Polymer-clay nanocomposites: a multiscale molecular modeling approach

A hierarchical procedure bridging the gap between atomistic and mesoscopic simulation for polymer-clay nanocomposite (PCN) design is presented. The dissipative particle dynamics (DPD) is adopted as the mesoscopic simulation technique, and the interaction parameters of the mesoscopic model are estimated by mapping the corresponding energy values obtained from atomistic molecular dynamics (MD) simulations. The predicted structure of the nylon 6 PCN system considered is in excellent agreement with previous experimental and atomistic simulation results.     

Constant-pressure simulations with dissipative particle dynamics

Dissipative particle dynamics (DPD) is a mesoscopic simulation method for studying hydrodynamic behavior of complex fluids. Ideally, a mesoscopic model should correctly represent the thermodynamic and hydrodynamic properties of a real system beyond certain length and time scales. Traditionally defined DPD quite successfully mimics hydrodynamics but is not flexible enough to accurately describe the thermodynamics of a real system. The so-called multibody DPD (MDPD) is a pragmatic extension of the classical DPD that allows one to prescribe the thermodynamic behavior of a system with only a small performance impact. In an earlier paper [S. Y. Trofimov, E. L. F. Nies, and M. A. J. Michels, J. Chem. Phys. 117, 9383 (2002)] we much improved the accuracy of the MDPD model for strongly nonideal systems, which are of most practical interest. The ability to correctly reproduce the equation of state of realistic systems in turn makes simulations at constant pressure sensible and useful. This situation of constant-pressure conditions is very common in experimental studies of (soft) condensed matter but has so far remained unexplored with the traditional DPD. Here, as a proof of concept, we integrate a modified version of the Andersen barostat into our improved MDPD model and make an evaluation of the performance of the new model on a set of single- and multicomponent systems. The modification of the barostat suppresses the "unphysical" volume oscillations after a sudden pressure change and simplifies the equilibration of the system.     

Dissipative Particle Dynamics Simulations of Polymer Brushes: Comparison with Molecular Dynamics Simulations

Summary: The structure of polymer brushes is investigated by dissipative particle dynamics (DPD) simulations that include explicit solvent particles. With an appropriate choice of the DPD interaction parameters , we obtain good agreement with previous molecular dynamics (MD) results where the good solvent behavior has been modeled by an effective Lennard–Jones potential. The present results confirm that DPD simulation techniques can be applied for large length scale simulations of polymer brushes. A relation between the different length scales and is established.

Polymer brush at a solid–liquid interface.     

水溶液中嵌段共聚物的耗散颗粒动力学模拟

用耗散颗粒动力学(dissipative particle dyanmics)模拟方法研究了Pluronic L64(PL64)和Pluronic 25R4(25R4)三嵌段共聚物水溶液中的介观相分离,模拟了聚合物聚集的动力学变化过程. 结果发现,在水溶液中,不同浓度的聚合物溶液表现出不同的介观结构,如分散相、球形胶束、双连续相(bicontinuous)等；而Pluronic L64在低浓度时更容易形成双连续相. 耗散颗粒动力学模拟可以作为实验的一个辅助,提供介观层次上的信息,对实验起到指导作用.     

Semi-bottom-up coarse graining of water based on microscopic simulations

The generalized dissipative particle dynamics (DPD) equation derived from the generalized Langevin equation under Markovian approximations is used to simulate coarse-grained (CG) water cells. The mean force and the friction coefficients in the radial and transverse directions needed for DPD equation are obtained directly from the all atomistic molecular dynamics (AAMD) simulations. But the dissipative friction forces are overestimated in the Markovian approximation, which results in wrong dynamic properties for the CG water in the DPD simulations. To account for the non-Markovian dynamics, a rescaling factor is introduced to the friction coefficients. The value of the factor is estimated by matching the diffusivity of water. With this semi-bottom-up mapping method, the radial distribution function, the diffusion constant, and the viscosity of the coarse-grained water system computed with DPD simulations are all in good agreement with AAMD results. It bridges the microscopic level and mesoscopic level with consistent length and time scales.     

A single-site anisotropic soft-core model for the study of phase behavior of soft rodlike particles

A novel mesoscopic simulation model is proposed to study the liquid crystal phase behavior of the anisotropic rodlike particles with a soft repulsive interaction,which possesses a modified anisotropic conservative force type used in dissipative particle dynamics.The influences of the repulsion strength and the particle shape on the phase behavior of soft rodlike particles are examined.In the simulations,we observe the formation of the nematic phase and smectic-A phase from the initially isotropic phase.More...     

The phase behavior, structure, and dynamics of rodlike mesogens with various flexibility using dissipative particle dynamics simulation

We present a systematic dissipative particle dynamics (DPD) study on the phase behavior, structure, and dynamics of rodlike mesogens. In addition to a rigid fused-bead-chain model with RATTLE constraint method, we also construct a semirigid model in which the flexibility is controlled by the bending constant of k(φ). Using this notation, the rigid model has an infinite bending constant of k(φ)=∞. Within the parameter space studied, both two kinds of models exhibit the nematic and smectic-A phases in addition to the isotropic and solid phases. All of the phase transitions are accompanied by the discontinuities in the thermodynamical, structural, and dynamical quantities and the hysteresis around the transition points, and are therefore first order. Note that the obtained solid state exhibits an in-layer tetragonal packing due to the high density. For the rigid model, the simulations show that the liquid crystal phases can be observed for mesogens with at least five beads and the nematic phase is the first one to appear. More importantly, the phase diagram of seven-bead-chain models is obtained as a function of k(φ) and temperature. It is found that decreasing the value of k(φ) reduces the anisotropy of molecular shape and the orientational ordering, and thereby shifts the liquid crystal phases to the lower temperature end of the phase diagram. Due to the different k(φ) dependence of phase transition temperatures, the nematic phase range exhibits a more marked narrowing than the smectic-A phase as k(φ) is reduced, implying that the flexibility has a destabilizing effect on the nematic and smectic-A phases. We also have investigated the anisotropic translational diffusion in liquid crystal phases and its temperature and flexibility dependence. In our study, we find that the phases formed, their statical and dynamic properties, as well as the transition properties are in close accord with those observations in real thermotropic liquid crystals. It is clear that both the rigid and semirigid models we used are valuable models with which to study the behavior of thermotropic liquid crystals using DPD algorithm.     

The effects of Lowe-Andersen temperature controlling method on the polymer properties in mesoscopic simulations

Lowe-Andersen (LA) temperature controlling method [C. P. Lowe, Europhys. Lett. 47, 145 (1999)] is applied in a series of mesoscopic polymer simulations to test its validity and efficiency. The method is an alternative for dissipative particle dynamics simulation (DPD) technique which is also Galilean invariant. It shows excellent temperature control and gives correct radial distribution function as that from DPD simulation. The efficiency of LA method is compared with other typical DPD integration schemes and is proved to be moderately efficient. Moreover, we apply this approach to diblock copolymer microphase separation simulations. With LA method, we are able to reproduce all the results from the conventional DPD simulations. The calculated structure factors of the microphases are consistent with the experiments. We also study the microphase evolution dynamics with increasing chiN and find that the bath collision frequency Gamma does not affect the order of appearing phases. Although the thermostat does not affect the surface tension, the order-disorder transition (ODT) is somewhat sensitive to the values of Gamma, i.e., the ODT is nonmonotonic with increasing Gamma. The dynamic scaling law is also tested, showing that the relation obeys the Rouse theory with various Gamma.     

Self-organization process of ordered structures in linear and star poly(styrene)-poly(isoprene) block copolymers: Gaussian models and mesoscopic parameters of polymeric systems

Mesoscopic simulations of linear and 3-arm star poly(styrene)-poly(isoprene) block copolymers was performed using a representation of the polymeric molecular structures by means of Gaussian models. The systems were represented by a group of spherical beads connected by harmonic springs; each bead corresponds to a segment of the block chain. The quantitative estimation for the bead-bead interaction of each system was calculated using a Flory-Huggins modified thermodynamical model. The Gaussian models together with dissipative particle dynamics (DPD) were employed to explore the self-organization process of ordered structures in these polymeric systems. These mesoscopic simulations for linear and 3-arm star block copolymers predict microphase separation, order-disorder transition, and self-assembly of the ordered structures with specific morphologies such as body-centered-cubic (BCC), hexagonal packed cylinders (HPC), hexagonal perforated layers (HPL), alternating lamellar (LAM), and ordered bicontinuous double diamond (OBDD) phases. The agreement between our simulations and experimental results validate the Gaussian chain models and mesoscopic parameters used for these polymers and allow describing complex macromolecular structures of soft condensed matter with large molecular weight at the statistical segment level.     

Bottom-up coarse-graining of a simple graphene model: the blob picture

The coarse-graining of a simple all-atom 2D microscopic model of graphene, in terms of "blobs" described by center of mass variables, is presented. The equations of motion of the coarse-grained variables take the form of dissipative particle dynamics (DPD). The coarse-grained conservative forces and the friction of the DPD model are obtained via a bottom-up procedure from molecular dynamics (MD) simulations. The separation of timescales for blobs of 24 and 96 carbon atoms is sufficiently pronounced for the Markovian assumption, inherent to the DPD model, to provide satisfactory results. In particular, the MD velocity autocorrelation function of the blobs is well reproduced by the DPD model, provided that the effect of friction and noise is taken into account. However, DPD cross-correlations between neighbor blobs show appreciable discrepancies with respect to the MD results. Possible extensions to mend these discrepancies are briefly outlined.     

A coarse-grained explicit solvent simulation of rheology of colloidal suspensions

We use a simple extension of the dissipative particle dynamics (DPD) model to address the dynamical properties of macrosolutes immersed in complex fluid solvents. In this approach, the solvent particles are still represented as DPD particles, thereby retaining the time and length scale advantages offered by the DPD approach. In contrast, the solute particles are represented as hard particles of the appropriate size. We examine the applicability of this simulation approach to reproduce the correct hydrodynamical characteristics of the mixture. Our results focus on the equilibrium dynamics and the steady-state shear rheological behaviors for a range of volume fractions of the suspension, and demonstrate excellent agreement with many published experimental and theoretical results. Moreover, we are also able to track the glass transition of our suspension and the associated dynamical signatures in both the diffusivities and the rheological properties of our suspension. Our results suggest that the simulation approach can be used as a one-parameter model to examine quantitatively the rheological properties of colloidal suspensions in complex fluid solvents such as polymeric melts and solutions, as well as allied dynamical phenomena such as phase ordering in mixtures of block copolymers and particles.     

Ordered packing of soft discoidal system

A novel mesoscopic simulation method is adopted to study the ordered packing of the anisotropic disklike particles with a soft repulsive interaction, which possesses a modified anisotropic conservative force type used in dissipative particle dynamics. We examine the influence of the shape of the particles, the angular width of the repulsion, and the strength of the repulsion on the packing structures. Specifically, an ordered hexagonal columnar structure is obtained in our simulations. Our study demonstrates that an anisotropic repulsive potential between soft discoidal particles is sufficient to produce a relatively ordered hexagonal columnar structure.     

Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics

The authors analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer dynamics. It has been argued that a low Schmidt number in a DPD fluid can lead to underdevelopment of the hydrodynamic interaction in polymer solutions. The authors' analyses reveal that equilibrium polymer dynamics in dilute solution, under typical DPD simulation conditions, obey the Zimm [J. Chem. Phys. 24, 269 (1956)] model very well. With a further reduction in the Schmidt number, a deviation from the Zimm model to the Rouse model is observed. This implies that the hydrodynamic interaction between monomers is reasonably developed under typical conditions of a DPD simulation. Only when the Schmidt number is further reduced, the hydrodynamic interaction within the chains becomes underdeveloped. The screening of the hydrodynamic interaction and the excluded volume interaction as the polymer volume fraction is increased are well reproduced by the DPD simulations. The use of soft interaction between polymer beads and a low Schmidt number do not produce noticeable problems for the simulated dynamics at high concentrations, except for the entanglement effect which is not captured in the simulations.     

On Coarse-Graining by the Inverse Monte Carlo Method: Dissipative Particle Dynamics Simulations Made to a Precise Tool in Soft Matter Modeling

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD) simulations, which are then used in coarse-grained dissipative particle dynamics (DPD) simulations. Here, the effective potentials were obtained by applying the inverse Monte Carlo method [Lyubartsev and Laaksonen, Phys. Rev. E. 52, 3730 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. In our first application of the method, the effective potentials were used in DPD simulations of aqueous NaCl solutions. With the same computational effort we were able to simulate systems of one order of magnitude larger than the MD simulations. The results from the MD and DPD simulations are in excellent agreement.     

Mesoscopic model for diffusion-influenced reaction dynamics

A hybrid mesoscopic multiparticle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum, and energy so that hydrodynamic effects are fully taken into account. Reactive and nonreactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for large-scale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A + C <==> B + C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction phi of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.     

Adsorption and disjoining pressure isotherms of confined polymers using dissipative particle dynamics

The adsorption and disjoining pressure isotherms of polymers confined by planar walls are obtained using Monte Carlo (MC) simulations in the Grand Canonical (GC) ensemble in combination with the mesoscopic technique known as dissipative particle dynamics (DPD). Two models of effective potentials for the confining surfaces are used: one with both an attractive and a repulsive term and one with a purely repulsive term. As for the polymer, seven-bead linear model of polyethylene glycol (PEG) dissolved in water is used. The results indicate remarkably good agreement between the trends shown by our adsorption isotherms and those obtained from experiments of PEG on oxide surfaces. Additionally, the disjoining pressure isotherm of water shows oscillations, while those of PEG display the same trend for both wall models. Moreover, it is found that the disjoining pressure isotherms are in qualitative agreement with those from experiments on confined linear polymers.     

重质油胶体聚集结构的耗散粒子动力学模拟

重质油是以沥青质为胶核分散于饱和油分中形成的极其复杂的胶体体系.本文采用耗散粒子动力学(DPD)方法研究重质油的胶体结构及其影响因素.根据重质油各组分的分子结构特征,构建了描述重质油组分的粗粒化模型化合物.模拟结果表明,本文构建的粗粒化模型能很好地反映重质油的胶体聚集结构.沥青质分子结构对胶体聚集结构有序性有显著影响,较高稠合程度的芳香环结构将使胶束结构有较高的有序性,烷基侧链则表现出分散作用.重质油中的胶质具有胶溶作用,胶质与沥青质的浓度比存在一个极限,当小于这个极限时,重质油将出现聚沉.     

Phase behavior of lyotropic rigid-chain polymer liquid crystal studied by dissipative particle dynamics

The phase behavior of lyotropic rigid-chain liquid crystal polymer was studied by dissipative particle dynamics (DPD) with variations of the solution concentration and temperature. A chain of fused DPD particles was used to represent each mesogenic polymer backbone surrounded with the strongly interacted solvent molecules. The free solvent molecules were modeled as independent DPD particles, where each particle includes a lump of solvent molecules with the volume roughly equal to the solvated polymer segment. The simulation shows that smectic-B (S(B)), smectic-A (S(A)), nematic (N), and isotropic (I) phases exist within certain regions in the temperature and concentration parameter space. The temperature-dependent S(B)∕S(A), S(A)∕N, and N∕I phase transitions occur in the high concentration range. In the intermediate concentration range, the simulation shows coexistence of the anisotropic phases and isotropic phase, where the anisotropic phases can be the S(B), S(A), or N phases. Mole fraction and compositions of the coexisted phases are determined from the simulation, which indicates that concentration of rigid rods in isotropic phase increases as the temperature increases. By fitting the orientational distribution function of the systems, the biphasic coexistence is further confirmed. From the parameter α obtained for the simulation, the distribution of the rigid rods in the two coexistence phases is quantitatively evaluated. By using model and simulation methods developed in this work, the phase diagrams of the lyotropic rigid-chain polymer liquid crystal are obtained. Incorporating the solvent particles in the DPD simulation is critical to predict the phase coexistence and obtain the phase diagrams.     

Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.