Interaction thermodynamic

The relationship between the physical properties of a blend and those of its components can depend on the thermodynamic interaction between the components and many other factors. Some generalizations are possible, but exceptions are common and fundamental understanding for some properties remains incomplete in spite of the central importance of this issue in blend technology. 

The thermodynamic linear expansion factor has been related to Flory or thermodynamic interaction parameter, %, and the entropy of dilution parameter, Xs, through the Flory-Fox [10] equations. 

Guner, A., Kibarer, G. 2001. The important role of thermodynamic interaction parameter in the determination of theta temperature, dextran/water system. European Polymer Journal, 37, 619-622. 

It is worth while to present in some detail the derivation of appropriate expressions for the thermodynamic interactions between segments occurring in the same volume element. Not only are such expressions essential for the present objective, they will be used also in the treatment of intramolecular interactions given in Chapter XIV. 

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 the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

Secondly, a depends on the intensity of the thermodynamic interaction as expressed by t/ i(1 —0/T), which is equal to ypi—Ki (see Chap. XII, p. 523). The larger this factor, the greater the value of a for a given M. As should have been expected, therefore, the better the solvent the greater the swelling of the molecule. Conversely, the... 

The estimation of f from Stokes law when the bead is similar in size to a solvent molecule represents a dubious application of a classical equation derived for a continuous medium to a molecular phenomenon. The value used for f above could be considerably in error. Hence the real test of whether or not it is justifiable to neglect the second term in Eq. (19) is to be sought in experiment. It should be remarked also that the Kirkwood-Riseman theory, including their theory of viscosity to be discussed below, has been developed on the assumption that the hydrodynamics of the molecule, like its thermodynamic interactions, are equivalent to those of a cloud distribution of independent beads. A better approximation to the actual molecule would consist of a cylinder of roughly uniform cross section bent irregularly into a random, tortuous configuration. The accuracy with which the cloud model represents the behavior of the real polymer chain can be decided at present only from analysis of experimental data. 

If we now calculate Cm from Eq. (7), the results of the foregoing analysis yield numerical values for the entropy of dilution parameters ypi in the various solvents. From the 0 s obtained simultaneously, the heat of dilution parameter Ki — 0 pi/T may be computed. To recapitulate, the value of in conjunction with gives at once Cm i(1--0/T). Acceptance of the value of Cm given by Eq. (7) as numerically correct makes possible the evaluation of the total thermodynamic interaction i(l —0/7"), which is equal to ( i—/ci). If the temperature coefficient is known, this quantity may be resolved into its entropy and energy components. 

In order to understand polymer solution behaviour, the samples have to be characterised with respect to their molecular configuration, their molar mass and polydispersity, the polymer concentration and the shear rate. Classical techniques of polymer characterisation (light scattering, viscometry, ultracentrifugation, etc.) yield information on the solution structure and conformation of single macromolecules, as well as on the thermodynamic interactions with the solvent. In technical concentrations the behaviour of the dissolved polymer is more complicated because additional intramolecular and intermolecular interactions between polymer segments appear. 

The value of 3.5 x 10 / for the solubility product of CaS0o l/2 H20(s) was derived from 1imestone/magnesia scrubber inlet liquor analyses obtained at the Environmental Protection Agency (EPA) Shawnee test facility (9), and may include kinetic, as well as thermodynamic, interaction between slurry solids and liquor. 

All measurements, of course, have to be made at a finite concentration. This implies that interparticle interactions cannot be fully neglected. However, in very dilute solutions we can safely assume that more than two particles have only an extremely small chance to meet [72]. Thus only the interaction between two particles has to be considered. There are two types of interaction between particles in solution. One results from thermodynamic interactions (repulsion or attraction), and the other is caused by the distortion of the laminar fiow due to the presence of the macromolecules. If the particles are isolated only the laminar flow field is perturbed, and this determines the intrinsic viscosity but when the particles come closer together the distorted flow fields start to overlap and cause a further increase of the viscosity. The latter is called the hydrodynamic interaction and was calculated by Oseen to various approximations [3,73]. Figure 7 elucidates the effect. 

In all hydrodynamic methods we have the effect of both the hydrodynamic and thermodynamic interactions and these do not contribute additively but are coupled. This explains why the theoretical treatment of [77] and of the concentration dependence of has been so difficult. So far a satisfactory result could be achieved only for flexible linear chains [3, 73]. Fortunately, the thermodynamic interaction alone can be measured by static scattering techniques (or osmotic pressure measurement) when the scattering intensity is extrapolated to zero scattering angle (forward scattering). Statistical thermodynamics demonstrate that this forward scattering is given by the osmotic compressibility dc/dn as [74,75]... 

The rapid transport of the linear, flexible polymer was found to be markedly dependent on the concentration of the second polymer. While no systematic studies were performed on these ternary systems, it was argued that the rapid rates of transport could be understood in terms of the dominance of strong thermodynamic interactions between polymer components overcoming the effect of frictional interactions this would give rise to increasing apparent diffusion coefficients with concentration 28-45i. This is analogous to the resulting interplay of these parameters associated with binary diffusion of polymers. 

The size of a polymer molecule in solution is influenced by both the excluded volume effect and thermodynamic interactions between polymer segments and the solvent, so that in general =t= . The Flory (/S) expansion factor a is introduced to express this effect, by writing ... 

Edsman, K., Sundelof, L.-O. (1987). Determination of thermodynamic interaction in mixed polymer solutions by a rapid and precise osmotic method the system dex-tran/polyvinyl-pyrrolidone/water. Polymer, 28, 2261-2214. 

Tager and co-workers (51) have invoked bundle structures to explain correlations between the viscosities of concentrated polymer solutions and the thermodynamic interactions between polymer and solvent. They note, for example, that solutions of polystyrene in decalin (a poor solvent) have higher viscosities than in ethyl benzene (a good solvent) at the same concentration, and quote a number of other examples. Such results are attributed to the ability of good solvents to break up the bundle structure the bundles presumably persist in poor solvents and give rise to a higher viscosity. It seems possible that such behavior could also be explained, at least in part, by the effects of solvent on free volume (see Section 5). Berry and Fox have found, for example, that concentrated solution data on polyvinyl acetate in solvents erf quite different thermodynamic interaction could be reduced satisfactorily by free volume considerations alone (16). Differences due to solvent which remain after correction for free volume... 

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