|
Absorption:
inflection point
Finds the inflection point in the diffusion-relaxation absorption model.
|
|
|
| xF |
|
Weight of Fickian diffusion (fraction,
in [0–1]). |
| kF, kR |
s−1 |
Diffusivity rate, relaxation rate
(both [T]−1). • |
| timef, step |
(min)
(s) |
Final time, graph step. • |
| Transform |
|
Transform function. • |
| tol, .prt |
|
Tolerance, print intermediate results. • |
| Show values |
|
Shows the graph coordinates. |
|
Computes the absorption curve with “Fickian diffusion”
and “relaxation” contributions, following
the Berens-Hopfenberg model, to find its inflection point.
Plots three curves versus √t (option) for:
the function, s (fraction swelling), and its 1.st
(D1) and 2.nd (D2) derivatives.
In the transform option, it is:
D1 = 2 √t ds(t)⁄dt and
D2 = 2 ds⁄dt +
4t d²s⁄dt².
(.xls)
As xF (φ in the program) tends to 0,
the inflection point, tinflect,
tends to 1⁄(2 kR). |
| References: |
Plate: AbsorInflect |
• Rosa, F.,
J. Bordado, M. Casquilho, 2002,
"Kinetics of water absorbency in AA/AMPS copolymers:
applications of a diffusion-relaxation model", Polymer, 43,
pp 63-70 (doi:10.1016/S0032-3861(01)00596-1).
• Fick, Adolf Eugen
(1828-04-01–1901-08-21): Fick's law of diffusion
Wikip., Google
search...
• 1704-07-31: Cramer, Gabriel (1752-01-04). |
