Mesoscopic simulation of metastable microphases in the order–order transition from gyroid-to-lamellar states of PS–PI diblock copolymer

The formation of metastable microphases during the order–order transition (OOT) from gyroid-to-lamellar states of a poly(styrene)–poly(isoprene) (PS–PI) copolymer has been investigated on a mesoscopic level using dissipative particle dynamics simulations. The formation of the gyroid microphase was obtained via an order–disorder transition process (ODT). The microphase was then subjected to thermal heating cycles. A thermodynamic instability of poly(styrene) microdomains due to temperature effects induces anisotropic composition fluctuations in the gyroid structure and a microphase transformation from gyroid-to-lamellar takes place via an OOT. Two metastable microphases (hexagonal perforated layers and cylinders) were detected during the thermal process. Results are consistent with experimental and theoretical studies.     

Temperature‐dependent changes in the hydrogen bonded hard segment network and microphase morphology in a model polyurethane: Experimental and simulation studies

Hydrogen bonding between hard segments has a critical effect on the morphology and properties of polyurethanes. Influence of temperature on hydrogen bonded urethane network and melting behavior of a model semicrystalline segmented polyurethane was investigated by experiments and simulations. Polyurethane was synthesized by the stoichiometric reaction between p‐phenylene diisocyanate and poly(tetramethylene oxide) (PTMO) with a molecular weight of 1000 g/mol. Simulations were carried out using dissipative particle dynamics (DPD) and molecular dynamics (MD) approaches. Experimental melting behavior obtained by various techniques was compared with simulations. DPD simulations showed a room temperature microphase morphology consisting of a three‐dimensional hydrogen‐bonded urethane hard segment network in a continuous and amorphous PTMO matrix. The first‐order melting transitions of crystalline urethane hard segments observed during the continuous isobaric heating in DPD and MD simulations (340–360 K) were in reasonably good agreement with those observed experimentally, such as AFM (320–340 K), WAXS (330–360 K), and FTIR (320–350 K) measurements. Quantitative verification of the melting of urethane hard segments was demonstrated by sharp discontinuities in energy versus temperature plots obtained by MD simulations due to substantial decrease in the number of hydrogen bonds above 340 K. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 182–192     

A practical method to avoid bond crossing in two-dimensional dissipative particle dynamics simulations

Dissipative particle dynamics (DPD) simulation technique is an effective method targeted on mesoscopic simulations in which the interactions between particles are soft. As a result, it inevitably causes bond crossing and interpenetration between particles. Here we develop a practical method based on the two-dimensional DPD model which can extremely reduce the possibility of bond crossing. A rigid core is added to each particle by modifying the form of the conservative force in DPD so that the particles cannot penetrate each other. Then by adjusting the spring constant of the bond, we can impose a simple geometry constraint so that the bond crossing can hardly take place. Furthermore, we take into account an analytic geometry constraint in the polymerization model of DPD by which we can successfully avoid the severe bond crossing problem during bond generation in two dimensions. A parabola fitting between the pressure and the particle number density shows that our modified DPD model with small rigid cores can still be mapped onto the Flory-Huggins model, and the mesoscopic length scale of our simulations does not change. By analyzing the mean-square displacement of the innermost monomer and the center of mass of the chains, we find a t(8/15) power law of the polymer dynamics in our model instead of the Rouse prediction supporting the recent results in literature.     

Finite-size effects in dissipative particle dynamics simulations

We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.     

耗散粒子动力学模拟Nafion-[Bmim][TfO]离子液体复合膜的介观结构

采用耗散粒子动力学方法模拟研究了离子液体的含量和温度对Nafion-[Bmim][TfO]离子液体复合膜的介观结构的影响。模拟发现了微相分离现象。对不同条件下的微相分离形成的孔径分析表明,随着离子液体在复合膜中含量的增加,离子液体在膜中的聚集状态由分散的团簇转变为连续的通道,但过高的含量会产生腔室结构。随着温度的上升,离子液体通道的结构变得更加复杂,原有的腔室结构转化为通道的新支路,即高温下离子液体通道变得更加连通。界面分布几率和径向分布函数的计算结果表明,离子液体的阳离子烷基链嵌进Nafion主链中,侧链磺酸基团分布的变化直接影响咪唑基团和阴离子在微相界面的分布。本工作在介观水平上探索了Nafion-离子液体复合膜结构,可为开发高温聚电解质燃料电池材料提供一定的参考。     

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.     

梳型嵌段共聚物微观相分离的耗散粒子动力学模拟

利用耗散粒子动力学(Dissipative particle dynamics, DPD)模拟方法研究了二维梳型嵌段共聚物的微观相分离, 得到了相形貌与侧链长度及链段间相互作用的依赖关系, 进一步与线型和星型嵌段共聚物微观相分离进行了对比. 模拟结果揭示了本体中影响梳形嵌段共聚物微观相分离的主要因素, 包括嵌段共聚物的组成\, 拓扑结构以及不同粒子间的排斥力.     

Dissipative particle dynamics at isothermal, isobaric, isoenergetic, and isoenthalpic conditions using Shardlow-like splitting algorithms

Numerical integration schemes based upon the Shardlow-splitting algorithm (SSA) are presented for dissipative particle dynamics (DPD) approaches at various fixed conditions, including a constant-enthalpy (DPD-H) method that is developed by combining the equations-of-motion for a barostat with the equations-of-motion for the constant-energy (DPD-E) method. The DPD-H variant is developed for both a deterministic (Hoover) and stochastic (Langevin) barostat, where a barostat temperature is defined to satisfy the fluctuation-dissipation theorem for the Langevin barostat. For each variant, the Shardlow-splitting algorithm is formulated for both a velocity-Verlet scheme and an implicit scheme, where the velocity-Verlet scheme consistently performed better. The application of the Shardlow-splitting algorithm is particularly critical for the DPD-E and DPD-H variants, since it allows more temporally practical simulations to be carried out. The equivalence of the DPD variants is verified using both a standard DPD fluid model and a coarse-grain solid model. For both models, the DPD-E and DPD-H variants are further verified by instantaneously heating a slab of particles in the simulation cell, and subsequent monitoring of the evolution of the corresponding thermodynamic variables as the system approaches an equilibrated state while maintaining their respective constant-energy and constant-enthalpy conditions. The original SSA formulated for systems of equal-mass particles has been extended to systems of unequal-mass particles. The Fokker-Planck equation and derivations of the fluctuation-dissipation theorem for each DPD variant are also included for completeness.     

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.     

Budding dynamics of individual domains in multicomponent membranes simulated by N-varied dissipative particle dynamics

We study the budding dynamics of individual domains in flat, multicomponent membranes using dissipative particle dynamics (DPD) simulations with varied bead number N, in which addition and deletion of beads based on their density at the membrane boundary is introduced. The budding process of a tubular bud, accompanied by a dynamical transition reflected in the energy and morphology evolutions, is investigated. The simulations show that budding duration is shortened with increasing line tension and depends on the domain size quadratically. At low line tension, increasing bending modulus accelerates budding at first, but suppresses the process as it increases further. In addition, the controlling role of the surface tension in the budding process is also explored. Finally, we use the N-varied DPD to simulate the experimentally observed multicomponent tubular vesicles, and the three bud growth modes are confirmed.     

Modeling gas permeation through membranes by kinetic Monte Carlo: applications to H2, O2, and N2 in hydrated Nafion®

We present a simulation tool in order to predict gas permeation through heterogeneous, microphase separated structures. The method combines dissipative particle dynamics (DPD) with kinetic Monte Carlo (KMC). Morphologies obtained from DPD are mapped onto a high density grid on which gas diffusion takes place. Required input parameters for the KMC calculations are the gas solubility and gas diffusion constant within each of the pure phase components. Our method was tested and validated for permeation of H(2), O(2), and N(2) gasses through hydrated Nafion membranes at various temperatures and water contents. We predict that membranes that contain an equal volume fraction of water, those with the highest ion exchange capacity exhibit the largest N(2) and O(2) permeation rates. For membranes of the same ion exchange capacity the H(2), O(2), and N(2) and permeability increases approximately linearly with Bragg spacing. We also predict that O(2) gas permeation depends much more on bottleneck phenomena within the phase separated morphologies than H(2) gas permeation. Overall, the calculated H(2) and O(2) permeability is found to be slightly lower than experimental values. This is attributed to the robustness of DPD resulting in ～7% larger Bragg spacing as compared with experiment and∕or increased gas solubility within the polymer phase with water uptake.     

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.     

淀粉微球形成过程的介观模拟及实验

以环己烷为油相、淀粉乳液为水相、Span60和Tween60为乳化剂,对淀粉微球的形成过程进行了耗散粒子动力学(DPD)模拟及实验研究.模拟结果表明,淀粉微球的形成过程存在四个阶段,即淀粉与乳化剂分子无规则分散阶段、小聚集体形成阶段、球状聚集体形成阶段和稳定平衡阶段,并且发现油水比是影响聚集体是否能形成球状的关键因素.油水比小于7的条件下,油水两相分离较难,水相呈现片状、十字型状、柱状及椭球状等形状;当油水比增加到8,水相能形成微球且微球粒径随油水比增加而减小.同时实验结果表明,油水比为8时,微球粘连,几乎看不清球状形貌,油水比为10～20时,微球的粒径随油水比的增大而减小.实验结果很好地吻合了模拟结果.     

Computer Simulations on the Channel Membrane Formation by Nonsolvent Induced Phase Separation

The formation of channel membrane of polystyrene‐block‐poly(4‐vinyl pyridine) block copolymer is studied by computer simulations with the nonsolvent induced phase separation (SNIPS) method. Dissipative particle dynamics is employed to study the microphase separation process and the SNIPS mechanism. Simulation results indicate that polymer concentration has a significant effect on the membrane structure. Channel membranes form in the copolymer concentration range of 44–58%. Block ratio plays an important role in shaping the membrane structure. Solvent exchange rate also affects the degree of microphase separation at each evolution stage of simulation. The time evolution of morphologies shows that the microphase separation processes happen with the following sequences: the polymer self‐assembled and many small pores appear, then they form irregular cavities and cross‐link gradually, finally the channel membrane forms. These results throw light on the formation mechanism of polymer membranes and provide insightful guidance for future membrane design and preparation.     

Cell dynamics simulations of block copolymers

Cell dynamics simulations are a powerful tool to simulate kinetic processes in phase separating systems. Here we review the technique and its application to block copolymers. Its advantages and disadvantages compared to other simulation methods for block copolymer structure and dynamics are reviewed. Results on the dynamics of microphase separation and interface propagation, and on the rate of order‐order phase transitions are reviewed. The use of the method to model certain shear‐induced structural and flow effects is also summarised.     

A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows

The purpose of this study is to compare the results from molecular-dynamics and dissipative particle dynamics (DPD) simulations of Lennard-Jones (LJ) fluid and determine the quantitative effects of DPD coarse graining on flow parameters. We illustrate how to select the conservative force coefficient, the cut-off radius, and the DPD time scale in order to simulate a LJ fluid. To show the effects of coarse graining and establish accuracy in the DPD simulations, we conduct equilibrium simulations, Couette flow simulations, Poiseuille flow simulations, and simulations of flow around a periodic array of square cylinders. For the last flow problem, additional comparisons are performed against continuum simulations based on the spectral/hp element method.     

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.     

Effects of interaction range and compressibility on the microphase separation of diblock copolymers: Mean-field analysis

Using the random-phase approximation and self-consistent field calculations, we have investigated the effects of finite interaction range and compressibility on the order-disorder transition (ODT) and the lamellar structure of symmetric diblock copolymers. While the compressibility does not affect the ODT, both the values of chiN and bulk lamellar period at the ODT increase with increasing interaction range. On the other hand, both the free-energy density and bulk period of the lamellae increase with either increasing interaction range or decreasing compressibility. Even with a finite compressibility, the mean-field ODT is still a second-order phase transition. The scaling exponent of bulk lamellar period with chiN, however, decreases with increasing compressibility. Our mean-field analysis provides a well understood reference for the study of fluctuation effects in diblock copolymers with finite interaction range and compressibility.     

Mesoscale simulation of polymer reaction equilibrium: combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations.     

Thermal Effect on Positive Patterned Self-Assembled Monolayer Grown from a Droplet of Alkanethiol

Atomic force microscope technique is widely used for the spatial narrow deposition of molecules inside the bare space of preexisting self-assembled monolayer (SAM) matrix. Using molecular dynamics simulation, we studied the formation of positively patterned SAM from a globule of 1-octadecanethiol (ODT) on predesigned SAM matrix of 1-dodecanethiol (DDT) and effect of temperature on it. The alkyl chains of ODT SAM were densely packed and ordered by means of chemisorption through sulfur atoms. The circular SAM of ODT contained defects due to the molecules those were standing upside down or trapped inside ODT SAM. We found that with the increase of temperature, these defects moved out by flipping of inverted ODT molecules or building spaces to be adsorbed on Au surface. The ODT molecules on the top of the pile of stable circular SAM or those are upside down and trapped disperse in a unique fashion namely serial pushing through which molecules firstly make a free space to enter inside the adsorbed thiol molecules and then push neighboring molecules to get enough space to be adsorbed on the gold surface. The stability of ODT SAM was confirmed by analyzing different structural properties such as tilt angle, tilt orientation. and backbone orientation. We also calculated the diffusion coefficient of the ODT molecules which were on the top of SAM island. © 2019 Wiley Periodicals, Inc.