Perturbed-chain equation of state for the solid phase

A perturbed chain equation of state for the solid phase has been derived. Although the equation is general with respect to intermolecular potential, we incorporate the Lennard-Jones potential in this work in order to compare results from the model with available Monte Carlo simulation data. Two forms of the radial distribution function for the hard-sphere solid chain reference state are used in the model. First, a theoretically rigorous approach is taken by using a correlation of actual solid-phase Monte Carlo hard-sphere chain data for the radial distribution function. This results in good agreement with the Monte Carlo data only at high density. Second, a simple extended-density approximation was used for the radial distribution function. This second approach was found to work well across the entire density range including the vicinity of the solid-fluid equilibrium.     

Monte Carlo calculations on polypeptide chains. VIII. Distribution functions for the end-to-end distance and radius of gyration for hard-sphere models of randomly coiling poly(glycine) and poly(L-alanine).

A Monte Carlo study of the distribution functions for the end-to-end distance and radius of gyration for hard-sphere models of poly(glycine) and poly(L-alanine) random coils has been conducted in the chain-length range n = 3 to 100 monomer units for both unperturbed chains and chains perturbed by long-range interactions (excluded volume effects). The distribution functions for the radius of gyration in all cases have been very precisely calculated, those for the perturbed end-to-end distance less precisely, and those for the unperturbed end-to-end distance least precisely. Empirical distribution functions of the form W(p) = ap-b exp(-cp-d) for the reduced end-to-end distance p = r/"r-2"-one-half and a similar form for the reduced radius of gyration could be least-squares fit to the Monte Carlo data. The expansion factors alpha-r and alpha-s were calculated vs. chain length and were used to test various versions of the two-parameter theory of the excluded volume effect. To be consistent with the chain-length dependence of alpha-r and alpha-s as determined by the Monte Carlo calculations, each of these theories required two different binary cluster integrals, a beta-r based on alpha-r and a beta-s based on alpha-s, both of which were strongly chain-length dependent. Both of these results suggest that the two-parameter theory is not applicable to the models used in this study. It was also found that, except for very short chain lengths, plots of ln alphs-r vs. ln n were linear, and thus that alpha-r could be estimated for long chain lengths. Comparison of these estimates with the experimental data on four polypeptide chains in one-earth solvents that the hard-sphere models used in this study yield expansion factors that do not seriously overestimate the magnitude of the excluded volume effect.     

Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.     

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.     

Fatty acids influence "solid" phase formation in models of stratum corneum intercellular membranes

Stacked intercellular lipid membranes in the uppermost epidermal layer, the stratum corneum (SC), are responsible for skin's barrier function. These membranes are unique in composition, the major lipids being ceramides (Cer), cholesterol, and free fatty acids (FFA) in approximately equimolar proportions. Notably, SC lipids include chains much longer than those of most biological membranes. Previously we showed that Cer's small hydrophilic headgroup enabled SC model membranes composed of bovine brain ceramide (BBCer), cholesterol, and palmitic acid in equimolar proportion to solidify at pH 5.2. In order to determine the influence of FFA chain length on the phase behavior of such membranes, we used 2H NMR and FT-IR to study BBCer/cholesterol/FFA dispersions containing linear saturated FFA 14-22 carbons long. Independent of chain length, the solid phase dominated the FFA spectrum at physiological temperature. Upon heating, each dispersion underwent phase transitions to a liquid crystalline phase (only weakly evident for the membrane containing FFA-C22) and then to an isotropic phase. The phase behavior, the lipid mixing properties, and the transition temperatures are shown to depend strongly on FFA chain length. A distribution of FFA chain lengths is found in the SC and could be required for the coexistence of a proportion of solid lipids with some more fluid domains, which is known to be necessary for normal skin barrier function.     

Structure of hard-sphere fluid and precursor structures to crystallization

The structural origin of the commonly observed split second peak of the radial distribution function of a supercooled or glassy liquid is examined in this work using the hard-sphere fluid as an example. A novel approach to the analysis of the microscopic structure of a fluid is described, which permits the decomposition of both the radial distribution function and bond-angle distribution function of a system of particles into contributions from a small number of ring structures. The method uses a modified shortest-path definition of rings appropriate to the analysis of the medium-range structure of dense systems. It is shown that the split peak is an indicator of the emergence of precursor structures to crystal formation. The origin of the split peak provides a structural link between fluid and crystalline phases and our results suggest that it is neither a structural feature peculiar to glassy phases nor a smooth structural continuation of the stable-fluid phase. This structural feature of simple glassy systems is more appropriately described as a signifier of the frustration of emerging crystalline order in a fluid.     

Deblurred observation of the molecular structure of an oil-water interface

We simulated the interface between liquid water and a stationary phase of tethered n-C18 alkyl chains at a thermodynamic state of low pressure and water vapor-liquid coexistence. The interfacial water (oxygen atom) density profile so obtained is compared with a precisely defined proximal density of water molecules (oxygen atoms) conditional on the alkyl chain configurations. Though the conventional interfacial density profile takes a traditional monotonic form, the proximal radial distribution of oxygen atoms around a specific methyl (methylene) group closely resembles that for a solitary methane solute in liquid water. Moreover, this proximal radial distribution function is sufficient to accurately reconstruct the water oxygen density profile of the oil-water interface. These observations provide an alternative interpretation to collective drying or vaporization interpretations of commonly observed oil-water interfacial profiles for which water penetration into the interfacial region plays a role.     

A practical integral equation for the structure and thermodynamics of hard sphere Coulomb fluids

A closure for the Ornstein-Zernike equation is presented, applicable for fluids of charged, hard spheres. From an exact, but intractable closure, we derive the radial distribution function of nonlinearized Debye-Hückel theory by subsequent approximations, and use the information to formulate a new closure by an extension of the mean spherical approximation. The radial distribution functions of the new closure, coined Debye-Hückel-extended mean spherical approximation, are in excellent agreement with those resulting from the hyper-netted chain approximation and molecular dynamics simulations, in the regime where the latter are applicable, except for moderately dilute systems at low temperatures where the structure agrees at most qualitatively. The method is numerically more efficient, and more important, convergent in the entire temperature-density plane. We demonstrate that the method is accurate under many conditions for the determination of the structural and thermodynamic properties of homogeneous, symmetric hard-sphere Coulomb systems, and estimate it to be a valuable basis for the formulation of density functional theories for inhomogeneous or highly asymmetric systems.     

Structural properties of a model system with effective interparticle interaction potential applicable in modeling of complex fluids

We report grand canonical ensemble Monte Carlo (MC) simulation and theoretical studies of the structural properties of a model system described by an effective interparticle interaction potential, which incorporates basic interaction terms used in modeling of various complex fluids composed of mesoscopic particles dispersed in a solvent bath. The MC results for the bulk radial distribution function are employed to test the validity of the hard-sphere bridge function in combination with a modified hypernetted chain approximation (MHNC) in closing the Ornstein-Zernike (OZ) integral equation, while the MC data for the density profiles in different inhomogeneous environments are used to assess the validity of the third-order+second-order perturbation density functional theory (DFT). We found satisfactory agreement between the results predicted by the pure theories and simulation data, which classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids. The present investigation indicates that the bridge function approximation and density functional approximation, which are traditionally used for the study of neutral atomic fluids, also perform well for complex fluids only on condition that the underlying effective potentials include a highly repulsive core as an ingredient.     

A simple theory of liquid—solid phase transitions

A simple phenomenological theory of liquid—solid phase transitions, based on the use of perturbation theory about a hard-sphere fluid, is examined. A temperature dependent hard-sphere diameter is determined which permits the prediction of solid and liquid densities and melting pressures. Calculations presented here for the Lennard-Jones 12-6 fluid show good agreement with the computer simulation results. Provided pair potentials are available, the theory may also be used for other fluids, including liquid metals.     

Specific low-shear viscosity of a liquid dispersion of solid particles from variational theory for the Fuchs stability ratio

The contribution of a solid phase to the low-shear viscosity of a solid–liquid dispersion, i.e., the specific viscosity, η_SP, is investigated theoretically by applying a variational procedure. The Fuchs stability ratio has been interpreted as a general steady-state equilibrium constant for aggregation and has been extended to a functional form which describes the motion of two Brownian units in a dispersion. Application of the Euler–Lagrange equation under the validity of an adiabatic-like approximation for the Hamiltonian (approximately Brownian kinetic energy and inertial potential field) yields a constraint that involves specific viscosity, solid volume fraction, φ, interparticle energy and correlation functions of the dispersed phase. The Einstein formula is found as the limit of the Saito equation when an infinitely dilute hard-sphere suspension is considered, while a general closed form expression, η_SP=η_SP(φ), is proposed for a concentrated suspension. It depends on the particle coordination number and affinity, returns the low density expansion predicted by effective-medium-type theories for the viscosity, and can be represented as the sum of two dominant contributions, associated respectively with the first peak of the radial distribution function and the second peak of the total correlation function. Application to experimental data, concerning latex particles in cis-decalin and interacting silica–water systems, is presented and discussed. Received: 31 March 2000/Accepted: 13 July 2000     

Solid-fluid and solid-solid phase equilibrium in a model of n-alkane mixtures

Solid-fluid and solid-solid phase equilibrium for binary mixtures of hard sphere chains modeling n-hexane, n-heptane, and n-octane has been calculated using Monte Carlo computer simulations. Thermodynamic integration was used to calculate the Gibbs free energy and chemical potentials in the solid and fluid phases from pure component reference values. A multiple stage free energy perturbation method was used to calculate the composition derivative of the Gibbs free energy. Equation of state and free energy data for the fluid phase indicate ideal solution behavior. Nonideality is much more significant in the solid phase with only partial solubility of shorter chains in the longer chains and essentially no solubility at the other end of the composition range. The miscibility decreases with increasing chain length difference between the components. For the model of n-hexane/n-octane mixtures solid--solid phase separation has been observed directly in some of the simulations, with the components segregating between the layers of the solid structure. The behavior is similar to that seen in some binary n-alkane mixtures with longer chain lengths but comparable chain length ratios between the components. Such phase separation, although indicated thermodynamically, is not seen directly in the simulations of the n-heptane/n-octane mixture due to the difference in the pure component crystal structures.     

Configurational statistics of macromolecules in solution from correlations of liquid molecules

We address the relevant quest for a simple formalism describing the microstructure of liquid solutions of polymer chains. On the basis of a recent relativistic-type picture of self-diffusion in (simple) liquids named Brownian relativity (BWR), a covariant van Hove's distribution function in a Vineyard-like convolution approximation is proposed to relate the statistical features of liquid and chain molecules forming a dilute polymer solution. It provides an extension of the Gaussian statistics of ideal chains to correlated systems, allowing an analysis of macromolecular configurations in solution by the only statistical properties of the liquid units (and vice versa). However, the mathematical solution to this issue is not straightforward because, when the liquid and polymer van Hove's functions are equated, an inverse problem takes place. It presents some conceptual analogies with a scattering experiment in which the correlation of the liquid molecules acts as the radiation source and the macromolecule as the scatterer. After inverting the equation by a theorem coming from the Tikhonov's approach, it turns out that the probability distribution function of a real polymer can be expressed from a static Ornstein-Uhlenbeck process, modified by correlations. This result is used to show that the probability distribution of a true self-avoiding walk polymer (TSWP) can be modeled as a universal Percus-Yevick hard-sphere solution for the total correlation function of the liquid units. This method suits in particular the configurational analysis of single macromolecules. The analytical study of arbitrary many-polymer systems may require further mathematical investigation.     

Phase behavior of polyampholytes from charged hard-sphere chain model

A molecular thermodynamic theory is developed for polyampholytes from the coarse-grained charged hard-sphere chain model. The phase behavior of polyampholytes with variations in sequence and chain length is satisfactorily predicted by the theory, consistent with simulation results and experimental observations. At a fixed chain length, the phase envelope expands as the sequence of charge distribution becomes less random. With increasing chain length, the phase envelope expands for diblock and random polyampholytes, but shrinks for zwitterionic polyampholytes. The predicted critical temperature, density, and pressure exhibit scaling relations with chain length for all the three (diblock, random, and zwitterionic) polyampholytes.     

Semi-empirical insertion probability for hard-spheres and hard-sphere chains

In spite of its simplicity and a well-defined theoretical basis, the Flory–Guggenheim approach is conventionally regarded as inapplicable to off-lattice system since the insertion probability of the approach does not account for the excluded region, existing in the off-lattice system. In this work, we propose the insertion probability accounting for the excluded region of off-lattice fluids and derive a new version of equation of state (EOS) for hard-sphere chains basing on the Flory–Guggenheim approach. To investigate the behavior of the excluded regions, a Monte Carlo sampling was performed for hard disks and the various excluded regions were found to have different density dependence. On the basis of the simulation result, we formulated the insertion probability for hard-sphere and that of hard-sphere chain which accounts for the effect of chain-connectivity on the monomer insertion. The proposed insertion probability was found to correctly predict the simulation data for monomer and correctly correlate the simulation data for chain fluids. The resulting EOS was found to meet closed-packed limit and predict the simulation data of compressibility factor for monomer and chains with a reasonable degree of accuracy. When compared with other off-lattice based EOS, it shows a comparable or better result. For second virial coefficient of chain molecules, the model was found to reasonably predict the simulation data.     

Conformation of a polymer chain in solution: an exact density expansion approach

The conformation of a polymer chain in solution is intrinsically coupled to the thermodynamic and structural properties of the solvent. Here we study such solvent effects in a system consisting of a flexible interaction-site n-mer chain immersed in a monomeric solvent. Chain conformation is described with a set of intramolecular site-site probability functions. We derive an exact density expansion for these intramolecular probability functions and give a diagrammatic representation of the terms contributing at each order of the expansion. The expansion is tested for a short hard-sphere chain (n=3 or 4) with site diameter sigma in a hard-sphere solvent with solvent diameter D. In comparison with Monte Carlo simulation results for 0.2< or =D/sigma< or =100, the expansion (taken to second order) is found to be quantitatively accurate for low to moderate solvent volume fractions for all size ratios. Average chain dimensions are predicted accurately up to liquidlike solvent densities. The hard-sphere chains are compressed with both increasing solvent density and decreasing solvent size. For small solvent (D相似文献   

Phase transition of short linear molecules adsorbed on solid surfaces from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on strongly attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the layering transitions change with the change of the chain length and with relative strength of the fluid-solid interaction. The critical temperature of the first layering transition, rescaled by the bulk critical temperature, increases slightly with an increase of the chain length. We have found that for longer chains the layering transitions within consecutive layers are shifted toward very low temperatures and that their sequence is finally replaced by a single transition.     

Conformation of a flexible chain in explicit solvent: exact solvation potentials for short Lennard-Jones chains

The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent.     

Theoretical scheme for the shear viscosity of Lennard-Jones fluids

We use the shear viscosity expression from the Enskog theory of dense gases in a perturbative scheme for the Lennard-Jones (LJ) fluid. This perturbative scheme is formulated by combining the analytic rational function approximation method of Bravo Yuste and Santos [Phys. Rev. A 43, 5418 (1991)] for the radial distribution function of hard-sphere fluids and the well known Mansoori-Canfield/Rasaiah-Stell perturbation theory to determine an effective diameter for the LJ fluid. The scheme is reliable on a wide range of temperatures and densities, and is very accurate around the critical point. Using this information, we build an accurate empirical formula for the shear viscosity in the liquid phase, which fits the recent data [K. Meier et al., J. Chem. Phys. 121, 3671 (2004)] in the whole simulation range.     

Thermodynamic perturbation theory for fused sphere hard chain fluids using nonadditive interactions

A model is developed for the equation of state of fused chains based on Wertheim thermodynamic perturbation theory and nonadditive size interactions. The model also assumes that the structure (represented by the radial distribution function) of the fused chain fluid is the same as that of the touching hard sphere chain fluid. The model is completely based on spherical additive and nonadditive size interactions. The model has the advantage of offering good agreement with simulation data while at the same time being independent of fitted parameters. The model is most accurate for short chains, small values of Delta (slightly fused spheres) and at intermediate (liquidlike) densities.