Penetrant concentration

Some concerns directly related to a tomizer operation include inadequate mixing of Hquid and gas, incomplete droplet evaporation, hydrodynamic instabiHty, formation of nonuniform sprays, uneven deposition of Hquid particles on soHd surfaces, and drifting of small droplets. Other possible problems include difficulty in achieving ignition, poor combustion efficiency, and incorrect rates of evaporation, chemical reaction, solidification, or deposition. Atomizers must also provide the desired spray angle and pattern, penetration, concentration, and particle size distribution. In certain appHcations, they must handle high viscosity or non-Newtonian fluids, or provide extremely fine sprays for rapid cooling. 

A typical sorption experiment involves exposing a polymer sample, initially at an equilibrium penetrant concentration of c to a bathing penetrant concentration of Ci. The weight gain or loss is then measured as a function of time. The term sorption used in this context includes both absorption and desorption. The sorption is of the integral type if c° = 0 in the case of absorption or if cf = 0 in the case of desorption. Details of the experimental setup for the sorption measurement are discussed elsewhere [4],... 

In the absense of any dependence of S and DT on penetrant concentration, the sorption and steady-state permeation properties of the membrane are described by effective solubility and permeability or diffusion coefficients given by... 

At such extraordinarily low penetrant concentrations, plasticization of the overall matrix is certainly not anticipated. Motions involving relatively few repeat units are believed to give rise to most short term glassy state properties. In rubbery polymers, on the other hand, longer chain concerted motions occur over relatively short time scales, and one expects plasticization to be easier to induce in these materials. Interestingly, no known transport studies in rubbers have indicated plasticization at the low sorption levels noted above for PVC and PET. 

The permeability of a polymer to a penetrant depends on the multiplicative contribution of a solubility and a mobility term. These two factors may be functions of local penetrant concentration in the general case as indicated by the dual mode model. Robeson (31) has presented data for CO2 permeation in... 

Crank, Park, Long, Barrer and their co-workers (5) have shown that D and D can be represented as exponential functions of penetrant concentration. Aitken and Barrer (33) used successfully a linear expression to describe the concentration... 

Salicylic acid can be helpful as a monotherapy. Witman reported that it is most commonly used in combination with corticosteroids, enhancing their penetration. Concentration of salicylic acid used for this purpose is 2 to 10%.2 Such combinations require compounding by a pharmacist and carry the risk of imprecise formulations that are potentially unstable, unsafe, or ineffective.2... 

Having mentioned the correlative capabilities of this model, one can consider its semi-predictive abilities. It was mentioned that a number of diffusion data taken from a limited range of penetrant concentrations are required to calculate two of the parameters of the model. Once these parameters have been determined, one can make theoretical predictions for diffusion coefficients over a wider range of penetrant concentration or temperature variation. This is a critical test for any theoretical model,... 

Pi)si, and D all converge to the same value at the limit of zero penetrant concentration. This limiting value shall be denoted by a symbol D0. It is important to observe that Eqs. (2) and (3) are valid for one-dimensional diffusion. It appears that no corresponding equation is as yet known for diffusion in higher dimensions. 

One of the central problems in the study of diffusion is to evaluate D for a given system as a function of such parameters as penetrant concentration and temperature. For polymer-penetrant systems with which we are concerned in this article two experimental methods are typical for this purpose. They are the sorption method and the permeation method. 

According to the thermodynamics of irreversible processes, the mutual diffusion coefficient D may be a function of penetrant concentration ct, position x, and time t. In the present chapter we shall discuss sorption behavior of systems in which D varies with cx only, and shall use the notation D (cx) to indicate this condition. It is assumed that the sample film is so thin that diffusion takes place effectively in the direction of its thickness. At the beginning of an absorption or a desorption experiment the film is conditioned so that Cj is uniform everywhere in it. This initial concentration is denoted by cf. Then we have... 

Various methods have been proposed for the evaluation of D as a function of penetrant concentration from sorption measurements. They all are applicable only for sorption data of the Fickian type, and may be classified into two groups. Methods belonging to one group utilize data for the initial slope of the reduced sorption curve, while the ones belonging to the other group resort to rates at which M (<) approaches the equilibrium value Since little work has yet been done to adapt the approach-to-equihbrium data for concentration-dependent D, the subsequent discussion will be confined to methods of the former group only. 

Fig. 2. Plots of various diffusion coefficients against penetrant concentration for the system polymethyl acrylate — benzene at 30° C o jD fromDa. D fromDj. (x) CfromD (determined from 5teady state permeabilities). Taken from unpublished paper of Kishimoto and Enda...

Fig. 3. Plots of D against penetrant concentration for the system polymethyl acrylate — ethyl acetate at different temperatures [Fujita, Kishimoto and Matsumoto (I960)]...

Here it is assumed that y > ft for all values of penetrant concentration. In Fig. 10 is shown the family of successive differential curves calculated from Eq. (1) with Eq. (17) as the boundary equation in these calculations... 

The quantity f(0,T), which is the value of / at zero penetrant concentration, represents the average fractional free volume in the pure polymer. As will be expected from its definition, the quantity y(T) may be compared with the fractional free volume of the diluent. A similar conclusion has been deduced by Ferry and Stratton (1960). 

By combining Eqs. (29) and (30) and then specifying the resulting relation for zero penetrant concentration one can derive for D0... 

Fig. 14. Correlation between D9 D value at zero penetrant concentration) and (viscosity of pure polymer) o polymethyi...

A final advantage of rubbery, amorphous polymers is that their sorption isotherms are often linear over relatively large ranges in penetrant concentration. Appendix C lists some common polymers that have been used as sensor coatings along with their Tg, Tfn, and monomer repeat unit structure. 

Case II transport occurs when the sorption is entirely controlled by stress-induced relaxations taking place at a sharp boundary separating an outer swollen shell, essentially at equihbrium penetrant concentration, from an unpenetrated glassy core. Ideally, this sharp boundary moves through the polymer at a constant velocity during case II transport. Super-case II transport occurs when the velocity of the case II sorption boundary is sufficiently slow so that a Fickian tail may develop ahead of the sorption discontinuity [63]. 

In the limit of low penetrant concentration, it reduces to the following form (Vrentas and Duda, 1978) ... 

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