0000000000022275
AUTHOR
Peter Nielaba
Elastic properties, structures and phase transitions in model colloids
The nature of the melting transition for a system of hard discs with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft discs in external periodic (light-) fields show rich phase diagrams including freezing and melting transitions when the density of the syst…
Locally Frozen Defects in Random Sequential Adsorption with Diffusional Relaxation
Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation allows the deposition process to reach full coverage. The coverage approaches the full occupation value, 1, as a power-law with convergence exponent near 1/2. For a periodic lattice of finite (even) size $L$, the final state is a frozen random rectangular grid of domain walls connecting single-site defects. The domain sizes saturate at L**0.8. Prior to saturation, i.e., asymptotically for infinite lattice, the domain growth is power-law with growth exponent ne…
Continuum limit in random sequential adsorption.
We develop analytical estimates of the late-stage (long-time) asymptotic behavior of the coverage in the D-dimensional lattice models of irreversible deposition of hypercube-shaped particles. Our results elucidate the crossover from the exponential time dependence for the lattice case to the power-law behavior with a multiplicative logarithmic factor, in the continuum deposition. Numerical Monte Carlo results are reported for the two-dimensional (2D) deposition, both lattice and continuum. Combined with the exact 1D results, they are used to test the general theoretical expectations for the late-stage deposition kinetics. New accurate estimates of the jamming coverages in 2D rule out some e…
Irreversible Multilayer Adsorption
Random sequential adsorption (RSA) models have been studied due to their relevance to deposition processes on surfaces. The depositing particles are represented by hard-core extended objects; they are not allowed to overlap. Numerical Monte Carlo studies and analytical considerations are reported for 1D and 2D models of multilayer adsorption processes. Deposition without screening is investigated, in certain models the density may actually increase away from the substrate. Analytical studies of the late stage coverage behavior show the crossover from exponential time dependence for the lattice case to the power law behavior in the continuum deposition. 2D lattice and continuum simulations r…
Path-integral Monte Carlo study of crystalline Lennard-Jones systems.
The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate $^{40}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of $^{20}\mathrm{Ne}$ and $^{22}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo result…
The liquid-solid transition of hard discs: first-order transition or Kosterlitz-Thouless-Halperin-Nelson-Young scenario?
We consider the question of whether a two-dimensional hard-disc fluid has a first-order transition from the liquid state to the solid state as in the three-dimensional melting-crystallization transition or whether one has two subsequent continuous transitions, from the liquid to the hexatic phase and then to the solid phase, as proposed by Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). Monte Carlo (MC) simulations of the fluid that study the growth of the bond orientational correlation length, and of the crystal are discussed. The emphasis is on a recent consistency test of the KTHNY renormalization group (RG) scenario, where MC simulations are used to estimate the bare elastic c…
Gradual freezing of orientational degrees of freedom in cubicAr1−x(N2)xmixtures
The mixed crystal ${\mathrm{Ar}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ is studied by Monte Carlo (MC) methods for x=0.33, 0.67, and 1.0 over a wide range of temperatures. For x=1 we find first-order transition from ordered cubic to disordered cubic, while for x=0.33 and x=0.67 we find broad nonuniform distribution functions of the local quadrupole Edwards-Anderson order parameter at low temperature. The short-range order of the quadrupolar mass distribution of the ${\mathrm{N}}_{2}$ molecules in the mixed systems is different from that observed in the pure ${\mathrm{N}}_{2}$ crystal, although the fcc symmetry has been chosen for the translational degrees…
Reply to “Comment on ‘Elastic constants from microscopic strain fluctuations’ ”
We agree with Coupier et al. [Phys. Rev. E 81, 013101 (2010)] that their technique for extracting elastic constants from microscopic strain fluctuations improves upon ours because of a more accurate computation of the integral of the elastic correlation function over sub-blocks. However, we believe that their interpretation of the physical relevance of the elastic correlation length extracted from the fits is misleading.
Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange : A Monte Carlo study
,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor ±Ĵ-interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (T/Ĵ ≥ 0.6). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function…
Quantum simulations in materials science: molecular monolayers and crystals
Low temperature properties and anomalies in crystals and molecular monolayers are studied by path integral Monte Carlo (PIMC) simulations. For light particles (H 2 , D 2 ) adsorbed on graphite anomalies in the transition to the low temperature √3-phases have been observed in experiments and are analyzed by PIMC. The computed thermal expansion of various crystalline materials (Si, N 2 ) is in much better agreement with experiments compared to the results obtained with purely classical simulations.
Low-temperature anharmonic lattice deformations near rotator impurities: A quantum Monte Carlo approach.
At zero temperature the equilibrium structures of a system consisting of a quantum rotator (${\mathrm{N}}_{2}$) embedded in a relaxing lattice (Ar) surrounding are studied with a variational approach. With symmetric wave functions (para-${\mathrm{N}}_{2}$), we obtain a cubic lattice deformation near the rotator, while with antisymmetric wave functions (ortho-${\mathrm{N}}_{2}$), we obtain a tetragonal lattice deformation forming a stable oriented ground state. At low temperatures, we investigate the properties of this system with a quantum Monte Carlo simulation. On top of the tetragonal deformation the width of the nearest-neighbor oscillations follows classical ``scaling'' laws according …
Low-energy excitations from interacting tunneling units in the mean-field approximation
Abstract The low-energy excitation spectrum of dilute concentrations of interacting tunneling quadrupoles randomly distributed in a non-polar medium was studied in the mean-field approximation. In particular the case of six-orientational tunneling quadrupoles (TQs) with a r−3 (elastic) interaction was considered. Because of the random position of the TQs, the internal field in a random variable and for relatively low concentrations has a Lorenzian probability distribution. The low-energy density of states is a constant and the low-energy excitations arise from the large internal fields, i.e. strongly interacting tunneling quadrupoles. The low-energy excitations were compared with those obta…
Quantum effects and orientational ordering in adsorbed layers of linear molecules
We study the influence of quantum fluctuations on the herringbone transition in adsorbed complete √3-mono-layers of diatomic molecules. Using Path-Integral Monte Carlo simulations for rotations, we can quantify the shift of the transition temperature for a highly realistic model to describe N2 on graphite. In addition, the zero-point motion of the librating molecules depresses the ground-state order parameter. We compare the benchmark data to quadratic Feynman-Hibbs effective potential simulations and to a quasiharmonic approximation. Using a simplified model for this transition, we study systematically quantum effects being relevant for lighter molecules. Depending on the rotator's rotatio…
Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis
The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionPL(ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities . Particular attention is paid to the qu…
Confined Crystals on Substrates: Order and Fluctuations in Between One and Two Dimensions
The effect of lateral confinement on a crystal of point particles in d = 2 dimensions in a strip geometry is studied by Monte Carlo simulations and using phe- nomenological theoretical concepts. Physically, such systems confined in long strips of width D can be realized via colloidal particles at the air-water interface, or by adsorbed monolayers at suitably nanopatterned substrates, etc. As a generic model, we choose a repulsive interparticle potential decaying with the twelfth inverse power of distance. This system has been well studied in the bulk as a model for two- dimensional melting. The state of the system is found to depend very sensitively on the boundary conditions providing the …
Numerical investigations of complex nano-systems
The nature of the melting transition for a system of hard disks with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft disks in external periodic (light) fields show rich phase diagrams, including freezing and melting transitions when the density of the syst…
Path integral Monte Carlo study of the internal quantum state dynamics of a generic model fluid
We study the quantum dynamics of a generic model fluid with internal quantum states and classical translational degrees of freedom in two spatial dimensions. The path integral Monte Carlo data for the imaginary time correlation functions are presented and analyzed by the maximum entropy method. A comparison of the frequency distribution with those of a mean field approximation and virial expansion shows good agreement at high and low densities, respectively. \textcopyright{} 1996 The American Physical Society.
Ordering of two-dimensional crystals confined in strips of finite width.
Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential $\ensuremath{\propto}{r}^{\ensuremath{-}12}$ in $d=2$ dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width $D$) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and suc…
Elastic moduli, dislocation core energy and melting of hard disks in two dimensions
Elastic moduli and dislocation core energy of the triangular solid of hard disks of diameter $\sigma$ are obtained in the limit of vanishing dislocation- antidislocation pair density, from Monte Carlo simulations which incorporates a constraint, namely that all moves altering the local connectivity away from that of the ideal triangular lattice are rejected. In this limit, we show that the solid is stable against all other fluctuations at least upto densities as low as $\rho \sigma^2 = 0.88$. Our system does not show any phase transition so diverging correlation lengths leading to finite size effects and slow relaxations do not exist. The dislocation pair formation probability is estimated …
A finite size scaling study of the five-dimensional Ising model
For systems above the marginal dimension d*, where mean field theory starts to become valid, such as Ising models in d = 5 for which d* = 4, hyperscaling is invalid and hence it was suggested that finite size scaling is not ruled by the correlation length ξ (∝ |t| −1/2 in Landau theory, t being the distance from the critical point) but by a “thermodynamic length” l (∝ |t| −2/d). Early simulation work by Binder et al. using nearest neighbor hypercubic L5 lattices with L ⩽ 7 yielded some evidence for this prediction, but the renormalized coupling constant gL = −3 + 〈M4〉/〈M2〉2 at Tc was gL ≈ −1.0 instead of the prediction of Brezin and Zinn-Justin, gL(Tc) = −3 + Γ4(1/4)/(8 π2) ≈ −0.812. In the…
Dynamical block analysis in a non-equilibrium system
Abstract We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equilibrium state into equilibrium was analyzed with a dynamical block analysis. This can lead to a new approach in the study of non-equilibrium phenomena. We show that with such an analysis one can obtain results on the dynamic evolution as the system evolves, consistent with those obtained from and analysis of the pair-distribution function, structure factor and excess energy. The simulations were carried out on the parallel computer of the condensed matter theory group at the University of Mainz.
Quantum effects on the herringbone ordering ofN2on graphite
The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.
Computer simulations of a Lennard-Jones model for Ar1—x(N2)x: A prototype system for quadrupolar glasses
Abstract Recent theoretical studies of orientational ordering in pure and diluted nitrogen crystals are summarized. While pure N2 has a first order phase transition from a plastic crystal to a phase with long-range orientational order, dilution with argon atoms leads to a quadrupolar glass phase. Monte Carlo simulations are used to study these phases, considering also the behavior of isolated N2 impurities in Ar crystals. It is shown that a simple model that neglects electrostatic interactions and takes only Lennard-Jones interactions into account can describe already many properties in qualitative agreement with experiment. Even the slow dynamics of the quadrupole moments can be modeled by…
Elastic constants from microscopic strain fluctuations
Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general e…
Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice
We use Monte Carlo techniques and analytical methods to study the phase diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M greater or equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M) while for z > z_d(M) there are M demixed phases each consisting mostly of one species. For M=2 there is a direct second order transition from the gas phase to the demixed phase while for M greater or equal 3 the transition at z_d(M) appears to be first order putting it in the Potts model universality class. For M large, …
Phase diagram of a model anticlustering binary mixture in two dimensions: A semi-grand-canonical Monte Carlo study
The temperature-density phase diagram of a model binary mixture in two dimensions is investigated using a semi-grand-canonical Monte Carlo simulation scheme which allows for exchange between the two species while keeping the total number of atoms fixed. The gas-liquid and the gas-solid regions of the phase diagram are mapped out using the efficient block analysis method incorporating finite-size scaling of the various coexisting densities. An ordered square lattice structure is seen to be stable at low temperatures. Interesting short-range ordering phenomena resulting in a ``disorder line'' in the fluid phase are also analyzed and compared with results from liquid-state integral equation th…
Interactions of membranes with coarse-grain proteins: a comparison
We study the interactions between lipid bilayers and rigid transmembrane proteins by Monte Carlo simulations of generic coarse-grain models. Different popular protein models are considered and compared with each other, and key parameters such as the hydrophobicity and the hydrophobic mismatch are varied systematically. Furthermore, the properties of the membrane are manipulated by applying different tensions. The response of the membrane to the insertion of single proteins is found to be mostly generic and independent of the choice of the protein model. Likewise, the orientational distributions of single proteins depend mainly on the hydrophobic mismatch and the hydrophobicity of the protei…
On the order of the herringbone transition of N2 on graphite: a Monte Carlo study
Using the anisotropic planar-rotor model we investigate the herringbone phase transition of N2 in the (√3 × √3)R30° commensurate phase on graphite by large scale Monte Carlo simulations. The effective correlation length ξ is measured near the transition temperature T0. The data, extrapolated to T0, yield a large but finite ξ at T0 demonstrating that the herringb ordering is a weak first order transition.
Phase Transitions in Multicomponent Widom-Rowlinson Models
We use Monte Carlo techniques to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. For M between two and six there is a direct transition from the gas phase at z z d (M). For M ≥ 7 there is an intermediate ordered phase in which the even (or odd) sublattice is occupied preferentially by particles chosen at random from any of the species. The existence of such an intermediate phase was proven earlier for M ≥ M 0, M 0 very large. Exact calculations on the Bethe lattice give M0 = 4.
Diffusional Relaxation in Dimer Deposition
In deposition of dimers on a 1D lattice substrate, we find by analytical arguments, supported by numerical Monte Carlo simulations, that the effect of added diffusional relaxation is to allow the full, saturation coverage, 100%, for large times. This limiting coverage is approached according to the ~ 1/√t power law preceded, for fast diffusion, by the mean-field crossover regime with the intermediate ~ 1/t behavior.
Liquid-vapour phase behaviour of a symmetrical binary fluid mixture
Using Monte-Carlo simulation and mean field calculations, we study the liquid-vapour phase diagram of a square well binary fluid mixture as a function of a parameter $\delta$ measuring the relative strength of interactions between particles of dissimilar and similar species. The results reveal a rich variety of liquid-vapour coexistence behaviour as $\delta$ is tuned. Specifically, we uncover critical end point behaviour, a triple point involving a vapour and two liquids of different density, and tricritical behaviour. For a certain range of $\delta$, the mean field calculations also predict a `hidden' (metastable) liquid-vapour binodal.
Ordering and demixing transitions in multicomponent Widom-Rowlinson models.
We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not …
N2monolayers physisorbed on graphite: the herringbone transition revisited
Monte Carlo simulations were undertaken of the orientational herringbone phase transition of N2 adsorbed on graphite in the complete monolayer (✓3 × ✓3) R30° structure. The non-universal aspects (c...
Field-induced ordering phenomena and non-local elastic compliance in two-dimensional colloidal crystals
Ordering phenomena in colloidal dispersions exposed to external one-dimensional, periodic fields or under confinement are studied systematically by Monte Carlo computer simulations. Such systems are useful models for the study of monolayers on a substrate. We find that the interaction with a substrate potential completely changes the miscibility of a binary, hard disc mixture at low external field amplitudes. The underlying ordering mechanisms leading to this laser-induced de-mixing differ, depending on which components interact with the substrate potential. Generic effects of confinement on crystalline order in two dimensions are studied in a model system of point particles interacting via…
Tricritical universality in a two-dimensional spin fluid
Monte Carlo simulations are used to investigate the tricritical point properties of a 2d spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2d Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point properties are also compared with the simulation measurements.
Two-dimensional model colloids and nano wires: phase transitions, effects of external potentials and quantum effects
Abstract Quantum effects, structures and phase transitions in Nano-systems have been analyzed. An overview is given on the results of our computations on structural and elastic properties of model colloids, on phase transitions of model colloids in external fields, and on structural and electronic properties of stretched atomic wires.
Line shifts and broadenings in polarizable liquids
We present a new dynamical derivation of the approximation used by Thompson, Schweizer, and Chandler and by Ho/ye and Stell for the frequency dependent polarizability of a quantum fluid with harmonically bound dipole moments; the Drude model. The derivation is the same for classical and quantum liquids—as is of course the result which agrees with that of these authors. We then refine the theory by taking account of the limited number of energy levels available, i.e., we replace the harmonic approximation by a two level approximation, for the target atom. This leads to a prefactor ω0I/ω0 in the line shift of an impurity atom in a fluid computed by Chandler, Schweitzer, and Wolynes: ω0 and ω0…
Quantum Effects and Phase Transitions in Adsorbed Molecular Layers
Phase transitions in adsorbed (two dimensional) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo (PIMC), Gibbs ensemble Monte Carlo (GEMC) and finite size scaling techniques. Entropy driven phase transitions in systems with purely repulsive interactions are analyzed as well phase diagrams of fluids with internal quantum states. Adsorbed layers of H 2 molecules at a full monolayer coverage in the \(\sqrt 3 \times \sqrt 3 \) structure have a higher transition temperature to the disordered phase compared to the system with the heavier D 2 molecules, this effect is analyzed by PIMC. Linear N 2 molecules adsorbed on graphite show a transition…
Collective Effects in Random Sequential Adsorption of Diffusing Hard Squares
We study by Monte Carlo computer simulations random sequential adsorption (RSA) with diffusional relaxation, of lattice hard squares in two dimensions. While for RSA without diffusion the coverage approaches its maximum jamming value (large-time fractional coverage) exponentially, added diffusion allows the deposition process to proceed to the full coverage. The approach to the full coverage is consistent with the t**(-1/2) power law reminiscent of the equilibrium cluster coarsening in models with nonconserved order-parameter dynamics.
Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality
In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder.We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a control…
ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS
In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator…
Lack of long-range order in confined two-dimensional model colloidal crystals.
We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance $D$ in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced (``layering''), but destroyed parallel to the wall.
RANDOM SEQUENTIAL ADSORPTION ON A LINEAR LATTICE: EFFECT OF DIFFUSIONAL RELAXATION
In this paper, the authors offer phenomenological arguments, supported by numerical Monte Carlo data, suggesting that the asymptotic large-time behavior of the coverage in the 1D lattice deposition of k-mers with k {gt} 3, accompanied by k-mer diffusion, is governed by the same mean-field dynamics as the lattice chemical reaction kA {yields} inert. The latter reaction is considered to occur with partial probability. The coverage in the deposition process approaches full saturation for any nonzero diffusion rate, and the void fraction decreases according to the power-law t{sup {minus}1/(k{minus}1)}.
Membrane-mediated Protein-protein Interaction: A Monte Carlo Study
We investigate membrane-mediated interactions between transmembrane proteins using coarse-grained models. We compare the effective potential of mean force (PMF) between two proteins, which are always aligned parallel to the z-axis of the simulation box, with those PMFs obtained for proteins with fluctuating orientations. The PMFs are dominated by an oscillatory packing-driven contribution and a smooth attractive hydrophobic mismatch contribution, which vanishes if the hydrophobic length of the protein matches the thickness of the membrane. If protein orientations are allowed to fluctuate, the oscillations are greatly reduced compared to proteins with fixed orientation. Furthermore, the hydr…
Spin-one-Ising model for (CO)1?x (N2) x mixtures: A finite size scaling study of random-field-type critical phenomena
A qualitative model for solid mixtures of diatomic molecules, where one species (called CO, to be specific) carries both a dipole moment and a quadrupole moment, while the other species (calledN 2) has only a quadrupole moment, is studied by Monte Carlo methods. We use spinsS i =±1 to represent the orientations of the CO electric dipole moment, if the lattice sitei is taken by a CO molecule, whileS i =0 if the site is taken by anN 2 molecule. Assuming nearest-neighbor antiferroelectric interactions between CO molecules, and a bilinear dipole-quadrupole coupling between CO andN 2, the randomly quenchedN 2 molecules act like random fields do in the random field Ising model. In previous work i…
Monte Carlo investigation of head-tail ordering of CO monolayers on graphite
Abstract Heat capacity measurements recently showed that CO physisorbed on graphite undergoes a head-tail ordering transition at roughly 5 K. The present paper is a detailed Monte Carlo study of this phase transition and the ordered state. The simulations are based on an ab initio pair potential and rely crucially on a thorough finite-size scaling study of various quantities. In agreement with experiments we find that the transition belongs to the universality class of the Ising model in two dimensions. We go beyond experimental knowledge by revealing the particular ferrielectric structure of the ground state, and show that the transition is due to the molecule's shape asymmetry rather than…
Monte Carlo Simulations of Growth Kinetics and Phase Transitions at Interfaces: Some Recent Results
ABSTRACTIn the first part Monte Carlo studies of the kinetics of multilayer adsorption (without screening) are described. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limit value according to a power law. In the second part, studies of phase transitions in two dimensional fluids are reviewed. With a combination of Monte Carlo and finite size scaling block analysis techniques, accurate values are obtained for the critical temperatures, coexistence densities and the compressibilities of an adsorbed fluid layer in an NVT ensemble.