Diffusion solubility coefficient

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 ...

Figures 4 and 5 show how the diffusion coefficient and solubility coefficient vary for a series of linear esters in low density polyethylene film. The trends are generally tme for other permeants in other films. As the size of the permeant increases, the diffusion coefficient decreases and the solubility coefficient increases. Since the increase in solubility coefficient is larger than the decrease in the diffusion coefficient, the permeability actually increases as the permeant size increases.

The temperature dependence of the permeability arises from the temperature dependencies of the diffusion coefficient and the solubility coefficient. Equations 13 and 14 express these dependencies where and are constants, is the activation energy for diffusion, and is the heat of solution... 

It should be recognized that all plastic materials over a time period allow a certain amount of water vapor, organic gas, or liquid to permeate the thickness of the material. It is only a matter of degree of permeation between various materials used as barriers against vapors and gases. It has been found that the permeability coefficient is a function of the solubility coefficient and diffusion coefficient. The process of permeation is explained as the solution of the vapor into the incoming surface of the barrier, followed by diffusion through the barrier thickness, and evaporation on the exit side. 

R is the gas constant Dq and activation energy Eu are constants derived from an Arrhenius plot for diffusion coefficients applying at different temperatures, and solubility coefficient was obtained from a separate permeation test at TiK. Suitable testing using a specially constmcted permeation cell water-cooled at one end provided good validation data. 

For gases, both permeation and diffusion data are best measured by permeation tests, many different types been described elsewhere. The same sheet membrane permeation test can quantify permeation coefficient Q, diffusion coefficient D, solubility coefficient s, and concentration c. The membrane, of known area and thickness, must be completely sealed to separate the high-pressure (initial) region from that containing the permeated gas it may need an open-grid support to withstand the pressure. The permeant must be suitably detected and quantified (e.g., by pressure or volume buildup, infrared (IR) spectroscopy, ultraviolet (UV), gas chromatography, etc.). 

Permeability (P) is usually defined as the product of a thermodynamic property and a transport property which are, respectively, the partition or solubility coefficient, K, and the diffusion coefficient, D. This partition coefficient is defined as the ratio at equilibrium of the solute concentration inside the gel to that in solution. A value of K less than 1 indicates that the solute favors the solution... 

Diffusion is generally measured as increase in mass, increasing and then levelling off at a saturation level which depends on the solubility coefficient. As a general rule the rate of mass increase and the time to equilibrium are proportional to the square of thickness. When the diffusion coefficient is known a suggested estimation of the time to reach equilibrium to a depth b is ... 

Both the diffusion coefficient and the solubility coefficient vary with temperature in accordance with an Arrhenius relationship. The diffusion coefficient increases with temperature, but the solubility coefficient increases for gases and decreases for vapours. For a full treatment of absorption a text on mass transport should be consulted. 

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... 

Contaminant precipitation involves accumulation of a substance to form a new bulk solid phase. Sposito (1984) noted that both adsorption and precipitation imply a loss of material from the aqueous phase, but adsorption is inherently two-dimensional (occurring on the solid phase surface) while precipitation is inherently three-dimensional (occurring within pores and along solid phase boundaries). The chemical bonds that develop due to formation of the solid phase in both cases can be very similar. Moreover, mixtures of precipitates can result in heterogeneous solids with one component restricted to a thin outer layer, because of poor diffusion. Precipitate formation takes place when solubility limits are reached and occurs on a microscale between and within aggregates that constitute the subsurface solid phase. In the presence of lamellar charged particles with impurities, precipitation of cationic pollutants, for example, might occur even at concentrations below saturation (with respect to the theoretical solubility coefficient of the solvent). 

The permeability coefficient P is related to the diffusion coefficient D, and the solubility coefficient S as shown by Henry s law ... 

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. 

If the component phases denoted by A and B are of sufficient, but still microscopic, size (cf. introductory section) and do not interact appreciably, their individual sorption and diffusion properties may be deduced from measurements on the pure bulk phases. Then, the overall solubility coefficient is given by an additive relation analogous to Eq. (5), except that the volume fractions vA, vB( = 1 — vA) of the respective components in the membranes must be taken into account ... 

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). 

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... 

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