A Simple Mathematical Model for Diffusional Sampler Operation

A simple mathematical model of the molecular basis for the function of a diffusional sampler for dilute mixtures of gaseous contaminants in supporting gases is presented. The model is based on the movement of single molecules of the contaminant between sections of a tubular diffusion path on a step-by-step basis; the length of the step and of each section of the tube are equal to the mean free path, λ, under the specified conditions. When the model is used, the coefficient of diffusion, D, can be calculated from λ and the average velocity, v¯, of the contaminant molecule. Both λ and v¯ were calculated independently using equations which involved the minimum number of assumptions. The value of D so estimated was of the same order as that in the literature, differing by a factor of <2. It should be emphasized that the model represents a statistical, thermodynamic approach to understanding diffusional samplers, and its utility is independent of the means of estimating λ and v¯ for specific gas pairs.