Solubility coefficients

The solubility coefficient indicates the sorption capacity of a polymer with respect to a particular sorbate. The simplest solubility coefficient is defined by Henry s law of solubility, which is valid at low concentration values for most substances. For other combinations, such as CO2 in PET at high pressure, Henry s and Langmuir s laws must be combined. These are also discussed in Chapter 14. 

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Solubility, aqueous Solubility coefficient Solubility coefficients Solubility diagrams Solubility parameter Solubility parameters Solubility products... 

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.

Fig. 5. Solubility coefficient at 30°C versus boiling point of ester in a low density polyethylene film (18). For unit conversion see equation 6.

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... 

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 solubility coefficient S is used as a measure of water solubility. It is the ratio between the concentrations in water and air phases at equilibrium. Ethanol, a very soluble gas, has a solubility coefficient of 1 100 at, 37 C while the coefficient for nitrous oxide, a poorly soluble gas, is 0.1.5. 

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. 

These relative solubility coefficients completely define the character of the partial and total pressure curves of binary mixtures. 

Adsorption of a fluid quantified by the surface solubility coefficient according to Henry s law... 

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. 

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 ... 

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.). 

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. 

Solubility coefficient (4) Response function x, y, z Cartesian coordinates... 

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. 

The Ostwald solubility coefficient is, therefore, independent of the partial pressure. 

Potency is described by the minimum alveolar concentration (MAC) of an agent and lipid solubility by the oil gas solubility coefficient. 

Xenon 131 kDa boiling point —108 °C blood gas solubility coefficient 14 oibgas solubility coefficient 1.9 MAC 71 odourless. 

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