Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for complex systems with a highly diffusive character. Based on the recently developed transition interface sampling (TIS) algorithm this procedure increases the efficiency by sampling only parts of complete transition trajectories. The algorithm assumes the loss of memory for diffusive progression along the reaction coordinate. We compare the new partial path technique to the TIS method for a simple diatomic system and show that the computational effort of the new method scales linearly, instead of quadratically, with the width of the diffusive barrier. The validity of the memory loss assumption is also discussed.     

Simulation of non-equilibrium energy distributions of current carriers in proton-conducting oxides with perovskite structure

A simulation method based on the integral equation for the sticking probability of ion in well was discussed for its application to study energy distributions of protons carried in simple and complex perovskite-like structures. In the terms of the Wiener—Hopf computational technique, a numerical algorithm was developed to detect deviations of the energy distribution function from the Boltzmann distribution near the potential barrier peak due to random interaction of ion with the nearest environment. Being considered as non-equilibrium in this sense, the derived distributions essentially deviated from the equilibrium distribution for a wide energy loss range of protons carried from one lattice position to another. The developed simulation algorithm may be of methodological interest in general practice for numerical solution of the Wiener—Hopf equations, because the known solution techniques for integral equations of this type are inapplicable to the studied problems of electrochemical kinetics due to their essentially different boundary conditions.     

Sedimentation and electrophoresis of a porous floc and a colloidal particle coated with polyelectrolytes

Sedimentation and electrophoresis of porous colloid complex; a colloidal floc and a colloidal particle covered with adsorbed polyelectrolytes are visited to examine the characteristic length of the transport phenomena. In the sedimentation, the overall size of a floc is dominative in the determination of Stokes drag, while the permeability is determined by the largest pore in the floc. This picture is important when break-up of flocs in a turbulent flow is considered. When a colloidal particles is coated with polyelectrolytes, the characteristic length for diffusion is that of the diameter of colloidal particle plus protruding part of polymer chain adsorbed onto the particle. On the other hand, when the porous colloid complex is placed in the electric field, fluid surrounding the complex can easily penetrate into the complex by means of electro-osmosis. The diffusive part of electric double layer located inside of the complex is the source of strong driving force of this osmotic flow. Flow generated in this regime can be treated as a sort of shear driven. The characteristic length scale for transport phenomena is the Debye length or the distance between charged segments. These lengths are much shorter than the case of sedimentation and Brownian diffusion.     

Fluorescence correlation spectroscopy simulations of photophysical phenomena and molecular interactions: a molecular dynamics/monte carlo approach

Fluorescence correlation spectroscopy (FCS) is being applied increasingly to study diffusion and interactions of fluorescently labeled macromolecules in complex biological systems. Fluctuations in detected fluorescence, deltaF(t), are expressed as time-correlation functions, G(tau), and photon-count histograms, P(k;DeltaT). Here, we developed a generalized simulation approach to compute G(tau) and P(k;DeltaT) for complex systems with arbitrary geometry, photophysics, diffusion, and macromolecular interactions. G(tau) and P(k;DeltaT) were computed from deltaF(t) generated by a Brownian dynamics simulation of single-molecule trajectories followed by a Monte Carlo simulation of fluorophore excitation and detection statistics. Simulations were validated by comparing analytical and simulated G(tau) and P(k;DeltaT) for diffusion of noninteracting fluorophores in a three-dimensional Gaussian excitation and detection volume. Inclusion of photobleaching and triplet-state relaxation produced significant changes in G(tau) and P(k;DeltaT). Simulations of macromolecular interactions and complex diffusion were done, including transient fluorophore binding to an immobile matrix, cross-correlation analysis of interacting fluorophores, and anomalous sub- and superdiffusion. The computational method developed here is generally applicable for simulating FCS measurements on systems complicated by fluorophore interactions or molecular crowding, and experimental protocols for which G(tau) and P(k;DeltaT) cannot be computed analytically.     

Aggregation of Charged Particles under Electrophoresis or Gravity at Arbitrary Péclet Numbers

Collision efficiencies are considered for colloidal suspensions of solid spheres moving in a viscous fluid under the influence of electrophoresis or gravity, Brownian motion, and electrostatic and van der Waals forces. The results are compared to those for convection (electrophoresis or gravity) and diffusion (Brownian motion) acting independently. The collision efficiency increases by many orders of magnitude over that predicted by simply adding diffusive and convective efficiencies in a specific parameter regime. This regime occurs when there is a large energy barrier in the interparticle potential, causing a stable region of parameter space if there is no diffusion. Brownian motion alone will only cause small amounts of aggregation under these conditions. However, for electric fields or buoyancy effects which are only slightly too weak to allow particles to overcome the potential barrier, the addition of weak Brownian motion to a system with convection can cause significant numbers of particles to overcome the energy barrier and aggregate. Copyright 2000 Academic Press.     

基于随机行走的二维空间扩散模拟研究

分子的扩散行为是微观化学的重要研究领域. 影响扩散行为的因素很多,但是目前各个因素的具体影响效果还不明确. 作者基于随机行走理论建立了分子在二维空间的扩散模型,依据此模型自主开发了模拟软件以及数据分析系统,并利用该模拟软件系统研究了势垒尧横向速度等因素对扩散行为的影响,验证了该模型的可靠性,证明根据该模型可以得到和实验尧理论相吻合的结果. 该软件有望成为模拟微观化学扩散行为的潜在平台,如电化学以及膜过滤过程中的扩散.     

New algorithms for processing and peak detection in liquid chromatography/mass spectrometry data

Two new algorithms for automated processing of liquid chromatography/mass spectrometry (LC/MS) data are presented. These algorithms were developed from an analysis of the noise and artifact distribution in such data. The noise distribution was analyzed by preparing histograms of the signal intensity in LC/MS data. These histograms are well fit by a sum of two normal distributions in the log scale. One new algorithm, median filtering, provides increased performance compared to averaging adjacent scans in removing noise that is not normally distributed in the linear scale. Another new algorithm, vectorized peak detection, provides increased robustness with respect to variation in the noise and artifact distribution compared to methods based on determining an intensity threshold for the entire dataset. Vectorized peak detection also permits the incorporation of existing algorithms for peak detection in ion chromatograms and/or mass spectra. The application of these methods to LC/MS spectra of complex biological samples is described.     

Carbon nanotube formation and growth via particle-particle interaction

Carbon nanotubes are observed to form under a wide range of temperatures, pressures, reactive agents, and catalyst metals. In this paper we attempt to rationalize this body of observations reported in the literature in terms of fundamental processes driving nanotube formation. Many of the observed effects can be attributed to the interaction of three key processes: surface catalysis and deposition of carbon, diffusive transport of carbon, and precipitation effects. A new nanotube formation mechanism is proposed that describes the nanotube structures observed experimentally in a premixed flame and can account for certain shortcomings of the prevailing mechanism that has been repeatedly applied to explain nanotube formation in nonflame environments. The interacting particle model (IPM) attributes the initiation of nanotube growth to the physical interaction between catalyst particles. Coalescence of two (or more) catalyst particles leads to partial blocking of the particle surface, causing a disparity in carbon deposition over the particle surface. The resulting concentration gradient generates a net diffusive flux toward the interparticle contact point. Dimers that separate in this condition can support continuous nanotube growth between the particles. The model can also be extended to multiple particles to account for more complex morphologies. The IPM is consistent with many of the structures observed in the flame-produced material. The validity of the model is evaluated through analysis of diffusion dynamics and a force analysis of particle binding and separation. The IPM is also discussed in relation to identifying the requirements and best conditions to support nanotube growth in the premixed flame. The formation of nanotubes between particles as described by the IPM indicates that a single mechanism cannot completely describe nanotube synthesis; more likely, multiple pathways exist with varying rates that depend on specific process conditions.     

Equilibrium, Kinetics, Diffusion and Self-Association of Proteins at Membrane Surfaces: Measurement by Total Internal Reflection Fluorescence Microscopy

Abstract— The equilibrium, kinetics, diffusion and self-association of proteins at membrane/solution interfaces may deviate substantially from these processes in bulk solution. A set of methods for examining these phenomena combines substrate-supported planar model membranes and the use of evanescent illumination with laser-based, quantitative fluorescence microscopy. Measurement of the steady-state, surface-associated fluorescence can be used to examine the thermodynamic properties of proteins at membranes. When combined with fluorescence photobleaching recovery, this technique provides information about membrane-binding kinetics; and when combined with fluorescence pattern photobleaching recovery, measurement of the translational diffusion coefficients of proteins weakly bound to membranes is possible. The use of polarized evanescent illumination can provide information about the orientation distributions of adsorbed fluorophores. Fluorescence correlation spectroscopy provides information about the self-association ( e.g. dimerization) of membrane-associated proteins.     

Magnetophoresis, sedimentation, and diffusion of particles in concentrated magnetic fluids

A dynamic mass transfer equation for describing magnetophoresis, sedimentation, and gradient diffusion of colloidal particles in concentrated magnetic fluids has been derived. This equation takes into account steric, magnetodipole, and hydrodynamic interparticle interactions. Steric interactions have been investigated using the Carnahan-Starling approximation for a hard-sphere system. In order to study the effective interparticle attraction, the free energy of the dipolar hard-sphere system is represented as a virial expansion with accuracy to the terms quadratic in particle concentration. The virial expansion gives an interpolation formula that fits well the results of computer simulation in a wide range of particle concentrations and interparticle interaction energies. The diffusion coefficient of colloidal particles is written with regard to steric, magnetodipole and hydrodynamic interactions. We thereby laid the foundation for the formulation of boundary-value problems and for calculation of concentration and magnetic fields in the devices (for example, magnetic fluid seals and acceleration sensors), which use a concentrated magnetic fluid as a working fluid. The Monte-Carlo methods and the analytical approach are employed to study the magnetic fluid stratification generated by the gravitational field in a cylinder of finite height. The coefficient of concentration stratification of the magnetic fluid is calculated in relation to the average concentration of particles and the dipolar coupling constant. It is shown that the effective particle attraction causes a many-fold increase in the concentration inhomogeneity of the fluid if the average volume fraction of particles does not exceed 30%. At high volume concentrations steric interactions play a crucial role.     

Analysis of barrier scattering with real and complex quantum trajectories

In this study, an analysis of the one-dimensional Eckart and Gaussian barrier scattering problems is undertaken using approximate quantum trajectories. Individual quantum trajectories are computed using the derivative propagation method (DPM). Both real-valued and complex-valued DPM quantum trajectories are employed. Of interest are the deep tunneling and the higher energy barrier scattering problems in cases in which the scattering barrier is "thick" by comparison to the width of the initial wave packet. For higher energy scattering problems, it is found that real-valued DPM trajectories very accurately reproduce the transmitted probability densities at low orders when compared to large fixed-grid calculations. However, higher orders must be introduced to obtain good probabilities for deep tunneling problems. Complex-valued DPM is found to accurately reproduce transmitted probability densities at low order for both the deep tunneling and the higher energy scattering problems. Of particular note, complex-classical trajectories are found to very nearly give the exact result for the deep barrier tunneling scattering problem, and the complex DPM converges well at high orders for these thick barrier scattering problems. A variety of analyses are performed to elucidate the dynamics of complex-valued DPM trajectories. The complex-extended barrier potentials are examined in detail, including an analysis of the complex force. Of particular interest are initial conditions for complex-valued DPM trajectories known as isochrones. All trajectories launched from an isochrone arrive on the real axis on the transmitted side of the barrier at the same time. The computation and properties of isochrones as well as the behavior of the initial wave packet in the complex plane are also examined.     

Diblock copolymer membranes investigated by single-particle tracking

We report a study on particle diffusion in membranes formed from polystyrene-block-poly(2-(dimethylamino)ethyl methacrylate) (PS-b-PDMAEMA) diblock copolymers. The membranes were investigated by scanning electron microscopy and by single-particle tracking employing carboxy-functionalized polystyrene beads loaded with a fluorophore as spectroscopic probes. From the diffusion trajectories we extracted the domain size distribution of the membranes and the local diffusion coefficient of the beads as a function of the size of the beads. The single-particle tracking data revealed that the effective domain sizes of the membranes are reduced with respect to the domain sizes obtained from scanning electron microscopy, reflecting the confined diffusion of the probe particles due to interactions with the domain walls. This is corroborated by a clear correlation between the diffusion coefficient of an individual polystyrene bead and the size of the actual domain to which it is confined.     

Dispersion of discrete sample signals within aerosol spray chambers: preliminary investigations

A barrel-type spray chamber with a baffle system and various other structures were used for characterization of band-broadening phenomena occurring within aerosol spray chambers, with an ICP-AES detector used in this case. Absolute values of aerosol particle size distributions from nebulizer/spray chamber systems were measured and found to be affected by the relative positions of impact surfaces with respect to the nebulizer. Smaller particles, but less total mass was observed as the baffle was moved closer to the nebulizer tip. However, based on measurements herein, it does not appear that particle sizes in any case will be small enough within the spray chamber for diffusion to influence band broadening for the bulk of the aerosol mass, as particularly important for mass sensitive detectors such as ICP-AES, although diffusion is likely to be important to particle number sensitive detectors.

Dispersion within the turbulent gas-phase regions of spray chambers appears to be relatively small. Geometries which introduce stagnant gas flow regions appear to have larger effects on band-broadening. The smoke tests utilized in these studies were found to be useful aids for visualization of spray chamber flow phenomena that influence dispersion of discrete signals.

Recirculation phenomena can also play a role in band broadening. Recirculation of aerosol re-entrained into the nebulizer jet appears to have an effect on dispersion, as represented by the full width at half maximum values. On the other hand, recirculation renebulization leads to substantial peak tailing.     

An electrodynamics-based model for ion diffusion in microbial polysaccharides

An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides. The fixed charges and electrostatic double layers that may associate with microbial polysaccharides and their effects on ion diffusion were explicitly built into the model. The model extends a common multicomponent ion diffusion formulation that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a cation exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. An illustrative example was also provided to simulate dynamic behavior of ionic current during ion diffusion within a charged bacterial cell wall polysaccharide and the effects of the ionic current on the compression or expansion of the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.     

Fluorescence correlation spectroscopy of gold nanoparticles,and its application to an aptamer-based homogeneous thrombin assay

We have studied the fluorescence properties and diffusion behaviors of gold nanoparticles (GNPs) in solution by using fluorescence correlation spectroscopy (FCS) at single molecule level. The GNPs display a high photo-saturation feature. Under illumination with strong laser light, they display higher brightness per particle (BPP) despite their low quantum yields. Based on the unique fluorescence properties and diffusion behaviors of GNPs, we have developed a sensitive and homogenous thrombin assay. It is based on a sandwich strategy and is making use of GNPs to which two different aptamers are conjugated. When the differently aptamer-labeled GNPs are mixed with solutions containing thrombin, the affinity reaction causes the GNPs to form dimers or oligomers. This leads to an increase in the diffusion time of the GNPs in the detection volume that is seen in FCS. The FCS method enables sensitive detection of the change in the characteristic diffusion time of the GNPs before and after the affinity reaction. Quantitative analysis of thrombin is based on the measurement of the change in the diffusion time. Under optimal conditions, the calibration plot is linear in the 0.5 nM to 110 nM thrombin concentration range, and the detection limit is 0.5 nM. The method was successfully applied to the direct determination of thrombin in human plasma.

Slow adsorption reaction between arsenic species and goethite (alpha-FeOOH): diffusion or heterogeneous surface reaction control

The slow stage of phosphate or arsenate adsorption on hydrous metal oxides frequently follows an Elovich equation. The equation can be derived by assuming kinetic control by either a diffusion process (either interparticle or intraparticle) or a heterogeneous surface reaction. The aim of this study is to determine whether the slow stage of arsenic adsorption on goethite is more consistent with diffusion or heterogeneous surface reaction control. Adsorption kinetics of arsenate and dimethylarsinate (DMA) on goethite (alpha-FeOOH) were investigated at different pH values and inert electrolyte concentrations. Their adsorption kinetics was described and compared using Elovich (Gamma vs ln time) plots. Desorption of arsenate and DMA was studied by increasing the pH of the suspension from pH 4.0 to pH 10.0 or 12.0. The effective particle sizes and zeta-potential of goethite were also determined. Effective particle size increased rapidly as the pH approached pH(IEP), both in the absence and presence of arsenic. Inert electrolyte concentrations and pH had no effect on the slow stage of arsenate adsorption on goethite, while the kinetics of DMA adsorption on goethite was influenced by both parameters. The slow stage of arsenate adsorption on goethite follows an Elovich equation. Since effective particle size changes with both pH and inert electrolyte concentrations, and effective particle size influences interparticle diffusion, the arsenate adsorption kinetics indicate that the slow adsorption step is not due to interparticle diffusion. DMA also has complex adsorption kinetics with a slow adsorption stage. DMA desorbed completely and rapidly when the pH was raised, in contrast to the slow adsorption kinetics, indicating that the slow adsorption step is not due to intraparticle diffusion. The slow adsorption is not the result of diffusion, but rather is due either to the heterogeneity of the surface site bonding energy or to other reactions controlling arsenic removal from solution.     

Determination of cluster composition in heteroaggregation of binary particle systems by flow cytometry

Cluster composition in aggregation processes of multiple particle species can be dynamically determined by flow cytometry if particle populations are fluorescently labeled. By flow cytometric single particle analysis, aggregates can be characterized according to the exact amount of constituent particles, allowing the detailed and separate quantification of homo- and heteroaggregation. This contribution demonstrates the application of flow cytometry for the experimental detection of heteroaggregation in a binary particle mixture of oppositely charged polystyrene (PS) particles and Rhodamine-B labeled melamine-formaldehyde (MF-RhB) particles. Experiments with different particle concentration, temperature, mixing mode, ionic strength and particle mixing ratio are presented. Aggregation kinetics are enhanced with increasing particle concentration and temperature as well as by increased shear of mixing. These results represent well-known behavior published in previous investigations and validate the performance of flow cytometry for probing heteroaggregation processes. Physical insight with a novel level of detail is gained by the quantification of de- and restabilization phenomena. At low ionic strength, "raspberry"-type aggregates with PS cores are formed by primary heteroaggregation. At moderate particle number ratios, these aggregates are electrostatically destabilized and form more complex aggregates in a secondary heteroaggregation process. At high particle number ratios (> or =50:1), the raspberry-type aggregates are electrostatically restabilized and secondary heteroaggregation is prevented. The dynamic change of aggregate charge was verified by zeta-potential measurements. The elevation of salt concentration over several orders of magnitude retards aggregation dynamics, since attractive interparticle forces are diminished by an electrostatic double layer. This indicates that heteroaggregation induced by attractive interparticle forces is faster than aggregation due to random Brownian motion. Destabilization at high ionic strength is facilitated by charged ions and no longer by MF-RhB coverage. This results in a species independent one step aggregation process.     

Aggregation and gelation kinetics of fumed silica-ethanol suspensions

The kinetics of aggregation and gelation of fumed silica suspended in ethanol were investigated as a function of volume fraction. At low particle concentrations, gelation is well described by aggregation into a primary minimum arising from hydrogen bonding and dispersion forces. The gelation is extremely slow due to an energetic barrier (approximately 25 kT) in the interparticle potential associated with solvation forces. The solvation forces also contribute to the formation of a secondary minimum in the interparticle potential. The depth of this minimum (approximately 3 kT) is sufficient that, at a critical particle concentration, long-range diffusion is arrested due to the short-range attractions and the cooperative nature of particle interactions, as described by mode coupling theory. The presence of the secondary minimum is also observed in the microstructure of the gels studied using X-ray scattering. These observations reinforce the importance of understanding the role of solvent-particle interactions in manipulating suspension properties.     

Modeling of asymmetric membrane formation by dry-casting method

Many polymeric membranes are produced by phase inversion technique invented by Loeb and Sourirajan in 1962. The dry-casting method is one of the major phase inversion techniques in which a homogeneous polymer solution consisting of solvent(s) and nonsolvent(s) is cast on a support and then evaporation of the casting solution takes place under convective conditions. In this paper, we model membrane formation by the dry-casting method. The model takes into account film shrinkage, evaporative cooling, coupled heat, and mass transfer and incorporates practical and reliable diffusion theory as well as complex boundary conditions especially at the polymer solution/air interface. The predictions from the model provide composition paths, temperature, and thickness of the solution. By plotting the composition paths on the ternary phase diagram, we ascertain the general structural characteristics of the membranes prepared from particular casting conditions. The predictive ability of the model was evaluated by comparing the results with the experimental data obtained from gravimetric measurements for cellulose acetate (CA)–acetone–water system. In an attempt to illustrate the importance of diffusion formalism on the predictions, recently proposed multicomponent diffusion theory and its simplified forms were utilized in the model. The computational results show that the critical factor for capturing the accurate behavior of membrane formation is the diffusion formalism utilized in the model.     

Packing density,permeability, and separation efficiency of packed microchips at different particle-aspect ratios

HPLC microchips are investigated experimentally with respect to packing density, pressure drop–flow rate relation, hydraulic permeability, and separation efficiency. The prototype microchips provide minimal dead volume, on-chip UV detection, and a 75 mm long separation channel with a ca. 50 μm × 75 μm trapezoidal cross-section. A custom-built stainless-steel holder allowed to adopt optimized packing conditions. Separation channels were slurry-packed with 3, 5, and 10 μm-sized spherical, porous C8-silica particles. Differences in interparticle porosity, permeability, and plate height data are analyzed and consistently explained by different microchannel-to-particle size (particle-aspect) ratios and particle size distributions.