Control of aggregation of nanoparticles by double-hydrophilic block copolymers: a dissipative particle dynamics study

Double-hydrophilic block copolymer (DHBC)-directed mineralization is investigated by dissipative particle dynamics (DPD) simulation. By mineralization, we refer to the formation of inorganic crystals from the solution. In the current study, the DHBCs are modeled as chains of A and B blocks with repulsion between unlike blocks, while the mineralization is approximated by aggregation of hydrophobic nanoparticles from the solution. Depending on the relative concentrations of nanoparticles and DHBC, dispersed spherical aggregates, hexagonally packed cylinders, and ordered lamellae structures are obtained. The structures formed are seen to be controlled by competing forces between aggregation of nanoparticles, the interaction of DHBC with nanoparticles, and the self-assembly of DHBC in the solution. The time evolutions of hexagonally packed cylinders and ordered lamellae are studied. For the development of cylinders, nanoparticles first aggregate into orientationally disordered small cylinders, then these cylinders slowly grow into hexagonally packed long cylinders. For the development of ordered lamellae, nanoparticles first form a disordered structure, then grow into disordered lamellae, and at last evolve into ordered lamellae. The simulation demonstrates that addition of DHBC can effectively control the aggregation of inorganic particles and lead to formation of a variety of nanostructures.     

Dissipative particle dynamics simulation of gold nanoparticles stabilization by PEO–PPO–PEO block copolymer micelles

Dissipative particle dynamics (DPD) was used to simulate the formation and stabilization of gold nanoparticles in poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) (PEO–PPO–PEO) block copolymer micelles. Primary gold clusters that were experimentally observed in the early stage of gold nanoparticle formation were modeled as gold bead in DPD simulation. It showed that gold beads were wrapped by the block copolymer and aggregated into spherical particles inside the micelles and forming stable Pluronic–gold colloids with two-layer structures. Increasing Pluronic concentration, molecular weight, and PPO block length led to the formation of more uniform and more stable gold nanoparticles. Density profiles of water beads suggested that the micelles, especially the hydrophobicity of the micellar cores, played an important role in stabilizing gold nanoparticles. Dynamic process indicated that the formation of gold nanoparticles was controlled by the competition between aggregation of primary gold clusters and the stabilization by micelles of block copolymers.. The DPD simulation results of gold–copolymer–water system agree well with previous experiments, while more structure information on microscopic level could be provided.     

Dissipative particle dynamics study on the interfaces in incompatible A/B homopolymer blends and with their block copolymers

Dissipative particle dynamics, a simulation technique appropriate at mesoscopic scales, has been applied to investigate the interfaces in immiscible binary A/B homopolymer blends and in the ternary systems with their block copolymers. For the binary blends, the interfacial tension increases and the interface thickness decreases with increasing Flory-Huggins interaction parameter chi while the homopolymer chain length is fixed. However, when the chi parameter and one of the homopolymer chain length is fixed, increasing another homopolymer chain length will induce only a small increase on interfacial tension and slight decrease on interface thickness. For the ternary blends, adding the A-b-B block copolymer will reduce the interfacial tension. When the mole number of the block copolymer is fixed, longer block chains have higher efficiency on reducing the interfacial tension than the shorter ones. But for the block copolymers with fixed volume fraction, shorter chains will be more efficient than the longer ones on reducing the interfacial tension. Increasing the block copolymer concentration reduces interfacial tension. This effect is more prominent for shorter block copolymer chains.     

Monte-Carlo simulation of ternary blends of block copolymers and homopolymers

We perform a theoretically informed coarse grain Monte-Carlo simulation in the nPT-ensemble and the Gibbs ensemble on symmetric ternary mixtures of AB-diblock copolymers with the corresponding homopolymers. We study the lamellar period by varying the length and amount of homopolymers. The homopolymer distribution within the lamellar morphology is determined as is the maximum amount of homopolymer within the lamellae. Gibbs ensemble simulations are used to locate the three-phase coexistence between two homopolymer-rich phases and a lamellar phase.     

Dissipative particle dynamics simulation study of the bilayer-vesicle transition

A bilayer structure is an important immediate for the vesicle formation. However,the mechanism for the bilayer-vesicle transition remains unclear. In this work,a dissipative particle dynamics(DPD) simulation method was employed to study the mechanism of the bilayer-vesicle transition. A coarse-grained model was built based on a lipid molecule termed dimyristoylphosphatidylcholine(DMPC). Simulations were performed from two different initial configurations:a random dispersed solution and a tensionless bilayer. It was found that the bilayer-vesicle transition was driven by the minimization of the water-tail hydrophobic interaction energy,and was accompanied with the increase of the position entropy due to the redistribution of water molecules. The bulk pressure was reduced during the bilayer-vesicle transition,suggesting the evolved vesicle morphology was at the relatively low free energy state. The membrane in the product vesicle was a two-dimensional fluid. It can be concluded that the membrane of a vesicle is not interdigitated and most of the bonds in lipid chains are inclined to orient along the radical axis of the vesicle.     

Dissipative particle dynamics simulation of phase behavior of aerosol OT/water system

The phase behaviors of the binary mixture of an anionic surfactant aerosol OT (AOT) and water are investigated on a mesoscopic level using dissipative particle dynamics (DPD) computer simulations. With a simple surfactant model, various aggregation structures of AOT in water including the lamellar, viscous isotropic, and reverse hexagonal phases are obtained, which agree well with the experimental phase diagram. Special attention is given on the unusual lamellar regions. Water diffusivity shows much useful information to understand how the phase behaviors varied with concentration and temperature. It is proposed that the anomalous lamellar phenomena at intermediate AOT concentration (about 40%) are due to the formation of a defective structure, pseudoreversed hexagonal phase, which evidently decreases the water diffusivity. After increasing temperature above 328 K, the pseudoreversed hexagonal structure will be partly transformed to a normal lamellar phase structure and the system lamellar ordering is therefore enhanced.     

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.     

Dissipative particle dynamics simulation study on the binary mixture phase separation coupled with polymerization

The influence of polymerization on the phase separation of binary immiscible mixtures has been investigated by the dissipative particle dynamics simulations in two dimensions. During polymerization, the bulk viscosity increases, which consequently slows down the spinodal decomposition process. The domain size growth is monitored in the simulations. The absence of 23 exponent for inertial hydrodynamic mechanism clearly reflects the suppressing effect of polymerization on the phase separation. Due to the increasing viscosity, the individual phase may be trapped in a metastable stage instead of the lamellar morphology identified for symmetric mixtures. Moreover, the polymerization induced phase separation in the binary miscible mixture has been studied. The domain growth is strongly dependent on the polymerization probability, which is naturally related to the activation energy for polymerization. The observed complex phase separation behavior is attributed to the interplay between the increasing thermodynamic driving force for phase separation and the increasing viscosity that suppresses phase separation as the polymerization proceeds.     

Interfacial fluctuations of block copolymers: a coarse-grain molecular dynamics simulation study

The lamellar and cylindrical phases of block copolymers have a number of technological applications, particularly when they occur in supported thin films. One such application is block copolymer lithography, the use of these materials to subdivide or enhance submicrometer patterns defined by optical or electron beam methods. A key parameter of all lithographic methods is the line edge roughness (LER), because the electronic or optical activities of interest are sensitive to small pattern variations. While mean-field models provide a partial picture of the LER and interfacial width expected for the block interface in a diblock copolymer, these models lack chemical detail. To complement mean-field approaches, we have carried out coarse-grain molecular dynamics simulations on model poly(ethyleneoxide)-poly(ethylethylene) (PEO-PEE) lamellae, exploring the influence of chain length and hypothetical chemical modifications on the observed line edge roughness. As expected, our simulations show that increasing chi (the Flory-Huggins parameter) is the most direct route to decreased roughness, although the addition of strong specific interactions at the block interface can also produce smoother patterns.     

Dissipative particle dynamics simulation of contact angle hysteresis on a patterned solid/air composite surface

We have studied two types of topological substrates--the continuous solid substrates (CSS) and the discontinuous solid substrates (DSS)--by using the dissipative particle dynamics (DPD) method for a better understanding of the contact angle hysteresis on two such substrates. After the validation of DPD in the system, we found that DSS has a different distribution of the metastable states from that of CSS and that DSS has relatively larger contact angle hysteresis at lower temperature. Obtained results also show that CSS is more suitable for making an ultrahydrophobic or ultralyophobic surface than DSS from the point of view of dynamic wettability.     

Dissipative particle dynamics simulation of microphase separation behaviors in graft-diblock copolymer films

Dependence of the microphase separation behaviors of graft-diblock copolymers (A _x )g(B _y ) in thin films on composition fraction, thickness of film and A–B repulsing strength is investigated preliminarily by dissipative particle dynamics. Several kinds of ordered mesostructures have been observed and the simulated phase diagrams show evident asymmetries, besides, the center of lamellas region shifts away from f _A = 0.5. Some of the mesostructures in the film can correspond to those in bulk. Decreasing the thickness of film as well as strengthening the A–B repulsion help the mesostructures enhance the degree of order.     

Molecular bottle brushes in a solution of semiflexible polyelectrolytes and block copolymers with an oppositely charged block: a molecular dynamics simulation

Using a coarse-grained model, we performed molecular dynamics simulations of the electrostatically driven self-assembly of strongly charged polyelectrolytes and diblock copolymers composed of oppositely charged and neutral blocks. Stoichiometric micelle-like complexes formed in a dilute solution represent cylindrical brushes whose conformation is determined by the linear charge density on the polyelectrolyte and by temperature. The core-shell morphology of the cylindrical brushes is proven. The core of these anisotropic micelles consists of an insoluble complex coacervate formed by the ionic chains and a shell made up of the neutral solvophilic blocks. As the concentration of macromolecules increases, the orientational ordering of ionic micelles takes place. The complexation can induce effective steric stiffening of the polyelectrolyte chains.     

Micellization behavior of star-block copolymers in a selective solvent: A Brownian dynamics simulation approach

Micellization behavior of (AB)n type star-block copolymer in a selective solvent for its outer block is investigated by using a Brownian dynamics simulation. Micellar properties are compared in terms of the arm number (n) of star-block copolymer. It is observed that the critical micelle concentration (cmc) shows a minimum when the cmc is plotted against the arm number. The star-block copolymer with longer soluble block shows the cmc minimum at smaller arm number than that with shorter soluble block. Although the star-block copolymer with multiple arms forms more compact core as compared to diblock copolymer, the average aggregation number is inversely proportional to the arm number (approximately 1/n), which implies that the micelle size is invariant with the arm number. Theoretical predictions based on a simple mean field theory agree qualitatively well with the simulation results.     

Molecular dynamics simulation of the forces between colloidal nanoparticles in n-decane solvent

Molecular dynamics is utilized to simulate solvation forces between two nanoparticles immersed in liquid n-decane. Three types of solvophilic nanoparticles are investigated with sizes in the 1-6 nm range: small and large amorphous spheres and crystalline cubes. We find that the solvation forces are negligible for the small spheres, which have diameters comparable to the end-to-end distance of all-trans decane, and we attribute this to the inability of the small spheres to induce decane ordering in the interparticle gap. The cubic nanoparticles (and to a lesser extent, the large spheres) are able to induce the formation of solidlike, n-decane layers in their gap for certain nanoparticle separations, and the transition between layered and disordered structures leads to solvation forces that oscillate between repulsion and attraction as the nanoparticle separation is varied. We find that the Derjaguin approximation [B. V. Derjaguin, Kolloid-Z. 69, 155 (1934)] is not effective at describing the dependence of the solvation forces on nanoparticle size and shape-contrasting results from a previous study involving these nanoparticles in Lennard-Jones solvent [Y. Qin and K. A. Fichthorn, J. Chem. Phys. 119, 9745 (2003)]. In particular, we find that for decane, the magnitude of the repulsive solvation forces is sensitive to nanoparticle size and shape, a phenomenon we attribute to the size and rigid-rod structure of n-decane, which makes its ordering in the interparticle gap sensitive to the size and the surface roughness of the nanoparticles.     

Ultraslow dynamics in asymmetric block copolymers with nanospherical domains

Low shear rate and low frequency measurements focused on the extremely slow dynamics of a three-dimensional body-centered cubic (BCC) structure of an asymmetric block copolymer under nanophase-separated conditions. The material studied was poly(styrene-b-ethylene-co-butylene-b-styrene) swollen in a hydrocarbon oil selective for the midblock. Transient viscosities during start-up of shear flow at extremely low shear rates are governed by very long relaxation times and by a modulus that is nearly the same as the plateau modulus obtained from oscillatory shear experiments. Only at extremely low shear rates a zero shear viscosity could be attained. Its very high value is close to the viscosity calculated from stress relaxation experiments. The steady shear viscosity decreases by several orders of magnitude when increasing the shear rate. SAXS experiments on samples sheared even at very low rates indicated loss of the BCC order that was present in the annealed samples before shearing. The SAXS profile recorded on such a sample showed a first-order maximum followed by a broad shoulder indicating a liquid-like short-range order of PS nanospheres in the swollen EB matrix.     

Brownian dynamics simulation study on the self-assembly of incompatible star-like block copolymers in dilute solution

We study the self-assembly of symmetric star-like block copolymers (A(x))(y)(B(x))(y)C in dilute solution by using Brownian dynamics simulations. In the star-like block copolymer, incompatible A and B components are both solvophobic, and connected to the center bead C of the polymer. Therefore, this star-like block copolymer can be taken as a representative of soft and deformable Janus particles. In our Brownian dynamics simulations, these "soft Janus particles" are found to self-assemble into worm-like lamellar structures, loose aggregates and so on. By systematically varying solvent conditions and temperature, we build up the phase diagram to illustrate the effects of polymer structure and temperature on the aggregate structures. At lower temperatures, we can observe large worm-like lamellar aggregates. Upon increasing the temperature, some block copolymers detach from the aggregate; this phenomenon is especially sensitive for the polymers with less arms. The aggregate structure will be quite disordered when the temperature is high. The incompatibility between the two parts in the star-like block copolymer also affects the self-assembled structures. We find that the worm-like structure is longer and narrower as the incompatibility between the two parts is stronger.     

Molecular dynamics simulation with a continuum electrostatic model of the solvent

The accuracy and simplicity of the Poisson-Boltzmann electrostatics model has led to the suggestion that it might offer an efficient solvent model for use in molecular mechanics calculations on biomolecules. We report a successful merger of the Poisson-Boltzmann and molecular dynamics approaches, with illustrative calculations on the small solutes dichloroethane and alanine dipeptide. The algorithm is implemented within the program UHBD. Computational efficiency is achieved by the use of rather coarse finite difference grids to solve the Poisson-Boltzmann equation. Nonetheless, the conformational distributions generated by the new method agree well with reference distributions obtained as Boltzmann distributions from energies computed with fine finite difference grids. The conformational distributions also agree well with the results of experimental measurements and conformational analyses using more detailed solvent models. We project that when multigrid methods are used to solve the finite difference problem and the algorithm is implemented on a vector supercomputer, the computation of solvent electrostatic forces for a protein of modest size will add only about 0.1 s computer time per simulation step relative to a vacuum calculation. © 1995 by John Wiley & Sons, Inc.     

Preliminary communication Lyotropic mesomorphism of AB block copolymers in a nematic solvent

A lyotropic hexagonal mesophase is identified in a mixture of a low molecular mass nematic solvent and an AB block copolymer with a liquid crystalline block A and an isotropic block B by polarizing microscopy. A highly ordered striated texture evolves spontaneously that exhibits an additional striated fine structure within the stripe domains.     

Dissipative particle dynamics simulation of depletion layer and polymer migration in micro- and nanochannels for dilute polymer solutions

The flows of dilute polymer solutions in micro- and nanoscale channels are of both fundamental and practical importance in variety of applications in which the channel gap is of the same order as the size of the suspended particles or macromolecules. In such systems depletion layers are observed near solid-fluid interfaces, even in equilibrium, and the imposition of flow results in further cross-stream migration of the particles. In this work we employ dissipative particle dynamics to study depletion and migration in dilute polymer solutions in channels several times larger than the radius of gyration (Rg) of bead-spring chains. We compare depletion layers for different chain models and levels of chain representation, solvent quality, and relative wall-solvent-polymer interactions. By suitable scaling the simulated depletion layers compare well with the asymptotic lattice theory solution of depletion near a repulsive wall. In Poiseuille flow, polymer migration across the streamlines increases with the Peclet and the Reynolds number until the center-of-mass distribution develops two symmetric off-center peaks which identify the preferred chain positions across the channel. These appear to be governed by the balance of wall-chain repulsive interactions and an off-center driving force of the type known as the Segre-Silberberg effect.