# mono_gauss_coil

Scattering from monodisperse polymer coils

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
i_zero Intensity at q=0 cm-1 70

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

$I(q) = \text{scale} \cdot I_0 \cdot P(q) + \text{background}$

where

\begin{align}\begin{aligned}I_0 &= \phi_\text{poly} \cdot V \cdot (\rho_\text{poly} - \rho_\text{solv})^2\\P(q) &= 2 [\exp(-Z) + Z - 1] / Z^2\\Z &= (q R_g)^2\\V &= M / (N_A \delta)\end{aligned}\end{align}

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

$q = \sqrt{q_x^2 + q_y^2}$

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