Pair force distributions in simple fluids

Analytic expressions are derived for the frequency distribution, P(f), of pair forces, f, and those of their α-Cartesian component, f(α), or P(f(α)), for some typical model simple fluids, expressed in terms of the radial distribution function and known constants. For strongly repulsive inverse power (IP), exponential and Yukawa purely repulsive potentials, P(f) diverges at the origin approximately as ～f(-1), but with different limiting analytic forms. P(f(α)) is also shown to diverge as ～f(-1) as f → 0 for the IP fluid. For the Lennard-Jones potential fluid, P(f) is finite for all f ≥ 0 but has two singularities for negative f, corresponding to the zero force limit (i.e., f → 0(-)) and the point of inflection in the potential. The corresponding component force distribution is singular as f(α) → 0 from both positive and negative force sides. The large force limit of P(f), which originates from the close neighbor interactions, is nearly exponential for the IP and LJ fluids, as is also found for granular materials. A more complete picture of force distributions in off-lattice particulate systems as a function of force law and state point (particularly the extent of "thermalization" of the particles) is provided.     

Single particle scattering and momentum distributions in solid hydrogen

The incoherent inelastic neutron scattering function of solid para-hydrogen was recorded. It was shown that at momentum transfers above 5Å⁻¹ the data can be interpreted as recoil spectra from single particle scattering at hydrogen molecules. The evaluation of the momentum distribution and kinetic energy of the scattering particles from such data is discussed.     

Non-Newtonian behavior in simple fluids

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheology of a microscopic sample of simple fluid. The calculations were performed using a configurational thermostat which unlike previous nonequilibrium molecular dynamics or nonequilibrium Brownian dynamics methods does not exert any additional constraint on the flow profile. Our findings are in agreement with experimental results on concentrated "hard sphere"-like colloidal suspensions. We observe: (i) a shear thickening regime under steady shear; (ii) a strain thickening regime under oscillatory shear at low frequencies; and (iii) shear-induced ordering under oscillatory shear at higher frequencies. These results significantly differ from previous simulation results which showed systematically a strong ordering for all frequencies. They also indicate that shear thickening can occur even in the absence of a solvent.     

Shear-dependent viscosity in simple fluids

Computer simulation results are used to examine the shear-dependent viscosity of simple fluids. The prime purpose of the investigation was to examine the possible non-newtonian effects when the particles in a fluid interact through central forces. A range of spherical interactions was examined, including both potentials with a barrier and simple colloidal models, and in all cases the fluids were shear-thinning. The non-equilibrium radial distribution function for a soft potential is considerably more sensitive to shear rate than is that for the strongly repulsive model. Calculations of the hydrostatic pressure show that it increases with shear rate, demonstrating that the phenomena of shear thickening and shear dilatency — used interchangeably in the literature — are separate phenomena.     

Quantum dynamics in simple fluids

We use quantum-correction factors to calculate approximately the quantum velocity time-correlation function (TCF) of supercritical Lennard-Jones argon from the classical TCF. We find that for this quite classical system, several different quantum-correction schemes yield essentially identical results for the real and imaginary parts of the quantum TCF, and also agree well with the recent forward-backward semiclassical dynamics (FBSD) results of Wright and Makri [J. Chem. Phys. 119, 1634 (2003)]. We also consider a more quantum-mechanical fluid of lighter atoms (neon) at a lower temperature. In this case different quantum-correction schemes give different results. FBSD calculations show that the harmonic quantum correction factor works the best for this system     

Single particle analysis using fluidic, optical and electrophoretic force balance in a microfluidic system

A unique microfluidic system is developed which enables the interrogation of a single particle by using multiple force balances from a combination of optical force, hydrodynamic drag force, and electrophoretic force. Two types of polystyrene (PS) particles with almost identical size and refractive index (plain polystyrene (PS) particle - mean diameter: 2.06 μm, refractive index: 1.59; carboxylated polystyrene (PS-COOH) particles - mean diameter: 2.07 μm, refractive index: 1.60), which could not be distinguished by optical chromatography, reveal different electrokinetic behaviors resulting from the difference in their surface charge densities. The PS-COOH particles, despite their higher surface charge density when compared to the PS particles, experience a lower electrophoretic force, regardless of ionic strength. This phenomenon can be understood when the more prominent polarization of the counter ion cloud surrounding the PS-COOH particles is considered. The surface roughness of the carboxylated particles also plays an important role in the observed electrokinetic behavior.     

Single particle confocal fluorescence spectroscopy in microchannels: dependence of burst width and burst area distributions on particle size and flow rate.

This article presents a non-invasive, optical technique for measuring particulate flow within microfluidic channels. Confocal fluorescence detection is used to probe single fluorescently labeled microspheres (200-930 nm diameter) passing through a focused laser beam at a variety of flow rates (100 - 1000 nL/min). Simple statistical methods are subsequently used to investigate the resulting fluorescence bursts and generate single-particle burst width and burst area distributions. Analysis of such distributions demonstrates that the average burst width and burst area decrease as particle size increases. In addition, both burst width and burst area (for a given particle size) are observed to decrease as volumetric flow rate is increased. The dependence of such distributions on particle size is proposed as a potential route to sizing single particles and molecules in microfluidic systems.     

Single aerosol particle studies

This paper surveys the research carried out on single aerosol particles in the micron and submicron size range with emphasis on the work performed by the authors. The principles and design of the electrodynamic and electrostatic balances are reviewed, and experimental data for evaporating droplets in a stagnant gas at various total pressures and various temperature are compared with theoretical results for Knudsen aerosol evaporation and are used to determine Lennard-Jones interaction parameters, diffusivities and vapor pressures for relatively nonvolatile compounds. The use of the electrodynamic balance or “picoblance” developed to study aerosol particles of the order of a piogram is illustrated for diffusion-controlled droplet evaporation measurements, and new data and an analysis for binary dorplet evaporation are presented.     

Single particle powder patterns

A-19-mm diameter insert has been built for a Gandolfi X-ray powder diffraction camera. The camera makes it possible to obtain good X-ray diffraction patterns on a single 2-μm particle in 20 hr and in a few hours time with larger particles.     

Determination of maximum particle size in magnetic fluids

Higher-order moments of particle size distribution functions are determined for magnetic fluids from analysis of initial segments of magnetization curves. It is shown that the higher-order moments calculated using approximation of real particle size distributions by the Γ distribution are strongly overestimated. Agreement between the measured and calculated moments can be radically improved by truncating maximum particle size X_max. A relation between X_max and the parameters of the Γ distribution is proposed taking into account the degree of polydispersity of a magnetic fluid. Namely, the ratio between the maximum and most probable particle diameters is equal to the ratio between the mean-square magnetic moment of a particle and its squared average magnetic moment.     

Velocity distributions of camphor particle ensembles

The spatial distribution of ensembles of camphor particles on a water surface can be classified into four phases with the following properties, for increasing density: (I) no clustering of particles and a minimum distance distribution similar to that of a 2D ideal gas; (II) reminiscent of a gas with clustering of particles; (III) net-like structure with occasional rearrangements; and (IV) motionless. While single particles have varying velocity distributions, the overall velocity distribution is Laplacian (the width decreasing with increasing camphor density) for all phases.     

Stokes-Einstein relation for pure simple fluids

The authors employed the equilibrium molecular dynamics technique to calculate the self-diffusion coefficient and the shear viscosity for simple fluids that obey the Lennard-Jones 6-12 potential in order to investigate the validity of the Stokes-Einstein (SE) relation for pure simple fluids. They performed calculations in a broad range of density and temperature in order to test the SE relation. The main goal of this work is to exactly calculate the constant, here denominated by alpha, present in the SE relation. Also, a modified SE relation where a fluid density is raised to a power in the usual expression is compared to the classical expression. According to the authors' simulations slip boundary conditions (alpha=4) can be satisfied in some state points. An intermediate value of alpha=5 was found in some regions of the phase diagram confirming the mode coupling theory. In addition depending on the phase diagram point and the definition of hydrodynamics radius, stick boundary condition (alpha=6) can be reproduced. The authors investigated the role of the hydrodynamic radius in the SE relation using three different definitions. The authors also present calculations for alpha in a hard-sphere system showing that the slip boundary conditions hold at very high density. They discuss possible explanations for their results and the role of the hydrodynamic radius for different definitions in the SE relation.     

Model for the free-volume distributions of equilibrium fluids

We introduce and test via molecular simulation a simple model for predicting the manner in which interparticle interactions and thermodynamic conditions impact the single-particle free-volume distributions of equilibrium fluids. The model suggests a scaling relationship for the density-dependent behavior of the hard-sphere system. It also predicts how the second virial coefficients of fluids with short-range attractions affect their free-volume distributions.     

Charge distributions and chemical effects in simple alkanes

A simple parametric procedure for calculating the electronic structure of hydrocarbons has been tested using a set of parametric relations suggested by Fliszár. The calculated inductive charges are satisfactory and are compared with values derived from a least-squares analysis of theoretical charges. Further improvement is possible by applying the least-squares analysis first and then the parametric equations. The procedure is also used to calculate the energy of atomization of the hypothetical vibrationless state, giving results which agreee well with experimental values.     

Physical properties of soft repulsive particle fluids

Molecular dynamics computer simulation has been applied to inverse power or soft-sphere fluids, in which the particles interact through the soft-sphere pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The focus of the study is on very soft particles with n values down to 4 considered, at densities up to and along the fluid-solid co-existence density. It is shown that in the soft-particle limit the local structure is dominated by the lengthscale associated with the average nearest neighbour distance of a random structure, which is proportional, variantrho(-1/3) and increasingly only very weakly dependent on n. This scaling is also manifest in the behaviour of the average energy per particle with density. The self-diffusion coefficient and shear viscosity are computed along the fluid-solid co-existence line as a function of n, for the first time. The product Deta(s) steadily increases with softness for n < 10, whereas the modified Stokes-Einstein relationship of Zwanzig, Deta(s)/rho(1/3), where rho is the number density, is within statistics constant over the same softness range. This is consistent with our observation that the static properties are determined by a characteristic lengthscale (i.e., l) which is proportional, variantrho(-1/3) in the soft-particle limit. The high frequency elastic moduli of these fluids are examined, which reveals that the mechanical properties become more 'rubbery' as the particles get softer.     

Elastic deformation during dynamic force measurements in viscous fluids

Understanding and harnessing the coupling between lubrication pressure and elasticity provides materials design strategies for applications such as adhesives, coatings, microsensors, and biomaterials. Elastic deformation of compliant solids caused by viscous forces can also occur during dynamic force measurements in instruments such as the surface forces apparatus (SFA) or the atomic force microscope (AFM). We briefly review hydrodynamic interactions in the presence of soft, deformable interfaces in the lubrication limit. More specifically, we consider the scenario of two surfaces approaching each other in a viscous fluid where one or both surfaces is deformable, which is also relevant to many force measurement systems. In this article the basic theoretical background of the elastohydrodynamic problem is detailed, followed by a discussion of experimental validation and considerations, especially for the role of elastic deformation on surface forces measurements. Finally, current challenges to our understanding of soft hydrodynamic interactions, such as the consideration of substrate layering, poroelasticity, viscoelasticity, surface heterogeneity, as well as their implications are discussed.     

Particle adhesion force distributions on rough surfaces

The effect of roughness on adhesion force distribution was studied in the gas phase. Spherical gold particles with diameters between 5 and 20 microm were generated in a flame process and glued onto atomic force microscope (AFM) cantilevers directly after. Nanostructured substrates with defined roughness were produced by a dip-coating process. The geometry of the adhering partners was determined by AFM imaging, and the adhesion force was measured with the AFM. Depending on the roughness of the particles and the substrates, three types of distribution functions can be identified; two of them can be explained with a simple model. The obtained adhesion force distributions not only agree with those experimentally recorded in previous studies of commercially important powders (e.g., alumina, toner, and gold on different substrates) but also agree with distributions reported in the literature.     

Bulk modulus for some simple molecular fluids

The bulk modulus B of several molecular fluids composed of rigid molecules has been calculated from p-p-T data obtained with a high-pressure vibrating tube densitometer. The data of all the substances studied, including Ar, can be described by a single master curve when plotted versus the reduced density *, in agreement with the predictions of the Gubbins-Gray perturbation theory for fluids with the same reference system. Combination of p-p-T and C_v data with the virial theorem has allowed the calculation of the exponent characterizing the repulsive branch of the intermolecular potential n. The different values of n suggest that different reference systems should be used for each substance, in contradiction with the conclusions obtained from the B versus * curves. This indicates that p-p-T data are less sensitive to the details of the intermolecular potential than their combination with other thermal properties like C_v, internal energy or residual entropy.     

Optimized theory for simple and molecular fluids

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.     

Approximative "one particle" bridge function B(1)(r) for the theory of simple fluids

New properties for the one particle bridge function B(1)(r), which are necessary to the calculation of the excess chemical potential betamue), are derived for the hard sphere fluid. The method, which only requires the knowledge of the bridge function B(2)(r), is based on an investigation of the correlation function dependence on the Kirkwood charging parameter. In this framework, the unavoidable question of topological homotopy is addressed. As far as B(2)(r) is considered as exact, this work provides useful information on B(1)(r) in the well identified dynamical regimes of the hard sphere fluid. Signatures of the transitions between these regimes are identified on the trends of B(1)(r). This approach provides self-consistent results for betamue) that agree very well with simulation data.