(2n,n) potential and sticky-sphere fluids

The authors investigate the behavior of a model fluid for which the interaction energy between molecules at a separation r is of the form 4epsilon[(sigma/r)2n-(sigma/r)n], where epsilon and sigma are constants and n is a large integer. The particular properties they study are the pressure p, the mean square force F2, the elastic shear modulus at infinite frequency Ginfinity, the bulk modulus at infinite frequency Kinfinity, and the potential energy per molecule u. They show that if n is sufficiently large it is possible to derive the properties of the system in terms of two parameters, the values of the cavity function and of its derivative at the position r=sigma. As an example they examine in detail the cases with n=144 and n=72 for three different temperatures and they test the theory by comparison with a computer simulation of the system. They use the simulated pressure and the average mean square force to determine the two parameters and use these values to evaluate other properties; it is found that the theory produces results which agree with computer simulation to within approximately 3%. It is also shown that the model, when the parameter n is large, is equivalent to Baxter's sticky-sphere model with the strength of the adhesion determined by the value of n and the temperature. They use Baxter's solution of the Percus-Yevick equations for the sticky-sphere model to determine the cavity function and from that the values of the same properties. In this second approach there are no free parameters to determine from simulation; all properties are completely determined by the theory. The results obtained agree with computer simulation only to within approximately 6%. This suggests that for this model one needs a better approximation to the cavity function than that provided by the Percus-Yevick solution. Nevertheless, the model looks promising for the study of (typically small) colloidal liquids where the range of attraction is short but finite when compared to its diameter, in contrast to Baxter's sticky-sphere limit where the attractive interaction range is taken to be infinitely narrow. The continuous function approach developed here enables important physical properties such as the infinite shear modulus to be computed, which are finite in experimental systems but are undefined in the sticky-sphere model.     

Thermodynamic stability of type-I and type-II clathrate hydrates depending on the chemical species of the guest substances

The free energy differences are calculated for various type-I and type-II clathrate hydrates based on molecular-dynamics simulations, thereby evaluating the thermodynamic stability of the hydrates depending on the chemical species of the guest substances. The simulation systems consist of 27 unit cells, that is, 1242 water molecules and 216 guest molecules for type-I hydrates, and 3672 water molecules and 648 guest molecules for type-II hydrates. The water molecules are described by TIP4P potential, while the guest molecules are described by one-site Lennard-Jones potential, U=4epsilon{(sigma/r)12-(sigma/r)6}, where U is the potential energy, r is the particle distance, sigma is the particle diameter, and epsilon is the energy well depth. The optimal values of sigma that yield the minimum free energy (the best thermodynamic stability) were determined to be 0.39 nm for the type-I hydrates and 0.37 nm for the type-II hydrates.     

Physical properties of soft repulsive particle fluids

Molecular dynamics computer simulation has been applied to inverse power or soft-sphere fluids, in which the particles interact through the soft-sphere pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The focus of the study is on very soft particles with n values down to 4 considered, at densities up to and along the fluid-solid co-existence density. It is shown that in the soft-particle limit the local structure is dominated by the lengthscale associated with the average nearest neighbour distance of a random structure, which is proportional, variantrho(-1/3) and increasingly only very weakly dependent on n. This scaling is also manifest in the behaviour of the average energy per particle with density. The self-diffusion coefficient and shear viscosity are computed along the fluid-solid co-existence line as a function of n, for the first time. The product Deta(s) steadily increases with softness for n < 10, whereas the modified Stokes-Einstein relationship of Zwanzig, Deta(s)/rho(1/3), where rho is the number density, is within statistics constant over the same softness range. This is consistent with our observation that the static properties are determined by a characteristic lengthscale (i.e., l) which is proportional, variantrho(-1/3) in the soft-particle limit. The high frequency elastic moduli of these fluids are examined, which reveals that the mechanical properties become more 'rubbery' as the particles get softer.     

Monte Carlo simulations of fluids whose particles interact with a logarithmic potential

Monte Carlo simulations of a model fluid in which the particles interact via a continuous potential that has a logarithmic divergence at a pair separation of sigma, which we introduced in J. G. Powles et al., Proc. R. Soc. London, Ser. A 455, 3725 (1999), have been carried out. The potential has the form, phi(r)= -epsilon ln(fr), where epsilon sets the energy scale and fr=1-(sigma/r)m. The value of m chosen was 12 but the qualitative trends depend only weakly on the value of m, providing it is greater than 3. The potential is entirely repulsive and has a logarithmic divergence as approximately -ln(r/sigma-1) in the r-->sigma limit. Predictions of the previous paper that the internal energy can be computed at all temperatures using the standard statistical mechanics formula for continuous potentials are verified here. The pressure can be calculated using the usual virial expression for continuous potentials, although there are practical limitations in resolving the increasingly important contribution from the r-->sigma limit at reduced temperatures greater than approximately 5. The mean square force F2 and infinite frequency shear Ginfinity and bulk Kinfinity moduli are only finite for T*=kBT/epsilon<1. The logarithmic fluid's physical properties become increasingly more like that of the hard sphere fluid with increasing temperature, showing a sharp transition in the behavior of the mean square force and infinite frequency elastic constants at T*=1. The logarithmic fluid is shown to exhibit a solid-fluid phase transition.     

Free-energy calculation of structure-H hydrates

A molecular-dynamics (MD) simulation of structure-H hydrates was performed under constant pressure and temperature with 6120 TIP4P water molecules, 900 OPLS-UA methane molecules, and 180 large molecular guest substance (LMGS) molecules. The LMGS molecules were represented in the form of a one-site Lennard-Jones (LJ) model using the LJ parameters sigma and epsilon. In order to clarify the thermodynamic stability of structure-H hydrates, we calculated the free-energy difference, changing on the sigma and epsilon only of the LMGS molecules. In this simulation, stable crystals of structure-H hydrates and a minimum value of DeltaG were obtained at sigma approximately 6.2 A and large values of epsilon. All simulations were performed using the special-purpose computer hardware MDGRAPE-2.     

Extended-range order, diverging static length scales, and local structure formation in cold Lennard-Jones fluids

We report molecular-dynamics simulations on a three-dimensional, two-component Lennard-Jones fluid. We used 125 000 particles (equal numbers of A and B) at density N/V=1.29 and 34 temperatures T covering 5 x 10(4) > or =T > or =0.56. The pair potential was 4epsilon[(sigma(ij)/r)(12)-(sigma(ij)/r)(6)] with sigma(AA)=1, sigma(AB)=11/12, and sigma(BB)=5/6. We computed specific and generic radial distribution functions g(ij)(r), and several density-momentum dynamic correlation functions whose static (t=0) parts vanish by symmetry. Evidence is presented that our systems were adequately annealed to eliminate remnant initial order and were adequately equilibrated at each temperature. Static spatial correlations in cold Lennard-Jones liquids have longer ranges than are often reported: g(r)-1 unequal to 0 is found out to r > or =7 at T=2 and out to r > or =10 at T=0.56. |g(r)-1| has an envelope function that simultaneously fits both crests and troughs of g(r). The envelope function implies a temperature-dependent static length scale l(1); over (0.56 < or =T< or =100), l(1) approximately T(-0.3), contrary to suggestions that g(r) is temperature independent as the glass is approached. The highest-melting-point crystal that we identified melts at T(m) approximately 1.08. In the fluid phase, we observe short-range noncrystalline local structure formation in g(r) as the glass is approached. Local structure is only found below a local structure melting temperature T(mc)=2.0. Local structure vanishes above T=2. Local structure becomes more pronounced as temperature is reduced. However, at all temperatures at which there is local structure in g(r), the local structure is confined to r < or =4. Within the region r < or =4, the amplitude of the local structure diminishes with distance r from the central atom approximately as exp(-r/l(2)), thereby defining a second distance scale in the fluid. l(2), while more difficult to measure, appears to scale with temperature as l(2) approximately T(-0.6); l(2) is not the same as l(1). The static and dynamic properties of the local structure match properties assigned by Kivelson's glass model [S. A. Kivelson et al., J. Chem. Phys. 101, 2391 (1994)] to that model's frustration-limited local clusters.     

How "sticky" are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range lambda at a given packing fraction eta and reduced temperature T* = kBT/epsilon can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter tau(T*,lambda). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r = sigma) in the SHS case, while it has a jump discontinuity at r = lambda sigma in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that [formula: see text]. Optimization of the agreement between y(SW) and y(SHS) to first order in density suggests the choice tau(T*,lambda) = [12(e(1/T* - 1)(lambda - 1)](-1). We have performed Monte Carlo (MC) simulations of the SW fluid for lambda = 1.05, 1.02, and 1.01 at several densities and temperatures T* such that tau(T*,lambda) = 0.13, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel[J. Phys.: Condens. Matter 16, S4901 (2004)]. Although, at given values of eta and tau, some local discrepancies between y(SW) and y(SHS) exist (especially for lambda = 1.05), the SW data converge smoothly toward the SHS values as lambda-1 decreases. In fact, precursors of the singularities of y(SHS) at certain distances due to geometrical arrangements are clearly observed in y(SW). The approximate mapping y(SW)-->y(SHS) is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y(SHS) the solution of the Percus-Yevick equation as well as the rational-function approximation, the radial distribution function g(r) of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.     

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).     

Simulating asymmetric colloidal mixture with adhesive hard sphere model

Monte Carlo simulation and Percus-Yevick (PY) theory are used to investigate the structural properties of a two-component system of the Baxter adhesive fluids with the size asymmetry of the particles of both components mimicking an asymmetric binary colloidal mixture. The radial distribution functions for all possible species pairs, g(11)(r), g(22)(r), and g(12)(r), exhibit discontinuities at the interparticle distances corresponding to certain combinations of n and m values (n and m being integers) in the sum nsigma(1)+msigma(2) (sigma(1) and sigma(2) being the hard-core diameters of individual components) as a consequence of the impulse character of 1-1, 2-2, and 1-2 attractive interactions. In contrast to the PY theory, which predicts the delta function peaks in the shape of g(ij)(r) only at the distances which are the multiple of the molecular sizes corresponding to different linear structures of successively connected particles, the simulation results reveal additional peaks at intermediate distances originating from the formation of rigid clusters of various geometries.     

Diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. V. The short time approximation for the memory function

The correlation function for density fluctuations in a monatomic fluid obeys a formally exact kinetic equation containing a memory function. A previously derived short time approximation (STA) for this memory function is tested by comparing its predictions with the results of molecular dynamic simulations of a dense Lennard-Jones fluid at a variety of temperatures. This approximation takes into account the contribution to the correlation function of uncorrelated repulsive binary collisions. The qualitative changes of predicted correlation functions with temperature and wave vector are generally correct. The major exception to this is the transverse current correlation function for small wave vector. The quantitative accuracy is better at short times than long times and better at high temperatures than low temperatures. The major failing of the STA is its underestimation of the amplitudes of the negative dips in the current autocorrelation functions and of the temperature dependence of the amplitudes of the dips. Despite its deficiencies in predicting the time dependence of current correlation functions, the STA gives accurate results for the self-diffusion coefficient and the shear viscosity coefficient at the highest temperatures studied.     

Transport coefficients of the Lennard-Jones model fluid. III. Bulk viscosity

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This third of a series of four papers presents the results for the bulk viscosity. With comprehensive simulation data at over 350 state points, the temperature and density dependences of the bulk viscosity are characterized in this work over a wide range of fluid states. The bulk viscosity exhibits a large critical enhancement similar to that known for the thermal conductivity, but it extends much farther into the supercritical region and can be observed even at 4.5 times the critical temperature. An investigation of the pressure-fluctuation autocorrelation functions shows that the enhancement is caused by extremely slowly decaying pressure fluctuations.     

Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules

We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.     

Photophysical aspects of single-molecule detection by two-photon excitation with consideration of sequential pulsed illumination.

An important goal in single molecule fluorescence correlation spectroscopy is the theoretical simulation of the fluorescence signal stemming from individual molecules and its autocorrelation function. The simulation approaches developed up to now are based exclusively on continuous-wave (cw) illumination and consequently on cw-excitation. However, this approximation is no longer valid in the case of two-photon excitation, for which pulsed illumination is usually employed. We present a novel theoretical model for the simulation of the fluorescence signal of single molecules and its autocorrelation function with consideration of the time dependence of the excitation flux and thus of all illumination-dependent photoprocesses: two-photon excitation, induced emission and photobleaching. Further important characteristics of our approach are the consideration of the dependence of the photobleaching rate on illumination and the low intersystem-crossing rates of the studied coumarins. Moreover, using our approach, we can predict quantitatively the effect of the laser pulse width on the fluorescence signal of a molecule, that is, the contributions of the photobleaching and saturation effects, and thus we can calculate the optimal laser pulse width. The theoretical autocorrelation functions were fitted to the experimental data, and we could ascertain a good agreement between the resulting and the expected parameters. The most important parameter is the photobleaching constant sigma, the cross section of the transition Sn<--S1, which characterises the photostability of the molecules independent of the experimental conditions. Its value is 1.7 x 10(-23) cm2 for coumarin 153 and 5 x 10(-23) cm2 for coumarin 314.     

Relaxation and short time dynamics of bulk liquids and fluids confined in spherical cavities and slit pores

The density of states for bulk and confined fluids have been modeled using a recently proposed gamma distribution (Krishnan, S. H.; Ayappa, K. G. J. Chem. Phys. 2004, 121, 3197). The gamma distribution results in a closed form analytical expression for the velocity autocorrelation function and the relaxation time of the fluid. The two parameters of the gamma distribution are related analytically to the second and fourth frequency moments of the fluid using short time expansions. The predictions by the proposed gamma model are compared with the velocity autocorrelation functions obtained using the theory of instantaneous normal modes (INMs) and from molecular dynamics simulations. The model is applied to a bulk soft sphere liquid and fluids confined in a spherical cavity and slit-shaped pores. The gamma model is able to capture the resulting changes in relaxation time due to changes in density and temperature extremely well for both the bulk liquid and confined inhomogeneous fluid situations. In all cases, the predictions by the gamma model are superior to those obtained from the INM theory. In the case of the fluid confined in a slit pore, the loadings were obtained from a grand canonical Monte Carlo simulation where the pore is equilibrated with a bulk fluid. This is similar to a confinement situation in a surface force apparatus. The predicted relaxation times vs pore widths from the gamma model are seen to accurately capture the oscillations due to formation and disruption of layers within the slit pore.     

Polymer brushes in solvents of variable quality: molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.     

Hard sphere perturbation theory for fluids with soft-repulsive-core potentials

The thermodynamic properties of fluids with very soft repulsive-core potentials, resembling those of some liquid metals, are predicted with unprecedented accuracy using a new first-order thermodynamic perturbation theory. This theory is an extension of Mansoori-Canfield/Rasaiah-Stell (MCRS) perturbation theory, obtained by including a configuration integral correction recently identified by Mon, who evaluated it by computer simulation. In this work we derive an analytic expression for Mon's correction in terms of the radial distribution function of the soft-core fluid, g(0)(r), approximated using Lado's self-consistent extension of Weeks-Chandler-Andersen (WCA) theory. Comparisons with WCA and MCRS predictions show that our new extended-MCRS theory outperforms other first-order theories when applied to fluids with very soft inverse-power potentials (n< or =6), and predicts free energies that are within 0.3 kT of simulation results up to the fluid freezing point.     

Density functional theory study of the properties of N-H...N, non-cooperativities, and intermolecular interactions in linear trans-diazene clusters up to ten molecules

We investigate aspects of N-H...N hydrogen bonding in the linear trans-diazene clusters (n=2-10) such as the N...H and N-H lengths, n(N) --> sigma(N-H) interactions, N...H strengths, and frequencies of the N-H stretching vibrations utilizing the DFT/B3LYP theory, the natural bond orbital (NBO) method, and the theory of atoms in molecules (AIM). Our calculations indicate that the structure and energetics are qualitatively different from the conventional H-bonded systems, which usually exhibit distinct cooperative effects, as cluster size increases. First, a shortening rather than lengthening of the N-H bond is found and thus a blue rather than red shift is predicted. Second, for the title clusters, any sizable cooperative changes in the N-H and N...H lengths, n(N) --> sigma(N-H) charge transfers, N...H strengths, and frequencies of the N-H stretching vibrations for the linear H-bonded trans-diazene clusters do not exist. Because the n(N) --> sigma(N-H) interaction hardly exhibits cooperative effects, the capability of the linear trans-diazene cluster to localize electrons at the N...H bond critical point is almost independent of cluster size and thereby leads to the noncooperative changes in the N...H lengths and strengths and the N-H stretching frequencies. Third, the dispersion energy is sizable and important; more than 30% of short-range dispersion energy not being reproduced by the DFT leads to the underestimation of the interaction energies by DFT/B3LYP. The calculated nonadditive interaction energies show that, unlike the conventional H-boned systems, the trans-diazene clusters indeed exhibit very weak nonadditive interactions.     

Equation of state and structural properties of the Weeks-Chandler-Andersen fluid

Molecular dynamics simulations have been carried out for the equation of state and percolation properties of the Weeks-Chandler-Andersen (WCA) system in its fluid phase as functions of density and temperature. The compressibility factor Z collapses well for the various isotherms, using an effective particle diameter for the WCA particle which is (in the usual WCA reduced units) sigma(e)=2(16)(1+T)(16), where T is the temperature. A corresponding "effective" packing fraction is zeta(e)=pisigma(e) (3)N6V, for N particles in volume V, which therefore scales out the effects of temperature. Using zeta(e) the simulation derived Z can be fitted to a simple analytic form which is similar to the Carnahan-Starling hard sphere equation of state and which is valid at all temperatures and densities where the WCA fluid is thermodynamically stable. The data, however, are not scalable onto the hard sphere equation of state for the complete packing fraction range. We explored the continuum percolation behavior of the WCA fluids. The percolation distance sigma(p) for the various states collapses well onto a single curve when plotted as sigma(p)sigma(e) against zeta(e). The ratio sigma(p)sigma(e) exhibits a monotonic decrease with increasing zeta(e) between the percolation line for permeable spheres and the glass transition limit, where sigma(p)sigma(e) approximately 1. The percolation packing fraction was calculated as a function of effective packing fraction and fitted to an empirical expression. The local coordination number at the percolation threshold showed a transition between the soft core and hard core limits from ca. 2:74 to 1:5, as previously demonstrated in the literature for true hard spheres. A number of simple analytic expressions that represent quite well the percolation characteristics of the WCA system are proposed.     

Spatial shape of electron delocalization: structure of the laplacian of the negative exchange-correlation density

The Laplacian of the negative exchange-correlation density (with respect to coordinate r(2)), nabla<(r)2>(2)[-Gamma(sigma1)(sigma2)(XC) (r(1),r(2))] = nabla(r)2(2)X(sigma1)(sigma2)(r(1),r(2)), is proposed as an instrument for the analysis of electron delocalization in real space. It determines local concentrations in the amount of electrons that are delocalized from a reference point r(1) over space. Integration of the reference coordinate r(1) over an atomic basin Omega(n) gives the function nabla(2)X(sigma1)(sigma2)(Omega(n);r), which contains detailed information about the spatial shape of the delocalization that originates from an atom in a molecule. Its isosurface representations are richly structured and resemble molecular orbitals in their complexity and partly also in their shape. The sum over all nabla(2)X(sigma1)(sigma2)(Omega(n);r) functions of a molecule equals the Laplacian of the electron density nabla(2)rho(r), for which it provides a meaningful partitioning into atomic contributions.