Effect of variable storage times on the calculation of diffusion coefficients characterizing small molecule migration in polymers

Abstract

The error which results from calculation of a diffusion coefficient from desorption measurements which fail to account for the nonuniform concentration profile developed during prior sample storage is determined for the case of migration from a plane sheet into an infinite, well-stlrred bath. The incorrectly calculated diffusion coefficient, D', neglecting prior storage time, is smaller than the actual diffusion coefficient, D. For small storage times, the ratio D'JD is close to unity; however, D'JD approaches an asymptotic value of 0.70 for very large storage times if the well-known "half-time'' method is employed for evaluating the diffusion coefficients. I f the so-called "initial slope" method is used for determination of diffusion coefficients, the calculational error is large, with the ratio D'lD approaching zero for large storage time. A sigmoid response in plots of fractional loss vs. the square root of time is sometimes taken as evidence for the existence of non-Fickian transport processes. It is shown here that such sigmoid plots are also observed when elution occurs prior to the initiation of the formal desorption experiment, even when Fickian transport controls the desorption process.

Hygrothermal analysis for the electrochemical migration failure in multi-chip packages during a highly accelerated stress test

“…Examples are the half-time method, part of the JEDEC standard [4], with only a few percent of error; and the initial slope method, which is derived from an approximation of Gaussian error function. [5][6] Exponential curve fitting [7] can also be used. In this work, each point of diffusivity D was obtained by exponential curve fitting with the equation below.…”

“…Second, the normalized analogy uses a normalized field variable known as the wetness variable. [10] w = M t /M sat ( 5 ) Last, the advanced analogy uses the modified solubility, as mentioned above. Therefore, the field variable in the advanced analogy is scaled by the boundary conditions.…”

Simulation of Water and Flavor Migration during Storage of Tobacco Products.

“…In particular, it is widely recognized as a serious problem that the migration of water and various flavors may fail to maintain desirable smoke odor and taste during storage inside a vending machine in the summer. In the food technologies field, many papers have been published with reference to the migrations or losses of flavors caused by sorption, as well as adsorption and permeation (Ayres et al, 1983;Farrell, 1988;Mohney et al, 1988;Ikegami et al, 1991; Letinski & Halek, 1992).…”

Permeation of Water and Volatile Flavors through Packaging Films.

“…In these papers, several types of equipment have been used for the measurement of the permeation and diffusion as well as sorption by means of the transient response or the steady-state transmission (Rogers et al, 1960;Pasternak et al, 1970;Paul & Kemp, 1973;Shimoda et al, 1987a). Furtherrnore, Rogers et al (1960) and Takeuchi & Okamura (1976) Other detailed studies in terms of the diffusion through the various films have also been published elsewhere (Frisch, 1957;Ayres et al, 1983). Salame & Steingiser (1977) predicted the effect of the chemical structure as well as the configuration of polymer molecules in the films on the permeation properties.…”