A dissipative particle dynamics description of liquid-crystalline phases. I. Methodology and applications

Controlling the transport of the mixture involving active and passive rods in confined channel

The transport of the binary mixture of self-propelled rods (SPRs) and passive rods in the asymmetric conjugate periodic channel is studied by dissipative particle dynamics (DPD) simulations. It is found that the autonomous pumping of the binary mixture of active and passive rods can be achieved by either the individual or collective behaviour of SPRs. More specifically, the transport of passive rods can be driven through the individual, collective jostlement of the active rods, and crowding out effect. The strength of self-propulsion, rod length, rod concentration, and geometric feature of the channel determines the mechanism of pumping. In addition, the drift of the binary mixture can be in the positive and negative directions of the channel or the currents of SPRs and passive rods in opposite directions and relies on the geometric feature of the channel and concentration of the two species. Overall, our simulation study offers an efficient approach of flow control for both species.

Enhancing directed collective motion of self-propelled particles in confined channel

The collective transport of the self-propelled rods (SPRs) is studied by dissipative particle dynamics simulations. Two types of channels (channel I and channel II) are taken into account for various rod concentrations. It is found that in channel I-the asymmetric corrugated channel with periodically varying width, some SPRs are trapped at the corners and form the hedgehog clusters. Other SPRs aggregate at the bottleneck and lead to a traffic jam. Consequently, channel I is inefficient for the directional SPR transport in the case of finite concentration. To achieve efficient collective particle transport, channel II-the channel with constant width and arrays of asymmetric obstacles within it, which can avoid the traffic clogging and hedgehog aggregate is suggested. It is found that the swimmer-obstacle interaction gives rise to the directional motion, the spacing between obstacles can avoid the formation of the hedgehog clusters. The high-efficiency directional collective motion of the SPRs is acquired in channel II. Overall, our simulation study offers an efficient approach for directional collective motion of SPRs.

Preferred penetration of active nano-rods into narrow channels and their clustering

In a channel connected to a reservoir, passive particles prefer staying in the reservoir than the channel due to the entropic effect, as the size of the particles is comparable to that of the channel. Self-propelled rods can exhibit out-of-equilibrium phenomena, and their partition behavior may differ from that of passive rods due to their persistent swimming ability. In this work, the distribution of active nano-rods between the nanoscale channel and reservoir is explored using dissipative particle dynamics. The ratio of the nano-rod concentration in the slit to that in the reservoir, defined as the partition ratio Ψ, is a function of active force, channel width, and rod length. Although passive nano-rods prefer staying in bulk (Ψ < 1), active rods can overcome the entropic barrier and show favorable partition toward narrow channels (Ψ > 1). As the slit width decreases to about the rod's width, active rods entering the slit behave like a quasi-two-dimensional system dynamically. At sufficiently high concentrations and Peclet numbers, nano-rods tend to align and move together in the same direction for a certain time. The distribution (PM) of the cluster size (M) follows a power law, PM ∝ M-2, for small clusters.

Engineered liquid crystal nano droplets: insights from multi-scale simulations

Liquid crystal (LC) droplets have been investigated for a wide range of applications, from displays to sensors. Over the years, a need has arisen for complete understanding of the behaviour of LCs in droplets under different conditions for the development of advanced devices, for which accurate modelling is necessary. We show here, for the first time, both qualitative and quantitative agreement between coarse-grained molecular models and Q-tensor theory calculations for liquid crystal (LC) droplets. The approach is demonstrated for two types of droplet surfaces, which possess strong planar degenerate and strong homeotropic anchoring, respectively. Once its reliability has been proven, our approach was used to identify defects due to changes in anchoring in a small region on the LC droplet surface, which could be triggered, for example, by the adsorption of a nano-particle or a protein. Both coarse-grained simulations and Q-tensor analysis show the appearance of defects in well-determined locations within the LC droplet, albeit sometimes affected by degeneracy due to the symmetry of the systems being investigated. These results suggest the possibility of using LC droplets, in the future, as platforms for advanced sensing as well as for signal intensification.

Defect dynamics in clusters of self-propelled rods in circular confinement

Rod-shaped active micro/nano-particles, such as bacterial and bipolar metallic micro/nano-motors, demonstrate novel collective phenomena far from the equilibrium state compared to passive particles. We apply a simulation approach --dissipative particle dynamics (DPD)-- to explore the collectively ordered states of self-propelled rods (SPRs). The SPRs are confined in a finite circular zone and repel each other when two rods touch each other. It is found that for a long enough rods system, the global vortex patterns, dynamic pattern oscillation between hedgehog pattern and vortex pattern, and hedgehog patterns are observed successively with increasing active force F_a. For the vortex pattern, the total interaction energy between the rods U is linear with active force F_a, i.e., U ∼ F_a . While the relation U ∼ F_a² is obtained for the hedgehog structure. It is observed that a new hedgehog pattern with one defect core is created by two ejections of polar cluster in opposite directions from the original hedgehog pattern, and then merges into one through the diffusion of the two aggregates, i.e., the creation and annihilation of topological charges.

Mechanical pressure, surface excess, and polar order of a dilute rod-like nanoswimmer suspension: role of swimmer-wall interactions

The mechanical pressure, surface excess, and polar order of a dilute rod-like nanoswimmer suspension confined by two parallel plates are explored by dissipative particle dynamics. The accumulation and preferred orientation of swimmers near the walls are distinctly shown through the density and polar order distributions for various active force, Fa, values and rod lengths. As Fa is increased, it is interesting to observe that there exists a maximum of the polar order, revealing that the dominant mechanism of the swimmer behavior can be altered by the coupling between the active force and the rod-wall interaction. As a result, the influences of the active force on the swim pressure Π(w)a contributed by the swimmers directly and the surface excess Γ* can be classified into two scaling regimes, natural rotation (weak propulsion) and forced rotation (strong propulsion). Π(w)a and Γ* are proportional to Fa2 in the former regime but become proportional to Fa in the latter regime. For all rod-wall repulsions, the swim pressure of active rods in confined systems Π(w)a always differs from that in unbounded systems Π(b)a which is simply proportional to Fa2 associated with the active diffusivity. That is, unlike thermal equilibrium systems, Π(w)a is not a state function because of the presence of the wall-torque.

Multi-particle collision dynamics algorithm for nematic fluids

Research on transport, self-assembly and defect dynamics within confined, flowing liquid crystals requires versatile and computationally efficient mesoscopic algorithms to account for fluctuating nematohydrodynamic interactions. We present a multi-particle collision dynamics (MPCD) based algorithm to simulate liquid-crystal hydrodynamic and director fields in two and three dimensions. The nematic-MPCD method is shown to successfully reproduce the features of a nematic liquid crystal, including a nematic-isotropic phase transition with hysteresis in 3D, defect dynamics, isotropic Frank elastic coefficients, tumbling and shear alignment regimes and boundary condition-dependent order parameter fields.

Induced polar order in sedimentation equilibrium of rod-like nanoswimmers

The active diffusion and sedimentation equilibrium of rod-like nanoswimmers with length L are investigated by dissipative particle dynamics. In the absence of propulsion, the nanorod has the rotational correlation time τθ and mobility μ0, which vary with L. On the basis of the mean squared displacement, the diffusive behavior of rod-like nanoswimmers subject to active force Fa is found to follow (D - D0) ∝ (μ0Fa)(2)τθ, where D0 depicts the Brownian diffusivity. When the nanoswimmer suspension is under the external force Fe, the balance between the downward migration and upward active diffusion yields the sedimentation length δ = D/(μ0Fe), which no longer obeys δ0 = kBT/Fe obtained from the Einstein-Smoluchowski relationship, D0 = μ0kBT. Different from the suspension of passive rods, the polar order is clearly seen for active rods. The local polar order is essentially constant within the distance of about 2δ from the bottom wall but decays as the distance is further increased. In this work, the active Peclet number is small compared to unity and the maximum polar order grows linearly with Fe/Fa. The polar order arises because it is easier for the nanoswimmer with the swimming direction opposite to the external force to escape from the bottom wall.

Mesoscale simulation of semiflexible chains. I. Endpoint distribution and chain dynamics

The endpoint distribution and dynamics of semiflexible fibers are studied by numerical simulation. A brief overview is given over the analytical theory of flexible and semiflexible polymers. In particular, a closed expression is given for the relaxation spectrum of wormlike chains, which determines polymer diffusion and rheology. Next a simulation model for wormlike chains with full hydrodynamic interaction is described, and relations for the bending and torsion modulus are given. Two methods are introduced to include torsion stiffness into the model. The model is validated by simulating single chains in a heat bath, and comparing the endpoint distribution of the chains with established Monte Carlo results. It is concluded that torsion stiffness leads to a slightly shorter effective persistence length for a given bending stiffness. To further validate the simulation model, polymer diffusion is studied for fixed persistence length and varying polymer length N. The diffusion constant shows crossover from Rouse (D [proportionality] N(-1)) to reptation behaviour (D [proportionality] N(-2)). The terminal relaxation time obtained from the monomer displacement is consistent with the theory of wormlike chains. The probability for chain crossing has also been studied. This probability is so low that it does not influence the present results.

Superiority of branched side chains in spontaneous nanowire formation: exemplified by poly(3-2-methylbutylthiophene) for high-performance solar cells

One-dimensional nanostructures containing heterojunctions by conjugated polymers, such as nanowires, are expected to greatly facilitate efficient charge transfer in bulk-heterojunction (BHJ) solar cells. Thus, a combined theoretical and experimental approach is pursued to explore spontaneous nanowire formation. A dissipative particle dynamics simulation is first performed to study the morphologies formed by rodlike polymers with various side-chain structures. The results surprisingly predict that conjugated polymers with branched side chains are well suited to form thermodynamically stable nanowires. Proof of this concept is provided via the design and synthesis of a branched polymer of regioregular poly(3-2-methylbutylthiophene) (P3MBT), which successfully demonstrates highly dense nanowire formation free from any stringent conditions and stratagies. In BHJ solar cells fabricated using a blend of P3MBT and [6,6]-phenyl-C71-butyric acid methyl ester (PC(71) BM), P3MBT polymers are self-organized into highly crystalline nanowires with a d(100) spacing of 13.30 Å. The hole mobility of the P3MBT:PC(71) BM (1:0.5 by weight) blend film reaches 3.83 × 10(-4) cm(2) V(-1) s(-1) , and the maximum incident photon-to-current efficiency reaches 68%. The results unambiguously prove the spontaneous formation of nanowires using solution-processable conjugated polymers with branched alkyl side chains in BHJ solar cells.

Time-resolved x-ray studies of the dynamics of smectic- A layer realignment by magnetic fields

While the rotation of smectic layers under an applied field may at first appear to be a relatively simple problem, the dynamic processes involved are rather complex. An applied field produces a torque on the liquid crystal director, but has no direct influence on the smectic layers. If the director is reoriented significantly, however, the layers must also reorient in order to accommodate this (the layered structure is produced by short-range molecular interactions). Indeed, if the liquid crystalline order is not maintained during the realignment then matters become even more complex. In this paper we use time-resolved x-ray scattering to investigate the realignment of smectic- A layers in thin-film devices using a magnetic field. No evidence is found for continuous rotation of the smectic layers under any circumstances in such devices, a result that is not found when using bulk samples. No evidence indicating the formation of the nematic phase is observed during realignment. A molecular-dynamics technique is used to model the system which indicates that the sample becomes significantly disorganized during the realignment process when large angular rotations are induced.

A new anisotropic soft-core model for the simulation of liquid crystal mesophases

A new anisotropic soft-core model is presented, which is suitable for the rapid simulation of liquid crystal mesophases. The potential is based on a soft spherocylinder, which can be easily tuned to favor different liquid crystal mesophases. The soft-core nature of the potential makes it suitable for long-time step molecular dynamics or dissipative particle dynamics simulations, particularly as a reference model for mesogens or as an anisotropic solvent for use in combination with atomistic models. Results are presented for two variants of the new potential, which show different mesophase behaviors. Variants of the potential can also be linked together to produce more complicated molecular structures. Here, as an example, results are provided for a model multipedal liquid crystal, which has eight liquid crystalline groups linked to a central core via semiflexible chains. Here, despite the complexity of molecular structure, the model succeeds in showing the spontaneous formation of a liquid crystal phase. The results also demonstrate that there is a very strong coupling between the internal structure of the multipedal mesogen and the molecular order of the phase, with the mesogen spontaneously undergoing major structural rearrangement at the transition to the liquid crystal phase.

Field-induced realignment of a smectic nanodroplet in an external magnetic field: a numerical investigation

The field-induced realignment of a smectic-A phase is in principle a complicated process involving the director rotation via the interaction with the field and the layer rotation via the molecular interactions. Time-resolved X-ray scattering experiments have revealed major phenomena concerning the maintenance of the integrity of the smectic-A layer structure during the alignment process. In order to obtain a deeper insight into this process, we have carried out a dissipative particle dynamics study of the realignment kinetics of a nanodroplet of a smectic-A liquid crystal suspended in an isotropic fluid following a switch in the direction of an applied magnetic field. The strength of the mesogen-field interaction is small compared to the inter-molecular interactions. The reaction of the smectic configuration to the field switch was found to depend on the balance between the inter-molecular interactions stabilising the formation of the smectic layering and the interaction of the mesogens with the external field. It is found that the rotational behaviour of the smectic layers under the influence of an external magnetic field arises from a combination of stochastic translational displacements and rotational motions of the centres of mass of the mesogens in the nanodroplets. The simulations indicate that X-ray scattering and NMR experiments monitoring the orientational order are sensitive to different aspects of the realignment process.

A dissipative particle dynamics study of the realignment of a nanodroplet of a nematic in a weak external magnetic field

We present a dissipative particle dynamics (DPD) approach for simulating the realignment of a nematic nanodroplet suspended in an isotropic fluid following a switch in the direction of an applied external magnetic field. The interaction of the mesogens with the external field is weak relative to the inter-molecular interactions. The simulations were used to investigate the way orientational equilibrium is re-established. The results reveal that the realignment process of the nanodroplet is consistent with its fluid structure. The reorientation of the nanodroplet as a whole is found to be caused by an internal structural rearrangement rather than a coherent rotation of the centres of mass of the mesogens about the centre of the nanodroplet. The switch in the field direction furthermore is found to induce a transient spatial variation in the orientational order of the long axes of the mesogens: the orientational order parameters decreases on moving from the core of the nanodroplet to the surface in contact with the isotropic environment. The results highlight differences between the time evolution of the orientation of the long molecular axes in the field and the rotations of the centres of mass of the mesogens about the centre of the nanodroplet.