Article pubs.acs.org/Langmuir

Mechanism of Nanoparticle Deposition on Polystyrene Latex Particles Marta Sadowska, Zbigniew Adamczyk,* and Małgorzata Nattich-Rak J. Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Science, Niezapominajek 8, 30-239 Cracow, Poland ABSTRACT: The deposition of positive amidine latex particles (98 nm in diameter) on negative polystyrene latex particles (820 nm in diameter) was studied by SEM imaging, microelectrophoretic and concentration depletion methods involving AFM. The role of ionic strength varied between 10−4 and 10−2 M and was systematically studied. The number of deposited positive latex particles (surface coverage) was evaluated by a direct counting procedure exploiting the SEM images. This allowed one to calibrate the results obtained from measurements of the electrophoretic mobility of larger latex particles covered by a controlled amount of the positive latex. These dependencies were quantitatively interpreted in terms of the 3D electrokinetic model previously used for planar interfaces. This allowed us to determine the coverage of nanoparticles on latex carriers under in situ conditions. Additionally, the maximum coverage of the positive latex was determined via AFM where the kinetics of the residual amidine latex deposition on mica was measured. The maximum coverage monotonically increased with ionic strength, attaining 0.52 for 10−2 M NaCl. This effect was interpreted in terms of reduced electrostatic repulsion among positive latex particles and theoretically accounted for by the random sequential adsorption model. The obtained results have significance for basic science, indicating that the results obtained for curved interfaces (polymeric carrier particles) by the microelectrophoretic method can be exploited to interpret the deposition of nanoparticles and proteins on planar interfaces and vice versa.

1. INTRODUCTION The attachment of colloid particles and proteins to larger microparticles is an interesting phenomenon from the basic science point of view. It is also an important step in many practically oriented processes, such as pickering emulsion stabilization, filtration, flotation, supporting catalyst formation, and the developing of microcapsule systems based on the colloidosome concept. In the realm of protein science, the efficient immobilization of enzymes and immunoglobulins on carrier polymeric particles is the critical step in enzymatic catalysis, immunological assays, and protein separation and purification. Despite its vital significance, only a few systematic publications devoted to elucidating the fundamentals of colloid particle immobilization onto microparticle surfaces are reported in the literature.1−7 For example, Vincent et al.1,2 studied the deposition of positively charged polystyrene latex particles (200 nm diameter) onto negative latex microspheres (3200 nm diameter). The role of the polymer (poly(vinyl alcohol)) and ionic strength in adsorption particle deposition kinetics and maximum coverage (adsorption isotherms) was evaluated using the concentration depletion method. As an interesting extension of these measurements, the electrophoretic mobility of larger latex particles was measured as a function of the smaller particle coverage. These results were theoretically interpreted in ref 8 in terms of the Monte Carlo random sequential adsorption (RSA) simulations that rigorously consider the curvature effect. © 2014 American Chemical Society

Extensive series of experiments were performed in refs 3−7 aimed at elucidating the deposition mechanisms of positively charged poly(amidoimine) PAMAM dendrimers of various generations (G2−G10) on larger negatively charged sulfate polystyrene latex particles. The reversibility of dendrimer deposition was studied, as was the effective charge, maximum coverage, electrophoretic mobility, and stability of latex particles at various ionic strengths. The dendrimer distribution on latex particle surfaces and specific force interaction profiles were evaluated by direct AFM measurements under wet conditions. However, because of the small size of dendrimers (below 13.5 nm) the curvature effects influencing the maximum coverage could not be observed in the above works. Also, the interesting dependencies of the electrophoretic mobility on the dendrimer dose were not interpreted because of the lack of an appropriate theoretical model. The release kinetics of various solutes from colloidosomes formed by self-assembling of colloid particles on hydrogel particles was theoretically and experimentally studied in refs 9−12. However, the self-assembly mechanisms of colloid particles and their maximum coverage were not considered in these works. The deficiency of systematic works devoted to particle deposition on curved interfaces is astonishing in view of the Received: October 20, 2013 Revised: December 19, 2013 Published: January 2, 2014 692

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frequencies of 47−150 kHz ±10%, the radius of curvature of the tip is 10 nm, and the cone angle is less than 20 °C. Typically, the number of latex molecules is determined over 10 equally sized areas randomly chosen over the mica sheets. The overall number of deposited S800 particles was 1000−2000.

large number of results available for the analogous problem of particle deposition on flat interfaces.13−16 Therefore, the primary goal of this article is to determine mechanisms of colloid particles immobilization on spherically shaped interfaces under the condition where the curvature effects play a significant role. The influence of ionic strength in this process is systematically studied, especially in determining the maximum coverage of colloid particles. The reliability of the data is increased by determining the coverage via direct enumeration by scanning electron microscopy (SEM) imaging of attached particles. Additionally, the solution depletion method is used based on the atomic force microscopy (AFM) determination of the residual latex concentration in the suspension after the attachment step. It should be mentioned that this method was previously applied to determine the adsorption mechanism of fibrinogen on latex particles.17 A precise determination of colloid particle coverage enables a proper interpretation of the zeta potential versus colloid particle coverage dependencies evaluated via microelectrophoretic measurements, which is another major goal of our work. In this way, the validity of the electrokinetic model18 for the interpretation of adsorption phenomena on curved interfaces (carrier particles) can be determined, that has not been attempted before in the literature. Besides being significant for basic science, the results obtained in this work for the model colloid particle system can be exploited as useful reference states for the quantitative analysis of protein adsorption on polymeric carrier particles extensively studied in the literature.19−27

3. RESULTS AND DISCUSSION 3.1. Bulk Characteristics of Latexes. Physicochemical characteristics of both latex suspensions were initially determined. These comprised the diffusion coefficients, electrophoretic mobilities, and electrokinetic (zeta) potentials. As measured by DLS, the diffusion coefficient D for the A100 latex (SEM micrograph of its monolayer is shown in Figure 1a)

Figure 1. SEM micrographs of (a) the A100 positive latex particles and (b) the negative S800 latex particles.

was practically constant for the ionic strength range of 10−4− 10−2 M and for pH 5.6, assuming an average value of 4.99 × 10−8 cm2 s−1. Knowing diffusion coefficient, the Stokes hydrodynamic diameter of the latex particles d was calculated using the dependence

2. MATERIALS AND METHODS Water was purified with a Milipore Elix 5 apparatus. Chemical reagents (sodium chloride and hydrochloric acid) were commercial products of Sigma-Aldrich and used without further purification. The temperature of the experiments was kept at a constant value equal to 298 ± 0.1 K. Positively charged amidine polystyrene latex, hereafter referred to as the A100 latex, and negatively charged sulfonate polystyrene latex (S800), both supplied by Invitrogen, were used in colloid deposition experiments. Stock suspensions of latexes of a well-defined concentration, determined by densitometry and the dry weight method, were diluted prior to deposition experiments to a desired weight concentration of 10 to 200 mg L−1. Ruby muscovite mica obtained from Continental Trade was used as a substrate. The solid pieces of mica were freshly cleaved into thin sheets prior to each experiment. The diffusion coefficients of latexes were determined by dynamic light scattering (DLS) using the Zetasizer Nano ZS instrument from Malvern, and their electrophoretic mobilities were measured using the laser Doppler velocimetry (LDV) technique. The margin of error of the electrophoretic mobility measurements was ±2%. The residual concentration of the positive A100 latex in the mixture acquired after deposition on the negative latex is determined via the indirect procedure previously described.13 It is based on a controlled adsorption of the residual A100 latex particles on mica quantified via AFM imaging. The mixture was transferred to a diffusion cell without centrifugation. A few freshly cleaved mica sheets are vertically immersed in the latex suspension. The deposition of the A100 latex from the mixture proceeds over the desired time period (typically 1200 min) under diffusion-controlled transport. It should be mentioned that larger S800 latex deposition is negligible during this time period because of its low number concentration and lower diffusion coefficient. The mica sheets covered with latex are rinsed and dried. Afterward, micrographs of latex monolayers are acquired by AFM imaging in air using the NT-MDT Solver device with an SMENA-B scanning head. The measurements are performed in semicontact mode using a silicon probe (NSG-03 polysilicon cantilevers) with resonance

d=

kT 3πηD

(1)

It was calculated from eq 1 that the hydrodynamic diameter of the A100 latex, donated by dA, was 98 nm. In an analogous way, the diffusion coefficient and the hydrodynamic radius of the S800 (negative latex whose SEM micrograph is also shown in Figure 1) were determined to vary between 5.9 × 10−9 and 6.0 × 10−9 cm2 s−1 for the ionic strength range of 10−4−10−2 M and for pH 5.6, which corresponds to the hydrodynamic diameters dS of 830 and 820 nm for the above ionic strength range. The electrophoretic mobility μe of the latexes was measured as a function of ionic strength using the microelectrophoretic method. The experimental data are shown in Table 1. In the case of the A100 latex, μe = 3.88 × 10−8 m2 = 3.88 μm cm (V s)−1 (the latter unit is commonly used in the literature) for Table 1. Electrophoretic Mobilities, Zeta Potentials (Calculated from Henry’s Model), and Charge Densities of A100 and S800 Latexes (pH 5.6, T = 298 K) latex (A100)

693

latex (S800)

NaCl concentration (M)

μe (μm cm/(V s)−1)

ζ (mV)

σ0 [e nm−2]

μe (μm cm/(V s)−1)

ζ (mV)

σ0 (e nm−2)

10−4 3 × 10−4 10−3 3 × 10−3 10−2

3.88 3.88 3.52 3.89 3.28

71 68 59 60 47

0.013 0.022 0.034 0.058 0.078

−5.04 −5.47 −6.58 −7.0 −8.4

−74 −77 −89 −92 −110

−0.015 −0.027 −0.064 −0.12 −0.31

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ionic strength of 10−4 M. This corresponds to the particle zeta potential of 71 mV (calculated from Henry’s model). The A100 latex mobility decreases with ionic strength, assuming 3.28 μm cm (V s)−1 for 10−2 M. This corresponds to a particle zeta potential of 47 mV. Analogous data determined for the S800 latex were −5.04 × 10−4 μm cm (V s)−1 (zeta potential −74 mV) for an ionic strength of 10−4 M and −8.4 × 10−4 μm cm (V s)−1 (zeta potential −110 mV) for an ionic strength of 10−2 M. The dependencies of latex zeta potentials on the ionic strength are graphically shown in Figure 2.

conditions lasted 300 s. It should be mentioned that this considerably exceeds the relaxation of 11 s for the above S800 latex concentration in the suspension as calculated from the formula given in ref 29. Subsequently, one part of the final suspension was used for SEM imaging, and the other was used for microelectrophoretic measurements. The SEM micrographs were acquired after the deposition of the S800 latex particles covered by A100 latex particles on mica surface carried out under diffusion conditions over 1 h. The latex particle monolayers obtained in this way were then sputtered with a thin layer of chromium, and an appropriate number of micrographs were taken (one of them is shown in Figure 3). The number of deposited A100 particles

Figure 2. Dependencies of the zeta potential of latexes calculated from Henry’s formula on the ionic strength at pH 5.6. (1) A100 latex. (2) S800 latex. The solid lines are the nonlinear fits of the experimental data.

Figure 3. Dependence of the surface concentration of the A100 latex, NA (μm−2), on its initial concentration after mixing with the S800 latex suspension, cA (initial concentration of S800 latex after mixing was 80 mg L−1). The points show experimental data obtained by the direct counting of single particles on SEM micrographs. The solid line denotes the theoretical results predicted for the irreversible deposition of latex, and the dashed horizontal line shows the linear interpolation of experimental data obtained for higher cA. The inset shows the S800 latex particle covered with a saturated layer of A100 latex (SEM micrography).

By knowing the zeta potential of latex particles, one can calculate their electrokinetic (uncompensated) charge using the Gouy−Chapman relationship for a symmetric 1:1 electrolyte.28 σ0 =

⎛ eζ ⎞ (8εkTnb)1/2 sinh⎜ l ⎟ ⎝ 2kT ⎠ 0.160

(2)

where σ0 is the electrokinetic charge density of latex particles expressed in e nm−2, k is the Boltzmann constant, ε is the dielectric permittivity of water, nb is the number concentration of the salt (NaCl) expressed in m−3, and ζ1 is the zeta potential of latex. Using the above zeta potential values, one obtains from eq 2 the following charge densities of the A100 latex: σ0 = 0.013 and 0.078 e nm−2 for ionic strength of 10−4 and 10−2 M, respectively. For the S800 latex, the charge densities are σ0 = −0.015 and −0.31 e nm−2 for ionic strengths of 10−4 and 10−2 M, respectively (Table 1). Because of high and opposite charge densities, especially for higher ionic strength, an irreversible attachment of the A100 latex to the S800 latex is expected as a result of favorable electrostatic interactions. 3.2. Measurements of Positive Latex Deposition on a Negative Latex. In the first series of experiments, the coverage of A100 latex particles on the S800 latex was determined by direct SEM imaging. As the first step in the procedure, monolayers of the A100 latex of a desired coverage were produced by mixing equal volumes of the latex of an appropriate concentration (dose) ranging between 10 and 200 mg L−1 with the S800 latex suspension of a fixed concentration of 160 mg L−1). The deposition carried out under stirring

was obtained via a direct counting procedure involving specialized image-analysis software. It should be mentioned that although this technique is rather tedious and timeconsuming it proved advantageous compared to the AFM measurements (as a result of curvature effects and tip artifacts), furnishing direct information about the A100 latex coverage. The results are plotted as a function of the surface concentration of A100 particles, normalized to a 1 μm2 area NA, with respect to its nominal bulk concentration in the mixture (before deposition started), cA. A typical example of such measurements obtained for an ionic strength of 10−2 M is shown in Figure 3. As can be observed, the experimental results (points) are adequately reflected by the theoretical dependence (solid straight line 1) derived from the mass balance having the form

NA =

ρL dL πρA dA 3c L

cA

(3)

where ρA and ρL are the specific densities of the A100 and S800 latexes, respectively, and cL is the bulk concentration of the S800 latex in the mixture before the deposition step (equal to 80 mg L−1). 694

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By knowing NA, one can calculate the dimensionless coverage of the A100 latex from the dependence ⎛ πd 2 ⎞ 1 ρL dL cA Θ = ⎜ A ⎟NA = 4 ρA dAc L ⎝ 4 ⎠

(4)

As can be seen in Figure 3, the theoretical results calculated from eq 3 (solid line) properly reflect the experimental data. This indicates that all of the A100 latex added to the suspension was irreversibly attached to the S800 latex particles. However, after exceeding a critical (saturation) concentration of cA, the surface concentration of A100 particles on the S800 latex attains a limiting value of 62 μm−2 and then remains constant. Using the value one obtains directly from eq 4, the coverage of the adsorbed A100 latex was 0.49. Additionally, the intersection of line 1 with horizontal line 2 fitting the experimental data for higher cA gives the critical A100 latex concentration of 20 mg L−1. Therefore, by virtue of eqs 3 and 4 one obtains 0.52 as the maximum coverage of the A100 latex at this ionic strength, which is close to the above obtained value given the experimental error, estimated to be 0.02. These results, confirming the irreversibility of latex deposition and furnishing the absolute coverage, are useful for the interpretation of the microelectrophoretic measurements. In these experiments, one part of the latex mixture prepared as above was used to measure the electrophoretic mobility of the S800 latex particles as a function of A100 latex dose cA. Knowing the electrophoretic mobility, the zeta potential of the S800 latex was calculated using Henry’s formula. In a few series of experiments performed for various ionic strengths and A100 latex coverages, it was determined that there were no changes in the electrophoretic mobilities (zeta potential) of latex for time periods of up to 48 h. This confirms, in accordance with previous results derived from SEM, that A100 deposition was irreversible for pH ionic strength varying between 10−4 and 10−2 M. The dependencies of the S800 latex zeta potential on cA and Θ calculated from eq 4 are shown in Figure 4 for ionic strengths of (a) 10−4, (b) 10−3, and (c) 10−2 M. It should be noted that, in all cases, ζ increases abruptly with the A100 latex coverage, resulting in the inversion of the negative potential of the S800 latex for Θ > 0.2. However, for higher Θ exceeding 0.3, the changes in the zeta potential become rather moderate. Finally, the limiting values of the zeta potentials are attained markedly below the bulk zeta potential of the A100 latex. Similar regularities were previously observed by Vincent et al.,1,2 who studied the deposition of positively charged polystyrene latex particles (200 nm diameter) onto 3200 nm negative latex particles at various ionic strengths. The electrophoretic mobility of the large latex particles abruptly increased with the small (positive) latex coverage, attaining positive values for Θ > 0.1. However, these interesting results were not theoretically interpreted. Analogous results were obtained by Lin et al.,3 who studied the deposition of positively charged dendrimers (G4−G6, particle size 4.5 to 13.5 nm) on negatively charged sulfate latex at pH 4. In the case of the G6 dendrimers, the overcharging of latex at pH 4 was observed for 0.7 mg L−1. From the data shown in Figure 4, one can estimate that the limiting coverages of the A100 latex, defined as the points on the Θ axis where the zeta potential of the S800 latex does not change, are 0.3, 0.42, and 0.50 for ionic strengths of 10−4, 10−3,

Figure 4. Dependencies of the zeta potential of S800 latex ζ on the A100 latex coverage Θ. (a) 10−4, (b) 10−3, and (c) 10−2 M. The solid lines denote the theoretical results calculated from eqs 5 and 6 derived from the 3D electrokinetic model.

and 10−2 M, respectively. The latter value agrees with that previously derived from the SEM measurements (Table 2). However, these maximum coverage estimates becomes less precise for higher ionic strength as a result of the small slope of ζ on Θ dependencies (Figure 4). The results shown in Figure 4 were interpreted in terms of the 3D model,18 whose validity for planar interfaces was previously confirmed in thorough experiments involving latex microparticles.30 In this model, the true electrostatic and hydrodynamic flow fields around deposited particles are evaluated using the multipole method.18 This allows one to formulate the following expression for the zeta potential of interfaces covered with particles ζ(Θ) = Fi(Θ)ζi + Fp(Θ)ζp

(5)

where Fi(Θ) and Fp(Θ) are dimensionless functions of particle coverage. 695

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Table 2. Maximum Coverage of the A100 Latex on the S800 Latex versus the Ionic Strength (pH 5.6) maximum A100 latex coverage on S800 latex obtained by various methods NaCl concentration (M) −4

10 3 × 10−4 10−3 3 × 10−3 10−2 ∞

κ(dA/2) 1.6 2.8 5.2 9.0 16 ∞

direct counting

electrophoretic mobility (EM)

0.44 ± 0.03

0.30 ± 0.02 0.37 ± 0.02 0.38 ± 0.02

0.51± 0.02

0.50 ± 0.05

As previously shown,31 functions Fi(Θ) and Fp(Θ) can be approximated by the following analytical expressions:

Fp(Θ) =

1 (1 − e− 2

(6) 2 C poθ

theoretical (RSA modeling)

± ± ± ± ±

0.16 0.25 0.36 0.45 0.53 0.69 (hard particles)

0.25 0.37 0.42 0.48 0.52

0.02 0.02 0.02 0.02 0.02

suspension and consequently its coverage on the S800 latex from the mass balance equation. In the first stage of these measurements, calibration experiments were performed where the A100 latex particle deposition kinetics on bare mica for a well-defined bulk concentration was studied for various ionic strengths. The results of these measurements are shown in Figure 5 as the

o

−C i θ F( i Θ) = e

depletion (AFM)

)

where the C°i and C°p constants depend on the κdA parameter, where κ−1 = (εkT/2e2I)1/2 is the double-layer thickness, I = 1 /2(∑icizi2) is the ionic strength, and ci represents the ion concentrations. For thin double layers where κdA > 1, Ci° and C°p attain constant values of 10.2 and 6.5, respectively.14 It should also be mentioned that for higher coverage the Fi(Θ) function vanishes and the Fp(Θ) function attains 1/(2)1/2. Hence, the limiting values of the zeta potential of the S800 latex, for high coverage of the A100 latex, should attain (1/ (2)1/2)ζA (where ζA is the A100 latex zeta potential in the bulk). The results calculated from eqs 5 and 6 by considering the curvature effect (i.e., by assuming that the effective surface area for depositing A100 particles is larger by the factor 1 + (dA/dS)2 than the geometrical surface area of the latex πdS2/4) are plotted in Figure 4 as solid lines. As can be seen, they quantitatively agree with the experimental data for higher ionic strengths of 10−2 and 10−3 M. The deviation observed for the lowest ionic strength of 10−4 M is probably caused by the partial penetration of the latex into the fuzzy layer on the S800 latex particles. It should be mentioned that results analogous to those shown in Figure 4 were obtained in ref 17 in the case of fibrinogen adsorption on the negative latex particles. A deviation from the 3D electrokinetic model was observed only for the lower ionic strength of 10−3 M, whereas for higher ionic strength quantitative agreement with this model was observed. The results shown in Figure 4 suggest that the 3D model, developed originally for stationary, planar interfaces, is also applicable for spherical interfaces undergoing electrophoretic motion. This is significant because deposition processes on carrier particles proceed more efficiently with respect to kinetics than deposition on stationary interfaces. Additionally, the high slope of the zeta versus Θ dependencies, especially for the high ionic strength demonstrated in Figure 4, shows that the microelectrophoretic measurements can be exploited for a robust determination of the coverage of nanoparticles on colloid carriers under in situ conditions. The limited precision of the maximum coverage determination for higher ionic strength can be improved by the AFM procedure described above that enables a direct determination of the deposition kinetics of A100 latex on mica via direct imaging of particles. From the kinetic runs obtained in this way, one can determine the bulk concentration of A100 latex in the

Figure 5. Kinetics of the A100 latex deposition on mica determined by AFM imaging (pH 5.6, latex bulk concentration 100 mg L−1). (1) 10−2, (2) 10−3, and (3) 3 × 10−4 M. The inset shows the AFM micrograph of the A100 monolayer on mica. The solid lines denote the theoretical results calculated from the RSA model for diffusioncontrolled transport.

dependence of latex coverage Θm on the square root of the deposition time t1/2. As can be seen, the experimental data (solid points) are well reflected by the theoretical results calculated by numerically solving the governing transport equation using the blocking function derived from the random sequential adsorption (RSA) approach.32−34 A characteristic feature of these measurements is the linear increase in the coverage with t1/2 for shorter times. However, for longer times exceeding 400 min (t1/2 > 20), maximum coverages are attained that systematically increase with the ionic strength. Accordingly, they were 0.16, 0.25, and 0.42 for ionic strengths of 3 × 10−4, 10−3, and 10−2 M, respectively. It should be mentioned that analogous results were previously reported by Johnson and Lenhoff,13 who studied the role of ionic strength in the adsorption of positively charged amidine latex particles (116 nm in diameter) on mica. The results shown in Figure 5, obtained for flat and homogeneous interfaces, represent useful reference data for determining the A100 latex bulk concentration and analyzing the deposition on latex microparticle surfaces. As mentioned, for the A100 coverage range below 0.1, the following equation adequately describes the adsorption kinetics 696

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Langmuir Θm =

πdA 2 ⎛ Dt ⎞1/2 ⎜ ⎟ cA 2 ⎝π ⎠

Article

threshold concentrations cAmx, which was 20 mg L−1 for the above case. This allows one to calculate the maximum coverage of A100 using eq 4. In this way, one obtains Θmx = 0.52, which agrees with previous data obtained via direct counting and microelectrophoretic measurements (Table 2). An analogous procedure was applied for systematically determining the dependence of Θmx on the ionic strength varying between 10−4 and 10−2 M. Higher ionic strength was inaccessible because of the aggregation of the latex suspension after mixing. The maximum coverages obtained in this way varied between 0.25 and 0.48 for ionic strengths of 10−4 and 3 × 10−3 M, respectively. (These data are collected in Table 2.) As can be noticed, the AFM data agree with previously obtained microelectrophoretic results (within error bounds estimated to be 0.02−0.04). For the sake of convenience, the experimental results obtained by various methods are graphically presented in Figure 7. As can be seen, the maximum

(7)

where Θm is the A100 coverage on mica. As can be deduced from eq 7, by measuring the coverage of the A100 latex on mica after a fixed deposition time, one can determine its bulk concentration. This is exploited to determine the maximum coverage of the A100 latex on the S800 latex. In these experiments, the original latex suspensions, acquired after the A100 deposition step, were not filtered or centrifuged. This significantly facilitates these measurements. It should be mentioned that the deposition of the larger latex particles (loaded with A100 latex) on mica was negligible over the time of these experiments (1200 min) because of their considerably lower number concentration and lower diffusion coefficient. This renders the A100 bulk concentration determination by the AFM imaging effective and quite precise. Typical results of these experiments, expressed as the dependence of the A100 coverage Θm on its concentration in the suspension cA, are shown in Figure 6 (the S800 latex

Figure 7. Dependence of the maximum coverage of A100 latex Θmax on the ionic strength and the κdA/2 parameter (upper axis). The points denote experimental results acquired by AFM imaging. Solid line 1 denotes the theoretical results calculated from the RSA model for a spherical interface, and dashed line 2 denotes the theoretical RSA results for a planar interface. The solid points show the experimental results obtained for the A100 deposition on the S800 latex, and the open points denote the results for A100 deposition on bare mica.

Figure 6. Dependencies of the coverage of A100 latex on Θm, determined by AFM imaging on the initial concentration in the suspension after mixing, cA (pH 5.5, bulk concentration of the S800 latex 80 mg L −1). The experimental procedure was such that after the initial adsorption step, the latex suspension was contacted for 1200 minutes with mica sheets in the diffusion cell. The ionic strength 10−2 M. Solid line 1 shows the reference results predicted for diffusioncontrolled transport of A100 latex (calculated by numerical solution of the transport equation) and dashed lines 2 shows the fit of the experimental data. The insets show the AFM micrograph of the A100 monolayer on mica for a surface concentration of ca. 100 (μm−2).

coverage of the A100 latex monotonically increases with the ionic strength (i.e., the κdA parameter). This strict correlation suggests that this effect is caused by the lateral electrostatic interactions among adsorbed molecules, whose range decreases proportionally to 1/(κdA)1/2. This hypothesis is further supported by the fact that analogous results were reported in the literature for colloid particles,13,36 dendrimers,37−39 gold nanoparticles,40 and human serum albumin.41 However, the maximum coverages obtained in the case of A100 deposition on carrier latex particles are significantly higher than the maximum coverage obtained in the reference case of the latex deposition on the flat mica interface (open points in Figure 7). This indicates that the interface curvature effects played a significant role in enhancing the maximum coverage because of the higher geometrical surface area available for particles. It is useful to analyze these results quantitatively in terms of the theoretical model developed in ref 8, where the maximum coverage of particle deposition on curved interfaces of spherical and cylindrical shape was analyzed. The particles interacted via the exponentially decaying, Yukawa-type potential (with the dimensionless decay length equal to κdA/2) describing the

concentration was 80 mg L−1). The insets of this figure show the AFM image of the latex monolayer on mica. Also, for comparison, the reference data for the pure A100 suspension of variable concentration are shown in Figure 6 (solid line number 1). As can be observed, for the lower range of the A100 concentration in the initial mixture, its deposition on mica is negligible because Θm remains close to zero (within error bounds). Only for cA exceeding a threshold value was there a linear increase in Θm with the slope identical to the reference line (initial part of curve 1). This confirms that A100 deposition on the S800 latex was irreversible. It is interesting that this behavior is analogous to a breakthrough curve of filtration columns observed in the case of the irreversible adsorption of particles.35 By extrapolating the linear dependence shown in Figure 6 to zero surface concentration of A100, one obtains accurate 697

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proceed more efficiently with respect to kinetics than deposition on stationary interfaces. Additionally, because of the large slope of the zeta potential, the nanoparticle coverage dependencies indicate that the microelectrophoretic measurements can be exploited for a robust determination of the coverage of nanoparticles on colloid carriers under in situ conditions. The obtained results hold significance for basic science, indicating that the results obtained for curved interfaces (polymeric carrier particles) by the microelectrophoretic method can be exploited for interpreting the deposition of nanoparticles and proteins on planar interfaces and vice versa.

repulsive electrostatic lateral interactions. The Monte Carlo modeling based on the random sequential adsorption concept enabled one to determine the maximum coverage of particles as a function of the κdH parameter. It was also shown that the exact numerical data for adsorption on a spherical interface can be interpolated in terms of the following equation Θmx = Θ∞

(1 + A)2 (1 +

2h * 2 ) dA

(8)

where Θ∞ is the maximum coverage for hard (noninteracting) particles on a flat interface, equal to 0.547,42 A = dA/dS is the aspect ratio parameter, and h* is the effective interaction range characterizing the repulsive double-layer interaction particles. It can be calculated from the equation28 ⎧ ⎫ ⎡ ϕ ⎤⎪ 2h* ⎛ 1 ⎞⎪ ϕ0 1 ⎨ln ⎬ ln 0 ⎥⎪ =⎜ − ln⎢1 + ⎟⎪ ⎢⎣ dA 2ϕch ⎥⎦⎭ κdA ⎝ κdA ⎠⎩ 2ϕch

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

(9)

The authors declare no competing financial interest.

■

where ϕ0 is the characteristic interaction energy of two deposited particles at close separation and ϕch is the scaling interaction energy close to the kT unit. The theoretical results calculated from eqs 8 and 9 are shown as the solid line in Figure 7. As can be noticed, the agreement between theoretical and experimental data obtained for A100 deposition on the S800 latex is satisfactory for the higher ionic strength range of 10−3 to 10−2 M. It is interesting that the maximum coverages in this case are significantly larger than for the A100 latex adsorption on the flat mica substrate (hollow points in Figure 7). This shows that the curvature effect played an significant role in the A100 latex deposition on the S800 latex. However, for ionic strength below 10−3 M the experimental results for the A100 latex deposition are significantly higher than theoretically predicted. It should be mentioned that an analogous trend was previously reported in the case of fibrinogen adsorption on negative latex particles.17 It was postulated in this work that this discrepancy can be attributed to the fuzzy layer on the S800 latex particles that increases the charge screening efficiency of adsorbed fibrinogen molecules. It seems that an analogous phenomenon is responsible for the increase in the maximum coverage of the A100 latex observed in this work. This conclusion is also supported by the electrokinetic data shown in Figure 4. It view of these experimental results, it is evident that analogies exist between colloid particle deposition and protein adsorption on microparticle carriers.

ACKNOWLEDGMENTS This work was supported by NCN grant UMO-2012/07/B/ ST4/00559 and POIG grant 01.01.02-12-028/09 FUNANO.

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REFERENCES

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4. CONCLUDING REMARKS A combination of SEM imaging and in situ microelectrophoretic and concentration-depletion methods involving AFM enabled one to evaluate quantitatively the deposition mechanism of nanoparticles on microparticle carriers. Significant roles of ionic strength and the interface curvature were confirmed in these experiments. The increase in the maximum coverage with ionic strength was interpreted in terms of reduced electrostatic repulsion among nanoparticles that was theoretically accounted for by the random sequential adsorption model. It was also confirmed that the 3D electrokinetic model, developed for stationary and planar interfaces, is also applicable for spherical interfaces undergoing electrophoretic motion. This is significant because deposition processes on carrier particles 698

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