Solubility coefficient effective

Many subtleties associated with ED, for instance, accompanying thermodynamic cooling issues, failure processes, and effects of localized stresses, are discussed in detail in the extensive review on this topic by Briscoe et al. Other workers have observed similar fracture effects arising from rapid temperature increases while maintaining pressure the connection with ED is via Henry s law linking dissolved gas concentration and solubility coefficient, and the fact that solubility coefficient decreases (in an Arrhenius fashion, as it happens) for readily condensable (i.e., less volatile) gases when temperature increases. 

Equation 1 implies that solubility is independent of solvent type, and is only a function of the equilibrium temperature and characteristic properties of the solid phase. In real systems the effect of non-ideality in the liquid phase can significantly impact the solubility. This effect can be correlated using an activity coefficient (y) to account for the non-ideal liquid phase interactions between the dissolved solute and solvent molecules. Eq. 1. then becomes [7,8] ... 

Table 5.3 Solute and solvent solubility isotope effects for (benzene-water) solutions at 306.2 K obtained from IE s on Henry s Law coefficients, Ki and Kn- [Isotope effects on free energies of transfer, ideal gas to solution in the limit of infinite dilution] (Dutta-Choudhury, M., Miljevic, N.

Levis KA, Lane ME and Corrigan OI (2003) Effect of Buffer Media Composition on the Solubility and Effective Permeability Coefficient of Ibuprofen. Int J Pharm 253 pp 49-59. 

The effect of temperature on the Bunsen solubility coefficients of the monoatomic atmospheric gases for seawater of 35%o. Molecular weights are shown in parentheses. 

How can this be No additional gas was added to the water. The answer lies in the nonlinear temperature effect on the Bunsen solubility coefficient (Figure 6.1). Because of the concave nature of the curves relating the Bunsen solubility coefficient to temperature, the result of this type of postequilibration temperature change is always supersaturation. 

Treatment of class (c) membranes, on the other hand, presents a considerably more complicated problem. Here, S and DT in Eqs. (1) and (2) are functions of the spatial coordinates. The problem becomes much more acute if S and DT are also dependent on C 4,5). Under these conditions, transformation of Eqs. (2) into (3) is not generally possible and there are no standard methods, as in the previous cases, of fully characterizing the membrane-penetrant system 3 "5). There is usually no difficulty in determining an overall or effective solubility coefficient but the definition of useful effective diffusion coefficients is a more difficult matter, which, not surprisingly, is a major concern of current research in the field. 

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). 

In terms of Eq. (1), the driving force is ApA and the resistance, f2 = L/Pa. Although the effective skin thickness L is often not known, the so-called permeance, PA/L can be determined by simply measuring the pressure normalized flux, viz., Pa/L = [flux of A]/A/j>a, so this resistance is known. Since the permeability normalizes the effect of the thickness of the membrane, it is a fundamental property of the polymeric material. Fundamental comparisons of material properties should be done on the basis of permeability, rather than permeance. Since permeation involves a coupling of sorption and diffusion steps, the permeability is a product of a thermodynamic factor, SA, called the solubility coefficient, and a kinetic parameter, DA, called the diffusion coefficient. 

The effect of copolymer composition on gas permeability is shown in Table 9. The inherent barrier in VDC copolymers can best be exploited by using films containing litde or no plasticizers and as much VDC as possible. However, the permeability of even completely amorphous copolymers, for example, 60% VDC—40% AN or 50% VDC—50% VC, is low compared to that of other polymers. The primary reason is that diffusion coefficients of molecules in VDC copolymers are very low. This factor, together with the low solubility of many gases in VDC copolymers and the high crystallinity, results in very low permeability. Permeability is affected by the kind and amounts of comonomer as well as crystallinity. A change from PVDC to 50 wt % VC or 40 wt % AN increases permeability 10-fold, but has little effect on the solubility coefficient. 

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. 

It is important to realize, however, that the determination of the substrate-micelle binding constant from solubility data relies entirely on data for saturated solutions and that, in the case of ionic surfactants, differences in the counterion interactions with the micelle and the micelle-substrate complex and activity coefficient effects may seriously complicate the results. In these respects, distribution studies with varying substrate and surfactant concentrations are certainly preferable. In view of the assumptions involved in the derivation and application of equations (10) and (11), the agreement between the K values obtained from kinetic data (equation 10) and those obtained from solubility measurements (equation 11) for several substrate-micelle interactions is certainly both remarkable and significant. 

Broadly considered, solubilities depend in part on nonspecific electrolyte effects and in part on specific effects. The nonspecific effects can be considered in terms of activity coefficients (Chapter 2). But activity-coefficient effects often are negligible compared with the uncertainties arising from disregarded or unknown side reactions and also with uncertainties arising from the crystalline state, the state of hydration, the extent of aging of the precipitate, and intrinsic solubility, all of which may contribute to the solubility of the precipitate. To the extent that each can be identified and measured, each can be accounted for. Nevertheless, the magnitude of unsuspected effects makes it expedient to assume activity coefficients of unity unless otherwise specifically indicated for relatively soluble salts or solutions containing moderate amounts of electrolytes. 

Equation (7-4) indicates that the solubility product includes an activity-coefficient term, a term which has been assumed to be unity up to this time. The introduction to this chapter pointed out that errors arising from neglect of the effects of the activity coefficient are usually small when compared with several uncertainties or side reactions. The activity coefficient in Equation (7-4) depends on the kind and concentration of all electrolytes in solution, not merely those involved directly with the precipitate. The correction to solubility calculations that must be made to account for the activity-coefficient effect is known as the diverse ion effect. The appropriate background is discussed in Chapter 2, and Problems 2-1,2-2, and 2-3 are examples of the calculations. For 1 1 electrolytes in solution, activity coefficients can usually be assumed to be unity when concentrations are much less than 0.1 M. Common ion and diverse ion effects can be significant at the same time, for example, when a large excess of common ion is added in a precipitation. The diverse ion effect is one of the reasons that the haphazard addition of a large excess of precipitant should be avoided. 

Transport through a dense polymer may be considered as an activated process, which can be represented by an Arrhenius type of equation. This implies that temperature may have a large effect on the transport rate. Equations 4.7 and 4.8 express the temperature dependence of the diffusion coefficient and solubility coefficient in Equation 4.5 ... 

Surface-active agents have been widely shown to enhance drug dissolution rates. This may be due to wetting effects, resulting in increased surface area, effects on solubility and effective diffusion coefficient or a combination of effects. Consequently surfactants have been included in tablet and capsule formulations to improve wetting and deaggregation of drug particles and thus increase the surface area of particles available for dissolution. 

When gases dissolve in water without chemical reaction there is generally an evolution of heat. Hence by Le Chatelier s principle an increase in temperature usually leads to a decreased solubility. The effect of temperature on the absorption coefficient may be determined from an equation analogous to the van t Hoff equation ... 

Ostwald solubility coefficient. The graph shows that an anaesthetic gas with a high oil solubility is effective at a low alveolar concentration and has a high potency. This relationship is the basis of the Meyer-Overton hypothesis of anaesthesia. 

The only tricky thing about Bunson and Ostwald solubility coefficients is that they represent a volume of gas per volume of solvent (not solution). Because gases increase the volume of the solution when they dissolve into it, a correction has to be made for this difference. The correction is significant and on the order of 0.14% (Weiss, 1971). The values presented in Table 3.6 have not been corrected for this effect, and since this is a potential point of confusion, we will use the Henry s Law coefficient most often in this book. 

In high-salinity waters such as seawater, both ion-pairing and activity-coefficient effects (see Chap. 4) increase the concentrations of species limited by the solubility of minerals. For example, in pure water saturated with respect to calcite, the molal solubility product ZmCa x ZmCOf" = 10 whereas in seawater this product equals 10 If the concentration of carbonate is constant, this corresponds to a 250-fold increase in the concentration of dissolved calcium in seawater relative to that in pure water. 

The more saline a water, the more soluble minerals tend to be in it, both because of complex formation and activity-coefficient effects (see Chap. 4). 

Increased crystallinity can reduce permeability values because the crystal regions of a polymer are impenetrable in most semicrystalline polymers. Hence, the average value of the solubility coefficient S is reduced. It also means that movement must occur around the crystallites, which means that a longer distance must be traveled. This lowers the effective value of D. 

Besides the above conventional effects, Chapter 3 summarizes data suggesting the ability of some gases to sorb and diffuse inside the actual crystals of poly(4-methyl-l-pentene) (68,69). Finally, Chapter 3 considers liquid crystalline polymers, which seem to form a new class of materials in terms of barrier responses(57). The high barrier nature of liquid crystal polymers appears to be largely due to their unusually low solubility coefficients for typical penetrants. This is quite different from the case for most high barriers like EVOH, and polyacrylonitrile that typically function due to the unusually low mobilities of penetrants in their matrices (70). ... 

Figure X. Effect of amorphous phase content on the solubility coefficients of various gases in semi-crystalline polyethylene. (Data taken from Ref. 19.)...

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