Monte Carlo simulation of micelle formation in block copolymer solutions

Short block copolymers in selective solvents (bad for A-block, good for B-block) are modeled by flexible bead-spring chains, where beads interact with short range Morse potentials of variable strength. It is shown that already very short chains (N_A = N_B = 2) exhibit a rather well-defined critical micelle concentration (cmc). The mass distribution of the micelles and their gyration tensor components as well as their internal structure are studied. It is shown that the relaxation time increases exponentially with the strength E_AA of the attractive energy between the A-monomers, and thus frozen-in micelles of medium size are obtained when E_AA is chosen too large. Our results are compared to studies of related but somewhat different models.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Monte Carlo simulation of segregation in ceramic thin films

A Monte Carlo exchange technique is used to study segregation in thin ceramic films with application to MgO/MnO. The approach is not restricted to the dilute limit. Surface concentrations as a function of temperature and film composition are determined directly from the simulations. For all compositions studied (Mn(chi)Mg(1-chi)O, 0 < or = chi < or = 1) the (001) surface is Mn(2+) rich; the occupancy of sites by Mn(2+) decreases rapidly with depth. The ratio of the number of Mn(2+) to Mg(2+) ions at the surface decreases as a function of temperature. The calculated enthalpies of segregation of Mn(2+) for the thin film are strongly dependent on the total Mn(2+) concentration at small Mn(2+) concentrations, with the enthalpy of segregation varying by a factor of two with surface coverage.     

Nonequilibrium Monte Carlo simulation of lattice block copolymer chains subject to oscillatory shear flow

This paper has extended nonequilibrium Monte Carlo (MC) approach to simulate oscillatory shear flow in a lattice block copolymer system. Phase transition and associated rheological behaviors of multiple self-avoiding chains have been investigated. Stress tensor has been obtained based upon sampled configuration distribution functions. At low temperatures, micellar structures have been observed and the underlying frequency-dependent rheological properties exhibit different initial slopes. The simulation outputs are consistent with the experimental observations in literature. Chain deformation during oscillatory shear flow has also been revealed. Although MC simulation cannot account for hydrodynamic interaction, the highlight of our simulation approach is that it can, at small computing cost, investigate polymer chains simultaneously at different spatial scales, i.e., macroscopic rheological behaviors, mesoscopic self-assembled structures, and microscopic chain configurations.     

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2相似文献   

Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts

Extensive Monte Carlo simulations are presented for the Fried-Binder model of block copolymer melts, where polymer chains are represented as self and mutually avoiding walks on a simple cubic lattice, and monomer units of different kind (A, B) repel each other if they are nearest neighbors (ε_AB > 0). Choosing a chain length N = 20, vacancy concentration Φ_v = 0,2, composition ƒ = 3/4, and a L × L × L geometry with periodic boundary conditions and 8 ≤ L ≤ 32, finite size effects on the collective structure factor S(q) and the gyration radii are investigated. It is shown that already above the microphase separation transition, namely when the correlation length ξ(T) of concentration fluctuations becomes comparable with L, a nonmonotonic variation of both S(q) and the radii with L sets in. This variation is due to the fact that the wavelength λ^*(T) of the ordering (defined from the wavenumber q^* where S(q) is maximal at λ^* = 2 π/q^*) in general is incommensurable with the box. The competition of two nontrivial lengths ξ(T), λ^* (T) with L makes the straigthforward application of finite size scaling techniques impossible, unlike the case of polymer blends. Since also the specific heat is found to have a broad rounded peak near the transition only, locating the transition accurately from Monte Carlo simulations remains an unsolved problem.     

Monte Carlo simulation of phase separations of block copolymers and of corresponding blends

The Monte Carlo method has been used to simulate the phase separations of block copolymers and of corresponding blends with very high concentration (sum of volume fractions of blocks A and B: ϕ_A + ϕ_B = 0,9545). Our main findings are as follows: (1) The mixing is nonrandom even in the athermal limit. (2) The nonselective good solvent molecules (ϕ_V = 0,0455) are mostly located at the interface between A- and B-rich phases, thus, it is not true that solvent and monomeric units will remain mixed at all temperatures. (3) Even for the same microscopic A-B interaction energy, ε, and at the same temperature, the Flory-Huggins parameter χ of block copolymers is always higher than that of corresponding blends, and the χ values of block copolymers and corresponding blends have different ε-dependencies. (4) The critical values of χ both for block copolymer and corresponding blend are obtained and compared with the meanfield theoretical predictions. It is found that the ratio of χ_c (block)/χ_c (blend) is qualitatively compatible with the prediction of the Flory-Leibler theory.     

Preparation and phase segregation of block copolymer nanotube multiblocks

Different nanotubes were prepared from two triblock copolymers. Chemistry was performed on the nanotubes so that one type contained amino terminal groups and the other bore carboxyl terminal groups. The amino and carboxyl groups were reacted by amidization to join the nanotubes head to tail to yield nanotube multiblocks. The block copolymer nanotube multiblocks (CONATUBLOCs) may be viewed as a macroscopic counterpart of block copolymers. Like block copolymers, the different blocks of the CONATUBLOCs segregated from one another not only in a block-selective solvent mixture but also in the solid state.     

Boltzmann bias grand canonical Monte Carlo

We derive an efficient method for the insertion of structured particles in grand canonical Monte Carlo simulations of adsorption in very confining geometries. We extend this method to path integral simulations and use it to calculate the isotherm of adsorption of hydrogen isotopes in narrow carbon nanotubes (two-dimensional confinement) and slit pores (one-dimensional confinement) at the temperatures of 20 and 77 K, discussing its efficiency by comparison to the standard path integral grand canonical Monte Carlo algorithm. We use this algorithm to perform multicomponent simulations in order to calculate the hydrogen isotope selectivity for adsorption in narrow carbon nanotubes and slit pores at finite pressures. The algorithm described here can be applied to the study of adsorption of real oligomers and polymers in narrow pores and channels.     

Dynamic Monte Carlo simulation of aggregation of nanoparticles in the presence of diblock copolymer

The aggregation of hydrophobic nanoparticles in the presence of diblock copolymers is investigated using dynamic Monte Carlo simulation on a simple cubic lattice. One nanoparticle occupies one lattice site, one block copolymer (A(m)B(m)) occupies 2m sequentially linked sites with m segments of A and m segments of B, and solvents are represented by any unoccupied sites. All of them are self-avoiding and nearest-neighbor interactions are considered. A compact big aggregate, dispersed aggregates wrapped by polymer chains, and an ordered lamellar structure are obtained by varying the concentration of copolymer. The structures are seen to be controlled by competing forces between the interaction of copolymer with nanoparticles and the self-assembly of copolymer in solution. The critical concentration of copolymer needed to form the lamellar structure, C(p,L), decreases with the chain length. It is also found that C(p,L) decreases roughly linearly with the concentration of nanoparticles C(n), which can be approximately expressed as C(p,L)=0.764-0.857C(n) when m=2. The simulation demonstrates that addition of diblock copolymer can effectively control the aggregation of nanoparticles and lead to the formation of a variety of nanostructures.     

Phase behavior and structure formation in linear multiblock copolymer solutions by Monte Carlo simulation

The solution phase behavior of short, strictly alternating multiblock copolymers of type (A(n)B(n))(m) was studied using lattice Monte Carlo simulations. The polymer molecules were modeled as flexible chains in a monomeric solvent selective for block type A. The degree of block polymerization n and the number of diblock units per chain m were treated as variables. We show that within the regime of parameters accessible to our study, the thermodynamic phase transition type is dependent on the ratio of m / n. The simulations show microscopic phase separation into roughly spherical aggregates for m / n ratios less than a critical value and first-order macroscopic precipitation otherwise. In general, increasing m at fixed n, or n at fixed m, promotes the tendency toward macroscopic phase precipitation. The enthalpic driving force of phase change is found to universally scale with chain length for all multiblock systems considered and is independent of the existence of a true phase transition. For aggregate forming systems at low amphiphile concentrations, multiblock chains are shown to self-assemble into intramolecular, multichain clusters. Predictions for microstructural dimensions, including critical micelle concentration, equilibrium size, shape, aggregation parameters, and density distributions, are provided. At increasing amphiphile density, interaggregate bridging is shown to result in the formation of networked structures, leading to an eventual solution-gel transition. The gel is swollen and consists of highly interconnected aggregates of approximately spherical morphology. Qualitative agreement is found between experimentally observed physical property changes and phase transitions predicted by simulations. Thus, a potential application of the simulations is the design of multiblock copolymer systems which can be optimized with regard to solution phase behavior and ultimately physical and mechanical properties.     

Monte Carlo simulation on symmetric ABA/AB copolymer blends in confined thin films

The effects of blend composition on morphology, order-disorder transition (ODT), and chain conformation of symmetric ABA/AB copolymer blends confined between two neutral hard walls have been investigated by lattice Monte Carlo simulation. Only lamellar structure is observed in all the simulation morphologies under thermodynamic equilibrium state, which is supported by theoretical prediction. When the composition of AB diblock copolymer (phi) increases, both lamellar spacing and the corresponding ODT temperature increase, which can be attributed to the variation of conformation distribution of the diblock and the triblock copolymer chains. In addition, both diblock and triblock copolymer, chains with bridge conformation extend dramatically in the direction parallel to the surface when the system is in ordered state. Finally, the copolymer chain conformation depends strongly on both the blend composition and the incompatibility parameter chiN.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Monte Carlo simulations of segregation in Pt-Re catalyst nanoparticles

We have investigated the segregation of Pt atoms to the surfaces of Pt-Re nanoparticles using the Monte Carlo method and modified embedded-atom method potentials that we have developed for Pt-Re alloys. The Pt(75)Re(25) nanoparticles (containing from 586 to 4,033 atoms) are assumed to have disordered fcc configurations and cubo-octahedral shapes (terminated by [111] and [100] facets), while the Pt(50)Re(50) and Pt(25)Re(75) nanoparticles (containing from 587 to 4,061 atoms) are assumed to have disordered hcp configurations and truncated hexagonal bipyramidal shapes (terminated by [0001] and [1011] facets). We predict that due to the segregation process the equilibrium Pt-Re nanoparticles would achieve a core-shell structure, with a Pt-enriched shell surrounding a Pt-deficient core. For fcc cubo-octahedral Pt(75)Re(25) nanoparticles, the shells consist of almost 100 at. % of Pt atoms. Even in the shells of hcp truncated hexagonal bipyramidal Pt(50)Re(50) nanoparticles, the concentrations of Pt atoms exceed 85 at. % (35 at. % higher than the overall concentration of Pt atoms in these nanoparticles). Most prominently, all Pt atoms will segregate to the surfaces in the hcp truncated hexagonal bipyramidal Pt(25)Re(75) nanoparticles containing less than 1000 atoms. We also find that the Pt atoms segregate preferentially to the vertex sites, less to edge sites, and least to facet sites on the shell of Pt-Re nanoparticles.     

Monte Carlo simulations of segregation in Pt-Ni catalyst nanoparticles

We have investigated the segregation of Pt atoms in the surfaces of Pt-Ni nanoparticles, using modified embedded atom method potentials and the Monte Carlo method. The nanoparticles are constructed with disordered fcc configurations at two fixed overall concentrations (50 at. % Pt and 75 at. % Pt). We use octahedral and cubo-octahedral nanoparticles terminated by {111} and {100} facets to examine the extent of the Pt segregation to the nanoparticle surfaces at T=600 K. The model particles contain between 586 and 4033 atoms (particle size ranging from 2.5 to 5 nm). Our results imply that a complete {100}-facet reconstruction could make the cubo-octahendral Pt-Ni nanoparticles most energetically favorable. We predict that at 600 K due to segregation the equilibrium cubo-octahedral Pt50Ni50 nanoparticles with fewer than 1289 atoms and Pt75Ni25 nanoparticles with fewer than 4033 atoms would achieve a surface-sandwich structure, in which the Pt atoms are enriched in the outermost and third atomic shells while the Ni atoms are enriched in the second atomic shell. We also find that, due to an order-disorder transition, the Pt50Ni50 cubo-octahedral nanoparticles containing more than 2406 atoms would form a core-shell structure with a Pt-enriched surface and a Pt-deficient homogenous core.     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

Self-assembled structures of block copolymers in selective solvents reproduced by lattice Monte Carlo simulation

A lattice Monte Carlo (MC) simulation was applied to the study of block copolymers in selective solvent or amphiphilic surfactant solution on the segment level, hydrodynamic interactions being neglected. The code was found to be very efficient, employing a partial reptation mode as the elementary movement of the self-avoiding lattice chains. Typical self-assembled structures of block copolymers such as micelle, lamellae, hexagonal cylinder and bicontinuous networks have been successfully reproduced without any priori specification of structure. Order–disorder and order–order transitions of diblock copolymers are systematically studied by adjusting the temperature, the concentration or the block length ratio in a series computer simulations. The structural differences between micelles composed of ABA and BAB triblock copolymers are also explicitly revealed by direct visualisation of the underlying chain configurations. The simulation results are consistent with the experimental observations in the literature. This simulation approach is thus a very useful tool in the extensive investigation of self-assembled structures. It has the advantage that both micro-domains and chain configurations can be studied with only a comparatively modest call on computational resources.     

Solid-liquid phase coexistence of the Lennard-Jones system through phase-switch Monte Carlo simulation

The phase-switch Monte Carlo method of Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] is extended to enable calculation of solid-liquid phase coexistence for soft potentials. The method directly accesses coexistence information about a system while avoiding simulation of the interfacial region. Order parameters are introduced that allow one to define a path that connects liquid and crystalline phases. Transition matrix methods are employed to bias the sampling such that both phases are sampled in a rapid and efficient manner. Coexistence properties are determined through an analysis of specific volume probability distributions, which are generated naturally during a biased simulation. The approach is demonstrated with the Lennard-Jones system. Finite-size effects are examined and compared to those for the hard sphere system. In addition, two techniques are considered for accounting for long-range interactions. The methodology presented here is general and therefore provides a basis for its application to other soft systems.     

Comparison of surface segregation and anticoagulant property in block copolymer blended evaporation and phase inversion membranes

In our recent study, an ABA amphiphilic triblock copolymer poly(vinyl pyrrolidone)‐b‐poly(methyl methacrylate)‐b‐poly(vinyl pyrrolidone) (PVP‐b‐PMMA‐b‐PVP) was synthesized and directly blended with polyethersulfone (PES) to prepare membranes. To further investigate the effects of surface energy and miscibility on the near‐surface composition profile of the membranes, evaporation membrane and phase inversion membrane of PES/PVP‐b‐PMMA‐b‐PVP were prepared by evaporating the solvent in a vacuum oven, and by a liquid–liquid phase separation technique, respectively. The surface composition and morphology of the membranes were investigated using XPS and tapping mode atomic force microscopy, and the surface segregations of the membranes were compared and discussed. For the evaporation membrane, PVP blocks were buried below the lower surface energy PMMA blocks and PES substrate at the airside surface. For the phase inversion membrane, however, the hydrophilicity of PVP blocks were the biggest driving force because of the high speed exchange between water and solvent, and present at the membrane surface. Thus, the modified PES membrane prepared by using phase inversion method has a layer of PVP block brushes on its surface and has the better anticoagulant property, which might improve the blood compatibility of the membrane and has potential to be used in blood purification. Copyright © 2012 John Wiley & Sons, Ltd.     

Histogram Monte Carlo simulation on phase transitions in single‐polymer systems

Applying the histogram Monte Carlo simulation method and the bond‐fluctuation model, various phase transitions in single‐polymer systems were investigated. The critical transition temperature (Θ point) in the coil‐globule collapse transition of a macromolecular chain is accurately determined. Finite‐size scaling results near the transition point are verified. The first‐order transition associated with the freezing/crystallization of a polymer at a temperature below the Θ point is also observed. The free energy profiles associated with these two transitions are explicitly computed. Furthermore, the unfolding phase transition associated with stretching a collapsed polymer chain is investigated. The free energy profile associated with the transition is explicitly computed. Results on the energy cumulants and free energy profiles provide direct evidences for the first‐order nature of the unfolding phase transition.