ARTICLE
Macromolecular Symposia
Terminal Viscoelastic Relaxation
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Rheology and Microscopic Heterogeneity of Poly(ethylene oxide) Solid Polymer Electrolytes Fatin Harun, Chin Han Chan,* and Qipeng Guo interaction.[3] Therefore, by combining Lack of precise thermal control in poly(ethylene oxide) (PEO)-based solid thermal properties extracted from differential scanning calorimetry (DSC) and polymer electrolytes (SPEs) with molar masses well above M > 104 g mol1 rheological study, the effects of polymerduring preparatory stage often demonstrates molar mass dependence on salt and salt-salt interactions in polymer thermal properties and ionic conductivities. In the earlier study, PEO-based chain behavior as a function of PEO SPEs were heated under inert atmosphere above the melting temperature of molar mass and lithium perchlorate PEO and then cooled down for subsequent isothermal crystallization. The (LiClO4) concentration can be systematically elucidated. Poly(ethylene oxide) system demonstrates insignificant variation with respect to molar mass of PEO (PEO)/lithium salt (Li) as a model for at constant salt concentration for thermal properties, ionic conductivity and SPE system was chosen here as PEO is intermolecular interaction. Here, we report the subsequent results of rheology known to have high solvating power and 5 and microscopic heterogeneity as a function of PEO molar mass (Mɳ ¼ 3 10 the related system shows acceptable ionic and 4 106 g mol1) and lithium salt concentration (0–13 wt.%). Above the conductivity.[4–12] solubility limit of PEO, the glass transition studied using differential scanning In general, the glass transition temperature (Tg) of SPEs[11,14–16] shows a gradual calorimetry shows the presence of microscopic heterogeneity of the systems as increase at low salt concentration where the indicated by the change in enthalpy of endothermic overshoot near the endset polymer continuously solvates the cations of glass transition. Rheological parameters were measured over a wide range of generated from the addition of salt. Upon frequency (0.01 to 100 Hz) at different temperatures (30, 60 and 80 C) using reaching solubility limit of polymer, Tg parallel plate geometry. Melt rheology system reveals that neat PEO at 80 C value levels off. At high salt concentration of PEO-based SPEs, the polymer chain in exhibits restriction in the long-range motion of the chains. When incorporated amorphous phase may become saturated with salt, it exhibits further deviation from the terminal viscoelastic relaxation with the cations coordination and the behaviour. This study agrees with our previous findings that influence of molar additional cations can hardly dissolve in mass of PEO in this range is insignificant on the melt rheology and microscopic PEO amorphous phase. At extremely high heterogeneity at constant salt concentration. salt concentration, two Tg values may be observed due to microphase separation between the ion-aggregates and polymer matrix as the salt-salt interaction is favoured over polymer-salt interaction.[11,17,18] According to 1. Introduction Prud’homme and co-workers,[11] PEO-based SPEs do not [1–2] Ratner and co-workers proposed Dynamic Bond Percolaundergo microphase separation even at very high salt tion Model to describe the conductivity mechanism of solid concentration but rather form small-sized labile heterogeneities polymer electrolytes (SPEs) in terms of cation hopping motion due to the weaker long-range Coulombic interaction and greater and dynamic motion of polymer. It is well established that the binding energy, as compared to other polymer host. Hence, this polymer chains coil around the cations (weak Coulombic study attempts to probe further the rest of the glass transition features from DSC results which may yield information on the interaction), facilitating ion-pair separation and dissolution heterogeneities that could not be extracted from the Tg value of salt in polymer matrix, thus, forming intermolecular alone. Referring to our earlier work,[8,9,19,20] the importance of F. Harun, C. H. Chan thermal pre-treatment on the samples comprising of semicrysFaculty of Applied Sciences talline polymer host (i.e. PEO) in order to obtain reproducible Universiti Teknologi MARA properties of SPEs which are independent of molar mass were 40450 Shah Alam, Selangor, Malaysia E-mail:
[email protected] highlighted. When the PEO-based SPEs were thermally treated under inert atmosphere above the melting temperature of PEO Q. Guo Institute for Frontier Materials and then cooled down for subsequent isothermal crystallization Deakin University for sufficient experimental time to develop morphology close to Geelong, Victoria 3220, Australia equilibrium condition, the samples show insignificant variation of thermal properties, ionic conductivity and intermolecular DOI: 10.1002/masy.201700040
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interaction with respect to molar mass of PEO at constant salt concentration.[20] In this subsequent rheological study, we focus on the viscoelastic of PEO chains in solid, solid-to-liquid and liquid state with addition of salt, as a function of molar mass of PEO at constant salt concentration and as a function of temperature. A number of rheological studies on SPEs shows that the variation of viscoelastic parameters in solid state resembles the results of Tg where the maximum of storage modulus is reached when the polymer reaches saturation limit with salt.[21,22] In melt state, the incorporation of salt may cause less effect on the viscoelastic parameters as a function of frequency[23–25] and longer polymer chain relaxation time.[26] In other words, addition of salt in polymer melt may result in the transition of liquid-like to solid-like viscoelastic behavior.
2. Experimental Section Different molar masses of PEO were purified before further use by dissolution in chloroform (Merck, Darmstadt, Hesse, Germany) followed by precipitation in n-hexane (Merck). LiClO4 salt was dried at 100 C for 24 h prior to usage. The characteristics of the polymers and salt used are summarized in Table 1. Thin films were prepared by adding different concentrations of LiClO4 of LiClO4 salt, Y S ¼ mass mass of PEO to PEO using tetrahydrofuran 1 (THF) (Merck) as solvent. The solution was poured in Teflon dish and left at room temperature until solvent evaporated. Then, the sample was dried at 50 C for 24 h for removal of residual solvent. This was followed by thermal treatment under nitrogen atmosphere at 80 C for 1/2 h. Finally, the samples were isothermally crystallized at 50 C for 24 h and kept in desiccators. Samples were vacuum dried again at 50 C for 24 h before sample characterizations.
3. Instrumentation 3.1. Differential Scanning Calorimetry (DSC) Approximately 7–15 mg of thin film samples were encapsulated in standard aluminium DSC pan (Perkin Elmer, Shelton,
Connecticut, USA). TA Q2000 (TA Instruments, New Castle, Delware, USA) was equipped with RCS90 refrigerator cooling system (TA Instruments) and nitrogen gas purging (purity: 99.9995%; flow rate: 50 mL min1). Glass transition parameters such as onset glass transition temperature (Tg,onset), endset glass transition temperature (Tg,endset), width of glass transition, change in heat capacity (ΔCp) and change in enthalpy of endothermic overshoot near the endset of glass transition (ΔHovershoot) were evaluated. The DSC was calibrated with high purity indium and sapphire standards. The samples were quenched-cooled to 90 C for 5 min and heated to 80 C at a rate of 10 C min1. A similar thermal procedure was applied in the sapphire run and baseline run. To determine the Cp value of sample, the heat flow signal from the sample was compared to the baseline of sapphire standard which is of known Cp. Both curves were corrected by zero or baseline correction experiment whereby an empty pan were placed in the furnace. The glass transition temperature (Tg) is taken at half extrapolated ΔCp value. For the estimation of Tg value, the tangent of the transition on the heat flow curve was extrapolated to the linear region before the onset and after the endset of the glass transition. In this manner, the estimated Tg value has closer approximation to the real value even for sample that displays endothermic overshoot. The width of the glass transition is defined as the temperature difference between the onset and the endset of the heat flow curve. ΔHovershoot value was calculated from the linear integration of the endothermic overshoot area.
3.2. Rheology Rheological measurements on thin film samples were performed using Physica MCR300 Rheometer (Anton Paar GmbH, Graz, Styria, Austria) operated with RheoPlus software (Anton Paar GmbH), equipped with 25 mm parallel-plate geometry. The gap was maintained using normal force control at 0.01 N to ensure that the sample is in good contact with the parallel plate probe. Neat PEO1 and PEO4 was subjected to strain sweeps ranging from 0.001 to 10% strain at 1.9 Hz with 20 points per decade for the selection of the suitable strain value within linear viscoelastic (LVE) range to be
Table 1. Characteristics of materials. Material 1
PEO1
PEO4
LiClO4
300,000
4,000,000
–
Tgb) ( C)
58
55
–
Tmc) ( C)
68
68
236d)
Mɳa)
(g mol )
Structure
Supplier
Sigma–Aldrich Chemical Co. (St. Louis, MO, USA)
Acr os Organics Co. (Geel, Antwerp, Belgium)
a) Viscosity-average molecular weight provided by supplier. b)Glass transition temperature during first heating cycle as determined in this study. c)Melting temperature during first heating cycle as determined in this study. d)Melting temperature adopted from O’Neil.[27]
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Figure 1. a) DSC thermograms of PEO1 at different salt concentrations YS and (b) determination of glass transition parameters for PEO1 at YS ¼ 0.15.
used in frequency sweep experiments. Frequency sweep varying from 0.01–100 Hz at 0.1% strain with 20 points per decade were performed at isothermal temperatures of 30, 60 and 80 C. The temperature was controlled using Peltier controller unit and waterbath Viscotherm VT2 (Anton Paar GmbH). The samples were equilibrated at their respective temperatures for 10 min before every measurement. Although rheological testing can be performed on both solid and molten states of the system, it is the rheological behaviour in the melt state that provides more insight on the structure, molar mass and flow properties of the materials. According to the theory of linear viscoelasticity,[28,29] a homogenous linear polymer melt is fully relaxed when the storage modulus (G0 ) and loss modulus (G00 ) obey the Power law dependence in the low frequency regime (terminal zone) with the slopes equal to 2 and 1, respectively: G0 ¼ af x ; G0 f 2 G00 ¼ af x ; G00 f
ð1Þ
where a is constant, f is frequency and x is power law exponent. Since the viscoelastic properties in the low frequency regime reflects the long-range motion of polymer chains, the deviation from terminal behaviour means that the long-range polymer motion is hindered, resulting in incomplete relaxation of polymer chains. Linear regression on double-logarithmic plots of moduli versus frequency after Eq. (1) allows estimation of power law exponent which are extracted from the slope values. Statistical error of linear regression based on 2-tailed student t-test in confidence level of 95% was estimated. Plot of G00 versus G0 (or modified Cole-Cole plot) can be used to illustrate terminal viscoelastic behaviour and miscibility of the system.[30–32] It provides a perfect semicircle fit when the slope values of G0 and G00 are 2 and 1, respectively.
4. Results and Discussion 4.1. Glass Transition Temperature In Figure 1(a), the DSC thermograms show a single Tg value that increases gradually with a sharper transition as more LiClO4 salt was added to PEO1 (as well for PEO4 which is not shown in
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Figure 1(a). The single Tg value affirms the absence of microphase separation between PEO and salt at all salt concentrations. To properly describe the glass transition behaviour, several parameters were extracted as shown in Figure 1(b). The values of Tg, ΔCp, width and ΔHovershoot are listed in Table 2. As presented in Figure 2(a), at Mɳ ¼ const, Tg value gradually shifts to higher temperature while the width becomes narrower with ascending LiClO4 salt concentration before levelling off. Due to the intermolecular interaction between PEO and salt, the polymer chain becomes more rigid, hence, resulting to an increase in Tg value.[20] The insignificant variation in Tg value at WS ¼ const suggests that the extent of intermolecular interaction between PEO and salt is independent of molar mass of PEO. Tg value reaches a maximum at YS ¼ 0.07 which marks the solubility limit of salt in PEO. If the polymer chain indeed becomes saturated with cations coordination, then this could also be observed from the relation between glass transition temperature and melting temperature. From Table 2, one can see that the Tg/Tm ratio exhibits significant increase up to YS 0.07 while at higher salt concentration, it stays constant.
Table 2. Parameters characterizing glass transition and ratio of Tg/Tm for PEO/LiClO4. Tg ( C)
ΔCp,
Width ( C)
ΔHovershoot
(J g1)
Tg/Tmb)
YS
PEO1
PEO4
PEO1
PEO4
PEO1
PEO4
PEO1
PEO4
PEO1
PEO4
0
57
55
0.097
0.11
6.4
6.6
–
–
0.63
0.64
0.02
51
51
0.14
0.17
5.9
6.0
–
–
0.65
0.65
0.05
47
47
0.18
0.18
5.8
5.9
–
–
0.66
0.66
0.07
49
48
0.22
0.23
5.7
5.8
0.029
0.031
0.67
0.67
0.10
49
48
0.27
0.26
5.7
5.8
0.081
0.091
0.67
0.67
0.12
48
48
0.32
0.29
5.6
5.7
0.10
0.11
0.68
0.68
0.15
48
47
0.37
0.34
5.4
5.6
0.12
0.13
0.68
0.69
ΔCp, PEO denotes change in heat capacity normalized to the mass fraction of PEO in the sample. b)Tm denotes melting temperature from the first heating run after DSC. Values were extracted from Ref. [20]. a)
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Figure 2. a) Variation of Tg and width of glass transition and (b) σDC value with salt concentrations YS for PEO1 (square) and PEO4 (star). The solid curves are for visual aid. Data of σDC were adopted from Ref. [20].
Moving on to the width of glass transition, it can be seen that the width of salt-added PEO is smaller than those of the neat PEO. The width of glass transition depends on the degree of cooperation between neighbouring molecules in large amplitude molecular motion. Therefore, below the solubility limit of PEO, the narrowing of width with ascending salt concentration is most likely associated to the greater extent of polymer-salt intermolecular interaction that hold the amorphous structure closer together, thus, restricting the independent mobility of the repeating units (stronger cooperative behavior). ΔCp is a measure of mass fraction of the amorphous microphase in the two-phase system (crystalline PEO and amorphous mixture of PEO þ Li). Below the solubility limit of PEO, ΔCp increases linearly with WS.[20] Since the change in heat capacity can also be correlated to the measure of non-crystalline material, it can be concluded that at Mɳ ¼ const, ΔCp increases with ascending salt concentration due to the increasing amount of amorphous phase. At WS ¼ const, the width and ΔCp are independent of the molar mass of PEO. Above the solubility limit, an endothermic overshoot appears after the endset of glass transition. Such endotherm, as noted in other studies[23,33] was not observed for neat and low salt concentration of PEO. Therefore, the magnitude of the endothermic overshoot can be used as a measure of microscopic heterogeneity formed in PEO amorphous phase at high salt concentrations. When the salt concentration increases, the endothermic overshoot at Mɳ ¼ const becomes more obvious implying higher degree of heterogeneity. It can be suggested that the presence of the microscopic heterogeneity may originate from the formation of ion-pairs and/or higher-order contact-ions that is/are known to become more apparent at high salt concentration. The insignificant differences in the magnitude of ΔHovershoot for different molar masses of PEO at WS ¼ const further supports that the dissolution of salt in the amorphous phase of PEO is independent of the molar mass of PEO. As shown in Figure 2(b), at WS ¼ const, the ionic conductivity (σDC) value is almost invariant of molar mass of PEO as reflected by Tg value. The changes in the σDC values, depicted in Figure 2 (b), are consistent with the variation of Tg value with salt content in Figure 2(a). It is clear that at lower salt content, the enhancement of σDC is led by the higher amount of polymer-salt
Macromol. Symp. 2017, 376, 1700040
intermolecular interaction in the amorphous phase of PEO-salt systems, which is independent of the molar mass of PEO.[20]
4.2. Rheology Figure 3 presents the plot of G’ and G“ versus frequency of PEO1 at YS ¼ 0, 0.07, 0.10 and 0.15 measured at three different temperatures. The same trend was observed for PEO4 which is not shown in Figure 3. The samples in solid (at T ¼ 30 C) and liquid (at T ¼ 80 C) states reveal distinct difference in viscoelastic properties. In solid state, neat PEO1 exhibits G0 curve independent of frequency (solid-like behavior). G0 is roughly one order of magnitude larger than loss modulus (G“) with both viscoelastic moduli are almost parallel throughout the frequency. This reflects that the stress generated does not relax over the time scale of experiment. On contrary, neat PEO1 shows strong dependence on frequency (liquid-like behavior) in melt state. At 30 C where all the samples remain in solid state, the incorporation of salt influences the magnitude of G’ and causes slight frequency dependence particularly at high frequency regime. The general trend of G0 magnitude is found to be similar to Tg trend. Both increase to a maximum value at YS ¼ 0.07 and then experience a reversal trend. This implies that below the solubility limit, the increasing extent of PEO Li intermolecular interaction from ascending salt concentration contributes to higher elasticity of polymer chain structure as represented by G0 . Beyond the solubility limit, the elasticity of the structure deteriorates due to the presence of excess cations which may not coordinate well with PEO chain. At 30 C, G0 > G00 throughout the whole salt compositions and frequency range tested. The dominance of G’ indicates that the material behaves elastic-like manner. The gap between G0 and G00 shrinks with increasing salt content and there are no cross-over between these moduli. At 60 C, the sample shows transition behavior between solid and melt state. Low salt content demonstrates solid-like behavior as observed at 30 C. When the amount of salt is high enough (e.g. PEO1 at YS ¼ 0.15) in reducing the melting temperature of PEO to around 60 C or below (data after Ref. [20]), the sample moves towards liquid-like behavior.
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Figure 3. Storage (solid marker) and loss moduli (open marker) of PEO1 at YS ¼ 0, 0.07, 0.10 and 0.15 measured at (a) 30 C, (b) 60 C and (c) 80 C.
At 80 C, addition of salt gradually increases the magnitude of G’ values of the fully developed liquid state. The elasticity of the polymer chain in melt state increases continuously with addition of salt. Initially, G00 > G0 in the low frequency region (also known as terminal zone), followed by moduli cross-over (G0 ¼ G00 ) and finally, G0 > G00 at high frequency region (also known as plateau zone). The frequency of G0 -G00 cross-over (fcross) shifts to lower value with increasing salt concentration. This can be explained by the presence of salt that restricts chain motion, or in other words, relaxation of the system. Above the fcross, G0 levels off and reaches apparent plateau value (characteristic of entangled molecules) whereas G00 decreases. This denotes the liquid-like viscoelastic behavior is turning into solid-like viscoelastic behavior.
allows estimation of power law exponent from the value of the slope as illustrated in Figure 4. The results are listed in Table 3. The power law exponent can be used to determine the deviation from terminal viscoelastic relaxation behavior.
4.3. Terminal Viscoelastic Relaxation Figure 4 depicts the double-logarithmic plots for G0 and G00 versus frequency of neat PEO4 measured at 80 C. For neat PEO (as well as for salt-added PEO which are not shown in Figure 4), both moduli display significant increase in slope (liquid-like behaviour) at low frequency, a typical feature of thermoplastic melts. Linear regression after Eq. (1) in low frequency region
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Figure 4. Power law approximation of G0 and G00 using linear fitting (r2 > 0.97) on the frequency sweep of neat PEO4 measured at 80 C. Solid curves are the regression curve after Eq. (1).
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Table 3. Power law exponent of G0 and G00 at 80 C, estimated after Eq. (1) from the low frequency slope. PEO1 YS
G0
PEO4 G00
G0
G00
0
1.08 0.12
0.88 0.08
1.44 0.23
0.89 0.14
0.02
0.91 0.37
0.71 0.24
1.13 0.11
0.73 0.10
0.05
0.90 0.04
0.74 0.10
1.12 0.06
0.73 0.03
0.10
0.92 0.08
0.64 0.07
0.99 0.02
0.70 0.04
It is noted that G0 is more sensitive towards structural changes in the system as compared to G00 . Lower exponent values of G0 and G00 are obtained for neat PEO as compared to the theoretical values which are 2 and 1, respectively. It is evident that neat PEO melt does not have ideal terminal viscoelastic relaxation as suggested by other studies.[34] This indicates that even in the absence of salt, the neat PEO melt is not homogenous. This restrains the long-range motion of PEO chains and thus, the neat PEO melt shows deviation in terminal viscoelastic relaxation. The results correspond well with the light scattering studies done by Selser and co-workers[35,36] that reported that PEO melts are not uniform on the microscopic scale due to the formation of transient physical network in different range of sizes from the extensive inter- and intra-polymer connections. At Mɳ ¼ const, the slope becomes less steep when added with salt. It shows a sharp decrease at YS ¼ 0.02. This implies a higher restriction in the long-range motion of PEO chains in PEO/Li. The sudden change in the slope of G0 means that at YS ¼ 0.02, PEO/Li establishes rheological percolation threshold. Above the rheological percolation threhold, the exponent of the moduli exhibits insignificant variation even though when more salt was added. The estimated power law exponent displays inappreciable effect of molar mass of PEO at WS ¼ const. At 60 C, G0 and G00 approached similar exponent values: G0 G00 f 0.5 at high salt concentration (e.g. PEO1 at YS ¼ 0.15), thus, confirming the transition from solid-like to liquid-like behavior. Figure 5 shows the plot of G00 versus G0 (or modified Cole-Cole plot) of PEO1 at YS ¼ 0 and 0.10, obtained at different
temperatures. The semicircles illustrated in Figure 5 point towards establishment of rheological percolation network formed in the systems. At 30 C, there is no formation of rheological network, even at high salt concentration. Hence, no semicircle can be observed in the plot. At 80 C, the plot exhibits semicircle for the whole salt concentration, including neat PEO. In other words, the rheological networks develop when PEO is in melt state, despite with or without the presence of salt. At 60 C, the semicircle can only be obtained at high salt concentrations. This demonstrates that the formation of rheological percolation network only occurs when PEO is in melt state. The same trend was observed for PEO4 which is not shown in Figure 5. One clearly sees a single circular arc, with the centre lying below G0 axis. Since the regression of moduli as a function of frequency does not comply strictly with the theoretical power law dependence, deviations from perfect semicircle shape of modified Cole-Cole plot are expected. Neat PEO melt can establish physical network on its own. According to Selser and co-workers,[35,36] the neat PEO melt in the range below and above the entanglement molar mass are able to form the physical networks. However, it is important to recognize that not all melts of linear polymers can form networks. The addition of LiClO4 salt may lead to formation of Li salt network in existing PEO network. Therefore, in PEO/Li system, the deviation of terminal viscoelastic relaxation behaviour may be due to the establishment of PEO network and the formation of Li salt network in PEO. This is in agreement with Selser et al. that concluded the network structure and behaviour of the PEO melt is still retained even after the addition of Li salt.
4.4. Distribution of Polymer Chain Relaxation Times The characteristic frequency for which G0 ¼ G00 is the reciprocal of the relaxation time of the temporary polymer network.[19] Figure 6 demonstrates how the values of frequency at G0 -G00 cross-over (fcross) and frequency at G00 max (fo) were determined. Selected values of cross-over frequency (fcross) and frequency at G00 max (fo) for PEO1 and PEO4 at 80 C are tabulated in Table 4. At Mɳ ¼ const, both frequencies shift to lower value with increasing salt concentration before levelling off when the solubility limit of
Figure 5. Plot of G00 versus G0 for neat PEO1 at 30, 60 and 80 C with different salt compositions at YS ¼ 0 and 0.10.
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Figure 6. An example of (a) fcross determination from G0 -G00 cross-over using third polynomial order fitting (r2 > 0.98) and (b) fo determination from G00 max using third polynomial order fitting (r2 > 0.98) for neat PEO4 at 80 C.
PEO is reached. This indicates the relaxation time increases with ascending salt content. The comparison of fcross and fo may provide insight on the distribution of relaxation time. The occurrence of G0 -G00 cross-over at a significantly lower frequency (fcross < fo) than G00 max further supports a broad distribution of relaxation as reflected by imperfect semicircle in G00 versus G0 plot. At WS ¼ const, the polymer chain relaxation time is nearly independent of molar mass. The discrepancy of fcross and fo values decreases upon addition of salt. This shows that the distribution of relaxation times is narrower for PEO/Li as compared to neat PEO.
network at 80 C for neat PEO and PEO/Li in melt state restricts the long-range relaxation of the polymer chains.
Acknowledgements The authors would like to acknowledge financial support from Ministry of Education, Malaysia for Fundamental Research Grant Scheme (FRGS) (600-RMI/FRGS 5/3 (67/2013)) and MyPhD scholarship. We would also like to extend our thanks to Universiti Teknologi MARA for UiTM Education Excellence Funding (bil. 35 (03/2014)). The rheological data by Nur Hajar Saadon are gratefully acknowledged.
5. Conclusions PEO-based SPEs with high molar masses exhibit insignificant variation of thermal and rheological (both solid and liquid) properties as a function of molar mass at constant salt concentration when the morphologies developed are close to equilibrium under the experimental condition. The DSC results reveal that PEO-based SPEs develop microscopic heterogeneities above the solubility limit of salt in PEO, which can be assessed from the width of Tg and the change in enthalpy of endothermic overshoot after the endset of Tg. The deviation in Power law exponent of storage and loss moduli as a function of frequency at 80 C as compared to the theoretical values indicates that neat PEO and PEO/Li does not exhibit perfect terminal viscoelastic relaxation behavior. The establishment of rheological percolation
Table 4. Frequency values of G0 -G00 cross-over and G00 max of PEO1 and PEO4 at 80 C. fcross (Hz)
fo (Hz)
YS
PEO1
PEO4
PEO1
PEO4
0
1.1
1.0
27
25
0.05
0.5
0.5
20
18
0.07
0.2
0.2
16
14
0.10
0.2
0.3
17
16
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Keywords glass transition, microscopic heterogeneity, poly(ethylene oxide), rheology, terminal viscoelastic relaxation
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