Near-Θ Polymers in a Cylindrical Space

Abstract

The advent of single-molecule manipulations has renewed our interest in understanding chain molecules in confined spaces. The conformation and dynamics of these molecules depend on the degree of confinement and self-avoidance. A distinguishing feature of weakly self-avoiding polymers (e.g., DNA) in a cylindrical space is the emergence of the so-called extended de Gennes regime. On the other hand, an earlier study indicates that slit confinement enhances the self-avoidance of a Θ-polymer, for which the two-body (monomer–monomer) interaction vanishes. Using molecular dynamics simulations, we study how cylindrical confinement modulates the self-avoidance of near-Θ polymers. Our results suggest that the confinement enhances self-avoidance, turning a near-Θ solvent into a good solvent. This finding has a number of nontrivial consequences. First, it induces the linear ordering of a near-Θ chain, as if the chain is in a good solvent. Second, under strong confinement, the chain size, R ∥, scales with the cylinder diameter, D, approximately as R ∥ ≈ Na(D/a – 1)−4/3, where N is the number of monomers and a the monomer size. This is distinct from R ∥ ≈ Na(D/a)−1 as suggested by the conventional picture, in which the second virial coefficient, B 2, remains unchanged upon confinement. In contrast, enhanced self-avoidance is not easily felt by the confinement free energy unless B 2 is large enough, outside the regime of a near-Θ solvent. Finally, we show how these findings are related to long-range bond–bond correlations observed for single polymers or polymer melts.

Solvent Quality Dependent Osmotic Pressure of Polymer Solutions in Two Dimensions

“…In two dimensions (2D), the correlation length exponent is ν normalΘ 2 normalD = 4 / 7 , which is different from that of the RW. Since the higher-order virial terms cannot be ignored in 2D, the Θ point of a polymer chain in 2D is defined under a more subtle condition than B 2 = 0 in 3D. − As a result, the Θ point of a 2D polymer, in practice, has numerically been attained by tuning the relevant parameters (see the Methods section). Historically, studies on geometrical fractal objects in 2D, in particular, the Θ chain in 2D and its exotic exponent ν normalΘ 2 normalD = 4 / 7 ≈ 0.571 , culminated in the 1980s.…”

Irregularity of Polymer Domain Boundaries in Two-Dimensional Polymer Solution

“…(ii) The configurations of the Θ chain differ from those of SAW (Figure B) in that some monomers are buried inside the domain, whereas others are exposed to the periphery constituting the external perimeter. Θ chains in dilute phase obey , characterized by the fractal dimension of percolating clusters ; ,,,,,,− however, Figure D indicates that the external perimeter of the Θ chain is still self-avoiding, such that . − …”

“…gm m e e g / c X Y X Y (28) For the correlation between two L-arm vertices of the watermelon geometry, the magnetic charges at X and Y are due to a vortex and anti-vortex pair with L/2 dislocations m X = −m Y = L/2, and the electric charges at X and Y are given as e X = e Y = 1 − g, and hence the scaling dimension x L = −(gm X m Y + e X e Y /g)/2 is expressed in terms of g and L 14 = x L g g g 8…”

“…Remarkably, scriptD ∂ in good solvents ( D SAW ∂ ) exhibits a nonmonotonic variation with ϕ, whereas scriptD ∂ of Θ chains ( D Θ ∂ ) remains constant over the same range of ϕ. The constant scriptD normalΘ ∂ can be understood as an outcome of the compensation between attraction and repulsion that characterizes the nature of the Θ chain. ,,− Despite a number of works that analyzed the irregularity of the polymer domain boundary in 2D polymer solution, ,,− , these studies are mainly focused on polymer melts or dense polymer systems. Our finding of the nonmonotonic variation of scriptD SAW ∂ ( ϕ ) , especially over intermediate concentrations, has not been reported elsewhere.…”

Theta Temperature Depression of Mechanically Interlocked Polymers: [2]catenane as a Model Polymer

“…Note that near θ-temperature and in the low molecular weight limit, large deviations from Gaussian chain properties have been reported, and the R g 2 deviates from the ideal chain behavior could have the square root correction format , or the logarithmic correction . For the logarithmic correction model, B = 37/363, −37/363 and 1.9/(44π) are reported by mean-field theory methods .…”