Translational Order Parameters Research Articles

A simple model for density anomaly and excess thermodynamic properties of alcohol-like in water-like mixture

ABSTRACT Molecular dynamics simulations were employed to gain insights into the density anomaly and excess thermodynamic properties of a binary mixture composed of a solvent resembling water and a solute resembling alcohol. In our model, both fluids were represented by spherical particles interacting through effective potentials: a two-length scale potential for the solvent–solvent interaction while purely repulsive potentials were used for the solute–solute and solute–solvent interactions. The temperature of maximum density (TMD) present in the pure solvent system is also observed in our mixture. The TMD exhibits a positive deviation in the mixture when compared to the pure solvent fluid under high-pressure conditions, while it shows a negative deviation under low-pressure conditions what is consistent with experiments. The excess volume, enthalpy and isobaric heat capacity show extreme values at x ≈ 0.4 . Using the radial distribution function and the translational order parameter we suggest that this behaviour can be explained in terms of solute particles caged in solvent network.

Optimization of the Domain Size in Stressed Liquid Crystals

The distributions of orientational and translational order parameters in liquid crystal polymer composites are studied using the methods of molecular-statistical physics. A model is considered in which the composite consists of liquid crystal (LC) domains separated by flat polymer sheets. The perturbation of the orientational and translational order parameters, which is caused by an arbitrary flat polymer sheet in a planar LC layer, is estimated. The effective distance over which this disturbance propagates is estimated. It is shown that it is proportional to the square root of the splay elastic constant of LC. It has been shown that in certain temperature ranges the polymer can induce a more ordered liquid crystal phase near itself (smectic phase inside of nematic phase and nematic phase – inside of isotropic liquid phase). In this case, the orientational order parameter of LC near the polymer can be significantly higher than far from it, and the “perturbation” of the order parameters can propagate over a distance of up to several micrometers with a sharp peak at a distance of the order of one micrometer. Based on the original theory, the methods have been proposed for optimizing the sizes of domains in stressed liquid crystals obtained by mechanical treatment in liquid crystal polymer composites.

Self-Organization of Two-Dimensional Systems: The Role of Translational and Orientational Order Parameters

Self-Organization of Two-Dimensional Systems: The Role of Translational and Orientational Order Parameters

Metastable hybridized structure transformation in amorphous carbon films during friction—A study combining experiments and MD simulation

Amorphous carbon films have attracted substantial interest due to their exceptional mechanical and tribological properties. Previous studies revealed that the amorphous carbon films exhibited lower coefficient of friction (COF) because of the transformation in bond structure from sp3-C to sp2-C during friction processes. However, the mechanism for such a transformation during friction is not well understood. This study is conducted to get an insight into the metastable transformation in amorphous carbon film during friction by means of experiments and molecular dynamics (MD) simulation. Relevant wear tests showed that wear of the film changed from an abrasive wear mode to a mixture of abrasion and adhesive wear, resulting in a decrease in growth rate of the wear rate after the running-in stage. It is worth noting that the sp3-C atoms were increased during the running-in stage when the films contained lower sp3/sp2 ratios. However, the formed sp3-C atoms could only be short-lived and gradually transformed to sp2-C atoms with the graphitization generated on the wearing surface of the films. The radial distribution function and translational order parameter indicated that the films’ high sp3/sp2 ratio led to an increased sp2-C proportion on the wear scar after friction, which caused an increased structural ordering.

Topological phase transition in a quasi-two-dimensional Coulomb gas.

A system with an equal number of positive and negative charges confined in a box with a small but finite thickness is modeled as a function of temperature using mesoscale numerical simulations for various values of the charges. The Coulomb interaction is used in its three-dimensional form, U(r)∼1/r. A topological phase transition is found in this quasi-two-dimensional (2D) system. The translational order parameter, spatial correlation function, specific heat, and electric current show qualitatively different trends below and above a critical temperature. We find that a 2D logarithmic Coulomb interaction is not essential for the appearance of this transition. This work suggests new experimental tests of our predictions, as well as novel theoretical approaches to probe quasi-2D topological phase transitions.

How Far Is "Bulk Water" from Interfaces? Depends on the Nature of the Surface and What We Measure.

Using systematic molecular dynamics (MD) simulations, we revisit the question: At what distance from an interface do the properties of "bulk water" get recovered? We have considered three different kinds of interfaces: nonpolar (hydrophobic; isooctane-water interface), charged (negative; AOT bilayer), and polar (zwitterionic; POPC bilayer). In order to interrogate the extent of perturbation of the interfacial water molecules as a function of the distance from the interface, we utilize a diverse range of structural and dynamical parameters. To capture the structural perturbations, we look into local density (translational order), local tetrahedral order parameter, and dipolar orientation of the water molecules. We also explore the anisotropic diffusion of the water molecules in the direction perpendicular to the interface as well as the planar diffusion parallel to the interface in a distance dependent manner. In addition, the orientational time correlation functions have been computed to understand the extent of slowdown in the rotational dynamics. As expected, the electrostatic field emanating from the charged AOT interface seems to have the highest long-range effect on the orientational order and dynamics of the water molecules, whereas specific interactions like hydrogen bonding and electrostatic interaction lead to significant trapping and kinetic slowdown for both AOT and POPC (zwitterionic) very close to the interface. Our analysis highlights that not only the length-scale of perturbation depends on the nature of the interfaces and specific interactions but also the type of water property that we measure/calculate. Different water properties seem to have widely different length-scale of perturbation. Orientational order parameters seem to be perturbed to a much longer length-scale as compared to translational order parameters. The global orientational order of water can be perturbed even up to ∼4-5 nm near the negatively charged AOT surface in the absence of any extra electrolyte. This observation has significant implication toward the interpretation of experimental measurements as well since different spectroscopic techniques would probe different parameters or water properties with possible mutual disagreement and inconsistency between different types of measurements. Thus, our study provides a broader and unifying perspective toward the aspect of "context dependent" structural and dynamical perturbation of "interfacial water".

Aroyloxycinnamates with wide mesophase temperature ranges

ABSTRACT A new series of eight asymmetric homologues was designed and synthesised by the reaction of aroyloxybenzaldehydes with Wittig salt of methyl bromoacetate, where the length of the alkoxy chain was varied. All the compounds were found thermally stable up to 220°C. Differential scanning calorimetry, polarising optical microscopy and X-ray diffraction were used to study the mesomorphic properties, where a mesophase range of up to 80°C was obtained. The two shorter homologues with C3–C4 were nematic, the intermediate lengths were nematic and smectic A (SmA) with a progressive increase of the SmA domains and the longest homologue with C12 was purely SmA. The translational order parameter of the SmA mesophases showed that the molecular order inside the smectic layers increases with molecular length, associated with the higher stabilisation and predominance of the SmA phase. All compounds dispersed in solution absorb light in the ultraviolet region.

Topographic Control of Order in Quasi-2D Granular Phase Transitions.

We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.

Liquid-Crystal Ordering and Microphase Separation in the Lamellar Phase of Rod-Coil-Rod Triblock Copolymers. Molecular Theory and Computer Simulations.

A molecular model of the orientationally ordered lamellar phase exhibited by asymmetric rod-coil-rod triblock copolymers has been developed using the density-functional approach and generalizing the molecular-statistical theory of rod-coil diblock copolymers. An approximate expression for the free energy of the lamellar phase has been obtained in terms of the direct correlation functions of the system, the Flory-Huggins parameter and the Maier-Saupe orientational interaction potential between rods. A detailed derivation of several rod-rod and rod-coil density-density correlation functions required to evaluate the free energy is presented. The orientational and translational order parameters of rod and coil segments depending on the temperature and triblock asymmetry have been calculated numerically by direct minimization of the free energy. Different structure and ordering of the lamellar phase at high and low values of the triblock asymmetry is revealed and analyzed in detail. Asymmetric rod-coil-rod triblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter and for several values of the triblock asymmetry. It has been found that the lamellar phase appears to be the most stable one at strong segregation. The density distribution of the coil segments and the segments of the two different rods have been determined for different values of the segregation strength. The simulations confirm the existence of a weakly ordered lamellar phase predicted by the density-functional theory, in which the short rods separate from the long ones and are characterized by weak positional ordering.

Different Mechanisms of Translational Symmetry Breaking in Liquid-Crystal Coil–Rod–Coil Triblock Copolymers

A molecular-statistical theory of coil-rod–coil triblock copolymers with orientationally ordered rod-like fragments has been developed using the density functional approach. An explicit expression for the free energy has been obtained in terms of the direct correlation functions of the reference disordered phase, the Flory–Huggins parameter and the potential of anisotropic interaction between rigid rods. The theory has been used to derive several phase diagrams and to calculate numerically orientational and translational order parameter profiles for different polymer architecture as a function of the Flory–Huggins parameter, which specifies the short-range repulsion and as functions of temperature. In triblock copolymers, the nematic–lamellar transition is accompanied by the translational symmetry breaking, which can be caused by two different microscopic mechanisms. The first mechanism resembles a low dimensional crystallization and is typical for conventional smectic liquid crystals. The second mechanism is related to the repulsion between rod and coil segments and is typical for block copolymers. Both mechanisms are analyzed in detail as well as the effects of temperature, coil fraction and the triblock asymmetry on the transition into the lamellar phase.

Shining rings: The effect of the rigid core and benzazole heterocycles on the properties of luminescent calamitic liquid crystals

We report the molecular designing of non-symmetrical luminescent liquid crystals based on the 1,2,3-benzotriazole (BTZ), 2,1,3-benzoxadiazole (BOX) and 2,1,3-benzothiadiazole (BTD) heterocycles. The compounds showed stable nematic and smectic mesophases in a wide range of temperatures (between 70 and 170 °C). Translational order parameter investigations based on X-ray diffraction experiments demonstrated high ordered layers, closely dependent of the molecular structure and the smectic organization. The molecules exhibited intense photoluminescence under UV–vis light excitation in solutions. The emission spectrum for BTZ revealed a maximum in the blue region (447 nm), while BOX and BTD emit in the yellow one (around 550 nm). The fluorescence quantum yields of the BTZ-based derivatives solution are up to 64%, significantly higher than BOX and BTD. Moreover, in solid films, the efficiencies remained in the same range of solution. DFT calculations indicate dihedral angles of 24-30° between the benzazole-phenyl rings, which may suppress π-stacking and consequently reduce fluorescence quenching in the solid phase. This work contributes to general knowledge, where asymmetric cores improve mesophase stabilization and photoluminescence preservation in the solid state compared to their symmetric pairs.

Structure and dynamics of the Lennard-Jones fcc-solid focusing on melting precursors

The Lennard-Jones potential is taken as a basis to study the structure and dynamics of the face centered cubic (fcc) solid along an isochore from low temperatures up to the solid/fluid transition. The Z method is applied to estimate the melting point. Molecular dynamics simulations are used to calculate the pair distribution function, numbers of nearest neighbors, and the translational order parameter, analyzing the weakening of the fcc-symmetry due to emerging premelting effects. A range of dynamic properties, such as the mean-squared displacement, non-Gaussian parameter, Debye-Waller factor, and vibrational density of states, is considered for the analysis of the solid state. All of these parameters clearly show that bulk mobility is activated at about 2/3 of the melting temperature, known as the Tammann temperature. This indicates that vibrational motion of atoms is not maintained exclusively in the entire stable solid state and that collective atomic motion constitutes a precursor of the melting process.

Density Functional Approach to the Molecular Theory of Rod-Coil Diblock Copolymers

The general density functional approach is used to develop a molecular-statistical theory of rod-coil diblock copolymers which is valid in the case of both weak and strong segregation. The free energy of the rod-coil copolymer is expressed as a functional of the number densities of rod and coil monomers which depend on the translational and orientational degrees of freedom. The equilibrium densities are determined by minimization of the free energy functional and depend on the orientational and translational order parameters of the monomers. The order parameters are calculated numerically by minimization of the free energy taking into account the incompressibility condition within the formalism of Lagrange multipliers. Phase diagrams are obtained and the profiles of orientational and translational order parameters are presented as functions of temperature and the fraction of coil fragments. It is shown that the lamellar phase possesses strong orientational order and the stability of the phase is increasing with the increasing fraction of rod monomers.

Insight into Out‐of‐Layer Fluctuations in the Smectic A Stability of 3,5‐Diarylisoxazole Liquid Crystals

Polar-terminated 3,5-diarylisoxazole liquid crystals (ILCs) were synthetized and characterized. ILCs are composed by rigid core 3,5-diarylisoxazol, alkyl chain and polar-terminated flexible spacer. Hydroxyl-, ketal- and 1,2-diol-terminated ILCs rendered smectic C and A mesophase, while bromine-terminated ILCs showed smectic A and B mesophase, for monosubstituted and linear ILCs. For branched alkyl chain monotropic SmA was detected and for disubstituted ILCs no mesophase was detected. Out-of-layer fluctuations (OLFs) are discussed based on X-ray diffraction date and textures. The OLFs are dependent on the bromine atom hardness, hydrogen bonding through collective actions and conformational effects at the interface between layers. Smectic translational order parameter (TOP) å was also obtained for orientated bromine- and hydroxyl-terminated ILCs and related it with OLFs. For 1,2-diol-terminated ILCs two SmC sublayers were founded, probably related to the intramolecular hydrogen bond favoring the 5-membered and 6-membered formation.

Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers.

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.

Effect of cross-link concentration on the isotropic to smectic-A phase transition in smectic elastomers

We describe the isotropic to smectic-A phase transition in smectic elastomers within Landau phenomenological theory. We analyze the effects of external mechanical stress and cross-link concentration on the isotropic to smectic-A phase transition. Both the orientational and translational order parameters decrease with the increase of cross-link concentration. The first order isotropic to smectic-A transition in low-molecular-weight materials, can become weak first order transition in smectic elastomers. The effect of cross-link concentration on the strain birefringence and correlation length in the isotropic phase of the transition is discussed.

Phase separations induced by translational and orientational order parameters

Phase separations induced by translational and orientational order parameters

Molecular theory of liquid-crystal ordering in rod-coil diblock copolymers.

Molecular-statistical theory of rod-coil diblock copolymers is proposed using the general density functional approach which enables one to consider the cases of both weak and strong segregation. The free energy of the system is expressed as a functional of the phase-space densities of rod and coil monomers, which depend on the orientational and translational order parameters. Temperature-concentration phase diagrams are obtained and the profiles of all order parameters are calculated numerically by minimizing the polymer free energy. The lamellar phase is shown to possess strong orientational order which is partially induced by the phase structural anisotropy. The enhanced stability of the lamellar phase is determined by a combination of the microphase separation effects and the emergence of long-range smectic order.

Molecular Electron Density Distribution and X-Ray Diffraction Patterns of Smectic A Liquid Crystals - A Simulation Study.

X-ray diffraction (XRD) is one of the most important methods to assess the long-range translational order in smectic A (SmA) liquid crystals. Nevertheless, the knowledge about the influence of the molecular electron density distribution (MEDD) on the XRD pattern is rather limited because it is not possible to vary the orientational order, the translational order and the MEDD independently in an experiment. We here present a systematic simulation study in which we examine this effect and show that the MEDD indeed has a major impact on the general appearance of the XRD pattern. More specifically, we find that the smectic layer peaks and the intensity ratios thereof strongly depend on the width of the MEDD. The classic approach by Leadbetter et al. to determine the smectic translational order parameter from XRD intensities works if the MEDD is quite narrow. In all other cases the influence of the MEDD has to be taken into account.

Structural and optical properties of free-standing smectic films.

We have carried out a complex numerical study of the structural, thermodynamic and optical properties of the partially fluorinated 5-n -alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) free-standing smectic film in air under the action of the external electric field [Formula: see text]. Calculations, based upon the extended McMillan's mean-field theory with anisotropic forces, show a stepwise reduction of the value of the Helmholtz free energy and the reflectivity of the partially fluorinated smectic film in air, as the temperature is raised above the bulk smectic-A-isotropic transition value. It has been shown, by solving the self-consistent nonlinear equations for the orientational and translational order parameters, that the electric field [Formula: see text] may not only affect the layer-thinning transition sequences, but also change the first multilayer jump in the film thickness, whereas practically does not affect the reflectivity R(N) of the partially fluorinated N -layer smectic film in air. In the range of film thicknesses investigated, the reduction of the R(N) is, at least, qualitatively in agreement with the experimentally observed decrease of the optical reflectivity with the decrease of N.