha mimic he human physiological condi-
ions, like human u ine.
P e ious wo ks by Bou opoulos and co-wo ke s [13] ha e used magne-
oelas ic senso s o moni o his kind o bio- eac ions, bu in he p esen
s udy se e al ac o s we e imp o ed:
• The amo phous e omagne ic ma e ial (Me glas 2826 alloy) was
subs i u ed by a ibbon o composi ion Fe73C 5Si10B12, which a oids
he need o p e- ea men o he su ace o p o ec i om he
co osion occu ing in he biological medium. This simpli ies he
p ocedu e and enhances he sensi i i y and quali y o he signals
(o g ea impo ance when using hese senso s in aqueous en i on-
men s).
• The nume ical i ings o he esonance cu es desc ibed in Chap e
2 we e used o o e come he nega i e e ec ha he damping o
he liquid media and he deposi ed mass ha e on he quali y o he
signal, and he e o e on he de e mina ion.
84
4.2. Calcium oxala e p ecipi a ion
• The magne ic elaxa ion co ec ion was applied o he measu e-
men s, specially o he low concen a ion eac ions (nea he sol-
ubili y limi o calcium oxala e, which has been epo ed o be
a ound 10−4M (0.1 mM) in pu e wa e a 25 ◦C [14]), in o de o
explo e he limi o de ec ion o he senso s.
4.2. Calcium oxala e p ecipi a ion
The moni o ing o he p ecipi a ion eac ion was ca ied ou by plac-
ing he magne oelas ic senso in a small ial (Figu es 4.2 and 4.3) wi h
a mix u e o equal pa s (0.6 mL) o oxalic acid (H2C2O4) and calcium
chlo ide (CaCl2) solu ions a he same concen a ion, leading o he o -
ma ion o he insoluble calcium oxala e c ys als (CaC2O4) acco ding o
he eac ion:
CaCl2(aq) + H2C2O4(aq)→CaC2O4(s)+2HCl(aq).(4.1)
C
Calcium oxala e c ys als
Magne oelas ic senso
Glass ial
Figu e 4.2: 3D ep esen a ion o he expe imen al p ocedu e, he senso
is placed in a glass ial wi h he eac an s, and he changes in he senso
signal a e acked while he p ecipi a e is o med and se led on he senso .
The p ecipi a ion eac ion occu s a e mixing he wo eac an s and
he o ma ion o he sal c ys als was acked in eal- ime by moni o -
ing he changes in he esonan equency o he magne oelas ic senso ,
which shi s as he p ecipi a e is deposi ed on i s su ace, as a di ec
consequence o he inc ease o i s o al mass.
85
Chap e 4. Moni o ing o p ecipi a ion eac ions
Equa ion 4.9 Simula ions
Ma e ial β1
2(β2−1) s
Ch omium 1.36 + 0.42 + 0.41
Aluminium 1.15 + 0.16 + 0.16
Sil e 0.63 - 0.30 - 0.29
Gold 0.45 - 0.39 - 0.37
Table 4.1: Compa ison be ween he sensi i i y coefficien s ob ained wi h
he exp ession 4.10 and hose ob ained wi h Comsol simula ions. The
coefficien 1
2(β2−1) in equa ion 4.10 is equi alen o s o he simula ions
(slope o he ∆ / -∆m/m0 ela ion).
i a e c ys als, so ha he elas ic modulus and he densi y a ec ing he
esona o would be he same as in he ac ual expe imen , and possible
e o s ob ained when calib a ing wi h o he ma e ials would be a oided.
4.4.2. E ec o he medium on he mass sensi i i y o he
senso
The medium in which he magne oelas ic senso is imme sed will
in luence he shape o he esonance cu e. This e ec is depic ed in
Figu e 4.7, which shows he esonance o he same senso placed in
di e en media (ai , dis illed wa e and glyce ol 50 %).
Figu e 4.7: E ec o he su ounding media on he esonance cu e.
Measu emen s pe o med wi h a Me glas 2826 ibbon o dimensions 12.7
×5 mm in ai , wa e and a glyce ol solu ion a 50 %.
92

4.4. Senso calib a ion
As i can be obse ed, wo king in mo e dense and iscous media
causes bo h he esonance equency and he ampli ude o he senso o
dec ease, and he quali y ac o Q o d op (due o he highe damping
su e ed by he ibbon). G imes e al. [19] al eady ga e an exp ession o
he obse ed dec ease in he magne oelas ic esonance equency when
he ib a ing senso is imme sed in a iscous liquid:
∆ =−√πηρl
2πdρs
( )1/2,(4.11)
whe e ηand ρla e he iscosi y and densi y o he liquid, and ρsand d
a e he densi y and hickness o he esona o , espec i ely.
The ∆ alues ob ained wi h his exp ession a e compa ed wi h he
expe imen al ones in Table 4.2. Fo he calcula ion, he ollowing alues
we e used: η(Wa e ) =0.89 ×10−3Pa·s, ρl(Wa e ) = 1000 kg/m3,
η(Glyce ol 50%) =6.8×10−3Pa·s, ρl(Glyce ol 50%) = 1130 kg/m3,
d= 25 µm, ρs= 7900 kg/m3and (Ai )= 174.8 kHz. I is clea
ha he heo e ical exp ession unde es ima es he ac ual change ha
su e s when he senso is imme sed in a liquid, which is sys ema ically
g ea e when i is expe imen ally measu ed.
∆ Expe imen al (kHz) ∆ Exp ession 4.11 (kHz)
Wa e -0.89 -0.56
Glyce ol 50 % -2.24 -1.65
Table 4.2: Compa ison o expe imen al and heo e ical alue (calcula ed
h ough exp ession 4.11) o he change in esonance equency o he senso
(∆ ) p oduced by he di e en media (wi h espec o i s alue in ai ).
In o de o elucida e i his e ec will also a ec he mass sensi i i y
o i will emain he same independen ly o he medium whe e he senso
is wo king, a es o calib a ion unde di e en media was pe o med.
To do ha , a magne oelas ic senso (Me glas 2826MB composi ion, di-
mensions 12.7 x 5 mm) was coa ed wi h polys y ene se e al imes and
i s esonance equency was measu ed a e each deposi ion while ib a -
ing in di e en media (ai , wa e and glyce ol 50 %). The polys y ene
coa ing was pe o med wi h a spin coa ing machine (using a dissolu ion
o polys y ene in ace one o concen a ion 0.5 g/ml), and he mass o
he coa ing was measu ed on each s ep on a high p ecision balance. The
esul s a e shown in Figu e 4.8.
93
Chap e 4. Moni o ing o p ecipi a ion eac ions
Figu e 4.8: Mass sensi i i y o he same senso in di e en media (ai ,
wa e and glyce ol 50 %).
I was ound ha he sensi i i y emained almos he same when
he senso was wo king in di e en media e en hough i s esonance was
damped. The e o e, ega dless o he ac ha he p ecipi a ion eac ion
senso will be ope a ing in a liquid medium, i s mass calib a ion in ai
p o ides a alid es ima ion o he mass o p ecipi a e.
4.4.3. Mass sensi i i y calib a ion
Taking he abo e-men ioned s udy in o accoun , he calib a ion o
he senso o moni o he p ecipi a ion eac ion was pe o med ollow-
ing wo condi ions. On he one hand, calcium oxala e c ys als we e
deposi ed on he senso su ace so ha he Young’s modulus and den-
si y o he coa ing a e he same as in he eal measu emen ; On he
o he hand, he calib a ion was pe o med in ai , since, as we ha e seen,
he alue o he sensi i i y is independen o he su ounding medium.
This ai calib a ion acili a es he p ocedu e since dealing wi h calcium
oxala e laye s in wa e would be e y complica ed.
The calib a ion o he senso sensi i i y o added mass was pe o med
by deposi ing, in successi e s eps, a known mass o calcium oxala e p e-
cipi a e on he senso su ace and measu ing he co esponding change
o i s esonance equency in ai . The measu emen s we e pe o med a
a bias ield co esponding o he aniso opy ield (Hk, in ou case Hk=
6.5 Oe, see Figu e 4.9a), which will be he ope a ion poin o he senso .
94
4.4. Senso calib a ion
Hk
(a) (b)
Figu e 4.9: (a) Dependence o he esonance equency wi h he applied
magne ic ield o he ibbon measu ed in ai and when i is imme sed
in dis illed wa e . The aniso opy ield (minimum esonance equency)
was measu ed as Hk= 6.5 Oe, and did no change when he senso was
imme sed in wa e . (b) Magne oelas ic esonance cu es measu ed in ai
and wa e a Hk.
The deposi ion o calcium oxala e c ys als on he senso su ace was
pe o med by p epa ing a p ecipi a ion solu ion (desc ibed in sec ion
4.2) and le ing he c ys als o o m. Then, by using a pipe e, he
su ace o he esona o was co e ed wi h his solu ion and le o d y.
A e wa ds, he senso was weighed on a p ecision balance (Figu e 4.10,
0.1 µg esolu ion), and i s magne oelas ic esonance equency was mea-
su ed a he aniso opy ield. This p ocess was epea ed se e al imes
in o de o ob ain di e en poin s o he mass calib a ion (shown in
Figu e 4.11).
Figu e 4.10: High p ecision balance (Sa o ius SE2) used o calib a e he
esponse o he senso o mass loadings.
As we ha e seen in he in oduc ion chap e , equa ion 4.3 is a i s
o de app oxima ion o he mo e gene al exp ession [20]:
95
Chap e 4. Moni o ing o p ecipi a ion eac ions
0
= (1 + ∆m
m0
)−1/2.(4.12)
This app oxima ion is alid o small mass loads, when he o he
he ms o he expansion a e negligible. Bu he mass changes su e ed
by he senso du ing he calcium oxala e p ecipi a ion p ocess can be
g ea e han 5 % o he ini ial weigh o he senso (m0= 7.6063 mg),
as we will see below. When mass loads a e conside able, he ela ion
be ween he esonance equency and he deposi ed mass is no linea
any mo e. The e o e, a second o de expansion o equa ion 4.12 has
been used o ob ain an app op ia e i o he calib a ion cu e (shown
in Figu e 4.11):
∆ = − 0≈ − 0
2m0
∆m+3 0
8m2
0
(∆m)2=a1∆m+a2(∆m)2.(4.13)
-14
-12
-10
-8
-6
-4
-2
0
00.5 11.5
∆ *(kHz)
∆m*(mg)
∆ *=*-9.8*(∆m)+*1.1*(∆m)2*
Figu e 4.11: Calib a ion cu e ob ained om he changes in he esonance
equency o he esona o (measu ed in ai ), caused by di e en calcium
oxala e mass deposi ions on i s su ace. Black do s ep esen he measu ed
calib a ion poin s. The solid ed line ep esen s he i o Equa ion 4.13,
wi h coefficien s a1= −9.8 kHz/mg and a2= 1.1 kHz/mg2.
The ob ained calib a ion cons an s a e:
a1=−9.8±0.4kHz/mg
a2= 1.1±0.3kHz/mg2
96
4.4. Senso calib a ion
Compa ing he senso sensi i i y epo ed by Bou opoulos e al. [13],
−1.38 kHz/mg, wi h he main mass calib a ion cons an (a1) ob ained
o he magne oelas ic esona o in his wo k, ou senso is abou se en
imes mo e sensi i e. The main eason ha accoun s o his ac is
he be e magne oelas ic coupling coefficien (k) o he magne oelas ic
ibbon. This is di ec ly ela ed o he leng h- o-wid h a io (R=L/w)
chosen o he esona o used in ou expe imen s (R= 10, ins ead o
R∼3o he p e ious wo k [13]).
We can compa e he expe imen ally ob ained calib a ion cons an s
wi h he heo e ical ones, which can be calcula ed o be a1=− 0
2m0=
−7.3kHz/mg and a2=3 0
8m2
0
= 0.7kHz/mg2( he mass and esonance
equency o he ba e magne oelas ic senso a e m0= 7.6063 mg and 0
= 111.85 kHz, espec i ely). I can be obse ed ha he expe imen al
calib a ion cons an s a e bo h highe han he expec ed alues (by 25 %
and 36 %, espec i ely).
In p inciple, we could es ima e he p ope ies o he coa ing ma e-
ial (E/ρ o calcium oxala e) h ough he expe imen al mass calib a-
ion, by compa ing i o equa ion 4.10. Using he main calib a ion
cons an ob ained in he expe imen s, a alue o β2=−0.28 is ob-
ained ((a≈1/2(β2−1), being a he dimensionless calib a ion cons an
a=a1m0/ 0=−0.64). This incong uence o he nega i e alue o
β2indica es ha his p ocedu e o ob ain he elas ic p ope ies o he
coa ing is no alid in ou case (al hough i s alidi y has been epo ed
by o he au ho s wi h o he coa ing ma e ials (sil e , aluminium) [17]).
Ac ually, obse ing equa ion 4.10, we ealize ha calib a ion cons an s
a < −0.5a e no explained by his app oxima ion (as hey will lead o
nega i e alues o β2), so he e ec o he coa ing densi y and elas ici y
explained in sec ion 4.4.1 does no comple ely explain he expe imen-
ally ob ained calib a ion cons an wi h calcium oxala e. This may be
due o he ac ha he elas ic p ope ies and homogenei y o calcium
oxala e coa ings a e no compa able o hose s udied in ha sec ion,
he e o e he applica ion o he elas ic heo y may no be adequa e o
s udy he e ec o his kind o coa ing ma e ials. O because he e a e
s ill o he ac o s a ec ing he sensi i i y ha a e no being conside ed.
We can conclude ha he di e ences obse ed be ween he expe -
imen al and he heo e ical mass calib a ion, may be pa ially due o
he e ec o he coa ing p ope ies, bu s ill no comple ely explained in
some expe imen al cases, as i is his case, so his is s ill an open subjec .
97

Chap e 4. Moni o ing o p ecipi a ion eac ions
4.5. Resul s o he moni o ing o he p ecipi a-
ion p ocess
Moni o ing o p ecipi a ion eac ions a high concen a ion
Fi s , he senso was es ed wi h high concen a ions o he eac an s
(30, 50 and 100 mM). The e ec o he di e en concen a ions in he
senso signal can be obse ed in Figu e 4.12.
30 mM
50 mM
100 mM
(a)
(b)
(c)
Figu e 4.12: Measu ed magne oelas ic esonance cu es o he senso a
di e en imes du ing he p ecipi a ion p ocess o solu ions o oxalic acid
and calcium chlo ide wi h concen a ions o : (a) 30 mM, (b) 50 mM and
(c) 100 mM.
98
4.5. Resul s o he moni o ing o he p ecipi a ion p ocess
In his case, he spec um analyze was se o pe o m a sweep o e
he equency ange (80 - 122 kHz) in 5 s, wi h a esolu ion bandwid h
o 105 Hz. The ampli ude o he exci a ion ield was se o h= 162 mOe
in o de o educe he magne ic elaxa ion. The measu ed esonance
cu es show, in he same ime window o 500 s, how quickly bo h he
magne oelas ic esonance equency (in kHz) and he ampli ude o he
de ec ed signal (in mV) dec eased as he calcium oxala e c ys als we e
o med in each eac ion. The a e a which his dec ease occu ed was
clea ly highe o he 100 mM han o he 30 mM concen a ion solu ion.
In addi ion, a dec ease o he quali y ac o (widening o he esonance
cu es, and hus a dec ease o he signal quali y) was obse ed as he
eac ion p og essed and he p ecipi a e mass was se led on he senso
su ace.
Figu e 4.13a shows he empo al e olu ion o he senso esonance
equency co esponding o he di e en concen a ion eac ions.
(a) (b)
Figu e 4.13: (a) Tempo al e olu ion o measu ed du ing he p ecipi a-
ion p ocess o di e en eac an concen a ions (30, 50 and 100 mM) and
o he con ol es (senso in a ial wi h dis illed wa e ). (b) Tempo al
e olu ion o ob ained h ough he nume ical i ing o he expe imen al
cu es (expe imen al da a shown in ligh colo s, and om i ings shown
in da k colo s).
As i can be obse ed, he change in esonance equency is di ec ly
ela ed o he kine ics o he eac ion and he quan i y o p ecipi a e
o med. No e ha he esul s o he 100 mM eac ion a e qui e noisy;
ha noise is due o he de e io a ion o he signal quali y (low Q) as
he p ecipi a e se les on he esona o and dampens i s ib a ion (see
Figu e 4.12c). A poo quali y signal educes he accu acy wi h which
99
Chap e 4. Moni o ing o p ecipi a ion eac ions
we can de e mine he esonance equency.
Thus, in o de o imp o e he esolu ion in de e mining he eso-
nance equency o he senso , he expe imen al da a ( esonance cu es)
we e nume ically i ed o equa ion 2.10 as desc ibed in Chap e 2 ( he
alues ob ained om he i ings a e aken om he maximum ampli-
ude o he i ing cu es). As he i ing equa ion no only depends on
he esonance equency bu on he hole esonance cu e (cha ac e ized
also by o he ac o s such as damping o backg ound pa ame e s), he
pa ame e s ob ained h ough i a e no as a ec ed by noise as i he eso-
nance equency is aken di ec ly om he maximum o he expe imen al
cu e. This imp o emen can be no iced in Figu e 4.13b.
The noise in de e mina ion in he con ol un was a ound 100
Hz (co esponding o an inc ease o he esona o mass o abou 10 µg
acco ding o equa ion 4.13 and he calib a ion cons an s a1and a2), and
inc eases as he esona o is damped wi h he p ecipi a e mass eaching
alues up o 2-3 kHz in he 100 mM concen a ion eac ion ( aising he
mass de ec ion limi o 200-300 µg.). Wi h he nume ical i ings, ha
noise was educed o 10 Hz (see Figu e 4.14), which imp o es he mass
esolu ion o 1 µg.
Figu e 4.14: Close up look a he con ol measu emen (g ay), and e-
duc ion o noise by he nume ical i ings (black).
In addi ion o he change in esonance equency, he e ec o he
p ecipi a e in he senso signal is also no iceable on o he esonance pa-
ame e s, o example on i s ampli ude, which dec eases as he eac ion
p og esses (see Figu e 4.15a). Mo eo e , he nume ical i ings allow
us o s udy he eac ions h ough he e olu ion o o he pa ame e s, as
he damping pa ame e s δ and δa, which inc ease as he p ecipi a e is
se led on he su ace o he senso (see Figu e 4.15).
100
4.5. Resul s o he moni o ing o he p ecipi a ion p ocess
(a) (b)
(c)
Figu e 4.15: Tempo al e olu ion du ing he eac ions ( o concen a ion
30, 50 and 100 mM) o (a) he maximum ampli ude o he signal ( eso-
nance ampli ude in mV ob ained h ough he nume ical i ings), and he
damping pa ame e s (b) δ and (c) δa.
Moni o ing o p ecipi a ion eac ions a low concen a ion
In o de o explo e he pe o mance o he senso a low concen a-
ions and he e o e de e mine i s limi o de ec ion, eac an solu ions
o concen a ion 1, 3, 5 and 10 mM we e nex used. When educing he
concen a ion, he mass o p ecipi a e o med is less, so he changes ob-
se ed in he esonance a e conside ably smalle (see Figu e 4.16); Also,
he a e o eac ion is educed. The e o e, in his case, he eac ion ime
moni o ed was inc eased o 2000 s. In addi ion, he bandwid h o he
equency sweep was educed o 36 Hz in o de o dis inguish smalle
equency shi s. The equency ange was also educed o 100 - 122 kHz,
since small equency changes a e expec ed. Wi h his con igu a ion he
sweep ime was 36 s, enough o ollowing hese eac ions, since hey
e ol e slowe han he p e ious ones.
101
Chap e 4. Moni o ing o p ecipi a ion eac ions
ne oelas ic senso in he eac ion a his concen a ion.
100 mM
(a)
10 mM
(b)
1 mM
(c) (d)
Figu e 4.22: Scanning Elec on Mic oscopy images o he p ecipi a ed
calcium oxala e c ys als (A mix u e o COM and COD c ys als we e ound).
The p edominan mo phology is he COM s uc u e. P ecipi a e o med in
he eac ion wi h eagen s o concen a ion (a) 100 mM (scale ba is 50
µm), (b) 10 mM (scale ba 20 µm), and (c) 1 mM (scale ba 20 µm). (d)
De ail o bo h mo phologies o he calcium oxala e c ys als, he hexagonal
pla e-like shape o COM c ys als, and he oc ahed al shape o COD c ys als.
In whi e, a schema ic 3D iew o bo h c ys als is shown. Scale ba is 10
µm.
4.7. Conclusions
The esul s p esen ed in his chap e demons a e he easibili y
o using magne oelas ic senso s in hose cases whe e emo e and non-
des uc i e de ec ion is equi ed, as i is he case o he p ecipi a ion e-
ac ion o physiological ino ganic sal s, such as calcium oxala e (CaC2O4).
108

4.7. Conclusions
MER de ec ion u ned ou o be a as de ec ion echnique, which al-
low he moni o ing o he p ecipi a ion p ocess and he s udy o i s
dynamics (p ecipi a e mass, a e o eac ion). The co osion esis an
alloy (Fe73C 5Si10B12) used in his expe imen has demons a ed o be
as capable as he comme cial Me glas 2826 alloy in moni o ing p ecip-
i a ion eac ions, wi h he ad an age ha no p e ea men is equi ed
o p e en oxida ion when used as a p ecipi a ion eac ion senso .
In addi ion, he use o he nume ical i ing o he senso esonance
cu es has imp o ed signi ican ly he senso esolu ion in he de e mi-
na ion o , and he e o e he esolu ion in mass quan i ica ion ( he
esolu ion was imp o ed om 10 µg o 1 µg). On he o he hand, he
co ec ion o he elaxa ion e ec by i ing he elaxa ion beha io and
sub ac ing i om he measu emen s has imp o ed he limi o de ec ion
o he senso s, so ha p ecipi a e masses as low as 2 µg a e disce nible
by ou sensing sys em.
To achie e a co ec mass calib a ion sensi i i y o he senso s, se -
e al ac o s ha e been analyzed in his chap e . I was ound ha he
su ounding medium (aqueous), al hough i a ec s he esonance sig-
nal, does no a ec he senso sensi i i y. This allows o pe o m ai
mass sensi i i y calib a ions which will be alid o he senso ope a -
ing in liquid. Howe e , ega ding he ma e ial used as coa ing o he
mass calib a ion, i s mechanical p ope ies g ea ly a ec he sensi i i y;
he e o e, he mass calib a ion should be pe o med wi h he speci ic
analy e ma e ial (whene e i is possible). The di e ence be ween he
heo e ically and he expe imen ally ob ained calib a ion cons an s is
no ye comple ely explained by he e ec o he coa ing p ope ies in
some cases, as is he case o calcium oxala e. Fu he in es iga ion could
be pe o med o elucida e o he ac o s a ec ing ha mass sensi i i y.
109
Chap e 4. Moni o ing o p ecipi a ion eac ions
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cu en concep s,” Ad ances in u ology, ol. 2018, 2018.
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[13] N. Bou opoulos, D. Kouzoudis, and C. G imes, “The eal- ime,
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Chap e 4. Moni o ing o p ecipi a ion eac ions
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112

CHAPTER 5
Me al O ganic F amewo ks
as ac i e laye s: wi eless
humidi y de ec ion
In his chap e , he unc ionaliza ion o he magne oelas ic esona o s
wi h Me al O ganic F amewo k (MOF) ac i e laye s is s udied wi h he
pu pose o de ec ing humidi y. Me al o ganic amewo k ma e ials a e
known o hei high adso p ion capaci y, which is due o hei high
po osi y and su ace a ea, and o hei unable selec i i y, which comes
om he ac ha hei po e chemis y and olume can be enginee ed
o abso b speci ic molecules. In he ollowing, di e en wa e -adso ben
MOF ma e ials we e syn hesized and in eg a ed as ac i e laye s on o
he MER esona o s. Thei wa e abso p ion capaci y and o e all pe -
o mance when in eg a ed in o he senso s we e e alua ed in e ms o
esponse ime, sensi i i y, s abili y, and selec i i y o wa e molecules.
The selec ed MOFs showed p omising wa e ha es ing capaci y, en-
abling a success ul senso esponse o humidi y in a wide ange o ela i e
humidi y (3 % – 85 %) wi h compe i i e esponse imes. In addi ion,
magne oelas ic esona o s ha e eme ged as a p omising ool o he cha -
ac e iza ion o he dynamic adso p ion capaci y o MOF ma e ials.
The wo k p esen ed in his chap e has esul ed in he ollowing publica ion:
• Sisniega, B., Fe nández de Luis, R., Gu ié ez, J. and Ga cía-A ibas, A.
“Magne oelas ic esona o s unc ionalized wi h me al–o ganic
amewo k wa e ha es e s as wi eless humidi y senso s”.APL
Ma e ials, 12(7) (2024).
5.1. In oduc ion
5.1. In oduc ion
Wi h he accele a ed p og ess o di e en indus ies and he aising
awa eness abou he necessi y o sus ainable and heal hy li es yles, he
de ec ion o he p esence o di e en gases and apo s ha e become im-
pe a i e. Among a wide a ie y o gases, he de ec ion o humidi y (o
i s quan i ying pa ame e , ela i e humidi y, RH) is o pa icula impo -
ance due o he ubiqui ous p esence o wa e apo in ou a mosphe e.
Rela i e humidi y de ec ion is key in many ields (Figu e 5.1), as
en i onmen al con ol, moni o ing o p ocessing indus ies, ood s o -
age, ag icul u e, o many domes ic applica ions, such as he au oma ed
con ol o li ing en i onmen s in buildings [1]. Humidi y de ec ion is
essen ial e en when i comes o he cap u e and de ec ion o o he gases
(e.g. CO2de ec ion) [2], as wa e is a common in e e ing molecule.
AIR
QUALITY
MONITORING
CONTROL OF
PROCESSING
INDUSTRIES
AGRICULTURE
AND
METEOROLOGY
FOOD
STORAGE
BIODETECTION
ADVANCED
FABRICATION
Figu e 5.1: Applica ion o humidi y de ec ion in se e al ields.
Humidi y senso s ansduce he amoun o wa e o some measu able
pa ame e and, up o da e, a e mos ly based on esis ance [3], capaci-
ance [4, 5] o e ac i e index changes [6, 7]. The deg ee o selec i i y,
sensi i i y, obus ness, compac ness, as esponse and cos equi ed o
humidi y senso s depend highly on he speci ic applica ion. Ideally,
115
Chap e 5. MOFs as ac i e laye s: wi eless humidi y de ec ion
washes. Finally, he ob ained whi e powde was d ied o 24 h a 80 ℃.
The s uc u e o MOF-808 a ises om he coo dina ion o imesic
acid molecules wi h six a oms o zi conium each. The zi conium a oms
a e hen o ganized in hexa-nuclea me allic clus e s (Z 6(OH)4O4) (Fig-
u e 5.7).
UiO-66-NH2
H
C
O
Z
N
BDC-NH2
z
x
y
z
x
y
z
x
y
z
y
Figu e 5.8: Fo ma ion p ocess o he UiO-66-NH2ma e ial.
In a glass ja , he linke , 0.362 g (2 mmol) o 2-amino e eph halic acid
(BDC-NH2(C8O4NH7)), was dissol ed wi h 20 mL o e hanol (E OH)
and 7 mL o o mic acid. In a beake , Z Cl4(0.47 g, 2 mmol) was
dissol ed wi h 16 mL o wa e . Then he zi conium chlo ide solu ion
was slowly added o he linke solu ion while s i ing, and inally le in
he o en du ing 24 h a 100 ℃.
A e ha , he esul ing p ecipi a e was cen i uged (7000 pm, 10
122

5.3. MOF syn hesis
minu es) and subjec ed o ou washing cycles wi h wa e ollowed by
ou me hanol washes. Finally, he ob ained whi e powde was d ied o
24 h a 80 ℃.
Again, as in he o he zi conium-based MOFs, hexa-nuclea zi co-
nium clus e s a e o med and connec ed h ough he o ganic linke s (in
his case, BDC-NH2) (see Figu e 5.8).
Al-Fum
H
C
O
Al
z
x
z
x
y
z
x
y
z
y
Fuma ic acid
Figu e 5.9: Fo ma ion p ocess o he Al-Fum ma e ial.
The syn hesis o Al-Fuma a e was escaled om he wo k o Zheng
e al. [32]. A mix u e o NaOH (0.24 g, 6 mmol) and uma ic acid
(C4H4O4, 0.232 g, 2 mmol) was dissol ed in 2.6 mL o dis illed wa e
in a sc ew-capped glass ja . The esul ing solu ion was s i ed un il he
solids we e comple ely dissol ed. Then, in a beake , AlCl3·6H2O (0.482
g, 2 mmol) was dissol ed in 2.4 mL o dis illed wa e . The aluminium
123
Chap e 5. MOFs as ac i e laye s: wi eless humidi y de ec ion
chlo ide solu ion was slowly added o he linke solu ion. The eac ion
was s i ed o 24 hou s in a 100 ℃ oil ba h.
A e he syn hesis, he sample was cen i uged (7000 pm, 10 min-
u es) and washed wi h aqueous 70 % e hanol (E OH) solu ion, and hen
cen i uged and washed again wi h E OH. Finally, i was d ied o e nigh
a 80 ℃.
The uma ic acid is coo dina ed wi h he aluminium a oms, which
hen o m chains (see Figu e 5.9).
CAU-23
S
H
C
O
Al
H2TDC z
x
y
z
x
y
z
x
z
y
Figu e 5.10: Fo ma ion p ocess o he CAU-23 ma e ial.
The syn hesis o CAU-23 was scale-down om he wo k o Zheng
e al. [32]. A mix u e o NaOH (0.24 g, 6 mmol) and 2,5- hiophenedi-
ca boxylic acid (H2TDC, C6H4O4S) (0.334 g, 2 mmol) was dissol ed
in 3.8 mL o dis illed wa e in a sc ew-capped glass ja . The esul ing
solu ion was s i ed un il he solids we e comple ely dissol ed. Then,
124
5.4. MOF Cha ac e iza ion
in a beake , AlCl3·6H2O (0.482 g, 2 mmol) was dissol ed in 1.2 mL o
dis illed wa e . The aluminum chlo ide solu ion was slowly added o he
linke solu ion and he p ecipi a e o med ins an aneously. The eac ion
was le o 6 hou s in an oil ba h a 100 ℃ while s i ing.
A e he syn hesis, he sample was cen i uged (7000 pm, 10 min-
u es) and washed wi h aqueous 70 % E OH solu ion, and hen cen-
i uged and washed again wi h E OH. Finally, he ob ained whi e pow-
de was d ied o 24 h a 80 ℃.
As in he case o Al-Fum, he aluminium a oms a e con igu ed in
chains, which a e in e connec ed wi h he o ganic linke s (H2TDC) (see
Figu e 5.10).
5.4. MOF Cha ac e iza ion
Once he MOFs we e syn hesized, and be o e hei in eg a ion as
ac i e laye s on o he MER senso s, a de ailed cha ac e iza ion o he
esul ed ma e ials was pe o med wi h se e al echniques in o de o
s udy hei c ys al s uc u e and assembly o he building blocks, he
numbe o s uc u al de ec s hey p esen and hei s abili y o wa e
p esence.
Such s udy was pe o med by means o X-Ray Di ac ion analysis,
In a-Red (IR) spec oscopy and he mog a ime ic analysis (TGA).
5.4.1. X-Ray Di ac ion analysis
In o de o e alua e he c ys alline pu i y o he MOF ma e ials,
which would con i m hei success ul syn hesis and quali y, hei c ys al
s uc u es we e s udied by X-Ray Di ac ion cha ac e iza ion.
The powde X-Ray Di ac ion (XRD) pa e ns o he MOF ma e ials
we e measu ed wi h a Panaly ical X’pe PRO di ac ome e (gene al
se ices o UPV/EHU, SGIke ), wi h CuKα adia ion (λ= 1.5406 Å) in
he ange o 5◦<2θ < 70◦, wi h a s ep size o 0.02◦(see de ails abou
he di ac ome e and X-Ray di ac ion echnique in Appendix A.5).
As i can be obse ed in Figu e 5.11, he measu ed di ac og ams
coincide wi h he pa e ns simula ed om he s uc u al in o ma ion
ob ained om he Camb idge S uc u al Da abase (Camb idge C ys al-
log aphic Da a Cen e , CCDC) o hese ma e ials. The da a coincide
as well wi h he pa e ns p e iously epo ed in he li e a u e [35–38].
125
Chap e 5. MOFs as ac i e laye s: wi eless humidi y de ec ion
Figu e 5.11: No malized powde X-Ray Di ac ion (XRD) pa e ns o
he syn he ized MOFs (measu ed wi h CuKα adia ion (λ= 1.5406 Å),
5◦<2θ < 70◦wi h s ep 0.02◦), and compa ison wi h he simula ed p o iles.
Fu he analysis o he da a by a ull-p o ile pa e n ma ching using
FullP o Sui e [39] (see de ails abou he pa e n-ma ching in Appendix
A.5), con i med he pu i y o he samples and he absence o addi ional
phases (Figu e 5.12).
The inal i ings o he pa e n ma ching analysis allow o es ima e
he cell pa ame e s o he samples, which a e esumed in Table 5.1 and
a e e y close o he ones epo ed in p e ious s udies.
The MOFs based on zi conium (MOF 801, MOF-808 and UiO-66-
126
5.4. MOF Cha ac e iza ion
NH2) p esen a cubic uni cell (wi h a=b=cand α=β=γ= 90◦).
Whe eas Al-Fum and CAU-23, belong o he monoclinic (a=b=cand
α=γ= 90◦=β) and o ho ombic (a=b=cand α=γ=β= 90◦)
sys ems espec i ely.
(a) (b)
(c) (d)
(e)
Figu e 5.12: Powde X-Ray di ac ion p o ile analysis o : (a) MOF-
801, (b) MOF-808, (c) UiO-66-NH2,(d) Al-Fum and (e) CAU-23.
127

Chap e 5. MOFs as ac i e laye s: wi eless humidi y de ec ion
The c ys allog aphic space g oups o he MOFs we e also con i med
(Table 5.2).
Table 5.1: Cell pa ame e s es ima ed wi h he ull-p o ile pa e n ma ching
o he XRD da a.
a(Å) b(Å) c(Å) α(◦)β(◦)γ(◦)
MOF-801 17.8910 ±0.0004 17.8910 ±0.0004 17.8910 ±0.0004 90 90 90
MOF-808 35.462 ±0.003 35.462 ±0.003 35.462 ±0.003 90 90 90
UiO-66-NH220.778 ±0.003 20.778 ±0.003 20.778 ±0.003 90 90 90
Al-Fum 6.8344 ±0.0008 12.139 ±0.001 14.231 ±0.002 90 122.53 90
CAU-23 15.4538 ±0.0009 24.0200 ±0.0009 14.2044 ±0.0009 90 90 90
Table 5.2: C ys allog aphic space g oup o he MOF ma e ials.
Space G oup Symbol
MOF-801 Pn¯
3
MOF-808 Fd¯
3m
UiO-66-NH2Fm¯
3m
Al-Fum P121/c1
CAU-23 P21212
5.4.2. Hyd oly ic s abili y o he MOF ma e ials
The e a e wo pa hways o he deg ada ion o MOFs in he p es-
ence o wa e : hyd olysis and linke displacemen . Hyd olysis occu s
when he me al-linke bond is b oken by addi ion o hyd oxyl g oups
esul ing in he libe a ion o a ee, p o ona ed linke , while he linke
displacemen mechanism in ol es he inse ion o a wa e molecule in o
he me al-linke bond, ollowed by he elease o a ee, dep o ona ed
linke [40]. The MOFs syn hesized a e, in p inciple, wa e -s able, bu in
o de o con i m hei s abili y o he exposu e o high humidi y le els
du ing long pe iods o ime (and p o e he co ec beha io o he sen-
so s unde ex eme humidi y condi ions), a hyd oly ic s abili y es was
pe o med.
The deg ada ion o MOFs in he p esence o wa e is o en accom-
panied by a pa ial loss o c ys allini y, which is why he compa ison
o X-Ray Di ac ion pa e ns collec ed be o e and a e exposu e o hu-
midi y is o en used o assess hei s abili y [40]. Uns able compounds
ypically show a b oadening o he di ac ion maxima o e en comple e
128
5.4. MOF Cha ac e iza ion
amo phiza ion upon exposu e o mois u e. The e o e, he hyd oly ic
s abili y o he MOFs was e alua ed by analyzing hei X-Ray Di ac-
ion pa e ns be o e and a e hey we e exposed o a wa e -sa u a ed
a mosphe e du ing 1 week (Figu e 5.13).
(a) (b)
(c) (d)
(e)
Figu e 5.13: Compa ison o he XRD pa e ns be o e and a e 1 week
o exposi ion o high humidi y o :(a) MOF-801, (b) MOF-808, (c) UiO-
66-NH2,(d) Al-Fum and (e) CAU-23.
129
Chap e 5. MOFs as ac i e laye s: wi eless humidi y de ec ion
The XRD pa e ns o he samples be o e and a e he wa e expo-
si ion ha e been compa ed quali a i ely, and he esul s show ha he
MOFs ha e a good wa e s abili y, as he pa e ns coincide wi h he
ones be o e he exposi ion. Only MOF-808 shows a sligh loss o c ys-
allini y as some o he e lec ions appea o be b oaden, bu s ill, i is
no conside ably deg aded. The e o e, he MOF ma e ials a e sui able
o be used as ac i e laye s wi h he pu pose o wa e de ec ion.
5.4.3. FTIR Spec oscopy analysis
In o de o con i m ha he MOFs a e well- o med, Fou ie T ans-
o m In a-Red (FTIR) spec oscopy can be used o s udy he main
ib a ional modes o he s uc u e o he ma e ials. The obse a ion
o he di e en modes o ib a ion can indica e he p esence o speci ic
bonds wi hin he s uc u e, which will con i m he success ul bonding o
he di e en s uc u al uni s.
The IR-spec a o he samples (Figu e 5.14), we e measu ed a e
d ying he samples a 125 ◦C du ing 12 h in a Jasco FT/IR-6100 spec-
ome e (see de ails abou he echnique and measu emen s in Ap-
pendix A.6).
Figu e 5.14: FTIR spec a o he syn hesized MOF ma e ials a e d ying
hem a 125 ◦C du ing 12 h.
130
5.4. MOF Cha ac e iza ion
The MOF ma e ials, specially MOF-801, MOF-808 and UiO-66-
NH2show a b oad signal a 3700 - 3200 cm−1associa ed o he wa e
molecules adso bed wi hin he MOF which a e no o ally emo ed by
d ying he samples. Ne e heless, he signa u e o he s uc u al hy-
d oxyl g oups a e easily loca ed wi hin his egion (s e ching ib a ion
peaks o O-H a e loca ed be ween 3700 and 3600 cm−1, ma ked wi h *
symbol in Figu e 5.14).
The mos impo an sec ion o he IR spec a is he one ha con-
ains he ypical bands a ound 1620, 1581 and 1380 cm−1(**), which
co espond o he s e ching modes o ca boxyla e g oups coo dina ed
wi h he Z and Al-based me al nodes, sugges ing he success ul bonding
o he linke s wi h he me al ions.
Signals a ound 983, and 796 cm−1can be a ibu ed o C-H and
C=C-H ou -o -plane bending ib a ions (***). Pa icula ly, o UiO-66-
NH2, he abso p ion band a 1258 cm−1is associa ed o he ib a ional
modes o amino g oups (#) in he BDC-NH2linke , and he signals a
3500 cm−1and 3400 cm−1, co espond o he asymme ic and symme ic
N–H s e ching (+).
5.4.4. The mog a ime ic analysis
Me al-o ganic amewo ks, and especially zi conium-based ones, a e
widely known o hei de ec i e chemis y [41]. Tha is, depending
on he syn hesis condi ions, di e en deg ees o missing linke can be
gene a ed andomly wi hin hei long- ange c ys al s uc u es. Some
linke s can be missing o can be eplaced by o he molecules (such as
wa e o sol en molecules). In ac , he de ec s can ha e a g ea impac
on he adso p i e p ope ies o he MOFs and he e o e, on hei wa e
ha es ing pe o mance [42]. The es ima ion o his linke de ec densi y
o he ma e ials was ca ied ou by he mog a ime ic analysis (TGA).
In gene al, TGA cu es p esen di e en weigh loss s eps in di e en
empe a u e anges associa ed wi h he e apo a ion o calcina ion o he
di e en molecules o ming he ma e ial. The e o e, he analysis o he
di e en weigh loss s eps in he TGA cu es gi es in o ma ion abou
he sample composi ion, and he compa ison wi h he heo e ical mass
loss alues allows us o es ima e he numbe o s uc u al de ec s o he
ma e ial.
TGA cu es o he samples we e measu ed using a NETZSCH-p o eus
STA 449 F3-Jupi e he mo-balance (de ails can be ound in Appendix
131