Homopolymer solutions thermodynamics

BER Bercea, M., Eckelt, J., and Wolf, B.A., Random copolymers Their solution thermodynamics as compared with that of the corresponding homopolymers (experimental data by M. Bercea), Ind. Eng. Chem. Res., 47, 2434, 2008. 

X10 Xiong, X., Eckelt, J., Zhang, L., and Wolf, B.A., Thermodynamics of block copolymer solutions as compared with the corresponding homopolymer solutions Experiment and theory (exp. data by J. Eckelt and B. A. WoU), Macromolecules, 42, 8398, 2009. 

A numerical calculation needs knowledge of the solvent activity of die corresponding homopolymer solution at the same equilibrium concentration (here characterized by the value of the Flory-Huggins %-function) and the assumption of a deformation model that provides values of the factors A and B. There is an extensive literature for statistical thermodynamic models which provide, for example, Flory A = 1 and B = 0.5 Hermans A = 1 and B = 1 James and Guttf or Edwards and Freed A = 0.5 and B = 0. A detailed explanation was given recently by Heinrich et al. ... 

For calculating the spinodal curve and the critical point, there are two possible ways in the framework of continuous thermodynamics. The most general one is the application of the stability theory of continuous thermodynamics [45-47]. The other way is based on a power series expansion of the phase equilibrium conditions at the critical point. Following the second procedure. Sole et al. [48] studied multiple critical points in homopolymer solutions. However, in the case of divariate distribution functions the method by Sole has to be modified as outlined in the text below. 

A third class of new polymer integral equation theories have been proposed by Kierlik and Rosinberg. Their work is an extension of a density functional theory of inhomogeneous polyatomic fluids to treat the homogeneous phase. The Wertheim thermodynamic pertubation theory of polymerization is employed in an essential manner. Applications to calculate the intermolecular structure of rather short homopolymer solutions and melts have been made. Good results are found for short chains at high densities, but the authors comment that their earlier theory appears to be unsuited for long chains at low to moderate (semidilute) densities. ... 

Fig. 2 Schematic of four thermodynamically stable states (random coil, crumpet coil, molten globule and collapsed globule) of a homopolymer chain in the coil-to-globule and the globule-to-coil transitions. There exists a hysteresis between the two transitions around the 0-temperature ( 30.6 °C) of the PNIPAM solution [37]...

Figure 24 shows that both (i g) and (jq,) decrease as the temperature increases. Each data point was obtained only after the solution had reached thermodynamically equilibrium and the measured value was stable. Note that in each curve there exists a small kink at 29.4 °C and that (Rg)/(Rh) remains constant at 1.15 in the range 29-30.6 °C, representing an additional transition prior to the collapse of the PNIPAM chain segments. The decreases of both (Rg) and (R ) after the kink become faster. As shown before, the coil-to-globule transition of PNIPAM homopolymer chains do not present such a kink [32-34,37-40]. The sharp decrease of (Rg)/(Rh) from 1.5 to 0.6 in the inset confirms the coil-to-globule transition of individual copolymer chains. However, a careful examination of Fig. 24 raises a number of questions. 

The solution properties of blocks and grafts are complicated since the copolymer components A and B behave differently in different solvents. In order to simplify the analysis, one usually starts with a solvent in which both A and B are soluble. In this case, the solution properties approach those of a homopolymer, for which accurate theories exist, e.g. in the thermodynamic treatment of Flory and Huggins (1, 2). The latter considers the free energy of mixing of pure polymer with pure solvent, AGmix in terms of two contributions, i.e. the enthalpy of mixing, A//mix, and the entropy of mixing, A mix, as follows ... 

However, traditional chemical thermodynamics is based on mole fractions of discrete components. Thus, when it is applied to polydisperse systems it has been usual to spht the continuous distribution function into an arbitrary number of pseudo-components. In many cases dealing, for example, with a solution of a polydisperse homopolymer in a solvent (the pseudobinary mixture), only two pseudo-components were chosen (reproducing number and mass averages of molar mass of the polymer) which, indeed, are able to describe some main features of the liquid-liquid equilibrium in the polydisperse mixture [1-3]. In systems with random copolymers the mass average of the chemical distribution is usually chosen as an additional parameter for the description of the pseudo-components. However, the pseudo-component method is a crude and arbitrary procedure for polydisperse systems. 

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