Isothermal compressibility, polymer glass

Figure 17. Specific volume Vt and isothermal compressibility (at the glass transition temperature Tg) calculated from the LCT as a function of the inverse number l/M of united atom groups in single chains for constant pressure (P = I atm 0.101325 MPa) F-F and F-S polymer fluids. Both quantities are normahzed by the corresponding high molar mass limits (i.e., by...

The study of glass transition is an important subject in current research, and simulations may well be suited to help our understanding of the phenomenon. An example is the application of Monte Carlo techniques by Wittman, Kremer, and Binder.The authors employed a lattice method in two dimensions to model the system. The glass transition was determined by monitoring the free volume changes as well as isothermal compressibility. The glasslike behavior was determined by evaluating the bond autocorrelation function. The authors found that both the dynamic polymer structure factor and the orienta-... 

Dielectric relaxation spectroscopy (DER), e.g. [103-105], DER monitors the mobility of dipolar groups in the polymer and also of small dipolar molecules (e.g. water) that may be dissolved in the polymer system. Corresponding to mechanical measurements, the maxima of dissipated energy indicate phase transition processes. Dilatometry, pVT measurements, e.g. [50,106]. These measurements unequivocally show a first order transition by a step in V T) and a bend if there is a glass transition. The important partial derivatives isobaric expansivity and isothermal compressibility can be derived from the corresponding measurements. The method is, however, quite time consuming and not widely used. 

Some of polymer properties change at the glass transition in discontinuous way (the coefficient of isobaric thermal expansion a, coefficient of isothermal compressibility kj, specific heat, etc), whereas the other ones change continuously (volume V, enthalpy H, and entropy S). As it is schematically shown in Figure 3, the onset of solidlike rigidity in an amorphous polymer at Tg is accompanied by sharp reductions in heat capacity Cp, thermal expansion coefficient up, and compressibility coefficient /cj (22). 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

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