Improved Gaussian self-consistent method—applications to homopolymers with different architectures in dilute solution

Abstract

A version of the Gaussian self-consistent (GSC) method, which avoids the use of the Edwards' virial expansion, is presented. Instead, the mean energy is evaluated directly via a convolution of the attractive part of the pair-wise non-bonded potential with the Gaussian trial radial distribution function. The hard sphere repulsion is taken into account via a suitably generalised Carnahan-Starling term. Comparison of the mean-squared inter-monomer distances and radius of gyration, as well as of the mean energy, between the results from the GSC calculations and Monte Carlo (MC) simulation in continuous space are made across the coil-to-globule transition for isolated ring, open and star homopolymers of varied lengths and flexibility. Importantly, both techniques utilise the same polymer model so that the data points could be directly superimposed. A surprisingly good overall agreement is found between these GSC and MC results. Caveats of the Gaussian technique and ways for going beyond it are also discussed.

Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains

“…This type of approach has already proven to be useful and accurate when studying copolymers (35,45). At each time point, the probability distribution function of the chain conformation is approximated by a multivariate Gaussian distribution whose parameters are determined using the maximum entropy principle (36) (see ‘Material and Methods’ section for details).…”

“…While numerical simulations of such stochastic system could be time demanding, we develop a Gaussian self-consistent approximation that allows a fast scanning of the parameter space and that enables the efficient computation of expectation values for the HiC-map of the copolymer. This type of approach has already proven to be useful and accurate when studying copolymers ( 35 , 45 ). At each time point, the probability distribution function of the chain conformation is approximated by a multivariate Gaussian distribution whose parameters are determined using the maximum entropy principle ( 36 ) (see ‘Material and Methods’ section for details).…”

Dendrimers in Solution: Insight from Theory and Simulation

“…Whereas the object of interest in the SCF theory of Boris and Rubinstein is the monomer density ρ ( r ),27 the main objects of the GSC approach are the mean‐square distances between the monomers [Eq. (12)] 47 …”

Characterization of stationary phases by a linear solvation energy relationship utilizing supercritical fluid chromatography

“…Während bei der SCF‐Theorie von Boris und Rubinstein27 die Monomerdichte ρ ( r ) im Mittelpunkt steht, zielt der GSC‐Ansatz auf den mittleren quadratischen Abstand zwischen den Monomeren [Gl. (12)] 47 …”