Polymer-solute interaction parameters

Condo, P.D., Sumpter, S.R., Lee, M.L. and Johnston, K.P. (1996) Partition Coefficients and Polymer-Solute Interaction Parameters by Inverse Supercritical Fluid Chromatography, Ind. Eng. Chem. Res. 35, 1115-1123. 

The global solubility parameters of polymers were determined from partial molar enthalpies of mixing [60, 71, 72], from partial molar free energies of mixing [60] and from the polymer-solute interactions parameters [60, 68, 101, 108, 109] all these functions were obtained by GLC. For normal, branched and cyclic alkanes, aromatic hydrocarbons and tetraline in polystyrene, eqns (5.40) and (5.42) yield Sj = 7.6 0.2 and 82 = 7.4 i 0.4 cali/2 "cm /z [60] at an average column temperature of 193°C. The same substances in poly(methyl acrylate) give 82 = 8.7 0.3... 

Polymer/solution interaction parameter, and 1)2,s Polymer volume fraction in swollen polymer. 

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. 

The Flory-Huggins interaction parameter, x Is the sum of enthalpic (xH) and entropic (x ) contributions to the polymer-solute interactions (28). xs is an emPitical constant related to the coordination of the polymer subunits (29). Chiou et al. (20) have selected a value of 0.25 for xs of humlc matter. From regular solution theory, xq is given by... 

Nonpolar Parameters. In a reverse osmosis system involving cellulose acetate membranes and aqueous solutions of hydrocarbon solutes, the adsorption of water and that of solute on the polar and nonpolar sites of the membrane surface respectively may be expected to take place essentially independently. Further, since the polymer-solute interaction forces are attractive in nature for the above case, the mobility of the solute molecules through the membrane pore is retarded, and they also tend to agglomerate... 

Specifically, he developed relationships for the free energy of mixing of solvent and solute (polymer) molecules with different solute axial ratios (length/width) and solute interaction parameters. In the absence of interactions between solute molecules, the free energy of the system lowers when rodlike molecules precipitate out of solution and form a separate solid phase. This is due to the fact that small water molecules must order themselves around large rodlike macromolecules in solution and therefore the system is most stable when the water molecules and rodlike molecules are separated in space into different phases, such as liquid and solid phases. 

This assumption is based on the fact that the polymer-solvent interaction parameter [see Eq. (8)] of the tributyrin-cellulose tributyrate system, as evaluated from melting-point depressions, is nearly zero at about 100° C [Mandelkern and Flory (160)]. It does not follow, however, that the system is athermal, for the parameter generally involves an entropy contribution. Furthermore, the heat and entropy parts of this parameter vary with the concentration in a complicated way, especially in polar systems [see, for example, Takenaka (243) Zimm (22) Kurata (154)]. Thus it is extremely hazardous to predict dilute solution properties from concentrated solution properties such as the melting-point depression, at least on a highly quantitative level as in the present problem. 

Charlet, G. Ducasse, R. Delmas, G., "Thermodynamic Properties of Polyolefin Solutions at High Temperature 2. Lower Critical Solubility Temperatures for Polybutene-1, Polypen-tene-1 and Poly(4-methylpentene-1) in Hydrocarbon Solvents and Determination of the Polymer-Solvent Interaction Parameter," Polymer, 22, 1190 (1981). 

In the case of polystyrene blends with poly(vinyl methyl ether) two phase behaviour was found for blends from various chlorinated solvents whereas single phase behaviour was found for blends from toluene The phase separation of mixtures of these polymers in various solvents has been studied and the interaction parameters of the two polymers with the solvents measured by inverse gas chromatography It was found that those solvents which induced phase separation were those for which a large difference existed between the two separate polymer-solvent interaction parameters. This has been called the A% effect (where A% = X 2 Xi 3)-A two phase region exists within the polymer/polymer/solvent three component phase diagram as shown in Fig. 2. When a dilute solution at composition A is evaporated, phase separation takes place at B and when the system leaves the two phase region, at overall... 

In his classic paper, Flory predicted the phase behavior in solutions of rod-like particles (5). The resulting phase diagram related the solvent-solute interaction parameter %i ( -5) to the volume fraction, V2, for polymer rods with an axial ratio of 100. A positive Xi makes a positive or excess free energy contribution to mixing. Good solvents are characterized by small Xi values. Two of Flory s major predictions are that the minimum polymer concentration required for mesophase formation will increase as Xi decreases, sharply at first, then more gradually, and at certain Xi values two different anisotropic phases coexist. Our microscopical observations of conjugated phases may reflect the validity of the latter prediction. 

The theory of Zimm (7) uses the assumptions of the Rouse theory and in addition considers hydrodynamic interactions between the moving submolecules and the solvent. The theory also makes use of the method formulated by Kirkwood and Riseman for the evaluation of the viscosity of dilute polymer solutions. A parameter h = where r is the... 

Problem 3.15 A polymer solution was cooled very slowly until phase separation took place to give two phases in equilibrium. Analysis of the phases showed that the volume fractions of polymer in the two phases were 2 = 0.01 and < 2 = 0.89, respectively. Using the Flory-Huggins equation for A/ri [cf. Eq. (3.53)], together with the equilibrium condition = A/i", calculate an estimate of the polymer-solvent interaction parameter for the conditions of phase separation. 

Although not normally detected, the third virial coeffident occasionally contributes to the nonideal behavior in ddnte solutions, and a curved plot is obtained, as shown in Figure 9.2(a). This increases the uncertainty of the extrapolation, bnt it can be overcome by recasting Equation 9.11 and introducing a polymer-solvent interaction parameter g... 

The binary interactirMi generally refers to the interactions between polymer-polymer and polymer-solvent The nature of solvent-polymer interaction plays an important role in the miscibility of blends. Many thermodynamic properties of polymer solutions such as solubility, swelling behavior, etc., depend on the polymer-solvent interaction parameter (y). The quantity was introduced by Flory and Huggins. Discussions of polymer miscibility usually start with Flory-Huggins equation for free energy of mixing of a blend (refer to Chap. 2, Thermodynamics of Polymer Blends ). 

For large n, the right-hand side of equation (4.1) reduces to 1/n . For n = Kf, V2c equals about 0.01, a very dilute solution. The critical value of the Flory-Huggins polymer-solvent interaction parameter, Zi, is given by... 

The adsorption of polymers from solutions strongly depends on the thermodynamic quality of solvent and the interaction energy between polymer and surface. All theories of adsorption include the thermodynamic parameter of interaction of the Flory-Huggins theory %i2. The thermodynamic interaction between polymer and solvent determines the conformation of macromolecules in solutions and thus the conditions of its interaction with the surface. The interaction between polymer and surface is characterized by the parameter of thermodynamic interaction, which was introduced by Silberberg, using the model of quasi-crystalline lattice of the surface layer, describing the properties of polymer solutions. This parameter may be determined as follows ... 

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