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

Parallel-tempering MD results for a CH3(CH2-O-CH2)mCH3 chain in water are exploited as a database 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 null water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple k → ∞ 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 ≈ 2π/0.6 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 Rg(2) is compared with the classic predictions for both the Gaussian model and freely jointed chains. ⟨Rg(2)(j)⟩, the contribution of the jth chain segment to ⟨Rg(2)⟩, depends on the contour index about as expected for Gaussian chains despite significant quantitative discrepancies that 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 to the close proximity of central elements to the globule center. However, that density structuring washes out for longer chains where many chain elements additively contribute to the density profiles. Gaussian chain models thus become more satisfactory for the density profiles for longer chains.