Chemical potential of a hard sphere fluid adsorbed in model disordered polydisperse matrices

We consider a model for adsorption of a simple fluid in disordered polydisperse adsorbents. The fluid consists of hard sphere particles. On the other hand, the adsorbents of this study are modeled as a collection of hard spheres with their diameter obeying a certain distribution function. Our focus is in the evaluation of the chemical potential of the fluid immersed in such a polydisperse material. It permits us to obtain porosity and pore size distribution for the adsorbent, as well as a set of adsorption isotherms. The latter have been calculated theoretically and by grand canonical Monte Carlo simulations. We observe that the width of assumed polydispersity distribution affects all the properties of the system. Nevertheless, the effect of matrix packing is dominant in determining adsorption for this class of models. We are convinced that the matrix structures generated via more sophisticated algorithms would exhibit stronger effects of polydispersity on the entire set of properties of adsorbed simple fluids.     

Isotropic-nematic transition of hard rods immersed in random sphere matrices

Using replica density functional theory and Monte Carlo computer simulations we investigate a system of annealed hard spherocylinders adsorbed in a matrix of quenched hard spheres. Theoretical predictions for the partition coefficient, defined as the ratio of density of rods in the matrix and that in a reservoir, agree well with simulation results. Theory predicts the isotropic-nematic transition to remain first order upon increasing sphere packing fraction, and to shift towards lower rod densities. This scenario is consistent with our simulation results that clearly show a jump in the nematic order parameter upon increasing the rod density at constant matrix packing fraction, corresponding to the isotropic-nematic transition, even for sphere matrix packing fractions < or approximately equal to 0.3.     

Fluids in porous media. III. Scaled particle theory

Based on a new and consistent formulation of scaled particle theory for a fluid confined in random porous media, a series of new approximations are proposed and one of them gives equations of state with excellent accuracy for a hard sphere fluid adsorbed in a hard sphere or an overlapping hard sphere matrix. Although the initial motivation was to remedy a flaw in a previous formulation of the scaled particle theory for a confined fluid, the new formulation is not a trivial and straightforward correction of the previous one. A few conceptual and significant modifications have to be introduced for developing the present formulation.     

Partitioning of Polymerizing Fluids in Random Microporous Media: Application of the Replica Ornstein-Zernike Equations

We have investigated a model for a polymerizing fluid in which each of the particles has two bonding sites, such that chains can be formed via a chemical association mechanism. The fluid model is considered to be in a random quenched microporous matrix. The matrix species are assumed to be either impermeable to adsorbed fluid particles or permeable, such that the surface of the matrix particles represents a permeable membrane of finite width. We have studied the influence of the matrix species on the formation of chains due to association. The model is investigated by means of the associative replica Ornstein-Zernike equations with the Percus-Yevick closure and the ideal chain approximation. We have observed that the average chain length is longer in the presence of an impermeable matrix than in the case where the matrix is absent. Matrix is therefore conducive to the growth of the polymerizing species in micropores. There is a decrease in the average chain length with increasing permeability of matrix species. This behavior reaffirms the attenuating role of the permeable matrix species as a whole. Copyright 1999 Academic Press.     

Negative linear compressibility in confined dilatating systems

The role of a matrix response to a fluid insertion is analyzed in terms of a perturbation theory and Monte Carlo simulations applied to a hard sphere fluid in a slit of fluctuating density-dependent width. It is demonstrated that a coupling of the fluid-slit repulsion, spatial confinement, and the matrix dilatation acts as an effective fluid-fluid attraction, inducing a pseudocritical state with divergent linear compressibility and noncritical density fluctuations. An appropriate combination of the dilatation rate, fluid density, and the slit size leads to the fluid states with negative linear compressibility. It is shown that the switching from positive to negative compressibility is accompanied by an abrupt change in the packing mechanism.     

Permeation of a hard sphere fluid into a quenched matrix

The permeation of a hard sphere fluid through a model membrane, composed of quenched (in space) hard spheres, is studied using molecular dynamics simulations. The fluid is initially placed outside the porous matrix and their initial intake is investigated and found to be non-Fickian. This non-Fickian behavior can be attributed to the high concentration difference between the fluid in the bulk and in the membrane. Once the system is equilibrated, the authors mark fluid particles that are outside the membrane and investigate their diffusion (color diffusion). Color diffusion is Fickian, and the mass intake and density profiles are well described by a continuum composite medium model with no adjustable parameters, i.e., with self-diffusion coefficients obtained from simulations. The matrix becomes impermeable when there are no percolating paths for the fluid.     

Elastic Behaviors of Adsorbed Protein-like Chains

Elastic behaviors of protein-like chains are investigated by Pruned-Enriched-Rosenbluth method and modified orientation-dependent monomer-monomer interactions model. The protein-like chain is pulled away from the attractive surface slowly with elastic force acting on it. Strong adsorption interaction and no adsorption interaction are both considered. We calculate the characteristic ratio and shape factor of protein-like chains in the process of elongation. The conformation change of the protein-like chain is well depicted. The shape of chain changes from “rod” to “sphere” at the beginning of elongation. Then, the shape changes from “sphere” to “rod”. In the end, the shape becomes a “sphere” as the chain leaves away from the surface. In the meantime, we discuss average Helmoholtz free energy per bond, average energy per bond, average adsorbed energy per bond, average α-helical energy per bond, average β-sheet energy per bond and average contact energy per bond.On the other hand, elastic force is also studied. It is found that elastic force has a long plateau during the tensile elongation when there exists adsorption interaction. This result is consistent with SMFS experiment of general polymers. Energy contribution to elastic force and contact energy contribution to elastic force are both discussed. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

Statistical associating Fluid Dimer Theory

Three modified versions of statistical associating fluid theory known as SAFT-D1, SAFT-D2 and SAFT-T for hard sphere chain molecules are used to test the approximation made in the derivation of the statistical associating fluid dimer theory (SAFT-D). The SAFT-D1 model accounts for the chain length independent site–site correlation function at contact, while SAFT-D2 and SAFT-T models account for chain length dependent site–site correlation function at contact. The residual chemical potentials are calculated for hard chain fluids containing chains of length m = 3, 4, 6, 8, 12, 16 and 32?mers and compared with the results obtained by configurational bias Monte Carlo (MC) method at various densities. We find that the approximation used in SAFT-D1 theory leads to an over prediction of residual chemical potential and its magnitude increases with increasing chain length.     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.     

A study of the phase behavior of a simple model of chiral molecules and enantiomeric mixtures

We present a study of the solid-fluid and solid-solid phase equilibrium for molecular models representative of chiral molecules and enantiomeric mixtures. The models consist of four hard sphere interaction sites of different diameters in a tetrahedral arrangement with the fifth hard sphere interaction site at the center of the tetrahedron. The volumetric properties and free energies of the pure enantiomers and binary mixtures were calculated in both fluid and solid phases using isobaric Monte Carlo simulations. The models exhibit essentially ideal solution behavior in the fluid phase with little chiral discrimination. In the solid phase the effects of chirality are much greater. Solid-fluid phase behavior involving the pure enantiomer solids and also racemic compounds was calculated. The calculations indicate that, depending on the relative sizes of the hard sphere interaction sites, packing effects alone can be sufficient to stabilize a racemic compound with respect to the pure enantiomer solids.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

流体熵相关性质的Monte Carlo模拟新方法

提出了用于计算实际体系熵相关性质的Monte Carlo多级取样分子模拟方法. 应用这一方法, 对硬球流体的化学势及Helmholtz自由能进行了估算, 得到了满意的结果. 计算化学势时, 不存在通常试验粒子方法所遇到的高密度问题. 该方法特别适合规律性的系统研究, 较之普通模拟方法要有效得多. 模拟得到的硬球体系无限稀释组份的超额化学势与对比直径的关系, 在相变区域为一条双凹曲线; 无论是在相变区还是在单相区, Carnahan-Starling公式对这一关系的描述均有较大偏差.     

流体熵相关性质的Monte Carlo模拟新方法

提出了用于计算实际体系熵相关性质的Monte Carlo 多级取样分子模拟方法.应用这一方法,对硬球流体的化学势及Helmholtz 自由能进行了估算,得到了满意的结果.计算化学势时,不存在通常试验粒子方法所遇到的高密度问题.该方法特别适合规律性的系统研究,较之普通模拟方法要有效得多.模拟得到的硬球体系无限稀释组份的超额化学势与对比直径的关系,在相变区域为一条双凹曲线;无论是在相变区还是在单相区,Carnahan-Starling 公式对这一关系的描述均有较大偏差.     

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.     

Electrochemical behaviour of mono- and oligonucleotides: IV. The adsorption of adenine oligonucleotides at the mercury-solution interface

The adsorption behaviour of some adenine oligonucleotides was studied at the hanging mercury drop electrode by phase sensitive a.c.-voltammetry and sweep voltammetry. These substances are adsorbed in the whole potential range from most positive potentials adjustable up to the potential of their reduction. The adsorbed layer is transformed at a fresh drop rather rapidly to a condensed film at all concentrations due to significant stacking forces acting between adjacent adenine base rings. The time dependence of the voltammetric reduction response under conditions where only the contribution due to the adsorbed species is measured shows that diffusion controlled adsorption takes place. Differences in adsorption behaviour for adsorption at a fresh surface and at a surface partially covered by slowly desorbing blocking reduction products have been elucidated. From the limiting value of the surface concentration an average surface area per adsozbed mononucleotide unit of about 40 Ų was found which is comparable to the value resulting under the same conditions for poly-A. It was concluded that in both cases the adsorption is occurring via the adenine base residues of the nucleotide chain. As the distance between adjacent bases in the chain is fixed by its backbone formed by sugar and phosphate residues the average adsorption area is essentially the same in both cases. The possible orientation of the bases attached to the electrode is discussed.     

Mesophase formation in a system of top-shaped hard molecules: density functional theory and Monte Carlo simulation

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.     

Geometrical cluster ensemble analysis of random sphere packings

We introduce a geometric analysis of random sphere packings based on the ensemble averaging of hard-sphere clusters generated via local rules including a nonoverlap constraint for hard spheres. Our cluster ensemble analysis matches well with computer simulations and experimental data on random hard-sphere packing with respect to volume fractions and radial distribution functions. To model loose as well as dense sphere packings various ensemble averages are investigated, obtained by varying the generation rules for clusters. Essential findings are a lower bound on volume fraction for random loose packing that is surprisingly close to the freezing volume fraction for hard spheres and, for random close packing, the observation of an unexpected split peak in the distribution of volume fractions for the local configurations. Our ensemble analysis highlights the importance of collective and global effects in random sphere packings by comparing clusters generated via local rules to random sphere packings and clusters that include collective effects.     

Prediction of a structural transition in the hard disk fluid

Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction η(?)～0.718, a value that is in substantial agreement with the packing fraction, η～0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations [Phys. Rev. E 73, 065104 (2006)]. Next, we show that the same method of analysis predicts that the exponential damping of oscillations in the hard sphere fluid becomes impossible when λ=4nπσ(3)[1+H(1)]≥34.81, where H(1) is the contact value of the correlation function, n is the number density, and σ is the sphere diameter in exact agreement with the condition, λ≥34.8, which is first reported in a numerical study of the Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing.