Interface Fluctuations Research Articles

Ion-specific induced fluctuations and free energetics of aqueous protein hydrophobic interfaces: toward connecting to specific-ion behaviors at aqueous liquid-vapor interfaces.

We explore anion-induced interface fluctuations near protein–water interfaces using coarse-grained representations of interfaces as proposed by Willard and Chandler (J. Phys. Chem. B2010, 114, 1954−195820055377). We use umbrella sampling molecular dynamics to compute potentials of mean force along a reaction coordinate bridging the state where the anion is fully solvated and one where it is biased via harmonic restraints to remain at the protein–water interface. Specifically, we focus on fluctuations of an interface between water and a hydrophobic region of hydrophobin-II (HFBII), a 71 amino acid residue protein expressed by filamentous fungi and known for its ability to form hydrophobically mediated self-assemblies at interfaces such as a water/air interface. We consider the anions chloride and iodide that have been shown previously by simulations as displaying specific-ion behaviors at aqueous liquid–vapor interfaces. We find that as in the case of a pure liquid–vapor interface, at the hydrophobic protein–water interface, the larger, less charge-dense iodide anion displays a marginal interfacial stability compared with that of the smaller, more charge-dense chloride anion. Furthermore, consistent with the results at aqueous liquid–vapor interfaces, we find that iodide induces larger fluctuations of the protein–water interface than chloride.

Determination of the origin and magnitude of logarithmic finite-size effects on interfacial tension: role of interfacial fluctuations and domain breathing.

The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions L parallel and Lz perpendicular to the interface with various boundary conditions in the canonical or grand canonical ensemble can be studied. Using two- and three-dimensional Ising models, the nature of the occurring logarithmic finite-size corrections is studied. It is found crucial to include interfacial fluctuations due to "domain breathing."

Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer

We consider the Kardar-Parisi-Zhang equation for a circular interface in two dimensions, unconstrained by the standard small-slope and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or two-dimensional vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small-noise amplitudes, scaling behavior is only of the latter type. Large noise is also seen to renormalize the bare physical parameters of the ring, akin to analogous parameter renormalization for equilibrium three-dimensional membranes. Our results bear particular importance on the relation between relevant universality classes of scale-invariant systems in two dimensions.

Numerical approach to unbiased and driven generalized elastic model

From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent β characterizing the growth of the mean squared displacement 〈(δh)(2)〉 of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments 〈∣δh∣(q)〉 with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.

Research and Application of Three‐Dimensional Density Interface Inversion

AbstractBased on the Fourier transform, the Parker‐Oldenburg algorithm in the frequency domain was extended to the three‐dimensional case in which the density changes with depth. From this, a gravity interface inversion formula was derived in which the assumed density varies laterally and vertically. Iterative convergence is assured by fixing a particular depth as the datum plane below the surface to reduce the interface fluctuation. The results of an example of synthetic gravity data indicate that the proposed method has high precision and rapid convergence, with high practical value for the inversion of density interfaces. This method was also used to determine the Moho depth beneath northern China. The results were verified by seismic sounding data.

Non-Equilibrium Phase Behaviour in Giant Lipid Vesicles Following Very Rapid Temperature Changes

Artificial lipid bilayers are useful models of biological membranes, appealing for applicative purposes, and an interesting example of quasi-2D liquid systems on which to investigate new physics. It is well known that ternary-component lipid membranes, depending on the relevant thermodynamic parameters (composition, temperature and pressure), can show phase coexistence between two liquid phases, Lo and Ld, that can be imaged by fluorescence microscopy.We have performed experiments observing both equilibrium and non-equilibrium morphology of lipid phases. Specifically we have investigated a new dynamical regime in which we follow the diffusive mixing of miscible phases, and observe pattern formation out of equilibrium. This has been possible thanks to the development of a method to induce rapid temperature changes, by infrared irradiation. In this fashion, a temperature change can be imposed faster (in about 1s) than the diffusive time over relevant lengthscales (several 10s).Our observations are that the line tension rapidly vanishes upon heating the system above the miscibility transition temperature. After a few seconds, the spectrum of the interface fluctuations becomes very different from the equilibrium capillary waves, growing in amplitude and losing the characteristic 1/wave-vector2 equilibrium form. The interface from then blurs out, resembling fractal growth fronts, until the phases are fully mixed.The same fast temperature change allows us to very rapidly cool the system. This extends previous measurements by other groups, giving insight into processes that take place over the first few seconds of phase separation.Investigating these non-equilibrium conditions is relevant because biological membranes in living systems are not in a steady state: they are continually subject to rapid changes in composition, temperature and curvature, and their response is known to couple into a variety of biochemical processes by mediating protein binding and interactions.

Temperature dependence of exciton localization in ZnO/Zn1−xMgxO multiple quantum wells with different barrier compositions

Temperature-dependent photoluminescence (PL) measurements are used to study two ZnO/Zn1−xMgxO multiple quantum well (MQW) structures with different barrier compositions. The PL band in the well layers is dominated by localized excitons (LEs), free excitons (FEs), and two longitudinal optical (LO) phonon replicas of the LE emission. The LE emission of higher Mg compositional barrier exhibits a significant blue shift of about 70meV with respect to the lower one. The mechanisms of carrier dynamics and localization are investigated within the temperature range 14–300K. As the temperature increases, luminescence from the excitons localized in the well layers shows an ‘S-shaped’ shift in the high-barrier MQWs, whereas a monotonic red shift is observed in the low-barrier MQWs. The ‘S-shaped’ shift behavior is associated with delocalization of the excitons in the potential minima induced by interface fluctuations or alloy disorder. Large exciton binding energies of 64 and 76meV were deduced, demonstrating efficient quantum confinement in the ZnO/ZnMgO MQWs.

Direct Probing of Solvent Accessibility and Mobility at the Binding Interface of Polymerase (Dpo4)-DNA Complex

Water plays essential structural and dynamical roles in protein-DNA recognition through contributing to enthalpic or entropic stabilization of binding complex and by mediating intermolecular interactions and fluctuations for biological function. These interfacial water molecules are confined by the binding partners in nanospace, but in many cases they are highly mobile and exchange with outside bulk solution. Here, we report our studies of the interfacial water dynamics in the binary and ternary complexes of a polymerase (Dpo4) with DNA and an incoming nucleotide using a site-specific tryptophan probe with femtosecond resolution. By systematic comparison of the interfacial water motions and local side chain fluctuations in the apo, binary, and ternary states of Dpo4, we observed that the DNA binding interface and active site are dynamically solvent accessible and the interfacial water dynamics are similar to the surface hydration water fluctuations on picosecond time scales. Our molecular dynamics simulations also show the binding interface full of water molecules and nonspecific weak interactions. Such a fluid binding interface facilitates the polymerase sliding on DNA for fast translocation whereas the spacious and mobile hydrated active site contributes to the low fidelity of the lesion-bypass Y-family DNA polymerase.

Simulation of Magnetohydrodynamic Multiphase Flow Phenomena and Interface Fluctuation in Aluminum Electrolytic Cell with Innovative Cathode

A three-dimensional (3D) transient mathematical model has been developed to understand the effect of innovative cathode on molten cryolite (bath)/molten aluminum (metal) interface fluctuation as well as energy-saving mechanism in aluminum electrolytic cell with innovative cathode. Based on the finite element method, the steady charge conservation law, Ohm’s law, and steady-state Maxwell’s equations were solved in order to investigate electric current field, magnetic field, and electromagnetic force (EMF) field. Then, an inhomogeneous multiphase flow model of three phases including bath, metal, and gas bubbles, based on the finite volume method, was implemented using the Euler/Euler approach to investigate melt motion and bath/metal interface fluctuation. EMF was incorporated into the momentum equations of bath and metal as a source term. Additionally, the interphase drag force was employed to consider different phase interactions. Thus, present work owns three main features: (1) magnetohydrodynamic multiphase flow are demonstrated in detail both in aluminum electrolytic cell with traditional cathode and innovative cathode; (2) bath/metal interface fluctuation due to different driving forces of gas bubbles, EMF, and the combined effect of the two driving forces is investigated, which is critical to the energy saving; and (3) the effect of innovative cathode on melt flow and motion of gas bubbles. A good agreement between the predicated results and measurement is obtained. The velocity difference leading to the melt oscillation decreases due to more uniform flow field. The average velocity of metal in the cell with innovative cathode decreases by approximately 33.98 pct. The gas bubbles in the cell with innovative cathode releases more quickly under the effect of protrusion on the cathode. The average bubble release frequency increases from 1.1 to 1.98 Hz. Hence, the voltage drop caused by gas bubbles would decrease significantly. In addition, the two large vortices are broken into many small vortices due to the protrusion. The final disappearance of the small vortices as a result of viscous dissipation is conducive to the suppression of bath/metal interface fluctuation. The average interface amplitude in the cell with innovative cathode reduces to 75.95 pct of that in the cell with traditional cathode.

Freezing point and solid-liquid interfacial free energy of Stockmayer dipolar fluids: A molecular dynamics simulation study

Stockmayer fluids are a prototype model system for dipolar fluids. We have computed the freezing temperatures of Stockmayer fluids at zero pressure using three different molecular-dynamics simulation methods, namely, the superheating-undercooling method, the constant-pressure and constant-temperature two-phase coexistence method, and the constant-pressure and constant-enthalpy two-phase coexistence method. The best estimate of the freezing temperature (in reduced unit) for the Stockmayer (SM) fluid with the dimensionless dipole moment μ*=1, √2, √3 is 0.656 ± 0.001, 0.726 ± 0.002, and 0.835 ± 0.005, respectively. The freezing temperature increases with the dipolar strength. Moreover, for the first time, the solid-liquid interfacial free energies γ of the fcc (111), (110), and (100) interfaces are computed using two independent methods, namely, the cleaving-wall method and the interfacial fluctuation method. Both methods predict that the interfacial free energy increases with the dipole moment. Although the interfacial fluctuation method suggests a weaker interfacial anisotropy, particularly for strongly dipolar SM fluids, both methods predicted the same trend of interfacial anisotropy, i.e., γ100 > γ110 > γ111.

Liquid–Vapor Interfacial Properties of Aqueous Solutions of Guanidinium and Methyl Guanidinium Chloride: Influence of Molecular Orientation on Interface Fluctuations

The guanidinium cation (C(NH2)3(+)) is a highly stable cation in aqueous solution due to its efficient solvation by water molecules and resonance stabilization of the charge. Its salts increase the solubility of nonpolar molecules ("salting-in") and decrease the ordering of water. It is one of the strongest denaturants used in biophysical studies of protein folding. We investigate the behavior of guanidinium and its derivative, methyl guanidinium (an amino acid analogue) at the air-water surface, using atomistic molecular dynamics (MD) simulations and calculation of potentials of mean force. Methyl guanidinium cation is less excluded from the air-water surface than guanidinium cation, but both cations show orientational dependence of surface affinity. Parallel orientations of the guanidinium ring (relative to the Gibbs dividing surface) show pronounced free energy minima in the interfacial region, while ring orientations perpendicular to the GDS exhibit no discernible surface stability. Calculations of surface fluctuations demonstrate that, near the air-water surface, the parallel-oriented cations generate significantly greater interfacial fluctuations compared to other orientations, which induces more long-ranged perturbations and solvent density redistribution. Our results suggest a strong correlation with induced interfacial fluctuations and ion surface stability. These results have implications for interpreting molecular-level, mechanistic action of this osmolyte's interaction with hydrophobic interfaces as they impact protein denaturation (solubilization).

Spherical Monovalent Ions at Aqueous Liquid–Vapor Interfaces: Interfacial Stability and Induced Interface Fluctuations

Ion-specific interfacial behaviors of monovalent halides impact processes such as protein denaturation, interfacial stability, and surface tension modulation, and as such, their molecular and thermodynamic underpinnings garner much attention. We use molecular dynamics simulations of monovalent anions in water to explore effects on distant interfaces. We observe long-ranged ion-induced perturbations of the aqueous environment, as suggested by experiment and theory. Surface stable ions, characterized as such by minima in potentials of mean force computed using umbrella sampling MD simulations, induce larger interfacial fluctuations compared to nonsurface active species, conferring more entropy approaching the interface. Smaller anions and cations show no interfacial potential of mean force minima. The difference is traced to hydration shell properties of the anions, and the coupling of these shells with distant solvent. The effects correlate with the positions of the anions in the Hofmeister series (acknowledging variations in force field ability to recapitulate essential underlying physics), suggesting how differences in induced, nonlocal perturbations of interfaces may be related to different specific-ion effects in dilute biophysical and nanomaterial systems.

Protein electron transfer: Dynamics and statistics

Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.

Biexcitons in semiconductor quantum dot ensembles

The effects of confinement on biexciton renormalization in self-assembled InAs and interfacial GaAs quantum dot (QD) ensembles are studied using two-dimensional Fourier-transform spectroscopy. We find that in thermally annealed InAs QDs, changes in the biexciton transition energy are strongly correlated with those of the exciton and that the biexciton binding energy is similar for all QDs in the ensemble. These results are in contrast to those from GaAs QDs formed from interfacial fluctuations of a narrow quantum well (QW). In both the GaAs QW and QDs, correlation is reduced and the biexciton binding exhibits a strong dependence on localization. Comparison with simulations reveals how confinement and Coulomb interactions modify biexciton renormalization.

Temperature Dependence and Energetics of Single Ions at the Aqueous Liquid–Vapor Interface

We investigate temperature-dependence of free energetics with two single halide anions, I(-) and Cl(-), crossing the aqueous liquid-vapor interface through molecular dynamics simulations. The result shows that I(-) has a modest surface stability of 0.5 kcal/mol at 300 K and the stability decreases as the temperature increases, indicating the surface adsorption process for the anion is entropically disfavored. In contrast, Cl(-) shows no such surface state at all temperatures. Decomposition of free energetics reveals that water-water interactions provide a favorable enthalpic contribution, while the desolvation of ion induces an increase in free energy. Calculations of surface fluctuations demonstrate that I(-) generates significantly greater interfacial fluctuations compared to Cl(-). The fluctuation is attributed to the malleability of the solvation shells, which allows for more long-ranged perturbations and solvent density redistribution induced by I(-) as the anion approaches the liquid-vapor interface. The increase in temperature of the solvent enhances the inherent thermally excited fluctuations and consequently reduces the relative contribution from anion to surface fluctuations, which is consistent with the decrease in surface stability of I(-). Our results indicate a strong correlation with induced interfacial fluctuations and anion surface stability; moreover, resulting temperature dependent behavior of induced fluctuations suggests the possibility of a critical level of induced fluctuations associated with surface stability.

CHARACTERIZATION OF HORIZONTAL GAS–LIQUID TWO-PHASE FLOW USING MARKOV MODEL-BASED COMPLEX NETWORK

Horizontal gas–liquid two-phase flow widely exists in many physical systems and chemical engineering processes. Compared with vertical upward gas–liquid two-phase flow, investigations on dynamic behavior underlying horizontal gas–liquid flows are quite limited. Complex network provides a powerful framework for time series analysis of complex dynamical systems. We use a network generation method based on Markov transition probability to infer directed weighted complex networks from signals measured from horizontal gas–liquid two-phase flow experiment and find that the networks corresponding to different flow patterns exhibit different network structure. To investigate the dynamic characteristics of horizontal gas–liquid flows, we construct a number of complex networks under different flow conditions, and explore the network indices for each constructed network. In addition, we investigate the sample entropy of different flow patterns. Our results suggest that the network statistic can well represent the complexity in the transition among different flow patterns and further allows characterizing the interface fluctuation behavior in horizontal gas–liquid two-phase flow.

Non-universal parameters, corrections and universality in Kardar–Parisi–Zhang growth

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar–Parisi–Zhang (KPZ) universality class, in d = 1 + 1, for both flat and curved geometries. We analyzed two classes of models. In the isotropic models the non-universal parameters are uniform along the surface, whereas in anisotropic growth they vary. In the latter case, which produces curved surfaces, the statistics must be computed independently along fixed directions. The ansatz h = v∞t + (Γt)1/3χ + η, where χ is a Tracy–Widom (geometry-dependent) distribution and η is a time-independent correction, is probed. Our numerical analysis shows that the non-universal parameter Γ determined through the first cumulant leads to a very good accordance with the extended KPZ ansatz for all investigated models in contrast with the estimates of Γ obtained from higher order cumulants that indicate a violation of the generalized ansatz for some of the studied models. We associate the discrepancies to corrections of an unknown nature, which hampers an accurate estimation of Γ at finite times. The discrepancies in Γ via different approaches are relatively small but sufficient to modify the scaling law t−1/3 that characterizes the finite-time corrections due to η. Among the investigated models, we have revisited an off-lattice Eden model that supposedly disobeyed the shift in the mean scaling as t−1/3 and showed that there is a crossover to the expected regime. We have found model-dependent (non-universal) corrections for cumulants of order n ≥ 2. All investigated models are consistent with a further term of order t−1/3 in the KPZ ansatz.

Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation

Experimental realizations of a one-dimensional (1D) interface always exhibit a finite microscopic width ξ>0; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description of the interface fluctuations below a characteristic temperature T(c)(ξ). Exploiting the exact mapping between the static 1D interface and a 1+1 directed polymer (DP) growing in a continuous space, we study analytically both the free-energy and geometrical fluctuations of a DP, at finite temperature T, with a short-range elasticity and submitted to a quenched random-bond Gaussian disorder of finite correlation length ξ. We derive the exact time-evolution equations of the disorder free energy F[over ¯](t,y), which encodes the microscopic disorder integrated by the DP up to a growing time t and an endpoint position y, its derivative η(t,y), and their respective two-point correlators C[over ¯](t,y) and R[over ¯](t,y). We compute the exact solution of its linearized evolution R[over ¯](lin)(t,y) and we combine its qualitative behavior and the asymptotic properties known for an uncorrelated disorder (ξ=0) to justify the construction of a "toy model" leading to a simple description of the DP properties. This model is characterized by Gaussian Brownian-type free-energy fluctuations, correlated at small |y|</~ξ, and of amplitude D̃(∞)(T,ξ). We present an extended scaling analysis of the roughness, supported by saddle-point arguments on its path-integral representation, which predicts D̃(∞)~1/T at high temperatures and D̃(∞)~1/T(c)(ξ) at low temperatures. We identify the connection between the temperature-induced crossover of D̃(∞)(T,ξ) and the full replica symmetry breaking in previous Gaussian variational method (GVM) computations. In order to refine our toy model with respect to finite-time geometrical fluctuations, we propose an effective time-dependent amplitude D̃(t). Finally, we discuss the consequences of the low-temperature regime for two experimental realizations of Kardar-Parisi-Zhang interfaces, namely, the static and quasistatic behavior of magnetic domain walls and the high-velocity steady-state dynamics of interfaces in liquid crystals.

Capillarylike fluctuations of a solid-liquid interface in a noncohesive granular system

One of the most noticeable collective motion of noncohesive granular matter is clustering under certain conditions. In particular, when a quasi-two-dimensional monolayer of monodispersed noncohesive particles is vertically vibrated, a solid-liquid-like transition occurs when the driving amplitude exceeds a critical value. Here the physical mechanism underlying particle clustering relies on the strong interactions mediated by grain collisions, rather than on grain-grain cohesive forces. In average, the solid cluster resembles a drop, with a striking circular shape. We experimentally investigate the coarse-grained solid-liquid interface fluctuations, which are characterized through the static and dynamic correlation functions in the Fourier space. These fluctuations turn out to be well described by the capillary wave theory, which allows us to measure the solid-liquid interface surface tension and mobility once the granular "thermal" kinetic energy is determined. Despite that the system is strongly out of equilibrium and that the granular temperature is not uniform, there is energy equipartition at the solid-liquid interface, for a relatively large range of angular wave numbers. Furthermore, both surface tension and mobility are consistent with a simple order of magnitude estimation considering the characteristic energy, length, and time scales, which is very similar to what can be done for atomic systems.

Critical Point Wedge Filling

We present results of a microscopic density functional theory study of wedge filling transitions, at a right-angle wedge, in the presence of dispersionlike wall-fluid forces. Far from the corner the walls of the wedge show a first-order wetting transition at a temperature T(w) which is progressively closer to the bulk critical temperature T(c) as the strength of the wall forces is reduced. In addition, the meniscus formed near the corner undergoes a filling transition at a temperature T(f)<T(w), the value of which is found to be in excellent agreement with macroscopic predictions. We show that the filling transition is first order if it occurs far from the critical point but is continuous if T(f) is close to T(c) even though the walls still show first-order wetting behavior. For this continuous transition the distance of the meniscus from the apex grows as ℓ(w)≈(T(f)-T)(-β(w)) with the critical exponent β(w)≈0.46±0.05 in good agreement with the phenomenological effective Hamiltonian prediction. Our results suggest that critical filling transitions, with accompanying large scale universal interfacial fluctuation effects, are more generic than thought previously, and are experimentally accessible.