Toward observation of single-file diffusion using the tracer zero-length column method

The tracer zero-length column (ZLC) method has been employed to study the diffusion of toluene in one-dimensional ZSM-12 and SAPO-5 zeolites. A significant deviation in the shape of the measured tracer exchange curves from monoexponential behavior was observed for toluene diffusion in both adsorbents in the limit of long-time asymptotes. In contrast, water/ZSM-12 and acetylene/SAPO-5 systems exhibit tracer exchange curves that are close to monoexponential behavior. Monoexponential curves are usually observed for systems obeying normal (Fickian) diffusion. Such diffusion is expected for the latter two systems because the diameters of both sorbates are less than the radii of their corresponding host channels. The differences in the shape of the tracer exchange curves for large and small sorbates can be explained by assuming the occurrence of anomalous, single-file diffusion for large sorbates in narrow, one-dimensional channels.     

Dynamics of chain molecules. Intramolecular diffusion controlled reactions for a pair of terminal reactive groups

The first order intramolecular rate constant for the reaction between the terminal groups of flexible macromolecules is calculated in the partial draining case, following the theory formulated by Wilemski and Fixman for diffusion controlled reactions. Substantial differences with respect to the nondraining and free-draining limits are evidenced, and it is shown that the rate constant in the partial-draining case has relevant contributions from all the modes of the bead-spring chain. The effects of chain flexibility and hydrodynamic interaction in macromolecules of increasing molecular weight are examined. The effective diffusion constant of the end groups increases with both the flexibility and the length of the chain. Numerical results for polystyrene (PS) and polydimethylsiloxane (PDMS) are presented and employed to calculate the relative quantum yield for fluorescence quenching. For highly flexible chains, like PDMS, quenching effects are expected in a range of molecular weight well above the limit of validity of the bead-spring model. On the contrary, for more rigid polymers, like PS, the quenching can be observed only at molecular weights lower than this limit. The calculated behavior is compared with some experimental results recently obtained by the authors.     

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

Stable colloidal dispersions of a lipase-perfluoropolyether complex in liquid and supercritical carbon dioxide

The technique of hydrophobic ion pairing was used to solubilize the lipase from Candida rugosa in a fluorinated solvent, perfluoromethylcyclohexane (PFMC), in complex with a perfluoropolyether (PFPE) surfactant, KDP 4606. The enzyme-surfactant complex was determined to have a hydrodynamic diameter of 6.5 nm at atmospheric pressure by dynamic light scattering (DLS), indicating that a single lipase molecule is stabilized by surrounding surfactant molecules. The complex formed a highly stable colloidal dispersion in both liquid and supercritical carbon dioxide at high CO2 densities (>0.92 and 0.847 g/mL, respectively), with 4% by volume PFMC as a cosolvent, yielding a fluid that was orange, optically translucent, and very nearly transparent. DLS demonstrated aggregation of the enzyme-surfactant complexes in CO2 at 25 and 40 degrees C and various pressures (2000-5000 psia) with hydrodynamic diameters ranging from 50 to 200 nm. The mechanism by which the enzyme-surfactant particles aggregate was shown to be via condensation due to very low polydispersities as characterized by the size distribution moments. Interparticle interactions were investigated with respect to density and temperature, and it was shown that on decreasing the CO2 density, the particle size increased, and the stability against settling decreased. Particle size also decreased as the temperature was increased to 40 degrees C, at constant CO2 density. Nanoparticle aggregates of an enzyme-surfactant complex in CO2, which are nearly optically transparent and stable to settling, are a promising new alternative to previous types of dispersions of proteins in CO2 that either required water/CO2 microemulsions or were composed of large particles unstable to settling.     

Electrophoretic properties of highly charged colloids: a hybrid molecular dynamics/lattice Boltzmann simulation study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.     

Percolation and jamming in structures built through sequential deposition of particles

The strength of attractive interaction among particles on a surface, which was studied in our previous work, leads to different degrees of clustering and ordering. A growing structure percolates when all clusters connect and become one and finally the structure is jammed when there is no space large enough to accommodate one more particle. The lowest jamming limit reported is for structures from the random sequential adsorption. We studied here, by means of Monte Carlo simulation, structures built through sequential deposition of particles, into which surface diffusion and various degrees of attractive forces are incorporated and reported jamming limits along with the percolation thresholds. The higher the strength of attractive interactions, the larger the percolation densities and jamming limits are. These results were shown in a diagram as a function of temperature (or equivalently the strength of attractive interaction), ranging from very low temperature to very high temperature (RSA limit).     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

Nanoparticle composition of a ferrofluid and its effects on the magnetic properties

Experiments were carried out on a water-based ferrofluid (gamma-Fe2O3 with carboxydextran shell) using photon correlation spectroscopy (PCS), atomic force microscopy, and magnetic nanoparticle relaxation measurements. The experiments were designed with the aim to relate the Néel signals that are in theory generated by large single core particles with nanoscopic properties, that is, particle size, particle size distribution, shell properties, and aggregation. For this purpose, the ferrofluid was fractionated by magnetic fractionation and size exclusion chromatography. Nanoparticles adsorbed onto positively charged substrates form a two-dimensional monolayer. Their mean core diameters are in the range of 6 to about 20 nm, and particles above 10 nm are mostly aggregates. The hydrodynamic particle diameters are between 13 and 80 nm. The core diameter of the smallest fraction is confirmed by X-ray reflectometry; the surface coverage is controlled by bulk diffusion. Comparison with the hydrodynamic radius yields a shell thickness of 3.8 nm. Considering the shell thickness to be constant for all particles, it was possible to calculate the apparent particle diameter in the original ferrofluid from the PCS signals of all fractions. As expected, the small cores yielded no Néel relaxation signals in freeze-dried samples; however, the fractions containing mostly aggregates yielded Néel relaxation signals.     

Tracer diffusion in colloidal suspensions under dilute and crowded conditions with hydrodynamic interactions

We consider tracer diffusion in colloidal suspensions under solid loading conditions, where hydrodynamic interactions play an important role. To this end, we carry out computer simulations based on the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) technique. Many details of the simulation method are discussed in detail. In particular, our choices for the SRD-MD parameters and for the different scales are adapted to simulating colloidal suspensions under realistic conditions. Our simulation data are compared with published theoretical, experimental and numerical results and compared to Brownian dynamics simulation data. We demonstrate that our SRD-MD simulations reproduce many features of the hydrodynamics in colloidal fluids under finite loading. In particular, finite-size effects and the diffusive behavior of colloids for a range of volume fractions of the suspension show that hydrodynamic interactions are correctly included within the SRD-MD technique.     

Voltammetric study and electrochemical detection of hexavalent chromium at gold nanoparticle-electrodeposited indium tinoxide (ITO) electrodes in acidic media

The voltammetric behavior of hexavalent chromium species (Cr(VI)) was respectively studied at ITO, bulk Au, and Au-electrodeposited electrodes in 0.01 M NaCl aqueous solutions containing 0.01 M HCl. It was found that performance degradation of the ITO electrodes toward the reduction of Cr(VI) can be suppressed by modifying the electrode surface with gold nanoparticles (AuNPs), which were formed on ITO electrodes by potential-sweeping or potential-step electrodeposition in a 0.01 M Na(2)SO(4) solution containing 1 mM HAuCl(4) x 3 H(2)O and 0.01 M H(2)SO(4). After the modification, the surface of ITO electrodes turned to the characteristically red or blue color exhibited by AuNPs. The gold nanoparticle-electrodeposited indium-tinoxide electrode (AuNP-ITO) demonstrates unique catalytic behavior, higher sensitivity and stability in the reduction of Cr(VI). Cr(VI) species was detected by either cyclic voltammetry or hydrodynamic amperometry. By cyclic voltammetry, the dependence of cathodic peak current on concentration was linear from 5 to 100 microM with a detection limit of 2 microM (sigma=3), and linearity was obtained from 0.5 to 50 microM by hydrodynamic amperometry where a constant potential of +0.2V (vs. Ag/AgCl) was applied and a batch-injection cell was employed. For hydrodynamic amperometry, the detection limit was 0.1 microM (sigma=3).     

Molecular dynamics simulation study of friction and diffusion of a tracer in a Lennard–Jones solvent

The friction and diffusion coefficients of a tracer in a Lennard–Jones (LJ) solvent are evaluated by equilibrium molecular dynamics simulations in a microcanonical ensemble. The solvent molecules interact through a repulsive LJ force each other and the tracer of diameter σ₂ interacts with the solvent molecules through the same repulsive LJ force with a different LJ parameter σ. Positive deviation of the diffusion coefficient D of the tracer from a Stokes–Einstein behavior is observed and the plot of 1/D versus σ₂ shows a linear behavior. It is also observed that the friction coefficient ζ of the tracer varies linearly with σ₂ in accord with the prediction of the Stokes formula but shows a smaller slope than the Stokes prediction. When the values of ratios of sizes between the tracer and solvent molecules are higher than 5 approximately, the behavior of the friction and diffusion coefficients is well described by the Einstein relation D = k _B T/ζ, from which the tracer is considered as a Brownian particle.     

Mechanical and frictional properties of nanoparticle monolayers grafted on functionalized mica substrates

Normal and lateral forces between two opposing monolayers of grafted polymer nanoparticles (NPs) were measured using the Surface Forces Apparatus in a humid atmosphere. The NPs made of N, N-diethylacrylamide and 2-hydroxyethyl methacrylate have a hydrodynamic diameter of ca. 660 nm at 25 degrees C. The effect of surface roughness was studied by creating surface asperities using different NP grafting densities ranging from 0.41 to 2.63 NPs/mum (2). An increase in the NPs grafting density gave rise to an increase in surface roughness and to a deformation of the nanoparticles caused by the lateral pressure between neighboring particles. An elastoplastic behavior of the nanoparticles was observed for large grafting densities, while a purely elastic behavior was observed for small grafting densities. The lateral forces measured between two opposing NP monolayers sliding past each other followed Amontons' law for all grafting densities. The friction coefficient between the surfaces appeared to increase significantly with an increase in surface roughness, which was inherent to an increase in the elastoplastic behavior of the NP monolayers.     

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.     

Equation of state and structural properties of the Weeks-Chandler-Andersen fluid

Molecular dynamics simulations have been carried out for the equation of state and percolation properties of the Weeks-Chandler-Andersen (WCA) system in its fluid phase as functions of density and temperature. The compressibility factor Z collapses well for the various isotherms, using an effective particle diameter for the WCA particle which is (in the usual WCA reduced units) sigma(e)=2(16)(1+T)(16), where T is the temperature. A corresponding "effective" packing fraction is zeta(e)=pisigma(e) (3)N6V, for N particles in volume V, which therefore scales out the effects of temperature. Using zeta(e) the simulation derived Z can be fitted to a simple analytic form which is similar to the Carnahan-Starling hard sphere equation of state and which is valid at all temperatures and densities where the WCA fluid is thermodynamically stable. The data, however, are not scalable onto the hard sphere equation of state for the complete packing fraction range. We explored the continuum percolation behavior of the WCA fluids. The percolation distance sigma(p) for the various states collapses well onto a single curve when plotted as sigma(p)sigma(e) against zeta(e). The ratio sigma(p)sigma(e) exhibits a monotonic decrease with increasing zeta(e) between the percolation line for permeable spheres and the glass transition limit, where sigma(p)sigma(e) approximately 1. The percolation packing fraction was calculated as a function of effective packing fraction and fitted to an empirical expression. The local coordination number at the percolation threshold showed a transition between the soft core and hard core limits from ca. 2:74 to 1:5, as previously demonstrated in the literature for true hard spheres. A number of simple analytic expressions that represent quite well the percolation characteristics of the WCA system are proposed.     

Transient ordering in a quasi-two-dimensional liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional colloid fluid. The fluctuations in the equilibrium state are monitored by the aperture cross-correlation function of radiation scattered by the fluid, as calculated from molecular dynamics simulations of near hard spheres with diameter sigma confined between smooth hard walls. These locally ordered fluctuations are transient; their decay can be monitored as a function of the time between the cross-correlated scattered radiation signals, but only the single-time cross-correlated signals are discussed in this paper. Systems with thicknesses less than two hard sphere diameters were studied. For wall separation H in the range 1 sigma/=1.57 sigma, hexagonal fluctuations persist in the dense liquid up to H=1.75 sigma, and fluctuations with square ordered symmetry, that of the solid to which the liquid freezes, only emerge at densities approximately 2% below freezing. For H=1.8 sigma and 1.85 sigma, hexagonal ordered flucuations are no longer found, and the square ordered fluctuations dominate the dense liquid region as the system freezes into a two layer square solid. For H=1.9 sigma and 1.95 sigma, where the liquid freezes into a two layer hexagonal solid, both square and hexagonal ordered fluctuations are observed. At lower densities, the ordered fluctuations only exhibit square symmetry. Hexagonal ordered fluctuations appear at densities approximately 7% below freezing and become more dominant as the density is increased, but the square ordered fluctuations persist until the system is converted into the solid.     

Phase behavior of semiflexible polymer chains

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01sigma and 1.05sigma (where sigma is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02sigma and 2.1sigma. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10相似文献   

The effect of rotational and translational energy exchange on tracer diffusion in rough hard sphere fluids

A study is presented of tracer diffusion in a rough hard sphere fluid. Unlike smooth hard spheres, collisions between rough hard spheres can exchange rotational and translational energy and momentum. It is expected that as tracer particles become larger, their diffusion constants will tend toward the Stokes-Einstein hydrodynamic result. It has already been shown that in this limit, smooth hard spheres adopt "slip" boundary conditions. The current results show that rough hard spheres adopt boundary conditions proportional to the degree of translational-rotational energy exchange. Spheres for which this exchange is the largest adopt "stick" boundary conditions while those with more intermediate exchange adopt values between the "slip" and "stick" limits. This dependence is found to be almost linear. As well, changes in the diffusion constants as a function of this exchange are examined and it is found that the dependence is stronger than that suggested by the low-density, Boltzmann result. Compared with smooth hard spheres, real molecules undergo inelastic collisions and have attractive wells. Rough hard spheres model the effect of inelasticity and show that even without the presence of attractive forces, the boundary conditions for large particles can deviate from "slip" and approach "stick."     

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.     

Diffusion of nanoparticles in dense fluids

The diffusion process of a single spherical nanoparticle immersed in a fluid solvent is studied by molecular dynamics simulations. When the nanoparticle mass stays constant, it is shown that, at short times, the decay of the nanoparticle velocity autocorrelation function is strongly modified when the particle diameter increases. It is also shown that, at large times, the characteristic algebraic decay induced by the hydrodynamic correlations between the solvated particle and the solvent presents a scaling behavior depending on the particle diameter.     

Radial diffusion and entrance effects in porous flow-through electrodes

Radial diffusion has two effects on the performance of a flow-through electrode: (a) it may limit the maximum experimentally attainable degree of conversion, and/or (b) the polarization at a certain current output may be lower for smaller than for larger pores. A dimensionless groupwas developed as a criterion of reactant conversion under certain conditions of flow rate, pore diameter and diffusion coefficient. The lengths of both diffusional and hydrodynamic entrance regions are calculated. The ratio between the length of the diffusional entrance region and the electrode thickness is related to the criterion of reactant conversion . It was shown that in all conditions of fully developed laminar flow inside the pores, radial diffusion must be fast with respect to axial convection: hence complete reactant conversion is possible. The effect of radial hydrodynamic dispersion is briefly outlined. It increases the rate of radial mass transfer, hence the degree of conversion and decreases the length of the diffusional entrance region. The length of the hydrodynamic entrance region would normally be much shorter than the diffusional entrance length. They become comparable only when the radial dispersion coefficient is of the same order as the kinematic viscosity of the electrolyte.