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Aggregation kinetics and surface charging properties of rod-like sulfated cellulose nanocrystals (CNCs) have been investigated in aqueous suspensions containing monovalent, divalent, or trivalent inorganic salts. Electrophoresis and time-resolved dynamic light scattering (DLS) were used to characterize the surface charge and colloidal stability of the CNCs, respectively. The surface charge and aggregation kinetics of the sulfated CNCs were found to be independent of solution pH (pH range 2-10). For the monovalent salts (CsCl, KCl, NaCl, and LiCl), the critical coagulation concentration (CCC) followed the order of Cs+ Ca2+ > Ba2+, which is in the reverse order of the counterion ionic size. For the trivalent salts (LaCl3, AlCl3, and FeCl3), the CNCs suspension was destabilized much more effectively. The observed complex stability curves with AlCl3 and FeCl3 are attributed to charge neutralization and charge reversal imparted by the adsorption of aluminum and ferric hydrolysis species on the CNC surface. The significant charge reversal induced by the ferric hydrolysis species led to the restabilization of suspensions. Our results on the colloidal stability of CNCs are of central importance to the nanotechnology and materials science communities working on various applications of CNCs.

The time-evolutions of nanoparticle hydrodynamic radius and aggregate fractal dimension during the aggregation of fullerene (C(60)) nanoparticles (FNPs) were measured via simultaneous multiangle static and dynamic light scattering. The FNP aggregation behavior was determined as a function of monovalent (NaCl) and divalent (CaCl(2)) electrolyte concentration, and the impact of addition of dissolved natural organic matter (humic acid) to the solution was also investigated. In the absence of humic acid, the fractal dimension decreased over time with monovalent and divalent salts, suggesting that aggregates become slightly more open and less compact as they grow. Although the aggregates become slightly more open, the magnitude of the fractal dimension suggests intermediate aggregation between the diffusion- and reaction-limited regimes. We observed different aggregation behavior with monovalent and divalent salts upon the addition of humic acid to the solution. For NaCl-induced aggregation, the introduction of humic acid significantly suppressed the aggregation rate of FNPs at NaCl concentrations lower than 150mM. In this case, the aggregation was intermediate or reaction-limited even at NaCl concentrations as high as 500mM, giving rise to aggregates with a fractal dimension of 2.0. For CaCl(2)-induced aggregation, the introduction of humic acid enhanced the aggregation of FNPs at CaCl(2) concentrations greater than about 5mM due to calcium complexation and bridging effects. Humic acid also had an impact on the FNP aggregate structure in the presence of CaCl(2), resulting in a fractal dimension of 1.6 for the diffusion-limited aggregation regime. Our results with CaCl(2) indicate that in the presence of humic acid, FNP aggregates have a more open and loose structure than in the absence of humic acid. The aggregation results presented in this paper have important implications for the transport, chemical reactivity, and toxicity of engineered nanoparticles in aquatic environments.

Biomaterials capable of suppressing microbial infection are of clear importance in various health care applications, e.g. implantable devices. In this study, we investigate the antimicrobial activity of single-walled carbon nanotubes (SWNT) layer-by-layer (LbL) assembled with the polyelectrolytes poly(L-lysine) (PLL) and poly(L-glutamic acid) (PGA). SWNT dispersion in aqueous solution is achieved through the biocompatible nonionic surfactant polyoxyethylene(20) sorbitan monolaurate (Tween 20), and the amphiphilic polymer phospholipid-poly(ethylene glycol) (PL-PEG). Absorbance spectroscopy and transmission electron microscopy (TEM) show SWNT with either Tween 20 or PL-PEG in aqueous solution to be well dispersed, at about the level of SWNT in chloroform. Quartz crystal microgravimetry with dissipation (QCMD) measurements show both SWNT-Tween and SWNT-PL-PEG to LbL assemble with PLL and PGA into multilayer films, with the PL-PEG system yielding the greater final SWNT content. Escherichia coli and Staphylococcus epidermidis inactivation rates are significantly higher (up to 90%) upon 24h incubation with SWNT containing films, compared to control films (ca. 20%). This study demonstrates the potential usefulness of SWNT/PLL/PGA thin films as antimicrobial biomaterials.

Injection of nanoscale zero-valent iron (NZVI) is potentially a promising technology for remediation of contaminated groundwaters. However, the efficiency of this process is significantly hindered by the rapid aggregation of the iron nanoparticles. The aim of this study was to enhance the colloidal stability of the nanoparticles through the addition of the "green" polymer guar gum. We evaluated the properties of guar gum and its influence on the surface properties, particle size, aggregation, and sedimentation of iron nanoparticles. Commercial iron nanoparticles were dispersed in guar gum solutions, and their aggregation and sedimentation behaviors were compared to those of bare iron nanoparticles and commercial nanoparticles modified with a biodegradable polymer (polyaspartate). High performance size exclusion chromatography, charge titration, and viscosity assessment showed that guar gum is a high molecular weight polymer which is nearly neutrally charged, rendering it suitable for steric stabilization of the iron nanoparticles. Electrophoretic mobility measurements demonstrated the ability of guar gum to adsorb on the nanoparticles, forming a slightly negatively charged layer. Dynamic light scattering experiments were conducted to estimate the particle size of the different nanoparticle suspensions and to determine the aggregation behavior at different ionic strengths. Guar gum effectively reduced the hydrodynamic radius of the bare nanoparticles from 500 nm to less than 200 nm and prevented aggregation of the nanoparticles even at very high salt concentrations (0.5 M NaCl and 3 mM CaCl(2)). Sedimentation profiles of the different nanoparticle suspensions confirmed the improved stability of the iron nanoparticles in the presence of guar gum. The results strongly suggest that guar gum can be used to effectively deliver stabilized zero-valent iron nanoparticles for remediation of contaminated groundwater aquifers.

Using variable substitution, we present a general method for the numerical solution of stiff, ordinary, linear, homogeneous differential equations characteristic of colloid particle adsorption/deposition over an energy barrier. For the example of the radial impinging jet system, we demonstrate the application of this method of calculating the colloid concentration profile and initial particle flux in the presence of repulsive electrostatic interactions between the particle and adsorption surface. We show that our method works well in systems with energy barriers up to the order of hundreds of kT, at which point the adsorption flux vanishes. The numerical results obtained with our method are in good agreement with the known limiting analytical approximations for the particle flux through an energy barrier and for a low Peclet number. The developed numerical code is very stable over a wide range of physical parameters, and its accuracy for the most challenging parameter sets is on the order of 10−4. To achieve this stability, we have derived and employed a single formula for the van der Waals dispersion interaction, working at both a small and a large separation distance. We show that this formula converges to the known available analytical expressions for dispersion forces in the limit of small and large separation distance. We also demonstrate that the maximum deviations between our formula and the other equations appear in the intermediate range of the separation distance and do not exceed 10%.

The early stage aggregation kinetics of fullerene C60 nanoparticles were investigated in the presence of Suwannee River humic acid and common monovalent and divalent electrolytes through time-resolved dynamic light scattering (DLS). In the absence of humic acid, the aggregation behavior of the fullerene nanoparticles in the presence of NaCl, MgCl2, and CaCl2 was found to be consistent with the classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability. In the presence of humic acid and NaCl or MgCl2 electrolytes, the adsorbed humic acid on the fullerene nanoparticles led to steric repulsion, which effectively stabilized the nanoparticle suspension. This behavior manifested in a dramatic drop in the rate of aggregation, an increase in the critical coagulation concentration (CCC), and an attained value of less than unity for the inverse stability ratio (or attachment efficiency) at high MgCl2 concentrations. While the increase in the nanoparticle stability was similarly observed in the presence of humic acid at low CaCl2 concentrations, enhanced aggregation occurred at higher CaCl2 concentrations. Measurement of scattered light intensities over time indicated significant aggregation of the humic acid macromolecules in solutions of high CaCl2 concentrations. Transmission electron microscopy (TEM) imaging of the fullerene aggregate structures in the presence of humic acid revealed that bridging of the fullerene nanoparticles and aggregates by the humic acid aggregates is the likely mechanism for the enhanced aggregation at high CaCl2 concentrations.

The transport and deposition dynamics of hematite (alpha-Fe(2)O(3)) colloids in packed quartz sand media are investigated. Column transport experiments were carried out at various solution ionic strengths, colloid concentrations, and flow velocities. A colloid transport model was proposed that includes the dynamics of blocking as well as multilayer deposition that takes place at high ionic strengths where particle-particle interactions are favorable. Blocking dynamics in the model are described by either Langmuirian adsorption (LA) or random sequential adsorption (RSA). Two important model parameters-the particle-matrix collision efficiency and the ionic strength dependent blocking (excluded area) parameter-are estimated from the colloid breakthrough curves using a nonlinear optimization procedure. The collision (attachment) efficiency for particle-particle interactions, on the other hand, was determined independently from colloid aggregation rate measurements. At very low ionic strength, only monolayer deposition is observed and the RSA model gives a better description of the experimental data than the LA model. At higher ionic strengths, multilayer deposition becomes significant and both models yield comparable results. Calculated maximum surface coverages at low ionic strengths were in good agreement with experimentally observed values obtained by scanning electron microscopy. Copyright 2000 Academic Press.

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.

We consider a dilute homogeneous suspension of rigid spherical particles with different size and density in a motionless Newtonian fluid. These particles are moving under gravity at low Reynolds and Stokes numbers (negligible fluid and particle inertia) and high Peclet numbers (negligible Brownian diffusion). Doublets are formed when two particles in relative motion are brought into contact by the action of the attractive van der Waals force. Trajectory calculations for particles with different densities indicate that as the reduced density ratio increases above unity, the percentage of particles captured on the front hemisphere decreases, and this generally results in smaller collision efficiencies. Furthermore, in contrast to the case of particles with equal density, a maximum of the collision efficiency occurs for a particle size ratio smaller than unity. Above a critical value of the reduced density ratio, the occurrence of a closed region of relative trajectories confines the capture sites mostly to the "rear" hemisphere of each particle. As the reduced density ratio increases above the critical value, this region grows larger and the collision efficiency may be estimated by a closed-form asymptotic solution. Copyright 1998 Academic Press. Copyright 1998Academic Press

A novel method, the surface element integration (SEI), is developed to determine the van der Waals and electrostatic double layer interactions between a particle and an infinite flat plate from the corresponding interactions per unit area between two infinite flat plates. Comparison with the Hamaker expression for nonretarded van der Waals interaction reveals that the new technique gives the exact interaction energy between a spherical particle and a flat plate. Available analytical expressions for the electrostatic double layer interaction energy between two infinite flat plates, based on the linearized Poisson-Boltzmann equation, are used in SEI to obtain the sphere-flat plate interaction energy. These sphere-flat plate interaction energies determined using SEI are compared with the corresponding interaction energies obtained from a detailed numerical solution of the Poisson-Boltzmann equation based on finite element analysis. The comparisons reveal that SEI scales the flat plate interaction to the corresponding sphere-flat plate geometry exactly, while the scaling based on the conventional Derjaguin approximation technique grossly overpredicts the interaction energy for small particles and low electrolyte concentrations. Copyright 1997 Academic Press. Copyright 1997Academic Press

A theoretical investigation of particle deposition onto a permeable surface in a parallel-plate channel is presented in this paper. The convective diffusion equation is rigorously formulated with the inclusion of lateral transport due to permeation drag and inertial lift, and transport due to gravitational, double layer, and van der Waals forces. A numerical procedure for solving the governing equation is also presented. The effects of particle size, permeation velocity, solution ionic strength, cross-flow velocity, and particle density on the initial rate of particle deposition are investigated. Results point out that the local and average particle deposition rates onto a permeable surface are determined by an interplay between several transport and interaction mechanisms, among which permeation drag, electric double layer repulsion, and inertial lift are most important.

A general theoretical model for particle deposition and transport in heterogeneous porous media is developed. The model can describe the transient particle deposition and the nonuniform particle coverage of porous media surfaces, resulting from surface charge heterogeneity, surface roughness, or other unevenly distributed surface properties. The model is applied to a packed-bed column with spherical collectors whose surfaces are hetero geneously charged. Results indicate that, under unfavorable chemical conditions, it is the degree of surface charge heterogeneity that mainly determines the transient (dynamic) deposition behavior. This transient behavior can be predicted by the flux-correcting function, a function strongly dependent on the charge heterogeneity of solid surfaces. It is further shown that the effect of surface charge heterogeneity on particle deposition dynamics can be quantitatively represented by a few parameters. These parameters are λ, the fraction of favorable surface sites, and α, the collision efficiency of colloidal particles with the unfavorable surface in the patchwise charge distribution model; and ψ0, the average surface potential, and σ, the standard deviation of surface potential in the normal charge distribution model.

The effect of particle size on the kinetics of particle deposition in the presence of attractive double layer interactions has been studied theoretically and experimentally. Particle deposition experiments were carried out with several model suspensions of positively charged latex particles and negatively charged glass beads using the packed bed column technique. The model particles used in the deposition experiments covered a wide size range, from 0.08 to 2.51 μm. Experimental deposition rates were compared to theoretical predictions based on a numerical solution of the convective diffusion equation with colloidal, hydrodynamic, and gravitational forces fully incorporated. Theoretical and experimental results reveal that the enhancement in particle deposition rate (i.e,, the deposition rate in the presence of double layer interaction divided by the rate in the absence of double layer interaction) is dependent on particle size. At low ionic strengths, the enhancement in deposition rate passes through a maximum as the particle size increases. This maximum corresponds to particles with a size around 1 μm. It is also concluded that this maximum is determined by the interplay between the size of the particles and the range of the attractive double layer interactions.

The use of simultaneous, multiangle static light scattering measurements for studying the kinetics of coagulation of monodisperse spherical colloids is reported. Absolute coagulation rate constants were determined from analysis of the change in the angular dependence of the scattered light intensity with time, at the early stage of the aggregation process. This method is advantageous to current light scattering methods which provide relative coagulation rates.

Modified boundary conditions for solving the convective diffusion equation for Brownian particles as applied in the Happel sphere-in-cell porous medium model are presented. With the modified boundary conditions, the convective diffusion equation correctly predicts the deposition rates of Brownian particles at low Peclet numbers. At moderate and large Peclet numbers, colloid deposition rates are similar to those calculated with existing models.

The kinetics of capture of suspended colloidal particles in a packed bed of granular material in the presence of attractive double layer interactions have been investigated. Colloid deposition experiments were carried out with positively charged polystyrene latex colloids and negatively charged glass beads packed in a laboratory scale column. A notable increase in colloid deposition rates was observed when the ionic strength of the aqueous solution was reduced from 0.1 M to a value of 10−6−10−5 M. The experimental results were generally in good agreement with theoretical deposition rates, which were calculated from a numerical solution of the convective diffusion equation with colloidal and hydrodynamic interactions fully incorporated. The enhancement of the colloid deposition rates is attributed to the increase in the range and magnitude of the attractive double layer interactions as the ionic strength decreases. When attractive double layer interactions extend to large distances from the collector surface, the transport of particles toward the collector increases beyond that of pure convective diffusion, and, as a result, colloid deposition rates also increase.

The influence of depletion interactions on the transport of micrometer-sized, negatively charged polystyrene latex particles through porous media was studied by analysis of particle breakthrough curves as a response to short-pulse particle injections to the inlet of a packed column of glass beads. The column outlet latex particle concentration profiles and the total amount of particles exiting the column were determined as a function of the concentration of small, silica nanoparticles in the solution and the bulk flow rate. Because of similar charges, the silica particles do not adsorb to either the latex particles or glass beads and thus induce an attractive depletion force between the latex particles and glass bead collectors. The total column outlet latex particle amount was calculated by integrating the measured breakthrough concentration curve and compared to the known amount of injected particles at the column inlet. It was found that the particle recovery was a decreasing function of the silica nanoparticle concentration and the carrier fluid residence time, and an increasing function of the velocity in the bed. In addition, removing the silica nanoparticles from the flowing solution caused a second outlet peak to appear, suggesting that some of the polystyrene particles were captured in secondary energy wells. The experimental data were interpreted using the predicted potential energy profile between a single particle and a glass bead, which was assumed to consist of electrostatic, van der Waals, and depletion components. The results indicate that secondary energy wells significantly affect particle transport behavior through porous media.

The influence of electrostatic double-layer and hydrodynamic interactions on random sequential adsorption (RSA) of colloidal particles onto packed spherical collectors was investigated using inverse analysis of colloid breakthrough data obtained from well-controlled particle deposition experiments. Deposition experiments were carried out using monodisperse aqueous suspensions of positively charged latex colloids and packed columns of negatively charged uniform glass beads for different combinations of ionic strength, particle size, and approach velocity. From the experimental particle breakthrough data, the initial particle deposition rates and the virial coefficients of the dynamic blocking function based on RSA mechanics were determined. The magnitudes of the virial coefficients were observed to increase from the hard sphere values with increasing flow rates and decreasing ionic strengths of the background electrolyte. Particle size also plays a significant role in governing the deposition dynamics. The deviation from the hard sphere RSA behavior becomes more prominent for larger particles. Copyright 2000 Academic Press.

A systematic study on the effect of electrostatic double layer interaction on permeate flux decline and deposit cake formation in crossflow membrane filtration of colloidal suspensions is reported. Three monodisperse silica suspensions with diameters of 47, 110, and 310 nm were used as model colloids, and a tubular zirconia membrane with an average pore diameter of 20 nm was used as a model membrane. The magnitude and range of the electrostatic double layer interactions were controlled via changes in solution ionic strength and pH. The coupling between colloidal interactions and hydrodynamic forces was investigated by changing the transmembrane pressure and particle size. The results indicate that the rate of flux decline is strongly dependent on solution ionic strength and, to a much lesser degree, on solution pH (for the investigated pH range 6.1-10.0). Variations in flux decline rate with solution ionic strength are especially significant as the particle size decreases. Particle cake thickness, permeability, and porosity generally increased with a decrease in solution ionic strength for a given particle size. For given physical and chemical conditions, the cake layer porosity increased with decreasing particle size, while cake permeability decreased with decreasing particle size. These trends are consistent with the increased importance of double layer repulsive forces in controlling the cake layer structure as the solution ionic strength and particle size decrease. Pressure relaxation experiments indicated that the particle cake layer is reversible, implying no irreversible deposition (attachment) of silica colloids onto the zirconia membrane surface. Copyright 1998 Academic Press.

A series of well-controlled membrane filtration experiments are performed to systematically investigate the dynamic behavior of permeate flux in crossflow membrane filtration of colloidal suspensions. Results are analyzed by a transient permeate flux model which includes an approximate closed-form analytical expression for the change of permeate flux with time. The model is based on a simplified particle mass balance for the early stages of crossflow filtration before a steady-state flux is attained, and Happel's cell model for the hydraulic resistance of the formed particle cake layer. The filtration experiments demonstrate that permeate flux declines faster with increasing feed particle concentration and transmembrane pressure and with a decrease in the particle size of the suspension. It is also shown that crossflow velocity (shear rate) has no effect on permeate flux at the transient stages of crossflow filtration. Pressure relaxation experiments indicate that the particle cake layer is reversible, implying no irreversible deposition (attachment) of particles onto the membrane surface or the accumulated (retained) particles. The experimental results are shown to be in very good agreement with the theoretical predictions, thus verifying the validity of the model for the transient permeate flux in crossflow filtration and the underlying assumptions in the derivation of the model. Copyright 1997 Academic Press.