Towards composite spheres as building blocks for structured molecules.

In order to design a flexible molecular model that mimics the chemical moieties of a polyatomic molecule, we propose the 'composite-sphere' model that can assemble the essential elements to produce the structure of the target molecule. This is likened to the polymerization process where monomers assemble to form the polymer. The assemblage is built into the pair interaction potentials which can 'react' (figuratively) with selective pieces into various bonds. In addition, we preserve the spherical symmetries of the individual pair potentials so that the isotropic Ornstein-Zernike equation (OZ) for multi-component mixtures can be used as a theoretical framework. We first test our approach on generating a dumbbell molecule. An equimolar binary mixture of hard spheres and square-well spheres are allowed to react to form a dimer. As the bond length shrinks to zero, we create a site-site model of a Janus-like molecule with a repulsive moiety and an attractive moiety. We employ the zero-separation (ZSEP) closure to solve the OZ equations. The structure and thermodynamic properties are calculated at three isotherms and at several densities and the results are compared with Monte Carlo simulations. The close agreement achieved demonstrates that the ZSEP closure is a reliable theory for this composite-sphere fluid model.

The test-particle induced inhomogeneous direct correlation functions and extensions of Widom's theorem: impacts on the incremental chemical potentials and high-order correlation functions.

We develop the potential distributions of several test particles to obtain a hierarchy of the nonuniform singlet direct correlation functions (s-DCFs). These correlation functions are interpreted as the segmental chemical potentials or works of insertion of successive test particles in a classical fluid. The development has several interesting consequences: (i) it extends the Widom particle insertion formula to higher-order theorems, the first member gives the chemical potential as in the original theorem, the second member gives the incremental energy for dimer formation, with higher members giving the energies for forming trimers, tetramers, etc. (ii) The second and third order s-DCFs can be related to the cavity distribution functions y((2)) and y((3)) in the liquid-state theory. Thus we can express the triplet cavity function y((3)) in terms of these s-DCFs in an exact form. This enables us to calculate, as an illustration of the above theoretical developments, the numerical values of the s-DCFs via Monte Carlo (MC) simulation data on hard spheres. We use these data to critically analyze the commonly used approximations, the Kirkwood superposition (KSA) and the linear approximation (LA) for triplet correlation functions. An improved rule over KSA and LA is proposed for triplet hard spheres in the rolling-contact configurations. (iii) The s-DCFs are naturally suited for analyzing the chain-incremental Ansatz or hypothesis in the calculation of the chemical potentials of polymeric chain molecules. The first few segments of a polymer chain have been shown from extensive Monte Carlo simulations to not obey this Ansatz. By examining the insertion energies of successive segments through the s-DCFs, we are able to quantitatively decipher the decay of the segmental chemical potentials for at least the first three segments. Comparison with MC data on 4-mer and 8-mer hard-sphere fluids shows commensurate behavior with the s-DCFs. In addition, an analytical density functional theory is derived, through the potential distribution theorem, for obtaining these nonuniform direct correlation functions.

Constructing a new closure theory based on the third-order Ornstein-Zernike equation and a study of the adsorption of simple fluids.

The third-order Ornstein-Zernike equation (OZ3) is used in the construction of a bridge functional that improves over conventional liquid-theory closures (for example, the hypernetted chain or the Percus-Yevick equations). The OZ3 connects the triplet direct correlation C((3)) to the triplet total correlation h((3)). By invoking the convolution approximation of Jackson and Feenberg, we are able to express the third-order bridge function B(3) as a functional of the indirect correlation γ. The resulting expression is generalized to higher-order bridge terms. This new closure is tested on the adsorption of Lennard-Jones fluid on planar hard surfaces by calculating the density profiles and comparing with Monte Carlo simulations. Particular attention is paid to the cases where molecular depletion on the substrate is evident. The results prove to be highly accurate and improve over conventional closures.

Liquid water can slip on a hydrophilic surface.

Understanding and predicting the behavior of water, especially in contact with various surfaces, is a scientific challenge. Molecular-level understanding of hydrophobic effects and their macroscopic consequences, in particular, is critical to many applications. Macroscopically, a surface is classified as hydrophilic or hydrophobic depending on the contact angle formed by a water droplet. Because hydrophobic surfaces tend to cause water slip whereas hydrophilic ones do not, the former surfaces can yield self-cleaning garments and ice-repellent materials whereas the latter cannot. The results presented herein suggest that this dichotomy might be purely coincidental. Our simulation results demonstrate that hydrophilic surfaces can show features typically associated with hydrophobicity, namely liquid water slip. Further analysis provides details on the molecular mechanism responsible for this surprising result.

Crystallization limits of the two-term Yukawa potentials based on the entropy criterion.

We examine the fluid-solid transition for the potential with two Yukawa terms (one attractive and the other repulsive) and a hard core by exploration of the parameter space of (K(1), Z(1), and Z(2)), i.e., the parameters of interaction strength and interaction ranges, respectively. We apply the single-phase crystallization rule of Giaquinta and Giunta (1992) by searching for the conditions where the residual entropy reaches zero. To obtain accurate entropy properties, we adopt the self-consistent closure theory of the zero-separation genre. This closure gives accurate thermodynamic properties. The Ornstein-Zernike equation is solved to obtain the correlation functions. The structure factor S(q) is examined with respect to its cluster-cluster peak, whose value is another indication of phase transition according to Hansen and Verlet (1969). We discover that the parameter Z(1) (which determines the range of attractive forces) is important in crystal formation, so long as sufficient attraction (parameter K(1)) is present. If the range of attraction is too narrow, strength alone is not adequate to satisfy the Giaquinta rule or to solidify at given concentration and temperature. The control of the range of repulsion rests with the Z(2)-parameter. Its variations can bring about a high peak in S(q) at zero wave number (i.e., at q=0). Implications for the crystallization of protein and colloidal solutions are discussed.

The mean activity coefficients of 2:2 electrolyte solutions: an integral equation study of the restricted primitive model.

We apply the closure theory ZSEP (self-consistent zero-separation based closures) developed earlier to the restricted primitive model (RPM) of 2:2 electrolytes in order to (i) obtain the activity coefficient information via the direct formula for chemical potentials [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] and (ii) test the performance of this flexible ZSEP closure at high-coupling strengths (i.e., high valency and low temperatures) for cases of 2:2 electrolytes where other closure schemes have encountered difficulties [e.g., the hypernetted chain (HNC) equation]. In particular, we shall remedy the shortcomings of the HNC theory at low concentrations (from 0.001M to 0.2M). The ZSEP closure is found to perform well at coupling strengths beta(') = absolute value(z(1)z(2))e(2)/(epsilon(m)kTd) approaching approximately 10 where some other closure theories cease to give good results. In addition, by applying the direct chemical potential formula, we demonstrate numerically that, in the RPM cases examined, the logarithm of the mean activity coefficients of electrolytes are closely approximated by the electrostatic internal energy, an easily accessible quantity, a fact that shall afford ready access to the chemical potentials for phase equilibrium and electrochemical calculations on electrolytic systems.

Phase separation of model adsorbates in random matrices.

The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.

Boundary slip and wetting properties of interfaces: correlation of the contact angle with the slip length.

Correlations between contact angle, a measure of the wetting of surfaces, and slip length are developed using nonequilibrium molecular dynamics for a Lennard-Jones fluid in Couette flow between graphitelike hexagonal-lattice walls. The fluid-wall interaction is varied by modulating the interfacial energy parameter epsilonr=epsilonsfepsilonff and the size parameter sigmar=sigmasfsigmaff, (s=solid, f=fluid) to achieve hydrophobicity (solvophobicity) or hydrophilicity (solvophilicity). The effects of surface chemistry, as well as the effects of temperature and shear rate on the slip length are determined. The contact angle increases from 25 degrees to 147 degrees on highly hydrophobic surfaces (as epsilonr decreases from 0.5 to 0.1), as expected. The slip length is functionally dependent on the affinity strength parameters epsilonr and sigmar: increasing logarithmically with decreasing surface energy epsilonr (i.e., more hydrophobic), while decreasing with power law with decreasing size sigmar. The mechanism for the latter is different from the energetic case. While weak wall forces (small epsilonr) produce hydrophobicity, larger sigmar smoothes out the surface roughness. Both tend to increase the slip. The slip length grows rapidly with a high shear rate, as wall velocity increases three decades from 100 to 10(5) ms. We demonstrate that fluid-solid interfaces with low epsilonr and high sigmar should be chosen to increase slip and are prime candidates for drag reduction.

Chemical potentials and phase equilibria of Lennard-Jones mixtures: a self-consistent integral equation approach.

We explore the vapor-liquid phase behavior of binary mixtures of Lennard-Jones-type molecules where one component is supercritical, given the system temperature. We apply the self-consistency approach to the Ornstein-Zernike integral equations to obtain the correlation functions. The consistency checks include not only thermodynamic consistencies (pressure consistency and Gibbs-Duhem consistency), but also pointwise consistencies, such as the zero-separation theorems on the cavity functions. The consistencies are enforced via the bridge functions in the closure which contain adjustable parameters. The full solution requires the values of not only the monomer chemical potentials, but also the dimer chemical potentials present in the zero-separation theorems. These are evaluated by the direct chemical-potential formula [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] that does not require temperature nor density integration. In order to assess the integral equation accuracy, molecular-dynamics simulations are carried out alongside the states studied. The integral equation results compare well with simulation data. In phase calculations, it is important to have pressure consistency and valid chemical potentials, since the matching of phase boundaries requires the equality of the pressures and chemical potentials of both the liquid and vapor phases. The mixtures studied are methane-type and pentane-type molecules, both characterized by effective Lennard-Jones potentials. Calculations on one isotherm show that the integral equation approach yields valid answers as compared with the experimental data of Sage and Lacey. To study vapor-liquid phase behavior, it is necessary to use consistent theories; any inconsistencies, especially in pressure, will vitiate the phase boundary calculations.