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Non-exponential nature of calorimetric and other relaxations: Effects of 2 nm-size solutes, loss of translational diffusion, isomer specificity, and sample size
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83.According to the manufacturer and others [Q. Li, S. Hutcheson, G. B. McKenna, and S. L. Simon, J. Polym. Sci., Part B: Polym. Phys. 46, 2719 (2008)], the distribution of molecular sizes in EP0409 is approximately: 60% T10, 18% T12, 4% T8 and the balance consists of larger sized silsesquioxanes, which are not necessarily cage-structure molecules. To estimate its average mol wt, and average functionality, i.e., the average number of epoxides per molecule, we assumed that the “larger sized, less defined silsesquioxanes” are also cage-structure molecules comprised of 9% T14 and 9% T16. This gives an average mol. wt. of 1.867 kg and functionality of 11.2, which we use here. The same value of functionality was found from measurement of rubbery modulus for the same EP0409 by Li et.al. They noted that the value of 11.2 for the effective functionality of the EP0409 is slightly lower than the value of 11.8 expected, based on the functionality and distribution of the EP0409 cages in the mixture. In their calculation of n = 11.2 all of the increase in the rubbery modulus was attributed to an increase in crosslink density and it was assumed that the rubber density changes with nanoparticle concentration in a way similar to the change measured in the glass density.
92.These formalism are either empirical or based on a particular concept and all apparently fit a set of DSC data. The equations used for fitting are based on the description of (i) enthalpy (Refs. 9 and 12), (ii) configurational entropy (Refs. 1 and 12), (iii) distribution of relaxation times [F. L. Cumbrera and A. Munoz, Thermochim. Acta 196, 137 (1992)],
92.T. S. Chow, Adv. Polym. Sci. 103, 149 (1992)],
92.(vii) a multiparameter description known as the KAHR model (Ref. 10) [A. J. Kovacs, J. J. Aklonis, and J. M. Hutchinson, in Structure of Non-Crystalline Materials, edited by P. H. Gaskell (Taylor & Francis, London, 1977), pp. 153–163],
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193.The fixed frequency scans (isochrones) of κCp′ and κCp″ against T are usually broader when the frequency is high and the features appear at high temperatures. This is seen in Figs. 1 and 2, Ref. 84. Similar features appear in (i) the dielectric permittivity and loss isochrones for poly(propylene oxide) (Fig. 14.26, Ref. 58), (ii) in the tan δ isochrones (Fig. 1, Ref. 157, and Fig. 1 in G. P. Johari and M. Goldstein, J. Chem. Phys. 55, 4245 (1971), and (iii) in mechanical compliance of poly(vinyl acetate) in Fig. 9.9, Ref. 58. This broadening is attributable to (i) an increase in the strength of the JG relaxation relative to that of the α-relaxation, (ii) decrease in the separation of the JG and the α-relaxation features, and (iii) the fact that the real and imaginary components of a property measured for a fixed frequency change with T mainly because the relaxation time changes and hence a larger change in T is needed to affect the same change in the relaxation time when the relaxation features appear at high temperatures (at a high frequency) than at low temperatures (at a low frequency).
194. E. Donth, H. Huth, and M. Beiner, J. Phys.: Condens. Matter 13, L451 (2001). Use of the Donth's fluctuation formula gave a size of the cooperatively rearranging region that approached the size of an individual molecule in the bifurcation, or relaxation-splitting, region. The size of the cooperatively rearranging region seems consistent with Donth's interpretation in terms of density inhomogeneity which fluctuates in space and time, i.e., in snapshots they would appear as density pattern with a temperature-dependent, intrinsic length scale of 0.5-3 nm and fluctuating on the time scale of the α-process. Reinsberg et al. (Ref. 73) compared the length scale of dynamic heterogeneity against this size.
201. S. Corezzi, M. Beiner, H. Huth, K. Schröter, S. Capaccioli, R. Casalini, M. Fioretto, and E. Donth, J. Chem. Phys. 117, 2435 (2002).
202. K. L. Ngai, P. Lunkenheimer, C. León, U. Schneider, R. Brand, and A. Loidl, J. Chem. Phys. 115, 1405 (2001). Even at high pressures the JG relaxation peak in glycerol is only partly resolved (Ref. 69).
219. W. Oldekop, Glastech. Ber. 30, 8 (1957).
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