Theory of wormlike polymer chains in confinement

Chen, Jeff Z. Y.

doi:10.1016/j.progpolymsci.2015.09.002

Cited by 75 publications

(73 citation statements)

References 139 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another interesting direction of extension of the current work would be to consider semiflexible chains rather than rigid rods, as "molecules" in most biological experiments are not exactly rigid. This extension is already built into the self-consistent field theory by using a finite persistence length λ [34]. The introduction of these effects would make the theory depend on a/b, a/L, L 2 ρ, d/L, and λ/L, resulting a much larger parameter space to explore.…”

Section: Discussionmentioning

confidence: 99%

“…The two terms compete with each other as one prefers isotropic state and the other nematic state. The actual numerical calculation to minimize the free energy was carried out by using the mathematically equivalent self-consistent field theory [24,34]. Appendix A summarizes the main formalism.…”

Section: A Extended Onsager Modelmentioning

confidence: 99%

“…The proof for mathematical equivalence is carefully addressed in both Refs. [24] and [34]. The formalism requires the introduction of a path variable s, continuously varying from one end of the molecule where s = 0 to another end where s = 1.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Topological defects in two-dimensional liquid crystals confined by a box

2018

View full text Add to dashboard Cite

When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: A Extended Onsager Modelmentioning

confidence: 99%

See 1 more Smart Citation

Topological defects in two-dimensional liquid crystals confined by a box

2018

View full text Add to dashboard Cite

show abstract

“…The rich phase behavior of hard body fluids depends very strongly on the shape of the particles [1] and the confining dimension [2,3]. It is now well understood that the anisotropic shape of particles is responsible for the formation of mesophases such as the the nematic, smectic, and columnar.…”

Section: Introductionmentioning

confidence: 99%

Ordering, clustering, and wetting of hard rods in extreme confinement

Basurto

Gurin

Varga

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

The effect of out-of-plane orientational and positional fluctuations is examined in the phase behavior of hard spherocylinders confined between two parallel walls. The stability of isotropic, nematic, and solid phases is studied for aspect ratios (κ = 1 + L/σ , where σ and L are the diameter and length of the cylinder) of 8, 10, and 16, while the width of the slitlike pore, H , is set in the quasi-two-dimensional regime, σ < H 2σ. Using replica exchange Monte Carlo (REMC) simulations and Onsager theory we provide evidence for the stabilization of the nematic order with increasing pore width. The minimum surface density necessary to exhibit nematic order remains nearly the same with increasing H , while the upper bound of nematic order is postponed to higher densities in detriment of the single-layer-solid phase. We prove that a drying-out effect takes place in the pore as the density increases linearly from the wall to the middle of the pore in the ideal gas limit. This behavior is kept for the isotropic phase and partially in the nematic one, while a wetting behavior is observed at the walls mostly for the solid phases. For κ = 8, we have also observed a compressibility signal of a transition between an isotropic fluid and a cluster-like fluid. This cluster phase is destabilized by increasing H. Finally, we build a master diagram, where the drying-wetting, solid-solid, and close packing density curves are independent from κ.

show abstract

“…Rod-coil BCP models assume one block is flexible while one is fully rigid, and the rigid rods exhibit liquid-crystalline orientational interactions 13,14 . Other BCP models consider semiflexible chains in which the persistence length is most often taken to be comparable to the chain length 12,[15][16][17] . Maier-Saupe interactions have been used to model orientational interactions in semi-flexible and rigid BCPs [18][19][20][21] .…”

Section: Introductionmentioning

confidence: 99%

Intradomain phase transitions in flexible block copolymers with self-aligning segments

Burke

Grason

2018

The Journal of Chemical Physics

View full text Add to dashboard Cite

We study a model of flexible block copolymers (BCPs) in which there is an enlthalpic preference for orientational order, or local alignment, among like-block segments. We describe a generalization of the self-consistent field theory of flexible BCPs to include inter-segment orientational interactions via a Landau-de Gennes free energy associated with a polar or nematic order parameter for segments of one component of a diblock copolymer. We study the equilibrium states of this model numerically, using a pseudo-spectral approach to solve for chain conformation statistics in the presence of a self-consistent torque generated by inter-segment alignment forces. Applying this theory to the structure of lamellar domains composed of symmetric diblocks possessing a single block of "self-aligning" polar segments, we show the emergence of spatially complex segment order parameters (segment director fields) within a given lamellar domain. Because BCP phase separation gives rise to spatially inhomogeneous orientation order of segments even in the absence of explicit intra-segment aligning forces, the director fields of BCPs, as well as thermodynamics of lamellar domain formation, exhibit a highly non-linear dependence on both the inter-block segregation (χN) and the enthalpy of alignment (ε). Specifically, we predict the stability of new phases of lamellar order in which distinct regions of alignment coexist within the single mesodomain and spontaneously break the symmetries of the lamella (or smectic) pattern of composition in the melt via in-plane tilt of the director in the centers of the like-composition domains. We further show that, in analogy to Freedericksz transition confined nematics, the elastic costs to reorient segments within the domain, as described by the Frank elasticity of the director, increase the threshold value ε needed to induce this intra-domain phase transition.

show abstract

Theory of wormlike polymer chains in confinement

Cited by 75 publications

References 139 publications

Topological defects in two-dimensional liquid crystals confined by a box

Topological defects in two-dimensional liquid crystals confined by a box

Ordering, clustering, and wetting of hard rods in extreme confinement

Intradomain phase transitions in flexible block copolymers with self-aligning segments

Contact Info

Product

Resources

About