DETERMINATION OF PARAMETERS FOR DYEING KINETICS FROM CONCENTRATION PROFILES
1985 Volume 41 Issue 9 Pages T390-T395
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1985 Volume 41 Issue 9 Pages T390-T395
The diffusion coefficients, D, of dyes in cellulose show a profound concentration dependence at low concentration of electrolytes. At higher concentration of electrolytes, the concentration dependence of D becomes small and the values of D can be regarded to be constant. Although the values of D are often evaluated by an appropriate averaging from the experimental diffusion profiles in the substrate, the reliability and confidence interval of their values have not always been clear.
A method of least squares for finding the fittest values of the constant diffusion coefficient and surface concentration, Co, from the concentration profiles obtained from the method of cylindrical cellophane film roll was presented by reducing the multiple regression analysis to the univariable one [eq. (9)]. Using the initial value of D estimated from the permeation distance, the fittest values of D and Co could be easily obtained. The variance, V, was defined as the weighted residual sum of squares in order to standardize the experimental errors which originated from the large concentration differences in the diffusion profiles [eq. (10)]. The weight, w_??_, was defined by both of the estimated errors for the thickness of a film and absorbance [eqs. (11) and (12)]. It is, therefore, not necessary to make so many measurements for each layer that the value of standard deviation could be obtained. The convergence criterion was checked by the F-test. The validity of assumptions was tested by the value of V. Since main experimental errors were attributed to the local micro-scattering in the thickness of a film, a% of the measured values in the absorbance was estimated to be the standard deviation. The minimal standard deviation, b (absorbance), was estimated from the accuracy of spectrophotometer.
Two examples of calculation for C. I. Direct Yellow 12 and Reactive Red 1 were presented. The D of Yellow 12 was not constant at I=0.1 (ionic strength) and 90°C. That of Red 1 was concluded to be constant at I=0.15, pH 6.7 and 30°C.
