A simple “Width” Method for easy determination of diffusion coefficients with maximum utilization of data

✍ Scribed by G.J. Wei; W.C. Deal Jr.

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 700 KB
• Volume: 87
• Category: Article
• ISSN: 0003-2697
• DOI: 10.1016/0003-2697(78)90693-0

✦ Synopsis

This paper extends the study of Gaussian curves and describes a simple, fast, and reliable Width Method for evaluating diffusion coefficients from the spreading of dcidx vs x curves with time. The procedure involves measuring the widths as a function of time at a number of different heights that are fixed fractions of the maximum heights of the curves. A major advantage of the Width Method is that it allows use of virtually all of the available data, instead of only one height, or one height and one width, from each curve. As a result, with the data from a single experiment, the method can be used to calculate a large number of independent values of the diffusion coefficient, one for each fixed fractional height used: in comparison, most other methods yield only a single value ofD. It is also shown that certain other methods, including the Area'Height Method, the Width/Height Method and the Error Function Method, are mathematically special cases of this more general and, in most cases, simpler method. Finally, procedures are also described by which these principles can be used to calculate diffusion coefficients from c vs x curves. Although more involved than the analysis using dcidx vs x curves, the c vs x method is still simpler than the methods used in analyzing data from fringe patterns using Rayleigh interference optics.