Scaling Exponent and Effective Interactions in Linear and Cyclic Polymer Solutions: Theory, Simulations, and Experiments

Abstract

Cyclic polymers have garnered increasing attention in the materials community as lack of free-chain ends in cyclic polymers results in significant differences in structure, thermodynamics, and dynamics compared to their linear counterparts. Yet, key open questions remain about how cyclic polymer chain conformations and effective interactions in solution change as a function of solvent quality, ring closure chemistry, and the presence/absence of common synthetic impurities. We use coarse-grained molecular dynamics simulations, polymer reference interaction site model theory, and small-angle neutron-scattering experiments on polystyrene in d-cyclohexane to demonstrate how linear and cyclic polymer chain configurations, scaling, and effective interactions are influenced by solvent quality and polymer concentration. We find that the balance between the available intraversus interchain contacts in solution dictate the trends in cyclic polymer size scaling and effective polymer−solvent and polymer−polymer interactions; these results are largely insensitive to the ring closure chemistry and the presence of linear or cyclic dimer impurities. This study provides the broader polymer science and engineering community fundamental insights into how synthesis, purification, and assembly of cyclic polymers in solvent(s) impact the resulting chain structure and polymer solution thermodynamics.

Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features

“…Samples were synthesized with deuterated sidechains to provide backbone contrast by SANS and elucidate scaling relationships of ξ. The interpretation of our scattering experiments is aided by largescale molecular-dynamics (MD) simulations of coarse-grained polymer model (32). We show that the scaling of ξ with sidechain length, backbone length, and backbone concentration all display behavior surprisingly similar to polyelectrolyte solution scaling.…”

Cyclic polymers: Advances in their synthesis, properties, and biomedical applications

“…[114] As polymers are characterized by a very close structure-property relationship, in solution as well as in bulk, the elimination of these impurities is crucial when determining the properties of cyclic polymers. [2,[115][116][117] The most traditional technique used to get rid of these impurities is the preparative SEC. In fact, because of its limited conformational freedom, a cyclic polymer will present a lower hydrodynamic volume when compared to its linear analogue.…”

“…[ 114 ] As polymers are characterized by a very close structure–property relationship, in solution as well as in bulk, the elimination of these impurities is crucial when determining the properties of cyclic polymers. [ 2,115–117 ]…”

Local Effects of Ring Topology Observed in Polymer Conformation and Dynamics by Neutron Scattering—A Review

“…In some of the literature, authors have chosen to discuss the so-called the g -factor rather than the Flory exponent, ν of the rings or chains. As recently noted by Gartner et al [ 65 ], for ideal Gaussian chains this ratio is expected to be equal to 0.5, but values ranging from 0.5 to 0.6 have been reported from both experiments and computations [ 50 ]. For PS samples with molecular weight from 17 to 570 k in benzene-d 6 , Takano et al reported g -factors varying from 0.589 to 0.647.…”

“…Large variations between g -factors may be related to different solvent conditions, but sample purity is also believed to contribute to discrepancies between data reported by different groups. Gartner et al [ 65 ] while coupling coarse-grained molecular dynamics simulations and SANS measurements on PS in d-cyclohexane studied the effect of solvent quality and concentrations on chain conformation, scaling, and interactions of linear chains and cyclics. Interestingly, these authors concluded that scaling is the result of a delicate balance between intra- and inter-chain contacts, and this is relatively insensitive to the ring closure chemistry and the presence of linear or other impurities.…”