Interaction parameters solution

In polymer solutions and blends, it becomes of interest to understand how the surface tension depends on the molecular weight (or number of repeat units, IV) of the macromolecule and on the polymer-solvent interactions through the interaction parameter, x- In terms of a Hory lattice model, x is given by the polymer and solvent interactions through... 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

Although the emphasis in these last chapters is certainly on the polymeric solute, the experimental methods described herein also measure the interactions of these solutes with various solvents. Such interactions include the hydration of proteins at one extreme and the exclusion of poor solvents from random coils at the other. In between, good solvents are imbibed into the polymer domain to various degrees to expand coil dimensions. Such quantities as the Flory-Huggins interaction parameter, the 0 temperature, and the coil expansion factor are among the ways such interactions are quantified in the following chapters. 

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. 

Polyisobutylene is readily soluble in nonpolar Hquids. The polymer—solvent interaction parameter Xis a. good indication of solubiHty. Values of 0.5 or less for a polymer—solvent system indicate good solubiHty values above 0.5 indicate poor solubiHty. Values of X foi several solvents are shown in Table 2 (78). The solution properties of polyisobutylene, butyl mbber, and halogenated butyl mbber are very similar. Cyclohexane is an exceUent solvent, benzene a moderate solvent, and dioxane a nonsolvent for polyisobutylene polymers. 

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

Because the appearance of a superlattice is usually well characterized qualitatively in terms of an interaction parameter w which has nothing to do, in the usual treatments, with the melting of the parent solid solution, one does not expect to find a simple relationship between the critical temperature for disordering of the superlattice, and Ts, the solidus temperature of the corresponding solid... 

By a statistical model of a solution we mean a model which does not attempt to describe explicitly the nature of the interaction between solvent and solute species, but simply assumes some general characteristic for the interaction, and presents expressions for the thermodynamic functions of the solution in terms of an assumed interaction parameter. The quasi-chemical theory is of this type, and we have noted that a serious deficiency is its failure to consider the vibrational effects in the solution. It is of interest, therefore, to consider briefly the average-potential model which does include the effect of vibrations. 

For gas-liquid solutions which are only moderately dilute, the equation of Krichevsky and Ilinskaya provides a significant improvement over the equation of Krichevsky and Kasarnovsky. It has been used for the reduction of high-pressure equilibrium data by various investigators, notably by Orentlicher (03), and in slightly modified form by Conolly (C6). For any binary system, its three parameters depend only on temperature. The parameter H (Henry s constant) is by far the most important, and in data reduction, care must be taken to obtain H as accurately as possible, even at the expense of lower accuracy for the remaining parameters. While H must be positive, A and vf may be positive or negative A is called the self-interaction parameter because it takes into account the deviations from infinite-dilution behavior that are caused by the interaction between solute molecules in the solvent matrix. 

Figure 10. Adsorbed cation coverage as a function of electrode potential, assuming a cation interaction parameter / = 6.18 The solid line is the steady-state solution, whereas the broken line is the quasi-steady solution. Open circles indicate the unstable area. (From G. L. Griffin, J. Electrochettu Soc. 131, 18, 1984, Fig. 1. Reproduced by permission of The Electrochemical Society, Inc.)...

According to Flory-Huggins theory, the heat of mixing of solvent and polymer is proportional to the binary interaction parameter x in equation (3). The parameter x should be inversely proportional to absolute temperature and independent of solution composition. 

We have recently extended the Flory model to deal with nonpolar, two-solvent, one polymer soltulons (13). We considered sorption of benzene and cyclohexane by polybutadiene. As mentioned earlier, a binary Interaction parameter Is required for each pair of components In the solution. In this Instance, we required Interaction parameters to represent the Interactions benzene/cyclohexane, benzene/polybutadlene, and cyclohexane/ polybutadiene. 

This stipulation of the interaction parameter to be equal to 0.5 at the theta temperature is found to hold with values of Xh and Xs equal to 0.5 - x < 2.7 x lO-s, and this value tends to decrease with increasing temperature. The values of = 308.6 K were found from the temperature dependence of the interaction parameter for gelatin B. Naturally, determination of the correct theta temperature of a chosen polymer/solvent system has a great physic-chemical importance for polymer solutions thermodynamically. It is quite well known that the second viiial coefficient can also be evaluated from osmometry and light scattering measurements which consequently exhibits temperature dependence, finally yielding the theta temperature for the system under study. However, the evaluation of second virial... 

Fig. 111.—Experimental values of the interaction parameter %i plotted against the volume fraction of polymer. Data for polydi-methylsiloxane M =3850) in benzene, A (New-ingi6). polystyrene in methyl ethyl ketone, (Bawn et aV ) and polystyrene in toluene, O (Bawn et alP) are based on vapor pressure measurements. Those for rubber in benzene, T (Gee and Orr ) were obtained using vapor pressure measurements at higher concentrations and isothermal distillation equilibration with solutions of known activities in the dilute range.

The thermodynamic behavior of the dilute polymer solution depends on three factors (1) the molecular weight, (2) the thermodynamic interaction parameters and ki, or ipi and 0, which characterize the segment-solvent interaction, and (3) the configuration, or size, of the... 

Gee ° has applied this method to the determination of the interaction parameters xi for natural rubber in various solvents. Several rubber vulcanizates were used. The effective value of VelV for each was determined by measuring its extension under a fixed load when swollen in petroleum ether. Samples were then swollen to equilibrium in other solvents, and xi was calculated from the swelling ratio in each. The mean values of xi for the several vulcanizates in each solvent are presented in Table XXXVI, where they are compared with the xi s calculated (Eq. XII-30) from vapor pressure measurements on solutions of unvulcanized rubber in some of the same solvents. The agreement is by no means spectacular, though perhaps no worse than the experimental error in the vapor pressure method. 

If the system separates, it can be extended to a model for the interface between two solutions by introducing ions. In the basic case the system contains a salt composed of cations and anions which is preferentially solvated by the solvent 5], but badly solvable in solution 2, and a salt K2A2 that is preferentially dissolved in solvent 2. This can be achieved by choosing suitable interaction parameters between the ions and the two solvents. 

Using the estimated interaction parameters phase equilibrium computations were performed. It was found that the EoS is able to represent the VL2E behavior of the methane-n-hexane system in the temperature range of 198.05 to 444.25 K reasonably well. Typical results together with the experimental data at 273.16 and 444.25 K are shown in Figures 14.14 and 14.15 respectively. However, the EoS was found to be unable to correlate the entire phase behavior in the temperature range of 195.91 K (Upper Critical Solution Temperature) and 182.46K (Lower Critical Solution Temperature). 

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