Dynamic Effects of the Conformational Isomerism

A quantitative description of sudi sittiations can be obtained for the simpk thermomechanical system whose molecules can assume only two conformational isomers The thermodynamic states for this system are usimlly uniquely ddined by temperature T, pressure p and the internal variable x, where x is the concentration of one conformational isomer and 1 — x is the concentration of the othw. The differences between the response functions under conditions of frozen and completely thawed conformational isomerism are given by Davies rebtionships 2.43)  

Incidentally, the thermal expansivity measured at constant temperature and pressure, viz. Oj and a, and the thermal pressure coefficients measured at constant temperature and volume, viz. and P, remain the same in arrested as well as in internal equilibrium, i.e. a.j. = ttp = a and p.j, = p = p. In non-equilibrium, i.e. in the states between the two extremes of arrested and internal equilibrium, one finds in general that ol and p.. p.  

The Eqs. (2.1a) and (2.1b) apply thus actually to a rate scale and, in the frequait case of cyclic exposure, to a frequency scale co. If a thermorheologically simple system is considei ed the fr juency scale can be replaced by a temperature sale 1/T. Steps A that satisfy Eqs. (2.1a) and (2.1b) appear then in the response-functions for systmis of this nature that are measured as a function of temperatiue at pven, fixed paturbation rate. The temperature at whidi the steps occur depends, however, on the rate of external i rturbution. The temperature-dependent thawing of conformational isomers in thermorheologically complicated systems can be similariy observed in the response-functions, but the steps no longer satisfy Eqs. (2.1 a) and (2.1 b). These two equations lose, in addition, their validity with rrapect to the rate scale if, as is the case of polymers, several mutually independent, internal variables are required in order to uniquely define the conformational isomerism. In this case. Eqs. (2.1a) and (2.1b) become inequalities 

Dynamic relationships such as the Davies equations have no significance whatever if the system is always in internal equilibrium with respect to the conformational isomerism, or if the conformational isomerism is frozen in the temperature range investi ted. Since for systems in internal equilibrium the internal variables are functions of the external variables, the former can be eliminated and the functions of state can be represented solely by the external variables. This dimination entails, however, a lo in information, and it is thus fiequently advisable to retain the inn variables also in the case of thermodynamic equilibrium (cf. Sect. 2.2). Arrested or frozen internal degrees of freedom have no thermodynamic significance whatsoever and can be ignored. 

The existence of a crystal condis crystal transition is the main question to be dealt with in this section. This is primarily a question of thermostatics. It is thus assumed that the relevant conformational isomers in the crystal concerned are in internal equilibrium. Conformational isomers that are arrested in the crystalline state can be eliminated from consideration. Conformational isomers that thaw in the temperature range of the transition may substantially distort the character of the transition because it would be experimentally difficult to attain internal equilibrium. 

---