Polymers entropy

The successful preparation of polymers is achieved only if tire macromolecules are stable. Polymers are often prepared in solution where entropy destabilizes large molecular assemblies. Therefore, monomers have to be strongly bonded togetlier. These links are best realized by covalent bonds. Moreover, reaction kinetics favourable to polymeric materials must be fast, so tliat high-molecular-weight materials can be produced in a reasonable time. The polymerization reaction must also be fast compared to side reactions tliat often hinder or preclude tire fonnation of the desired product. 

The modulus increases with temperature. This behavior is verified by experiment. By contrast, the modulus of metals decreases with increasing T. The difference arises from the fact that entropy is the origin of elasticity in polymers but not in metals. 

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... 

We concluded the last section with the observation that a polymer solution is expected to be nonideal on the grounds of entropy considerations alone. A nonzero value for AH would exacerbate the situation even further. We therefore begin our discussion of this problem by assuming a polymer-solvent system which shows athermal mixing. In the next section we shall extend the theory to include systems for which AH 9 0. The theory we shall examine in the next few sections was developed independently by Flory and Huggins and is known as the Flory-Huggins theory. 

This is the entropy of the disordered polymer when the latter entirely fills the lattice. 

Since the 0 s are fractions, the logarithms in Eq. (8.38) are less than unity and AGj is negative for all concentrations. In the case of athermal mixtures entropy considerations alone are sufficient to account for polymer-solvent miscibility at all concentrations. Exactly the same is true for ideal solutions. As a matter of fact, it is possible to regard the expressions for AS and AGj for ideal solutions as special cases of Eqs. (8.37) and (8.38) for the situation where n happens to equal unity. The following example compares values for ASj for ideal and Flory-Huggins solutions to examine quantitatively the effect of variations in n on the entropy of mixing. 

A plot of these values is shown in Fig. 8.1. Note the increase in the entropy of mixing over the ideal value with increasing n value. Also note that the maximum occurs at decreasing mole fractions of polymer with increasing degree of polymerization. 

The thermodynamic ceiling temperature (26) T for a polymerization is computed by dividing the AfTp by the standard entropy of polymerization, The T is the temperature at which monomer and polymer are in equHibrium in their standard states at 25°C (298.15 K) and 101.3... 

Obviously, B can never be negative in these cases to the extent that equation 5 is vaUd, miscibility can only be driven by combinatorial entropy, and this possibihty is maximized by matching the values of 5 and 5g as nearly as possible. In general, high molecular weight, nonpolar polymers are rarely miscible with each other. 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

The ring-opening polymerization of is controUed by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cycHzation equihbrium constants of dimethyl siloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equihbrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equihbrium constant of the formation of each cycHc is approximately equal to the equihbrium concentration of this cycHc, [(SiR O) Thus the total... 

The actual amount and stmcture of this "bound" water has been the subject of debate (83), but the key factor is that in water, PVP and related polymers are water stmcture organi2ers, which is a lower entropy situation (84). Therefore, it is not unexpected that water would play a significant role in the homopolymeri2ation of VP, because the polymer and its reactive terminus are more rigidly constrained in this solvent and termination k is reduced... 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

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