Orlando Guzmán

Polymer-particle mixtures: Depletion and packing effects

The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.

Quenched disorder in a liquid-crystal biosensor: Adsorbed nanoparticles at confining walls

We analyze the response of a nematic liquid-crystal film, confined between parallel walls, to the presence of nanoscopic particles adsorbed at the walls. This is done for a variety of patterns of adsorption (random and periodic) and operational conditions of the system that can be controlled in experimental liquid-crystal-based devices. We compute simulated optical textures and the total optical output of the sensor between crossed polars, as well as the correlation function for the liquid-crystal tensor order parameter; we use these observables to discuss the gradual destruction of the original uniform orientation. For large concentrations of particles adsorbed in random patterns, the liquid crystal at the center of the sensor adopts a multidomain state, characterized by a small correlation length of the tensor order parameter, and also by a loss of optical anisotropy under observation through crossed polars. In contrast, for particles adsorbed in periodic patterns, the nematic at the center of the cell can remain in a monodomain orientation state, provided the patterns in opposite walls are synchronized.

Slow dynamics of thin nematic films in the presence of adsorbed nanoparticles

Recent experiments indicate that liquid crystals can be used to optically report the presence of biomolecules adsorbed at solid surfaces. In this work, numerical simulations are used to investigate the effects of biological molecules, modeled as spherical particles, on the structure and dynamics of nematic ordering. In the absence of adsorbed particles, a nematic in contact with a substrate adopts a uniform orientational order, imposed by the boundary conditions at this surface. It is found that the relaxation to this uniform state is slowed down by the presence of a small number of adsorbed particles. However, beyond a critical concentration of adsorbed particles, the liquid crystal ceases to exhibit uniform orientational order at long times. At this concentration, the domain growth is characterized by a first regime where the average nematic domain size LD obeys the scaling law LDt approximately t1/2; at long times, a slow dynamics regime is attained for which LD tends to a finite value corresponding to a metastable state with a disordered texture. The results of simulations are consistent with experimental observations.

Monte Carlo simulations and dynamic field theory for suspended particles in liquid crystalline systems

Monte Carlo simulations and dynamic field theory are used to study spherical particles suspended in a nematic liquid crystal. Within these two approaches, we investigate the binding of the defects to the particles, the adsorption of a particle at a solid surface, and two particles interacting with each other. Quantitative comparisons indicate good agreement between the two approaches. A Monte Carlo method based on the combination of canonical expanded ensemble simulations with a density-of-state formalism is used to determine the potential of mean force between one particle and a hard wall. On the other hand, the potential of mean force is evaluated using a dynamic field theory, where the time-dependent evolution of the second rank tensor includes two major aspects of liquid crystalline materials, namely the excluded volume and the long-range order elasticity. The results indicate an effective repulsive force that acts between the particle and the wall. Layer formation at the surface of the hard wall gives rise to local minima in the potential of mean force. The director profile for a particle at contact with a solid surface is characterized by a disclination line distorted and attracted towards the wall. The structure of the nematic for two particles at short distances is also investigated. Our results indicate a structure where the two particles are separated by a circular disclination line. The potential of mean force associated with this configuration indicates an effective attractive interaction between the two particles.

An effective-colloid pair potential for Lennard-Jones colloid-polymer mixtures

We propose an effective one-component model that accurately reproduces the colloid–colloid radial distribution function gcc(r) of a colloid–polymer mixture. The particles of this effective model interact through an effective potential ueff(r), obtained by inversion of the Ornstein–Zernike equation and a closure suited for fluids with repulsive cores. The consistency of this approach was tested by simulation of the effective one-component fluid and comparison to the original radial distribution function. The effective potential can be separated into a repulsive part (corresponding to the “bare” pair potential between colloids), and a depletion potential, v(r). The strength and range of v(r) are well represented by simple functions of the total volume fraction.

Effective potential for three-body forces in fluids

We develop a model for an effective Axilrod–Teller–Muto (ATM) triple-dipole interaction based on accurate calculations of three-body effects on the third virial coefficient. The effective ATM interaction is written as a two-body density-dependent potential and is obtained by averaging the ATM function over the position of the third particle. It is shown that the addition of the mean ATM potential does not affect much the form of the binary interaction and so it can be incorporated as an effect on the minimum of the potential (position and depth). The underlying binary potentials are modelled by Approximate Non-Conformal (ANC) functions that have been proven to be highly accurate in accounting for effective pair interactions in many fluids of interest. The final total effective potential, binary plus ternary, is expressed in terms of the same ANC functions. The adequacy of the effective three-body force thus found is tested by looking at the pressure and specific heat of various fluids, formed by small nonpolar molecules, in the region of moderate densities where a third-virial approximation is reliable, and then comparing them against experimental results. The critical temperatures and volumes of those fluids are also calculated and the three-body effects on them are assessed.

Third virial coefficient of nonpolar gases from accurate binary potentials and ternary forces

An explicit model for the third virial coefficient C(T) is presented, based on accurate binary interactions plus three-body forces; its predictions are compared to experimental data for 15 fluids (argon, krypton, xenon, nitrogen, oxygen, fluorine, carbon monoxide, carbon dioxide, perfluoromethane, methane, ethene, ethane, propane, n-butane, and n-pentane). Three-body interactions are represented by the Axilrod–Teller–Muto (ATM) triple-dipole potential, while the binary potential profile is systematically varied using approximate non-conformal (ANC) potentials. Non-conformality affects significantly both two- and three-body contributions to C(T). A formula for C(T) of ANC+ATM systems is obtained in terms of all interaction parameters; the three-body contribution is proportional to the parameter ν of the ATM potential while its temperature dependence is proportional to that of a reference fluid (argon). The ANC+ATM model reproduces C(T) within experimental error for most of the fluids considered, with a small negative deviation in some cases, which may be ascribed to the need of a complement to the ATM term.

Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.

Analytical equation of state with three-body forces: Application to noble gases

We developed an explicit equation of state (EOS) for small non polar molecules by means of an effective two-body potential. The average effect of three-body forces was incorporated as a perturbation, which results in rescaled values for the parameters of the two-body potential. These values replace the original ones in the EOS corresponding to the two-body interaction. We applied this procedure to the heavier noble gases and used a modified Kihara function with an effective Axilrod-Teller-Muto (ATM) term to represent the two- and three-body forces. We also performed molecular dynamics simulations with two- and three-body forces. There was good agreement between predicted, simulated, and experimental thermodynamic properties of neon, argon, krypton, and xenon, up to twice the critical density and up to five times the critical temperature. In order to achieve 1% accuracy of the pressure at liquid densities, the EOS must incorporate the effect of ATM forces. The ATM factor in the rescaled two-body energy is most important at temperatures around and lower than the critical one. Nonetheless, the rescaling of two-body diameter cannot be neglected at liquid-like densities even at high temperature. This methodology can be extended straightforwardly to deal with other two- and three-body potentials. It could also be used for other nonpolar substances where a spherical two-body potential is still a reasonable coarse-grain approximation.

Separating the effects of repulsive and attractive forces on the phase diagram, interfacial, and critical properties of simple fluids

Molecular simulations in the canonical and isothermal-isobaric ensembles were performed to study the effect of varying the shape of the intermolecular potential on the phase diagram, critical, and interfacial properties of model fluids. The molecular interactions were modeled by the Approximate Non-Conformal (ANC) theory potentials. Unlike the Lennard-Jones or Morse potentials, the ANC interactions incorporate parameters (called softnesses) that modulate the steepness of the potential in their repulsive and attractive parts independently. This feature allowed us to separate unambiguously the role of each region of the potential on setting the thermophysical properties. In particular, we found positive linear correlation between all critical coordinates and the attractive and repulsive softness, except for the critical density and the attractive softness which are negatively correlated. Moreover, we found that the physical properties related to phase coexistence (such as span of the liquid phase between the critical and triple points, variations in the P-T vaporization curve, interface width, and surface tension) are more sensitive to changes in the attractive softness than to the repulsive one. Understanding the different roles of attractive and repulsive forces on phase coexistence may contribute to developing more accurate models of liquids and their mixtures.