Polymer-solvent interaction parameter molecular weight dependence

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Swelling The first step in the solubilization of a polymer. The degree of swelling depends on the polymer-solvent interaction parameter and the molecular weight of the polymer. In the case of a cross-linked polymer, solubilization cannot take place, and an equilibrium degree of swelling is attained. 

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... 

Equations (3.125) and (3.126) together with Eq. (3.120) show that the expansion factor depends significantly on two molecular parameters. The first is molecular weight. At conditions far removed from unperturbed conditions, a increases without limit as the square root of the molecular weight. The second parameter determining a is A2, which chracterizes polymer-solvent interaction. Under theta conditions at which z becomes zero, a becomes unity. Physical measurements made under these conditions will reflect the characteristics of the unperturbed molecule. The overall dimensions of such a molecule will be determined solely by bond lengths... 

Table V was prepared from Figure 5. The critical PEG molecular weight is that molecular weight below which some penetration can occur into the substance. For untreated wood, it is about 3000. However, the meaning of this value must be interpreted with caution. According to the theory of gel permeation chromatography, the important single solute parameter is effective molar volume rather than molecular weight (9). The molar volume of a polymer depends on polymer-polymer and polymer-solvent interactions this is illustrated schematically in Figure 9 (36). The total chain lengths are the same for all the polymer systems, yet the configurations and bulkiness vary considerably.

Osmotic pressure data can, therefore, be used for the determination of the number-average molecular weight, M , or the solvent-polymer interaction parameter Xj. This depends, of course, on knowing the values of the densities and specific volumes of the polymer and the solvent. In good solvents, g is approximately 1/4 in which case Equation 12.50 becomes... 

The viscosity dependence on polymer molecular weight is demonstrated in Figure 2.21 whereas Figure 2.22 shows the effect of polymer/solvent interaction. In the latter, the viscosity of solutions of a thermoplastic rubber at constant concentration and temperature is given in various hydrocarbon(blend)s. In this example hydrogen bonding or polar effects play no or only a very limited role. It is clear that in this case the solution viscosity is very much influenced by the Hildebrand solubility parameter of the solvent in relation to that of the polymer (8.2-9.1). 

BCA2 Kaddour, L.O., Anasagasti, M.S., and Strazielle, C., Molecular weight dependence of interaction parameter and demixing concentration in polymer-good solvent systems. Comparison with theory, MaAro/wo/. Chem., 188, 2223,1987. 

Recently, renormalization group calculations have been used to derive new scaling laws for the molecular weight dependence of the interaction parameter, Xab between unlike polymers (A and B) in a good solvent and the critical demixing concentration. The purpose of this paper is to present some experimental results which verify this theory for several mixtures of two polymers polystyrene (PS) - poly(dimethyl-siloxane) (PDMS), poly(methyl-methacrylate) (PMMA)-PDMS, PS-PMMA and PS-poly (vinylacetate) (PVAc). 

If the monomers are uniformly distributed within the polymer chain, the ratio of monomers will define the flexibility of the polymer chain. Because many properties depend on this chain mobility, polymer composition is carefully controlled. In addition to chain mobility, polymer composition also defines the solubility parameter of the polymer, which is a critical property relative to the type of solvents in which the polymer is soluble, the ability of the polymer to accept and hold oil, and the relative compatibility of the polymer with other polymers. Basically, these properties all involve polymer/solvent interaction, with the difference being the increasing molecular weight of the solvent. 

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... 

In those cases in which V2/Vi is known, both gv° and g ° are given. For the rest of the systems, only gv° is given. Prediction of thermodynamic properties on ternary systems formed by a polymer and two solvents or two polymers and a solvent requires the knowledge of the parameter g°, characteristic of the interaction of the corresponding binary pairs [9], However, due to the variety of sources for the several systems studied, the data correspond to different polymer molecular weights, m, and to different temperatures. Since the variation of x with concentration may depend on M for low M s, it has selected data only for M > 2 x 109, where no M dependence is detected. 

Another possible variable for the characterization of the goodness of solvents is the interaction parameter x values, expressing the measure of deviations of actual solutions from ideal ones. This value can be determined by several methods, which are, mostly experimentally demanding and time-consuming, x is dependent on both the polymer concentration and molecular weight and information provided about the specific interactions in the solution is of no particular interest [11,30,31], Solvents, obviously different in quality, yield quite close values and thus the resolving capability is low. Comparison of results obtained by various methods and/or experimenters is thus fairly difficult [30,32-34],... 

Here a mixture of sterically stabilized colloidal particles, solvent, and free polymer molecules in solution is considered. When two particles approach one another during a Brownian collision, the interaction potential between the two depends not only on the distance of separation between them, but also on various parameters, such as the thickness and the segment density distribution of the adsorbed layer, the concentration and the molecular weight of the free polymer. The various types of forces that are expected lo contribute to the interaction potential are (i) forces due to the presence of the adsorbed polymer, (ii) forces due to the presence of the free polymer, and (iii) van der Waals forces. It is assumed here that there are no electrostatic forces. A brief account of the nature of these forces as... 

The number-average molecular weight (MJ of polymers can be easily determined from methods based on colligative properties, which are dependent on the number of molecules in the solution [28]. Thus, the addition of a number of solute molecules to a solvent produces a change in the chemical potential (A/Ui) of the solvent from which the molecular and interactional parameters can be deduced. 

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