Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Analogy in the adsorption of random copolymers and homopolymers at solid-liquid interface: a Monte Carlo simulation study

The adsorption of random copolymers at solid-liquid interface from a nonselective solvent has been studied by Monte Carlo simulation in a cubic lattice. The polymeric molecules are modeled as self-avoiding linear chains composed of two types of segments A and B. The effects of copolymer composition (A/B ratio), segment-surface interaction, and bulk concentration are examined on the thermodynamic and structural adsorption properties including surface coverage, adsorption amount, adsorption layer thickness, and microscopic density distribution. At a given newly introduced effective adsorption energy, random copolymers are found to behave quantitatively as homopolymers regardless of the copolymer composition and surface affinity. This remarkable analogy provides an efficient way in predicting the adsorption of random copolymers from homopolymers.     

A benchmark quantum Monte Carlo study of the ground state chromium dimer

We report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A superionic state in nano-porous double-layer capacitors: insights from Monte Carlo simulations

Recently observed anomalous properties of ionic-liquid-based nanoporous supercapacitors [C. Largot et al., J. Am. Chem. Soc., 2008, 130, 2730-2731] have attracted much attention. Here we present Monte Carlo simulations of a model ionic liquid in slit-like metallic nanopores. We show that exponential screening of the electrostatic interactions of ions inside a pore, as well as the image-charge attraction of ions to the pore surface, lead to the 'anomalous' increase of the capacitance with decreasing the pore width. The simulation results are in good agreement with the experimental data. The capacitance as a function of voltage is almost constant for low voltages and vanishes above a certain threshold voltage. For very narrow pores, these two regions are separated by a peak. With increase of the pore size the peak turns into a bump and disappears for wide pores. This effect, related to a specific character of the voltage-induced filling of nanopores with counterions at high densities, is yet to be verified experimentally.     

A Monte Carlo study of liquid benzene

A Monte Carlo study for liquid benzene, where the pair potential is described as a sum of Lennard-Jones (12, 6) interactions acting between six equivalent centres of each molecule, has been carried out. The potential parameters have been chosen in such a way that the internal energy and virial pressure were in agreement with the experimental values. The liquid structure has been examined in detail by computing several distribution functions: the radial, the angular correlations and the radial-angular distribution between molecular planes.     

A Monte Carlo study of water clusters

The free energy, internal energy and entropy for water clusters of 8 and 64 molecules have been calculated using the Monte Carlo method and both the Lie-Clementi (C-XII) and Stillinger (ST2) potential functions. Detailed structural data for a cluster of 64 water molecules was also obtained by averaging over a large number of configurations. Average dipole orientations and radial density distributions indicated that individual water molecules were not particularly restricted to fixed orientations and that general ordering tendencies were small.     

A Monte Carlo study of fluctuating polymer-grafted membranes

Using Monte Carlo simulations of an off-lattice model, we study the elastic properties of polymer-grafted membranes. Our results are found to be in good agreement with those predicted by the classical path approximation of the self-consistent field theory and scaling theory based on de Gennes' blob picture. In particular, we found that when the membrane is grafted on both sides by brushes with same molecular weight N and grafting density sigma, the excess bending modulus induced by the polymers scales as N3 sigmaalpha where alpha is consistent with 7/3, as predicted by the self-consistent field theory, and 5/2, as predicted by the scaling theory. When the polymers are grafted to one side of the membrane only, the membrane bends away from the polymers with a spontaneous curvature with a scaling that is consistent with both scaling and self-consistent field theories. When the thickness of the brush exceeds the membrane's spontaneous radius of curvature, the bending modulus approaches a constant which is of the same order as the bending modulus of the bare membrane.     

A Monte Carlo simulation study of branched polymers

Monte Carlo simulations are presented for the static properties of highly branched polymer molecules. The molecules consist of a semiflexible backbone of hard-sphere monomers with semiflexible side chains, also composed of hard-sphere monomers, attached to either every backbone bead or every other backbone bead. The conformational properties and structure factor of this model are investigated as a function of the stiffness of the backbone and side chains. The average conformations of the side chains are similar to self-avoiding random walks. The simulations show that there is a stiffening of the backbone as degree of crowding is increased, for example, if the branch spacing is decreased or side chain length is increased. The persistence length of the backbone is relatively insensitive to the stiffness of the side chains over the range investigated. The simulations reproduce most of the qualitative features of the structure factor observed in experiment, although the magnitude of the stiffening of the backbone is smaller than in experiment.     

Self-assembling of chain molecules in low dimensions: A Monte Carlo study

We studied the self-assembling of linear chain molecules in insoluble monolayers due to attractive interactions. We used lattice Monte Carlo simulations in a two-dimensional system. The molecules consist of segments occupying adjacent lattice sites. The head segments are confined to move along a line whereas the chain segments can arrange in a plane above the heads. Only one interaction parameter is applied. At high densities and small interaction energy the system shows percolation behavior. At moderate and small densities it can be characterized by a monotonous cluster size distribution. Self-assembling occurs at small densities for strong attractive interactions. The corresponding cluster size distributions indicate preferred cluster sizes which depend upon density and interaction strength. With increasing density the clusters grow. The internal cluster structure depends on the cluster size and the interaction parameter. The clusters tend to minimize their total energy. Molecules at cluster margins contribute less to the cluster energy and are mainly disordered. They cause that the cluster properties strongly depend on the cluster size. Large clusters only have minimum energy if the molecules in the cluster are in stretched-out conformation. With decreasing interaction strength the clusters get disordered thereby producing less energy-minimized domain boundaries.     

Condensation phenomena in nanopores: a Monte Carlo study

The nonequilibrium dynamics of condensation phenomena in nanopores is studied via Monte Carlo simulations of a lattice-gas model. Hysteretic behavior of the particle density as a function of the density of a reservoir is obtained for various pore geometries in two and three dimensions. The shape of the hysteresis loops depend on the characteristics of the pore geometry. The evaporation of particles from a pore can be fitted to a stretched exponential decay of the particle density. Phase-separation dynamics inside the pore is effectively described by a random walk of the non-wetting phases. Domain evolution is significantly slowed down in the presence of a random wall-particle potential and gives rise to a temperature-dependent growth exponent. A geometric roughness of the pore wall only delays the onset of a pure domain growth.     

Interfacial properties of glassy polymer melts: A Monte Carlo study

The properties of the interface between a polymer melt and a solid wall are studied over a wide range of temperatures by dynamic Monte Carlo simulations. It is shown that in the supercooled state near the glass transition of the melt an “interphase” forms, the structure of which is influenced by the wall. The thickness of this interphase is determined from the monomer density profile near the surface and is strongly temperature dependent. At low glass-like temperatures it is larger than the bulk radius of gyration of the chains.     

Protection of nano-powders by adsorbed surfactants: A Monte Carlo study

The production of high-performance ceramics requires the protection of powder particles against chemical reactions. Hydrolysis and oxidation of nanoscaled non-oxidic powders can be impeded by a coating consisting of a dense adsorbed layer of amphiphilic molecules. Using Monte Carlo simulations for a coarse grained model the adsorption equilibrium of differently shaped amphiphiles in apolar and polar solvents is investigated. For estimating the protection capability of the adsorbed surfactant film in aqueous environment we study the diffusion of small hydrophilic particles through the adsorbed surfactant film. The surfactants considered as coating agents differ in the number of hydrocarbon tails. It is found that amphiphiles with a single hydrocarbon tail or at most two branches are more suitable to protect particle surfaces than amphiphiles with three or four branches, although the adsorption energy of amphiphiles with many branches is higher.     

Diffusion Monte Carlo study of the equation of state of solid ortho-D2

The authors present results of diffusion Monte Carlo calculations for a system of solid ortho-D2 at different densities, for pressure ranging from 0 up to 350 MPa. They compare the equation of state obtained using two of the most used effective intermolecular potentials, i.e., the Silvera-Goldman and the Buck potentials, with experimental data, in order to assess the validity of the model interactions. The Silvera-Goldman potential has been found to provide a satisfactory agreement with experimental results, showing that, as opposed to what recently found for p-H2, three-body forces can be efficiently accounted for by an effective two-body term.     

Structures of stiff macromolecules of finite chain length near the coil‐globule transition: A Monte Carlo simulation

Using a coarse‐grained model of a semiflexible macromolecule, the equilibrium shapes of the chain have been studied varying both the temperature and the chain stiffness. We have applied Monte Carlo techniques using the bond fluctuation model for a chain length of N = 80 effective monomers, and two different types of interactions: a potential depending on the angle between successive bonds along the chain to control the chain stiffness, and an attractive interaction between non‐bonded effective monomers to model variable solvent quality. In a diagram of states where chain stiffness and inverse temperature are used as variables, we find regions where the chain exists as coil, as spherical globule, and as toroidal globule, respectively. Some of these regions are not limited by sharply defined boundaries, but rather wide two‐state coexistence regions occur in between them, where also intermediate metastable structures (such as rods and disks) occur. Recording histograms of energy, orientational order parameters, etc., which exhibit a two‐peak structure in the two‐state coexistence regions, we perform a subensemble analysis of the individual structures corresponding to these peaks.     

Ground state of small mixed helium and spin-polarized tritium clusters: a quantum Monte Carlo study

We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.     

Monte Carlo study of polyelectrolyte gels

The discontinuous transition between dense and dilute phases in polyelectrolyte gels is observed in Bond-Fluctuation Method Monte Carlo simulations of gels. The transition is driven by the competition between local attractive interactions of a poor-quality solvent and global repulsive interactions from counter-ion pressure. A procedure is introduced that prevents local attractive interactions from destroying ergodicity. Under good solvent conditions, lengths and volumes of gels are found to follow self-avoiding random walk scaling. © 1996 John Wiley & Sons, Inc.     

Grafting of maleic anhydride onto linear polyethylene: A Monte Carlo study

Monte Carlo simulation was used to study the graft of maleic anhydride (MAH) onto linear polyethylene (PE‐g‐MAH) initiated by dicumyl peroxide (DCP). Simulation results revealed that major MAH monomers attached onto PE chains as branched graft at higher MAH content. However, at extremely low MAH content, the fraction of bridged graft was very close to that of branched graft. This conclusion was somewhat different from the conventional viewpoint, namely, the fraction of bridged graft was always much lower than that of branched graft under any condition. Moreover, the results indicated that the grafting degree increased almost linearly to MAH and DCP concentrations. On the other hand, it was found that the amount of grafted MAH dropped sharply with increasing the length of grafted MAH, indicating that MAH monomers were mainly attached onto the PE chain as single MAH groups or very short oligomers. With respect to the crosslink of PE, the results showed that the fraction of PE‐(MAH)_n‐PE crosslink structure increased continuously, and hence the fraction of PE‐PE crosslink decreased with increasing MAH concentration. Finally, quantitative relationship among number average molecular weight of the PE, MAH, and DCP contents was given. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5714–5724, 2004     

Stochastic theory of interfacial enzyme kinetics: A kinetic Monte Carlo study

In the spirit of Gillespie’s stochastic approach we have formulated a theory to explore the advancement of the interfacial enzyme kinetics at the single enzyme level which is ultimately utilized to obtain the ensemble average macroscopic feature, lag-burst kinetics. We have provided a theory of the transition from the lag phase to the burst phase kinetics by considering the gradual development of electrostatic interaction among the positively charged enzyme and negatively charged product molecules deposited on the phospholipid surface. It is shown that the different diffusion time scales of the enzyme over the fluid and product regions are responsible for the memory effect in the correlation of successive turnover events of the hopping mode in the single trajectory analysis which again is reflected on the non-Gaussian distribution of turnover times on the macroscopic kinetics in the lag phase unlike the burst phase kinetics.     

Hydrogen storage in sH hydrates: a Monte Carlo study

Grand canonical Monte Carlo simulations are performed to evaluate the hydrogen-storage capacity of the recently discovered hydrogen hydrates of the sH type, at 274 K and up to 500 MPa. First, the pure H2 hydrate is investigated in order to determine the upper limit of H 2 content in sH hydrates. It is found that the storage capacity of the hypothetical pure H2 hydrate could reach 3.6 wt % at 500 MPa. Depending on pressure, the large cavity of this hydrate can accommodate up to eight H2 molecules, while the small and medium ones are singly occupied even at pressures as high as 500 MPa. Next, the binary H2-methylcyclohexane sH hydrate is examined. In this case, the small and medium cavities are again singly occupied, resulting in a maximum H2 uptake of 1.4 wt %. Finally, the results from simulations on pure H2 and binary hydrates are utilized to investigate the potential of H2 storage in sH hydrates where the promoter molecules occupy the medium instead of the large cavities.