Solubility coefficient, polymer

Table 11. Diffusion Coefficients and Solubility Coefficients of Selected Penetrants in Polymers at 25°C ...

Table 5. Diffusion and Solubility Coefficients for Oxygen and Carbon Dioxide in Selected Polymers at 23°C, Dry ...

The solubihty coefficients are more difficult to predict. Although advances are being made, the best method is probably to use a few known solubility coefficients in the polymer to predict others with a simple plot of S vs ( poiy perm Y where and are the solubility parameters of the polymer and permeant respectively. When insufficient data are available, S at 25°C can be estimated with equation 19 where k = 1 and the resulting units of cal/cm are converted to kj /mol by dividing by the polymer density and multiplying by the molecular mass of the permeant and by 4.184 (16). 

The interrelationships of the various coefficients associated with fluid uptake (Section 23.4.2) mean that it should be possible to estimate a rate for one of the uptake phenomena from test data for another of them. Campion proposed using this approach to estimate permeation coefficient Q from solubility coefficient s. The form of a liquid absorption plot (Figure 23.6, Section 23.4.4.1) is such that s should be obtainable from it, and inspection showed that this link was via Henry s law with concentration corrected by the polymer density p. The following expression was derived for s ... 

K., The correlation of polymer-water and octanol-water coefficients Estimation of drug solubilities in polymers, Int. J. Pharm., 45, 1-11, 1988. 

By using a PES with a different thickness, one can conveniently change the AV ratio. This approach permits some control over the time required to reach equilibrium concentrations. Bartkow et al. (2004) has reported an excellent example of the impact of ratio or thickness on the time to equilibrium. These investigators showed that a 200 pm thick PE sheet took twice as long to reach equilibrium in air as a 100 pm thick PE sheet. In theory, changing membrane thickness will not affect polymer diffusivity and equilibrium membrane-water partition coefficients (I mwS) or solubility coefficients ( p). However, in practice different values of (membrane-air partition coefficient) and membrane... 

For both HA and its esters, the solubility coefficient, defined as the ratio between water concentration in the polymer and the water relative pressure (S = cw/relative pressure), did not strictly increase with concentration (Tables 1-4). For example, at low water concentrations the solubility coefficient decreased with concentration, whereas an opposite trend was shown at higher water concentrations. The solubility coefficient attained a minimum relative pressure of about 0.6 for all the materials tested. 

According to the Flory-Huggins theory of polymer solutions, if the mixing process were driven only by an entropic gradient (nonpolar solvent) the solubility coefficient... 

Among the many industrial applications, one can recall the analyses on carbon black, where FIFFF and SdFFF were used in synergy, and on carbon nanotube, for which a frit inlet AsFlFFF channel was used. Water-soluble polydisperse polymers were fractionated, with a very high selectivity, according to differences in the diffusion coefficient, yielding a diffusion coefficient spectrum which was then converted into a molecular weight (M) distribution curve based on the relationship between D and molecular weight [36]. 

He also showed that the size of the gas molecule is an important factor and that the solubility coefficient S of gases in amorphous polymers can be calculated from the following expression, which relates the critical temperature Tcl and boiling point Tb ... 

TABLE 2 DIFFLTSION AND SOLUBILITY COEFFICIENTS FOR OXYGEN AND CARBON DIOXIDE IN SELECTED POLYMERS AT 2LC, DRY... 

Polyethylene terephthalate) (PET), with an oxygen permeability of 8 iiiuol/(ius-GPa), is not considered a barrier polymer by die old definition however, it is an adequate barrier polymer for holding carbon dioxide in a 2-L bottle for carbonated soft drinks. The solubility coefficients for carbon dioxide are much larger than for oxygen. For the case of the PET soft drink bottle, the principal mechanism for loss of carbon dioxide is by sorption in the bottle walls as 500 kPa (5 atm) of carbon dioxide equilibrates with the polymer. For an average wall thickness of 370 pm (14.5 mil) and a permeabdity of 40 nmol/(m-s-GPa), many months are required to lose enough carbon dioxide (15% of initial) to be objectionable. 

The diffusion and solubility coefficients for oxygen and carbon dioxide in selected polymers have been collected in Table 2. 

Table 4 contains some selected permeability data, including diffusion and solubility coefficients foT flavors in polymers used in food packaging. Generally, vtuylidene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation, whereas the polyolefins are poor barriers. Comparison to Table 2 shows lhat the large-molecule diffusion coefficients are 1000 or more times lower tli an the small-molecule coefficients. 

Reasonable prediction can be made of the permeabilities of low molecular weight gases such as oxygen, nitrogen, and carbon dioxide in many polymers. The diffusion coefficients arc not complicated by the shape of the penneant, and the solubility coefficients of each of these molecules do not vary much from polymer to polymer. Hence, all that is required is some correlation of the penneant size and the size of holes in the polymer matrix. Reasonable predictions of the pemieabilides of larger molecules such as flavors, aromas, and solvents are not easily made, The... 

Flavor and Aroma Transport. Many methods are used to characterize the transport of flavor, aroma, and solvent molecules in polymers. Each lias some value, and no one method is suitable for all situations. Any experiment should obtain the permeability, the diffusion coefficient, and the solubility coefficient. Furthermore, experimental variables might include the temperature, the humidity, the flavor concentration, and the effect of competing flavors. 

Nonlinear, pressure-dependent sorption and transport of gases and vapors in glassy polymers have been observed frequently. The effect of pressure on the observable variables, solubility coefficient, permeability coefficient and diffusion timelag, is well documented (1, 2). Previous attempts to explain the pressure-dependent sorption and transport properties in glassy polymers can be classified as concentration-dependent and "dual-mode models. While the former deal mainly with vapor-polymer systems (1) the latter are unique for gas-glassy polymer systems (2). 

The solubility coefficients of gases in glassy polymers are not constant, but decrease with increasing concentration of the gas in the polymers (2). Calculations of the isosteric enthalpy of sorption in several gas-polymer systems confirm that the gas-polymer affinity is reduced with increasing sorbed gas concentrations (24, 25, 26). The change in the isosteric enthalpy of sorption is a result of the changes in the polymer matrix induced by the presence of the sorbed gas. 

We have shown previously (10) that based on Geefs thermodynamic analysis of gas solubility in polymers (12) and the theory of corresponding states (14), the solubility coefficient, a, can be expressed as,... 

In the limit of zero-concentration, gas-glassy polymer systems behave "ideally. As the gas concentration in the membrane approaches zero the solubility coefficient becomes constant with the value ao [eqs. (1), (3) and (4)]. In the same limit, the diffusion coefficients are constant and equal to the diffusion coefficient Do, [eqs. (5), (7), (8) and (9)]. As typical of limiting values, ao and Do have no correspondence to... 

The concentration of sorbed gas in the polymer is the product of the solubility coefficient and the gas pressure p,... 

In the following sections the factors that determine the magnitude of diffusion and solubility coefficients in polymers are discussed. 

Figure 4.1 Schematic illustration of how the (a) diffusion coefficient of penetrants depend on their size in rubbery and glassy polymers and (b) solubility coefficients for penetrants depend on their condensability.

The factors affecting the selectivity and permeability of polymer membranes to different gases are best discussed on the basis of Eqs. (12) and (14). As noted in Eq. (12), the permeability coefficient, P, of a penetrant gas in a polymer membrane is the product of a (concentration-averaged) diffusion coefficient, D, and of a solubility coefficient,... 

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