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.     

Self-consistent field modeling of non-ionic surfactants at the silica-water interface: incorporating molecular detail

We have constructed a model to predict the properties of non-ionic (alkyl-ethylene oxide) (C(n)E(m)) surfactants, both in aqueous solutions and near a silica surface, based upon the self-consistent field theory using the Scheutjens-Fleer discretisation scheme. The system has the pH and the ionic strength as additional control parameters. At high ionic strength, the solvent quality for the surfactant head groups is affected, which changes both the bulk and the adsorption behavior of the surfactant. For example, with increasing ionic strength, the CMC drops and the aggregation increases. Surfactants adsorb above the critical surface association concentration (CSAC). The CSAC is a function of the surfactant and the surface properties. Therefore, the CSAC varies with both the ionic strength and the pH. We predict that with increasing ionic strength, the CSAC will first slightly increase but then drop substantially. The charge on the surface is pH dependent, and as the head groups bind through H-bonding to the silanol groups, the CSAC increases with increasing pH. We focus on adsorption/desorption transitions for the surfactants and compare these to the experimental data. Both the equilibrium predictions and the consequences for the kinetics of adsorption follow experimental findings. Our results show that molecularly realistic models can reveal a much richer interfacial behavior than anticipated from more generic models.     

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.     

Th(IV) adsorption on alumina: effects of contact time, pH, ionic strength and phosphate

Adsorption of Th(IV) (total concentration, 10(-5)-10(-4) mol/L) was studied by a batch technique. The effects of pH, ionic strength, contact time, and phosphate on the adsorption of Th(IV) onto alumina were investigated. Adsorption isotherms of Th(IV) on alumina at approximately constant pH and three ionic strengths (0.05, 0.1, 0.5 mol/L KNO3) were determined. It was found that the pH values of aqueous solutions of both the Th(IV)-alumina and phosphate-alumina adsorption systems increase with increasing contact time, respectively. Adsorption of Th(IV) on alumina steeply increases with increasing pH from 1 to 4.5 and the adsorption edge consists of three regions. The phosphate added clearly enhances Th(IV) adsorption in the pH range 1-4. From the adsorption isotherms at approximately constant pH and three different ionic strengths, a reduced ionic strength effect was observed and is contradictory to the insensitive effect obtained from the adsorption edges on three oxides of Fe, Al, and Si at different ionic strengths. Compared with the adsorption edges at different ionic strengths, the adsorption isotherms at approximately constant pH and different ionic strengths are more advantageous in the investigation of ionic strength effect. The significantly positive effect of phosphate on Th(IV) adsorption onto alumina was attributed to strong surface binding of phosphate on alumina and the subsequent formation of ternary surface complexes involving Th(IV) and phosphate.     

Controlled association in suspensions of charged nanoparticles with a weak polyelectrolyte

The properties of high-pH suspensions of mixtures of silica with low-molecular-weight samples of the water-soluble polymer polyethylenimine (PEI) have been studied. At pH > 10 and low ionic strength, silica nanoparticles are stabilized by a negative surface charge, and PEI has only a very low positive charge. The adsorption of PEI induces a localized positive charge on the segments of polymer closest to the silica surface. The parts of the molecule furthest away from the surface have little charge because of the high pH of the medium. The polymer-covered particle remains negatively charged, imparting some electrostatic stabilization. Suspensions of silica and low-molecular-weight PEI are low-viscosity fluids immediately after mixing, but aggregation occurs leading to the eventual gelation (or sedimentation at lower concentrations) of these mixtures, indicating colloidal instability. The gelation time passes through a minimum with increasing surface coverage. The rate of gelation increases exponentially with molecular weight: for molecular weight > or = 10,000 Da PEI, the instability is so severe that uniform suspensions cannot be produced using simple mixing techniques. The gelation rates increase rapidly with temperature, ionic strength, and reduction in pH. The rate of gelation increases with increasing particle concentration at low surface coverage but decreases at high coverage as a consequence of a small increase in pH. Gels are broken by application of high shear into aggregates that re-gel more rapidly than the original discrete coated particles.     

Energetics of protein adsorption on amine-functionalized mesostructured cellular foam silica

The energetics of lysozyme adsorption on aminopropyl-grafted MCF silica (MCF-NH2) are compared to the trends observed during lysozyme adsorption on native MCF silica using flow microcalorimetry (FMC). Surface modification on MCF silica affects adsorption energetics significantly. All thermograms consist of two initial exothermic peaks and one later endothermic peak, but the heat signal trends of MCF-NH2 are opposite from those observed for adsorption onto native MCF silica in salt solutions of sodium acetate and sodium sulfate. At low ionic strength (0.01 M), LYS adsorption onto MCF-NH2 was accompanied by a large exotherm followed by a desorption endotherm. With increasing ionic strength (0.1 and 3.01 M), the magnitude of the thermal signal decreased and the total process became less exothermic. Also a higher protein loading of 14 μmol g(-1) was obtained at low ionic strength in batch adsorption isotherm measurements. Taken together, the FMC thermograms and batch adsorption isotherms reveal that MCF-NH2 has the nature of an ion exchange adsorbent, even though lysozyme and the aminopropyl ligands have like net charges at the adsorption pH. Reduced electrostatic interaction, reduced Debye length, and increased adsorption-site competition attenuate exothermicity at higher ionic strengths. Thermograms from flow microcalorimetry (FMC) give rich insight into the mechanisms of protein adsorption. A two-step adsorption mechanism is proposed in which negatively charged surface amino acid side chains on the lysozyme surface make an initial attachment to surface aminopropyl ligands by electrostatic interaction (low ionic strength) or van der Waals interaction (high ionic strength). Secondary attachments take place between protruding amino acid side chains and silanol groups on the silica surface. The reduced secondary adsorption heat is attributed to the inhibitory effect of the enhanced steric barrier of aminopropyl group on MCF silica.     

Polyelectrolyte adsorption on charged surfaces: study by electrokinetic measurements

In order to describe the influence of cationic polyelectrolytes on flocculation of disperse systems the adsorption of poly (diallyldimethylammonium chloride) (PDADMAC) onto silica, mica and acidic polymer latex was investigated. The plateau value of the adsorption isotherms grows with increasing surface charge density of the substrates and electrolyte concentration. The adsorbed layer of the polycation was characterized by zeta potential measurements with KCl solutions of constant ionic strength and varied pH. The zero point of the charge as well as the shape of the zeta potential–pH plot depends on the coverage of the surface with polycations. For fully covered substrates the zero point of the charge as well as the pK_A and pK_B values calculated by a stochastic search programme are independent of the substrate. Maximum flocculation was observed at about 30% of the plateau value of the adsorption isotherms.     

Self-consistent field modeling of poly(ethylene oxide) adsorption onto silica: the multiple roles of electrolytes

In technological applications, it is increasingly important to understand and predict interfacial phenomena. Using a self-consistent field model within the Scheutjens-Fleer discretization scheme, we have developed a molecularly realistic model of the adsorption of poly(ethylene oxide) (PEO) onto silica from an aqueous solution. The bulk solution consists of water, PEO, 1:1 electrolyte, protons, and hydroxyl ions. The solvent quality is good below and becomes poor above a threshold ionic strength (of around 1 M). The silica surface features a number of silanol groups that have an affinity for PEO (by means of H bonding) when these groups are not dissociated. In line with experimental data, the surface changes from adsorbing to nonadsorbing at a sufficiently high pH. Even though PEO is uncharged, there is a complex effect of the ionic strength on the interfacial characteristics. For example, we report a non-monotonic behavior of the adsorbed amount as a function of ionic strength. Going from a low to a high ionic strength at a neutral or slightly basic pH, the adsorbed amount initially decreases as the surface affinity decreases (caused by the reduction of adsorption sites when, as a result of screening, the surface is increasingly charged) but then increases as a result of a reduction in solvent quality. These results indicate that molecularly realistic models can reveal much richer interfacial behavior than anticipated from generic models. The predictions follow many experimental findings.     

Am(III) adsorption on oxides of aluminium and silicon: effects of humic substances,pH, and ionic strength

The adsorption of Am(III) (total concentration 10(-9) mol/l) on alumina, silica, and hematite was studied by a batch technique. The effects of pH, ionic strength, and humic substances on the adsorption of Am(III) on alumina and silica were investigated, and the adsorption isotherms of Am(III) on alumina and silica at different pH values were determined. It was found that compared with the adsorption of Am(III) on alumina, the adsorbability of silica on the basis of mass is less, the relative adsorption rate on silica is slower, the sensitivity of adsorption on silica to ionic strength is less, the dependence of adsorption on silica on pH is gentler, and consequently that the adsorption characteristics of Am(III) on alumina and silica are distinctly different. The negative effect of fulvic acid on the adsorption on silica and the positive effect of humic acid on the adsorption on alumina were found. In contrast to the Am(III) adsorption on alumina and silica, a tremendously high adsorbability of Am(III) on hematite was found. The sequence of adsorbabilities of Am(III) on the basis of mass is Fe2O3 > Al2O3 > SiO2.     

The adsorption-desorption process of bovine serum albumin on carbon nanotubes

The aim of this work is to study the adsorption-desorption process of bovine serum albumin (BSA) on carbon nanotubes (CNT) by reflectometry. The effect of the surface properties was analyzed by comparing the behavior of BSA on silica. The experiments were performed by reflectometry at different BSA concentrations, at pH 3.0, 4.8, and 7.0 and at two ionic strengths. Protein desorption was induced by either dilution with buffer or the addition of SDS. The initial adsorption rate is controlled by the attachment of BSA molecules to the surface, and strongly diminishes at pH 7. Adsorption isotherms reflect the high affinity of BSA for both sorbent surfaces and reach well-defined plateau values that depend on the pH, being the highest at pH 4.8 on CNT. Experiments performed at different ionic strengths (NaCl added) showed a less pronounced effect. Dilution does not induce desorption on either surface however, the addition of SDS removes protein only from the silica surface.     

Adsorption of polyelectrolyte-nanoparticle systems on silica: influence of ionic strength

In this work the effect of ionic strength on the adsorption behavior of cationic polyelectrolyte (acrylamide-acrylamidopropyltrimethylammonium chloride) and negatively charged silica particles has been studied by means of ellipsometry. The adsorption of the polyelectrolyte was observed to increase with increasing salt concentration, a behavior typical for polyelectrolytes with a screening-reduced solvency and a nonelectrostatic affinity for the surface. A similar dependence on the ionic strength was observed when studying the electrolyte effect on the nanoparticle adsorption to the preadsorbed polyelectrolyte film, suggesting that the polyelectrolyte surface conformations largely govern the binding capacity of the particles to the surface.     

The impact of ionic strength and background electrolyte on pH measurements in metal ion adsorption experiments

Our understanding of metal ion adsorption to clay minerals has progressed significantly over the past several decades, and theories have been promulgated to describe and predict the impacts of pH, ionic strength, and background solution composition on the extent of adsorption. Studies evaluating the effects of ionic strength on adsorption typically employ a broad range of background electrolyte concentrations. Measurement of pH in these systems can be inaccurate when pH values are measured with liquid junction pH probes calibrated with standard buffers due to changes in the liquid junction potential between standard, low ionic strength (0.05 M) buffers and high ionic strength solutions (>0.1 M). The objective of this research is to determine the extent of the error in pH values measured at high ionic strength, and to develop an approach for accurately measuring pH over a range of ionic strengths using a combined pH electrode. To achieve this objective, the adsorption of cobalt (10(-5) M) onto gibbsite (10 g/L) from various electrolyte solutions (0.01-1 M) was studied. The pH measurements were determined from calibrations with standard buffers and ionic strength corrected buffer calibrations. The results show a significant effect of the aqueous solution background electrolyte anion and ionic strength on pH measurement. The 0.5 and 1 M ionic strength metal ion adsorption edges shifted to lower pH with increasing ionic strength when pH was calibrated with standard buffers whereas no shift in the adsorption edges was observed when calibrated with ionic strength corrected buffers. Therefore, to obtain an accurate pH measurement, pH calibration should contain the same electrolyte and ionic strength as the samples.     

Adsorption studies of cationic starch onto quartz surface through an electrode-separated piezoelectric sensor

In the construction of an electrode-separated piezoelectric sensor (ESPS), the quartz surface is in direct contact with the liquid phase. The negatively charged quartz crystal surface can adsorb cationic starch. This adsorption process was in situ monitored from the frequency shift of the ESPS. It was shown that the adsorption of cationic starch onto the quartz surface is reversible with respect the dilution of the bulk phase. The adsorption behavior can be described by Langmuir model. The adsorption density and kinetics parameters were estimated from the frequency responses of the ESPS. The influence of pH and ionic strength on adsorption parameters was investigated. It was shown that the influence of pH on the adsorption rate was slight. With increasing ionic strength, the rate constants for adsorption and desorption increase, but the adsorption equilibrium constant and saturation adsorption density decrease. The adsorption equilibrium constant and adsorption density reach a maximum in buffer of pH 10.     

An in situ FTIR-ATR study of polyacrylate adsorbed onto hematite at high pH and high ionic strength

FTIR-ATR was used to examine in situ the interaction of polyacrylate and hematite at pH 13. Static light scattering and mobility measurements were used to assess solution polyacrylate dimensions and hematite surface charge, respectively. Polyacrylate adsorption occurred only with the addition of electrolyte (e.g., NaCl), and it was found that excess cations, up to approximately 1 M, facilitated adsorption, above which the effect was found to plateau. At pH 13 and at low ionic strength, adsorption of polyacrylate onto hematite is facilitated by cations in solution shielding both the negative acrylate functionality of the polymer and the negative hematite surface. The shielding of the hematite surface continues to increase with increasing salt concentration up to a measured 3 M. Similarly, the shielding of the polymer increased with electrolyte concentration up to approximately 1 M salt, beyond which no further increase in shielding was observed. At this concentration the polymer assumes a finite minimum size in solution that ultimately limits the amount adsorbed. The dimension of the polymer in solution was found to be independent of monovalent cation type. Thus, at high pH and high ionic strength adsorption is determined by the degree of hematite surface charge reduction. The cation-hematite surface interaction was found to be specific, with lithium leading to greater polyacrylate adsorption than sodium, which was followed by cesium. The stronger affinity of lithium for the hematite surface over sodium and cesium is indicative of the inverse lyotropic adsorption series and has been rationalized in the past by the "structure-making-structure-breaking" model. These results provide a useful insight into the likely adsorption mechanism for polyacrylate flocculants at high pH and ionic strength onto residues in the Bayer processing of bauxite.     

Diffusion into and adsorption of polyethylenimine on porous silica gel

The polyethyleneimine (PEI)–water–silica gel absorption system was used as a model system to investigate the relationship between diffusion into the porous structure, adsorption rate, and molecular weight of the polymer. Three silica gels, Porasil A, B, and and C having a range of characteristic porosity were used as adsorbents. Adsorption of PEI on Porasil C, which has the majority of its pores much larger than the dimensions of the adsorbate molecule, increased initially with increased molecular weight but became nearly constant at higher molecular weight. Little increase in adsorption occurred for this silica gel with increased ionic strength or with increased pH between 9.5 and 10.8. In contrast, adsorption increased sharply with increased ionic strength and for the same pH range on Porasil A. Molecular weight dependence was reversed. Adsorption decreased with increased molecular weight on Porasil A. In this case, the molecular size of PEI investigated was the same as the majority of pore apertures in the adsorbent. Solution environments (i.e., pH and ionic strength) that decrease the size of the PEI molecule and its affinity for the anionic silica gel surface, thus enabling it to more readily diffuse into the smaller porous regions of the adsorbent, are the apparent causes of the very large adsorption increase. Electrostatic repulsion between PEI molecules do not appear greatly to affect adsorption. Similar adsorption behavior has been reported in the literature for the PEI–cellulosic fiber adsorption system. Maximum adsorption on Porasil A occurred at pH 10.8, the same maximum generally reported for adsorption of PEI on cellulosic fibers. In this case, the silica gel (Porasil A) was found to have a pore size distribution and specific surface area of the same magnitude as cellulosic fibers prepared in the expanded state.     

Effect of polyelectrolytes and polyelectrolyte mixtures on the electrokinetic potential of dispersed particles. 2. Electrokinetic potential of silica particles in electrolyte, polyelectrolyte and polyelectrolyte mixtures solutions

The effect pH, ionic strength (KCl concentration), weakly and medium charged anionic and cationic polyelectrolytes (PEs) as well as their binary mixtures on the electrokinetic potential of silica particles as a function of the polyelectrolyte/mixture dose, its composition, charge density (CD) of the PE, and way of adding the polymers to the suspension has been studied. It has been shown that addition of increasing amount of anionic PEs increases the absolute value of the negative zeta-potential of particles at pH > pH isoelectric point (IEP = 2.5); this increase is stronger the charge density of the polyelectrolyte is higher. Adsorption of cationic polyelectrolytes at these pH values gives a significant decrease in the negative ζ-potential and overcharging the particles; changes in the ζ-potential are more pronounced for PE samples with higher CD. In mixtures of cationic and anionic PE at pH > pHIEP, the ζ-potential of particles is determined by the adsorbed amount of the anionic polymer independently of the CD of PEs, the mixture composition and the sequence of addition of the mixture components. Unexpectedly, the ζ-potential of silica at pH = 2.1, i.e. < pHIEP, turned out to be positive in the presence of both anionic PE and cationic + anionic PE mixtures. This is explained by formation (and adsorption onto positively charged silica surface) of pseudo-cationic PEs from anionic ones due to transfer of protons from the solution to the amino-group of the anionic polymer. Considerations about the role of coulombic and non-coulombic forces in the mechanism of PE adsorption are presented.     

Adsorption of poly(styrene sulfonate) of different molecular weights on alpha-alumina: effect of added sodium dodecyl sulfate

The adsorption of poly(styrene sulfonate), PSS, of different molecular weights (70,000, 500,000, and 1,000,000 mol/kg), from aqueous solutions on alpha-alumina has been investigated. PSS of the lower molecular weight adsorbs less than the others whose adsorption isotherms overlap. The adsorption is found to increase with increasing ionic strength of the solutions indicating that both electrostatic and non-electrostatic contributions are involved in the adsorption process. Upon addition of the anionic surfactant, sodium dodecyl sulfate, SDS, PSS is found to adsorb less the more SDS added. SDS is found to be preferentially adsorbed as shown both from the simultaneous adsorption of the components and also from the sequential adsorption process where SDS in all cases displaces preadsorbed PSS from the solid surface. The displacement of preadsorbed polyelectrolyte by surfactant is a very slow process and the displacement is less pronounced as the molecular mass of the polyelectrolyte increases indicating the fewer number of contact points to the surface. This is further underlined by the effect on the displacement of PSS by SDS upon increasing the ionic strength of the solutions.     

Adsorption of zwitterionic drugs onto oxidized cellulose

Adsorption of zwitterionic drugs (beta-lactam antibiotics and amino acids) onto samples of oxidized cellulose (OC) with various carboxyl contents and structural characteristics from aqueous and water/alcohol solutions was investigated. The adsorption process can be described according to the theory of localized stoichiometric adsorption and represented by Langmuir isotherms. It was established that the constants of interfacial distribution mainly increase with increased relative sorbate hydrophobicity. The dependencies of adsorption on pH of equilibrium drug solution have a maximum at pH 3-3.5, which is caused by peculiarities of dissociation of OC and sorbates. The drug uptake is shown to increase with an increase of alcohol mole fraction in the solution and transfer to the binary water/isopropanol from water/ethanol solutions. The dominant contribution to the increase of uptake is the desolvation of ionic groups of zwitterions in the solution, which increases with increased alcohol content. The degree of crystallinity of the sorbent has no considerable effect on drug adsorption from aqueous solutions. In water/alcohol solutions the adsorption of drugs by OC samples with similar exchange capacity increases with reducted uniformity of carboxylic group distribution in the volume of the polymer, which is connected with increased accessibility of carboxylic groups for sorbate molecules.     

Adsorption of atrazine on soils: model study

The adsorption of the widely used herbicide atrazine onto three model inorganic soil components (silica gel, gamma-alumina, and calcite (CaCO(3)) was investigated in a series of batch experiments in which the aqueous phase equilibrated with the solid, under different solution conditions. Atrazine did not show discernible adsorption on gamma-alumina (theta=25 degrees C, 3.8相似文献   

Ionic strength effects on silicic acid (H4SiO4) sorption and oligomerization on an iron oxide surface: an interesting interplay between electrostatic and chemical forces

The effect of ionic strength on reactions at aqueous interfaces can provide insights into the nature of the chemistry involved. The adsorption of H(4)SiO(4) on iron oxides at low surface silicate concentration (Γ(Si)) forms monomeric silicate complexes with Fe-O-Si linkages, but as Γ(Si) increases silicate oligomers with Si-O-Si linkages become increasingly prevalent. In this paper, the effect of ionic strength (I) on both Γ(Si) and the extent of silicate oligomerization on the ferrihydrite surface is determined at pH 4, 7, and 10, where the surface is, respectively, positive, nearly neutral, and negatively charged. At pH 4, an increase in ionic strength causes Γ(Si) to decrease at a given H(4)SiO(4) solution concentration, while the proportion of oligomers on the surface at a given Γ(Si) increases. At pH 10, the opposite is observed; Γ(Si) increases as I increases, while the proportion of surface oligomers at a given Γ(Si) decreases. Ionic strength has only a small effect on the surface chemistry of H(4)SiO(4) at pH 7, but at low Γ(Si) this effect is in the direction observed at pH 4 while at high Γ(Si) the effect is in the direction observed at pH 10. The pH where the surface has zero charge decreases from ≈8 to 6 as Γ(Si) increases so that the surface potential (Ψ) is positive at pH 4 for all Γ(Si) and at pH 7 with low Γ(Si). Likewise, Ψ < 0 at pH 10 for all Γ(Si) and at pH 7 with high Γ(Si). The diffuse layer model is used to unravel the complex and subtle interactions between surface potential (Ψ) and chemical parameters that influence interfacial silicate chemistry. This analysis reveals that the decrease in the absolute value of Ψ as I increases causes Γ(Si) to decrease or increase where Ψ is, respectively, positive or negative. Therefore, at a given Γ(Si), the solution H(4)SiO(4) concentration changes with I, and because oligomerization has a higher H(4)SiO(4) stoichiometry coefficient than monomer adsorption, this results in the observed dependence of the extent of silicate oligomerization on I.