Enthalpy polymer solutions

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... 

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. 

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

FIG. 7.7 Typical curves of free enthalpy G vs. volume fraction ip as a function of temperature, from above the critical temperature Tc to temperatures below Tc. The diagram below is obtained with the aid of the double tangent curves and the inflection points to construct the binodal curves (phase diagram) and spinodal curves (stability diagram), respectively. It has to be emphasised that this is the result for low molecular weight liquids, for polymer solutions the critical point would be very close to ip = 0. 

To calculate AWm (the enthalpy of mixing) the polymer solution is approximated by a mixture of solvent molecules and polymer segments, and AW is estimated from the number of 1,2 contacts, as in Section 12.2.1. The terminology is somewhat different in the Flory-Huggins theory, however. A site in the liquid lattice is assumed to have z nearest neighbors and a line of reasoning similar to that developed above for the solubility parameter model leads to the expression... 

Subsequent development has led to a variety of applications, including liquid/hquid equilibria [Magnussen, Rasmussen, and Fredenslund, Ind. Eng. Chem. Process Des. Dev. 20 331—339 (1981)], solid/hquid equilibria [Anderson and Prausnitz, Ind. Eng. Chem. Fun-dam. 17 269-273 (1978)], solvent activities in polymer solutions [Oishi and Prausnitz, Ind. Eng. Chem. Process Des. Dev. 17 333-339 (1978)], vapor pressures of pure species [Jensen, Fredenslund, and Rasmussen, Ind. Eng. Chem. Fundam. 20 239-246 (1981)], gas solubilities [Sander, Slqold-Jprgensen, and Rasmussen, Fluid Phase Equilib. 11 105—126 (1983)], and excess enthalpies [Dang and Tas-sios, Ind. Eng. Chem. Process Des. Dev. 25 22-31 (1986)]. 

In the above considerations, the hydrophobic portions of both the membrane polymer and the small molecules that enter the membrane are expected to interact in the hydrophobic microphases in the membrane. It therefore becomes useful to find a numerical measure of the miscibility of these hydrophobic portions of molecules. In the case of complete molecules, both small and polymeric, the solubility parameter concept has been useful in the past. This concept is related to the enthalpy change which occurs on mixing in regular solution theory as developed by Hildebrand and coworkers (10) and as used for polymer solution theory by Flory (11). The Hildebrand solubility parameter is a measure of the attraction between molecules of the same kind, including dispersion forces, polar forces, and hydrogen bonding... 

When X = 2 th e two effects compensate each other, (/ii — / l) = 0 and the dilute polymer solution behaves ideally, i.e., as if Hrmx — 0 and the polymer chain segments were not connected. Flory used the term theta conditions to describe this ideal state of dilute polymer solutions and developed the concept further by defining the excess partial molar enthalpy,, and entropy, AS, of mixing as... 

The effect of temperature on the flow behaviour of polymethacrylate and polyacrylate blends in mineral oil demonstrated that it is strongly controlled by the entropy of activation for viscous flow [51], confirming early speculations [52]. The increased negative entropy was presumably a result of the very sluggish translational motion of the polymer coils. On the other hand, the enthalpy of activation for viscous flow of the polymer solutions was, for the most part, very nearly the same as that of the oil solvent. Only the most efficient systems exhibited decreased enthalpy, suggesting that coil expansion at high temperatures may be a factor, but the effect was very small relative to the entropy effect. 

Thus, there is no temperature difference between them. Exchanging the solvent droplet of one of the probes by a droplet of the solution leads to condensation of solvent vapor due to the lower vapor pressure of the solvent above the solution. Thereby, the released condensation enthalpy increases the temperature of the solution droplet, which simultaneously leads to an increase of the vapor pressure. After reaching the vapor pressure equilibrium of the solution droplet, a relatively stable temperature is obtained at the solution droplet. This temperature is converted by the measuring system to a direct voltage signal and is thereby at the user s disposal as a measuring value. The resulting relative measured value is nearly proportional to the osmolal concentration of the solutions. However, it may be affected by heat loss and the nonideal behavior of the polymer solutions. 

In dilute polymer solutions, the polymer molecules are isolated from each other by regions of pure solvent, i.e., the polymer segments are not uniformly distributed in the lattice. In view of this, the Flory-Huggins theory is least satisfactory for dilute polymer solutions and only applies to concentrated solutions or mixtures. Furthermore, the interaction parameter introduced to account for the effects of polymer-solvent contact interactions is not a simple parameter and should contain both enthalpy and entropy contributions. Additionally, as noted earlier, it has also been shown to be dependent on the solution concentration. 

Enthalpies of solution or mixing, expressed as the enthalpy change per unit mass of polymer, are given in the table at infinite dilution, i.e., a very small amount of polymer and a large excess of solvent were mixed isothermaUy to form a homogeneous solution. By thermodynamics, or A H "" are obtained from the fol-... 

The state of the polymer before dissolution can significantly affect the enthalpy of solution. The dissolving of a semicrystalline polymer requires an additional amount of heat associated with the disordering of crystalline regions. Consequently, its enthalpy of... 

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