Isobaric glass transitions, polymers

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... 

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. 

Isobaric (constant pressure) and isochoric (constant volume) glass transitions in polymers were first observed by Colucci and co-workers (66) for bisphenol-A polycarbonate. A molecular dynamics study of such transitions in a model amorphous poljmier was reported by Yang and co-workers (67). This study showed that the glass transition is primarily associated with the fi-eezing of the torsional degrees of freedom of polymer chains (related to chain stiffness), which are strongly coupled to the degree of fi-eedom associated with the nonbonded Lennard-Jones potential (related to interchain cohesive forces). 

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). 

For describing thermally stimulated current associated with transitions in amorphous polymers, the multiple order parameter concept has been used. This concept has been widely discussed in past years and a good fit of volume recovery under isothermal and isobaric conditions through the glass transition has been presented by Kovacs et al. The relative volume departure of the system from equilibrium, 5, has been assumed to have a rate of change t,- of... 

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