Gold Nanoparticle Monolayers of Controlled Coverage and Structure

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Gold Nanoparticle Monolayers of Controlled Coverage and Structure Katarzyna Kubiak, Zbigniew Adamczyk, Julia Maciejewska, and Magdalena O#wieja J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02683 • Publication Date (Web): 08 May 2016 Downloaded from http://pubs.acs.org on May 9, 2016

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The Journal of Physical Chemistry

Gold Nanoparticle Monolayers of Controlled Coverage and Structure

Katarzyna Kubiak, Zbigniew Adamczyk*, Julia Maciejewska, Magdalena Oćwieja

E-mail addresses: [email protected], [email protected], [email protected], [email protected]

Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8, 30 - 239 Cracow, Poland.

*Corresponding author Zbigniew Adamczyk phone: +48126395134 fax: +48124251923 e-mail: [email protected]

1 ACS Paragon Plus Environment


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ABSTRACT Deposition mechanism of gold nanoparticles on polly(allylamine chloride) modified gold sensor was investigated by the quartz crystal microbalance (QCM) and the scanning electron microscopy (SEM). The influence of the suspension concentration, flow intensity, ionic strengths and pH was systematically studied. It was shown that the deposition kinetics for lower coverage range was characterized by a linear increase of the coverage with the time. A general kinetic equation was formulated for calculating the particle deposition rates pertinent to the linear regime. Extensive measurements were also carried out for longer times at different ionic strengths and pHs. Negligible desorption of particles was observed that enabled one to precisely determine the maximum coverage of monolayers. These results were quantitatively interpreted in terms of the generalized random sequential adsorption (eRSA) model that considers the bulk and surface transfer steps in a rigorous way. It was proven, by comparing the QCM data with the SEM results, that the monolayer hydration was negligible. The structure of monolayers obtained for various ionic strength was also analyzed in terms of the radial distribution function by using the SEM micrographs of deposited particles.

Highlights: • Mechanism of gold nanoparticles deposition at PAH covered gold sensor was determined • Gold nanoparticle monolayers of controlled coverage and structure were prepared • Reference results for calculating macromolecule (protein) adsorption kinetics were obtained


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1. INTRODUCTION Gold nanoparticles belong to nanomaterials which attract major interest reflected by numerous literature reports devoted to the methods of their preparation, biofunctionalization and applications in various fields of sciences and industry1-4. In recent years, the main attention was focused on the synthesis of gold nanoparticles of desired optical and surface properties, useful for biological detection (biosensing), diagnostic immunoassays and in vivo imaging1-3. Since gold nanoparticles of suitable size and morphology, exhibit fluorescence and surface plasmon resonance (SPR), which is related to the collective oscillations of electrons induced by the visible light2, they are widely used in colorimetric sensing, fluorescence-based sensing, electrochemical sensing and surface enhanced Raman scattering (SERS)-based sensing1,4. In many of these applications a sensitive detection of target biomolecules was attained by using gold nanoparticle mono- and multilayers deposited on surfaces of electrodes4,5, glasses6-8 and quartz crystal microbalance (QCM) sensors9-17. Such chip-based sensors6,7 were successfully applied for label-free detection of microorganisms17, cells14, carbohydrates5,18, proteins8,16, antigens7,19 and DNA molecules9-13. However, despite of an extensive range of practical applications, relatively few experimental works were devoted to systematic studies of gold nanoparticle monolayer and film formation, especially to the kinetic aspects of these processes. Graber et al.20, by applying the UV-Vis, TEM and SERS measurements, studied selfassembly of 12 nm in diameter gold nanoparticles on quartz, glass and silica surfaces functionalized by alkoxysilanes. In another work21 the efficiency of various surface techniques to quantitatively study of gold monolayers was compared. It was suggested that a combination of scanning probe method (AFM or NSOM) with TEM or FE-TEM is required in order to obtain reliable data. However, in these works no information about the kinetics of gold particle self-assembly and the structure of the monolayers was provided.



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Schmitt et al.22 investigated self-assembly of 15 nm in diameter gold nanoparticles under diffusion transport on fused silica, silicon and mica substrates functionalized by various polymeric layers. Interesting kinetic dependencies were reported showing a linear increase in the coverage of gold particles with the square root of immersion time whose slope was proportional to the bulk suspension concentration. Systematic kinetic and structural studies of citrate stabilized gold nanoparticle monolayers on (aminopropyl)triethoxysilane (APTES)-modified silicon wafers, were performed by Kooij et al.23-27. Spectroscopic ellipsometry and AFM studies showed that the maximum coverage of the particles (12.8 nm in diameter) monotonically increased with the ionic strength of the suspension attaining ca. 28% for the ionic strength of 15 mM25. In Ref. 24 interesting kinetic data obtained by using the single wavelength reflectometry under flow conditions (stagnation point flow) were reported for the same gold nanoparticles and APTES modified substrate. The results were quantitatively interpreted in terms of the random sequential adsorption (RSA) model. On the other hand, in Ref.23,26 Kooij et al. determined by using AFM the structure of gold nanoparticle monolayers for various ionic strengths, quantitatively analyzed in terms of the radial distribution function. Electrochemical and optical properties of gold nanoparticle monolayers on gold electrodes modified by poly-L-lysine, protein and dithiols monolayers have been extensively studied in Refs.28-31 by cyclic voltammetry, electrochemical impedance spectroscopy SEM and AFM. Particle deposition kinetics in Refs.28,30,31 was interpreted in terms of the Langmuir model by using the adsorption constant as an adjustable parameter. Additionally, in Ref.31 thorough AFM measurements of the maximum coverage of gold nanoparticles were carried out with the aim of elucidating the role of ionic strength. The results, interpreted in terms of the random sequential adsorption (RSA) model, unequivocally proved the decisive role of ionic strength whose increase reduced the surface to surface distance among deposited


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particles. However, for higher ionic strength approaching 10-2 M, a significant aggregation of particles was observed that complicated the interpretation of experimental data. Winkler et al.32 determined by UV-vis spectroscopy the deposition kinetics of positively charged gold nanoparticles on glass and oxidized silicon substrates under diffusioncontrolled transport. The influence of ionic strength, for a broad range up to 2 M, was systematically studied and the experimental data were interpreted in terms of the Langmuir adsorption model. This interesting study unequivocally showed that by increasing ionic strength one can obtain gold particle monolayers of high density. However, the structure of monolayers was rather irregular because of the aggregation of gold particles for higher ionic strength. Given a high density and shape stability of gold nanoparticles, it can be expected that their deposition kinetics can be efficiently studied by using the quartz crystal microbalance (QCM) technique. However, despite a considerable significance, there are few works focused on fundamental aspects of gold monolayer formation under various conditions. Most of QCM studies were performed with the aim to develop efficient sensors with embedded gold nanoparticles as signal enhancement probes15. This allowed to increase the immobilization capacity and detection limit of some biomolecules1,4,9,15. Lin et al.9 showed that the deposition of citrate-stabilized gold nanoparticles with the diameter of 12 nm onto thiol-modified QCM sensor caused an efficient attachment of HS-DNA to the surface. It was confirmed that the amount of immobilized DNA strongly depended on the coverage of gold nanoparticles. These results represent a novel strategy for the development of efficient nucleic acid and oligonucleotid sensors. Zhao et al.10 as well as Liu with coworkers11,12 studied the applicability of gold nanoparticles of various sizes and surface properties as signal amplifiers in DNA detection.



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In an approach developed by Kim and coworkers15, a highly sensitive detection of biomolecules was achieved by their deposition onto QCM sensor and a subsequent deposition of gold nanoparticles as signal amplification probes. However, in these QCM oriented studies, the gold nanoparticle deposition onto macromolecule monolayers have not been quantitatively analyzed by considering the influence of their concentration, pH and ionic strength, transport conditions (flow rate), etc. No adequate kinetic models have been developed that can be used to systematize the results and derive conclusions of a general validity. Because of the lack of reliable information, the aim of this work is to elucidate mechanisms of gold nanoparticle monolayer formation at macromolecule covered surfaces by applying the QCM-D method, previously used for silver nanoparticles33. It should be mentioned that the gold nanoparticles significantly differ from previously studied silver nanoparticle system in respect to the density, surface properties and suspension stability. Because of much higher density, the hydration degree of gold monolayers is expected to be lower than the hydration of silver nanoparticles. This increases the precision of the mass transfer coefficient determination and facilitates to derive a universal formula enabling one to determine the dry mass of macromolecules, e.g. proteins, for arbitrary transport conditions. As a result the macromolecule hydration function can be calculated without using additional ex situ measurements. Additionally, in this work unique two-stage kinetic measurements are performed that directly prove the significance of the electrostatic interactions and the irreversibility of gold particle deposition. Finally, in contrast to the previous Ag nanoparticle work, the structure of monolayers obtained for various ionic strengths is quantitatively analyzed in terms of the radial distribution function by using the SEM micrographs of deposited particles. In this way, the significance and the range of electrostatic interactions is proven. The experimental data


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are theoretically interpreted in terms of the generalized random sequential adsorption model (eRSA)33,34 that allows one to determine in a precise way the mass transfer coefficients under various physicochemical and flow transport conditions.

2. EXPERIMENTAL SECTION

2.1 Materials and Methods Hydrogen tetrachloroaurate (HAuCl4, 99.999%), trisodium citrate, sodium chloride, sodium hydroxide, hydrochloric acid, phosphate-buffered saline (PBS), Trizma® base (2-amino-2-(hydroxymethyl)-1,3-propanediol) were commercial products of Sigma Aldrich. Sulfuric acid (95%) and hydrogen peroxide (30 %) were obtained from Avantor Performance Materials Poland S.A. Poly(allylamine hydrochloride) (PAH) having a molecular weight of 70 kDa was purchased from Polysciences. Ultrapure water, used in this work, was obtained using the Milli-Q Elix&Simplicity 185 purification system from Millipore SA Molsheim, France. In the electrophoretic mobility measurements, pH of the gold particle suspensions was regulated by the addition of NaOH or HCl by keeping the ionic strength constant. On the other hand, in the deposition experiments, pH was fixed at precisely controlled value of either 7.4 or 9 by using the PBS or Trizma buffers, respectively. The synthesis of gold nanoparticles was performed according to the chemical reduction method by exploiting trisodium citrate as a reducing and stabilizing agent35-37. Briefly, 100 ml of 1mM hydrogen tetrachloroaurate aqueous solution was heated to 88oC under refluxing conditions. While stirring vigorously, 10 mL of 38.8 mM sodium citrate solution was quickly added, resulting in the color changes of the originally yellow solution to burgundy red. The mixture was kept at 88oC for 15 minutes and subsequent cooled to room temperature while stirring continuously. After the synthesis, the gold suspension was purified 7 ACS Paragon Plus Environment


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from ions excess using a stirred membrane filtration cell (Millipore, model 8400) with a regenerated cellulose membrane (Millipore, NMWL: 100 kDa). The filtration procedure was continued until the conductivity of the suspension decreased to 15 µS/cm at pH of 5.5-6.0. The mass concentration of the gold particle suspension after the purification was determined by using the densitometer DMA 5000 (Anton Paar) according to the procedure described in Ref. 35. The hydrodynamic diameter of particles and the stability of their suspensions under controlled conditions of pH and ionic strength were determined by the dynamic light scattering (DLS) measurements of the diffusion coefficient using the Nano ZS Zetasizer from Malvern. UV-vis spectra of nanoparticle suspension were recorded by the Shimadzu UV-1800 spectrometer. The electrophoretic mobility of particles was measured using the LDV method (Nano ZS Zetasizer apparatus). The zeta potential was afterward calculated from the Henry’s equation 35. Quartz QCM sensors covered by the gold layer (Q-Sense, Gothenburg, Sweden) had a basic frequency of 4.95 MHz. The sensors were cleaned in a mixture of 95 % sulfuric acid (H2SO4) and hydrogen peroxide (30 %) at the volume ratio 2:1. Afterward, the sensor was rinsed by deionized water at 80° C for 30 minutes and dried out in a stream of a nitrogen gas. The topology and roughness of the sensor was examined by atomic force microscopy (AFM), by using the NT-MDT Solver Pro instrument with the SMENA SFC050L scanning head. It was confirmed that the sensors were homogeneous and exhibited the root mean square roughness of 3 nm. Quartz crystal microbalance with dissipation monitoring was used for real-time investigations of gold particle deposition kinetics. Initially, in each measurement, a stable base line for the pure electrolyte (PBS or Trizma buffers) of controlled ionic strength was obtained. After the stabilization of the baseline, the cationic polyelectrolyte poly(allylamine


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hydrochloride) (PAH) was adsorbed on the sensor at pH 5.6, ionic strength 10-2 M NaCl, from solutions having the concentration of 10 mg L-1 under flow rate of 0.0133 cm3 s-1. In the next step, gold particle suspension of controlled concentration was flushed. Upon obtaining a stable signal, the pure electrolyte solution was flushed through the cell in order to study particle desorption. The bulk concentration of gold particle suspensions in the experiments was 10 - 50 mg L-1, and the flow rates were varied between 1.33 10-3 cm3 s-1 to 6.16 10-3 cm3 s-1. The mass of deposited particles was calculated from the Sauerbrey’s equation ∆m = − C

∆f n

33,38-40

(1)

where ∆m is particle mass per unit area, ∆f is the frequency change, n is the overtone number and C is the mass sensitivity constant depending on the physical property of sensor. For a 4.95 MHz AT-cut quartz crystals, it is equal to 0.177 mg m-2 Hz 38-40. The particle size distribution on QCM sensors after the deposition experiments was determined by scanning electron microscopy (SEM, JEOL JSM-7500F). Additionally, their surface concentration (coverage) was calculated from the SEM micrographs by using an image-analysis software.

3. RESULTS AND DISCUSSION

3.1. Characteristics of particle and the substrate

The mass concentration of gold particles in the purified stock suspension was 178 mg L-1 as determined by densitometry 35. The size distribution of particles was characterized by TEM imaging, see Fig. 1. The average particle size derived from the histogram obtained in this was 14.1 ±2 nm. 9 ACS Paragon Plus Environment


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Fig. 1. The histogram of gold nanoparticle size distribution acquired from SEM measurements of monolayer deposited on the PAH modified gold sensor (shown in the inset).

Additionally, the size of gold particles was determined by DLS via the diffusion coefficient measurements. From the diffusion coefficient, the hydrodynamic diameter of particles was calculated by using the Stokes-Einstein formula. It was equal to 13 ±3 nm at pH range 7-9 and ionic strength range 10-4

to 10-2 M. It should be mentioned that the

hydrodynamic diameter of particles remained constant for prolonged time periods up to 2000 hours for these pHs and ionic strengths, that confirmed the stability of particle suspensions over the time of the deposition experiments, typically lasting 5-40 minutes.


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µe

-1

-20

-1

ζ [mV]

[µmcm(Vs) ]

-2

-40

-3 -60

-4 -80

-5 2

4

6

8

10

12

pH

Fig. 2. The electrophoretic mobility of gold nanoparticles vs. pH regulated by addition of either HCl or NaOH for the ionic strength of 10-3 M. The hollow points show the results obtained for buffered solutions.

Except for DLS, extensive measurements of the electrophoretic mobility of gold nanoparticles were carried out by applying the micro-electrophoretic method. The result shown in Fig. 2 indicate that the particles exhibit a negative electrophoretic mobility monotonically decreasing with pH from -2.2 to – 3.0 µm cm (V s)-1 for pH 3 and 11, respectively (for ionic strength of 10-3 M). Analogous results were obtained for other ionic strengths. Knowing the mobility, the zeta potential of particles was calculated from the Henry’s equation35. Accordingly, for pH 3 the zeta potential was equal to -40 mV and for pH 11, - 57 mV (for ionic strength of 10-3 M). These results are collected in Table 2.



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Table 1. Physicochemical characteristics of gold nanoparticles used in this work.

Property [unit], symbol

Value

Remarks

Specific density [g cm-3], ρ p

19.3

Literature data41

Diffusion coefficient [cm2 s-1], D

-7

3.7x10 ± 0.5 x10

Determined by DLS for T = 298 K, pH 6-9 I = 10-4 – 10-2 M, NaCl

-7

Hydrodynamic diameter [nm], dH

13±3

Calculated by using the diffusion coefficient

Particle size [nm], dp

14.1±2

From TEM imaging

Geometrical cross-section area [nm2], Sg

156

from geometry

Plasmon absorption maximum [nm], λp

521

Measured for pH 4-9 I = 10-4 - 10-2 M, suspension concentration 20 mg L-1

Table 2. Electrophoretic mobility and zeta potential of gold nanoparticles for various ionic strengths, pH 7.4 (PBS) and 9 (Trizma), T = 298 K.

Ionic strength [M] 10-4 pH 7.4 9 10-3 pH 7.4 9 10-2 pH 7.4 9

µe µm cm (V s)-1

ζp [mV] Henry’s model

0.23

-3.01± 0.1 -3.26± 0.1

-58 -63

0.73

-2.78 ± 0.1 -2.93± 0.1

-52 -55

2.30

-2.61 ± 0.1 -2.87± 0.2

-47 -52

κdp


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3.2. The kinetics of particle deposition

Extensive measurements were performed by using the QCM-D method with the aim of thoroughly determine the kinetics of gold nanoparticle deposition on the PAH modified gold sensor. A primary run acquired in these experiments is shown in Fig. 3 as the dependence of the frequency shift and dissipation on the time. In the first stage, a stable PAH monolayer was adsorbed over the time of 20 minutes. Afterwards, the pure electrolyte was flushed through the cell and the desorption run was recorded. Negligible desorption of PAH was observed in all these runs. The zeta potential of PAH monolayers was assumed to change between 60 and 45 mV as deduced from previous results obtained for mica42. After establishing a stable signal stemming from the PAH monolayer, the deposition run was initiated by pumping the gold nanoparticle suspension at the flow rate of 2.5 10-3 cm3 s-1. The decrease in the frequency shift (see Fig. 3) indicated a rapid deposition of the gold particles. After the frequency shift attained a steady-state value the desorption run was initiated by flushing a pure electrolyte through the cell at the same flow rate. Negligible change in the frequency shift confirmed that the desorption of gold particles was minimal. Additionally, as one can observe in Fig. 3, the dissipation function assumed very low values, of the order of 10-6 for the entire deposition/desorption run. This confirms the validity of the Sauerbreys’s equation used for calculating ∆m that is usually expressed in ng cm-2

43,44

.

However, it is more convenient to express the ∆m in mg m-2 as usually done in the protein oriented literature34 . For the sake of convenience this parameter, corresponding to the particle coverage, is denoted hereafter by Γ. In order to increase the precision of measurements, the particle coverage was calculated as average from the third, fifth and seventh overtone.



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Fig. 3. The primary QCM measurements of gold nanoparticle deposition at the PAH modified Au sensor expressed as the frequency change [Hz] and the relative dissipation (right hand axis) vs. the time for the average third, fifth and seventh overtone, pH 7.4 (PBS), bulk suspension concentration 30 mg L-1, ionic strength 10-2 M, flow rate 2.5 10-3 ml s-1. By using the Sauerbrey’s equation, the primary frequency changes derived from QCM measurements were converted to the dependence of the coverage on the deposition time. The kinetics of particle deposition on PAH modified gold sensor obtained in this way at pH 7.4 (fixed by the PBS buffer), I = 10-2 M and the flow rate of 1.33x10-3 cm3 s-1 is shown in Fig. 4. The kinetic runs derived for gold suspension concentration of 50, 30 and 10 mg L-1, respectively, indicate that after a short transition time lasting ca. 0.2 min. the particle coverage increased linearly with the time for all bulk suspension concentrations. This confirms that gold particle deposition under the steady state was bulk transport controlled and the surface blocking effects were negligible. Additionally, the linearity of deposition kinetics suggests a minor hydration of the gold particle monolayer, in accordance to what was previously observed for silver nanoparticles33.


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Fig. 4. Gold nanoparticle deposition kinetics (PAH modified Au sensor, pH 7.4, PBS) for various bulk suspension concentrations 1) 50 mg L-1, 2) 30 mg L-1, 3) 10 mg L-1, I = 10-2 M , flow rate 1.33x10-3 cm3 s-1. It should also be mentioned that the slope of the linear dependencies Γ vs. t shown in Fig. 4 increases proportionally to the bulk suspension concentration cb that also confirms the bulk transport controlled deposition regime of gold nanoparticles. In order to study this aspect in more detail, extensive kinetic measurements were carried out for other ionic strengths and pHs. Results of these experiments shown in Fig. 5 indicate that for all ionic strengths, pH 7.4 and 9, the slopes of the Γ vs. the time dependencies are identical. This confirms that the electrostatic interactions between the sensor and gold nanoparticles did not influence the rate of particle deposition that was, therefore, bulk transport controlled.



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Fig. 5. Gold nanoparticle deposition kinetics (PAH modified Au sensor), bulk suspension concentration 30 mg L-1, flow rate 1.33x10-3 cm3 s-1, (1) 10-4 M, pH 7.4 (PBS), (2) 10-2 M, pH 7.4 (PBS), (3) 10-2 M, pH 9 (Trizma), (4) 10-3 M, pH pH 7.4 (PBS). From the experimental data shown in Figs. 4-5 the mass transfer rate constant kco, defined as ∆Γ/ (∆t cb ), was precisely calculated. For the flow rate of 1.33x10-3 cm3 s-1, kco was equal to 1.02·10-4 ± 4·10-6 L m-2 s-1 = 1.02·10-5 ± 4·10-7 cm s-1. Hence, by knowing kco, the kinetics of particle deposition under the linear, bulk controlled regime is given by the expression: Γ = kco cb t

(2)

However, as shown in the case of silver nanoparticle deposition33, the mass transfer rate constant depends on the volumetric flow rate of the suspension. Therefore, a series of kinetic experiments was carried out for various ionic strength and pHs where the influence of the flow rate was systematically studied. Typical results obtained for pH 7.4 (PBS), bulk suspension concentration 10 mg L-1, I = 10-2 M are shown in Fig. 6.


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Fig. 6. Gold nanoparticle deposition kinetics (PAH modified Au sensor, pH 7.4, PBS), bulk suspension concentration 10 mg L-1, I = 10-2 M:1) 6.16x10-3 cm3 s-1, 2) 2.5x10-3 cm3 s-1, 3) 1.33x10-3 cm3 s-1. As can be seen, the particle deposition kinetics is a linear function of time with the slope monotonically increasing with the flow rate. A thorough regression analysis showed that the results obtained for various flow rates can be well fitted by the expression 1

kc = kco (Q / Qo ) 3

(3)

where Qo = 1.33x10-3 cm3 s-1. This result can be generalized by considering that for convection driven transport in the QCM cell, the surface averaged mass transfer rate constant can be expressed as45,46

1

2

kc = C f Q 3 D 3

(4)

where Cf is the constant depending on the cell’s geometry and D is the diffusion coefficient of the solute (nanoparticle). It is interesting to mention that the validity of Eq.(4) for QCM cell flows was confirmed by Zhang et al.47.



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By using the diffusion coefficient calculated from the SEM diameter of gold nanoparticles one can calculate from Eq.(4) that the Cf constant is equal to 1.9 cm- 4/3. This is close to the previously determined value for silver nanoparticles that was equal to 1.99 cm- 4/3 33. Given the significantly higher density of gold compared to silver, one can expect a higher accuracy of the Cf constant determined in this work compared to the previous one. Accordingly, under the linear adsorption regime, the dry mass of a solute can be calculated from the dependence 1

2

Γ = 10 C f Q 3 D 3 cb t

(5)

where Γ is expressed in mg m-2 and cb in mg L-1. It should be mentioned that Eq.(5) can be used for predicting the dynamic hydration degree of various macromolecules, e.g., proteins if the wet QCM coverage is known without performing additional ex situ experiments34. After precisely determining the mass transfer rates for the linear deposition regime, nanoparticle deposition for longer times was studied where the surface blocking effects play a significant role. The primary goal of these investigation was obtaining the maximum coverage for various ionic strengths. Typical kinetic runs obtained in this case for pH 7.4 (PBS) and ionic strength of 10-2 M and 10-3 M are presented in Fig. 7. One can observe that for longer deposition time, a stationary coverage Γmx of the gold nanoparticle is attained independently of the bulk suspension concentration. As discussed in previous works45,46,48 this behaviour unequivocally indicates that the deposition process was irreversible. However, Γmx abruptly decreases for lower ionic strength being equal to 53 mg m-2 for ionic strength of 10-2 M and 27 mg m-2 for ionic strength of 10-3 M that unequivocally confirms an essential role of the electrostatic interactions. Analogous effect was also observed for the lowest ionic strength of 10-4 M as discussed later on.


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b)

Fig. 7. Gold nanoparticle deposition kinetics on PAH modified Au sensor, pH 7.4 (PBS) flow rate 2.5 x 10-3 cm3 s-1, determined by QCM-D for bulk suspension concentration of (1) 50 mg L-1, (2) 30 mg L-1, (3) 10 mg L-1. Part a, experimental data obtained for ionic strength 10-2 M. Part b, experimental data obtained for ionic strength 10-3 M. The dashed-dotted lines show the theoretical results calculated from the eRSA model and the dotted line shows the results calculated from the usual RSA model by neglecting the coupling between bulk and surface transport.

A quantitative interpretation of the kinetic runs was performed in terms of the random sequential adsorption (RSA) approach

49-54

extended in Refs.46,55,56 by considering the

coupling of the bulk and surface transport steps. RSA is on a stochastic process governed by the following rules49-54 (i) a particle is generated having its position and orientation selected at 19 ACS Paragon Plus Environment


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random within an isotropic adsorption domain, (ii) if the particle fulfills prescribed criteria it becomes irreversibly adsorbed (deposited) and its position remains unchanged during the entire simulation process, (iii) if the deposition criteria are violated, a new attempt is made that is fully uncorrelated with previous attempts. There are two major deposition criteria (i) the lack of overlapping of any previously adsorbed particle and (ii) a contact with the substrate surface. It should be mentioned that RSA is a flexible approach enabling to determine the available surface function50-54 called in the colloid oriented literature less accurately surface blocking function, denoted by B(Γ), and the maximum coverage of particles interacting via the screened Coulomb potential. In order to account for the correlation between consecutive deposition events that occur under convective-diffusion transport conditions, we have used the available surface function (blocking function) as the boundary conditions for the for the bulk transport equation

46, 55-56

. This hybrid approach is referred to as the extended RSA

model. It physically reflects the situation that a particle approaching the interface upon a failed deposition attempt does not disappears as the classical RSA model postulates but is able to undertake other deposition attempts in close vicinity. In this way, for convection driven transport, one can formulate the following kinetic equation where this correlation between deposition events is consider33

Γ

∫ Γ

0

( ka − kc ) B ( Γ ' ) + kc ka nb B ( Γ ' ) − kd Γ '

d Γ ' = kc t

(6)

where, Γ is the time-dependent coverage of particles, Γ0 is the initial coverage Γ’ is the dummy integration variable, ka and kd are the kinetic adsorption and desorption constants, kc is the mass transfer constant.


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Eq.(6) represents a general solution of the convective mass transfer kinetics valid for arbitrary particle size. If the coupling is neglected, by assuming that ka = kc, Eq.(6) reduces to the simpler dependence:

Γ

1

∫ k n B( Γ ) − k '

Γ0

a b

' dΓ

dΓ ' = t

(7)

By considering that the desorption of gold nanoparticle was negligible, i.e., kd = 0, the deposition kinetics was calculated from Eqs.(6-7) by using a four-point numerical integration algorithm. For efficiently performing calculations, it is useful to introduce the absolute (thermodynamic) coverage of particles defined as

θ = S g N s = 1.5 ⋅10−7

1 Γ ρs d p

(8)

By using this definition, one can express the blocking function for spherical particles in the following form46,48

2

3

B (θ ) = (1 + a1θ + a2 θ + a3θ )(1 − θ )3

where θ =

(9)

θ −7 1 Γ is the maximum coverage, is the normalized coverage, θmx = 1.5 ⋅10 ρs d mx θmx

and a1 – a3 are the dimensionless coefficients equal to 0.812, 0.426 and 0.0717, respectively. The maximum coverage of particles that is dependent on ionic strength and particle zeta potential was calculated in Refs.46,48,56 by numerical modeling. The exact theoretical data derived by applying a Monte-Carlo algorithm were approximated by a useful analytical formula48 21 ACS Paragon Plus Environment


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θ mx = θ ∞

1

(1 + 2h

*

/d

)

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(10)

2

where θ∞ is the maximum coverage for hard particles that is equal to 0.547 for spheres46,48,56 and h* is the effective interaction range characterizing the electrostatic repulsion among particles in the monolayer46,56 . The effective interaction range can be calculated for spherical particles interacting via exponentially decaying potential from the formula

h* =

 φ  1  φo 1 − ln  1 + ln o   ln κ d  φch φch    κd

(11)

where φo is the interparticle electrostatic energy at contact that depends on the particle zeta potential and φch is the characteristic interaction energy close to one kT unit 46,48. It is to mention that in contrast to the widely used Langmuir model, in our calculation scheme no adjustable parameters are used since they can be either theoretically predicted, for example the maximum coverage the blocking function, adsorption constant, or can be measured, e.g., the diffusion coefficient, particle size and density, electrophoretic mobility, zeta potential, etc. One can observe in Fig. 7 that the theoretical results properly reflect the experimental data for the entire range of bulk suspension concentration and deposition time. In contrast, the results calculated from Eq.(7) by exploiting the standard RSA model, where the bulk transport step is neglected (depicted in Fig. 7 as dotted lines), significantly underestimate the experimental data. This shows that the eRSA model used in this work, where correlations between particle deposition attempts are considered in an exact way, is more appropriate for interpreting nanoparticle deposition kinetics.


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Interestingly, the experimental maximum coverages, equal to 0.29 and 0.15 for ionic strength of 10-2 and 10-3, respectively, agree to within error bounds with the theoretically predicted values of 0.28 and 0.14. This indicates that the lateral electrostatic interactions among particles exert a decisive influence on their adsorption mechanism for the higher coverage regime. This hypothesis is supported by the results of a composite experiment shown in Fig. 8. In the first stage, nanoparticle deposition was carried out at lower ionic strength of 10-3 (at pH 7.4, PBS). Afterwards, when a saturated monolayer of lower coverage was attained, the ionic strength was abruptly changed to 10-2 M by flushing a more concentrated NaCl solution of the same pH. All other governing parameters of this deposition run remained unchanged. As seen in Fig. 8, an abrupt deposition of gold nanoparticles appeared and a much higher maximum coverage was attained. It almost matched the value pertinent to primary experiments carried out at fixed ionic strength of 10-2 M from the very beginning. Therefore, the experimental data presented in Fig. 8 unequivocally confirm the electrostatic mechanism of particle deposition and the irreversibility of this process.

Fig. 8. A two-stage kinetics of gold nanoparticle deposition on PAH modified Au sensor, pH 7.4 (PBS), ionic strength change from 10-3 M to 10-2 M at the time of 60 min., line 2. Lines 1 and 3 show the results obtained for single step gold nanoparticle deposition for ionic strength 10-2 M (line 2) and 10-3 M (line 3).



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It should be mentioned that experiments of this type, directly confirming the significance of electrostatic interactions and irreversibility of gold particle deposition have not been before reported in the literature. Additional measurements yielding the maximum coverage were also performed for different pHs and ionic strength. In order to quantitatively calibrate the QCM results, the coverage of gold nanoparticles on the sensor after the deposition run was also determined by ex situ SEM imaging. In this way, by analyzing the micrographs acquired by SEM, the surface concentration of particles, denoted by Ns, was determined. Then, the particle coverage was calculated from the dependence

Γ = (π d p3 ρ p / 6 ) N s

(12)

The results derived from SEM are compared with the QCM data and the RSA theoretical results in Table 3. In all cases the agreement between experimental and theoretical data is satisfactory, even for the lowest ionic strength of 10-4 M. This indicates that the supporting PAH layer exerts a negligible influence on the gold particle deposition process. This is physically explained by observing that the thickness of the PAH layer is less than a few nanometers 33, 39,42 .


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Table 3. Maximum coverages of gold nanoparticles θ mx derived from QCM, SEM measurements and RSA modeling.

θ mx [1] I [M]

10

10

10

pH QCM

SEM

RSA (theoretical)

7.4

0.10± 0.005

0.098 ± 0.002

0.10

9

0.09± 0.005

0.09±0.003

0.095

7.4

0.15± 0.003

0.15 ± 0.003

0.14

9

0.13± 0.003

0.14± 0.002

0.13

7.4

0.29± 0.005

0.28 ± 0.0052

0.28

9

0.26± 0.005

0.27± 0.005

-4

-3

-2

0.27

One can observe that the maximum coverages obtained at pH 9 are slightly smaller than the corresponding coverages at pH 7.4. This effect is attributed to the lower zeta potential of the PAH/gold monolayer at pH 9. It should be mentioned that the agreement of QCM and SEM results observed for all ionic strengths confirms that the hydration of the gold monolayer is also negligible for the high coverage range. This has an essential practical significance indicating that Eqs.(5,6) can be used for calculating the dry mass of adsorbed solutes. In this way, a quantitative interpretation of the QCM measurements for macromolecules (proteins) is facilitated whose degree of hydration depends on the substrate topology (roughness), protein shape, monolayer coverage and molecule orientation, viscosity of the monolayer, etc. By knowing the dry mass, the deconvolution of the primary QCM signal aimed at deriving the ‘dry’ mass of the protein can be done ab initio without accepting empirical models of the monolayer structure and without performing ex situ adsorption measurements for the same substrate by using ellipsometry, OWLS , etc. 25 ACS Paragon Plus Environment


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Another conclusion of practical significance, that can be derived by analyzing the data show in Table 3, is that one can precisely regulate the coverage of gold nanoparticle monolayers by the adjustment of the ionic strength that changes the range of electrostatic interactions. One can also expect that the ionic strength should influence the structure of particle monolayers. This has been confirmed by performing extensive SEM studies of the structure of nanoparticle monolayers deposited under various conditions. Typical monolayers obtained for ionic strength of 10-4, 10-3 and 10-2 M are presented in Fig. 9. One can directly observe that the 10-4 M monolayer is characterized by a very uniform particle distribution with average distance among their centers considerably exceeding their diameter. For increasing ionic strength, the monolayers become more dense and the distances among particles decrease. Analogously as in Refs.23,25 these effects were quantitatively analyzed in terms of the radial distribution function g (called also the pair correlation function) by exploiting the SEM micrographs. This function is calculated according to the procedure described in our previous works57 by taking assembly averages of the number of particles at given radial distance normalized to the bulk uniform number of particles. In order to attain a proper statistics, typically the positions of ca. 5000 particles were determined by image analyzing software. The radial distribution functions obtained in this way are shown in Fig. 9. One can observe that in all cases a well-pronounced maximum appeared at the distance ca. 3, 2.5 and 1.9 dp for ionic strength of 10-4, 10-3 and 10-2 M, respectively. By considering that the average particle size is 14.1 nm this corresponds to the physical distance between particle surfaces equal to 28, 21 and 13 nm and the effective interaction range h* equal to 14, 10.5 and 6.5 nm. Accordingly, for ionic strengths of 10-3 and 10-2 M, the effective range h* is twice the double layer double-layer thickness equal to 9.6 and 3.1 nm, respectively. However, for the lowest ionic strength of 10-4 M (double-layer thickness 31 nm) this proportionality does not


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hold that can be attributed to influence of the positively charged substrate that decreases, at longer distances, the repulsive interaction among particles.

a)

b)

c)



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Fig. 9. SEM micrographs of gold nanoparticle monolayers deposited at QCM gold sensor (pH 7.4) and corresponding radial distribution functions obtained for ionic strength “a” 10-4 M, ( θ = 0.098), “b” 10-3 M ( θ = 0.15) and “c” 10-2 M ( θ = 0.28). The arrows show the position of the maximum of the radial distribution function. The solid lines represent a least square interpolations of the experimental data.

Although the radial distribution function pair correlation for monolayers obtained under flow conditions in QCM cells have not been reported before, the surface to surface distance was determined by SEM in Ref.28 to be equal to 25 nm for gold particles having the diameter of 18 nm. Ionic strength was not specified in this work but one can estimate that it was ca. 10-3 M, hence this result reasonably agrees with our measurements. Analogously, the surface to surface distances among gold nanoparticles 13 nm in diameter were determined by AFM in Ref. 31 For higher ionic strength of ca. 10-2 M the interparticle distance approached 19 nm, whereas for lower ionic strength range it was considerably larger. Therefore, the results shown in Fig. 9 confirm that by changing ionic strength one can adjust in a continuous way both the averaged distance among deposited particles and the coverage of monolayers. This has essential practical significance in the perspective of producing biosensors having controlled structure of surfaces matching the structure of the analyte, e.g., protein molecules.

4. CONCLUSIONS Extensive measurements performed in this work confirmed that the kinetics of gold nanoparticle deposition for the low coverage regime was determined by the bulk transport rather than the surface mass transfer step. In consequence, the particle coverage increased linearly with the time independently of ionic strength and pH. This enabled one to derive Eq.(5) for calculating mass transfer rates for various flow rates and diffusion coefficients without using adjustable parameters. Given a much larger density of gold than silver, the precision of this formula is higher than previously derived for the silver nanoparticles. 28 ACS Paragon Plus Environment

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Kinetic measurements performed for longer times showed that there was no desorption of particles that allowed to precisely determine the maximum coverage of monolayers for various physicochemical conditions. It was confirmed that that the maximum coverage of nanoparticles increased with ionic strength because of decreasing extension of repulsive electrostatic interactions. This effect was directly confirmed by statistically analyzing the distribution of particles in the monolayers carried out in terms of the radial distribution function. The kinetics of particle deposition were quantitatively interpreted in terms of the theoretical model (eRSA) where the bulk and surface transfer steps were rigorously taken into account. Also, the two-stage kinetic measurements confirmed in a direct way the significance of the electrostatic interactions and the irreversibility of gold particle deposition. It was also confirmed, by comparing the QCM and SEM results that the hydration degree of the gold nanoparticle monolayer was minimal. By considering this finding, it was postulated that Eqs.(6-7) can be used for precisely calculating the coverage of macromolecules adsorbing in the QCM cell under various conditions. In this way, the macromolecule hydration degree can be unequivocally determined without applying additional measurements. The structure of monolayers obtained for various ionic strength under flow conditions that was not determined before was analyzed in terms of the radial distribution function by using the SEM micrographs of deposited particles. In this way, the significance of electrostatic interactions was confirmed and the interparticle distance was directly determined. Besides significance to basic sciences, the obtained results can be exploited for developing an efficient procedure of preparing gold-nanoparticle monolayers of desired coverage and structure having potential applicability as biosensors.



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ACKNOWLEDGMENTS Financial support from the NCN Research project: UMO-2012/07/B/ST4/00559 is acknowledged. The authors are grateful to Dr. Małgorzata Zimowska for her assistance in the SEM measurements.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

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(53) Tarjus, G.; Schaaf, P.; Talbot, J.; Random sequential addition: A distribution function approach. J. Stat. Phys. 1991, 63, 167-202. (54) Talbot, J.; Tarjus, G.; van Tassel, P.R.; Viot, P; From car parking to protein adsorption: an overview of sequential adsorption processes. Colloid Surf. A 2000, 165, 287-324. (55) Adamczyk, Z.; Barbasz, J.; Cieśla, M.; Mechanisms of fibrinogen adsorption at solid substrates. Langmuir 2011, 27, 6868–6878. (56) Adamczyk, Z.; Modelling adsorption of colloids and proteins. Curr. Opin. Colloid Interface Sci. 2012, 17, 173–185. (57) Adamczyk, Z.; Zembala, M.; Siwek, B.; Structure and ordering in localized adsorption of particles. J. Colloid Interface. Sci. 1990, 140, 123-137.


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GRAPHICAL ABSTRACT


Gold Nanoparticle Monolayers of Controlled Coverage and Structure

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