Weight polymer-solvent interaction parameter

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. 

Equations (3.46) and (3.47) can be used in two different ways. First, if the polymer-solvent interaction parameter, Xi27 is known and the value of V2 at swelling equilibrium is measured, then the molecular weight between cross-links, can be calculated using Eq. (3.46). Second, if the value of Mf. is known and V2 is measured at equilibrium, the polymer-solvent interaction parameter xi2 at polymer concentration V2 can be determined. 

Data Specific volume of the PMMA network = 0.81 cm /g x (polymer-solvent interaction parameter) = 0.47 density of EtAc = 0.900 g/cm (molecular weight = 88.12). 

Where q = The Ratio of the Volumes In the Swollen and Dry States V = The Specific Volume of the Polymer Vf = The Molar Volume of the Solvent Mg = The Molecular Weight Between Crosslinks M = The Molecular Weight of the Polymer X = Polymer-Solvent Interaction Parameter Figure 12. Swelling of the resist layer... 

Inverse gas chromatography can be used to obtain the polymer-solvent interaction parameter in the limit of 2 = 1. Here x is found from the retention volume of the low molecular-weight component in the vapor phase as it is eluted over the polymer which is the stationary component in a gas-phase chromatography experiment. 

Solubility parameters can also be estimated from intrinsic viscosity. Flory [101] related intrinsic viscosity to polymer molecular weight and the chain-expansion factor. The chain-expansion factor can, in turn, be related to the polymer-solvent interaction parameter using the Flory-Hug-gins theory. A variety of models can be used to relate the interaction parameter to solubility parameters [87,102,103] these equations have the form... 

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. 

Estimate (a) polymer molecular weight, M , (b) second virial coef cients Ai and F2, and (c) polymer-solvent interaction parameter... 

Here, Mp >s the number average molecular weight before crosslinking, v is the specific volume of the polymer, V, is the molar volume of the swelling agent, 1)2.5 is the polymer volume fraction in the equilibrium-swollen polymer and is the Flory polymer-solvent interaction parameter. 

Values of the polymer-solvent interaction parameters, defined by Eq. (El) in terms of volume fractions, have been collected. They are tabulated as a function of polymer eoncentration for various temperatures. Data given on the basis of segment fractions, sj, or weight fractions, W2, were eonverted into volume fractions ifj. 

The degree to which a cross-linked polymer will swell when immersed in a solvent depends upon the polymer-solvent interaction parameter at the test temperature and the average moleeular weight of the chain segments separating crosslinks (effective chains). This relationship is defined by the Floiy-Rehner equation [89,90]. 

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... 

For high molecular-weight polymer-solvent systems, the polymer critical concentration is close to zero and the interaction parameter has a value close to 0.5. Thus, a good solvent (polymer soluble in the solvent at all proportions) is obtained if < 0.5, whereas values greater than 0.5 indicate poor solvency. Since we mentioned that the model is only an approximate representation of the physical picture and that the FH parameter is often not a constant at all, this empirical rule is certainly subject to some uncertainty. Nevertheless, it has found widespread use and its conclusions are often in good agreement with experiment. 

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.

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). 

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