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.     

Ionic microgels as model systems for colloids with an ultrasoft electrosteric repulsion: structure and thermodynamics

We present a theoretical analysis of the structural properties and phase behavior of spherical, loosely cross-linked ionic microgels that possess a low monomer concentration. The analysis is based on the recently derived effective interaction potential between such particles [A. R. Denton, Phys. Rev. E 67, 011804 (2003)]. By employing standard tools from the theory of the liquid state, we quantitatively analyze the pair correlations in the fluid and find anomalous behavior above the overlap concentration, similar to the cases of star-branched neutral and charged polymers. We also employ an evolutionary algorithm in order to predict the crystalline phases of the system without any a priori assumptions regarding their symmetry class. A very rich phase diagram is obtained, featuring two reentrant melting transitions and a number of unusual crystal structures. At high densities, both the Hansen-Verlet freezing criterion [J.-P. Hansen and L. Verlet, Phys. Rev. 184, 151 (1969)] and the Lindemann melting criterion [F. A. Lindemann, Phys. Z. 11, 609 (1910)] lose their validity. The topology of the phase diagram is altered when the steric interactions between the polymer segments become strong enough, in which case the lower-density reentrant melting disappears and the region of stability of the fluid is split into two disconnected domains, separated by intervening fcc and bcc regions.     

One-dimensional cluster growth and branching gels in colloidal systems with short-range depletion attraction and screened electrostatic repulsion

We report extensive numerical simulations of a simple model for charged colloidal particles in suspension with small nonadsorbing polymers. The chosen effective one-component interaction potential is composed of a short-range attractive part complemented by a Yukawa repulsive tail. We focus on the case where the screening length is comparable to the particle radius. Under these conditions, at low temperature, particles locally cluster into quasi one-dimensional aggregates which, via a branching mechanism, form a macroscopic percolating gel structure. We discuss gel formation and contrast it with the case of longer screening lengths, for which previous studies have shown that arrest is driven by the approach to a Yukawa glass of spherical clusters. We compare our results with recent experimental work on charged colloidal suspensions (Phys. Rev. Lett. 2005, 94, 208301).     

Competing interactions in two dimensional Coulomb systems: surface charge heterogeneities in coassembled cationic-anionic incompatible mixtures

A binary mixture of oppositely charged components confined to a plane such as cationic and anionic lipid bilayers may exhibit local segregation. The relative strengths of the net short range interactions, which favors macroscopic segregation, and the long range electrostatic interactions, which favors mixing, determine the length scale of the finite size or microphase segregation. The free energy of the system can be examined analytically in two separate regimes, when considering small density fluctuations at high temperatures and when considering the periodic ordering of the system at low temperatures [F. J. Solis, S. I. Stupp, and M. Olvera de la Cruz, J. Chem. Phys. 122, 054905 (2005)]. A simple molecular dynamics simulation of oppositely charged monomers, interacting with a short range Lennard-Jones potential and confined to a two dimensional plane, is examined at different strengths of short and long range interactions. The system exhibits well-defined domains that can be characterized by their periodic length scale as well as the orientational ordering of their interfaces. By adding salt, the ordering of the domains disappears and the mixture macroscopically phase segregates in agreement with analytical predictions.     

Depletion potentials induced by charged colloidal rods

We present direct depletion potential measurements for a single colloidal sphere close to a wall in suspensions of charged colloidal rods. In contrast to earlier studies of purely entropic systems (Helden et al. Phys. Rev. Lett. 2003, 90, 048301), here electrostatic interactions are important. These enhance the depletion attraction and lead to repulsive parts in the interaction potentials, indicating correlation effects between the rods.     

Molecular dynamics study of polarizability anisotropy relaxation in aromatic liquids and its connection with local structure

The collective polarizability anisotropy dynamics in a set of three aromatic liquids, benzene (Bz), hexafluorobenzene (HFB), and 1,3,5-trifluorobenzene (TFB), has been studied by molecular dynamics simulation. These liquids have very similar shapes, but different electrostatic interactions due to opposite polarities of C-H and C-F bonds, giving rise to different local intermolecular structures in the liquid phase. We have investigated how these structural arrangements affect polarizability anisotropy dynamics observed in optical Kerr-effect (OKE) spectroscopy. We have modeled the interaction-induced polarizability with the first-order dipole-induced dipole approximation, with the molecular polarizability distributed over the carbon sites. Local contributions to the librational OKE spectrum were computed separately for molecules participating in parallel or perpendicular relative orientations within the first coordination shell. We found that the relative locations of parallel and perpendicular librational bands of the OKE spectra are closely related to the corresponding pair energy distributions of the closest four neighbors of a given molecule, corresponding to a model of a harmonic oscillator in a cage of nearest neighbors. This model predicts higher librational frequencies for more attractive intermolecular interactions, which in all three liquids correspond to parallel local arrangements. On the diffusive orientational time scale, all three liquids exhibit slower relaxation of molecules in parallel arrangements, although the difference in relaxation rates is substantial only in TFB, which has the strongest tendency toward parallel stacking. The analysis of the collective polarizability relaxation was performed using two different approaches, the projection scheme (J. Chem. Phys. 1980, 72, 2801) and the theory developed by Steele (Mol. Phys. 1987, 61, 1031) for the second time derivatives applied to collective time correlations. Both approaches allow the decomposition of the OKE response into contributions from orientational relaxation and other dynamical processes. We find that they lead to different predictions on how the response depends on collective reorientation and processes arising from fluctuations in the interaction-induced polarizability. We discuss the reasons for these differences and the advantages and disadvantages of the two analysis schemes.     

Molecular insight into the electrostatic membrane surface potential by 14n/31p MAS NMR spectroscopy: nociceptin-lipid association

Exploiting naturally abundant (14)N and (31)P nuclei by high-resolution MAS NMR (magic angle spinning nuclear magnetic resonance) provides a molecular view of the electrostatic potential present at the surface of biological model membranes, the electrostatic charge distribution across the membrane interface, and changes that occur upon peptide association. The spectral resolution in (31)P and (14)N MAS NMR spectra is sufficient to probe directly the negatively charged phosphate and positively charged choline segment of the electrostatic P(-)-O-CH(2)-CH(2)-N(+)(CH(3))(3) headgroup dipole of zwitterionic DMPC (dimyristoylphosphatidylcholine) in mixed-lipid systems. The isotropic shifts report on the size of the potential existing at the phosphate and ammonium group within the lipid headgroup while the chemical shielding anisotropy ((31)P) and anisotropic quadrupolar interaction ((14)N) characterize changes in headgroup orientation in response to surface potential. The (31)P/(14)N isotropic chemical shifts for DMPC show opposing systematic changes in response to changing membrane potential, reflecting the size of the electrostatic potential at opposing ends of the P(-)-N(+) dipole. The orientational response of the DMPC lipid headgroup to electrostatic surface variations is visible in the anisotropic features of (14)N and (31)P NMR spectra. These features are analyzed in terms of a modified "molecular voltmeter" model, with changes in dynamic averaging reflecting the tilt of the C(beta)-N(+)(CH)(3) choline and PO(4)(-) segment. These properties have been exploited to characterize the changes in surface potential upon the binding of nociceptin to negatively charged membranes, a process assumed to proceed its agonistic binding to its opoid G-protein coupled receptor.     

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

Coarse-graining intermolecular interactions in dispersions of highly charged colloids

Effective pair potentials between charged colloids, obtained from Monte Carlo simulations of two single colloids in a closed cell at the primitive model level, are shown to reproduce accurately the structure of aqueous salt-free colloidal dispersions, as determined from full primitive model simulations by Linse et al. (Linse, P.; Lobaskin, V. Electrostatic Attraction and Phase Separation in Solutions of Like-Charged Colloidal Particles. Phys. Rev. Lett.1999, 83, 4208). Excellent agreement is obtained even when ion-ion correlations are important and is in principle not limited to spherical particles, providing a potential route to coarse-grained colloidal interactions in more complex systems.     

The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations

We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/-0.02k(B)Tsigma(-2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inverse-power potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].     

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.     

Charged particles at fluid interfaces as a probe into structural details of a double layer

Electrostatic interactions between charged, distant colloids in a bulk electrolyte solution do not depend on the inherent structure of ions and a solvent forming a double layer. For charged colloids trapped at an interface between an electrolyte and air this no longer holds; as the electrostatic interactions are mediated via air and the field lines determining the interactions originate at the charged surface, these details come into prominence. Using the Langevin-Poisson-Boltzmann equation we investigate how steric effects and the polarization saturation of a solvent effect the contact potential at the colloid surface and, in consequence, the long range interactions between colloids trapped at an interface. For a surface charge 0.4 C m(-2) the combination of these effects can increase the interactions by up to ～40 times when compared to Poisson-Boltzmann calculations. The validity of these enhancement mechanisms is supported by recent experimental data (K. Masschaele et al., Phys. Rev. Lett., 2010, 105, 048303).     

Local biaxiality in cholesteric liquid crystals from the surface interaction model

The feature of local biaxiality of the orientational order in twisted nematics and cholesteric liquid-crystalline phases is faced by modeling the mean field orientational potential on the basis of the surface interaction model [A. Ferrarini, G. J. Moro, P. L. Nordio, and G. R. Luckhurst, Mol. Phys. 77, 1 (1992)]. Here we present a tool for the complete parameterization of the potential for general molecular structures and recover the long-pitch approximation usually invoked to model the molecular order in these phases. The method is applied to archetype molecular geometries (an ellipsoidal object, a conical object, a lath-shaped molecule, and the shape's enantiomers of a propellerlike molecule) in order to evaluate the dependence of the second-rank orientational order parameters on the pitch of the phase. Special emphasis is given to the so-called biaxiality parameter B [Z. Yaniv, N. A. P. Vaz, G. Chidichimo, and J. W. Doane, Phys. Rev. Lett. 47, 46 (1981)], which can be experimentally determined by the analysis of time-averaged (2)H-NMR spectra of deuterated probes dissolved in the twisted phase. The model calculations show how probes with different geometries are sensitive to the local biaxiality.     

Brownian dynamics simulations of simplified cytochrome c molecules in the presence of a charged surface

Simulations were performed for up to 150 simplified spherical horse heart cytochrome c molecules in the presence of a charged surface, which serves as an approximate model for a lipid membrane. Screened electrostatic and short-ranged attractive as well as repulsive van der Waals forces for interparticle and particle-membrane interactions are utilized in the simulations. At a distance from the membrane, where particle-membrane interactions are negligible, the simulation is coupled to a noninteraction continuum analogous to a heat bath [Geyer et al., J. Chem. Phys. 120, 4573 (2004)]. From the particles' density profiles perpendicular to the planar surface binding isotherms are derived and compared to experimental results [Heimburg et al. (1999)]. Using a negatively charged structureless membrane surface a saturation effect was found for relatively large particle concentrations. Since biological membranes often contain membrane proteins, we also studied the influence of additional charges on our model membrane mimicking bacterial reaction centers. We find that the onset of the saturation occurs for much lower concentrations and is sensitive to the detailed implementation. Therefore we suggest that local distortion of membrane planarity (undulation), or lipid demixing, or the presence of charged integral membrane proteins create preferential binding sites on the membrane. Only then do we observe saturation at physiological concentrations.     

Orientational anisotropy of bead-spring star chains during creep process

The bead-spring model for star chains (Rouse–Ham model) is a fundamental model for the polymer dynamics. Despite the importance of this model, its dynamics under the stress-controlled condition was not analyzed so far. For completeness of the model, the equation of motion of the Rouse–Ham chain was solved to derive an analytical expression of the orientation function S(n,t) for the stress-controlled creep process. This expression indicated that the segments near the free end of the star arm exhibit overshoot of their orientational anisotropy to compensate for the slow growth of the anisotropy near the branching point and that the distribution of the anisotropy along the arm contour becomes more heterogeneous with increasing arm number f. This correlation/interplay of the segments at different locations along the arm, not seen under the strain-controlled condition, is a natural consequence of the constant-stress requirement during the creep process. The corresponding interplay was noted also for respective Rouse–Ham eigenmodes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3501–3517, 2006     

Liquid crystal phases of charged colloidal platelets

The liquid crystal phase behavior of a suspension of charged gibbsite [Al(OH)3] platelets is investigated. By variation of the ionic strength, we are able to tune the effective thickness-to-diameter ratio of the platelets in suspension. This enables us to experimentally test the liquid crystal phase transition scenario that was first predicted a decade ago by computer simulations for hard platelets (Veerman, J. A. C.; Frenkel, D. Phys. Rev. A 1992, 45, 5632), that is, the isotropic (I) to nematic (N) and isotropic to columnar (C) phase transitions in one colloidal suspension. In addition to the shape-dependent thermodynamic driving force, the effect of gravity is important. For example, a biphasic (I-N) suspension becomes triphasic (I-N-C) on prolonged standing. This effect is described by a simple osmotic compression model.     

Quantum Monte Carlo study of helium clusters doped with nitrous oxide: quantum solvation and rotational dynamics

Dynamical and structural properties of small (4)He(N)-N(2)O complexes have been analyzed using ground-state and finite-temperature Monte Carlo simulations. The effective rotational constants resulting from the ground-state calculations are in excellent agreement with the results of a recent spectroscopic study [Y. Xu et al., Phys. Rev. Lett. 91, 163401 (2003)]. After an initial decrease for cluster sizes up to N=8, the rotational constant increases, signaling a transition from a molecular complex to a quantum-solvated system. Such a turnaround is not present in the rotational constants extracted from the finite-temperature Monte Carlo calculations, performed for Boltzmann statistics, thus highlighting the importance of exchange effects to explain the decoupling between a solvated dopant and the helium motion.