Interaction parameters, polymer

The algorithm we used for solvent/polydisperse polymer equilibria calls for only one solvent/polymer interaction parameter. The interaction parameter (pto) i ed in the algorithm can be determined from essentially any type of ethylene/polyethylene phase equilibrium data. Cloud-point data have been used (18). while Cheng (16) and Harmony ( ) have done so from gas sorption data. 

Vr = Volume fraction of polymer in swollen gel f.1 = Huggins solvent/polymer interaction parameter V0 = Molar volume of solvent (cm3)... 

Light scattering from macromolecules is used routinely to obtain molecular weights, radii of gyration and polymer-solvent and polymer-polymer interaction parameters. A closely related technique, electric field induced light scattering (EFLS) (13,14) has received less attention, but is also potentially useful for polymer characterization. 

Melting Point Depression. A more quantitative evaluation of the relationships existing between lignin structure and blend miscibility is possible through the Tm depression observed in these materials. For semi-crystalline blend systems, such as these, the polymer-polymer interaction parameter, B , can be determined through the following simplified expression (15) ... 

Figure 4. Variation in the polymer-polymer interaction parameter, B with hydroxy content of ethyl lignin (X), lignin acetate (O), unmodified lignin ( ), and hydroxypropyl lignin (—).

Fig. 8. Dependence of the volume traction of network chains within the network, On, on the network-polymer interaction parameter, xnp, for p < p (curve /) and p > pcr (curve 2). Reproduced with permission from Ref. [35]...

Taking into account the modes in which the water can be sorbed in the resin, different models should be considered to describe the overall process. First, the ordinary dissolution of a substance in the polymer may be described by the Flory-Huggins theory which treats the random mixing of an unoriented polymer and a solvent by using the liquid lattice approach. If as is the penetrant external activity, vp the polymer volume fraction and the solvent-polymer interaction parameter, the relationship relating these variables in the case of polymer of infinite molecular weight is as follows ... 

In conclusion, studies of the equilibria between living polymers and their monomers provide means of determining monomer-polymer interaction parameters, and interaction parameters of monomer and polymer with a solvent. 

Analyzes the ability of a paste to spread over a biological surface and calculates the interfacial tension between the two [110], The tension is considered proportional to X1/2, where X is the Flory polymer-polymer interaction parameter. Low values of this parameter correspond to structural similarities between polymers and an increased miscibility... 

Evaluation of the Polymer-Polymer Interaction Parameter from the Equation of State Thermodynamic Theory... 

The values of the polymer-polymer interaction parameter A, calculated by use of the Xi2 and s /s2 values discussed above for the three polymer pairs, are tabulated in Table I. To show the concentration dependence, these values are given for each pair at three different concentrations, corresponding to the weight fraction Wi of the first component equal to 0.1, 0.5, and 0.9. 

In describing the polymer-polymer interaction parameters for pairs which are normally incompatible as those discussed in this work, it therefore appears that the free volume (or the equation-of-state) contribution can usually be neglected except when the pair is on the verge of compatibility. This is in a marked contrast to polymer-solvent systems where the free volume effect is usually very large. From this follows that the dependence of A for polymer-polymer pairs on concentration or on temperature would also be fairly small. Table I shows only a modest variation of A with a change in Wi from 0.1 to 0.9. The relatively more pronounced variation of A for NR/PS as compared with other two pairs still arises mostly from the contact enthalpy term and reflects the larger Sx/s2 ratio for this system. 

Table I. Polymer-Polymer Interaction Parameter A and Its Components ...

Because of these uncertainties, equations 1, 2, 3, 4, and 5 may not be relied upon as a means of quantitative evaluation of A until more data for other polymer-solvent systems become available. The equation-of-state thermodynamics is, however, useful in its ability to give us insight into the physical factors and their relative magnitudes which contribute to the polymer-polymer interaction parameter. The results in this work clearly show that the dependence of A on concentration and temperature is moderate. This gives a justification as a good approximation to the use of a constant polymer-polymer interaction parameter in the polymer interface theories where the polymer concentration encompasses the whole range Wi = 0 to 1 across the phase boundary. 

Kruse, R. L., "Styrene-Polymer Interaction Parameters in High Impact Polystyrene," 141 (1975). 

Narasimhan, V. Huang, R. Y. M. Burns, C. M., "Polymer-Polymer Interaction Parameters of Polystyrene and Polybutadiene from Studies in Solutions of Toluene or Tetrahydro-furan," J. Polym. Sci., Polym. Phys. Ed., 21, 1993 (1983). 

Paxton, T. R., "The Miscibility of Polymers Interaction Parameter for Polybutadiene with Polystyrene," J. Appl. Polym. Sci., 7, 1499 (1963). 

Calculate the melting point of pure PCL and the value of the polymer-polymer interaction parameter, knowing that A//2 = 3690 cal/mol. 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

Polymer-polymer interaction parameters (X23 were calculated using the following expression ... 

Polymer-polymer interaction parameters are summarized for three systems ... 

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