.. _mono-gauss-coil: 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 |Ang| 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 :ref:`poly-gauss-coil` model. **Definition** .. math:: I(q) = \text{scale} \cdot I_0 \cdot P(q) + \text{background} where .. math:: 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) 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 .. math:: q = \sqrt{q_x^2 + q_y^2} .. figure:: img/mono_gauss_coil_autogenfig.png 1D plot corresponding to the default parameters of the model. **Source** :download:`mono_gauss_coil.py ` $\ \star\ $ :download:`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 **Authorship and Verification** * **Author:** * **Last Modified by:** * **Last Reviewed by:**