Influence of adsorbed polymers on the removal of mineral particles from a planar surface

 Experimental results on the role of adsorbed polymers on the particle adhesion are presented. Both Brownian (silica particles) and non-Brownian (glass beads) particles were used. The particles were deposited onto the internal surface of a glass parallelepiped cell, and then submitted to increasing laminar flow rates. The pH and the ionic strength of the electrolytes were fixed. The adhesive force was related to the hydrodynamic force required to dislodge 50% of the initially attached beads. We found that high molecular weight PEO had little effect on the adhesion of small silica beads due to the low affinity of the polymer for silica or glass surfaces. On the contrary, PEO greatly enhanced the adhesion of bigger glass beads forced to deposit on the capillary surface because of gravity. The increase was all the more pronounced as the molecular weight of the polymer was high. The effect of high molecular weight cationic copolymers on the adhesion of silica particles was drastic. The maximal force (1500 pN) applied by the device could not enable any particle detachment even using polymers of low cationicity rate (5%), showing the efficiency of electrostatic attractions. When copolymers were adsorbed on both surfaces (particles and plane), the adhesive force exhibited a maximum at intermediate coverage of particles. This optimum was related to the optimum flocculation concentration classically observed in flocculation of suspensions by polymers. Received: 16 February 1996 Accepted: 10 September 1996     

Salt concentration influence on the efficiency of two cationic polymeric flocculants

The influence of the increase of the solution ionic strength on the flocculation of charged latex particles in the presence of cationic polymers is reported. Empirical flocculation rate constants are experimentally determined using particle counting and for two cationic polymers, one linear and the second with two branches. Comparisons are made with a solution containing monovalent salt only at different ionic concentrations in the absence of polymers. In all cases, polymer-induced flocculation is significantly more efficient than charge screening effects using salt only. Analysis of zeta potential measurements indicates that the charge neutralization and surface charge variations dictate the stability of the latex suspensions. Moreover, the addition of a small amount of salt in the polymer–particle mixtures results in a dramatic decrease of the polymer efficiency which is more pronounced for the linear polymeric flocculant. By increasing further the ionic strength, the rates of polymer flocculation are found to increase again but remain smaller than in the absence of salt.     

Aggregation and charging of colloidal silica particles: effect of particle size

We studied systematically aqueous suspensions of amorphous well-characterized silica particles by potentiometric titration, electrophoretic mobility, and time-resolved light scattering. Their charging behavior and aggregation rate constants were measured as a function of pH and ionic strength in KCl electrolytes for three types of particles of approximately 30, 50, and 80 nm in diameter. The charging behavior was consistent with the basic Stern model; the silica particles carry a negative charge, and its magnitude gradually increases with increasing pH and ionic strength. On the other hand, their early-stage aggregation (or coagulation) behavior is complex. The aggregation of the largest particles shows features resembling predictions of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory. On one hand, the rate constant decreases sharply with increasing pH at low ionic strengths and attains fast aggregation conditions at high ionic strengths. On the other hand, we observe a characteristic slowing down of the aggregation at low pH and high ionic strengths. This feature becomes very pronounced for the medium and the small particles, leading to a complete stabilization at low pH for the latter. Stabilization is also observed at higher pH for the medium and the small particles. From these aggregation measurements we infer the existence of an additional repulsive force. Its origin is tentatively explained by postulating hairy layers of consisting of poly(silicilic acid) chains on the particle surface.     

Self-organization of polymer particles on hydrophobic solid substrates in aqueous media. II. Self-organization of cationic polymer particles on polymer films and wettability control with particle monolayers

Self-organization of cationic polymer particles through hydrophobic interaction on polymer films in aqueous system and characteristic properties of the resulting particle monolayers were investigated. Cationic polymer particles bearing quaternary ammonium groups on their surfaces effectively self-organized on polymer films. With an increase of the particle surface charge density, the surface coverage and average aggregate size (N _a) decreased. The surface coverage control was accomplished by tuning the ionic strength of the media. The wettability of polymer films for water was imparted by the formation of particle monolayers on them. Annealing of the particle monolayers resulted in the increase of the adhesive strength, while the wettability for water was lost. Further improvements of both wettability and adhesive strength of particle monolayers were achieved by the immobilization of silica colloids on the particle monolayers. This method would be effective for the hydrophilization of polymer films.     

Coagulation kinetics of amorphous colloidal silica suspensions with and without hydroxypropyl cellulose polymer

The coagulation rate constant of submicron silica has been measured as a function of solution pH, salt concentration and hydroxypropyl cellulose (HPC) polymer concentration. Results show that the colloidal stability of silica is dominated by the cation concentration in the presence of salt in the pH range 3–9.5. The stability increases as cation concentration decreases. At low salt concentration and a minimum colloid stability was found in the intermediate pH range 4–8. These results show that differences in the literature values of the critical coagulation constant by relative light-scattering experiments can be explained by the use of the coagulation rate constant analysis. When HPC polymer was present in the solution, the colloid stability of the silica increased. The adsorption of polymer stabilizes the silica suspensions, both at low pH near the isoelectric point and at high ionic strength where it coagulates without the polymer. A monolayer coverage was necessary to provide steric stabilization. At 10^–3 M KCl a smaller equilibrium concentration of HPC in solution is needed to give monolayer coverage and steric stabilization than at 1 M KCl and pH 4.2.     

Characterization of poly(ethylene imine) layers on mica by the streaming potential and particle deposition methods

Deposition kinetics of polystyrene latex (averaged particle size of 0.66 microm) on mica covered by poly(ethylene imine) (PEI), a cationic polyelectrolyte having an average molecular mass of 75,000 g mol(-1), was studied using the impinging-jet method. The hydrodynamic radius of PEI, determined by PCS measurements, was 5.3 nm. The electrophoretic mobility of PEI was measured as a function of pH for ionic strengths of 10(-3) and 10 (-2) M, which made it possible one to determine the amount of electrokinetic charge of the molecule and its zeta potential. Formation of the polyelectrolyte layer on mica was followed by measuring the streaming potential in the parallel-plate channel. From these measurements, the dependence of the apparent zeta potential of mica on the surface coverage of PEI was determined. The amount of adsorbed PEI on mica was calculated from the convective diffusion theory. These results were quantitatively interpreted in terms of the theoretical model postulating a particle-like adsorption mechanism for PEI with not too significant shape deformation upon adsorption. On the other hand, the Gouy-Chapman model postulating the adsorption in the form of flat disks was proved inappropriate. After the surface was fully characterized, particle deposition experiments were carried out with the aim of finding the correlation between the polymer coverage and the initial rate of latex particle deposition. In the range of small polyelectrolyte coverage, a monotonic relation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For Theta(PEI)>0.25, the initial particle deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. These results were interpreted theoretically by postulating that an effective immobilization of colloid particles occurred on local polyelectrolyte assemblages containing between two and three PEI molecules.     

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.     

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.     

Adsorption of poly(ethyleneimine) on silica surfaces: effect of pH on the reversibility of adsorption

The role of polymer charge density in the kinetics of the adsorption and desorption, on silica, of the polyelectrolyte poly(ethyleneimine) (PEI) was investigated by stagnation-point flow reflectometry. In the first series of experiments, PEI solutions were introduced at the same ionic strength and pH as the background solvent. It was found that the adsorbed amount of PEI increased by increasing pH. In the second series of investigations, several PEI solutions with ascending pH were introduced consecutively into the cell. In these cases, a stepwise buildup of the adsorbed amount was observed and the "final" adsorbed amounts were observed to be roughly equal with the adsorbed amounts of the first series of measurements at the same pH. Finally, adsorption/desorption experiments were performed where the preadsorption of PEI was followed by the introduction of PEI solutions of descending pH. No desorption was detected when the pH changed from pH = 9.7 to pH = 5.8. However, when there was a 9.7 --> 3.3 or 5.8 --> 3.3 decrease in the pH, the kinetic barriers of desorption seemed to completely disappear and roughly the same adsorbed amount as in the first series of experiments at pH = 3.3 was quickly attained by desorption of the PEI. This study reveals the high impact of pH, affecting parameters such as charge density of the surface and polyelectrolyte as well as the structure of the adsorbed macromolecules, on the desorption properties of weak polyelectrolytes. The observed interfacial behavior of PEI may have some important consequences for the stability of alternating polyelectrolyte multilayers containing weak polyelectrolytes.     

PAA/PEO comb polymer effects on rheological properties and inter-particle forces in aqueous silica suspensions

The effects of a poly(acrylic acid) (PAA)-poly(ethylene) (PEO) comb polymer dispersant on the rheological properties and inter-particle forces in aqueous silica suspensions have been studied under varying pH conditions. The comb polymer was found to adsorb more strongly under acidic than basic conditions, indicating that the PAA backbone of the copolymer preferentially adsorbs onto silica surfaces with the PEO "teeth" extending out from the surface into the solution. In the presence of low concentrations of copolymer, the silica suspensions were stable due to electrostatic repulsions between the silica surfaces. At higher copolymer concentrations and under neutral and basic conditions, where the copolymer interacted only weakly with silica, the suspensions showed a transition from a dispersed to weakly flocculated state and attractive forces were measured between silica surfaces. Under acidic conditions, the silica dispersion also destabilized at intermediate copolymer adsorbed density and then was re-stabilized at higher adsorbed coverage. The silica suspensions were stable at high copolymer coverage due to steric repulsions between the particles. The destabilization at intermediate coverage is thought to be due to polymer bridging between particles or possibly depletion forces.     

Surface modification for stability of nano-sized silica colloids

The surfaces of commercial 30-nm colloidal silica particles were modified by reacting with functional silanes. The high specific surface area and reactivity of the particles due to the small size make the process susceptible to irreversible aggregation not found previously with larger particles. This study compares surface charge results from different reaction conditions and characterization methods. Measurements of the zeta potential as a function of pH and gelation kinetics shed light on the mechanism of instability in nano-sized silica suspensions. Experimental results showed that very stable particles can be suspended in a nonaqueous solvent after refluxing of the silica particles, while maintaining the original particles physical properties of size and electrochemical behavior. Extremely stable particles are obtained by aminosilane surface modification. Factors affecting susceptibility of small particles to irreversible aggregation caused by a nonaqueous solvent or a high concentration of a trialkoxysilane, including the large amount of reactive silanol groups on the surface gel layer of the particles, are discussed.     

Effect of poly(ethylene oxide)-silane graft molecular weight on the colloidal properties of iron oxide nanoparticles for biomedical applications

The size, charge, and stability of colloidal suspensions of magnetic nanoparticles with narrow size distribution and grafted with poly(ethylene glycol)-silane of different molecular weights were studied in water, biological buffers, and cell culture media. X-ray photoelectron spectroscopy provided information on the chemical nature of the nanoparticle surface, indicating the particle surfaces consisted of a mixture of amine groups and grafted polymer. The results indicate that the exposure of the amine groups on the surface decreased as the molecular weight of the polymer increased. The hydrodynamic diameters correlated with PEG graft molecular weight and were in agreement with a distributed density model for the thickness of a polymer shell end-grafted to a particle core. This indicates that the particles obtained consist of single iron oxide cores coated with a polymer brush. Particle surface charge and hydrodynamic diameter were measured as a function of pH, ionic strength, and in biological buffers and cell culture media. DLVO theory was used to analyze the particle stability considering electrostatic, magnetic, steric, and van der Waals interactions. Experimental results and colloidal stability theory indicated that stability changes from electrostatically mediated for a graft molecular weight of 750 g/mol to sterically mediated at molecular weights of 1000 g/mol and above. These results indicate that a graft molecular weight above 1000 g/mol is needed to produce particles that are stable in a wide range of pH and ionic strength, and in cell culture media.     

Interactions of PEI (polyethylenimine)–silica particles with citric acid in dispersions

Adsorbed polyethylenimine (PEI) of M _w 1,800 and 70,000 on silica (SiO₂) dispersions produced flocculated slurry in the pH range of 5 to 12. Adsorbed citrate widens this flocculated pH regime. It also increases the strength of the interparticle attractive force or the yield stress over the pH range of between 3 and 8. The stronger attractive force is due to particle bridging by the citrate anions bonding with positively charge sites of the adsorbed PEI layer of the interacting particles at the closest point of interaction. The higher M _w PEI being more strongly attached to the silica particle produced a stronger attractive interparticle force with adsorbed citrate anions. Via charge balance calculation using contributions from SiO₂, PEI, and citrate, the pH of zero charge was found to correspond to the pH of zero zeta potential for PEI of M _w 70,000. This suggests 100% adsorption of PEI and citrate on SiO₂. The bridging interaction was confirmed by a linear relationship between yield stress and the square of the limiting citrate charge content. Adsorbed citrate was found for the first time to play the role of a bridging agent, a result of the positive charges being located on a more flexible adsorbed layer rather than being fixed to a rigid surface.     

Control of specific attachment of proteins by adsorption of polymer layers

This study concerns the design of protein-resistant polymer adsorbed layers for the control of surface binding of biospecific recognition entities. Polymer surface layers were prepared using the adsorption of poly(allylamine hydrochloride) (PAH), poly(l-lysine) (PL), and branched and linear polyethyleneimine (PEI) and further modified by the covalent attachment of biotin for specific avidin attachment. The adsorption of PAH, PL, and PEI on silicon substrates was studied as a function of pH and ionic strength using ellipsometry. Average dry layer thicknesses of approximately 10, approximately 5, approximately 9, and approximately 3 A (+/-1 A) were obtained when polymer adsorption occurred from solutions at pH 9.5 that contained 0.5 M NaCl for PAH, PL, branched PEI, and linear PEI, respectively. These polymers showed significant differences in their efficiency to suppress nonspecific avidin adsorption. At low ionic strength, avidin adsorption occurred on all polymer-coated surfaces at basic pH values, despite the same positive electrostatic charge for protein globules and the surface. Though the net electrostatic repulsion between avidin molecules and branched PEI was efficiently screened in a protein solution of pH 7 and 0.15 M NaCl, branched-PEI coatings of high molecular weight were unique in their ability to provide avidin-resistant surfaces as a result of steric hindrance from the branched architecture of adsorbed polymer chains. All polymers studied were effective in suppressing avidin adsorption at pH 3 as a result of protonation of the avidin surface functional groups at this pH. Branched-PEI-coated surfaces were also effective for the suppression of smaller positively charged proteins such as lysozyme and ribonuclease A at pH 7 and 0.15 M NaCl. They were also resistant to the adsorption of negatively charged proteins such as BSA and fibrinogen at pH 7 and 0.75 M NaCl. Furthermore, by using PEI-modified protein-repellent surfaces, selective binding of avidin was achieved to surface-bound silver nanoparticles, which should provide a promising application for the label-free detection of biological species using surface-enhanced Raman scattering (SERS).     

Stability and Adsorption Properties of Suspensions of Finely Dispersed Silica in the Presence of Cationic Surfactants

Interrelation between the coagulation rate, adsorption and electrokinetic properties of silica polydisperse suspensions in the presence of cationic surfactants is studied. The highest coagulation rate is observed in a certain concentration range of the cationic surfactants. When pH values increases, an increasing amount of cationic surfactant is required to achieve maximal coagulation rate. For bisquaternary cationic surfactants, ethonium and decamethoxine, maximal coagulation rate is observed at concentrations by an order of magnitude lower than for monoquaternary cetyltrimethylammonium bromide. It is concluded that the suspensions lost their stability as a result of both neutralization of particle surface charge and flocculating effect of the cationic surfactants. Moreover, the flocculation mechanism depends on the cationic surfactant nature and physicochemical parameters of the medium, ionic strength and pH.     

Flocculation and stabilization of colloidal silica by the adsorption of poly-diallyl-dimethyl-ammoniumchloride (PDADMAC) and of copolymers of DADMAC with N-methyl-N-vinyl- acetamide (NMVA)

 The stabilization and flocculation behavior of colloidal silica-particles with cationic polyelectrolytes (PE) is investigated. The zetapotentials, diffusion coefficients and flocculation rate constants of silica particles have been measured as a function of the adsorbed amount of cationic polyelectrolytes poly(diallyl-dimethyl-ammoniumchloride) (PDADMAC) of different molar masses and of statistic copolymers of DADMAC and N-methyl-N-vinyl-acetamide (NMVA) of various compositions at different salt concentrations and pH-values. Very fast flocculation due to van der Waals attraction occurs if the zetapotential is small. At low ionic strength this condition occurs just below the plateau of the adsorption isotherms where the surface charges are screened by adsorbed polycations. Additionally with high molecular polycations slow mosaic flocculation is observed at lower PE concentrations. At high ionic strength fast flocculation takes place at low macroion concentration due to the screening of the surface charges by adsorbed polycations and salt ions. At medium concentrations of polycations below plateau adorption slow bridging flocculation is observed. At plateau adsorption the suspensions become stabilized up to high ionic strength. At low salt concentration charge reversal at full coverage with polycations results in electrostatic repulsion. At high ionic strength the particles are stabilized sterically due to the osmotic repulsion of the long adsorbed PE tails. Therefore macroions of high molar mass are necessary to stabilize the suspension at high ionic strength. Received: 27 January 1998 Accepted: 23 March 1988     

Direct surface force measurements of polyelectrolyte multilayer films containing nanocrystalline cellulose

Polyelectrolyte multilayer films containing nanocrystalline cellulose (NCC) and poly(allylamine hydrochloride) (PAH) make up a new class of nanostructured composite with applications ranging from coatings to biomedical devices. Moreover, these materials are amenable to surface force studies using colloid-probe atomic force microscopy (CP-AFM). For electrostatically assembled films with either NCC or PAH as the outermost layer, surface morphology was investigated by AFM and wettability was examined by contact angle measurements. By varying the surrounding ionic strength and pH, the relative contributions from electrostatic, van der Waals, steric, and polymer bridging interactions were evaluated. The ionic cross-linking in these films rendered them stable under all solution conditions studied although swelling at low pH and high ionic strength was inferred. The underlying polymer layer in the multilayered film was found to dictate the dominant surface forces when polymer migration and chain extension were facilitated. The precontact normal forces between a silica probe and an NCC-capped multilayer film were monotonically repulsive at pH values where the material surfaces were similarly and fully charged. In contrast, at pH 3.5, the anionic surfaces were weakly charged but the underlying layer of cationic PAH was fully charged and attractive forces dominated due to polymer bridging from extended PAH chains. The interaction with an anionic carboxylic acid probe showed similar behavior to the silica probe; however, for a cationic amine probe with an anionic NCC-capped film, electrostatic double-layer attraction at low pH, and electrostatic double-layer repulsion at high pH, were observed. Finally, the effect of the capping layer was studied with an anionic probe, which indicated that NCC-capped films exhibited purely repulsive forces which were larger in magnitude than the combination of electrostatic double-layer attraction and steric repulsion, measured for PAH-capped films. Wherever possible, DLVO theory was used to fit the measured surface forces and apparent surface potentials and surface charge densities were calculated.     

Coupling between polymer adsorption and colloidal particle aggregation

Studies of the adsorption of high molecular weight polymers on colloidal latex and silica particles and their subsequent flocculation were carried out. Neutral polyethylene oxide samples with both a narrow and a broad molecular weight distribution were used together with low charged cationic copolymers. The influence of the particle concentration and polymer dose on the flocculation were systematically investigated under quiescent conditions.Equilibrium bridging only occurred with polyelectrolyte, even in very dilute suspensions, at high particle coverage. In contrast to this, non-equilibrium bridging occurred with both neutral polymer and polyelectrolytes but only for more concentrated suspensions and small amounts of adsorbed polymer. Polymer adsorption in dilute suspensions, which did not show particle aggregation was measured an electrophoretic technique. In more concentrated suspensions, where flocculation takes place, we found that aggregation prevents further polymer adsorption and induces both an excluded volume and a surface effect. The consequences on the shape of the isotherms differ according to the aggregation mechanism.A significant decrease of the amount, , of adsorbed polymer is observed with non-equilibrium bridging. When both mechanisms simultaneously contribute to the aggregation, the value of depends on their relative importance. In the intermediate range of copolymer dose their respective contributions are critically sensitive to the details of the mixing step and stirring, leading to non reproducible experimental results.     

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.     

Electrostatic interactions of colloidal particles at vanishing ionic strength

Electrostatic interactions of colloidal particles are typically screened by mobile ions in the solvent. We measure the forces between isolated pairs of colloidal polymer microspheres as the density of bulk ions vanishes. The ionic strength is controlled by varying the concentration of surfactant (NaAOT) in a nonpolar solvent (hexadecane). While interactions are well-described by the familiar screened-Coulomb form at high surfactant concentrations, they are experimentally indistinguishable from bare Coulomb interactions at low surfactant concentration. Interactions are strongest just above the critical micelle concentration, where particles can obtain high surface potentials without significant screening, kappaa < 1. Exploiting the absence of significant charge renormalization, we are able to construct a simple thermodynamic model capturing the role of reverse micelles in charging the particle surface. These measurements provide novel access to electrostatic forces in the limit where the particle size is much less than the screening length, which is relevant not just to the nonpolar suspensions described here, but also to aqueous suspensions of nanoparticles.