6.2

\(\renewcommand\AA{\unicode{x212B}}\)

EISFDiffSphereAlkyl

Description

../../_images/EISFDiffSphereAlkyl_1.png

This fitting function models the elastic incoherent intensity of a linear polycarbon chain (alkyl) where the local diffusion of each unit in the chain is modeled as undergoing continuous diffusion but confined to a spherical volume whose radius varies from a minimal value \(r\) to a maximum value \(R\) [1].

\[ \begin{align}\begin{aligned}R_i = (R -r) * (i/M) + r\\EISF(Q) = \frac{1}{M} \sum_{i=1}^{M} (3 \frac{j_1(QR_i)}{QR_i})^2(Q\cdot R_i)\end{aligned}\end{align} \]

\(r\) and \(R\) units are inverse of \(Q\) units. Because of the spherical symmetry of the problem, the structure factor is expressed in terms of the \(j_l(z)\) spherical Bessel functions.

Related functions: - EISFDiffSphere - ElasticDiffSphere - InelasticDiffSphere - DiffSphere

References

[1]
    1. Sharma, et al., J. Phys. Chem. B 120(1):154-163.

Usage

Example - fit of Q-dependence:

q =  [0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9]
# A=2.0, r=0.12, R=1.6, M=9
eisf = [1.96561499215648, 1.90667574712235, 1.82327109734092,
        1.72075639596568, 1.60529662348532, 1.48322421137169,
        1.36043655237770, 1.24191091785048, 1.13138963884055]
w = CreateWorkspace(q, eisf, NSpec=1)
results = Fit('name=EISFDiffSphereAlkyl, M=9', w, WorkspaceIndex=0)
print(results.Function)

Output:

name=EISFDiffSphereAlkyl,M=9,A=2,Rmin=0.12,Rmax=1.6

Properties (fitting parameters)

Name Default Description
A 1.0 Amplitude
Rmin 1.0 Minimum radius, inverse units of Q.
Rmax 2.0 Maximum radius, inverse units of Q.

Categories: FitFunctions | QuasiElastic

Source

Python: EISFDiffSphereAlkyl.py (last modified: 2020-03-27)