gel_fit¶
Fitting using fine-scale polymer distribution in a gel.
Parameter |
Description |
Units |
Default value |
---|---|---|---|
scale |
Scale factor or Volume fraction |
None |
1 |
background |
Source background |
cm-1 |
0.001 |
guinier_scale |
Guinier term scale |
cm^-1 |
1.7 |
lorentz_scale |
Lorentz term scale |
cm^-1 |
3.5 |
rg |
Radius of gyration |
Å |
104 |
fractal_dim |
Fractal exponent |
None |
2 |
cor_length |
Correlation length |
Å |
16 |
The returned value is scaled to units of cm-1 sr-1, absolute scale.
This model was implemented by an interested user!
Unlike a concentrated polymer solution, the fine-scale polymer distribution in a gel involves at least two characteristic length scales, a shorter correlation length (\(\xi\)) to describe the rapid fluctuations in the position of the polymer chains that ensure thermodynamic equilibrium (based on an Ornstein-Zernicke, or Lorentz, model), and a longer distance (denoted here as \(R_g\)) needed to account for the static accumulations of polymer pinned down by junction points or clusters of such points (based on a simple Guinier model). The relative contributions of these two contributions, \(I_L(0)\) and \(I_G(0)\), are parameterised as lorentz_scale and guinier_scale, respectively.
See also the lorentz model and the gauss_lorentz_gel model.
Definition
The scattered intensity \(I(q)\) is calculated as
Note that the first term reduces to the Ornstein-Zernicke equation when the fractal dimension \(D = 2\); ie, when the Flory exponent is 0.5 (theta conditions). In gels with significant hydrogen bonding \(D\) has been reported to be ~2.6 to 2.8.
Source
gel_fit.py
\(\ \star\ \) gel_fit.c
References
Mitsuhiro Shibayama, Toyoichi Tanaka, Charles C Han, J. Chem. Phys. 1992, 97 (9), 6829-6841. DOI: 10.1063/1.463637
Simon Mallam, Ferenc Horkay, Anne-Marie Hecht, Adrian R Rennie, Erik Geissler, Macromolecules 1991, 24, 543-548. DOI: 10.1021/MA00002A031
Authorship and Verification
Author:
Last Modified by: Steve King Date: November 22, 2022
Last Reviewed by: Paul Kienzle Date: November 21, 2022