Elastic properties of liquid-crystalline bilayers self-assembled from semiflexible–flexible diblock copolymers

Abstract

The elastic properties of bilayers self-assembled from rod–coil diblock copolymers are strongly affected by the liquid-crystalline order of the rods.

Analytical Calculation of the Elastic Moduli of Self-Assembled Liquid-Crystalline Bilayer Membranes

“…The circles and squares are the excess free energy of cylindrical and spherical bilayers calculated in the cylindrical and spherical coordinate systems, respectively. 18 Under this model parameter, the bilayer is self-assembled to A phase and its thickness is about 2.2R g when the bilayer is slightly curved. Therefore, the curvature of spherical and cylindrical bilayers has an upper bound c max ∼ 1/2.2 ≈ 0.45.…”

“…These geometries are easy to simulate since we can reduce the computation domain to dimension one in their corresponding coordinate systems. Furthermore, MDEs 3−5 are now in one-dimensional planar, cylindrical, and spherical coordinate systems, which can be written in unified forms 18 (omit the superscripts and subscripts)…”

“…We consider the model system (used in ref ) as a binary mixture of A­(flexible)­B­(semiflexible)-diblock copolymers and A-homopolymers. In this generic model, the amphiphilic molecules are modeled by the diblock copolymers and the amphiphilic solvent molecules are modeled by the homopolymers.…”

“…Although many amphiphilic molecules contain a rigid or semiflexible component, the elastic properties for semiflexible bilayers are less explored. Cai et al 18 extended the PFM to a semiflexible chain model described by the wormlike chain to study the elastic properties of liquidcrystalline bilayers and found that the liquid-crystalline order of the bilayers could have significant effects on the elastic properties of the membranes. Since the AEM could provide the analytical expression of elastic moduli and allows one to design more efficient numerical schemes, 13 it is valuable to extend the AEM to semiflexible bilayers and verify its numerical efficacy compared with the PFM.…”

“…Since the energies F C (c) and F S (c) are polynomials when the curvature c is small, their coefficients can be extracted from two datasets, {(c i , F C (c i ))} and {(c i , F S (c i ))}, by the standard polynomial fitting method. 16,18 Here, for each curvature c i in the set {c i }, the free energy F(c i ) (F C (c i ) or F S (c i )) is calculated by solving the SCFT model with the geometric constraint at r 1 corresponding to c i .…”