Mingge Deng

Dissipative particle dynamics simulations of toroidal structure formations of amphiphilic triblock copolymers.

In this paper, the dynamic assembly of toroidal micelle structures of amphiphilic triblock copolymers in dilute solution has been investigated using dissipative particle dynamics simulations. The amphiphilic molecule is represented by a coarse-grained model, which contains hydrophilic and hydrophobic particles. Some microstructures of complex morphology having toroidal micelles have been observed in the simulations; the toroidal micelle formation is in accordance with the theoretical prediction of the toroidal structure in cylindrical micelle suspensions by Pochan et al. (Science 2004, 306, 94). These findings are very interesting, and these complex morphologies enrich our knowledge of the potential products obtained from the self-assembly of block copolymers.

Complex micelles from the self-assembly of amphiphilic triblock copolymers in selective solvents.

The self-assembled microstructures of amphiphilic block copolymers depend on the selectivity of solvents for each block. By changing the selectivity of solvents, defined in terms of the repulsive interactions between the solvent and the hydrophilic/hydrophobic particles, an extensive simulation study on the spontaneous formation of complex micelles from amphiphilic triblock copolymers in a dilute solution is presented. The dynamic pathways in the formation of these assemblies have been investigated using a particle-based dissipative particle dynamics approach. In addition, the potential mechanism behind the formation of these microstructures has also been studied, which may be helpful in explaining how these aggregates are formed and in understanding the general principle of amphiphilic molecules.

Complex micelles from the self-assembly of coil-rod-coil amphiphilic triblock copolymers in selective solvents

We report an extensive simulation study on the spontaneous formation of complex micelles from coil-rod-coil amphiphilic triblock copolymers in dilute solution resulting from solvent selectivity. The amphiphilic molecule is built from one hydrophilic block on each side and a hydrophobic block in the middle. The rigidity of the rod block is introduced by adding a bond-bending potential of the angle among three subsequent particles in the hydrophobic block. The incorporation of rigid-rod block into the amphiphilic block copolymer results in the self-assembled microstructures and their corresponding properties that differ from those built from fully flexible amphiphilic molecules with the same conditions. By changing the selectivity of solvents, defined in terms of the repulsive interactions between the solvent and the hydrophilic/hydrophobic particles, we find that the aggregation morphology changes from bundle-like micelles to spherical and cylindrical micelles to elongated micelles and then to ring-like toroidal micelles, revealing that the selectivity of solvents is a key factor that determines aggregation morphology. In addition, we observe that the formation of toroidal micelles from coil-rod-coil amphiphilic triblock copolymers proceeds via the growth pathway, which is quite distinct from the conventional toroidal micelle coalescence pathway observed in the self-assembling process of fully flexible amphiphilic triblock copolymer systems. Chain packing in toroidal micelles formed from amphiphilic triblock copolymers with fully flexible hydrophobic and rigid-rod hydrophobic blocks is likewise investigated. The simulation results show that the rigid-rod middle blocks adopt only extended conformations while flexible-coil middle blocks can adopt both folded and extended conformations in toroidal micelles. These findings demonstrate that the bond-bending potential in amphiphilic molecules is an effective and relatively simple method to model the behavior of coil-rod-coil amphiphilic block copolymers.

Fluctuating hydrodynamics in periodic domains and heterogeneous adjacent multidomains: Thermal equilibrium

We first study fluctuating hydrodynamics (FH) at equilibrium in periodic domains by use of the smoothed dissipative particle dynamics (SDPD) method. We examine the performance of SDPD by comparing it with the theory of FH. We find that the spatial correlation of particle velocity is always the Dirac δ function, irrespective of numerical resolution, in agreement with the theory. However, the spatial correlation of particle density has a finite range of r(c), which is due to the kernel smoothing procedure for the density. Nevertheless, this finite range of correlation can be reduced to an arbitrarily small value by increasing the resolution, that is, reducing r(c), similarly to how the smoothing kernel converges to the Dirac δ function. Moreover, we consider temporal correlation functions (CFs) of random field variables in Fourier space. For sufficient resolution, the CFs of SDPD simulations agree very well with analytical solutions of the linearized FH equations. This confirms that both the shear and sound modes are modeled accurately and that fluctuations are generated, transported, and dissipated in both thermodynamically and hydrodynamically consistent ways in SDPD. We also show that the CFs of the classical dissipative particle dynamics (DPD) method with proper parameters can recover very well the linearized solutions. As a reverse implication, the measurement of CFs provides an effective means of extracting viscosities and sound speed of a DPD system with a new set of input parameters. Subsequently, we study the FH in truncated domains in the context of multiscale coupling via the domain decomposition method, where a SDPD simulation in one subdomain is coupled with a Navier-Stokes (NS) solver in an adjacent subdomain with an overlapping region. At equilibrium, the mean values of the NS solution are known a priori and do not need to be extracted from actual simulations. To this end, we model a buffer region as an equilibrium boundary condition (EBC) at the truncated side of the SDPD simulation. In the EBC buffer, the velocity of particles is drawn from a known Gaussian distribution, that is, the Maxwell-Boltzmann distribution. Due to the finite range of spatial correlation, the density of particles in the EBC buffer must be drawn from a conditional Gaussian distribution, which takes into account the available density distribution of neighboring interior particles. We introduce a Kriging method to provide such a conditional distribution and hence preserve the spatial correlation of density. Spatial and temporal correlations of SDPD simulations in the truncated domain are compared to that in a single complete domain. We find that a gap region between the buffer and interior is important to reduce the extra dissipation generated by the artificial buffer at equilibrium, rendering more investigations necessary for thermal fluctuations in the multiscale coupling of nonequilibrium flows.

Analysis of hydrodynamic fluctuations in heterogeneous adjacent multidomains in shear flow.

We analyze hydrodynamic fluctuations of a hybrid simulation under shear flow. The hybrid simulation is based on the Navier-Stokes (NS) equations on one domain and dissipative particle dynamics (DPD) on the other. The two domains overlap, and there is an artificial boundary for each one within the overlapping region. To impose the artificial boundary of the NS solver, a simple spatial-temporal averaging is performed on the DPD simulation. In the artificial boundary of the particle simulation, four popular strategies of constraint dynamics are implemented, namely the Maxwell buffer [Hadjiconstantinou and Patera, Int. J. Mod. Phys. C 08, 967 (1997)], the relaxation dynamics [O’Connell and Thompson, Phys. Rev. E 52, R5792 (1995)], the least constraint dynamics [Nie et al.,J. Fluid Mech. 500, 55 (2004); Werder et al., J. Comput. Phys. 205, 373 (2005)], and the flux imposition [Flekkøy et al., Europhys. Lett. 52, 271 (2000)], to achieve a target mean value given by the NS solver. Going beyond the mean flow field of the hybrid simulations, we investigate the hydrodynamic fluctuations in the DPD domain. Toward that end, we calculate the transversal autocorrelation functions of the fluctuating variables in k space to evaluate the generation, transport, and dissipation of fluctuations in the presence of a hybrid interface. We quantify the unavoidable errors in the fluctuations, due to both the truncation of the domain and the constraint dynamics performed in the artificial boundary. Furthermore, we compare the four methods of constraint dynamics and demonstrate how to reduce the errors in fluctuations. The analysis and findings of this work are directly applicable to other hybrid simulations of fluid flow with thermal fluctuations.

Flow in complex domains simulated by Dissipative Particle Dynamics driven by geometry-specific body-forces

We demonstrate how the quality of simulations by Dissipative Particle Dynamics (DPD) of flows in complex geometries is greatly enhanced when driven by body forces suitably tailored to the geometry. In practice, the body force fields are most conveniently chosen to be the pressure gradient of the corresponding Navier-Stokes (N-S) flow. In the first of three examples, the driving-force required to yield a stagnation-point flow is derived from the pressure field of the potential flow for a lattice of counter-rotating line vortices. Such a lattice contains periodic squares bounded by streamlines with four vortices within them. Hence, the DPD simulation can be performed with periodic boundary conditions to demonstrate the value of a non-uniform driving-force without the need to model real boundaries. The second example is an irregular geometry consisting of a 2D rectangular cavity on one side of an otherwise uniform channel. The Navier-Stokes pressure field for the same geometry is obtained numerically, and its interpolated gradient is then employed as the driving-force for the DPD simulation. Finally, we present a third example, where the proposed method is applied to a complex 3D geometry of an asymmetric constriction. It is shown that in each case the DPD simulations closely reproduce the Navier-Stokes solutions. Convergence rates are found to be much superior to alternative methods; in addition, the range of convergence with respect to Reynolds number and Mach number is greatly extended.

Adsorption of a wormlike polymer in a potential well near a hard wall: Crossover between two scaling regimes

We consider the adsorption of a semiflexible wormlike polymer to the surface of a flat wall by a square potential well of width W and depth v. Using a wormlike chain formalism that couples the orientational and positional degrees of freedom, for a wormlike chain much longer than the persistence length, we numerically calculate the adsorption phase diagram and analyze the scaling behavior near the phase transition. Our numerical results over a wide range of W can be used to identify scaling behaviors valid in the large and small width-to-persistence-length ratio as well as near the adsorption phase transition.

Dissipative Particle Dynamics: Foundation, Evolution, Implementation, and Applications

Dissipative particle dynamics (DPD) is a particle-based Lagrangian method for simulating dynamic and rheological properties of simple and complex fluids at mesoscopic length and time scales. In this chapter, we present the DPD technique, beginning from its original ad hoc formulation and subsequent theoretical developments. Next, we introduce various extensions of the DPD method that can model non-isothermal processes, diffusion-reaction systems, and ionic fluids. We also present a brief review of programming algorithms for constructing efficient DPD simulation codes as well as existing software packages. Finally, we demonstrate the effectiveness of DPD to solve particle-fluid problems, which may not be tractable by continuum or atomistic approaches.

Electrostatic correlations near charged planar surfaces

Electrostatic correlation effects near charged planar surfaces immersed in a symmetric electrolytes solution are systematically studied by numerically solving the nonlinear six-dimensional electrostatic self-consistent equations. We compare our numerical results with widely accepted mean-field (MF) theory results, and find that the MF theory remains quantitatively accurate only in weakly charged regimes, whereas in strongly charged regimes, the MF predictions deviate drastically due to the electrostatic correlation effects. We also observe a first-order like phase-transition corresponding to the counterion condensation phenomenon in strongly charged regimes, and compute the phase diagram numerically within a wide parameter range. Finally, we investigate the interactions between two likely-charged planar surfaces, which repulse each other as MF theory predicts in weakly charged regimes. However, our results show that they attract each other above a certain distance in strongly charged regimes due to significant electrostatic correlations.

Anisotropic single-particle dissipative particle dynamics model

We have developed a new single-particle dissipative particle dynamics (DPD) model for anisotropic particles with different shapes, e.g., prolate or oblate spheroids. In particular, the conservative and dissipative interactions between anisotropic single DPD particles are formulated using a linear mapping from the isotropic model of spherical particles. The proper mapping operator is constructed between each interacting pair of particles at every time step. Correspondingly, the random forces are properly formulated to satisfy the fluctuation-dissipation theorem (FDT). Notably, the model exactly conserves both linear and angular momentum. We demonstrate the proposed models accuracy and efficiency by applying it for modeling colloidal ellipsoids. Specifically, we show it efficiently captures the static properties of suspensions of colloidal ellipsoids. The isotropic-nematic transition in an ellipsoidal suspension is reproduced by increasing its volume fraction or the aspect ratio of ellipsoid particles. Moreover, the hydrodynamics and diffusion of a single colloidal ellipsoid (prolate or oblate with moderate aspect ratios) are accurately captured. The calculated drag force on the ellipsoid and its diffusion coefficients (both translational and rotational) agree quantitatively with the theoretical predictions in the Stokes limit.