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Explicit expressions of self-diffusion coefficient, shear viscosity, and the Stokes-Einstein relation for binary mixtures of Lennard-Jones liquids
Explicit expressions of the self-diffusion coefficient, D{sub i}, and shear viscosity, η{sub sv}, are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m{sup −3}. The scaling equations obtained by multiplying all the single-variable dependences can well express D{sub i} and η{sub sv} evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for D{sub i} can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the “isotope effect” on D{sub i}. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.
Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation
The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261–290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16–29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375–400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1–29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.
Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics
We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables, we select the position of the nanoparticle and the total mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic ordinary differential equations that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic partial differential equations which resemble previously used phenomenological models based on fluctuating hydrodynamics. Key to this connection between our “bottom-up” and previous “top-down” approaches is the use of the same dual orthogonal set of linear basis functions familiar from finite element methods (FEMs), both as a way to coarse-grain the microscopic degrees of freedom and as a way to discretize the equations of fluctuating hydrodynamics. Another key ingredient is the use of a “linear for spiky” weak approximation which replaces microscopic “fields” with a linear FE interpolant inside expectation values. For the irreversible or dissipative dynamics, we approximate the constrained Green-Kubo expressions for the dissipation coefficients with their equilibrium averages. Under suitable approximations, we obtain closed approximations of the coarse-grained dynamics in a manner which gives them a clear physical interpretation and provides explicit microscopic expressions for all of the coefficients appearing in the closure. Our work leads to a model for dilute nanocolloidal suspensions that can be simulated effectively using feasibly short molecular dynamics simulations as input to a FEM fluctuating hydrodynamic solver.
Multi-channel lock-in amplifier assisted femtosecond time-resolved fluorescence non-collinear optical parametric amplification spectroscopy with efficient rejection of superfluorescence background
Superfluorescence appears as an intense background in femtosecond time-resolved fluorescence noncollinear optical parametric amplification spectroscopy, which severely interferes the reliable acquisition of the time-resolved fluorescence spectra especially for an optically dilute sample. Superfluorescence originates from the optical amplification of the vacuum quantum noise, which would be inevitably concomitant with the amplified fluorescence photons during the optical parametric amplification process. Here, we report the development of a femtosecond time-resolved fluorescence non-collinear optical parametric amplification spectrometer assisted with a 32-channel lock-in amplifier for efficient rejection of the superfluorescence background. With this spectrometer, the superfluorescence background signal can be significantly reduced to 1/300–1/100 when the seeding fluorescence is modulated. An integrated 32-bundle optical fiber is used as a linear array light receiver connected to 32 photodiodes in one-to-one mode, and the photodiodes are further coupled to a home-built 32-channel synchronous digital lock-in amplifier. As an implementation, time-resolved fluorescence spectra for rhodamine 6G dye in ethanol solution at an optically dilute concentration of 10{sup −5}M excited at 510 nm with an excitation intensity of 70 nJ/pulse have been successfully recorded, and the detection limit at a pump intensity of 60 μJ/pulse was determined as about 13 photons/pulse. Concentration dependent redshift starting at 30 ps after the excitation in time-resolved fluorescence spectra of this dye has also been observed, which can be attributed to the formation of the excimer at a higher concentration, while the blueshift in the earlier time within 10 ps is attributed to the solvation process.
Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation
Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this paper, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (l E ) with salt concentration c s and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, l E ~ c s -0.5 as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Inspired by Cohen’s extraction of Warner’s force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.
Investigation of HCl-based surface treatment for GaN devices
Surface treatments of GaN in HCl-based solutions are studied by X-ray photoelectron spectroscopy (XPS) and electrical characterization of fabricated GaN surfaces. A dilute-HCl treatment (HCl:H{sub 2}O=1:1) at room temperature and a boiled-HCl treatment (undiluted HCl) at 108°C are made on high-temperature annealed n-GaN. From the XPS study, removal of surface oxide by the dilute-HCl treatment was found, and more thoroughly oxide-removal was confirmed in the boiled-HCl treatment. Effect of the surface treatment on electrical characteristics on AlGaN/GaN transistor is also studied by applying treatment processes prior to the surface SiN deposition. Increase of drain current is found in boiled-HCl treated samples. The results suggest that the boiled-HCl treatment is effective for GaN device fabrication.
Revisiting the formation of cyclic clusters in liquid ethanol
The liquid phase of ethanol in pure and in non-polar solvents was studied at room temperature using Fourier transform infrared (FT-IR) and {sup 1}H nuclear magnetic resonance (NMR) spectroscopies together with theoretical approach. The FT-IR spectra for pure ethanol and solution in cyclohexane at different dilution stages are consistent with {sup 1}H NMR results. The results from both methods were best explained by the results of the density functional theory based on a multimeric model. It is suggested that cyclic trimers and tetramers are dominated in the solution of cyclohexane/hexane with the concentration greater than 0.5M at room temperature. In liquid ethanol, while the primary components at room temperature are cyclic trimers and tetramers, there is a certain amount (∼14%) of open hydroxide group representing the existence of chain like structures in the equilibria. The cyclic cluster model in the liquid and concentrated solution phase (>0.5M) can be used to explain the anomalously lower freezing point of ethanol (159 K) than that of water (273 K) at ambient conditions. In addition, {sup 1}H NMR at various dilution stages reveals the dynamics for the formation of cyclic clusters.
Temperature of maximum density and excess thermodynamics of aqueous mixtures of methanol
In this work, we present a study of representative excess thermodynamic properties of aqueous mixtures of methanol over the complete concentration range, based on extensive computer simulation calculations. In addition to test various existing united atom model potentials, we have developed a new force-field which accurately reproduces the excess thermodynamics of this system. Moreover, we have paid particular attention to the behavior of the temperature of maximum density (TMD) in dilute methanol mixtures. The presence of a temperature of maximum density is one of the essential anomalies exhibited by water. This anomalous behavior is modified in a non-monotonous fashion by the presence of fully miscible solutes that partly disrupt the hydrogen bond network of water, such as methanol (and other short chain alcohols). In order to obtain a better insight into the phenomenology of the changes in the TMD of water induced by small amounts of methanol, we have performed a new series of experimental measurements and computer simulations using various force fields. We observe that none of the force-fields tested capture the non-monotonous concentration dependence of the TMD for highly diluted methanol solutions.
Simulations of the infrared, Raman, and 2D-IR photon echo spectra of water in nanoscale silica pores
Vibrational spectroscopy is frequently used to characterize nanoconfined liquids and probe the effect of the confining framework on the liquid structure and dynamics relative to the corresponding bulk fluid. However, it is still unclear what molecular-level information can be obtained from such measurements. In this paper, we address this question by using molecular dynamics (MD) simulations to reproduce the linear infrared (IR), Raman, and two-dimensional IR (2D-IR) photon echo spectra for water confined within hydrophilic (hydroxyl-terminated) silica mesopores. To simplify the spectra the OH stretching region of isotopically dilute HOD in D{sub 2}O is considered. An empirical mapping approach is used to obtain the OH vibrational frequencies, transition dipoles, and transition polarizabilities from the MD simulations. The simulated linear IR and Raman spectra are in good general agreement with measured spectra of water in mesoporous silica reported in the literature. The key effect of confinement on the water spectrum is a vibrational blueshift for OH groups that are closest to the pore interface. The blueshift can be attributed to the weaker hydrogen bonds (H-bonds) formed between the OH groups and silica oxygen acceptors. Non-Condon effects greatly diminish the contribution of these OH moieties to the linear IR spectrum, but these weaker H-bonds are readily apparent in the Raman spectrum. The 2D-IR spectra have not yet been measured and thus the present results represent a prediction. The simulated spectra indicates that it should be possible to probe the slower spectral diffusion of confined water compared to the bulk liquid by analysis of the 2D-IR spectra.
Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface
Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structural defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.
Communication: The origin of many-particle signals in nonlinear optical spectroscopy of non-interacting particles
Nonlinear spectroscopy signals detected by fluorescence from dilute samples of N non-interacting molecules are usually adequately described by simply multiplying the single molecule response by N . Here, we show that signals that scale with higher powers of N are generated by the joint detection of several particles. This can be accomplished by phase sensitive detection such as phase cycling, photo-acoustic modulation, or by Hanbury-Brown Twiss photon coincidence. Such measurements can dissect the ensemble according to the number of excited particles.
The near-infrared spectrum of ethynyl radical
Transient diode laser absorption spectroscopy has been used to measure three strong vibronic bands in the near infrared spectrum of the C{sub 2}H, ethynyl, radical not previously observed in the gas phase. The radical was produced by ultraviolet excimer laser photolysis of either acetylene or (1,1,1)-trifluoropropyne in a slowly flowing sample of the precursor diluted in inert gas, and the spectral resolution was Doppler-limited. The character of the upper states was determined from the rotational and fine structure in the observed spectra and assigned by measurement of ground state rotational combination differences. The upper states include a {sup 2}Σ{sup +} state at 6696 cm{sup −1}, a second {sup 2}Σ{sup +} state at 7088 cm{sup −1}, and a {sup 2}Π state at 7110 cm{sup −1}. By comparison with published calculations [R. Tarroni and S. Carter, J. Chem. Phys 119, 12878 (2003); Mol. Phys. 102, 2167 (2004)], the vibronic character of these levels was also assigned. The observed states contain both X{sup 2}Σ{sup +} and A{sup 2}Π electronic characters. Several local rotational level perturbations were observed in the excited states. Kinetic measurements of the time-evolution of the ground state populations following collisional relaxation and reactive loss of the radicals formed in a hot, non-thermal, population distribution were made using some of the strong rotational lines observed. The case of C{sub 2}H may be a good place to investigate the behavior at intermediate pressures of inert colliders, where the competition between relaxation and reaction can be tuned and observed to compare with master equation models, rather than deliberately suppressed to measure thermal rate constants.
Fluctuating hydrodynamics of reactive liquid mixtures
Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.
Electromodulation spectroscopy of highly mismatched alloys
The electronic band structure of highly mismatched alloys (HMAs) was very successfully explored using electromodulation (EM) spectroscopy, i.e., photoreflectance (PR), electroreflectance, and contactless electroreflectance (CER). With these techniques, the optical transitions between the valence band and the E – and E + bands, which are formed in the conduction band of dilute nitrides and dilute oxides, were observed and used to formulate the band anticrossing model, which well describes the electronic band structure of HMAs. In this tutorial, principles of EM spectroscopy are presented and shortly discussed. Special attention is focused on PR and CER techniques, which are nondestructive and have recently been widely applied to study the electronic band structure of HMAs and low dimensional heterostructures containing HMAs. For these methods, experimental setups are described, and theoretical approaches to analyze the experimental data are introduced. Finally, to show the utility of EM spectroscopy, selected examples of the application of this method to study various issues in HMAs are presented and briefly discussed.
On the new universality class in structurally disordered n -vector model with long-range interactions
We study a stability boundary of a region where nontrivial critical behavior of an n-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g., weak quenched dilution). This boundary is given by the marginal dimension of the order parameter nc dependent on space dimension, d, and a control parameter of the interaction decay, σ, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field theoretical renormalization group results for the pure model with long-range interactions, we get nc as a three loop ɛ = 2σ – d-expansion. We provide numerical values for nc applying series resummation methods. Our results show that not only the Ising systems (n = 1) can belong to the new disorder-induced long-range universality class at d = 2 and 3.
Polyamorphism in a solute-lean Al–Ce metallic glass
Polyamorphism discovered in lanthanide-rich metallic glasses (MGs) has been attributed to the electronic transition of the lanthanide element as a solvent element. In this work, we report that pressure-induced polyamorphism still exists in a Ce-poor Al 93 Ce 7 binary MG where the 4f electron element serves as a solute and solute–solute avoidance is expected. The polyamorphic transition, observed by in situ high-pressure synchrotron x-ray diffraction, is accompanied by a volume collapse of ~0.78% and occurs over a narrow pressure range from ~0.8 to ~1.8 GPa. Further synchrotron Ce L 3 -edge x-ray absorption spectroscopy measurements reveal that pressure-induced 4f electron delocalization underlies the polyamorphic transition. Molecular dynamics simulations confirm that the Ce atoms in the MG are completely isolated by the solvent Al atoms. This result demonstrates that 4f element-bearing alloys with extremely dilute concentrations can also exhibit polyamorphic states originating from electronic transitions, extending the compositional space of polyamorphism of MGs into very dilute regions. Our work suggests that tunable properties under compressive stress could be achieved in MGs by even minor doping of elements prone to electronic transitions.
Effect of surface properties and polymer chain length on polymer adsorption in solution
In polymer nanoparticle composites (PNCs) with attractive interactions between nanoparticles (NPs) and polymers, a bound layer of the polymer forms on the NP surface, with significant effects on the macroscopic properties of the PNCs. The adsorption and wetting behaviors of polymer solutions in the presence of a solid surface are critical to the fabrication process of PNCs. In this study, we use both classical density functional theory (cDFT) and molecular dynamics (MD) simulations to study dilute and semi-dilute solutions of short polymer chains near a solid surface. Using cDFT, we calculate the equilibrium properties of polymer solutions near a flat surface while varying the solvent quality, surface–fluid interactions, and the polymer chain lengths to investigate their effects on the polymer adsorption and wetting transitions. Using MD simulations, we simulate polymer solutions near solid surfaces with three different curvatures (a flat surface and NPs with two radii) to study the static conformation of the polymer bound layer near the surface and the dynamic chain adsorption process. Additionally, we find that the bulk polymer concentration at which the wetting transition in the poor solvent system occurs is not affected by the difference in surface–fluid interactions; however, a threshold value of surface–fluid interaction is needed to observe the wetting transition. We also find that with good solvent, increasing the chain length or the difference in the surface–polymer interaction relative to the surface–solvent interaction increases the surface coverage of polymer segments and independent chains for all surface curvatures. Finally, we demonstrate that the polymer segmental adsorption times are heavily influenced only by the surface–fluid interactions, although polymers desorb more quickly from highly curved surfaces.