A Simple Analytical Model for Predicting the Collapsed State of Self-Attractive Semiflexible Polymers

Abstract

Abstract:We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of dimensionless ratios of the three energy parameters, namely solvent-water surface energy (γ s ), energy of bundle end folds (γ e ), and bending energy per unit length in a torus (γ b ). Our phase diagram captures the general phase behavior of a single long chain (>10 Kuhn lengths) at moderately high (order unity) dimensionless temperature, which is the ratio of thermal energy to the attractive interaction between neighboring monomers. We find that the phase behavior approaches an asymptotic limit when the dimensionless chain length to diameter ratio (L*) exceeds 300. We successfully validate our analytical results with Brownian Dynamics (BD) simulations, using a mapping of the simulation parameters to those used in the phase diagram. We evaluate the effect of three different bending potentials in the range of moderately high dimensionless temperature, a regime not been previously explored by simulations, and find qualitative agreement between the model and simulation results. We, thus, demonstrate that a rather simplified analytical model can be used to qualitatively predict the final collapsed state of a given polymer chain.

Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

“…In the following, we focus on the effect of bending stiffness, where the energy and length scales of the self- and mutual-attraction are fixed, but the strength of the bending penalty is varied. This includes mean-field studies [ 89 ], numerical studies of lattice models [ 90 , 91 , 92 ] and off-lattice models [ 93 , 94 , 95 , 96 , 97 , 98 ], analytical approaches [ 99 ] and experimental studies [ 100 ]. It was shown that the variation of a single parameter, such as the stiffness, may strongly influence the arising structural motifs and, moreover, may affect the order of the accompanying transitions.…”

“…Details of the models become relevant again for the low-temperature conformations. For off-lattice models, this includes the formation of stable knots [ 98 ] (see Section 4.3 ), toroidal loops [ 97 , 99 ] and the arrangement of the compact frozen states, which may form icosahedral structures [ 97 , 108 ]. This appears to depend on many details, such as the explicit relations between the bonded and non-bonded length and energy scales, with many open questions remaining.…”

“…The influence of stiffness on the collapse transition, more explicitly the morphological variation or the type, has been a long-standing subject of investigation [ 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 ]. The collapse transition of a flexible polymer is a second-order phase transition in the limit [ 2 ].…”

Conformation of Methylcellulose as a Function of Poly(ethylene glycol) Graft Density

“…Methylcellulose (MC) is an abundant and sustainable cellulose derivative that enjoys an impressive range of consumer applications, from clinical excipients to construction materials. , One of the most interesting and rheologically significant properties of MC is its ability to self-assemble into highly elastic fibrous networks, upon heating in aqueous solution. − Interestingly, the detailed mechanism and internal structure of the fibrils is still an open fundamental question; − further addition of relatively few hydroxypropyl groups, to produce hydroxypropyl methylcellulose (HPMC), suppresses fibril formation. , Other straightforward chemical modifications to the MC backbone could also tune physical properties and thereby broaden the breadth of applications. For example, small molecular grafts are predicted to increase the stiffness of an otherwise flexible or semiflexible polymer. − Increasing stiffness is expected to modify MC self-assembly, thereby enabling new application opportunities, and also could ultimately contribute to a more detailed understanding of the nature of MC fibril formation.…”

Modeling the Interplay of Conformational and Electronic Structure in Conjugated Polyelectrolytes

“…K A > 12). 38,75 Helices have been observed previously in neutral phenylene ethynylene oligomers and the conformation was also attributed to the presence of strong π-stacking interactions. 76 We briefly investigated the impact side chains have on conformations by removing the side chains and transferring the +1 charge to each backbone bead, producing three main observations.…”