Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.     

Confinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments.     

Tunable effective interactions between dendritic macromolecules

We employ extensive Monte Carlo and molecular-dynamics simulations to investigate the effective interactions between the centers of mass of dendritic macromolecules of variable flexibility and generation number. Two different models for the connectivity and steric interactions between the monomers are employed, the first one being purely entropic in nature and the second explicitly involving energetic interactions. We find that the effective potentials have a generic Gaussian shape, whose range and strength can be tuned via modifications in the generation number and flexibility of the spacers. We supplement our simulation analysis by a density-functional approach in which the connectivity between the monomers is approximated by an external confining potential that holds the monomer beads together. Using a simple density functional for the interactions between the monomers, we find semiquantitative agreement between theory and simulation. The implications of our findings for the interpretation of scattering data from concentrated dendrimer solutions are also discussed.     

Surface phase separation in complex mixed adsorbing systems: an interface-bulk coupling effect

The interfacial thermodynamics and structure of ternary mixtures of the type A+B+solvent are investigated. According to the Gibbs phase rule, the coupling between the bulk phase and the interfacial region-which is related to the reversibility of the adsorption of the corresponding species-is a determinant as to whether phase separation can be observed at the interface. For an n-component adsorbing solution, at least one of the species has to adsorb irreversibly over the experimental time scales in order not to fix more intensive variables than those required to observe surface phase separation. We present results for a lattice model planar interface consisting of the ternary mixture A+B+solvent. The solvent molecules and the type A molecules have fixed chemical potentials at the interface since they are equilibrated with a bulk solution. In contrast, the type B molecules are irreversibly adsorbed at the interface and do not equilibrate with the bulk. Mean-field theory is compared with Monte Carlo simulation. Interestingly, the spinodal line in the interaction-composition plane shows a reentrant on the B-rich phase side. We discuss the implications of these results for surface phase separation of adsorbing mixtures of proteins and low-molecular-weight surfactants.     

The phase behavior of comblike block copolymer A(m+1)B(m)/homopolymer A mixtures

The phase behaviors of comblike block copolymer A(m+1)B(m)/homopolymer A mixtures are studied by using the random phase approximation method and real-space self-consistent field theory. From the spinodals of macrophase separation and microphase separation, we can find that the number of graft and the length of the homopolymer A have great effects on the phase behavior of the blend. For a given composition of comblike block copolymer, increasing the number of graft does not change the macrophase separation spinodal curve but decreases the microphase separation region. The addition of a small quantity of long-chain homopolymer A increases the microphase separation of comblike block copolymer/homopolymer A mixture. However, the addition of short-chain homopolymer A will decrease the phase separation region of comblike block copolymer/homopolymer A mixture. It is also found that the microstructure formed by diblock copolymer is easier to be swelled by homopolymer than that formed by comblike block copolymer. This can be attributed to the architecture difference between the comblike block copolymer and linear block copolymer.     

Capillary condensation of a binary mixture in slit-like pores

We investigate the capillary condensation of two model fluid mixtures in slit-like pores, which exhibit different demixing properties in the bulk phase. The interactions between adsorbate particles are modeled by using Lennard-Jones (12,6) potentials and the adsorbing potentials are of the Lennard-Jones (9,3) type. The calculations are performed for different pore widths and at different concentrations of the bulk gas, by means of density functional theory. We evaluate the capillary phase diagrams and discuss their dependence on the parameters of the model. Our calculations indicate that a binary mixture confined to a slit-like pore may exhibit rich phase behavior.     

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.     

Molecular simulation investigation into the performance of Cu-BTC metal-organic frameworks for carbon dioxide-methane separations

We report a molecular simulation study for Cu-BTC metal-organic frameworks as carbon dioxide-methane separation devices. For this study we have computed adsorption and diffusion of methane and carbon dioxide in the structure, both as pure components and mixtures over the full range of bulk gas compositions. From the single component isotherms, mixture adsorption is predicted using the ideal adsorbed solution theory. These predictions are in very good agreement with our computed mixture isotherms and with previously reported data. Adsorption and diffusion selectivities and preferential sitings are also discussed with the aim to provide new molecular level information for all studied systems.     

Decay of correlation functions in hard-sphere mixtures: structural crossover

We investigate the decay of pair correlation functions in a homogeneous (bulk) binary mixture of hard spheres. At a given state point the asymptotic decay r-->infinity of all three correlation functions is governed by a common exponential decay length and a common wavelength of oscillations. Provided the mixture is sufficiently asymmetric, size ratios q less than or approximately 0.7, we find that the common wavelength reflects either the size of the small or that of the big spheres. By analyzing the (complex) poles of the partial structure factors we find a sharp structural crossover line in the phase diagram. On one side of this line the common wavelength is approximately the diameter of the smaller sized spheres whereas on the other side it is approximately the diameter of the bigger ones; the wavelength of the longest ranged oscillations changes discontinuously at the structural crossover line. Using density functional theory and Monte Carlo simulations we show that structural crossover also manifests itself in the intermediate range behavior of the pair correlation functions and we comment on the relevance of this observation for real (colloidal) mixtures. In highly asymmetric mixtures, q< or =0.1, where there is metastable fluid-fluid transition, we find a Fisher-Widom line with two branches. This line separates a region of the phase diagram where the decay of pair correlations is oscillatory from one in which it is monotonic.     

聚合物链长及表面吸附强度对三维受限下嵌段共聚物微观相分离的影响

利用动态密度泛函(Dynamic density functional theory, DDFT)方法研究了三维受限下嵌段共聚物的微观相分离, 讨论了共聚物链长和表面吸附强度对微观相形成与取向的影响. 体系中随机分布的等径微球提供三维限制结构, 体积分数为0.6. 增加微球的半径和体积分数, 能够使其从破坏微相规整结构的纳米掺杂过渡到提供三维限制结构. 调整嵌段共聚物与微球表面的相互作用对微相形成与取向有重要影响.     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

Long-range interactions between soft colloidal particles in slit-pore geometries

Combining theoretical and experimental techniques, we investigate the structure formation of charged colloidal suspensions of silica particles in bulk and in spatial confinement (slit-pore geometry). Our focus is to identify characteristic length scales determining typical quantities, such as the position of the main peak of the bulk structure factor and the period of the oscillatory force profile in the slitpore. We obtain these quantities from integral equations/SANS experiments (bulk) and Monte Carlo simulations/colloidal probe-AFM measurements (confinement), in which the theoretical calculations are based on the Derjaguin-Landau-Verwey-Overbeck (DLVO) potential. Both in bulk and in the slitpore, we find excellent qualitative and quantitative agreement between theory and experiment as long as the ionic strength chosen in the DLVO potential is sufficiently low (implying a relatively long-ranged interaction). In particular, the bulk properties of these systems obey the widely accepted density scaling of xi proportional to phi(-1/3). On the other hand, systems with larger ionic strengths and, consequently, more short-ranged interactions do not obey such power law behavior and rather resemble an uncharged hard-sphere fluid, in which the relevant length scale is the particle diameter.     

Direct correlation functions of binary mixtures of hard Gaussian overlap molecules

We study the direct correlation function (DCF) of a classical fluid mixture of nonspherical molecules. The components of the mixture are two types of hard ellipsoidal molecules with different elongations, interacting through the hard Gaussian overlap (HGO) model. Two different approaches are used to calculate the DCFs of this fluid, and the results are compared. Here, the Pynn approximation [J. Chem. Phys. 60, 4579 (1974)] is extended to calculate the DCF of the binary mixtures of HGO molecules, then we use a formalism based on the weighted density functional theory introduced by Chamoux and Perera [J. Chem. Phys. 104, 1493 (1996)]. These results are fairly in agreement with each other. The pressure of this system is also calculated using the Fourier zero components of the DCF. The results are in agreement with the Monte Carlo molecular simulation.     

Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO(2) and poly(methyl methacrylate) CO(2) systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

Molecular Modeling of Adsorption in Activated Carbon: Comparison of Monte Carlo Simulations with Experiment

We present Mont Carlo computer simulation results for a molecular model of fluids adsorbed in porous carbon materials. The model carbon used is based on the platelet model for carbon of Segarra and Glandt (1994). The model we use has a single basal plane per platelet and the structure is isotropic, disordered, with weak short-range correlations between the platelets. We have performed grand canonical Monte Carlo simulations of the adsorption isotherms for methane, ethane, and their mixtures in this model carbon. We find generally good agreement with experimental and the mixture results are quite accurately described by the ideal adsorbed solution theory. An exception to this is the behavior for the mixture at the highest pressures. In this case the experimental data show significant deviations from ideal adsorbed solution theory and the simulation results.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.