mono_gauss_coil¶
Scattering from monodisperse polymer coils
Parameter |
Description |
Units |
Default value |
---|---|---|---|
scale |
Scale factor or Volume fraction |
None |
1 |
background |
Source background |
cm-1 |
0.001 |
i_zero |
Intensity at q=0 |
cm-1 |
70 |
rg |
Radius of gyration |
Å |
75 |
The returned value is scaled to units of cm-1 sr-1, absolute scale.
This Debye Gaussian coil model strictly describes the scattering from monodisperse polymer chains in theta solvents or polymer melts, conditions under which the distances between segments follow a Gaussian distribution. Provided the number of segments is large (ie, high molecular weight polymers) the single-chain form factor P(Q) is that described by Debye (1947).
To describe the scattering from polydisperse polymer chains see the poly_gauss_coil model.
Definition
where
Here, \(\phi_\text{poly}\) is the volume fraction of polymer, \(V\) is the volume of a polymer coil, M is the molecular weight of the polymer, \(N_A\) is Avogadro’s Number, \(\delta\) is the bulk density of the polymer, \(\rho_\text{poly}\) is the sld of the polymer, \(\rho\text{solv}\) is the sld of the solvent, and \(R_g\) is the radius of gyration of the polymer coil.
The 2D scattering intensity is calculated in the same way as the 1D, but where the q vector is redefined as
Source
mono_gauss_coil.py
\(\ \star\ \) mono_gauss_coil.c
References
P Debye, J. Phys. Colloid. Chem., 51 (1947) 18.
R J Roe, Methods of X-Ray and Neutron Scattering in Polymer Science, Oxford University Press, New York (2000).
http://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_28.pdf
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