Influence of humic acid on the aggregation kinetics of fullerene (C60) nanoparticles in monovalent and divalent electrolyte solutions

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

Study of the colloidal stability of an amphoteric latex

We have studied the colloidal stability of an amphoteric latex (–COOH and NH ₂ surface groups) with a low-angle light scattering technique (nephelometry). Measurements were carried out at different pH values and electrolyte concentrations (NaCl or CaCl ₂). The results show a behaviour in agreement with DLVO theory when the pH of the medium is below the isoelectric point (i.e.p.) of the latex: at low ionic strengths the latex is stable, but it becomes completely unstable and coagulates when electrolyte concentration goes over a particular value (the critical coagulation concentration). However, when pH is raised above the isoelectric point, the latex is completely stable even at high electrolyte concentrations, showing a behaviour clearly opposite to the theory. This could be explained by means of an additional short-range repulsive "hydration force" due to the structure of water molecules that accompany hydrated cations around the hydrophilic latex surface. The morphology and electrical properties of the latex surface have been studied by different methods: dynamic light scattering, electrophoretic mobility, potentiometric and conductometric titrations.     

Kinetic determination of critical coagulation concentrations for sodium- and calcium-montmorillonite colloids in NaCl and CaCl2 aqueous solutions

The stability of the sodium and calcium forms of montmorillonite was studied at different NaCl and CaCl2 concentrations. The aggregation kinetics was determined from the decrease in particle concentration with time at different electrolyte concentrations. The DLVO theory defines the critical coagulation concentration (CCC) value as the electrolyte concentration that balances the attractive and repulsive potential energies between the particles, making aggregation diffusion-controlled. Therefore CCC values were obtained by extrapolation of the aggregation rate constants measured as a function of ionic strength to conditions where the rate constant value is determined by diffusion only. When the electrolyte was CaCl2, the CCC value was found to be approximately two orders of magnitude lower than the CCC values obtained using NaCl as electrolyte.     

Aggregation kinetics and dissolution of coated silver nanoparticles

Determining the fate of manufactured nanomaterials in the environment is contingent upon understanding how stabilizing agents influence the stability of nanoparticles in aqueous systems. In this study, the aggregation and dissolution tendencies of uncoated silver nanoparticles and the same particles coated with three common coating agents, trisodium citrate, sodium dodecyl sulfate (SDS), and Tween 80 (Tween), were evaluated. Early stage aggregation kinetics of the uncoated and coated silver nanoparticles were assessed by dynamic light scattering over a range of electrolyte types (NaCl, NaNO(3), and CaCl(2)) and concentrations that span those observed in natural waters. Although particle dissolution was observed, aggregation of all particle types was still consistent with classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The aggregation of citrate-coated particles and SDS-coated particles were very similar to that for the uncoated particles, as the critical coagulation concentrations (CCC) of the particles in different electrolytes were all approximately the same (40 mM NaCl, 30 mM NaNO(3), and 2 mM CaCl(2)). The Tween-stabilized particles were significantly more stable than the other particles, however, and in NaNO(3) aggregation was not observed up to an electrolyte concentration of 1 M. Differences in the rate of aggregation under diffusion-limited aggregation conditions at high electrolyte concentrations for the SDS and Tween-coated particles, in combination with the moderation of their electrophoretic mobilities, suggest SDS and Tween imparted steric interactions to the particles. The dissolution of the silver nanoparticles was inhibited by the SDS and Tween coatings, but not by the citrate coating, and in chloride-containing electrolytes a secondary precipitate of AgCl was observed bridging the individual particles. These results indicate that coating agents could significant influence the fate of silver nanoparticles in aquatic systems, and in some cases these stabilizers may completely prevent particle aggregation.     

Influence of surface oxidation on the aggregation and deposition kinetics of multiwalled carbon nanotubes in monovalent and divalent electrolytes

The aggregation and deposition kinetics of two multiwalled carbon nanotubes (MWNTs) with different degrees of surface oxidation are investigated using time-resolved dynamic light scattering (DLS) and quartz crystal microbalance with dissipation monitoring (QCM-D), respectively. Carboxyl groups are determined to be the predominant oxygen-containing surface functional groups for both MWNTs through X-ray photoelectron spectroscopy (XPS). The aggregation and deposition behavior of both MWNTs is in qualitative agreement with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The critical coagulation concentration (CCC) of the highly oxidized MWNTs (HO-MWNTs) is significantly higher than the lowly oxidized MWNTs (LO-MWNTs) in the presence of NaCl (210 and 53 mM, respectively) since HO-MWNTs have a higher surface charge density. In contrast, the aggregation inverse stability profiles of HO-MWNTs and LO-MWNTs are identical and yield comparable CCCs (0.9 and 1.0 mM, respectively) in the presence of CaCl(2). Similar to the results obtained from the aggregation study, HO-MWNTs are considerably more stable to deposition on silica surfaces compared to LO-MWNTs in the presence of NaCl. However, both MWNTs have the same propensity to undergo deposition in the presence of CaCl(2). The remarkable similarity in the aggregation and deposition kinetics of HO-MWNTs and LO-MWNTs in CaCl(2) may be due to Ca(2+) cations having a higher affinity to form complexes with adjacent carboxyl groups on HO-MWNTs than with isolated carboxyl groups on LO-MWNTs.     

Mucin-electrolyte interactions at the solid-liquid interface probed by QCM-D

The interaction between mucin and ions has been investigated by employing the quartz crystal microbalance technique with measurement of energy dissipation. The study was partially aimed at understanding the adsorption of mucin on surfaces with different chemistry, and for this purpose, surfaces exposing COOH, OH, and CH(3) groups were prepared. Mucin adsorbed to all three types of functionalized gold surfaces. Adsorption to the hydrophobic surface and to the charged hydrophilic surface (COOH) occured with high affinity despite the fact that in the latter case both mucin and the surface were negatively charged. On the uncharged hydrophilic surface exposing OH groups, the adsorption of mucin was very low. Another aim was to elucidate conformational changes induced by electrolytes on mucin layers adsorbed on hydrophobic surfaces from 30 mM NaNO(3). To this end, we investigated the effect of three electrolytes with increasing cation valance: NaCl, CaCl(2) and LaCl(3). At low NaCl concentrations, the preadsorbed layer expands, whereas at higher concentrations of NaCl the layer becomes more compact. This swelling/compacting of the mucin layer is fully reversible for NaCl. When the mucin layer instead is exposed to CaCl(2) or LaCl(3), compaction is observed at 1 mM. For CaCl(2), this process is only partially reversible, and for LaCl(3), the changes are irreversible within the time frame of the experiment. Finally, mucin interaction with the DTAB cationic surfactant in an aqueous solution of different electrolytes was evaluated with turbidimetry measurements. It is concluded that the electrolytes used in this work screen the association between mucin and DTAB and that the effect increases with increasing cation valency.     

Aggregation and deposition kinetics of fullerene (C60) nanoparticles

The aggregation and deposition kinetics of fullerene C60 nanoparticles have been investigated over a wide range of monovalent and divalent electrolyte concentrations by employing time-resolved dynamic light scattering (DLS) and quartz crystal microbalance (QCM), respectively. Aggregation kinetics of the fullerene nanoparticles exhibited reaction-limited (slow) and diffusion-limited (fast) regimes in the presence of both electrolytes, having critical coagulation concentrations (CCC) of 120 and 4.8 mM for the monovalent (NaCl) and divalent (CaCl2) salts, respectively. The measured stability ratios of the aggregating fullerene nanoparticles were in very good agreement with Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, with a derived Hamaker constant of 6.7 x 10-21 J for the fullerene nanoparticles in aqueous medium. For the deposition kinetics studies, the rate of fullerene nanoparticle deposition increased with increasing electrolyte concentrations, as was indicated in the aggregation kinetics results. However, at electrolyte concentrations approaching or exceeding the CCC, the rate of deposition dropped sharply due to significant concurrent aggregation of the fullerene nanoparticles. The deposition of the fullerene nanoparticles was further shown to be mostly irreversible, with immediate detachment of the nanoparticles observed only when exposed to a solution of high pH.     

Effect of clay aggregation on water diffusivity using low field NMR

Water diffusivity D measured by using NMR techniques in Na-smectite suspensions decreases with increasing smectite fraction (up to 50 wt%), but increases with increasing salinity (NaCl or CaCl(2) aqueous solutions) at a fixed clay fraction. The increase, larger for CaCl(2) solutions, is explained by aggregation of clay particles when high salinities are reached. Macroscopic organisation of dense mixtures of clay and aqueous solutions can be inferred by T(2) transverse NMR relaxation times which are sensitive to the volume to surface ratio. Dispersed suspensions exhibit mono-modal T(2) distributions, whereas bimodal T(2) distributions are observed for flocculated systems. The bimodal T(2) distributions are interpreted as a measurement of the spacing between clay particles within aggregates and between aggregates. Finally, the diffusion data can be gathered in an unique curve using the Debye length and the measured spacing between particles. When the thickness of the electro-diffuse layer (Debye length) is of the same order as the spacing between clay particles, the water diffusivity decreases. Otherwise it is constant at about 2.22+/-0.25x10(-9) m(2)/s. This last result illustrates clearly the effect of electro-chemical properties of smectite on water diffusivity.     

Intrinsic viscosity of aqueous suspensions of cellulose nanofibrils

Cellulose nanofibrils (CNF) from wood fibers are of increasing interest to industry because they are from renewable sources and are biodegradable. Owing to their high aspect ratio, they produce viscous suspensions and stiff gels that are strengthened by interfibrillar hydrogen bonds. In this study, the viscosity of aqueous CNF suspensions, at dilute concentrations ( \(nL^{3}<1\) ), was measured at various pH values by addition of HCl, and at various ionic strengths by addition of NaCl and \(\hbox {CaCl}_{2}\) . The results show that the primary electroviscous effect significantly increases the intrinsic viscosity. The intrinsic viscosity under conditions where the surface charge of nanofibrils is fully screened is in good agreement with the predictions of classical theory for dispersions of rodlike particles at low shear rates. Increasing the ionic strength up to \(\kappa d\approx 1\) decreases the intrinsic viscosity; at \(\kappa d>1\) , the intrinsic viscosity increases because of fibril aggregation and increase of the effective volume fraction.     

Adsorption of oppositely charged polyelectrolyte/surfactant complexes at the air/water interface: formation of interfacial gels

The adsorption and complexation of polystyrene sulfonate (a highly charged anionic polyelectrolyte) and dodecyltrimethylammonium bromide (a cationic surfactant) at the air-water interface can lead to interfacial gels that strongly influence foam-film drainage and stability. The formation and characteristics of these gels have been studied by combining surface tension, ellipsometry, and foam-film drainage experiments. Simultaneously, the solution electromotive force is measured and used to track the polymer-surfactant interactions in the bulk solution. We find that surface gelation occurs above the critical aggregation concentration in solution but before bulk precipitation of the polymer-surfactant complexes. Furthermore, we reveal that strong readsorption of polymer-surfactant complexes occurs during the resolubilization of the precipitated complexes at high surfactant concentrations (i.e., >critical micelle concentration). Seemingly overlooked in the past, this readsorption significantly influences the surface rheological properties and foam-film drainage of these systems.     

高温及超临界条件下 MgCl2与CaCl2水溶液中离子水化与缔合的量子化学计算

对NaCl等碱金属水溶液的研究表明,室温条件下,离子在溶液中以水合形式存在,而在高温及超临界时,阴阳离子将结合成为离子对．采用量子化学计算,研究了MgCl2与CaCl2水溶液中水化与缔合的情况．通过Gaussian98软件包计算了阳离子的水化自由能以及离子对的生成能,从而获得水合离子与离子对的热力学稳定性及其随温度、压力的变化情况．通过比较热力学稳定性,考察了两种溶液中水化与缔合的变化情况．研究结果表明,MgCl2与CaCl2水溶液中离子水化与缔合的变化趋势与碱金属溶液基本一致,但是存在一个过渡区域,该区域内离子对与水合离子共存,因此需要采用不同于碱金属溶液的方法处理MgCl2与CaCl2水溶液．     

Interactions between cationic starch and anionic surfactants

The surface tensions and the phase equilibria of dilute aqueous cationic starch (CS)/surfactant systems were investigated. The degree of substitution of the CS varied from 0.014 to 0.772. The surfactants investigated were sodium dodecyl sulphate (SDS), potassium octanoate (KOct), potassium dodecanoate (KDod) and sodium oleate (NaOl). The concentrations of CS were 0.001, 0.01 and 0.1 w%.Critical association concentrations (cac) occur at surfactant concentrations well below the critical micelle concentrations of the surfactants, except for KOct, KDod and NaOl at the lowest CS concentrations investigated (0.001 w%). The surface tensions of CS/surfactant solutions decrease strongly already below the cac. This is attributed to the formation of surface active associates by ion condensation. Associative phase separation of gels formed by CS and surfactant takes place at extremely low concentrations when the surfactant/polymer charge ratio is somewhat larger than 1. The gel is higly viscous and contains 40–60% water, depending on the concentration of electrolyte, the surfactant hydrocarbon chain length and the nature of the polar head of the surfactant.The concentration at which the phase separation occurs decreases with increasing surfactant chain length and the concentration of simple electrolyte, factors that promote micelle formation. This indicates that the gels are formed by association of CS to surfactant micelles. When surfactant well in excess of charge equivalence is added, the gels dissolve because the CS/surfactant complexes acquire a high charge.     

Interface tension of silica hydroxylated nanoparticle with brine: a combined experimental and molecular dynamics study

We have used molecular dynamics simulations to calculate the interfacial tension of hydroxylated SiO(2) nanoparticles under different temperatures and solutions (helium and brine with monovalent and divalent salts). In order to benchmark the atomistic model, quartz SiO(2) interfacial tension was measured based on inverse gas chromatography under He atmosphere. The experimental interfacial tension values for quartz were found between 0.512 and 0.617 N/m. Our calculated results for the interfacial tension of silica nanoparticles within helium atmosphere was 0.676 N/m, which is higher than the value found for the system containing He∕α-quartz (0.478 N/m), but it is similar to the one found for amorphous silica surface. We have also studied the interfacial tension of the nanoparticles in electrolyte aqueous solution for different types and salts concentrations (NaCl, CaCl(2), and MgCl(2)). Our calculations indicate that adsorption properties and salt solutions greatly influence the interfacial tension in an order of CaCl(2) > MgCl(2) > NaCl. This effect is due to the difference in distribution of ions in solution, which modifies the hydration and electrostatic potential of those ions near the nanoparticle.     

Adsorption of guar gum onto quartz from dilute mixed electrolyte solutions

The effect of potassium, sodium, calcium, magnesium, and hydrogen cations on adsorption of guar gum onto quartz was investigated at natural pH. The role of the background ions was analyzed in terms of their water-structure making or breaking capabilities. In dilute solutions (0.01 mol/L) of structure-makers (NaCl, HCl, CaCl2, and MgCl2), the guar gum adsorption density did not change compared to the adsorption densities obtained in distilled water. Potassium, the only structure-breaking ion (chaotrope) among the tested cations, significantly enhanced guar gum adsorption. The results obtained in mixed electrolytes demonstrate that the strong structure-breaking properties of K+ overcome any contributions from weak structure making ions (kosmotropes), and guar gum adsorption remains at the levels observed in KCl alone. Only when strongly hydrated Mg2+ ions are mixed with KCl, the overall effect becomes additive and the influence of potassium is proportionally reduced by increasing concentrations of magnesium cations. In this approach, guar gum adsorption on quartz is viewed as a competition between polysaccharide and water molecules for silanol surface sites. The hydration of the quartz surface inhibits the adsorption process but the competition equilibrium, and hence polysaccharide adsorption, can be affected by the presence of chaotropes or kosmotropes.     

Aggregation of ionic liquids [C(n)mim]Br (n = 4, 6, 8, 10, 12) in D2O: a NMR study

Aqueous solutions of five ionic liquids (ILs) of the 1-n-alkyl-3-methylimidazolium bromide family, [C(n)mim]Br (n = 4, 6, 8, 10, 12), were investigated by NMR measurements at 298.2 K as a function of IL concentrations. Critical aggregation concentrations and aggregation numbers of these ILs were determined by 1H NMR except for [C4mim]Br in D2O. The effects of the alkyl chain length of the cations were examined on the aggregation behavior of the ILs. 1H NMR data of the solvent D2O were used to investigate the hydration of the ILs in D2O, and it was found that the ionic hydration and the cation-anion association or aggregation of the ILs offset each other. The microenvironment of different protons of cations of the ILs in the aggregates was probed by determining the spin-lattice relaxation rate (1/T1). It is suggested that the imidazolium rings in the aggregates are exposed to water and that the molecular motion of the aggregates is more restricted than that of the monomers of the ILs. Furthermore, a stair-like microscopic aggregation structure is suggested for the [C(n)mim]Br/D2O (n = 6, 8, 10) systems from 2-D 1H-1H NOESY measurements.     

Hofmeister effects in the restabilization of IgG--latex particles: testing Ruckenstein's theory

The hydration interaction is responsible for the colloidal stability observed in protein-coated particles at high ionic strengths. The origin of this non-DLVO interaction is related not only to the local structure of the water molecules located at the surface but also to the structure of those molecules involved in the hydration of the ions that surround the colloidal particles. Ruckenstein and co-workers have recently developed a new theory based on the coupling of double-layer and hydration interactions. Its validity was contrasted by their fitting of experimental data obtained with IgG-latex particles restabilized at high salt concentration. The theory details the important role played by the counterions in the stability at high salt concentrations by proposing an ion pair reaction forming surface dipoles. These surface dipoles are responsible of repulsive interactions between two approaching surfaces. This paper checks the theory with recent data where some ions associated with the Hofmeister series (NO(3)(-), SCN(-) and Ca(2+)) restabilize the same kind of IgG-latex systems by means of hydration forces. Surprisingly, these ions induce stability acting even as co-ions, likely by modifying the water structure at the surface, but not forming surface ion pairs. Therefore, this experimental evidence would question Ruckenstein's theory based on the surface dipole formation for explaining the observed restabilization phenomena.     

Reduced aggregation and sedimentation of zero-valent iron nanoparticles in the presence of guar gum

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

Molecular dynamics study of the effect of calcium ions on the monolayer of SDC and SDSn surfactants at the vapor/liquid interface

The effect of Ca(2+) ions on the hydration shell of sodium dodecyl carboxylate (SDC) and sodium dodecyl sulfonate (SDSn) monolayer at vapor/liquid interfaces was studied using molecular dynamics simulations. For each surfactant, two different surface concentrations were used to perform the simulations, and the aggregation morphologies and structural details have been reported. The results showed that the aggregation structures relate to both the surface coverage and the calcium ions. The divalent ions can screen the interaction between the polar head and Na(+) ions. Thus, Ca(2+) ions locate near the vapor/liquid interface to bind to the headgroup, making the aggregations much more compact via the salt bridge. The potential of mean force (PMF) between Ca(2+) and the headgroups shows that the interaction is decided by a stabilizing solvent-separated minimum in the PMF. To bind to the headgroup, Ca(2+) should overcome the energy barrier. Among contributions to the PMF, the major repulsive interaction was due to the rearrangement of the hydration shell after the calcium ions entered into the hydration shell of the headgroup. The PMFs between the headgroup and Ca(2+) in the SDSn systems showed higher energy barriers than those in the SDC systems. This result indicated that SDSn binds the divalent ions with more difficulty compared with SDC, so the ions have a strong effect on the hydration shell of SDC. That is why sulfonate surfactants have better efficiency in salt solutions with Ca(2+) ions for enhanced oil recovery.     

Gelation of cellulose nanocrystal suspensions in glycerol

Aqueous suspensions of cellulose nanocrystals (NCC) produced by sulfuric acid hydrolysis of natural cellulose fibres display a number of unique properties. In addition to forming equilibrium chiral nematic phases above some critical concentration, cellulose nanocrystal suspensions tend to gel or aggregate if the stability of the suspension decreases, for example because of a decrease in the surface charge density of sulfate ester groups, or a change in the properties of the suspending medium. Direct incorporation of unmodified nanocrystals into organic media usually leads to aggregation. We have found that it is possible to circumvent this difficulty and form clear thixotropic gels of unmodified NCC in glycerol, by careful evaporation of water from aqueous glycerol suspensions of NCC. The physical gels form at a fairly low (<3 wt%) concentrations of cellulose. The initial composition of the suspension, the temperature and rate of evaporation, and the time resting at room temperature all influence the formation of thixotropic gels. Desulfation of the acid-form nanocrystals, enhanced in the glycerol-rich suspensions, is shown to be a key step in this gelation process.     

Deswelling kinetics of polyacrylate gels in solutions of cetyltrimethylammonium bromide

The deswelling kinetics of single sodium polyacrylate gel beads (radius 40-160 microm) in aqueous solutions of cetyltrimethylammonium bromide under conditions of forced convection are investigated using micromanipulator assisted light microscopy. The purpose of the study is to further evaluate a previously published model (J. Phys. Chem. B 2003, 107, 9203) using a higher homolog surfactant. For gels with expected fast deswelling (small gel size/low surfactant concentration) and/or in low electrolyte concentration, the model is found to correctly predict the deswelling characteristics of the gel beads. However, for some gels with expected slow deswelling, especially in high electrolyte concentration (10 mM NaBr), the model widely underestimates the required deswelling time. The reason for this is argued to be the longer time frame and high bromide concentration allowing the formation of a denser, more ordered structure in the surface phase, which resists the deformation and reorganization of material necessary for deswelling. Unexpectedly long lag times before the start of deswelling are also found for gels in low surfactant concentration, indicating that a relatively high surfactant concentration in the gel, greatly exceeding the critical aggregation concentration, is needed to start formation of a collapsed surface phase. This critical surfactant concentration is found to be dependent on initial gel radius, as small gels require a relatively higher concentration to initiate collapse.