Aggregation Rate Constants Research Articles

Recognition of silver nanoparticles surface-adsorbed citrate anions by macrocyclic polyammonium cations: a spectrophotometric approach to study aggregation kinetics and evaluation of association constant.

In this report, we have studied the recognition of citrate anions adsorbed on the surface of silver nanoparticles (cit-Ag-NPs), by macrocyclic polyammonium cations (MCPACs): Me6 [14]ane-N4 H8 (4+) (Tet-A/Tet-B cations) and [32]ane-N8 H16 (8+) , which are well reputed anion recognizers and are treated as to mimic of biological polyamines. The study was monitored on ultraviolet-visible spectroscopy by performing a titration of the aqueous dispersion of the cit-Ag-NPs by the aqueous solution of MCPACs. The ultraviolet-visible time-scan plots over the reduction of the absorption band of surface plasmon resonance of cit-Ag-NPs at 390 nm are well fitted with fourth-order polynomial equation and are employed to determine the initial aggregation rate constants. It has been stated that the aggregation is the result in electrostatic attraction followed by H-bond formation between the surface-adsorbed citrate anions and added MCPACs. The atomic force microscopy results have evidenced aggregation of cit-Ag-NPs in presence of MCPACs. The evaluated H-bonded association constant (Kasso ) using Benesi-Hildebrand method reveals that [32]ane-N8 H16 (8+) cations form stronger association complex, as expected, with the citrate anions than the Me6 [14]ane-N4 H8 (4+) cations. The study would thus provide the insight of molecular interactions involved in nanoparticle surface-adsorbed anions with biological polyamines. Copyright © 2016 John Wiley & Sons, Ltd.

Kinetics of Monoclonal Antibody Aggregation from Dilute toward Concentrated Conditions.

Gaining understanding on the aggregation behavior of proteins under concentrated conditions is of both fundamental and industrial relevance. Here, we study the aggregation kinetics of a model monoclonal antibody (mAb) under thermal stress over a wide range of protein concentrations in various buffer solutions. We follow experimentally the monomer depletion and the aggregate growth by size exclusion chromatography with inline light scattering. We describe the experimental results in the frame of a kinetic model based on population balance equations, which allows one to discriminate the contributions of the conformational and of the colloidal stabilities to the global aggregation rate. Finally, we propose an expression for the aggregation rate constant, which accounts for solution viscosity, protein-protein interactions, as well as aggregate compactness. All these effects can be quantified by light scattering techniques. It is found that the model describes well the experimental data under dilute conditions. Under concentrated conditions, good model predictions are obtained when the solution pH is far below the isoelectric point (pI) of the mAb. However, peculiar effects arise when the solution pH is increased toward the mAb pI, and possible explanations are discussed.

230Th and 234Th as coupled tracers of particle cycling in the ocean: A maximum likelihood approach

We applied maximum likelihood estimation to measurements of Th isotopes (234,230Th) in Mediterranean Sea sediment traps that separated particles according to settling velocity. This study contains two unique aspects. First, it relies on settling velocities that were measured using sediment traps, rather than on measured particle sizes and an assumed relationship between particle size and sinking velocity. Second, because of the labor and expense involved in obtaining these data, they were obtained at only a few depths, and their analysis required constructing a new type of box-like model, which we refer to as a “two-layer” model, that we then analyzed using likelihood techniques. Likelihood techniques were developed in the 1930s by statisticians, and form the computational core of both Bayesian and non-Bayesian statistics. Their use has recently become very popular in ecology, but they are relatively unknown in geochemistry.Our model was formulated by assuming steady state and first-order reaction kinetics for thorium adsorption and desorption, and for particle aggregation, disaggregation, and remineralization. We adopted a cutoff settling velocity (49m/d) from Armstrong et al. (2009) to separate particles into fast- and slow-sinking classes. A unique set of parameters with no dependence on prior values was obtained. Adsorption rate constants for both slow- and fast-sinking particles are slightly higher in the upper layer than in the lower layer. Slow-sinking particles have higher adsorption rate constants than fast-sinking particles. Desorption rate constants are higher in the lower layer (slow-sinking particles: 13.17±1.61, fast-sinking particles: 13.96±0.48) than in the upper layer (slow-sinking particles: 7.87±0.60y−1, fast-sinking particles: 1.81±0.44y−1). Aggregation rate constants were higher, 1.88±0.04, in the upper layer and just 0.07±0.01y−1 in the lower layer. Disaggregation rate constants were just 0.30±0.10y−1 in the upper layer and higher, 3.01±0.35y−1, in the lower layer. For rapid-sinking particles, adsorption of Th from solution and aggregation of slow-sinking particles are the main source, and particle sinking is the main sink. For slow-sinking particles, adsorption is also the main source, but radioactive decay (for 234Th) and desorption are the main sinks. Sinking and aggregation are small compared to adsorption and decay, and the contribution of disaggregation is negligible.

Protein A chromatography increases monoclonal antibody aggregation rate during subsequent low pH virus inactivation hold

Protein A chromatography is a near-ubiquitous method of mAb capture in bioprocesses. The use of low pH buffer for elution from protein A is known to contribute to product aggregation. Yet, a more limited set of evidence suggests that low pH may not be the sole cause of aggregation in protein A chromatography, rather, other facets of the process may contribute significantly. This paper presents a well-defined method for investigating this problem. An IgG4 was incubated in elution buffer after protein A chromatography (typical of the viral inactivation hold) and the quantity of monomer in neutralised samples was determined by size exclusion chromatography; elution buffers of different pH values predetermined to induce aggregation of the IgG4 were used. Rate constants for monomer decay over time were determined by fitting exponential decay functions to the data. Similar experiments were implemented in the absence of a chromatography step, i.e. IgG4 aggregation at low pH. Rate constants for aggregation after protein A chromatography were considerably higher than those from low pH exposure alone; a distinct shift in aggregation rates was apparent across the pH range tested.

Denaturation Kinetics of Whey Protein Isolate Solutions and Fouling Mass Distribution in a Plate Heat Exchanger

Few investigations have attempted to connect the mechanism of dairy fouling to the chemical reaction of denaturation (unfolding and aggregation) occurring in the bulk. The objective of this study is to contribute to this aspect in order to propose innovative controls to limit fouling deposit formation. Experimental investigations have been carried out to observe the relationship between the deposit mass distribution generated in plate heat exchangers (PHE) by a whey protein isolate (WPI) mainly composed ofβ-lactoglobulin (β-Lg) and the ratio between the unfolding and aggregation rate constants. Experiments using a PHE were carried out at a pilot scale to identify the deposit distribution of a model fouling solution with different calcium contents. In parallel, laboratory experiments were performed to determine the unfolding/aggregation rate constants. Data analysis showed that (i)β-Lg denaturation is highly dependent on the calcium content, (ii) for each fouling solution, irrespective of the imposed temperature profile, the deposit mass in each channel and the ratio between the unfolding and aggregation rate constants seem to be well correlated. This study demonstrates that both the knowledge of the thermal profile and theβ-Lg denaturation rate constants are required in order to predict accurately the deposit distribution along the PHE.

Protein-silver nanoparticle interactions to colloidal stability in acidic environments.

We report a kinetic study of Ag nanoparticles (AgNPs) under acidic environments (i.e., pH 2.3 to pH ≈7) and systematically investigate the impact of protein interactions [i.e., bovine serum albumin (BSA) as representative] to the colloidal stability of AgNPs. Electrospray-differential mobility analysis (ES-DMA) was used to characterize the particle size distributions and the number concentrations of AgNPs. Transmission electron microscopy was employed orthogonally to provide visualization of AgNPs. For unconjugated AgNPs, the extent of aggregation, or the average particle size, was shown to be increased significantly with an increase of acidity, where a partial coalescence was found between the primary particles of unconjugated AgNP clusters. Aggregation rate constant, kD, was also shown to be proportional to acidity, following a correlation of log(kD) = -1.627(pH)-9.3715. Using ES-DMA, we observe BSA had a strong binding affinity (equilibrium binding constant, ≈ 1.1 × 10(6) L/mol) to the surface of AgNPs, with an estimated maximum molecular surface density of ≈0.012 nm(-2). BSA-functionalized AgNPs exhibited highly-improved colloidal stability compared to the unconjugated AgNPs under acidic environments, where both the acid-induced interfacial dissolution and the particle aggregation became negligible. Results confirm a complex mechanism of colloidal stability of AgNPs: the aggregation process was shown to be dominant, and the formation of BSA corona on AgNPs suppressed both particle aggregation and interfacial dissolution of AgNP samples under acidic environments.

Nonideal Diffusion Effects and Short-Range Ordering Lead to Higher Aggregation Rates in Concentrated Hard-Sphere Dispersions

Brownian aggregation in concentrated hard-sphere dispersions is studied using models and Brownian dynamics (BD) simulations. Two new theoretical models are presented and compared to several existing approaches and BD simulation results, which serve as benchmarks. The first new model is an improvement over an existing local density approximation (LDA)-based model. The other is based on the more rigorous Fundamental measure theory (FMT) applied to the "liquid-state" dynamic density-functional theory (DDFT). Both models provide significant improvements over the classical Smoluchowski model. The predictions of the new FM-DDFT-based model for aggregation kinetics are in excellent agreement with BD simulation results for dispersions with initial particle volume fractions, ϕ, up to 0.35 (close to the hard-sphere freezing transition at ϕ = 0.494). In contrast to previous approaches, the nonideal particle diffusion effects and the initial and time-dependent short-range ordering in concentrated dispersions due to entropic packing effects are explicitly considered here, in addition to the unsteady-state effects. The greater accuracy of the FM-DDFT-based model compared to that of the LDA-based models indicates that nonlocal contributions to particle diffusion (only accounted for in the former) play important roles in aggregation. At high concentrations, the FM-DDFT-based model predicts aggregation half-times and gelation times that are up to 2 orders of magnitude shorter than those of the Smoluchowski model. Moreover, the FM-DDFT-based model predicts asymmetric cluster-cluster aggregation rate constants, at least for short times. Overall, a rigorous mechanistic understanding of the enhancement of aggregation kinetics in concentrated dispersions is provided.

The use of amino acids to prepare physically and conformationally stable spray-dried IgG with enhanced aerosol performance

This study investigated the effect of various amino acids on the molecular and thermodynamic stability of IgG (immune globulin G) as well as its aerosol performance. The antibody was spray-dried in the presence of different amino acids (leucine, phenylalanine, cysteine, glycine, lysine and arginine) using 20% and 50% (w/w) amino acid. SEC-HPLC, SDS-PAGE and IR-spectroscopy were performed to evaluate the stability of spray-dried IgG. The in-vitro aerosol performance of the well-stabilized formulations was subsequently assessed. IgG containing phenylalanine at 20 and 50% w/w produced the lowest content of aggregated antibody (1.35 ± 0.24%) and (1.12 ± 0.15%). The application of phenylalanine and cysteine at 50% (w/w) demonstrated the best storage stability (2 month at 45°C) with a rate constant of 0.006/month and enhanced fine particle fractions of 62.43 ± 0.34% and 70.51 ± 0.23%, respectively. Samples containing 50% arginine exhibited significantly perturbed conformation and, consequently, the highest aggregation rate constant of 0.019/month following storage. These results indicate that phenylalanine and cysteine serve as efficacious amino acids for the preparation of IgG dry powder with regard to stability and aerodynamic properties.

Gauging Colloidal and Thermal Stability in Human IgG1–Sugar Solutions through Diffusivity Measurements

Monoclonal antibodies are the fastest growing class of biotherapeutics. Ensuring their colloidal and conformational stability in liquid dispersions is crucial for maintaining therapeutic efficacy and economic viability. Sugars are often added to increase the colloidal and thermal stability of protein; however, determining which sugar is the most stabilizing requires time and sample-consuming stability tests. Here we show for a human IgG1 that the extent of stabilization by different sugars can be gauged by analyzing the proteins' diffusive virial coefficient kD. This protein interaction parameter is measured conveniently in a noninvasive, high-throughput manner using dynamic light scattering. It is found to correlate closely with experimental aggregation rate constants at the onset of aggregation and with melting temperatures for antibodies in different sugar solutions. The proposed analysis thus provides a rapid test of the subtle differences between inherently similar sugar-protein interactions; it should greatly facilitate the formulation of protein therapeutics. For the antibody investigated in this study, circular dichroism spectroscopy also yields clues about the mechanism by which sugars improve the thermal stability.

Stimulus-Responsive Au@(MeO2MAx-co-OEGMAy) Nanoparticles Stabilized by Non-DLVO Interactions: Implications of Ionic Strength and Copolymer (x:y) Fraction on Aggregation Kinetics

Functionalized nanoparticles can assist in stabilizing fluid-fluid interfaces; however, developing and applying the appropriate surface modification presents a challenge because successful application of these nanomaterials for biotechnological, food processing, and environmental applications requires their long-term stability in elevated ionic strength media. This work studies stimulus responsive polymeric materials based on random copolymers of di(ethylene glycol) methyl ether methacrylate (x = MeO2MA) and oligo(ethylene glycol) methyl ether methacrylate (y= OEGMA) which, when grafted to gold nanoparticles, show significant, tunable, colloidal stability. The nanoparticles Au@(MeO2MAx-co-OEGMAy) display tunable, reversible aggregation that is highly dependent on the (x:y) ratio and ionic strength. Effects of these parameters on the initial rate constant of aggregation (k11) are studied by time-resolved dynamic light scattering (TR-DLS) experiments. At the same nanoparticle concentration, a strong sensitivity to salt concentration is observed. Over less than 300 mM increase in NaCl concentration, we observed a two-order of magnitude increase in aggregation rate constants, 4.2 × 10(-20) < k11 < 1.8 × 10(-18) m(3)s(-1). Additionally, for the same gold nanoparticles, a higher fraction of OEGMA requires a higher salt concentration to induce aggregation. A linear relationship between the critical NaCl coagulation concentration (CCC) and the copolymer composition is observed. Analysis of the experimental data with an extended Derjaguin-Landau-Verwey-Overbeek (xDLVO) theory that includes hydration and osmotic forces is used to explain the stability of these systems. We find the hydration pressure, 2.4 < P(h,0) < 7.2 MPa, scales linearly both with the osmotic pressure and the OEGMA monomer concentration (5 < y < 20%). Specific knowledge of P(h,0)(y, C(NaCl)) enables design of both aggregation kinetics and stability as a function of the copolymer ratio and external stimuli.

The effect of double layer repulsion on the rate of turbulent and Brownian aggregation: experimental consideration

Coagulation rates of well-characterized carboxyl latex particles with a diameter of 1.5μm were measured to study the effect of double layer repulsion on the kinetics of aggregation in the presence and the absence of turbulent flow. The absolute coagulation rate constants were determined by the turbidity measurement with T-matrix method, which is a computational method to calculate the extinction cross section of doublets. Measurements were conducted as a function of pH and KCl concentration. Turbulent flow was generated by an end-over-end rotation. Brownian coagulation was performed in quiescent condition. Both turbulent and Brownian aggregation rate constants decreased with increasing pH in 2, 10, and 100mM KCl. In the case of 2 and 10mM KCl, the decrease of turbulent rate constant with pH was more gradual than that of Brownian ones. Turbulent rate constants in 100 mM KCl showed lower critical pH, above which the rate decreases, compared to that of Brownian coagulation. These results are qualitatively consistent with theoretical calculation of coagulation constant. We consider that the effect of double layer repulsion on the reduction of the rate becomes small in a flow field because higher kinetic energy in a turbulent flow overcomes the energy barrier. Also, we demonstrated that fast coagulation regime is attained by reducing the magnitude of ζ potential below 25mV; a good indicator is ζ potential, rather than surface potential and surface charge, when judging colloidal dispersion is stable or not.

Probing Colloidal Particle Aggregation by Light Scattering

The present article reviews recent progress in the measurement of aggregation rates in colloidal suspensions by light scattering. Time-resolved light scattering offers the possibility to measure absolute aggregation rate constants for homoaggregation as well as heteroaggregation processes. We further discuss the typical concentration dependencies of the aggregation rate constants on additives. Addition of simple salts containing monovalent counterions leads to screening of the electrostatic repulsion of the charged particles and a transition from slow to rapid aggregation. Addition of salts containing multivalent counterions may lead to a charge reversal, which results in a sequence of two instability regions. Heteroaggregation rates between oppositely charged particles decrease with increasing salt level. This decrease is caused by screening of the electrostatic attraction between these particles.

On two-compartment population balance modeling of spray fluidized bed agglomeration

The present work focuses on the modeling and analysis of a spray fluidized bed granulation (SFBG) process based upon the concept that particles are communicating between the two compartments at some steady state mass flow rate. A numerical technique for solving the proposed two-compartment model (2CM) is developed and validated against some newly derived analytical solutions. Moreover, the inverse technique for extracting the rate constant of one-compartment model (1CM) is extended to 2CM. A correlation of aggregation rate constant of 2CM with the rate constant of conventional 1CM under some restrictions is investigated and it is found that the 1CM cannot be used, in general, to predict results of 2CM. Furthermore, it is observed that the existence of two zones in SFBG is responsible to certain extent for time dependent behaviour of aggregation rate constant. Finally, influence of compartment sizes and particles residence times on particle size distribution is investigated.

Trehalose Limits BSA Aggregation in Spray-Dried Formulations at High Temperatures: Implications in Preparing Polymer Implants for Long-Term Protein Delivery

Polymer implants are promising systems for sustained release applications but their utility for protein delivery has been hindered because of concerns over drug stability at elevated temperatures required for processing. Using bovine serum albumin (BSA) as a model, we have assessed whether proteins can be formulated for processing at elevated temperatures. Specifically, the effect of trehalose and histidine-HCl buffer on BSA stability in a spray-dried formulation has been investigated at temperatures ranging from 80°C to 110°C. When both the sugar and buffer are present, aggregation is suppressed even when exposed to 100°C, the extrusion temperature of poly(lactide-co-glycolide) (PLGA), a bioresorbable polymer. Estimation of aggregation rate constants (k) indicate that though both trehalose and histidine-HCl buffer contribute to BSA stability, the effect because of trehalose alone is more pronounced. BSA-loaded PLGA implants were prepared using hot-melt extrusion process and in vitro release was conducted in phosphate buffered saline at 37°C. Comparison of drug released from implants prepared using four different formulations confirmed that maximal release was achieved from the formulation in which BSA was least aggregated. These studies demonstrate that when trehalose and histidine-HCl buffer are included in spray-dried formulations, BSA stability is maintained both during processing at 100°C and long-term residence within implants.

A priori prediction of aggregation efficiency and rate constant for fluidized bed melt granulation

This paper presents a predictive aggregation rate model for spray fluidized bed melt granulation. The aggregation rate constant was derived from probability analysis of particle–droplet contact combined with time scale analysis of droplet solidification and granule–granule collision rates. The latter was obtained using the principles of kinetic theory of granular flow (KTGF). The predicted aggregation rate constants were validated by comparison with reported experimental data for a range of binder spray rate, binder droplet size and operating granulator temperature. The developed model is particularly useful for predicting particle size distributions and growth using population balance equations (PBEs).

Programming nanoparticle aggregation kinetics with poly(MeO2MA-co-OEGMA) copolymers

The ability to exert active control over the kinetic processes associated with dispersion stability is appealing for applications ranging from precision sensing to materials processing. Here, we demonstrate programmable aggregation dynamics using a system of gold nanoparticles sterically stabilized with a thermoresponsive copolymers consisting of di(ethylene glycol) methyl ether methacrylate (x = MeO2MA) and poly(ethylene glycol) methyl ether methacrylate (y = OEGMA). The copolymer ratio (x : y) dictates macromolecule hydrophilicity enabling control of the physicochemical properties of these nanoparticles through external stimuli such as temperature and ionic strength. A detailed characterization of these polymers and the variables used to control their physicochemical properties are presented. We determine the initial aggregation rate constants (k11), a widely adopted measure of nanoparticle stability, of Au@(MeO2MAx-co-OEGMAy) NPs as a function of co-polymer composition, ionic strength, and temperature. For NPs functionalized with a distinct ratio of copolymers (x : y), we observed the onset of measureable aggregation at especially high ionic strengths, normally >300 mM NaCl. While holding copolymer ratio constant, we observed a two order of magnitude increase in aggregation rate constants over less than 300 mM increase in NaCl concentration, 3.0 × 10−20 m3 s−1 < k11 < 2.0 × 10−18 m3 s−1. The results highlight the impact of the polymer structure and its interaction with the media on the swelling behavior and kinetic stability of core–shell thermoresponsive nanoparticles. We compare the inverse stability ratio, W−1, to a theoretical reversible association model in order to extract the underlying thermodynamics associated with interfacial hydration as a function of the co-polymer ratio and stimulus fields.

Aggregation Behavior of Desulfurization Flux in Hot Metal Desulfurization with Mechanical Stirring

The aggregation behavior of desulfurization flux in hot metal desulfurization with mechanical stirring was investigated by small-scale hot metal experiments. Desulfurization flux added from the top aggregated in the hot metal during stirring, reducing the interfacial area between the flux and hot metal, which had a large effect on the desulfurization rate. The size of aggregated slag can be estimated using an aggregation model based on granulation theory. The obtained aggregation rate constant, ka, is 4.5–40.9×10–11 (m3/s). The interfacial area between flux and hot metal can be estimated using the aggregation model, which can also estimate desulfurization behaviors under various conditions. The obtained slag size after desulfurization agreed with the calculated slag size in the equilibrium state, which is highly dependent on stirring conditions. The aggregation rate in commercial-scale (270 ton) desulfurization is larger than that in small-scale experiments due to the difference of their stirring energies.

Influence of annealing treatment on as-grown Ib-type diamond crystal at a high temperature and high pressure

In this paper, we report on the influence of annealing treatment on as-grown Ib-type diamond crystal under high pressure and high temperature in a china-type cubic anvil high-pressure apparatus. Experiments are carried out at a pressure of 7.0 GPa and temperatures ranging from 1700 °C to 1900 °C for 1 h. Annealing treatment of the diamond crystal shows that the aggregation rate constant of nitrogen atoms in the as-grown Ib-type diamond crystal strongly depends on diamond morphology and annealing temperature. The aggregation rate constant of nitrogen remarkably increases with the increase of annealing temperature and its value in octahedral diamond is much higher than that in cubic diamond annealed at the same temperature. The colour of octahedral diamond crystal is obviously reduced from yellow to nearly colorless after annealing treatment for 1 h at 1900 °C, which is induced by nitrogen aggregation in a diamond lattice. The extent of nitrogen aggregation in an annealed diamond could approach approximately 98% indicated from the infrared absorption spectra. The micro-Raman spectrum reveals that the annealing treatment can improve the crystalline quality of Ib-type diamond characterized by a half width at full maximum at first order Raman peak, and therefore the annealed diamond crystals exhibit nearly the same properties as the natural IaA-type diamond stones of high quality in the Raman measurements.

Roles of Nucleation, Denucleation, Coarsening, and Aggregation Kinetics in Nanoparticle Preparations and Neurological Disease

Kinetic models for nucleation, denucleation, Ostwald ripening (OR), and nanoparticle (NP) aggregation are presented and discussed from a physicochemical standpoint, in terms of their role in current NP preparations. Each of the four solid-state mechanisms discussed predict a distinct time dependence for the evolution of the mean particle radius over time. Additionally, they each predict visually different particle size distributions (PSDs) under limiting steady-state (time-independent) conditions. While nucleation and denucleation represent phase transformation mechanisms, OR and NP aggregation do not. Thus, when modeling solid-state kinetics relevant to NP processing, either the time evolution of the mean particle radius or the fractional conversion data should be fit using appropriate models (discussed herein), without confusing/combining the two classes of models. Experimental data taken from the recent literature are used to demonstrate the usefulness of the models in real-world applications. Specifically, the following examples are discussed: the preparation of bismuth NPs, the synthesis of copper indium sulfide nanocrystals, and the aggregation of neurological proteins. Because the last process is found to obey reaction-limited colloid aggregation (RLCA) kinetics, potential connections between protein aggregation rates, the onset of neurological disease, and population lifespan dynamics are suggested by drawing a parallel between RLCA kinetics and Gompertz kinetics. The physical chemistry underpinning NP aggregation is investigated, and a detailed definition of the rate constant of aggregation, k(a), is put forth that provides insight into the origin of the activation energy barrier of aggregation. For the two nanocrystal preparations investigated, the initial kinetics are found to be well-described by the author's dispersive kinetic model for nucleation-and-growth, while the late-stage NP size evolution is dominated by OR. At intermediate times, it is thought that the two mechanisms both contribute to the NP growth, resulting in PSD focusing as discussed in a previous work [Skrdla, P. J. J. Phys. Chem. C2012, 116, 214-225]. On the basis of these two mechanisms, a synthetic procedure for obtaining monodisperse NP PSDs, of small and/or systematically targeted mean sizes, is proposed.

Does the hydrophobic attraction contribute to the interaction between colloidal silica spheres coagulated by an adsorbing cationic surfactant?

The character of the attractive interaction between hydrophobic surfaces, which is beyond the realm of the DLVO theory, is still under debate. The strength and extension of this non-DLVO, hydrophobic attraction (HA) between fixed macroscopic surfaces have been found to vary depending on the substrate type and, especially, the procedure adopted to render its surface hydrophobic. A related question is how HA manifests between hydrophobic colloidal particles in disperse systems. Here, the way of the particles’ hydrophobization is expected to be of utmost importance again. In the present article we compare experimentally determined absolute aggregation rate constants of uniform silica spheres at once hydrophobized and aggregated in water by a cationic surfactant (hexadecyltrimethylammonium bromide, CTAB) with their theoretical counterparts calculated from the DLVO theory in combination with hydrodynamic interactions and without any adjustable parameters. It has been found that both constants become identical when approaching a limiting magnitude in the specific situation of CTA+ cations adsorbed on the surface of silica colloids to such an extent that they compensate the negative charge and at the same time maximally hydrophobize the surface. Moreover, the limiting magnitude of the rate constants is comparable with that measured and predicted for silica colloids coagulated by K+ cations (KCl). It is concluded that the aggregation of hydrophobic silica particles initiated by the surfactant adsorption can be considered as the electrolytic coagulation in the fast (diffusion-limited) regime with no energy barrier due to the electrostatic repulsion, driven solely by the van der Walls attraction. Consequently, HA does not seem to influence the coagulation process at least in this colloidal system. Possible reasons of the disagreement of this finding with previous results of direct force experiments on similar surfactant-hydrophobized macroscopic systems are discussed.