Loop-Closure and Gaussian Models of Collective Structural Characteristics of Capped PEO Oligomers in Water

TL;DR

This study uses parallel-tempering MD simulations to analyze the structural characteristics of PEO oligomers in water, proposing a discrete-Gaussian model that aligns with experimental scattering data and reveals chain swelling and density structuring.

Contribution

It introduces a discrete-Gaussian model for PEO chains that accurately captures scattering behavior and chain structure, improving upon traditional continuum models.

Findings

Discrete-Gaussian model matches high-$k$ behavior.

Identifies 0.6 nm as a natural monomer size.

Swelling effects cause quantitative discrepancies from ideal Gaussian chains.

Abstract

Parallel-tempering MD results for a CH$_3$(CH$_2$-O-CH$_2$)$_m$CH$_3$ chain in water are exploited as a data-base for analysis of collective structural characteristics of the PEO globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of Corexit type. The chain structure factor, relevant to neutron scattering from a deuterated chain in neutral water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple $k \rightarrow \infty$ behavior, but we consider a discrete-Gaussian model that does achieve that consistency. Shifting-and-scaling the discrete-Gaussian model helps to identify the low-$k$ to high-$k$ transition near $k \approx 2\pi/0.6 \mathrm{nm}$ when an empirically matched number of Gaussian links is about one-third of the total number of effective-atom sites. This short distance-scale boundary of 0.6 nm is directly verified with the $r$-space distributions, and this distance is thus identified with a natural size for coarsened monomers. The probability distribution of $R_g{}^2$ is compared with the classic predictions for both Gaussian model and freely-jointed chains. $\left\langle R_g{}^2(j)\right\rangle$, the contribution of the $j$-th chain segment to $\left\langle R_g{}^2\right\rangle$, depends on contour index about as expected for Gaussian chains despite significant quantitative discrepancies which express the swelling of these chains in water. Monomers central to the chain contour occupy the center of the chain globule. The density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due close proximity of central elements to the globule center. But that density structuring washes-out for longer chains where many chain elements additively contribute to the density profiles.