Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal

Beyond the mean-field approximation for pair correlations in classical density functional theory: Reference inhomogeneous non-associating monomeric fluids for use with SAFT-VR Mie DFT

A free-energy functional is presented to explicitly take into account pair correlations between molecules in inhomogeneous fluids. The framework of classical density functional theory (DFT) is used to describe the variation in the density of molecules interacting through a Mie (generalized Lennard-Jones) potential. Grand Canonical Monte Carlo simulations are performed for the systems to validate the new functional. The statistical associating fluid theory developed for Mie fluids (SAFT-VR Mie) is selected as a reference for the homogeneous bulk limit of the DFT and is applied here to systems of spherical non-associating particles. The importance of a correct description of the pair correlations for a reliable representation of the free energy in the development of the equation of state is duly noted. Following the Barker-Henderson high-temperature expansion, an analogous formulation is proposed from the general DFT formalism to develop an inhomogeneous equivalent of the SAFT-VR Mie free energy as a functional of the one-body density. In order to make use of this new functional in adsorption studies, a non-local version of the DFT is considered, with specific weighted densities describing the effects of neighboring molecules. The computation of these quantities is possible in three-dimensional space for any pore geometry with repulsive or attractive walls. We showcase examples to validate the new functional, revealing a very good agreement with molecular simulation. The new SAFT-DFT approach is well-adapted to describe realistic complex fluids.

Molecular theory of the static dielectric constant of dipolar fluids

The link between the static dielectric constant and the microscopic intermolecular interactions is the Kirkwood g₁ factor, which depends on the orientational structure of the fluid. Over the years, there have been several attempts to provide an accurate description of the orientational structure of dipolar fluids using molecular theories. However, these approaches were either limited to mean-field approximations for the pair correlation function or, more recently, limited to adjusting the orientational dependence to simulation data. Here, we derive a theory for the dielectric constant of dipolar hard-sphere fluids using the augmented modified mean-field approximation. Qualitative agreement is achieved throughout all relevant thermodynamic states, as demonstrated by a comparison with simulation data from the literature. Excellent quantitative agreement can be obtained using a single empirical scaling factor, the physical origin of which is analyzed and accounted for. In order to predict the dielectric constant of the Stockmayer fluid (Lennard-Jones plus dipole potential), we use an adjusted version of the expression for the dipolar hard-sphere fluid. Comparing theoretical predictions with newly generated simulation data, we show that it is possible to obtain excellent agreement with simulation by performing the calculations at a corresponding state using the same scaling factor. Finally, we compare the theoretical orientational structure of the Stockmayer fluid with that obtained from simulations. The simulated structure is calculated following a post-processing methodology that we introduce by deriving an original expression that relates the proposed theory to the histogram of relative dipole angles.

Phase Behavior of Lyotropic Liquid-Crystalline Polymers under Varying Solvent Conditions: Effect of External Fields on the Phase Diagram

In this work, we report a Density Functional Theory based study of phase behavior of lyotropic liquid-crystalline polymers under both good and varying solvent conditions in the presence of external electric or magnetic field. Our microscopic model for the good solvent case is based on the tangent hard-sphere chain with bond-bending potential to account for the chain stiffness; the variable solvent quality is modeled by adding attractive monomer-monomer interactions. The phase diagrams are constructed in three intensive variables (temperature, pressure, and field strength), and are characterized by the presence of critical and triple lines, which originate from the critical and triple points of the corresponding zero-field case. The merging of critical and triple lines results in the appearance of the "double critical" and "critical triple" points, already known from the earlier studies of the phase behavior of spin fluids in magnetic fields. The important difference of the present model from the spin fluids is due to the finite stiffness of the polymer chains (characterized by their persistence length), which adds an additional parameter controlling the morphology of the phase diagrams.

Molecular theory of a ferromagnetic nematic liquid crystal

We employ a version of classical density functional theory to study the phase behavior of a simple model liquid crystal in an external field. The uniaxially symmetric molecules have a spherically symmetric core with superimposed orientation-dependent attractions. The interaction between the cores consists of a hard-sphere repulsion plus an isotropic square-well attraction. The anisotropic part of the interaction potential allows for the formation of a uniaxially symmetric nematic phase. The orientation of the molecules couples to an external polar field. The external field is capable of rotating the nematic director n[over ̂] in the x-z plane. The field is also capable of changing the topology of the phase diagram in that it suppresses the phase coexistence between an isotropic liquid and a nematic phase observed in the absence of the field. We study the transition from an unpolar to a polar nematic phase in terms of the orientation-distribution function (odf), nematic and polar order parameters, and components of n[over ̂]. If represented suitably the odf allows us to study orientational changes during the switching process between nonpolar and polar nematic phases. We also give a simple argument that explains why nematic order is lost whereas polar order persists up to the gas-liquid critical point along the coexistence curve. We also discuss the relevance of our theory for future experimental studies.

Manipulation of cholesteric liquid crystal phase behavior and molecular assembly by molecular chirality

Molecular simulation is used to study the effect of molecular chirality on liquid crystalline phase transition and molecular assembly behavior. Based on a flexible chain (FCh) model with helical arrangement of side beads, the phase behavior of FCh models with various molecular chiralities are studied as functions of pressure (or density). By modifying the molecular chirality of FCh, we can manipulate the relative stability of the nematic and cholesteric phases continuously; and we found that increasing molecular chirality may destabilize cholesteric order due to the effective reduction of chiral interactions. A semismectic phase is identified in the high-density region, in which the two-dimensional fluid layers overlap due to shift alignment formed by FCh particles. The global phase diagram of the FCh model is constructed and the potential energy surface is calculated to elucidate the formation of cholesteric phase in terms of two-body interactions.

Free energy of conformational isomers: The case of gapped DNA duplexes

Liquid-crystalline phases in all-DNA systems have been extensively studied in the past and although nematic, cholesteric and columnar mesophases have been observed, the smectic phase remained elusive. Recently, it has been found evidence of a smectic-A ordering in an all-DNA system, where the constituent particles, which are gapped DNA duplexes, resemble chain-sticks. It has been argued that in the smectic-A phase these DNA chain-sticks should be folded as a means to suppress aggregate polydispersity and excluded volume. Nevertheless, if initial crystalline configurations are prepared in silico with gapped DNA duplexes either fully unfolded or fully folded by carrying out computer simulations one can end up with two different phases having at the same concentration and temperature the majority of gapped DNA duplexes either folded or unfolded. This result suggests that these two phases have a small free energy difference, since no transition is observed from one to the other within the simulation time span. In the present manuscript, we assess which of these two phases is thermodynamically stable through a suitable protocol based on thermodynamic integration. Our method is rather general and it can be used to discriminate stable states from metastable ones of comparable free energy.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. II. The interplay between molecular packing and orientational order

As in Paper I of this series of papers [S. M. Cattes et al., J. Chem. Phys. 144, 194704 (2016)], we study a Heisenberg fluid confined to a nanoscopic slit pore with smooth walls. The pore walls can either energetically discriminate specific orientations of the molecules next to them or are indifferent to molecular orientations. Unlike in Paper I, we employ a version of classical density functional theory that allows us to explicitly account for the stratification of the fluid (i.e., the formation of molecular layers) as a consequence of the symmetry-breaking presence of the pore walls. We treat this stratification within the White Bear version (Mark I) of fundamental measure theory. Thus, in this work, we focus on the interplay between local packing of the molecules and orientational features. In particular, we demonstrate why a critical end point can only exist if the pore walls are not energetically discriminating specific molecular orientations. We analyze in detail the positional and orientational order of the confined fluid and show that reorienting molecules across the pore space can be a two-dimensional process. Last but not least, we propose an algorithm based upon a series expansion of Bessel functions of the first kind with which we can solve certain types of integrals in a very efficient manner.

Cholesteric ordering predicted using a coarse-grained polymeric model with helical interactions

The understanding of cholesteric liquid crystals at a molecular level is challenging. Limited insights are available to bridge between molecular structures and macroscopic chiral organization. In the present study, we introduce a novel coarse-grained (CG) molecular model, which is represented by flexible chain particles with helical interactions (FCh), to study the liquid crystalline phase behavior of cholesteric molecules such as double strand DNA and α-helix polypeptides using molecular dynamics (MD) simulations. The isotropic-cholesteric phase transitions of FCh molecules were simulated for varying chain flexibilities. A wall confinement was used to break the periodicity along the cholesteric helix director in order to predict the equilibrium cholesteric pitch. The left-handed cholesteric phase was shown for FCh molecules with right-handed chiral interactions, and a spatially inhomogeneous distribution of the nematic order parameter profile was observed in cholesteric phases. It was found that the chain flexibility plays an important role in determining the macroscopic cholesteric pitch and the structure of the cholesteric liquid crystal phase. The simulations provide insight into the relationship between microscopic molecular characteristics and the macroscopic phase behavior.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Phase Behavior of Magnetic Nanocolloids of Different Sizes Suspended in an Apolar Solvent

We employ classical density functional theory (DFT) to investigate the phase behavior and composition of binary mixtures; each compound consists of hard spheres of different sizes with superimposed dispersion attraction. In addition to the dispersion attraction, molecules of one component carry an additional three-dimensional magnetic "spin" where the orientation-dependent spin-spin interaction is accounted for by the Heisenberg model. We are treating the excess free energy using a modified mean-field approximation (second virial coefficient) for the orientation-dependent pair correlation function. Depending on the concentration of the magnetic particles, the strength of the spin-spin coupling, and the size ratio of the particles, the model predicts the formation of ordered (polar) phases in addition to the more conventional gas and isotropic liquid phases. Key features of our model are a particle-size dependent shift of the gas-liquid critical point (critical temperature and density) and a change in the width of the phase diagram. In the near-critical region, the latter can be analyzed quantitativly in terms of an effective critical exponent β_eff that may differ from the classical critical exponent [Formula: see text]; the classical value is attained in the immediate vicinity of the critical point as it must. The deviation between β_eff and β can be linked to nontrivial composition effects along the phase boundaries.