Free enthalpy, polymer thermodynamics

In view of thermodynamics the ceiling temperature looks like a melting point. Below and above this temperature the system consists of 100% polymer and of 100% monomer, respectively. This is shown in Fig. 20.2. If, however, the polymer is soluble in its monomer, then the free enthalpy of mixing also plays a role and the result will be that the "melting point" is not as sharp as shown there will be a gradual change (i.e. the dashed line) from 100% polymer to 100% monomer. The ceiling temperature is in this case defined as the temperature where the amount of monomer equals the amount of polymer (i.e. at 50%) and equal to (see, e.g. Ivin, 2000) ... 

Description of thermochemical properties of chemical compounds, including that of polymers can be done using a few thermodynamic functions. One basic function is Gibbs free enthalpy that is expressed as follows [1] ... 

Formation of polymers is governed by thermodynamic and kinetic factors (see also Section 2.3). The free enthalpy of polymerization is an important parameter, which is known for various monomers. Tables with values for AH° and AS are given in literature [4]. Several values for AH for the formation of some polymers having in the backbone chain only carbon atoms are given in Table 2.2.1 (1 cal = 4.1868 J international, 1 cal = 4.184 J thermochemical). Some of the values are given for ideal gas phase, although few monomers and no polymers are in gas phase. Since in a reaction the reactant and the product can be in different aggregation states, the state of both participants must be indicated. 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

In many applications it is of prime importance that plasticizer and polymer be completely miscible at the molecular level. Thermodynamic criteria for the solubility of additives in polymers are the same as those given for simple liquid mixtures [2-6]. When two liquid substances form a stable solution, classical thermodynamics shows that the free enthalpy of mixing, AG , is negative [7]. Furthermore, one can write... 

Two polymers are miscible when they form a thermodynamically stable single-phase system [6]. Such is the case when the mixing of two amorphous polymers at constant temperature and pressure is accompanied by a net decrease in the free enthalpy of mixing, i.e., AGm < 0 [1,5-8]. As mentioned in Chapter 1, this condition is easily realized for an exothermic mixing (AHm < 0), but when AHm > 0, the miscibility becomes possible only if AHm < T ASm -... 

Phase relationships in equilibrium are determined by the free enthalpy (Gibbs free energy) of the system. The thermodynamic bdiaviour of polymer solutions can be very well described with the free enthalpy of mixing function derived, independently, by Florv (6,7) and Huggins (8—10) on the basis of the lattice theory of the liquid state. For the simplest case conceivable — a solution of a polydisperse polymer in a single solvent quasi-binary system) — we have... 

During the cooling of a semi-crystalline thermoplastic polymer, the macromolecules are organized around a germ of nucleation. At a particular temperature of thermodynamic balance between crystal and liquid (Tm°), the molar free enthalpies are equal in the solid and liquid phases. Crystallization is theoretically possible as soon as the solid free enthalpy... 

Recently, the melting process of semicrystalline polymers was considered as fully irreversible due to small crystal size, entanglements, or crystal defects [1-6]. Discussion of irreversible and reversible thermodynamic melting of polymers can be started from the analysis of the free enthalpy in the melting region as is schematically shown in Figure 9.33. 

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. 

The effect of solvency for the polymer chain has been considered in the thermodynamic treatment of Flory and Huggins [6], usually referred to as the Flory- Huggins theory. This theory considers the free energy of mixing of a pure polymer with a pure solvent, in terms of two contributions, namely the enthalpy of... 

A new type of rotational degrees of freedom parameter will be defined for the backbones and side groups of polymers, and correlations for the heat capacity and related thermodynamic functions (enthalpy, entropy and Gibbs free energy) will be developed utilizing both the connectivity indices and the rotational degrees of freedom, in Chapter 4. 

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