Diffusion solubility parameter

C. M. Hansen, The Three-Dimensional Solubility Parameter and Solvent Diffusion Coefficient, Danish Technical Press, Copenhagen, Denmark, 1967. 

Plasticizers reduce hardness, enhance tack and reduce cost in rubber base adhesive formulations. A plasticizer must be easily miscible and highly compatible with other ingredients in the formulations and with the surfaces to which the adhesive is applied. The compatibility and miscibility of plasticizers can be estimated from the solubility parameter values. Most of plasticizers have solubility parameters ranging between 8.5 and 10.5 hildebrands. However, the high miscibility and compatibility also lead to easier diffusion of the plasticizer to the surface, decreasing the adhesion properties. Therefore, plasticizers should be carefully selected and generally combinations of two or more of them are used. 

In the high concentration regime, our SCP is different from a typical SCP observed in Case II diffusion. Specifically, our SCP lacks the sharp solvent front(fig.8). The abrupt increase in solvent concentration normally observed is due to the long relaxation time of the polymer chain in response to solvent plasticization. Then, the absence of this feature points to a very rapid relaxation of PMMA chains by MEK. This is probably due to a good match in the solubility parameters of PMMA and MEK ( =9.3 for both). 

Thus, the permeability values are high when the solubility parameters of the diffusion molecules are similar to that of the polymer film. 

The volatility, viscosity, diffusion coefficient and relaxation rates of solvents are closely connected with the self-association of the solvents, described quantitatively by their structuredness. This property has several aspects that can be denoted by appropriate epithets (Bennetto and Caldin 1971). One of them is stiffness expressible by the internal pressure, the cohesive energy density, the square of the solubility parameter, see Chapter 3, or the difference between these two. Another aspect is openness expressible by the compressibility or the fluidity, the reciprocal of the viscosity, of the solvent (see Chapter 3). A further... 

This approach to estimating solubilities and diffusion rates has not been applied to other classes of solutes, even though the solubility parameters can be easily estimated by group contribution methods and AHf and T can be determined by differential scanning calorimetry. 

Given information on the characteristic diffusion coefficients of the two polymers, it is then possible to estimate their relative permeabilities. The slope of the correlation line is a measure of the polarity of the polymer the lower the slope, the greater the solubility of a hydrophilic drug. The anticipated correlation between the slope and the solubility parameter of the polymer is approximately observed (cf Tables II, III). 

The various approaches to estimating diffusion coefficients and solubilities of drugs in polymers have been reviewed. The polymers typically used for drug delivery have diffusion coefficients that are characteristic of the polymer and relatively constant for drugs of a similar molecular size. Drug solubilities in a polymer can be estimated from the solubility parameters and melting points (steroids), from the melting point alone, or from the correlation of partition coefficients. 

Equations describing the release characteristics of the frustum-shaped cells correlate quite well with experiments involving the release of the test compound ethyl p-aminobenzoate dispersed in a Silastic matrix. Experimental parameters include diffusivity, solubility, suspension concentration, declination angle, and opening radius. 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

Prior to this discovery, in 1954 Silberberg and Kuhn (62) were first to study the polymer-in-polymer emulsion containing ethylcellulose and polystyrene in a nonaqueous solvent, benzene. The mechanisms of polymer emulsification, demixing, and phase reversal were studied. Wetzel and Hocks discovery would then equate the pressure-sensitive adhesive to a polymer-polymer emulsion instead of a polymer-polymer suspension. Since the interface is liquid-liquid, the adhesion then becomes one type of R-R adhesion (35, 36). According to our previous discussion, diffusion is not operative unless both resin and rubber have an identical solubility parameter. The major interfacial interaction is physical adsorption, which, in turn, determines adhesion. Our previous work on the wettability of elastomers (37, 38) can help predict adhesion results. Detailed studies on the function of tackifiers have been made by Wetzel and Alexander (69), and by Hock (20, 21), and therefore the subject requires no further elaboration. 

It can be anticipated that prediction of diffiisivities should be best with larger particles since the diffusion path is physically longer. A few simulation runs with different values of diffusivity, solubility and external mass transfer coefficient, show that the most sensitive parameter (or resistance) are intraparticle diffusivity and solubility while the effect of external mass transfer coefficient is small. 

Diffusion Theory. The diffusion theory of adhesion is mostly applied to polymers. It assumes mutual solubility of the adherend and adhesive to form a true interpliase. The solubility parameter, the square root of the cohesive energy density of a material, provides a measure of the intemiolecular interactions occurring witliin the material. Thermodynamically, solutions of two materials are most likely to occur when the solubility parameter of one material is equal to that of the other. Thus, the observation that "like dissolves like." In other words, the adhesion between two polymeric materials, one an adherend, the other an adhesive, is maximized when the solubility parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubility between adhesive and adherend. The diffusion theory is not applicable to substantially dissimilar materials, such as polymers on metals, and is normally not applicable to adhesion between substantially dissimilar polymers. 

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