Configurational entropy polymer melts

Let us now turn to a discussion of the relation of the temperature dependence of the polymer melt s configurational entropy with its glass transition and address the famous paradox of the Kauzmann temperature of glass-forming systems.90 It had been found experimentally that the excess entropy of super-cooled liquids, compared with the crystalline state, seemed... 

Given the above model and assumptions. Freed [50] has recently shown that the LCT configurational entropy Sc T) of a polymer melt is given by the expression... 

The experimental inaccessibility of the configurational entropy poses no problem for the LCT, apart from a consideration of whether to normalize the configurational entropy per lattice site or per monomer in order to provide a better representation of experiment within the AG model. Once the appropriate normalization of Sc has been identified, t can be calculated from Eq. (33) as a function of temperature T, molar mass Mmoi, pressure P, monomer structure, backbone and side group rigidities, and so on, provided that Ap is specified [54]. The direct determination of Ap from data for T > Ta is not possible for polymer systems because Ta generally exceeds the decomposition temperature for these systems. Section V reviews available information that enables specifying Ap for polymer melts. 

Unfortunately, reliable experimental estimates of the configurational entropy are unavailable to enable explicit application of the AG model for polymer fluids. Instead, the temperature dependence of t in polymer melts is often analyzed in terms of the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) equation [103],... 

Figure 6. LCT configurational entropy Sc per lattice site of a constant pressure (P = 1 atm 0.101325 MPa) polymer melt as a function of the reduced temperature ST = T - defined...

Our theory of polymer melt glasses distinguishes four characteristic temperatures of glass formation that are evaluated for a given pressure from the configurational entropy s T) or the specific volume v(T). Specifically, these four... 

Figure 22. The configurational entropy Sc per lattice site as calculated from the LCT for a constant pressure, high molar mass (M = 40001) F-S polymer melt as a function of the reduced temperature ST = (T — To)/Tq, defined relative to the ideal glass transition temperature To at which Sc extrapolates to zero. The specific entropy is normalized by its maximum value i = Sc T = Ta), as in Fig. 6. Solid and dashed curves refer to pressures of F = 1 atm (0.101325 MPa) and P = 240 atm (24.3 MPa), respectively. The characteristic temperatures of glass formation, the ideal glass transition temperature To, the glass transition temperature Tg, the crossover temperature Tj, and the Arrhenius temperature Ta are indicated in the figure. The inset presents the LCT estimates for the size z = 1/of the CRR in the same system as a function of the reduced temperature 5Ta = T — TaI/Ta. Solid and dashed curves in the inset correspond to pressures of P = 1 atm (0.101325 MPa) and F = 240 atm (24.3 MPa), respectively. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005, American Chemical Society.)...

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

Finally, melting point depression measurements have been conducted on several symmetrically substituted polysiloxanes, specifically the dimethyl, diethyl, di-n-propyl, and diphenyl polymers. Interpretation of such experimental results yields entropies of fusion. Although it is difib-cult to extract a reliable configurational entropy from this quantity, such results could help elucidate the configurational characteristics of the chains thus investigated. ... 

---