Order Parameter Profiles Research Articles

Critical surface adsorption of confined binary liquids with locally conserved mass and composition

Close to a solid surface, the properties of a fluid deviate significantly from their bulk values. In this context, we study the surface adsorption profiles of a symmetric binary liquid confined to a slit pore by means of molecular dynamics simulations; the latter naturally entails that mass and concentration are locally conserved. Near a bulk consolute point, where the liquid exhibits a demixing transition with the local concentration as the order parameter, we determine the order parameter profiles and characterise the relevant critical scaling behaviour, in the regime of strong surface attraction, for a range of pore widths and temperatures. The obtained order parameter profiles decay monotonically near the surfaces, also in the presence of a pronounced layering in the number density. Overall, our results agree qualitatively with recent theoretical predictions from a mesoscopic field-theoretical approach for the canonical ensemble.

A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics.

A singular potential method in the Q tensor order parameter representation of a nematic liquid crystal is used to study the equilibrium configuration of a disclination dipole. Unlike the well studied isotropic limit (the so called one constant approximation), we focus on the case of anisotropic Frank elasticity (bend/splay elastic constant contrast). Prior research has established that the singular potential method provides an accurate description of the tensor order parameter profile in the vicinity of a disclination core of a highly anisotropic lyotropic chromonic liquid crystal. This research is extended here to two interacting disclinations forming a dipole configuration. The director angle is shown to decay in the far field inversely with distance to the dipole as is the case in the isotropic limit, but with a different angular dependence. Therefore elastic constant anisotropy modifies the elastic screening between disclinations, with implications for the study of ensembles of defects as seen, for example, in active matter in the extended system limit.

Anisotropic particle multiphase equilibria in nonuniform fields.

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1-9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid-nematic, fluid-crystal, and fluid-nematic-crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal-nematic and crystal-fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications.

Demixing of homogeneous binary lipid membranes induced by protein inclusions.

We study a model of a lipid bilayer membrane described by two order parameters: the chemical composition described using the Gaussian model and the spatial configuration described with the elastic deformation model of a membrane with a finite thickness or, equivalently, for an adherent membrane. We assume and explain on physical grounds the linear coupling between the two order parameters. Using the exact solution, we calculate the correlation functions and order parameter profiles. We also study the domains that form around inclusions on the membrane. We propose and compare six distinct ways to quantify the size of such domains. Despite its simplicity, the model has many interesting features like the Fisher-Widom line and two distinct critical regions.

Mixtures of ultracold atomic gases in optical lattices with nonzero pair or counterflow hopping

We study the critical behavior of a mixture of two species of lattice bosons described by the extended Bose–Hubbard model. Our goal is to analyze in which conditions exotic orderings like pair superfluid or counterflow superfluid could be detected. We use a numerical method based on mean field approximation to calculate the phase diagram of the system, along with particle density, and order parameter profiles in selected multicritical points. We observe that the phase diagram becomes significantly renormalized in the presence of pair flow or counterflow. Furthermore, a critical particle density emerges, which isolates a new region of the phase diagram, in which the exotic order parameter exists for any value of single-particle hopping.

Predicting protein flexibility with AlphaFold.

AlphaFold2 has revolutionized protein structure prediction from amino-acid sequence. In addition to protein structures, high-resolution dynamics information about various protein regions is important for understanding protein function. Although AlphaFold2 has neither been designed nor trained to predict protein dynamics, it is shown here how the information returned by AlphaFold2 can be used to predict dynamic protein regions at the individual residue level. The approach, which is termed cdsAF2, uses the 3D protein structure returned by AlphaFold2 to predict backbone NMR NH S2 order parameters using a local contact model that takes into account the contacts made by each peptide plane along the backbone with its environment. By combining for each residue AlphaFold2's pLDDT confidence score for the structure prediction accuracy with the predicted S2 value using the local contact model, an estimator is obtained that semi-quantitatively captures many of the dynamics features observed in experimental backbone NMR NH S2 order parameter profiles. The method is demonstrated for a set nine proteins of different sizes and variable amounts of dynamics and disorder.

Packing and elasticity in membrane mechanical properties.

Here we address how membrane properties involving head group size, acyl chain unsaturation, and lipid packing affect their structure and dynamics. Strong out-of-plane proteolipid couplings considered by the flexible surface model (FSM) affect protein function through elastic forces described by the spontaneous curvature and the bending rigidity. We hypothesized that the mechanical properties and the molecular packing resulting from different lipid types are captured by introducing a perdeuterated POPC-d31 probe lipid. Di-monounsaturated phosphatidylcholine and phosphatidylethanolamine (DOPC, DOPE), and different ratios of DOPC/DOPE mixtures were studied using MD simulations combined with experimental solid-state 2H NMR spectroscopy. Residual quadrupolar couplings obtained from de-Paked powder-type spectra yielded order parameter (SCD) profiles for the individual acyl segments giving insights into average membrane structural properties such as area per lipid and bilayer thickness [1]. The corresponding spin-lattice relaxation rates (R1Z) for the resolved peaks followed a theoretical square-law dependence on SCD providing the bending rigidity [2]. Furthermore, MD simulations for the lipid systems were carried out and order parameters were calculated and compared against the NMR-observed SCD values. Utilization of the probe lipid POPC-d31 (1−10 mol%)affected the lamellar to hexagonal phase transition temperature of DOPE lipid systems but did not affect the quadrupolar splittings of DOPE and DOPC systems. Higher bending rigidity was observed for DOPE membranes versus DOPC supporting the idea that the membrane bending rigidity is primarily governed by increased lipid packing and is related to the area-compressibility modulus. Use of a probe lipid to capture membrane mechanical properties of complex lipid systems allow investigation of the relationship of membrane mechanics in vital biological functions.

Shape and interfacial structure of droplets. Exact results and simulations

We consider the fluctuating interface of a droplet pinned on a flat wall. For such a system we compare results obtained within the exact field theory of phase separation in two dimensions and Monte Carlo (MC) simulations for the Ising model. The interface separating coexisting phases splits and hosts drops whose effect is to produce subleading corrections to the order parameter profile and correlation functions. In this paper we establish the first direct measurement of interface structure effects by means of high-performance MC simulations which successfully confirm the field-theoretical results. Simulations are found to corroborate the theoretical predictions for interface structure effects whose analytical expression has recently been obtained. It is thanks to these higher-order corrections that we are able to correctly resettle a longstanding discrepancy between simulations and theory for the order parameter profile. In addition, our results clearly establish the long-ranged decay of interfacial correlations in the direction parallel to the interface and their spatial confinement within the interfacial region also in the presence of a wall from which the interface is entropically repelled.

High-precision anomalous dimension of three-dimensional percolation and spatial profile of the critical giant cluster.

In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile ϕ, which is obtained by raising the solution of the Yamabe equation to the scaling dimension Δ_{ϕ}. The latter can be fixed from outcomes of numerical simulations, from which we obtain Δ_{ϕ}=0.47846(71) and the corresponding value of the anomalous dimension η=-0.0431(14). The comparison with values of η determined by using scaling relations is discussed. A test of hyperscaling is also performed.

Effects of the preferential adsorption in a near-critical binary fluid mixture on dynamics of a droplet

A large amount of binary fluid mixture in the homogeneous phase near the demixing critical point can include a small spherical droplet of a third fluid-component confined by a sharp interface. Conversely, a droplet consisting of the mixture can be immersed in the third fluid-component. In either of the situations, we assume that the third component attracts one mixture component more than the other via short-range interactions. The adsorption layer, enriched with the preferred component, appears on the mixture side of the interface and can thicken significantly because of large susceptibility. The preferential adsorption affects flows, causing the drag coefficient to deviate. We use the hydrodynamics based on a coarse-grained free-energy functional to calculate the deviation, while neglecting the weak singularity of mixture viscosity. When the mixture lies inside the droplet, the ratio of the deviation changes nonmonotonically as the ratio of the ambient viscosity to the droplet viscosity increases. When the mixture lies outside, the deviation ratio increases with the viscosity ratio and can be considerably larger for a droplet than for a rigid sphere. Then, if a composition gradient is imposed, a force-free droplet undergoes diffusiophoresis, whose mobility can be considerably larger in magnitude than that of a rigid sphere. These results can be utilized in future applications in the droplet microfluidics. We also discuss probable power-law dependences of the drag coefficient and the mobility on the reduced temperature. The suggested power for the mobility is connected with the universal order-parameter profile in the surface critical behavior.

Effect of methanol as an amphiphile on water structuring around a hydrate forming gas molecule: Insights from molecular dynamics simulations

Gas hydrates (GH) are crystalline compounds composed of small hydrophobic molecules encapsulated within cavities formed by hydrogen bonded water molecules. These compounds are an important source of fuel and are of application in gas storage and transportation. Processes such as nucleation, crystal growth, stability and decomposition of GH are controlled by the introduction of molecules referred to as additives. A challenging aspect in the study of GH is to explain at a molecular level the influence of additives on these processes. An intriguing case of additives is that of amphiphilic molecules which influence hydrate processes through their complex effects on the organization of water as well as on gas solubility. In this study, we apply molecular dynamics simulations to examine the effect of CH3OH, the simplest amphiphile and the most commonly used additive, on the organization of H2O molecules in the hydration shell of CO2, a hydrate forming gas. The interface between methanol–water liquid mixture and CO2 is examined by applying the Identification of Truly Interfacial Molecules (ITIM) technique, thereby minimizing the errors due to molecular level roughness at the interface. The organizational order of hydration shell water (HSW) is examined by evaluating the F4 order parameter. The results show that the presence of CH3OH enhances the availability of aqueous CO2 near the interface which makes the arrangement of HSW in this region more hydrate-like, resulting in an increase in value of F4 on approaching the interface from the bulk. It is also observed that CH3OH molecules tend to orient their hydrophobic CH3 group towards aqueous CO2 thereby inducing hydrate-like ordering of water in the hydration shell. However, on approaching the liquid surface, hydrate-like organization of HSW is opposed by CH3OH molecules at the surface which, owing to their –OH group oriented towards the liquid phase, significantly influences water orientation near the interface and decreases the value of F4. The net outcome of these opposing effects of CH3OH on hydrate-like ordering of HSW is the observation of a maximum in the value of F4 order parameter at a distance beneath the surface of the liquid and a progressive decrease from this maximum on moving further closer to the surface. The observed features of the value of F4 order parameter profile are explained based on the analysis of the intrinsic structure of the liquid–gas interface. The results indicate that, the presence of CH3OH leads to a region beneath the liquid surface where the extent of hydrate-like organization of HSW becomes maximum. However, CH3OH molecules significantly limits the availability of water molecules around aqueous gas, justifying the action of methanol as an inhibitor for hydrate formation when present at high concentrations. The results indicate that the effect of an amphiphile on GH formation is determined by its interaction with dissolved gas as well as by the influence of surface adsorbed amphiphile on water orientation and gas availability near the interface.

Serotonergic drugs modulate the phase behavior of complex lipid bilayers

Serotonin is an endogenous neurotransmitter involved in both physiological and pathophysiological processes. Traditionally, serotonin acts as a ligand for G protein-coupled receptors (GPCRs) leading to subsequent cell signaling. However, serotonin can also bind to lipid membranes with high affinity and modulate the phase behavior in 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC)/N-palmitoyl-D-erythro-sphingosylphosphorylcholine (PSM)/cholesterol model membranes mimicking the outer leaflet of the plasma membrane. Here, we investigated if serotonergic drugs containing the pharmacophore from serotonin would also modulate phase behavior in lipid membranes in a similar fashion. We used 2H NMR spectroscopy to explore the phase behavior of POPC/PSM/cholesterol (4/4/2 molar ratio) mixtures in the presence of the serotonergic drugs aripiprazole, BRL-54443, BW-723C86, and CP-135807 at a lipid to drug molar ratio of 10:1. POPC and PSM were perdeuterated in the palmitoyl chain, respectively, and prepared in individual samples. Numerical lineshape simulations of the 2H NMR spectra were used to calculate the order parameter profiles and projected lengths of the saturated acyl chains. All serotonergic drugs induce two components in 2H NMR spectra, indicating that they increased the hydrophobic mismatch between the thickness of the coexisting lipid phases leading to larger domain sizes, relatively similarly to serotonin. AFM force indentation and Raman spectral studies, which interrogate membrane mechanical properties, also indicate changes in membrane order in the presence of these drugs. These findings highlight how serotonergic drugs alter membrane phase behavior and could modulate both target and other membrane proteins, possibly explaining the side effects observed for serotonergic and other clinically relevant drugs.

Experimental and computational investigation of hydrophilic monomeric substances as novel CO2 hydrate inhibitors and potential synergists

CO2 hydrate formation in the CO2 transmission pipelines for ocean or geological sequestration can result in pipeline blockage and rupture. Herein, monomeric substances (urea (U), acetamide (A), and glycine (G)) that are easily decomposable were evaluated as kinetic hydrate inhibitors and potential synergists for CO2 hydrate using experimental and computational approaches. The onset temperatures of CO2 + inhibitor hydrates were experimentally measured using a high-pressure autoclave reactor. G showed the best inhibition effect among single inhibitors, and combinations of U + A and A + G made the inhibition synergism for CO2 hydrate. Moreover, molecular dynamics simulations were also conducted to understand the nucleation and formation behaviors of CO2 hydrate in the presence of single and mixed inhibitors at a molecular level. The profiles of F4 order parameters and hydrate counts for each CO2 + inhibitor system followed the experimental results. Analyses of hydrogen bond distributions, radial distribution function, and mean squared displacement were carefully conducted to elucidate the inhibition mechanism of monomeric substances and their inhibition synergism for CO2 hydrate. The experimental and computational results would provide insights into the development of new biodegradable CO2 hydrate inhibitors and contribute to safe transportation and injection of CO2 for long-term storage.

Monte Carlo Simulations of Biaxial Molecules Near Hard Wall

A system of optimal biaxial molecules placed at the sites of a cubic lattice is studied in an extended Lebwohl-Lasher model. Molecules interact only with their nearest neighbors through the pair potential that depends on the molecule orientations. It is known that in the homogeneous system there is a direct second-order transition from the isotropic to the biaxial nematic phase, but properties of confined systems are less known. In the present paper the lattice has periodic boundary conditions in the X and Y directions and it has two walls with planar anchoring, perpendicular to the Z direction. We have investigated the model using Monte Carlo simulations on $N_x \times N_y \times N_z$ lattices, $N_x = N_y = 10, 16$, $N_z$ from 3 to 19, with and without assuming mirror symmetry. This study is complementary to the statistical description of hard spheroplatelets near a hard wall by Kapanowski and Abram [Phys. Rev. E 89, 062503 (2014)]. The temperature dependence of the order-parameter profiles between walls is calculated for many wall separations. For large wall separations there are the surface layers with biaxial ordering at both walls (4-5 lattice constants wide) and beyond the surface layers the order parameters have values as in the homogeneous system. For small wall separations the isotropic-biaxial transition is shifted and the surface layers are thinner. Above the isotropic-biaxial transition the preferable orientations in both surface layers can be different. It is interesting that planar anchoring for biaxial molecules leads to the uniaxial interactions at the wall. As a result we get the planar Lebwohl-Lasher model with additional (biaxial) interactions with the neighbors from the second layer, where the Kosterlitz-Thouless transition is present.

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.

Interface in presence of a wall. Results from field theory

We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge, we show how the problem can be studied analytically from first principles, starting from the degrees of freedom (particle modes) of the bulk field theory. After deriving the passage probability of the interface and the order parameter profile in the regime in which the interface is not bound to the wall, we show how the theory accounts at the fundamental level also for the binding transition and its key parameter.

Theory of Inhomogeneous Rod-like Coulomb Fluids

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson–Boltzmann and Maier–Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity to a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic–isotropic wetting phase with a Donnan potential difference.

Structure and Interaction of Lipid Bilayers in the Presence of ATP

Even in the absence of membrane receptors, adenosine triphosphate (ATP) has been shown to interact with lipid membranes and to affect their interactions. Measurements of zeta potentials by dynamic light scattering (DLS) show that ATP creates a positive zeta potential of phosphatidylcholine (PC) lipid vesicles. A similar effect is seen on phosphatidylserine (PS) bilayers in that the negative zeta potential of PS diminishes in magnitude in the presence of ATP. We further investigate the effect of ATP on lipid bilayers by 2H NMR spectroscopy which gives us an order parameter profile for the carbon-deuterium bonds along lipid acyl chains.

Experimental and Computational Investigation of Hydrophilic Monomeric Substances as Novel CO <sub>2</sub> Hydrate Inhibitors and Potential Synergists

CO2 hydrate formation in the CO2 transmission pipelines for ocean or geological sequestration can result in pipeline blockage and rupture. Herein, monomeric substances (urea (U), acetamide (A), and glycine (G)) that are easily decomposable were evaluated as kinetic hydrate inhibitors and potential synergists for CO2 hydrate using experimental and computational approaches. The onset temperatures of CO2 + inhibitor hydrates were experimentally measured using a high-pressure autoclave reactor. G showed the best inhibition effect among single inhibitors, and combinations of U + A and A + G made the inhibition synergism for CO2 hydrate. Moreover, molecular dynamics simulations were also conducted to understand the nucleation and formation behaviors of CO2 hydrate in the presence of single and mixed inhibitors at a molecular level. The profiles of F4 order parameters and hydrate counts for each CO2 + inhibitor system followed the experimental results. Analyses of hydrogen bond distributions, radial distribution function, and mean squared displacement were carefully conducted to elucidate the inhibition mechanism of monomeric substances and their inhibition synergism for CO2 hydrate. The experimental and computational results would provide insights into the development of new biodegradable CO2 hydrate inhibitors and contribute to safe transportation and injection of CO2 for long-term storage.

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.