The study of the structure factor of a wormlike chain in an orientational external field

Abstract

A precise representation of the structure factor of a wormlike chain for the arbitrary chain flexibility in an orientational external field is obtained by virtue of the numerical solution to the modified diffusion equation satisfied by the Green's function. The model is built from a standard wormlike chain formalism in a continuous version which crossovers from the rigid-rod limit to the flexible chain limit and the Maier-Saupe interaction which describes the orientational effects from the nematic field. The behaviors of the structure factor in the distinct wavevector k regimes are numerically investigated as functions of chain flexibility and tilt angle between the directors of the nematic field and k. The radius of gyration extracted from the structure factor in small-k regime is also carefully analysed in both the directions along and perpendicular to the nematic axis. Our calculations exactly recover the prediction of the structure factor undergoing an orientational field in the rigid rod limit.

Chain Dimensions and Stiffness of Cellulosic and Amylosic Chains in an Ionic Liquid: Cellulose, Amylose, and an Amylose Carbamate in BmimCl

“…Dashed lines in the figure indicate the initial slope to determine ⟨ S 2 ⟩ z and P ( q ). The second virial coefficient A 2 was estimated from the slope of [ c /Δ I (0)] 1/2 (filled squares) using the M w data mentioned in the former section with the same method reported in ref , in which the optical constant was estimated from [ c /Δ I (0)] c 0 1/2 and the M w value. The resultant ⟨ S 2 ⟩ z and A 2 data are listed in Table along with the M w values.…”

Polymer-Based Accurate Positioning: An Exact Worm-like-Chain Study

“…28−30 A good candidate for developing the general framework is the WLC model for semiflexible polymers. On the one hand, the exact solutions to the WLC model from the path integral scheme 31,32 and the green function scheme 33−38 become available recently to allow a precise counting of the conformational entropy, which remains difficult for other methods like atomic simulations. The new solutions are already applied to study polymer brush 36,38 and diblock copolymer melt.…”

Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

“…To solve the SCFT model for the isotropic-nematic transition, Spakowitz and Wang proposed an exact theoretical approach based on the Laplace-transformed partition function of a wormlike chain [67]. By examining the crossing of the isotropic and nematic branches of the free energy, Jiang et al numerically located the transition point in Nυ and the jump of the orientational order parameter S at the transition [45]. Letting L/2Lp=2.7848 yields Nυ=40.704 and S=0.353, exactly matching the transition point presented in Figure 3f.…”

“…SCFT schemes based on MS-type (Maier–Saupe) models have been applied to a broad range of systems: from solutions and melts of homopolymers [42,43,44,45], to nanostructured block-copolymer melts [46,47,48,49,50,51,52,53,54]. Currently there is an increased interest in employing mean-field approaches based on MS-type models for the description of nematic mesophases of conjugated polymers (e.g., see [9,15,55,56]).…”