Coupled Influence of Colloidal and Hydrodynamic Interactions on the RSA Dynamic Blocking Function for Particle Deposition onto Packed Spherical Collectors

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.     

Particle adsorption and deposition: role of electrostatic interactions

This work demonstrates how electrostatic interactions, described in terms of the classical DLVO theory, influence colloid particle deposition phenomena at solid/liquid interfaces. Electrostatic interactions governing particle adsorption in both non-polar and polar media (screened interactions) are discussed. Exact and approximate methods for calculating the interaction energy of spherical and non-spherical (anisotropic) particles are presented, including the Derjaguin method. Phenomenological transport equations governing particle deposition under the linear regime are discussed with the limiting analytical expressions for calculating initial flux. Non-linear adsorption regimes appearing for higher coverage of adsorbed particles are analysed. Various theoretical approaches are exposed, aimed at calculating blocking effects appearing due to the presence of adsorbed particles. The significant role of coupling between bulk transport and surface blocking is demonstrated. Experimental data obtained under well-defined transport conditions, such as diffusion and forced convection (impinging-jet cells), are reviewed. Various experimental techniques for detecting particles at interfaces are discussed, such as reflectometry, ellipsometry, streaming potential, atomic force microscopy, electron and optical microscopy, etc. The influence of ionic strength and flow rate on the initial particle deposition rate (limiting flux) is presented. The essential role of electrostatic interactions in particle deposition on heterogeneous surfaces is demonstrated. Experimental data pertinent to the high-coverage adsorption regime are also presented, especially the dependence of the maximum coverage of particles and proteins on the ionic strength. The influence of lateral electrostatic interactions on the structure of particle monolayers is elucidated, and the links between colloid and molecular systems are pointed out.     

Multiscale-linking simulation of irreversible colloidal deposition in the presence of DLVO interactions

An efficient multiscale-linking algorithm, based on the self-consistent integration of Brownian dynamics simulation of particle trajectories with the solution of the continuum-level conservation equation for particle concentration subject to an adaptive Neumann boundary condition that accounts for the blocking effect of deposition, is developed. The algorithm has been already validated in the case of deposition of noninteracting hard spheres [R.V. Magan, R. Sureshkumar, Multiscale Model. Simul. 2 (2004) 475]. In this study, the above algorithm is extended to incorporate particle interactions modeled by the DLVO theory. The simulations are used to identify a time scale at which the deposition process transitions from a power-law to an asymptotic regime. Detailed characterization of the two regimes is provided for a wide range of ionic strength, particle surface charge density, bulk volume fraction, and substrate potential values. The radial distribution functions obtained for various ionic strengths can be collapsed into a master curve when the radial distance is normalized with respect to a characteristic length scale of inter-particle repulsion. Moreover, simulation results suggest a rescaled, uniformly valid soft random sequential adsorption (RSA) model. Simulation results for the kinetics and monolayers structure compare favorably with experimental data, without the use of adjustable parameters. Comparison with other dynamic simulation techniques shows that while their predictions are qualitatively similar, notable quantitative differences exist especially for small ionic strengths.     

Multiscale simulation of irreversible deposition in presence of double layer interactions

Sequential lattice Monte Carlo simulations, in which the transition probabilities are derived from the discrete form of the continuum-level mass conservation law, are used to predict the morphology of colloidal deposits. The simulations account for particle-surface (P-S) and particle-particle (P-P) electrostatic and van der Waals interactions. Simulation results for maximum coverage for monolayer deposition are in quantitative agreement with the hard-sphere RSA jamming limit. Moreover, as reported in earlier studies, monolayer simulations in the absence of P-S interactions qualitatively predict the monotonic increases in fractional coverage with increasing ionic strength, characterized by the Debye screening length (kappa a). Monolayer simulations with P-S interactions show that the dependence of fractional coverage on kappa a is strongly influenced by the ratio of particle to surface potentials (Psi(p)/Psi(s)). P-S and P-P forces achieve their respective maximum at different values of kappa a leading to a nonmonotonic trend in surface coverage as a function of kappa a. These results indicate that the incorporation of P-S interactions into colloidal deposition studies allows more accurate interpretation of the experimental data. In multilayer deposition simulations, balance between long-ranged weak interactions and short-ranged strong interactions between P-P and P-S, coupled with physical screening effects, resulted in widely varying coverages with height of the deposit, ionic strength, and Psi(p)/Psi(s). Moreover, fractal dimension of the deposit ranged from approximately 1 (kappa a < 1) to 1.7 (kappa a > 1). Qualitative kinetic analysis showed widely varying deposition rates in different layers depending on Psi(p)/Psi(s) and ionic strength. The multilayer system approached the monolayer system in the limit kappa a--> infinity and Psi(p)/Psi(s)--> infinity.     

Biomimetic particles: optimization of phospholipid bilayer coverage on silica and colloid stabilization

The effect of ionic strength and pH on phosphatidylcholine (PC) adsorption from vesicles on silica nanoparticles was investigated over a range of NaCl concentrations (0.1-150 mM) at pH 6.3 and 7.4 from determination of adsorption isotherms, colloid stability, particle sizing, and zeta-potentials. At and above 10 mM ionic strength, pH 6.3, high-affinity adsorption isotherms with limiting adsorption indicative of one-bilayer deposition on each silica particle were obtained. At 10 mM ionic strength, adsorption isotherms indicated lower affinity between PC and silica at pH 7.4 than at pH 6.3, suggesting a role of hydrogen bonding between silanol on silica and phosphate on PC in promoting bilayer deposition at low pH. Under conditions where high affinity and bilayer deposition were achieved, silica sedimentation documented from photographs was absent, suggesting particle stabilization induced by bilayer coverage. However, at physiological (150 mM NaCl) or close to physiological ionic strength (140 mM NaCl), the large colloid stability similarly achieved at pH 6.3 or 7.4 suggested the major role of van der Waals attraction between the PC bilayer vesicle and silica particle in determining bilayer deposition. The effect of increasing ionic strength was increasing van der Waals attraction, which caused PC vesicle disruption with bilayer deposition and bilayer-induced silica stabilization.     

Atomic force microscopy study of the adsorption and electrostatic self-organization of poly(amidoamine) dendrimers on mica

The adsorption behavior of poly(amidoamine) dendrimers to mica surfaces was investigated as a function of ionic strength and pH. The conformation and lateral distribution of the adsorbed dendrimers of generations G8 and G10 were obtained ex situ by tapping mode atomic force microscopy (AFM). The deposition kinetics of the dendrimers was found to follow a diffusion-limited process. Fractional surface coverage and pair correlation functions of the adsorbed dendrimers were obtained from the AFM images. The data are interpreted in terms of the random sequential adsorption (RSA) model, where electrostatic repulsion due to overlapping double layers is considered. Although the general trends typical for an RSA-determined process are well-reproduced, quantitative agreement is lacking at low ionic strengths.     

High density silver nanoparticle monolayers produced by colloid self-assembly on polyelectrolyte supporting layers

A stable silver nanoparticle suspension was synthesized via the reduction of silver nitrate using sodium borohydride and sodium citrate. The particle's shape and size distribution were measured by various methods. The electrophoretic mobility measurements revealed that the zeta potential of particles was highly negative, increasing slightly with the ionic strength, from -52 mV for I=10(-5) M to -35 mV for I=3×10(-2) M (for pH=5.5). The zeta potential of mica modified by the adsorption of cationic polyelectrolytes: PEI and PAH was also determined using the streaming potential measurements. The modified mica sheets were used as substrates for particle monolayers formed via colloid self assembly. The kinetics of this process, proceeding under diffusion-controlled transport conditions, was quantitatively evaluated by a direct enumeration of particles using the AFM and SEM techniques. Both the kinetics of particle deposition and the maximum surface concentration were determined. From the slope of the initial deposition rates, the equivalent diameter of particles was determined to be 16 nm, in agreement with previous measurements. Based on this finding, an efficient method of determining particle size in suspension was proposed. It was also demonstrated that for higher ionic strengths, the maximum coverage of particle monolayers on PAH modified mica exceeded 0.39. The kinetic data were quantitatively interpreted in terms of the random sequential adsorption (RSA) model using the effective hard particle concept.     

Blocking and ripening of colloids in porous media and their implications for bacterial transport

A model accounting for the dynamics of colloid deposition in porous media was developed and applied to systems containing similarly charged particles and collectors. Colloid breakthrough and intracolumn retention data confirmed that blocking reduced overall colloidal adhesion to soil. The surface coverage at which blocking occurred varied for the type of colloid, as shown by changes in the clean-bed collision efficiency, _0, and the excluded area parameter, β. Excluded area parameters were relatively high due to unfavorable interactions between particles and collectors, and ranged from 11.5 for one bacterium (Pseudomonas putida KT2442) to 13.7 and 24.1 for carboxylated latex microspheres with differing degrees of charged groups on their surfaces. Differences in β values for the three colloids were correlated with electrophoretic mobility, with the most negatively charged colloid (carboxylated latex; CL microspheres) having the highest β. No correlation between hydrophobicity and ₀ or β was found. Besides using colloidal particles capable of blocking, the addition of chemical additives to the soil has been suggested as a means for reducing attachment of colloids to porous media. Dextran addition caused an order-of-magnitude reduction in the overall (for carboxylated-modified latex; CMLs). This reduction was not attributed to blocking, but to the sorption of dextran to the soil which lowered ₀. The filtration-based numerical model used to fit the ₀ and β parameters was used to demonstrate that blocking could result in significantly enhanced bacterial transport in field situations.     

Molecular dynamics simulations of multilayer polyelectrolyte films: effect of electrostatic and short-range interactions

The effect of the strength of electrostatic and short-range interactions on the multilayer assembly of oppositely charged polyelectrolytes at a charged substrate was studied by molecular dynamics simulations. The multilayer buildup was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in polymer surface coverage after the first few deposition steps. Furthermore, there is substantial intermixing between chains adsorbed during different deposition steps. We show that the polymer surface coverage and multilayer structure are each strongly influenced by the strength of electrostatic and short-range interactions.     

Adsorption and aggregation of cationic amphiphilic polyelectrolytes on silica

The adsorption of two cationic amphiphilic polyelectrolytes, which are copolymers of two charged monomers, triethyl(vinylbenzyl)ammonium chloride and dimethyldodecyl(vinylbenzyl)ammonium chloride (which is the amphiphilic one) with different contents of amphiphilic groups (40% (40DT) and 80% (80DT)), onto the hydrophilic silica-aqueous solution interface has been studied by in situ null ellipsometry and tapping mode atomic force microscopy (AFM). Adsorption isotherms for both polyelectrolytes were obtained at 25 degrees C and at different ionic strengths, and the adsorption kinetics was also investigated. At low ionic strength, thin adsorbed layers were observed for both polyelectrolytes. The adsorption increases with polymer concentration and reaches, in most cases, a plateau at a concentration below 50 ppm. For the 80DT polymer, at higher ionic strength, an association into aggregates occurs at concentrations at and above 50 ppm. The aggregates were observed directly by AFM at the surface, and by dynamic light scattering in the solution. The adsorption data for this case demonstrated multilayer formation, which correlates well with the increase in viscosity with the ionic strength observed for 80DT.     

Transport and retention of TiO2 rutile nanoparticles in saturated porous media under low-ionic-strength conditions: measurements and mechanisms

The mechanisms governing the transport and retention kinetics of titanium dioxide (TiO(2), rutile) nanoparticle (NP) aggregates were investigated in saturated porous media. Experiments were carried out under a range of well-controlled ionic strength (from DI water up to 1 mM) and ion valence (NaCl vs CaCl(2)) comparable to the low end of environmentally relevant solution chemistry conditions. Solution chemistry was found to have a marked effect on the electrokinetic properties of NP aggregates and the sand and on the resulting extent of NP aggregate transport and retention in the porous media. Comparable transport and retention patterns were observed for NP aggregates in both NaCl and CaCl(2) solutions but at much lower ionic strength with CaCl(2). Transport experimental results showed temporal and spatial variations of NP aggregate deposition in the column. Specifically, the breakthrough curves displayed a transition from blocking to ripening shapes, and the NP retention profiles exhibited a shift of the maximum NP retention segment from the end toward the entrance of the column gradually with increasing ionic strength. Additionally, the deposition rates of the NP aggregates in both KCl and CaCl(2) solutions increased with ionic strength, a trend consistent with traditional Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Upon close examination of the results, it was found that the characteristics of the obtained transport breakthrough curves closely followed the general trends predicted by the DLVO interaction-energy calculations. However, the obtained NP retention profiles were found to deviate severely from the theory. We propose that a NP aggregate reconformation through collision between NP aggregates and sand grains reduced the repulsive interaction energies of NP-NP and NP-sand surfaces, consequently accelerating NP deposition with transport distance and facilitating approaching NP deposition onto NPs that had already been deposited. It is further suggested that TiO(2) NP transport and retention are determined by the combined influence of NP aggregate reconformation associated with solution chemistry, travel distance, and DLVO interactions of the system.     

Resolving the coupled effects of hydrodynamics and DLVO forces on colloid attachment in porous media

Transport of colloidal particles in porous media is governed by the rate at which the colloids strike and stick to collector surfaces. Classic filtration theory has considered the influence of system hydrodynamics on determining the rate at which colloids strike collector surfaces, but has neglected the influence of hydrodynamic forces in the calculation of the collision efficiency. Computational simulations based on the sphere-in-cell model were conducted that considered the influence of hydrodynamic and Derjaguin-Landau-Verwey-Overbeek (DLVO) forces on colloid attachment to collectors of various shape and size. Our analysis indicated that hydrodynamic and DLVO forces and collector shape and size significantly influenced the colloid collision efficiency. Colloid attachment was only possible on regions of the collector where the torque from hydrodynamic shear acting on colloids adjacent to collector surfaces was less than the adhesive (DLVO) torque that resists detachment. The fraction of the collector surface area on which attachment was possible increased with solution ionic strength, collector size, and decreasing flow velocity. Simulations demonstrated that quantitative evaluation of colloid transport through porous media will require nontraditional approaches that account for hydrodynamic and DLVO forces as well as collector shape and size.     

Theoretical analysis of factors affecting the formation and stability of multilayered colloidal dispersions

A mathematical analysis of the major factors influencing the formation and stability of colloidal dispersions containing spherical particles surrounded by multilayered polymeric interfacial membranes formed by the layer-by-layer electrostatic deposition technique is carried out. The mathematical model assumes that (i) the colloidal dispersion initially consists of a mixture of electrically charged monodisperse spherical particles and oppositely charged polymer molecules, (ii) the adsorption of polymer molecules to the particle surfaces is diffusion-limited, and (iii) the dominant particle-particle collision mechanism is Brownian motion. This approach was used to produce stability maps that highlight conditions under which bridging flocculation, multilayer formation, or depletion flocculation occurs. The stability maps are derived from calculations of the critical polymer concentrations required to (i) saturate the particle surfaces (C(Sat)), (ii) ensure that polymer adsorption is faster than particle collisions (C(Ads)), and (iii) promote depletion flocculation (C(Dep)). In addition, the influence of interfacial properties on the stability of multilayer colloidal dispersions was assessed by calculating the colloidal interactions between the coated particles (i.e., van der Waals, electrostatic, steric, and depletion). These calculations indicated that the major factors are the interfacial charge and composition rather than the interfacial thickness. This article provides useful insights into the factors affecting the formation of stable multilayer colloidal dispersions.     

Role of interaction forces in controlling the stability and polishing performance of CMP slurries

Chemical mechanical polishing (CMP) is an essential step in metal and dielectric planarization in multilayer microelectronic device fabrication. In the CMP process it is necessary to minimize the extent of surface defect formation while maintaining good planarity and optimal material removal rates. These requirements are met through the control of chemical and mechanical interactions during the polishing process by engineering the slurry chemistry, particulate properties, and stability. In this study, the performance of surfactant-stabilized silica CMP slurries at high pH and high ionic strengths are investigated with particular emphasis on the particle-particle and particle-substrate interactions. It is shown that for the design of consistently high performing slurries, stability of abrasive particles must be achieved under the dynamic processing conditions of CMP while maintaining sufficient pad-particle-wafer interactions.     

Thin adsorbed films of a strong cationic polyelectrolyte on silica substrates

The adsorption of poly(diallyldimethyl ammonium chloride) (DADMAC) on planar silica substrates was examined as a function of ionic strength and pH. The study was carried out with reflectometry in an impinging-jet cell and complemented by atomic force microscopy (AFM) and ellipsometry investigations. The adsorption process is initially transport limited, whereby the adsorption rate increases somewhat with increasing ionic strength. This effect is caused by a simultaneous decrease of the hydrodynamic radius of the polymer. After a transient period, the adsorption process saturates and leads to an adsorption plateau. The plateau value increases strongly with increasing ionic strength. This increase can be explained by progressive screening of the electrostatic repulsion between the adsorbing polyelectrolyte chains, as can be rationalized by a random sequential adsorption (RSA) model. The adsorbed amount further increases with increasing pH, and this effect is probably caused by the corresponding increase of the surface charge of the silica substrate.     

Kinetics of localized adsorption of colloid particles

Methods of analyzing localized adsorption of colloid particles at solid/liquid interfaces were extensively reviewed. First, the initial adsorption fluxes calculated using the Levich-Smoluchowski approximation were discussed. The uniformly, and nonuniformly accessible interfaces were distinguished and the superiority of the former in experimental studies was pointed out. A criterion was introduced for estimating the relative significance of the bulk transfer and surface adsorption steps. It was shown that for the majority of experimental and practical situations the surface mass balance equation can be decoupled from the bulk continuity equation. Thus, in due course attention was focused on theoretical and experimental methods of determining the surface blocking parameter B. It was shown that for low and moderate surface concentration range the statistical mechanic approach can be effectively used for predicting B. By introducing the equivalent hard sphere radius r¹ it became possible to analyze quantitatively blocking effects of interacting as well as nonspherical particles. The analytical solutions were compared with numerical simulation methods valid for the entire range of surface concentrations. The Monte-Carlo algorithm based on the random sequential adsorption (RSA) concept was compared with the sequential Brownian-Dynamics (SBD) method. Theoretical results obtained using these approaches were extensively discussed especially the role of repulsive electrostatic interaction among adsorbing particles. It was shown that these interactions diminish profoundly both the particle adsorption rate and the maximum surface concentration of particles forming “random” monolayers. When the electrostatic forces were operating (lower ionic strength) two distinctive adsorption regimes were predicted (i) fast Langmuir-type adsorption for short times and then (ii) very slow RSA-type approach to the maximum surface concentrations. As discussed such long lasting transient adsorption states could erroneously be interpreted as equilibrium adsorption isotherms. Then, the indirect and direct experimental methods aimed at a quantitative determination of particle adsorption kinetics were described. Illustrative experimental results performed for model latex suspensions were evoked. A satisfactory agreement with theoretical predictions was found for a variety of important physicochemical parameters studied. The RSA approach was found useful for describing particle adsorption kinetics for low and moderate surface concentrations in the case when the flow induced effects could be neglected. On the other hand, the SBD method was found of general validity especially in describing the hydrodynamic scattering effect observed experimentally for higher shear rates. Finally, the theoretical and experimental results concerning structure formation in adsorption processes were presented. The experimentally measured two-dimensional (2D) pair correlation function g12 of adsorbed particles suggested a liquid-like short range ordering occurring for larger surface concentrations. The extent of the 2D ordering was influenced by the adsorption mechanisms of particles, especially the presence of external field of forces.     

Combined effect of spin speed and ionic strength on polyelectrolyte spin assembly

Polyelectrolyte spin assembly (PSA) of multilayers is a sequential process featuring adsorption of oppositely charged polyelectrolytes from dilute solutions undergoing spin-coating flow. Here, we report on the dependence of PSA multilayer buildup of poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride) on solution ionic strength and spin speed. We observed that at a given spin speed, the PSA coating growth rate (thickness/bilayer) and polymer surface coverage shows a nonmonotonic dependence on salt concentration, first increasing and then decreasing with increasing solution ionic strength. This is argued to be a manifestation of two competing mechanisms responsible for the layer formation. At low salt concentrations, the electrostatic interactions control the multilayer assembly process, while at high salt concentrations it is dominated by shear flow. We explain this nonmonotonic behavior in the framework of a Flory-like theory of multilayer formation from polyelectrolyte solution under shear flow. Additionally, the PSA process led to multilayer coatings with a radial dependence on thickness at lower spin speed in the shear-dominated regime. On increasing spin speed, such radial dependence subsided, eventually leading to uniform coatings by planarization. The surface topography of the multilayered coatings adsorbed at salt concentration less than 0.1 M was flat and featureless for all studied spin speeds. Unique morphological features in the films were formed at salt concentration higher than 0.1 M, the size of which depended on the spin speed and solution ionic strength.     

Adsorption behavior of DODAB/DPPC vesicles on silica

The interaction between composite dipalmitoylphosphatidylcholine (DPPC)/dioctadecyldimethylammonium bromide (DODAB) bilayer vesicles in the gel state and silica is investigated over the 0-20% DODAB range from determination of adsorption curves, silica sedimentation, particle sizing and zeta-potentials. At 1 mg/mL silica, 0% DODAB, pH 6.3, over the 0-150 mM NaCl range of ionic strengths, high affinity adsorption curves were barely affected by ionic strength and all of them exhibited limiting adsorption values above the level expected for single bilayer deposition. At 1 mg/mL silica, 2% DODAB, pH 6.3 and 1 mM NaCl, high affinity adsorption curves fortuitously presented limiting adsorption indicative of one bilayer deposition on each silica particle. At %DODAB<2% or %DODAB>2%, limiting adsorption was above and below the level expected for bilayer deposition, respectively. Increasing %DODAB in the vesicle composition negatively modulated the limiting adsorption on silica despite the increasing surface charge on vesicles and electrostatic attraction between vesicles and particles. The results point out the difficulty of closed vesicle disruption (required for bilayer deposition from vesicles) when the bilayer is tightly packed in the rigid gel state and might be of interest for analytical applications of immobilized vesicles on silica.     

Adsorption of poly(amido amine) (PAMAM) dendrimers on silica: importance of electrostatic three-body attraction

Adsorption of poly(amido amine) (PAMAM) dendrimers to silicon oxide surfaces was studied as a function of pH, ionic strength, and dendrimer generation. By combining optical reflectometry and atomic force microscopy (AFM), the adsorbed layers can be fully characterized and an unequivocal determination of the adsorbed mass becomes possible. For early stages, the adsorption process is transport limited and of first order with respect to the dendrimer solution concentration. For later stages, the surface saturates and the adsorbed dendrimers form loose but correlated liquidlike surface structures. This correlation is evidenced by a peak in the pair correlation function determined by AFM. The maximum adsorbed amount increases with increasing ionic strength and pH. The increase with the ionic strength is explained by the random sequential adsorption (RSA) model and electrostatic repulsion between the dendrimers. The adsorbing dendrimers interact by the repulsive screened Coulomb potential, whose range decreases with increasing ionic strength and thus leads to increasing adsorbed densities. The pH increase is interpreted as an effect of the substrate and is quantitatively explained by the extended three-body RSA model. This model stipulates the importance of a three-body interaction acting between two adsorbing dendrimers and the charged substrate. The presence of the charged substrate weakens the repulsion between the adsorbing dendrimers and thus leads to higher surface densities. This effect can be interpreted as an additional attractive three-body interaction, which acts in addition to the usual two-body repulsion and originates from the additional screening of the Coulomb repulsion by the counterions accumulating in the diffuse layer.     

Comparative analysis of the activity coefficients for the system NaBr+NaFormate+H2O at 25°C by the methods of scatchard,pitzer and lim

Activity coefficients for NaBr in the system NaBr+NaFormate+H₂O at 25°C were determined from emf measurements at different total ionic strengths. At each total ionic strength, the measurements were carried out at different Na-Formate/NaBr ionic strength ratios. The experimental activity coefficients were comparatively analyzed using Scatchard's, Pitzer's and Lim's methods. Although all these models can be successfully applied to the analysis of this mixed system, the All Mixing Coefficients (LA) and Consistency Test (LT) models lead to better fittings than the others.