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
rg Radius of gyration 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.


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


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

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

\[q = \sqrt{q_x^2 + q_y^2}\]

Fig. 96 1D plot corresponding to the default parameters of the model.


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).