Rheological response and dynamics of the amphiphilic diamond phase from kinetic lattice–Boltzmann simulations

Abstract

The purpose of the present paper is to report on the first computational study of the dynamical and rheological response of a self-assembled diamond mesophase under Couette flow in a ternary mixture composed of oil, water and an amphiphilic species. The amphiphilic diamond mesophase arises in a wide range of chemical and biological systems, and a knowledge of its rheological response has important implications in materials science and biotechnological applications. The simulations reported here are performed using a kinetic lattice–Boltzmann method. Lyotropic liquid crystals exhibit characteristic rheological responses in experiments that include shear-banding and a non-Newtonian flow curve as well as viscoelasticity under oscillatory shear. Their behaviour under steady and oscillatory shear is correctly reproduced in our simulations. On cessation of shear, as the morphology returns to the diamond phase, the relaxation of the stress response follows a stretched-exponential form for low initial strain rates.

Shear rheology of amphiphilic cubic liquid crystals from large-scale kinetic lattice–Boltzmann simulations

“…The self-assembly of bicontinuous sponge, cubic and non-cubic periodic mesophases has been simulated previously in ternary mixtures comprising oil, water and an amphiphilic species by means of the kinetic lattice-Boltzmann approach used in this work. 2,[17][18][19][20] Simulations of the rheology of the gyroid and diamond phase under applied steady shear on models comprising 128 3 and 64 3 lattice-sites have also been performed, 17,19,21 in agreement with rheological experiments on self-assembled amphiphilic systems. 15,[22][23][24][25] The cubic primitive phase is observed to form quite commonly in amphiphilic fluid mixtures, 1,11,26,27 However, the selfassembly and rheology of the primitive phase has not been studied experimentally although reports of the morphologically related micellar BCC and FCC phases in block copolymers exist.…”

“…In the current work, we will use composition, F b , F r and F g as per our previous simulations where self-assembly into the gyroid, primitive and diamond phase was observed purely by varying the interaction parameter values. 21 We will use the same interaction parameter sets g br , g bs and g ss for the gyroid and diamond phase as were used in the earlier work, 21 while an extended range of parameter sets will be used for the four different primitive systems studied here. The morphology of the self-assembled cubic phases is verified via reference to the idealized periodic nodal approximation (PNA) 3,54 by means of (a) direct visualisation and (b) comparison of the topological Euler characteristic.…”

“…The spatial resolution of these simulations of cubic amphiphilic systems is z2 nm per lattice unit while one lattice time-step corresponds to O(1)-O(10) ms. 2,21 According to this mapping, the applied strain rates in the steady shear simulations are in the range of 0.001 to 0.1 s À1 . As we are simulating a simplified generic amphiphilic model, quantitative comparison with specific systems will not be meaningful.…”

Rheology of lamellar liquid crystals in two and three dimensions: a simulation study

“…Guided by those results, we additionally report some very large three dimensional simulations at selected points in the parameter space. These 3D simulations are, we believe, of unprecedented scale for lamellar phases, although even larger ones have recently been used to address the rheology of cubic liquid crystals 29,30 .…”

“…These 3D simulations are, we believe, of unprecedented scale for lamellar phases, although even larger ones have recently been used to address the rheology of cubic liquid crystals. 29,30 Below, we describe smectics via a widely-used free energy functional. 23,28,31,32 This provides a robust generic framework for addressing lamellar ordering without being tied to any specific class of materials (although we do become more specific when estimating suitable parameters for the simulations).…”