Molecular dynamic in binary mixtures and polymer blends with large difference in glass transition temperatures of the two components: A critical review
Abstract
The dynamics in highly asymmetric mixtures with large difference in Tg of the two components are complex. At low values of the lower-Tg2 component only the a1-relaxation and its Tga1 were found together with a fast relaxation. Three different interpretations of the fast relaxation were given. The first one interpreted the fast relaxation as the JG ß-relaxation, and the a2-relaxation is present but not resolved. The second one interpreted it as localized and noncooperative a'-relaxation of the low-Tg2 component totally confined by the frozen high-Tg1 component. The third one interpreted it also as the confined a2-relaxation, but it is liquid-like and cooperative. We review exhaustively the experimental data of many highly asymmetric mixtures and polymer blends to show unequivocally that the observed fast relaxation is the JG ß-relaxation. Notwithstanding, the confined-but-cooperative a2-relaxation exists, albeit not resolved. Experimental data are exclusively considered and objectively utilized to arrive at the conclusions.
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Elsevier Editorial System(tm) for Journal of Non-Crystalline Solids Manuscript Draft Manuscript Number: Title: Molecular dynamic in binary mixtures and polymer blends with large difference in glass transition temperatures of the two components: a critical review Article Type: VSI: GUPTA Keywords: Dynamics; Mixtures; polymer blends; Johari-Goldstein relaxation; glasses Corresponding Author: Professor Kia L Ngai, PHD Corresponding Author's Institution: IPCF First Author: Kia Ngai Order of Authors: Kia Ngai; Sofia Valenti, M.S.; simone capaccioli, Ph D Abstract: By mixing a molecular or polymeric glass-former with another one, its dynamic and thermodynamic properties can be modified to various degrees depending on the composition. The study of the modifications is beneficial not only in basic research on glasses and glass transition but also in applications. When the difference in glass transition temperatures of the K), commonly observed in miscible mixtures is a single glass transition temperature coming from a single structural a-relaxation, which is accompanied by a Johari-Goldstein (JG) b-relaxation strongly connected in dynamic properties. Satisfactory explanation of the connected dynamics of the two relaxations and changes with composition have been given by the Coupling Model. The dynamics and thermodynamics in highly asymmetric e) are more complex. Two a-relaxations (a1 and a2) and correspondingly two glass transitions temperatures (T_g^α1 and T_g^α2) were clearly identified at high and moderate values of c2 of the lower-Tg2 component. However, at low values of c2, only the a1-relaxation and its glass transition at T_g^α1 were found together with a fast relaxation having approximately an Arrhenius temperature dependence for its relaxation time at low temperatures. There are two ways to interpret the data. One interpretation of the observed fast relaxation is the JG b- -relaxation is not resolved due to low c2. Some researchers interpretated the fast relaxation as the -relaxation, but its properties and the associated T_g^α2 are drastically modified at low c2, -relaxation is either unresolved or non-existent. They further proposed that the drastic -relaxation is due to confinement of the low-Tg2 component by the frozen high-Tg1 component. It is transformed to local relaxation within the confined spaces, and becomes identifiable with the observed fast relaxation having Arrhenius T-dependence. This view and interpretation of the dynamics of highly asymmetric mixtures and polymer blends are maintained to be valid up to the present time. In this paper we review exhaustively the experimental data of many highly asymmetric mixtures and blends to show unequivocally that the observed fast relaxation is the JG b-relaxation and not the a2-relaxation.
Notwithstanding, the a2-relaxation with its associated T_g^α2 is also present, albeit not easily resolved due to weak relaxation strength at low c2. The value of T_g^α2 increases monotonically on decreasing c2, without exhibiting a maximum as concluded by one group. The fast relaxation is demonstrated to be the JG b-relaxation from its connection to both the a1 and the a2 relaxations in its properties including the pressure dependence of its relaxation time. Established also is the significant increase of T_g^α2 with pressure, and hence also the relaxation time of the a2-relaxation, despite it is confined. Only experimental data are utilized in this review, and therefore the conclusions we arrived at are totally objective. Suggested Reviewers: Thomas Blochowicz Ph D Prof., Institut fur Festkorperphysik, TU-Darmstadt [email protected] He has done the most extensive studies using different spectroscopies including neutron scattering. His data are critical in this review. None of the authors have published with him. Osamu Urakawa PH D Prof., Department of Macromolecular Science, University of Osaka [email protected] His is the leader of the Japanese group working on dynamics and thermodynamics of polymer blends and mixtures of molecules with polymers. His data are important contributions and cited in the review. None of the authors has published paper with him. G GOULART SILVA PH D Prof., G. GOULART SILVA, ICEx/UFMG [email protected] He or she published important paper cited in the review. George Floudas PH D Prof., Physics, University of Ioannina [email protected] He published important data on this subject and his paper is cited in this review
K.L. Ngai Dipartimento di Fisica, Universita di Pisa, Largo Bruno Pontecorvo 3, I-56127, Pisa, Italy Telephone 39 050 221 4322 (lab), 4537(office) e-mail: kia.ngai@ pi.ipcf.cnr.it [email protected], [email protected] ___________________________________________________________________________ February 22nd, 2019 Prof. Edgar Dutra Zanotto Editor J.Non-Cryst.Solids Dear Prof. Zanotto, I am submitting the manuscript entitled “ Molecular dynamic in binary mixtures and polymer blends with large difference in glass transition temperatures of the two components: a critical review ” by K. L. Ngai, Sofia Valenti, and Simone Capaccioli, for your consideration of publication as a Review article in the special issues of “Frontiers of Glass Science” and “PK Gupta”. The dynamics of the equilibrium liquid and glassy states of mixtures of two molecular glass-formers, mixture of moleuclar glass-former with polymer, and polymer blends are active research areas for the past few decades and continues to the present time. Currently of particular interest are the highly asymmetric mixtures and blends, which are composed of two components with very large difference in their glass transition temperatures. As expected, novel phenomena emerge from the experimental studies of these systems, and are challenging for fundamental understanding. In the course of the last twenty years, several attempts were made to interpret the experimental data and explain the phenomena. However, no consensus of interpretation and explanation have been reached, possibly due not all experimental facts were taken into consideration in past attempts. Thus, in this review we collect and consider all relevant experimental data. This undertaking is instrumental in arrive at an interpretation consistent with all available experiments. Since only experimental data are considered, this review is totally objective, and can be used as a basis for others to make their contributions. For reviewers I suggest the following reserchers who made contributions to the subject, and are referred to in the review. Cover Letter
(1) Prof. Thomas Blochowicz, Institut fur Festkorperphysik, TU-Darmstadt, 64289 Darmstadt, Germany, who have done the most extensive studies using different spectroscopies including neutron scattering. [email protected] (2) Prof. George Floudas, University of Ioannina, Department of Physics, and Foundation for Research and Technology-Hellas (FORTH), [email protected] (3) G. Goulart Silva ([email protected]). (4) Prof. Osamu Urakawa, Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560-0043, Japan, [email protected] We did not have any publication with these researcher in publication. One exception is my collaboration with George Floudas, which was more than 30 years ago and when he was a graduate student. Sincerely,
Journal of Non-Crystalline Solids Confirmation of Authorship Please save a copy of this file, complete and upload as the “Confirmation of Authorship” file. As corresponding author, I K.L. Ngai , hereby confirm on behalf of all authors that: 1. This manuscript has not been published, was not, and is not being submitted to any other journal. If presented at a conference, the conference is identified. If published in conference proceedings, substantial justification for re-publication must be presented. 2. All necessary permissions for publication were secured prior to submission of the manuscript. 3. All authors listed have made a significant contribution to the research reported and have read and approved the submitted manuscript, and furthermore, all those who made substantive contributions to this work have been included in the author list. Confirmation of Authorship
By mixing a molecular or polymeric glass-former with another one, its dynamic and thermodynamic properties can be modified to various degrees depending on the composition. The study of the modifications is beneficial not only in basic research on glasses and glass transition but also in applications. When the difference in glass transition temperatures of the two components Tg is not too large (less than 100 K), commonly observed in miscible mixtures is a single glass transition temperature coming from a single structural -relaxation, which is accompanied by a Johari-Goldstein (JG) -relaxation strongly connected in dynamic properties. Satisfactory explanation of the connected dynamics of the two relaxations and changes with composition have been given by the Coupling Model. The dynamics and thermodynamics in highly asymmetric mixtures (i.e., when Tg is large) are more complex. Two -relaxations (1 and 2) and correspondingly two glass transitions temperatures ( and ) were clearly identified at high and moderate values of c2 of the lower-Tg2 component. However, at low values of c2, only the 1-relaxation and its glass transition at were found together with a fast relaxation having approximately an Arrhenius temperature dependence for its relaxation time at low temperatures. There are two ways to interpret the data. One interpretation of the observed fast relaxation is the JG -relaxation, and the 2-relaxation is not resolved due to low c2. Some researchers interpretated the fast relaxation as the 2-relaxation, but its properties and the associated are drastically modified at low c2, and the JG -relaxation is either unresolved or non-existent. They further proposed that the drastic modification of the 2-relaxation is due to confinement of the low-Tg2 component by the frozen high-Tg1 component. It is transformed to local relaxation within the confined spaces, and becomes identifiable with the observed fast relaxation having Arrhenius T-dependence. This view and interpretation of the dynamics of highly asymmetric mixtures and polymer blends are maintained to be valid up to the present *Abstract
time. In this paper we review exhaustively the experimental data of many highly asymmetric mixtures and blends to show unequivocally that the observed fast relaxation is the JG - relaxation and not the 2-relaxation. Notwithstanding, the 2-relaxation with its associated is also present, albeit not easily resolved due to weak relaxation strength at low c2. The value of increases monotonically on decreasing c2, without exhibiting a maximum as concluded by one group. The fast relaxation is demonstrated to be the JG -relaxation from its connection to both the 1 and the 2 relaxations in its properties including the pressure dependence of its relaxation time. Established also is the significant increase of with pressure, and hence also the relaxation time of the 2-relaxation, despite it is confined. Only experimental data are utilized in this review, and therefore the conclusions we arrived at are totally objective.
1 Molecular dynamic in binary mixtures and polymer blends with large difference in glass transition temperatures of the two components: a critical review K.L. Ngaia, Sofia Valentib , S. Capacciolia,b aCNR-IPCF, Largo Bruno Pontecorvo 3 ,I-56127, Pisa, Italy bDipartimento di Fisica, Università di Pisa, Largo Bruno Pontecorvo 3 ,I-56127, Pisa, Italy Abstract By mixing a molecular or polymeric glass-former with another one, its dynamic and thermodynamic properties can be modified to various degrees depending on the composition. The study of the modifications is beneficial not only in basic research on glasses and glass transition but also in applications. When the difference in glass transition temperatures of the two components Tg is not too large (less than 100 K), commonly observed in miscible mixtures is a single glass transition temperature coming from a single structural -relaxation, which is accompanied by a Johari-Goldstein (JG) -relaxation strongly connected in dynamic properties. Satisfactory explanation of the connected dynamics of the two relaxations and changes with composition have been given by the Coupling Model. The dynamics and thermodynamics in highly asymmetric mixtures (i.e., when Tg is large) are more complex. Two -relaxations (1 and 2) and correspondingly two glass transitions temperatures ( and ) were clearly identified at high and moderate values of c2 of the lower-Tg2 component. However, at low values of c2, only the 1-relaxation and its glass transition at were found together with a fast relaxation having approximately an Arrhenius temperature dependence for its relaxation time at *Manuscript Click here to download Manuscript: New Manuscript_9.docx Click here to view linked References
2 low temperatures. There are two ways to interpret the data. One interpretation of the observed fast relaxation is the JG -relaxation, and the 2-relaxation is not resolved due to low c2. Some researchers interpretated the fast relaxation as the 2-relaxation, but its properties and the associated are drastically modified at low c2, and the JG -relaxation is either unresolved or non-existent. They further proposed that the drastic modification of the 2-relaxation is due to confinement of the low-Tg2 component by the frozen high-Tg1 component. It is transformed to local relaxation within the confined spaces, and becomes identifiable with the observed fast relaxation having Arrhenius T-dependence. This view and interpretation of the dynamics of highly asymmetric mixtures and polymer blends are maintained to be valid up to the present time. In this paper we review exhaustively the experimental data of many highly asymmetric mixtures and blends to show unequivocally that the observed fast relaxation is the JG - relaxation and not the 2-relaxation. Notwithstanding, the 2-relaxation with its associated is also present, albeit not easily resolved due to weak relaxation strength at low c2. The value of increases monotonically on decreasing c2, without exhibiting a maximum as concluded by one group. The fast relaxation is demonstrated to be the JG -relaxation from its connection to both the 1 and the 2 relaxations in its properties including the pressure dependence of its relaxation time. Established also is the significant increase of with pressure, and hence also the relaxation time of the 2-relaxation, despite it is confined. Only experimental data are utilized in this review, and therefore the conclusions we arrived at are totally objective. Corresponding author: [email protected]; [email protected]
9 same interpretation is maintained in other papers [45-47,55,56] and in more recent reviews [58,86]. Such persistent interpretation may have led others including the authors of Refs.[81-84] to mistakenly identify the JG -relaxation in the case of the 8-20% TPP mixtures with PS as the confined 2-relaxation, and the additional wrong conclusion that does not continue the monotonic increase with decrease of c2 found at higher values of c2. Instead reaches a maximum at some low value of c20.35, and decrease on further decrease of c2. This result is false because the JG glass transition temperature Tg obtained by extrapolating the Arrhenius temperature dependence of to 100 s was wrongly taken as for c2 lower than 0.3. Efforts were made by us in 2013 [80] and 2018 [87] to demonstrate by experimental evidences and theoretical considerations that the JG -relaxation was mistaken as either the local -relaxation in the blends of PVME with PS [24,25] or the restricted 2-relaxation in mixtures of TPP with PS [81-83]. Furthermore, new dielectric measurements by Valenti et al. [87] on 20% TPP/80%PS mixture at elevated pressures and compared with NMR data have shown unequivocally that the purported 2-relaxation is the JG -relaxation. Hence proven wrong is the conclusion of exhibiting a maximum at c2=0.35 in the mixtures of TPP with PS. Notwithstanding, in a chapter of a book published in 2018, Bock et al. [85] acknowledged the publication of the paper by Valenti et al. but avoided mentioning or addressing the experimental evidences given therein. Instead, they reaffirmed their interpretation by reproducing the figure showing the existence of a maximum of the purported as a function of c2 of TPP in the mixtures with PS. In addition, to bolster the commitment to their interpretation, they show a similar figure from the mixture of m-tricresyl phosphate (m-TCP) with a nonpolymeric high-Tg glass formers DH based on spirobichroman derivatives in a paper published by Pötzschner et al. [84], which was not addressed in the paper by Valenti et al. The dielectric data and the
10 interpretation of Pötzschner et al. as confined 2-relaxation was made use by Alegria and Colmenero in a 2016 review [86] to support the interpretation by LAC [24,25] of a faster relaxation with Arrhenius T-dependence in the PVME/PS with c230% as confined 2- relaxation, which we had shown that it is actually the JG -relaxation [80]. It is disconcerting that Alegria and Colmenero had not so far responded to the experimental evidences and theoretical considerations we gave in ref.[80] to refute the interpretation of LAC. Instead they cited the meager data from Pötzschner et al.[84] for support, which we shall discuss later and show they made the same mistake of identifying the resolved JG -relaxation as the confined 2- relaxation.. From the discussions in the above, it is clear that the controversy in the interpretation of the relaxation processes in highly asymmetric binary mixtures with low concentration c2 of the low-Tg component remains unresolved since 2003. It calls for comprehensive, in-depth, and critical investigation into the experimental facts to uncover the true interpretation of the dynamics and to resolve the controversy once and for all. This is the objective of this paper. The first task is to demonstrate that the faster process with Arrhenius T-dependence identified by LAC and Pötzschner et al. as the confined 2-relaxation is actually and truly the JG -relaxation. This will be accomplished by providing multiple and indisputable experimental evidences combined with theoretical considerations. The second task is to uncover the true confined but cooperative 2-relaxation detectable by conventional DSC, temperature-modulated DSC (TMDSC) or thermally stimulated depolarization current (TSDC) in some mixtures and blends despite it has weak relaxation strength and sandwiched between the 1-relaxation and the JG - relaxation, and show it does exist and reveal its properties. The third and final task is to reassert the universal presence of the JG -relaxation and revive its fundamental importance by showing
11 the various strong connections in properties it has with the 1-relaxation as well as with the confined and still cooperative 2-relaxation. We deem our genuine effort and the materials presented in this review either settle the controversy or deserve conscientious response from others if they still maintain their own interpretations. Another way and perhaps the best to settle the controversy is to invoke direct evidences of the coexistence of the confined 2-relaxation and the JG -relaxation together with the undisputed 1-relaxation from experiments in highly asymmetric mixtures and polymer blend. It would be ideal if the thermodynamics and dynamic properties of all three processes and the relations between them are characterized in the experimental results, as well as the determination of the two glass transition temperatures, and . These facts can be used to unequivocally identify the processes in the mixtures and polymer blends, particularly in those cases where the confined 2-relaxation was not resolved and mistaken as the resolved JG -relaxation [24,25,45- 47,56,81-86]. Fortunately, such experiments had been performed by Blochowicz and coworkers and reported in a series of studies of either methyltetrahydrofuran or tetrahydrofuran in mixtures with tristyrene [77], polystyrene [79], oligo-PMMA [78]. Their results are presented first in the next section to pave the way in resolving the controversy in the interpretation of the other mixtures [81-85] and polymer blends [24,25,45-47,56,86]. 2. Evidences of coexistence of confined 2-relaxation, 1-relaxation, and JG -relaxation Examples of highly asymmetric mixtures and polymer blends are taken from the literature to show coexistence of the confined 2-relaxation, the 1-relaxation, and the JG -relaxation, and the two glass transition temperatures and . This expose should make easier for us to
12 demonstrate convincingly the mistake made by others [24,25,81-84] in identifying the resolved JG -relaxation as the confined 2-relaxation in the next section. 2.1 Highly asymmetric mixtures (A) MTHF and THF in tristyrene For highly asymmetric mixtures, the examples are taken from the comprehensive studies of methyltetrahydrofuran (MTHF, Tg2=90K) or tetrahydrofuran (THF) with tristyrene (Tg1 =233 K) [77,78] as well as MTHF with polystyrene having Mw=60 000 g/mol (PS60k, Tg1=373 K) [79] by Blochowicz and coworkers using a variety of experimental techniques including dielectric spectroscopy, differential scanning calorimetry, 2H nuclear magnetic resonance, depolarized dynamic light scattering, and incoherent quasielastic neutron scattering, which enable selectively probing the dynamics of the components over broad range of time or frequency. Present in dielectric spectra of the mixtures of MTHF with tristyrene [77] are two secondary relaxations, and . The slower -relaxation was identified as the JG -relaxation [103] with relaxation times (T) weakly dependent on concentration c2 of MTHF ranging from 70% down to 6% and having an activation energy of about 3000 K. This is an interesting property of the JG -relaxation in mixtures, which seems general as shown later on in mixtures of TPP with PS [81-85] and blends of PVME with PS [24,25,80]. The data of (T) plotted against reciprocal temperature are shown in Fig.2. The dashed lines emanating from the (T) data are the primitive relaxation times, 0, calculated from the -relaxation times of the 1- process 1 at c2 = 8%, 12%, 50% and 70% with coupling parameters n given in the figure. The 2- or -relaxation were resolved in the dielectric spectra times of mixtures with c2 = 6%, 12%, 25%, 40% and 50%. The 2 or are represented by closed dark grey symbols lying close to the grey dashed line: inverted triangles (6% MTHF), diamonds (12% MTHF), and circles (50%
13 MTHF). Evidently the data of 2 or are limited and are much shorter than 100 s in any of the three cases of c2= 6%, 12%, and 25% to allow determination of the dielectric without large uncertainty by extrapolating the assumed Arrhenius T-dependence of to 100 s. Nevertheless this was done by the authors of Ref.[77], and the results of the dielectric shows very small increase on decreasing c2 from 50% down to 12%. However there is a small decrease of from c2=12% to 6%. The mini ‘maximum’ at 12% should not be taken seriously due to scarcity of data and since error estimates were not given. We do not follow Blochowicz et al. in drawing a line to represent the common Arrhenius dependence of for mixtures with different c2 and extrapolate it to reach 100 s to determine (c2). For details, see Fig.3 in Ref.[77] or Fig.S3 in Supplementary Information (SI). This is because the data are too meagre to support that or τ2(T) as well as Tg 2(c2) is independent of c2. Despite the uncertainty of the Arrhenius T-dependence of , it can be seen from Fig.2 that E 2 for any c2 is much larger than E of the JG -relaxation, as it should be. On the other hand, deduced from DSC increases with decreasing c2 from 50% down to 25%, but decrease slightly at c2 =12%. Unfortunately the DSC data for c2 =12% were not presented, and there is no way to judge the value of the DSC reported. The analysis of the 25% DSC data and error estimate were not given either to judge the DSC reported. By no means we are implying that Blochowicz and coworkers advocated the existence of a maximum in . In fact they drew a line through the data points in their Fig.4 in Ref. [77] and reproduced as Fig.S1 in SI, and also in Fig.1 in ref.[79] or Fig.S2 in SI suggesting monotonic increase with decrease of c2. The purpose of this discussion is to preempt others to use the data as support of presence of maximum in mixtures of MTHF with tristyrene.
14 Blochowicz and coworkers also studied the mixtures of tetrahydrofuran (THF) with tristyrene at three c2 =33%, 20% and 10% by dielectric spectroscopy and observe all four relaxation, 1, 2 or , , and as in the mixtures of MTHF with tristryene. From the relaxation times of 1, 2, and relaxations reported in separate figures in Ref.[78], we have combined the data of 2, , and in one Fig.3 here. Values of 2(T) or τ(T) determined in the experiments have Arrhenius T-dependence of confined 2-relaxation for all three THF mixtures, and its concentration dependence in the THF mixtures is much clearer than from the data of the MTHF mixtures shown before in Fig.2. The activation energy E 2 of 2(T) for any c2 in Fig.3 is larger than E of the JG -relaxation. By extrapolating the Arrhenius T-dependence of τ(T) to 100 s, the of the three mixtures are determined. The were determined before in Ref.[78] from the VFT-dependence of τ1(T) as the temperature at which τ1(T)=100 s. The dependences of and on c2, the concentration of THF, are presented in the lower panel of Fig.3 to show the monotonic increase of with decrease of c2. The coexistence of the 1-relaxation, the confined 2-relaxation, and the JG -relaxation in the THF mixtures is clearer than in the MTHF mixtures. There is no doubt from the data of this highly asymmetric mixture that does not exhibit a maximum at some low value of c2. (B) 50%MTHF in PS60k Replacing tristyrene by PS60K (polystyrene with Mw= 60 kDa) the difference Tg = Tg1 - Tg2 is increased from 143 K to 283 K, and consequently increased is the difference, (c2) - (c2), and more separated is the - or 2-relaxation from the 1-relaxation to make it easier to
15 resolve. This trend can be seen by comparing the relaxation times τ2(T), τ2(T), and τ(T) of the MTHF-3styrene mixtures in Fig.2 with the MTHF-PS60K mixtures in the left panel of Fig.4 for c2=50%. The coexistence of the JG -relaxation and the confined 2-relaxation with τ2(T) having Arrhenius T-dependence is clear. Not pointed out before in Ref.[103] is the change of temperature dependence of τ(T) on crossing some temperature in the neighborhood of determined by either DSC (thinner vertical dashed line) or dielectrically (thicker vertical dashed line) from the definition, τ ( )=100 s. Brought out by the red full line and black dashed lines with different slopes in Fig.4, the crossover in temperature dependence of τ (T) at is proof of that the -relaxation is the JG -relaxation as usually found in binary mixtures of rigid dielectric probes [70, 72]. The separation of τ2(T) from τ(T) measured by the length of either one of the two vertical dashed lines is consistent with that calculated from the CM Eq.(2) for a value of n of 0.44. These properties indicate the 2-relaxation is a genuine cooperative -relaxation detected by DSC (see upper inset in Fig.S2), and connected to the JG -relaxation by the CM Eq.(2) like in single component glass-formers [92,93,96-102]. Thus the 2-relaxation of the low-Tg component MTHF still performs liquid-like dynamics despite being confined within the matrix of the immobilized high-Tg component PS60K. Not too far above , the temperature dependence of τ2(T) is Arrhenius as well as that of τ (T). It is evident from Fig.4 that the activation energy E 2 of τ2(T) is a few times larger than E of τ (T). The much larger size of E 2 than E can be used to identify the JG -relaxation and not to mistaken it as the confined 2- relaxation, especially in cases where the latter was not resolved [24,25,81-85]. It can be seen by inspection of the spectra in the upper right panel of Fig.4 that the dielectric strength 2(T) of the confined 2-relaxation increases with decrease of temperature according to the Curie-Weiss
16 law, while the opposite trend is shown by (T) of the JG -relaxation. Again, the contrasting T-dependences of the dielectric strength is another simple way to distinguish the two relaxations. At higher temperatures, the short relaxation times represented in Fig.4 by closed red circles were measured by quasielastic neutron scattering. Considered together with the dielectric τ2(T) and τ (T), these neutron scattering data suggest the 2-relaxation has already merged with the JG -relaxation, and hence the relaxation times τ2(T) are identifiable with τ (T). The dielectric frequency dispersions of the 1-relaxation measured at 190 and 200 K were fitted by the Fourier transform of the Kohlrausch function to determine the values of n=0.77 and 0.75 respectively in the right lower panel of Fig.4. The corresponding primitive relaxation times τ0(T) calculated by Eq.(2) with these n values and τ1(T) are shown by the two black triangles in left panel, and they are in approximate agreement with τ (T). This result shows the relaxation times of the JG -relaxation and the slowest 1-relaxation are also related by Eq.(2), in accord with the CM prediction. It is remarkable that Blochowicz et al. had been able to detect the 2-relaxation and determine τ2(T) over 15 decades from 104 to 10-11 s by the combinations of DSC, dielectric relaxation, and neutron scattering. Their data in Fig.4 indicate the 2-relaxation has merged with the JG -relaxation at higher temperatures, and there the short relaxation times τ2(T) probed by neutron scattering become τ (T). This is the reason why the temperature dependence of τ2(T) is so weak in the range 10-11< τ2(T) <10-9 s, and different from the stronger Arrhenius T- dependence of τ2(T) observed at longer times down to 103 s at temperature lower than from DSC of the truly confined 2-relaxation. By contrast, dielectric data of τ2(T) at long times and the DSC were absent in the neutron scattering studies of three highly asymmetric polymer
17 blends of 25%PEO in poly(meth methacrylate) (PMMA) (TgPEO=220 K, TgPMMA=400 K) by Genix et al. [45], 20%PEO in poly(vinylacetate) (PVAc) (TgPEO =220 K, TgPVAc =315 K) by Tyagi et al. [46,56], and 25%PEO in polyethersulfone (PES) (TgPEO=220 K, TgPES=382 K) by Genix et al. [47]. The neutron data of τ2(T) from PEO in the three blends with PMMA, PVAc, and PES have τ2(T) shorter than 10-9.5 s, and with weak temperature dependence like that of the neutron scattering τ2(T) in 50%MTHF in PS60k in Fig.4, which we had identified with τ (T). Without the benefit of this knowledge possible only from more complete set of data such as those of Blochowicz and coworkers, the authors of the neutron scattering studies of the three polymer blends [45-47] interpreted the neutron τ2(T) data of PEO component as confinement by the rigid environments. In fact they stated explicitly in Ref.[46] for τ2(T) of 20%PEO in PVAc by the statement: “The activation energy of the confined motions is of about 0.26 eV, much lower than those shown by the secondary relaxations in this system. Thus, the observed phenomenon cannot be identified with those processes.”. This interpretation is questionable because the neutron τ2(T) were taken at temperatures above and slightly below where the high-Tg1 component is at or near equilibrium respectively and is not hard frozen (see Fig.S4). Moreover, by extrapolating the Arrhenius temperature dependence of the τ2(T) from neutron scattering with its activation energy of 0.26 eV to lower temperatures, its value is many orders of magnitude shorter than the value of τ2(T) at the viscoelastic of 245 5 K determined by Urakawa et al. in the same blend [113]. The same interpretation of confined 2-relaxation based on the neutron τ2(T) with Arrhenius T-dependence of 25%PEO in PMMA [45] is contradicted by the observation of the calorimetric by several groups [16,39,54]. Moreover, as shown before for the mixture of 50%MTHF in PS60k in Fig.4, the neutron τ2(T) has merged with and becomes the JG relaxation time τ(T), supported by finding that τ(T) is the same as the primitive
18 relaxation time τ0(T). Therefore, the short τ2(T) from neutron scattering of 25%PEO in PVAc, PMMA, and PES is not associated with the confined 2-relaxation and cannot be interpreted as such in Refs.[45-47,56] and in the review [58]. High frequency deuteron NMR experiments have found that segmental relaxation times, 2, in the range, -8.5 log( 2/s) -11.5, of the fast PEO component in blends with PMMA are nearly independent of composition for blends from 3 to 30% d4PEO over the wide temperature regime studied, and 2 is hardly influenced by the presence of the PMMA [23,27,28]. Shown in Fig.S6 of SI, the result holds for a wide range of temperatures extending to well below the glass transition of the PMMA matrix, where the segmental relaxation times of PMMA are about 12 orders of magnitude longer than 2 of PEO. Similar behavior is observed by deuteron NMR in PEO blends with PVAc (polyvinyl acetate) [59]. In the range -9 log( 2/s) -11.8, the 2 of PEO in 2% PEO blend differs little from that in 50% PEO and 100%PEO blends by about half a decade and one decade respectively. The effect seems general, not only found in highly asymmetric polymer blends but also in all blends [80]. For instance, the same effect was found by quasielastic neutron scattering (QENS) in the PEO/PMMA blends by Sakai et al. [51,52]. The explanation was given by the CM in Refs.[28,80], and the details will be given later in the section on polymer blends. In the neutron scattering study of the blend of 25% of PEO in PES [47], Genix et al. pointed out that the PEO neutron τ2(T) seem to approach, within the experimental uncertainties, the extrapolation of the timescales obtained for the secondary -relaxation in semicrystalline PEO or the -relaxation in 10 and 20%PEO in PMMA as shown in their Fig.6 [47] or Fig.S5 in SI. By this they implied that the confined motion of PEO in the blend could correspond to those involved in the -relaxation of PEO. Although they said that this is a question that deserves
25 , which B&K and Pötzschner et al. interpreted as the 2-relaxation of TPP and m-TCP respectively subjected to confinement, i.e. ‘the more mobile (lower-Tg) component relaxes by a liquid-like motion in a matrix formed by the arrested (higher-Tg) component’[81-84]. To show that this is a mistake, we first take from their own published data as evidences. Afterwards we shall bring in our own dielectric relaxation data at ambient and elevated pressures to demonstrate convincingly that the resolved faster relaxation is the JG -relaxation by utilizing Properties (1)- (9) and (11). Presence of the unresolved 2-relaxation are shown by indirect evidences in accord with Properties (1)-(9). The NMR data from B&K are brought back for reconsideration and shown to be consistent with our identification of the resolved faster process is the JG - relaxation [87], and the confined 2-relaxation is mostly unresolved albeit present. 3.1 Dielectric data at ambient pressure 8% and 18%TPP mixtures with PS Kahlau et al. [81] made dielectric measurements of mixtures of tripropyl phosphate (TPP) with polystyrene (PS) with c2 over the whole range from 100% down to 0%. We consider their data labelled as c2=20, and 10% (but actually the dielectric measurements were made at 18% and 8% respectively) because the confinement of 2-relaxation is expected more pronounced, the separation between 2 and larger, and hence easier to distinguish it from the JG -relaxation. The dielectric spectra of the 18% TPP mixture are reproduced in Fig.7 from Ref.[81,83], where only two relaxations are resolved. The slower one is no doubt the 1-relaxation, but they interpret the faster relaxation as the confined 2-relaxation. It is clear by inspection of the figure that the dielectric strength of the faster process increases with increasing temperature consistent with that of the JG -relaxation, but at variation with that of the confined 2-relaxation (i.e.
26 Property 4). Had this been taken into consideration by B&K, perhaps they would hesitate interpret it as the confined 2-relaxation. The left panel of Fig.8 is the Arrhenius plot of the dielectric relaxation times of the two processes reproduced from Kahlau et al. [81]. We are interested mainly in the data of the mixtures with c2=20 (actually 18)%, and 10 (actually 8)% in which the slow one is the 1- relaxation and the fast one was interpreted as the confined 2-relaxation [81]. The two lines drawn in the figure are supposedly representing the Arrhenius temperature dependences of 2(T) of the 18 and 8% mixtures, and the intercepts with the horizontal broken line at 100 s were used to determine the dielectric glass transition temperature of the purported 2-relaxation. The value 137 K at c2=8% so obtained is shown in Fig.8b, which is also reproduced from Kahlau et al. It is only 2 degrees higher than Tg2=135 K of pure TPP, and hence violating Property (5). It is responsible for the existence of a maximum. Therefore this value of 137 K for the purported confined 2-relaxation in mixture with c2=8% is not consistent with the much higher value of than Tg2 (Property 5) established in mixtures where the confined 2- relaxation was clearly resolved and identified, i.e., Property (1). The broadening of the faster process with decreasing temperature can be seen from the spectra of the 20%TPP mixture in Fig.7, which is a well-known property of JG -relaxation. Notwithstanding, interpreting the fast process as the confined 2-relaxation, Kahlau et al. accounted for the broadening in mixtures with c2=8 and 18% by a broad distribution of relaxation times represented by a temperature independent distribution of activation energies g(E) so that its mean correlation time 2(T) has an Arrhenius temperature dependence governed by the mean activation energy EA. The value of EA for the 8%TPP mixture is 5241 K. Hence EA
27 /R17 falls within the bounds of the ratio for JG -relaxations [112,114]. This was recognized by Kahlau et al. but they still interpret the resolved fast process in Figs,7 and 8 as the confined 2-relaxation. By the way, the small value of EA violates Property (2) of the confined 2-relaxation becasue its activation energy E2 is appreciably larger than the activation energy E of the JG -relaxation time (T). The inconsistency with Properties 1 and 2 casts doubt on the interpretation of the resolved fast process as the confined -2 relaxation by Kahlau et al. It is natural for Kahlau et al. to fit 2(T) by the Arrhenius T-dependence in view of the interpretation that 2(T) are the relaxation times of 2-relaxation confined by the frozen matrix of the high-Tg component PS. However, there is no reason to expect a break from the Arrhenius T-dependence of the confined 2(T) at any temperature far below . By careful examination of the purported 2(T) data of the 8%TPP mixture (blue circles in Fig.8a), one can find that the temperature dependence actually is not strictly Arrhenius over the entire range. This becomes clearer by selecting the purported 2(T) data of the 8%TPP from the rest and replotting them together with the 1(T) data in the left panel of Fig.9. The two straight lines drawn through the 2(T) data of the 8%TPP mixture with different slopes demonstrate a change from a weaker Arrhenius T-dependence to a stronger one at 238 K far below the dielectric =314 K. While this property is not expected from the confined 2-relaxation, it manifestly belongs to that of the JG -relaxation (i.e., Property 6) at or near the glass transition temperature (8%)=238 K. Thus the resolved fast process in the 8%TPP mixture is the JG -relaxation and not the confined 2-relaxation mistakenly identified as such by Kahlau et al. Incidentally, the presence of the confined 2-relaxation in the 8%TPP mixture is revealed by this Property (6) of the JG -
28 relaxation, and hence we have an estimate of 2(T) of the unresolved 2-relaxation is about 100 s at T =238 K, i.e., the dielectric 2 glass transition temperature is 238 K. The value 238 K of the dielectric 2-glass transition temperature (8%) for the 8%TPP mixture is entered into the plot of and versus c2 or cTPP in the right panel of Fig.9. This helps to restore the monotonic increase of both the dielectric and with decreasing c2 at small c2 (i.e. Property 5), and replace the maximum of not found by anyone else except in Refs.[81-85]. In these papers, included are the supposedly determined from DSC data of the 20%TPP and 10%TPP mixtures to support the presence of the maximum. Although the DSC traces of these mixtures were published, they were not analyzed to support the DSC values of in Figs.8 and 9. If the features of the DSC traces of these mixtures at low temperatures were used by B&K to suggest the purported values of the DSC , it is worthwhile to point out similar feature is present in the pure PS used (see Fig.1a in Ref.[81]). Also even if the weak feature in the DSC trace truly reflects an enthalpy relaxation, it can very well be associated with the JG -relaxation [99]. The inset of the left panel of Fig.9 is a reproduction of the master curve of the dielectric loss spectra of the 1-relaxation taken at several temperatures close to together with the fit by the Fourier transform of the Kohlrausch function with n=0.73 performed by Kahlau et al. [81]. The open inverted triangles in the main figure are the values of the primitive relaxation times 0(T) calculated by the CM equation (2) from 1(T) with n=0.73 and tc=2 ps. The value of 0(T) at T= is in agreement with the extrapolation of the Arrhenius T-dependence of the (T) data for T> to , which further supports the resolved fast relaxation is the JG -relaxation according to Property 7. Also the stronger T-dependence of 0(T) (T) for T> together
29 with the weaker T-dependence of (T) for T< indicates another change of T-dependence of (T) at . In accord with Property 6. These results further confirm the confined 2-relaxation alleged by B&K is actually the JG -relaxation. The relaxation strength of 2 of the purported confined 2-process in the 18%TPP mixture obtained by Kahlau et al. is shown as a function of temperature in the left panel of Fig.10. It increases with increase of temperature at odds with the opposite trend of genuine confined 2- process according to Property 4, but consistent with the behavior of the dielectric strength of the JG -relaxation. The broken line in Fig.10 was drawn by Kahlau et al. [81] to show that there is change of T-dependence of 2 at 273 K identified with . No doubt this is correct because 273 K is the determined by DSC, We pointed out there is yet another change at T- dependence of 2 at 232 K we identified with for the 18%TPP mixture. It is 8 degrees lower than =238 K for the 8%TPP mixture as can be expected due to higher concentration of TPP. Thus for the 18%TPP mixture, the dielectric glass transition temperature of the truly confined 2-relaxation time is 232 K, and 2(T) is about 100 s at T= =232 K. These changes of 2 at and are another support of the resolved fast process is the JG -relaxation (from Property 6), and not the confined 2-relaxation misinterpreted by Kahlau et al. The value =232 K of the 18%TPP mixture is represented by the red ellipsoid in the right panel of Fig.10. On replacing the false dielectric 137 K from Ref.[81] by 232 K of the confined 2-relaxation, we restore the monotonic increase of with decrease in c2 (i.e., Property 1), and dismiss the purported maximum at c2 near 36% of B&K. The monotonic increase of on decreasing c2 at low values equal to 18 and 8%TPP is demonstrated in Fig.10.
30 20%TPP mixtures with PS We made our own dielectric relaxation measurements at ambient and elevated pressures of a truly 20%TPP mixture [87] with the same PS as used in the study of B&K [81-83]. The data from 140 K to 260 K at ambient pressure showing the 1-relaxation and the JG -relaxation are presented in Fig.11. Data at ambient pressure and temperatures higher than 260 K are shown in the two panels of Fig.12 together with some data taken at elevated pressures to be discussed later. The relaxation times 1(T) and (T) at ambient pressure are shown by black open and closed squares respectively in Fig.13, and the dielectric glass transition temperature = 268 K is determined by 1( ) = 100 s. The 1-loss peak can be well fit by the imaginary part of the Fourier transform of the KWW function with (1-n)=0.25, but the low frequency flank of the JG -loss peak is indeterminate. Therefore the loss from the 2-relaxation cannot be deduced by subtracting the sum of the 1 and JG losses from the measured loss spectra. The best one can do is to use the frequency of the measured loss minimum as an approximate guide to the location of the unresolved 2-relaxation and its peak frequency f2(T). The approximate 2-relaxation times 2(T) corresponding to f2(T) at four temperatures, 260, 268, 280, and 289 K are shown by the black diamonds in Fig.13. (T) From the spectra at ambient pressure of the JG -relaxation in Fig.11, we determined the T- dependence of its and the results are presented in Fig.14. There is a clear change of (T) within the neighborhood of 265 K, close to =268 K of the 1-relaxation dominated by the majority PS component. A weaker change of (T) at about 223 K is assigned to the of the truly confined 2-relaxation from the minority TPP component. This assignment is represented by the upper black closed diamond in the relaxation map (Fig.13) by assuming at =223 K
31 that 2=102 s. The line is the Arrhenius fit of the approximate 2(T) at four temperatures to include the value of 2( )=100 s at =223 K. The Arrhenius T-dependence of 2(T) of the confined 2-relaxation is expected from Property (2), and it is evidently stronger than that of (T), causing the two to merge at higher temperatures. The 1(T) and 2(T) increase monotonically with decrease in concentration of TPP in the three mixtures (i.e. Property 3), while (T) changes little (i.e. Property 11). This is like 8%, 12%, 50%, and 70% of MTHF in 3styrene (Fig.2) and 10%, 20%, and 33% THF in 3styrene, where the confined 2-relaxation was resolved in the dielectric spectra [77,78]. Altogether, the data of 1, the approximate 2, and and their relations in the 20% TPP mixture in Fig.13 resemble that found in 50% MTHF in PS60k by Blochowicz et al. [79] shown in Figs.4, and 6. Included in the relaxation map (Fig.13) are the values of 2=102 s at the glass transition temperatures =238 K (red diamond) and 233 K (blue diamond) of the true 2- relaxation in the 8% and 18% TPP mixtures respectively. As the reader may recall, the value of 238 K of for the 8%TPP mixture was deduced from the temperature at which (T) changes its T-dependence (Fig.9), while the value of 232 K for the 18%TPP mixture was deduced from the temperature at which (T) changes its T-dependence (Fig.10). Shown in the relaxation map (Fig.13) are the dielectric 1(T) and (T) of the 8% (red) and 18% (blue) TPP mixtures from Kahlau et al. [81]. The primitive relaxation times 0(T) calculated by the CM equation (2) from 1(T) and 1-n=0.27 determined from the Kohlrausch fit to the frequency dispersion and represented by inverted triangles in Fig.13 are consistent with the data of (T) obtained at lower temperatures. Thereby Property (7) is also verified.
32 The method of obtaining approximate 2(T) from the dielectric spectra of the 20%TPP mixture was applied to the 8%TPP and 18%TPP mixtures published by B&K [81-83]. The approximate 2(T) for the 8%TPP at 290 K and 298 K, and 2(T) for the 18%TPP mixtures at 317 K are presented in Fig.S8 in SI`. These values of 2(T) together with 2( )=100 s at =238 K and 232 K for the 8%TPP and 18%TPP mixtures respectively were fit to the Arrhenius T-dependences according to Property (2) and are represented by the red and blue lines in Fig.S8. 3.2 Mixtures of TCP with DH379 Pötzschner et al. [84] studied the component dynamics of the highly asymmetric mixtures of m-tri-cresyl phosphate (TCP) (Tg=206 K) with a spirobichroman derivative (DH379) (Tg=382 K) at concentrations of 34% and 20%. They observed two relaxations by dielectric spectroscopy. Dominated by the majority DH379 component, the temperature dependence of the slower 1- relaxation time 1(T) was used to determine Tg 1 in Fig.15a. Following the example of B&K, Pötzschner et al. interpreted the faster process as the confined 2-relaxation in the immobile matrix of DH379. The Arrhenius T-dependence fit to the relaxation times of the faster relaxation were extrapolated to 100 s to determine of the purported confined 2-relaxation as shown in Fig.15a. The values of the alleged of the 34% and 20% TCP mixtures produce a maximum when considered together with those determined at higher c2 in Fig.15b. The presence of the maximum is based solely on the dielectric data since no NMR or calorimetric data were presented for these two mixtures. This maximum, instead of monotonic increase of with decreasing c2, is the consequence of misidentifying the faster relaxation as the confined 2- relaxation, which is actually the JG -relaxation as we demonstrate below. The mistake can be
33 perceived from the 20% TCP mixture having the alleged the same as Tg of 100% TCP, violating Property (1). This is also surprising and impossible because the environment of the TCP in the two cases are drastically different. It also violates Property 2. We demonstrate the mistake made by producing more evidences from the experimental data of Pötzschner et al. Firstly, the isothermal dielectric loss spectra of the mixture with 34% TCP show the frequency dispersion of the α2-process narrows and the relaxation strength increases with increasing temperature (see Fig.S9), which is the signature of the JG -relaxation. Secondly, this identification of the resolved faster process in the 34%TCP mixture as the JG -relaxation is supported by its relaxation times changing at near 285 K from a non- Arrhenius high-temperature dependence to an Arrhenius dependence at lower temperatures, i.e. Property 6 (see left panel of Fig.16). Thirdly, the frequency dispersion of the dielectric 1-loss peak at 320 K in the 20%TCP mixture published by Pötzschner et al.[84] is fitted by the Fourier transform of the Kohlrausch function (Eq.1) with (1-n)=0.44 and shown in the upper right panel of Fig.16. If the broadening of the 1-loss peak by concentration fluctuations in this mixture is negligible, the value of (1- n)=0.44 can be used to calculate 0 by the CM Eq.(2), which gives an estimate of the JG . Indicated by the tip of the vertical arrow and marked by in the left panel of Fig.16, the order of magnitude of the calculated 0 at 320 K is in agreement with the observed relaxation time of the faster relaxation at the same temperature. This is another support of identifying the faster process with the JG -relaxation (i.e. Property 7), like demonstrated before in Figs. 2, 4, and 6 for mixtures of 10% and 20% TPP with PS respectively. Fourthly, by examining closely the temperature dependence of the relaxation time of the faster process at lower temperatures in the left panel of Fig.16, there is a change to a weaker
34 temperature dependence at above 250 K. With the faster process now correctly interpreted as the JG -relaxation, this change is evidence of the presence of the truly confined 2-relaxation having its glass transition temperature Tg 2 250 K (i.e. Property 6). This correct value of of the 20%TCP mixture is entered into the lower right panel of Fig.16 to replace the erroneous value of 206 K obtained by Pötzschner et al. in extrapolating the Arrhenius T-dependence of (T) to 100 s (Fig.15). The replacement restore the monotonic increase of Tg 2 with decrease of cm-TCP. 3.3 Dielectric data of 20%TPP mixture at elevated pressures In order to make quantitative comparison with the rich NMR data and DSC data of Bock et al. [82,83], we made our own dielectric relaxation measurements at elevated pressures on a mixture with exactly the same composition of 20%TPP [87]. The TPP and PS used were obtained from the same source as B&K. Only two relaxations are resolved in all experiments including ours at elevated pressures, with the slower one being definitely the 1-relaxation. By observing the change of the dynamics of the faster relaxation with applied pressure and how its relaxation time f is related to that of the slower 1-relaxation, we shall be able to ascertain its identity. Significant changes of the fast relaxation times f were observed on elevating pressure and are shown in Fig,S10 in SI. The sensitive pressure dependence of the faster relaxation is consistent with our interpretation of it as the JG -relaxation, i.e. Property (8). Furthermore, at temperatures above we can check if the ratio 1(P,T)/ f(P,T) is invariant to changes of pressure P and temperature T while either 1(P,T) or f(P,T) is kept constant. The latter is a general relation between the -relaxation time and the relaxation time of the JG -relaxation [70-76,91,97- 103], which is derived from the same relation between and 0 of the CM Eq.(1) and the
41 performing a spatially highly restricted reorientational motion on the same timescale. Also note that at T=225 K and 250 K, the values of JG(T)= 2(T)= se(T) is close to the mixing time tm=0.05 ms of (2D) 31P NMR spectra of the mixture with cTPP= 20% at 200 K. It can be seen from Fig.19 herein or Fig.10 of Bock et al.[82] for tm=0.05 ms that essentially the entire intensity is found on the diagonal, and hence no reorientation occurs on this time scale. Thus, the observation of a spatially highly restricted reorientational motion of PS on the same timescale as JG(T)= 2(T)= se(T) tm =0.05 ms is consistent with our interpretation of the faster process as the JG -relaxation, in which both TPP and PS participate (from 2H NMR solid-echo spectra of PS-d3), and naturally also in its successors, the 1 and the confined 2 relaxations. On the other hand, the observation poses a problem to identifying the faster process by Bock et al. entirely as the isotropic α2-process of the TPP. Consistency of the interpretations of dielectric and NMR data The dielectric relaxation data we obtained are in the mixture with 20% TPP exactly the same as that studied by various NMR techniques by Bock et al. This allows quantitative intercomparison of our dielectric spectra and interpretations given with that of the NMR data. Valenti et al.[87] have demonstrated in detail that the dielectric data and our interpretations are fully consistent with the NMR data. For a detailed comparison we refer the reader to Ref.[87].. 4. JG -relaxation mistaken as confined 2-relaxation in polymer blends We have convincingly shown in mixtures of molecular glass-formers with oligo-polymers and polymers that the resolved faster relaxation is the JG -relaxation but was misidentified as the confined 2-relaxation. The mistake was made by others in polymer blends, and it is necessary to rectify this problem by presenting experimental evidences.
42 4.1 Ambient pressure dielectric relaxation data of xPVME-(1-x)PS blends Bock et al, Kahlau et al.[81-83], and Pötzschner et al.[84] all mentioned the studies of binary polymer blends of poly(vinyl methylether) (PVME, Tg=250 K) and PS (Tg=373 K) with large Tg= 123 K of the two components by Lorthioir et al. [24,58]. DSC measurements detected only one transition in blends at all cPVME, which is the upper glass transition temperature = 337 K of the 1-relaxation. The isochronal dielectric loss data at 1 Hz for blends with various values of cPVME are reproduced from Ref.25 in Fig.20. Two relaxations were resolved in blends with cPVME 30%. For the blends with cPVME =20%, the orange-color arrow at 228 K serves to indicate the locations of the fast relaxation at 1 Hz, and the other arrow at 331 K indicates the 1 relaxation at 1 Hz consistently with = 337 K by DSC at a lower frequency. The dielectric strength of the faster relaxation at 228 K is significantly stronger than the slower one at 337 K. From the isothermal dielectric spectra of the fast relaxation in blends with cPVME 30% (to be shown later), the temperature dependence of its relaxation times f(T) changes to more like Arrhenius at low temperatures. Based on these dielectric properties, Lorthioir et al. interpreted the fast relaxation in blends of 10, 20, and 30% PVME with PS as coming from confined PVME in the frozen matrix of PS, and this interpretation was maintained in two reviews [58,86], and neutron scattering studies [45-47,56]. However, we have shown the fast relaxation, identified by Lorthioir et al. as the confined PVME relaxation, is actually the JG -relaxation in the blends of 10, 20, and 30% PVME with PS [80]. Notwithstanding in a recent review [86], Allegria and Colmenero (AC) cited the paper by Pötzschner et al. [84] in the mixtures of TCP with DH379, which we have discussed before in Section 3, and shown to have given a wrong assignment to the fast process. The interpretation of the fast dielectric relaxation as TCP confined by frozen DH379 given by Pötzschner et al. [84] is similar to that of Lorthioir et al., and AC used it as
43 another support in reaffirming their interpretation of the fast relaxation in 10, 20, and 30% PVME blends with PS as the confined PVME relaxation [24,25]. Thus there is a need to revisit the experimental data of the PVME blends with PS to demonstrate unequivocally that the resolved fast relaxation is the JG -relaxation as well as to uncover the confined 2-relaxation of PVME and its properties, which has not been done before. In this section we analyze the data of Lorthioir et al. in conjunction with the data of Urakawa et al. [31] obtained in the same blends, and demonstrate from the properties of the resolved fast relaxation that it is not the confined PVME relaxation, but instead it is the JG - relaxation. Although dielectrically unresolved, the confined PVME 2-relaxation in the 20% PVME blend was detected by thermally stimulated depolarization current (TSDC) by Leroy et al. [26] and the value of its =293 K determined directly, while =337 K was obtained by DSC. These values of by TSDC and by DSC of all blends are presented in Fig.21, where the data are taken from Ref.[26]. The values of and are entered into the relaxation map of <log (s)> in Fig.22b. Also shown are the averaged relaxation times <log f(T)> of the fast relaxation (filled green circles) taken from Ref.[58], which are related to f(T) in Fig.22d deduced from isothermal dielectric spectra of the fast relaxation in Fig.22c. The data in Figs.22c and 22d were taken from Lorthioir et al. and redrawn. This fast relaxation was interpreted by Lorthioir et al. as the PVME all confined by the frozen PS chains. The activation energy Ea of the f(T) for the 20%PVME blend in Fig.22d is 7869 K in temperature units, and the ratios, Ea/ =26.9 and Ea/ =23.3, all fall within the bounds of the values for JG -relaxation in pure glass-formers [112,114]. On decreasing temperature, the data of <log f(T)> in Fig.22b as well as f(T) in Fig.22d exhibit a crossover from a VFT-like T-dependence to an Arrhenius T- dependence after crossing a temperature nearly the same as =293 K. This is reminiscent of
44 Property 6 on the temperature dependence of the JG -relaxation time JG(T), and hence we label the <log f(T)> and the f(T) data by JG -relaxation in Figs.22b and 22d respectively, and the crossover temperature is identifiable with the glass transition temperature =293 K of the confined 2-relaxation. By contrast, according to Lorthioir et al., all PVME are confined by the frozen PS chains at low enough temperatures and contribute entirely to the fast relaxation observed (filled circles). Their proposal was already contradicted by the detection of the =293 K from TSDC measurements by Leroy et al. in Fig.21 and Fig.22b. This is because at =293 K there is another faction of PVME having relaxation time of the order of 100 s, in addition to the faction contributing to the fast relaxation with relaxation time f=10-4 s at the same temperature. Thus the interpretation by Lorthioir et al. of the fast relaxation originating from PVME all confined by the immobile PS chains is clearly invalid. On the other hand, the experimental data in Figs.21 and Fig.22(b) are fully consistent with our interpretation of presence of two separate relaxations at temperature below =337 K, namely the JG -relaxation to account for the fast relaxation and the confined 2-relaxation for the glass transition at =293 K. Notwithstanding, validity of the interpretation by Lorthioir et al. is still maintained by the authors to the present times [86], and were referred to by others [81- 85] despite the publication in 2013 [80] pointing out the mistake. Therefore we need to go deeper into the discussion of the experimental data of Lorthioir et al. and the complementary data of Urakawa et al. [31] to show that the entire data sets are inconsistent with the interpretation of Lorthioir et al. but consistent with ours. We also present in the next section data of other polymer blends with large difference in Tg of the two components to demonstrate consistency with our interpretation in all these cases.
45 We start by considering the dielectric loss data at 1 kHz, (T,1 kHz), of the blends of PVME with PS for widely different values of cPVME in Fig.22a from Urakawa et al. [31]. The low temperature peaks with maxima at about 130 K with peak intensity roughly proportional to cPVME is the intramolecular -relaxation of PVME, and it is unimportant and of no interest to us. The 1 kHz isochronal loss peak at about 280 K of the blend with cPVME=20% from Urakawa et al. is consistent with the 1 kHz peak frequency of isothermal loss spectra of the fast relaxation of the blend in Fig.22c, and also the temperature dependence of f(T) in Fig.22d. So is the 1 Hz isochronal loss peak at 228 K of Lorthioir et al., shown before in Fig.20, when compared with f(T) in Fig.22d. This fast relaxation is identifiable with the JG -relaxation from Property 6 since on increasing temperature f(T) changes its temperature dependence from Arrhenius to a stronger dependence on crossing =293 K. This behaviour can be seen from <log f(T)> in Fig.22b and better from log f(T) in Fig.22d where more data of f(T) are presented. Having identified the broadly resolved loss peak in the 1 kHz (T) data of the 20% PVME blend in Fig.22a unequivocally as the JG -relaxation, naturally the broad loss peaks in the 10%, 6%, and 4% PVME blends with reduced intensity are also the JG -relaxation, although the shift of the loss peak to lower temperature in the 6% and 4% PVME blends remains to be explained. In Fig.22b, the broken horizontal line indicates the relaxation time of 10-3.8 s corresponding to 1 kHz. The open green circle on the line corresponds to the JG -loss peak temperature at 280 K in Fig.22a, and it can be seen that it lies close to the data of <log f> or <log JG> at temperatures nearby. The temperature at which the confined 2-relaxation time is equal to 10-3.8 s, corresponding to 1 kHz, has to be higher than 280 K because at T= =293 K 2(T) is already the order of 100 s. Determined by the onset of the shoulder of the 1 kHz
46 isochronal (T) data in Fig.22a and indicated by the red arrow, it is approximately 320 K, and thus 2(T=320 K) 10-3.8 s. The red line in Fig.22b connecting the two data points, 2(T=320 K) = 10-3.8 s and 2( =293K) 102 s, should approximately represent the supposedly Arrhenius T-dependence of the confined 2(T) according to Property 2. The second shoulder with onset at T354 K is the temperature at which 1(T=354 K) =10-3.8 s. It is located in Fig.22b by the open blue diamond. The two data points, 1(T=354 K) =10-3.8 s and 1( =337 K) 102 s of the 1- relaxation are supposedly connected by a VFT temperature dependence, which is not provided. Summarizing the above, we are able to show the presence of three relaxations, and identify the fast one as the ubiquitous JG -relaxation, the slower one as the confined 2- relaxation, and the slowest one as the 1-relaxation in the 20% PVME blend with PS. The success is made possible by considering and analyzing the combined experimental data of by TSDC and by DSC by Leroy et al., the isothermal and the 1 Hz isochronal dielectric spectra of Lorthioir et al. and the 1 kHz isochronal spectra of Urakawa et al. The results in the PVME/PS blends are isomorphic to the other mixtures with large difference in the glass transition temperatures of the two components. 4.2 Dielectric relaxation of 25%PVME-75%PS blend at elevated pressures Dielectric relaxation measurements were made by Schwartz et al. [55] at ambient and elevated pressures on the 25% PVME/75% PS blend. As already been demonstrated in the above and in Figs.20-22 using data from similar blends studied by Lorthioir et al., the dielectrically resolved fast relaxation that Schwartz et al. observed in the 25% PVME blend is not from the confined α2-relaxation, but from the JG β-relaxation in the blend contributed in its dielectric strength from the PVME component. This can be confirmed by putting the ambient pressure data of log f(T) in
47 the 25% PVME blend from Schwartz et al. together with the 30% and 20% PVME blends of Lorthioir et al. in Fig22d. This is done in Fig.23 to show the good correspondence between the data from blends of similar compositions from two sources. Moreover, the relaxation time τf(T) of the 25% PVME blend of Schwartz et al. changes its temperature dependence from Arrhenius below some temperature 289 K to a stronger T-dependence above it, which we can identify as of the confined 2-relaxation from Property 6. This identification is supported by the actual value of obtained from the interpolation curve given by Leroy et al. of their TSDC data (see Fig.21), and is consistent with the larger value of 293-295 K for of the 20% PVME blend. The entire data of log f(T) for the 25%PVME blend from Schwartz et al. at ambient and elevated pressures are reproduced here as Fig.24 with illustrations added to make the following points clear. In this figure, the vertical dashed orange and the thinner orange continuous arrows indicate at ambient pressure the location of 1000/ with ≈ 289 K, obtained by interpolation of the TSDC data of Leroy et al.[26], and 1000/ with ≈ 321 K from DSC of the blend (see Fig.21). While there is a marked change in T-dependence of τJG(T) at the ≈ 289 K of the PVME component, the change at ≈ 321 K is more subtle. Nevertheless its presence is indicated by the VFT fit of τJG(T) at higher temperatures (orange curve) starting to deviate from the data at temperature near ≈ 321 K. This behavior reminds us of Property 6 and the same observation in the mixtures of mixture of 50%MTHF with PS60k in Figs.4 and 6, and in the mixture of 8% and 18% TPP in PS in Figs.9 and 13. It is an evidence of the connections of the JG -relaxation to both the 1-relaxation and the 2-relaxation in the blend, and hence it brings out the fundamental importance of the JG -relaxation in the blend. The same Property 6 also can be observed from the data of τJG(P, T) at elevated pressures. In Fig.24, lines are drawn to connect points at lower temperatures to show the change of
48 temperature dependence at , the 2 glass transition temperature at pressure P. Aided by these lines, the crossover seems to occur uniformly at the same value of the relaxation time, τ (P, T) ≈ 10−4.8 s, independent of P, which is indicated by open symbols in the figure. This behavior is the same as τ (P, T) of the 20% TPP in mixture with PS shown before in Figs.17 and 18, which is Property 8 showing once more the connection of the JG -relaxation to the 2- relaxation. Moreover, this relaxation time at the crossover of 25% PVME for all P is close to τ ≈ 10−5 s for the crossover at ambient pressure of the 20% PVME blend at ≈ 293 K shown previously in Fig.22d, The property of τ (P,T) found by Schwartz et al. is another proof that the observed process is the JG β-relaxation of the blend. The constancy of τ (P, T) at the crossover temperature, T(P) , is remarkable. Same as found in the 20%TPP mixture with PS, this property of the 25% PVME blend is shown explicitly by the inset of Fig.24, where the τ (P,T) data at different pressures are collapsed into a master-curve by plotting τ (P,T) against scaled reciprocal temperature, T(P)/T. The colored vertical arrows in Fig.24 mark the positions where the 1-relaxation enters into the glassy state, as determined by PVT data [116]. Note the approximate agreement between this location and 1000/ from DSC at ambient pressure. The data of τ (P,T) at higher pressures are too sparse to consider the constancy of τ (P,T) at the crossover temperature, T(P) . The valuable information coming from our analysis of the dielectric data at elevated pressure of Schwartz et al. in Fig.24 is the monotonic increase of with increase of pressure from 289 K at 0.1 MPa to about 351 K at 300 MPa. The increase in of the confined 2-relaxation with pressure indicates correspondingly large increase of τ 2(P,T) with pressure. This property of τ 2(P,T) is not expected a priori from the idea of confinement of
49 PVME by the frozen PS matrix by LAC. However, it can be reconciled by the cooperative nature of the 2-relaxation, as revealed by the detection of glass transition at by DSC in other highly asymmetric mixtures and blends [16,39,54,65,78,79], and the change of the temperature dependence of τ (T) on crossing . 5. Corroborating evidences from other polymer blends Solid evidences have been given to demonstrate the mistakes made by others in identifying the resolved fast relaxation as the confined 2-relaxation, instead of the JG -relaxation, in highly asymmetric blends [24,25,45-47,56,58,86] and mixtures [81-85] with large Tg. In these systems, the propensity of the high-Tg component makes it easy to detect the higher glass transition temperature by DSC, but not . The situation led others to assume that the low-Tg2 component are entirely confined by the frozen high-Tg1 component at temperatures sufficiently far below , and resulting in a single localized relaxation with Arrhenius temperature dependence for its relaxation times 2. Thus, a critical evidence to expose the mistake is the presence of a slower relaxation also originating from the low-Tg2 component coexisting with the resolved fast relaxation at temperatures sufficiently below . It comes from the detection of a second glass transition temperature lower than by TSDC [26], dielectric relaxation [29], adiabatic calorimetry [88], or conventional DSC [16,39,54,65,78,79], indicating the presence of another process below with relaxation time of the order of 100 s or longer. This process is distinctly different from the resolved fast relaxation since the value of its relaxation time f(T) at T= is many orders of magnitude shorter than 100 s (see Fig.22b). The fact that at we have two relaxations with widely different relaxation times clearly contradicts a single
50 relaxation from the hypothesis of the low-Tg component is entirely confined by the frozen high- Tg component [24,25,45-47,56,58,86]. In the following we present experimental observation of in other polymer blends, and in some cases the concurrent presence of the JG -relaxation, for the purpose of showing the generality of our interpretation. 5.1 xPEO-(1-x)PMMA blends These blends were studied by many different groups, and the various results are collected together in this section to bring out the facts in toto. We start with the DSC measurements of Floudas and coworkers [39] Lodge and coworkers [54], and Goulart Silva et al. [16], all of them detected two glass transitions at and . Shown in Fig.25a is the derivative dCp/dT of the specific heat taken from Ref.[39] whereby detected are the two glass transitions at and for two blends with cPEO=30 and 20%. These values together with those for other compositions are plotted against cPEO in Fig.25b. In the relaxation map of Fig.26, the magenta star placed at 100 s is supposed to represent the 2-relaxation time 2 of the PEO component at 1000/ with =245 K in the 20% PEO–80% PMMA blend. The 2-relaxation of the PEO component was not resolved in the dielectric studies of Runt and coworkers [21,22] because it is obscured by the dielectric loss over broad frequency range from the JG -relaxation of the PMMA component. However, it was observed in blends of perdeuteriopoly(ethylene oxide) (d4PEO) and PMMA using deuteron NMR over the concentration range from 0.5 to 100% d4PEO with Larmor frequencies ranging from 31 to 76 MHz [23,27,28] discussed before and shown in Fig.S6. The 2-relaxation times 2 of the 20%PEO-80%PMMA blends from deuteron NMR are shown again in Fig.26, together with QENS data of Sakai et al. [51,52]. The closed and open red circles are the faster and the slower 2-relaxation times found in QENS experiment of Sakai et
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66 [116] P. Zoller and D. J. Walsh, Standard Pressure-Volume Temperature Data for Polymers (Technomic Publishing Company, Lancaster, PA, 1995). 10-210-1 100101102103104105106 10-1 0100 200 300 400 500 200 250 300 10-2 KWW=0.47 =0.7 s '' 10% wt. Quinaldine in tristyrene f0 10% CNBz+ tristyrene f0 0100 200 300 220 240 260 280 T [K] P [MPa] (T)=0.7 s T (K); P (MPa) 223.0; 0.1 232.6; 60.0 243.0; 120.0 252.5; 180.0 258.2; 219.0 266.2; 273.6 274.2; 330.0 JG '' f (Hz) 290.2; 449.6 297.2; 500.0 303.0; 554.3 (a) (b) P [MPa] T [K] Figure 1 (a) (b). T-P superposition of isochronal loss spectra for (a) 10% wt. quinaldine in tyistyrene and (b) 10% molar fraction of cyanobenzene in trystyrene. Different pressure and temperature combinations keeping the same structural relaxation time are shown in the inset,
73 Figure 9. Left panel: relaxation map of 8%TPP in PS. Red open circles represent 1-relaxation times, red open inverted triangles represent the primitive relaxation times from CM. Red solid circles indicate 2- or JG - relaxation times. The vertical solid line indicates Tg 1 while the vertical dotted line indicate Tg 2. Inset shows the superposition of 2-loss peaks fitted with Fourier transformed KWW function (n=0.73). Right panel: Tg 1 and Tg 2 plotted versus concentration of TPP. The data represented by the black and red symbols are reproduced from Ref. [81]. Blue triangle indicates the Tg value estimated by the change in T-dependence of JG shown in left panel. Tg values estimated from dielectric strength crossovers are: green multiplication signs obtained in ref.[87] for cTPP=0.20 with (upper ) =268 K of 1- relaxation and (middle ) Tg 2 or =225 K of the true 2-relaxation; red ellipse symbol indicate =232 K of the true 2-relaxation for cTPP=0.20 [81]. The blue and red lines are Gordon-Taylor fits of using the value of the pure fast component as Tg,2 = 135 K (that of pure TPP) and that of the slow pure component as Tg,1 = 335 K (that of pure PS 2 kg/mol) or Tg1 = 291 K (Tg of the nano-confined PS with molecular mass=2000 g/mol), respectively.
74 Figure 10. Left panel: Dielectric strength 2 of the purported confined 2-process shown as a function of temperature in the 18%TPP in PS mixture obtained by Kahlau et al [81]. The broken black line indicates change of T-dependence of JG at 273 K identified with . The red dashdotted line indicates a change at T-dependence of JG at 232 K identified with . Figure reproduced from Ref.[81] with permission from AIP. Right panel: Tg 1 and Tg 2 plotted versus concentration of TPP, symbols are the same as in Figure 9.
75 10-1 100101102103104105106 -2 -1 T=190 K T=140 K T=5 K log '' Frequency/Hz Ambient pressure Temperature increase 140 K T=10 K 190 K 260 K T=260 K Figure 11. Dielectric loss spectra of the 20%TPP in PS mixture [87] at different temperatures from the liquid down to the glassy state.
76 10-4 10-2 100102104106 10-1 100 10-2 100102104106 10-1 100 KWW=0.25 ''/''max frequency (Hz) T= 270 K P=0.1 MPa T= 294K P=100 MPa T= 319 K P=210 MPa KWW=0.25 T = 288 K P=0.1 MPa T= 294 K P=17.3 MPa T= 310 K P=85.9 MPa frequency (Hz) Figure 12. Superposition of spectra at different pressures and temperatures, for two different frequencies of the maximum of the peak, for the 20%TPP in PS mixture [87]. The conductivity has been subtracted in both cases. Solid black lines are fits by the Fourier transform of the KWW function.
77 Figure 13. Relaxation map for the data of 8% (red symbols), 18% (blue symbols) and 20% (black symbols) TPP in PS mixture relaxation times: 1 are shown as open circles, open triangles and open squares, respectively. The 2 for 8%, 18% and 20%TPP are shown by red, blue and black diamonds. The s are shown by solid circles, triangles and squares, respectively. The inverted open triangles indicate the primitive relaxation time of the CM. The vertical dotted lines indicate or
78 160 180 200 220 240 260 4.0 4.5 5.0 5.5 160 180 200 220 240 260 280 0.4 0.6 0.8 1.0 1.2 1.4 x 10 T (K) Step in T (K) Figure 14. JG or 2 of 20%TPP in PS mixture as a function of temperature, zoom of the inset, which shows the whole set of temperatures. The inset shows a wider T-range where a sharp rise can be noticed in the neighborhood of 265 K close to =268 K of the 1-relaxation (black arrow), and another milder change is observable for at about 223 K (red arrow) which we assigned to the of the truly confined 2-relaxation from the minority TPP component.
79 Figure 15. (a) Arrhenius plot of the dielectric relaxation times of the two processes in TCP/ DH379 mixture at different TCP concentration. Solid and open symbols represent 1 and 2 (labelled as the relaxations dominated by the majority DH379 and TCP component), respectively. (b): Tg as obtained from dielectric spectroscopy or NMR experiments by extrapolating to 100 s the relaxation time. Figures reproduced from Pötzschner et al. [84] with permission from AIP.
80 Figure 16. Left panel: Arrhenius plot of the 1 and JG -relaxation times of TCP/ mixture at 20% (cyan symbols) and 34% (orange symbols) TCP concentration [84]. Solid and open symbols represent 1 and 2 (labelled as the relaxations dominated by the majority DH379 and TCP component), respectively. The black cross represents the primitive relaxation time predicted by CM. (upper right panel): Logarithm of dielectric susceptibility at 320 K for the cm-TCP = 20% sample plotted against log(f/fmax) taken from Ref.[84]. The line is the fit of the 1-relaxation by the Fourier transform of the Kohlrausch function with n=0.56. (lower right panel): Tg as obtained from dielectric spectroscopy or NMR experiments by extrapolating to 100 s the relaxation time. Figures reproduced from Pötzschner et al. [84] with permission from AIP.
81 Figure 17. Relaxation map for 20%TPP in PS mixture: isotherms are shown on the left panel, while isobars on the right. Solid points represent relaxation times of the α1-relaxation, while open points of the JG -relaxation. Also shown are the fits of the α1-relaxation with the Vogel- Fulcher-Tammann equation (solid lines), while the JG -relaxation times have been fitted with an Arrhenius law.
82 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -10 -8 -6 -4 -2 0 2 4 0100 200 300 260 280 300 320 P = 0.1 MPa P = 190 MPa T = 294 K T = 310 K T = 319 K log10(/s) Tg(P)/T Pg (MPa) Tg(K) Figure 18. Master plot of the relaxation times for all temperatures and pressures data shown in Fig.17, with temperature rescaled by Tg(P). Inset shows the dependence of Tg(P), the solid line is the fit by the Andersson - Andersson function, dashed lines mark the confidence bands.
89 Figure 25.(a) the derivative dCp/dT of the specific heat obtained from DSC curve for PEO/PMMA blends with PEO concentration cPEO=30%, 20% and 10%. (b). Values of the two glass transitions and for all compositions plotted against cPEO . Figures are reproduced from Ref.[39] with permission from ACS.
90 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 -12 -10 -8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 -12 -10 -8 -6 -4 -2 0 2 log10( /s) 1000/T (K-1) log10( /s) 1000/T (K-1) 20%PEO-80%PMMA Tg1 Tg2 JG Figure 26. In the main figure, the line defined by open black circles is the fit of 2H NMR data of segmental -relaxation time of the PEO component from Lutz et al. [27] in 20% PEO–80% PMMA blend. The magenta star is placed at 100 s to represent the 2-relaxation time 2 of the PEO component at =245 K in the 20% PEO–80% PMMA blend. The closed and open red circles are the fast and slow 2-relaxation times found in QENS experiment of Garcia-Sakai et al. at Q = 1.3 Å-1 [51, 52]. The vertical black arrow locates the position of =356 K for the PMMA component in the blend. The pale blue line is the VFT fit of the NMR data of the PEO component in 20% PEO–80% PMMA blend and requiring it to reach 2(T)=100 s at =245 K, which is not acceptable (see text). The blue line is the Arrhenius T-dependence of the confined 2-relaxation suggested to interpolate 2(T)=100 s at T= and the deuteron NMR data (open black circles). The short and thick magenta line represents the relaxation times of the JG -relaxation. In the inset, in addition to the same symbols and line in the main figure, it shows QENS data for PEO in the 25/75 blend from QENS at Q=1.02 Å-1 [52] (asterisks). Also from QENS data at Q=1.02 Å-1 [48] are open black squares indicating the slow relaxation, and the closed black squares the fast relaxation for the PEO component in 20%PEO-80%PMMA blend. The red closed and open triangles are the same for the 30%PEO-70%PMMA blend. The blue line is the primitive relaxation time of PEO obtained from NMR data of pure PEO.
91 Figure 27. Effective glass transition temperature Tg,eff of the PEO component (that is ) for poly(ethylene oxide)/poly(vinyl acetate)/ (x%PEO-(1-x)PVAc) and x%PEO-(1-x)PMMA blends plotted as a function of PEO fraction [113]. Continuous and dashed lines are from Fox-Flory and Lodge-McLeish model predictions. Figure reproduced from Ref.113 with permission from Elsevier.
92 Figure 28. (a) Values of and obtained by conventional and temperature-modulated DSC for miscible blends of polyisoprene (PI) and poly(4-tert-butylstyrene) (P4tBS) over a broad composition range [60]. Lines are fits to the Lodge-McLeish model [18]. Figure reproduced from ref.[60] by permission. (b) Sketch of the segmental dynamics of the slow (A) and fast (B) components in a miscible A/B polymer blend, reproduced from ref.[60] by permission and modified. The dotted line represents a segmental relaxation time of 100 s, and effective glass transition temperatures of the components are indicated. For component B, below the effective Tg of A, the dashed curve represents the VTF extension of its high-temperature dynamics, while the thick solid line represents the enhanced dynamics that result from the vitrification of the blend. The Tg2 of pure PI and two JG -relaxation times JG(T) are also shown. (c). Dielectric spectra of PI with molecular weight of 21 k [89].
93 Figure 29. The segmental -relaxation time 2 (closed symbols) of PI27 in 35%PI27 blend (red circles), and 20%PI27 blend (blue diamonds) with PtBS2300. Data from Refs.[65], and replotted as a new figure. The blue symbols represent 2 obtained from isochronal representation of the data for 20% PI blends. The locations of the 1000/ and 1000/ in each of the two blends are indicated by the arrows accompanied by the value. Right inset is reproduced from Ref.[65] with permission. Lower part shows the derivative of the heat flow with respect to T for PI2700 and PtBS2300 homopolymers and their blends at different compositions. The intensity of the curves was multiplied by 0.5, 0.5, 2.5, 4, and 5, for 100, 80, 43, 35, and 20% samples, respectively. In addition, curves have been shifted in the y axis for clearness. Continuous black lines represent fits to two Gaussian functions and dashed lines individual components of the fitting. Upper panel: Glass transition temperature of PI component in the blend as a function of
94 PI content (crosses); horizontal bars represent full width at half-maximum of the Gaussian fits; dashed line represents the expected global glass transition temperature for the blend according to a simple mixing rule.
95 Figure 30. The segmental -relaxation time 2 (closed symbols) of PI27 in 35%PI27 blend (green circles), and 20%PI27 blend (red diamonds) with PtBS1300. Data from Refs.[65], and replotted as a new figure. The red symbols represent 2 obtained from isochronal representation of the data for 20% PI blends. The locations of the 1000/ and 1000/ in each of the two blends are indicated by the arrows accompanied by the value. Right inset has the same information as in Figure 29 and is reproduced from Ref.[65] with permission from ACS.
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50% 70% τ0 12% 8% n=0.74 n=0.77 τ0 τβ n=0.63 n=0.39 xMTHF-(1-x)3S τ0 α2 α1 α1α2 4 5 6 7 8 9 10 1000 / T (K-1) -10 -8 -6 -4 -2 0 2 4 log(τ / s) Figure 2
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: *Declaration of Interest Statement