Star Polymer w/ Excluded Volume


This model describes scattering from a star-branched polymer where the arms of the polymer may have excluded volume, i.e., they need not be Gaussian chains.

Under this model, the form factor of the star polymer with $f$ arms having degree of polymerization $N$ is given by

P_{star}(q) = \frac{1}{f^{2}} \left[ fP_{sb}(q,N) + f(f-1)P_{ib}(q,N) \right]
$P_{sb}(q,N)$ is the single branch/arm form factor, given by:
P_{sb}(q,N) = \frac{1}{\nu U^{1/2\nu}}\gamma\left( \frac{1}{2v}, U \right) - \frac{1}{\nu U^{1/\nu}}\gamma\left( \frac{1}{\nu}, U\right)
where $\nu$ is the excluded volume parameter, $U = q^{2}b^{2}N^{2\nu}/6$ and $b$ is the Kuhn length. The interbranch/arm form factor is given by:
P_{ib}(q,N) = 2P_{sb}(q,2N) - P_{sb}(q,N)

The final scattering intensity that this model gives is
I(q) = scale \times (\rho_{P} - \rho_{S})^{2}P_{star}(q) + B
where $\rho_{P}$ and $\rho_{S}$ are the scattering length densities of the polymer and solvent, respectively, and $B$ is the incoherent background.


1. B. Hammouda, "Form Factors for Branched Polymers with Excluded Volume", J. of Research of NIST, 121, 139-164 (2016).

2. X. Lang, W. R. Lenart, J. E. P. Sun, B. Hammouda, and M. J. A. Hore, "Interaction and Conformation of Aqueous Poly(N-isopropylacrylamide) (PNIPAM) Star Polymers below the LCST", Macromolecules, 50, 2145-2154 (2017).

Example Data:


Created By mjahore
Uploaded Aug. 22, 2018, 7:56 p.m.
Category Shape-Independent
Score 0
Verified This model has not been verified by a member of the SasView team
In Library This model is not currently included in the SasView library. You must download the files and install it yourself.


No comments yet.

Please log in to add a comment.