A Methodology to Calculate Small-Angle Scattering Profiles of Macromolecular Solutions from Molecular Simulations in the Grand-Canonical Ensemble

Published

August 31, 2018

Author(s)

Marco A. Blanco Medina, Harold W. Hatch, Joseph E. Curtis, Vincent K. Shen

Abstract

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly-flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at fixed number of molecules) show equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value.

Citation

The Journal of Chemical Physics

Pub Type

Journals

Keywords

Small-angle scattering, SAXS, SANS, Molecular simulations, Grand-canonical Monte Carlo, Pair distribution functions

Citation

Blanco, M. , Hatch, H. , Curtis, J. and Shen, V. (2018), A Methodology to Calculate Small-Angle Scattering Profiles of Macromolecular Solutions from Molecular Simulations in the Grand-Canonical Ensemble, The Journal of Chemical Physics (Accessed April 26, 2024)