Chain conformations of ring polymers under theta conditions studied by Monte Carlo simulation

Giant Casimir Nonequilibrium Forces Drive Coil to Globule Transition in Polymers

We develop a theory to probe the effect of nonequilibrium fluctuation-induced forces on the size of a polymer confined between two horizontal, thermally conductive plates subject to a constant temperature gradient, ∇ T. We assume that (a) the solvent is good and (b) the distance between the plates is large so that in the absence of a thermal gradient the polymer is a coil, whose size scales with the number of monomers as N^ν, with ν ≈ 0.6. We find that above a critical temperature gradient, ∇ T_c ≈ N^-5/4, a favorable attractive monomer-monomer interaction due to the giant Casimir force (GCF) overcomes the chain conformational entropy, resulting in a coil-globule transition. Our predictions can be verified using light-scattering experiments with polymers, such as polystyrene or polyisoprene in organic solvents in which the GCF is attractive.

Dimensions of catenated ring polymers in dilute solution studied by Monte-Carlo simulation

Interaction between two simple ring chains catenated in a molecule was estimated by a Metropolis Monte Carlo simulation, and the result was compared with a model. We employed catenated ring chains in this study; they were composed of two simple ring chains, and the topology was kept as 2 1 2 . The temperature dependence of the distance between two ring chains in a molecule was discussed using Flory's scaling exponent, ν, in R _g ∝ N ^ν , where R _g is the radius of gyration of a simple ring chain catenated in a molecule. In the simulation, the topology of the component rings and their links were kept because chain crossing was prohibited. The excluded volume of chains was screened by the attractive force between polymer segments, and the strength of the attractive force depends on temperature, T. At the θ temperature for trivial ring polymers, where the condition ν = 1/2 holds, their trajectories can be described statistically as a closed-random walk, i.e., a closed-phantom chain model. The temperature at which interaction between trivial ring polymers, i.e., inter-molecular interaction, is repulsive; trivial ring polymer molecules show the excluded volume generated with keeping their own topology, 0₁. A catenated molecule is composed of two simple rings, and so forth a component ring can be affected by the existence of the counterpart rings. Under that temperature, the mean-square distance between two rings in a catenated molecule, ⟨L ²⟩, was obtained and compared with that of the simple model composed of two circles in three-dimensions, where interaction between circles is set as zero. It has been found that the simulated ⟨L ²⟩ values were constantly larger than those of the model owing to the excluded volume of rings in a molecule.

Morphology of symmetric ABCD tetrablock quaterpolymers studied by Monte Carlo simulation

Morphology of symmetric ABCD tetrablock quaterpolymers in melt was studied by the Monte Carlo (MC) simulation, where the volume fractions of the block chains, f, kept the relationships of f_A=f_D and f_B=f_C, and the volume fraction of the two mid-blocks φ was defined as φ=f_B+f_C. Previous self-consistent field theory for ABCD reported morphological change including several structures; however, the scope was limited within a two-dimensional system. To the contrary, in this paper, MC simulations were carried out in three dimensions with changing the φ value finely, which resulted in finding a tetracontinuous structure in the range of 0.625≤φ≤0.75. Moreover the tetracontinuous structure has been found to be the gyroid structure, and the mean curvature of the B/C interface is nearly zero. We concluded that the B/C interface must be the Schoen gyroid surface, one of three-dimensional periodic minimal surfaces. The geometrical nature of the A/B interface should be equivalent to that of the C/D interface, and they stand as level surfaces to the Schoen gyroid surface.

Interactions of complex polymers with nanoporous substrate

With the advance of polymer synthesis, polymers that possess unique architectures such as stars or cyclic chains, and unique chemical composition distributions such as block copolymers or statistical copolymers have become frequently encountered. Characterization of these complex polymer systems drives the development of interactive chromatography where the adsorption of polymers on the porous substrate in chromatography columns is finely tuned. Liquid Chromatography at the Critical Condition (LCCC) in particular makes use of the existence of the Critical Adsorption Point (CAP) of polymers on solid surfaces and has been successfully applied to characterization of complex polymer systems. Interpretation and understanding of chromatography behaviour of complex polymers in interactive chromatography motivates theoretical/computational studies on the CAP of polymers and partitioning of these complex polymers near the CAP. This review article covers the theoretical questions encountered in chromatographic studies of complex polymers.

Cyclic polymers revealing topology effects upon self-assemblies, dynamics and responses

A variety of single- and multicyclic polymers having programmed chemical structures with guaranteed purity have now become obtainable owing to a number of synthetic breakthroughs achieved in recent years. Accordingly, a broadening range of studies has been undertaken to gain updated insights on fundamental polymer properties of cyclic polymers in either solution or bulk, in either static or dynamic states, and in self-assemblies, leading to unusual properties and functions of polymer materials based on their cyclic topologies. In this article, we review recent studies aiming to achieve distinctive properties and functions by cyclic polymers unattainable by their linear or branched counterparts. We focus, in particular, on selected examples of unprecedented topology effects of cyclic polymers upon self-assemblies, dynamics and responses, to highlight current progress in Topological Polymer Chemistry.

Interactions between ring polymers in dilute solution studied by Monte Carlo simulation

The second virial coefficient, A2, for trivial-ring polymers in dilute condition was estimated from a Metropolis Monte Carlo (MC) simulation, and the temperature dependence of A2 has been discussed with their Flory's scaling exponent, ν, in Rg ∝ N(ν), where Rg is radius of gyration of a polymer molecule. A limited but not too small number of polymer molecules were employed in the simulation, and the A2 values at various temperatures were calculated from the molecular density fluctuation in the solution. In the simulation, the topology of ring polymers was kept, since chain crossing was prohibited. The excluded volume effects can be screened by the attractive force between segments, which depends on the temperature, Tα, defined in the Metropolis MC method. Linear and trivial-ring polymers have the ν value of 1/2 at Tα = 10.605 and 10.504. At Tα = 10.504, the excluded volume effects are screened by the attractive force generated between segments in a ring polymer, but the A2 value for ring polymers is positive. Thus, the temperature at A2 = 0 for a ring polymer is lower than that at ν = 1/2, and this fact can be explained with the following two reasons. (a) Rg value for a ring polymer is much smaller than that for a linear polymer at the same temperature and molecular weight, where interpenetration of a ring polymer chain into neighboring chains is apparently less than a linear chain. (b) The conformation of trivial rings can be statistically described as a closed random walk at ν = 1/2, but their topologies are kept, being produced topological constraints, which strongly relate not only to the long-distance interaction between segments in a molecule but also the inter-molecular interaction.