Enthalpy polymer thermodynamics

Polymers in the glassy sutc are seldom in thermodynamical equilibrium. By cooling an amorphous polymer down from above its glass transition temperature, a thermodynamically nonequUibrium state is formed, which, usually very slowly, relaxes toward equilibrium. This kind of relaxation process is referred to as volume-enthalpy or thermodynamical relaxation because it involves a decrease of the specific volume and enthalpy. The volume change can be measured dUatometrically, the enthalpy change calw-imetrically. Vblume relaxation is described quantitatively by the Kovacs [11] equatioo as... 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

The non-bonded interaction energy, the van-der-Waals and electrostatic part of the interaction Hamiltonian are best determined by parametrizing a molecular liquid that contains the same chemical groups as the polymers against the experimentally measured thermodynamical and dynamical data, e.g., enthalpy of vaporization, diffusion coefficient, or viscosity. The parameters can then be transferred to polymers, as was done in our case, for instance in polystyrene (from benzene) [19] or poly (vinyl alcohol) (from ethanol) [20,21]. 

The single most important factor that determines whether a cyclic monomer can be converted to linear polymer is the thermodynamic factor, that is, the relative stabilities of the cyclic monomer and linear polymer structure [Allcock, 1970 Sawada, 1976]. Table 7-1 shows the semiempirical enthalpy, entropy, and free-energy changes for the conversion of cycloalkanes to the corresponding linear polymer (polymethylene in all cases) [Dainton and Ivin, 1958 Finke et al. 1956]. The Ic (denoting liquid-crystalline) subscripts of AH, AS, and AG indicate that the values are those for the polymerization of liquid monomer to crystalline polymer. 

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... 

As to Eq. (7), it is to be remembered that AG, in a general case is a function of p. Therefore, the experimental dependencies of p on concentration, chain length of oligomer and temperature may be employed to find thermodynamic parameters only for a fixed value of p, e.g., for p = 0.5 using Eqs. (8 a- b). These equations have been taken by various authors to calculate the enthalpy and entropy of complex formation between simple synthetic oligomers and polymers 28). In a number of cases the correspondence between the values of complex formation enthalpy thus obtained and determined, either by calorimetry or by potentiometric titration 26), has been found satisfactory although it is obvious that in a general case these values do not necessarily coincide. 

The kinetic constants, calculated in the previous section, can immediately by applied to the investigation of the energetics of the flow-equilibrium, especially to the calculation of the activation enthalpy AH and entropy AS related to the coil relaxation in the actual gel phase as mentioned above, and to the coil release from segment-segment contacts with the gel, before the retarded rediffusion of these coils from the gel into the sol sets on. These thermodynamic functions can then be compared with those of the reversible polymer transfer gel - sol calculated in Section 3.1. 

Polymer catalysts showing interactions with the substrate, similar to enzymes, were prepared and their catalytic activities on hydrolysis of polysaccharides were investigated. Kinetical analyses showed that hydrogen bonding and electrostatic interactions played important roles for enhancement of the reactions and that the hydrolysis rates of polysaccharides followed the Michaelis-Menten type kinetics, whereas the hydrolysis of low-molecular-weight analogs proceeded according to second-order kinetics. From thermodynamic analyses, the process of the complex formation in the reaction was characterized by remarkable decreases in enthalpy and entropy. The maximum rate enhancement obtained in the present experiment was fivefold on the basis of the reaction in the presence of sulfuric acid. 

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