Stability of silver nanoparticle monolayers determined by in situ streaming potential measurements

All chemical reagents used in the experiments (silver nitrate, trisodium citrate, sodium chloride, sodium hydroxide, and hydrochloric acid) were commercial products of Sigma Aldrich and applied directly without further purification.

Natural ruby mica sheets were purchased from Continental Trade and used as a solid substrate for the colloidal particle adsorption. The solid pieces of mica were freshly cleaved into thin fragments of desired area and used in each experiment without any pretreatment. Ultrapure water obtained using the Milli-Q Elix&Simplicity 185 purification system from Millipore SA Molsheim, France was used to prepare all solutions and synthesize colloidal suspensions.

The cationic polyelectrolyte, poly(allylamine hydrochloride) (PAH), having a molecular weight of 70 kDa was purchased from Polysciences and used as supporting layer for silver nanoparticle deposition.

Silver nanoparticle suspensions were synthesized by a chemical reduction of AgNO₃ using trisodium citrate, which has been widely applied for the preparation of various metallic nanoparticles (Kamyshny and Magdassi 2009) and described in details in our previous work (Oćwieja et al. 2013). Briefly, a sample of silver nitrate (200 mg) was dissolved in distilled water to obtain silver ions concentration of 1.18 mM and then heated to 88 °C under stirring (the rate of stirring 300 rpm). Afterward, 4 mL of 1 % trisodium citrate solution was added rapidly to the silver solution. The mixture was kept at 88 °C for 35 min with continuous stirring. After this period of time, the silver suspension was immediately cooled to the room temperature. The silver sol was purified from ionic excess using a stirred membrane filtration cell (Millipore, model 8400) with a regenerated cellulose membrane (Millipore, NMWL 100 kDa). The procedure was continued until the conductivity of the supernatant solution stabilized at 15–20 μS/cm.

The weight concentration of the particle suspension was determined using a high precision densitometer: DMA 5000M (Anton Paar).

UV–Vis extinction spectrum was measured using the Shimadzu UV-1800 spectrometer.

Diffusion coefficients of silver nanoparticles (hydrodynamic diameter) were determined by dynamic light scattering (DLS) using the Zetasizer Nano ZS from Malver company.

The microelectrophoretic mobility of the nanoparticles was measured by the laser Doppler velocimetry technique (LDV) using the same equipment and additionally using the Brookhaven Zeta Pals apparatus.

The morphology of silver nanoparticles was investigated using the JEOL JSM-7500F microscope working in transmission mode. Samples for this examination were prepared by dispersing a drop of the silver colloid on a copper grid which was covered by a carbon film. Furthermore, the scanning electron microscope JEOL JSM-7500F was used to determine the coverage of silver monolayers. To ensure a sufficient conductivity, before the measurement, the silver nanoparticles samples were covered with a thin layer of chromium.

Independently, the surface concentration of silver particles on the modified mica substrate was quantitatively determined using AFM. These measurements were carried out using the NT-MDT Solver Pro instrument with the SMENA SFC050L scanning head. Imaging was done in the semicontact mode using silicon probe (polysilicon cantilevers with resonance 120 kHz ± 10 %, typical curvature radius tip was 10 nm, cont angle was <20°).

The zeta potentials of PAH-covered mica and silver particle monolayers were determined via streaming potential measurements using a home-made cell previously described (Adamczyk et al. 2010; Zembala et al. 2001). The main part of the cell is a parallel plate channel of dimensions 2b _c × 2 c _c  × L = 0.027 × 0.29 × 6.2 cm, formed by mica sheets separated by a perfluoroethylene spacer. A laminar flow of the electrolyte was forced by a regulated hydrostatic pressure difference. The streaming potential E _s was measured using a pair of Ag/AgCl electrodes as a function of the hydrostatic pressure difference ΔP which was driving the electrolyte flow through the channel. The cell electric conductivity K _e was determined by Pt electrodes. Knowing the slope of the E _s versus ΔP dependence, the apparent zeta potential of substrate surface (ζ _i ) can be calculated from the Smoluchowski relationship:where η is the dynamic viscosity of the solution; ε is the dielectric permittivity; R _e is the electric resistance of the cell governed mainly by the specific conductivity of the electrolyte in the cell, and K _e is the specific conductivity of the cell, connected with the electric resistance via constitutive relationship:where ΔS _c  = 2b _c  × 2 c _c is the channel cross-sectional area; K′ _e is the specific conductivity due to electrolyte, and K _s is the surface conductivity, depending in general on the channel shape. It is worth mentioning that the correction concerning the surface conductivity was practically negligible for the ionic strength of electrolytes above 10⁻³ M.

The procedure of preparing silver nanoparticle monolayers on PAH-covered mica was as follows:

The weight concentration of the stock silver suspension was determined by the densitometer as described in our previous works (Oćwieja et al. 2011, 2012b). The supernatant solution used in these measurements was acquired by membrane filtration. The stock silver particles suspension having the concentration 550 mg L⁻¹ was diluted prior to experiments.

The size distribution and morphology of the silver particles were determined from AFM images and SEM micrographs. The nanoparticle diameter (d _p) was calculated as the average value from two perpendicular directions and from the surface area of particles, as described before (Oćwieja et al. 2011, 2013). According to the histogram obtained from SEM micrographs, the mean diameter of particles was 28 nm with a standard deviation of 4 nm.

The average size distribution of particles was also determined by AFM. Silver particles were deposited from a dilute suspension (20 mg L⁻¹), pH = 5.5, I = 10⁻² M for 15 min, on a mica sheet precovered by a supporting PAH layer. The size of the particles was determined using the Nova 1152 software which is directly coupled to the AFM microscope. The average size of particles determined from the histogram was 29 nm, with a standard deviation of 5 nm.

The average particle size (hydrodynamic diameter, d _H) was also determined via diffusion coefficient (D) measurements performed using the DLS method. Knowing the diffusion coefficients, one can determine the hydrodynamic diameter using the Stokes–Einstein relationship:where k is the Boltzman constant; T is the absolute temperature, and η is the dynamic viscosity of the solvent. The hydrodynamic diameter can be interpreted as the size of an equivalent sphere having the same hydrodynamic resistance coefficient as the particle. The advantage of using this quantity in comparison to the diffusion coefficient is that it is independent of temperature and liquid viscosity, so it is an appropriate parameter for analyzing a suspension stability under various conditions (Oćwieja et al. 2013).

For the sake of convenience, PAH and silver particle sizes, determined by various technique, are collected in Table 1.

The electrophoretic mobility μ _e of PAH molecules and silver nanoparticles, defined as the average translation velocity under given electric field, was determined by micro-electrophoresis. This quantity is of an essential significance for characterizing particle stability and interactions with surfaces governing deposition/release processes.

Knowing the electrophoretic mobility and the hydrodynamic diameter, one can determine the effective (uncompensated) charge per polyelectrolyte molecule or colloidal particle q from the Lorentz–Stokes relationship:where μ _e is the averaged migration velocity of PAH molecules in the uniform electric field E.

Equation (4) can be directly used for calculations of the average number of elementary charges per molecule considering that e = 1.602 × 10⁻¹⁹ C, thus:where N _c is expressed as the number of elementary charge e per molecule; η is the solution dynamic viscosity expressed in g (cm s)⁻¹; d _H is hydrodynamic diameter of a particle or molecule, expressed in nm, and μ _e is electrophoretic mobility expressed in μm cm (V s)⁻¹.

The number of uncompensated (electrokinetic) charges calculated in this way for PAH molecules and silver nanoparticles for ionic strength ranging from 10⁻⁴ to 0.15 M NaCl, and various pH are collected in Table 2.

As mentioned, the streaming potential method enables in situ measurements, which was exploited in our work to monitor the formation of the PAH-supporting layer and the silver nanoparticle monolayer under various physicochemical conditions.

In the first stage of the experimental procedure, described above, the PAH monolayer of a controlled coverage was produced directly in the streaming potential cell under diffusion-controlled conditions. The nominal coverage of PAH (θ _PAH) was calculated considering the diffusion-controlled transport from finite volumes where the adsorption kinetics is governed by the equation (Adamczyk et al. 2006):where S _g is the characteristic cross-section of the PAH molecules determined to be 155 nm² (Adamczyk et al. 2006); 2h is the distance between the two mica sheets forming the channel; D _p is a diffusion coefficient of PAH; t is adsorption time; n _p is the polyelectrolyte number concentration, expressed in molecules per cm³, connected with the its concentration expressed in mg L⁻¹ by the following relationship: \(n_{p} = 10^{ - 6} c_{b} \frac{{A_{\text{v}} }}{{M_{w} }}\) (Adamczyk et al. 2006), A _v = 6.023 × 10²³ is the Avogadro number and M _w is the molar mass of PAH.

Afterward, the cell was flushed with pure electrolyte; the streaming potential of PAH-covered mica was measured, and the zeta potential was calculated using Eq. (1).

The dependence of the zeta potential of mica on the coverage of PAH derived from these measurements for pH 5.5 and ionic strength of 10⁻² M is shown in Fig. 1. These experimental results were interpreted in terms of the 3D electrokinetic model developed in Adamczyk et al. (2010). The following analytical expression was derived for calculating the zeta potential of polyelectrolyte covered surfaces:

where ζ(Θ) is the zeta potential of the polyelectrolyte-covered substrate; ζ _i is the zeta potential of bare mica; ζ _p is the zeta potential of PAH molecules in the bulk, and \(F_{i} \left( \Uptheta \right),\,F_{\text{p}} \left( \Uptheta \right)\) are the dimensionless functions of the coverage and the electrical double-layer thickness. In the case of thin double layers, the C _i , C _p approach the limiting values of \(C_{i}^{0} = 10.2\) and \(C_{p}^{0} = 6.51\), respectively (Adamczyk et al. 2010). As shown in Wasilewska and Adamczyk (2011), the \(F_{i} \left( \Uptheta \right),\,F_{\text{p}} \left( \Uptheta \right)\) functions can be approximated by the following analytical expressions:

Obviously, for bare surfaces, where θ = 0, F _i (θ) = 1, and F _p(θ) = 1. On the other hand, for high coverage range, the F _i (θ) function vanishes, and F _p(θ) tends to \(\frac{1}{\sqrt 2 }\). Thus, using Eq. (8), one can deduce that the limiting zeta potential for surfaces covered by particles is given by

Theoretic results calculated using Eqs. (7, 8) are plotted in Fig. 1 as a solid line. As can be seen, they reflect well the experimental data for the entire range of PAH coverage. Analogous results obtained for other ionic strength and pH are discussed in Morga and Adamczyk (2013).

After fully characterizing PAH monolayers on mica, a series of experiments was performed to determine the formation of silver nanoparticle monolayers. Hence, in the first stage, the supporting PAH monolayer of a desired coverage was formed. Afterward, the silver monolayer was formed under diffusion-controlled transport using suspensions of appropriate concentration. The coverage of silver particles was calculated from Eq. (6) using the characteristic cross-section area of 615 nm² (see Table 1). In the first series of experiments, the influence of the supporting PAH layer density on the silver monolayer formation was studied. Typical results of these experiments, performed for I = 10⁻² M, pH 5.5, and various supporting layer coverages, θ _PAH ranging from 0.07 to 0.5 are shown in Fig. 2.

As can be seen, in all cases, the decrease in the zeta potential of the supporting PAH layer upon silver particle deposition was observed, even for θ _PAH = 0.07. This is a rather unusual behavior, contradicting the mean-field DLVO theory, because negatively charged particles are deposited on negatively charged (on average) substrate. However, such deviations were often observed for colloid particle adsorption on protein supporting layers, e.g., fibrinogen (Adamczyk et al. 2011a) and albumin (Jachimska et al. 2012). They were quantitatively explained in terms of the heterogeneous charge distribution in the supporting layer stemming from molecule density fluctuations. This leads to formation of local adsorption sites exhibiting positive charge in contrast to the average negative charge of substrates.

As can be seen in Fig. 2, for higher PAH coverage, the variations in the zeta potential of silver monolayers are significantly more pronounced. This results in an abrupt decrease in the zeta potential that can be exploited for a sensitive monitoring of particle deposition process. It is interesting to mention that in all cases, the limiting zeta potential of silver particle monolayers approaches −29 mV. Considering that the bulk value of the silver particle zeta potential is −39 mV, one can deduce that this agrees with the theoretic value predicted from Eq. (9). It is also interesting to mention that the influence of the mica zeta potential and the supporting PAH layer on the final zeta potential of the silver monolayer is rather negligible. An analogous behavior was previously observed for the colloid particle bilayers at mica formed by deposition of positive amidine latex particles and negative polystyrene latex particles (Zaucha et al. 2011).

Since these results have a major significance for determining the effect of substrate and the supporting layer of polyelectrolyte films formation according in the widely used layer by layer (LbL) technique (Zaucha et al. 2011), we have presented them in Fig. 3, in the form of the “saw-like” graph.

As can be seen, even for the supporting layer coverage as low as 0.07, the electrokinetic properties of silver monolayer become fixed; that is, the zeta potential of the silver monolayer assumes 0.7 of the bulk zeta potential.

In order to estimate, the validity of Eq. (6), which was used to calculate the nominal coverage of silver particles, a series of experiments was performed where the true coverage was determined by SEM imaging. According to this procedure, after completing the streaming potential measurements, the mica sheets covered by silver particles were dried and transferred to the SEM chamber. A monolayer obtained for various PAH-supporting layers is shown in Fig. 4. The coverage of particles was calculated by a direct counting of their number over equal-sized surface areas chosen at random over the mica sheet. The total number of particle counted in this way was ca. 1,000 that ensures a relative accuracy of this measurement better that 3 %.

In the next two series of experiments, the influence of the ionic strength and pH on the silver particle monolayer formation was systematically studied. In all these experiments, the dense PAH monolayer, having the coverage of 0.5, was used.

Results of such measurements obtained for various ionic strength are shown in Figs. 5 and 6. The experimental results were interpreted in terms of electrokinetic model where both the molecules and particles adsorbed at the solid/liquid interface were treated as isolated entities exhibiting a 3D charge distribution (Adamczyk et al. 2010, 2011b; Morga et al. 2012).

As can be seen in Fig. 5, the formation of silver particle monolayers results in an abrupt decrease in the surface zeta potential with the slope ζ versus θ considerably exceeding 10 for θ below 0.1. The inversion in sign of the zeta potential is observed for θ _s = 0.08. For higher coverage of silver particles (θ _s > 0.1), the zeta potential variations become rather minor, and for θ _s > 0.25, the zeta potential of silver monolayers attains asymptotic values of −32, −27, and −23 mV for ionic strengths 10⁻³, 10⁻² and 0.15 M NaCl, respectively. Thus, it was confirmed in these measurements that the limiting zeta potential for the high coverage range of silver nanoparticles approaches 1/√2 = 0.71 of the bulk zeta potential of the nanoparticles.

In the second series of studies, the dependence of the zeta potential on the coverage of silver nanoparticles under different pH was studied. Typical results of these experiments, performed for I = 10⁻² M pH 5.5 and 9.0, T = 298 K are shown in Fig. 6.

As can be see seen, the formation of a silver monolayer results in an abrupt decreases in the zeta potential with the slope ζ _s versus θ _s considerably exceeding 10 for θ close to 0.1. For higher coverage of silver particles (θ > 0.1), the zeta potential variations become rather minor, and for θ _s  > 0.25, the zeta potentials of the silver layer attain the asymptotic value of −27 and −35 mV for pH 5.5 and 9.0, respectively that are close (within experimental error bounds) to the theoretic values of 1/√2 = 0.71 of the bulk zeta potential of the nanoparticles (see Table 2).

In order to determine the stability of silver monolayers obtained as described above, a few series of desorption experiments were performed. Firstly, silver particle monolayers of a defined initial coverage were produced at pH 5.5 and I = 10⁻² M, in the electrokinetic cell. As mentioned above, the initial coverage was adjusted by changing the suspension concentration and adsorption time. Afterward, the cell was flushed with pure electrolyte of appropriate ionic strength (10⁻⁴–0.1 M NaCl) and pH, and the particles were allowed to desorb under diffusion-controlled transport for a desired period of time up to 200 h. The final coverage of the silver nanoparticles remaining on the surface was determined in situ by direct streaming potential measurements. After the in situ measurements, the coverage of particles was also determined from SEM micrographs by a direct enumeration procedure. Although this method is tedious and time-consuming, it furnishes reliable data of high precision. Typical release kinetics runs obtained for the initial coverage of silver particles equal to θ ₀ = 0.20 for various ionic strengths are presented in Fig. 7.

As can be seen in Fig. 7, the particle release rate increases with ionic strength. Thus, for I = 10⁻⁴ M, the residue coverage of the monolayer after the time of 200 h is 90 % of the initial value, whereas for I = 0.1 M, the coverage decreases to 65 % of the initial value. Thus, for low ionic strength, the particle release can be considered as practically negligible.

Additionally, a series of experiments was performed in order to investigate the dependence of silver nanoparticle release rate on pH. Typical kinetic runs obtained for I = 10⁻² M, θ = 0.20, and pH 3.5, 5.5, and 9.0 are shown in Fig. 8.

As can be seen, the nanoparticle release rate decreases with pH. Thus, for pH 3.5, the residue coverage of the monolayer after the time of 200 h is 62 % of the initial value, whereas for pH 5.5 and 9.0, it remains at the level of 75 and 83 %, respectively.

The experimental runs shown in Figs. 7 and 8 are quantitatively interpreted in terms of the RSA model previously developed (Adamczyk 2006; Oćwieja et al. 2012a). The kinetic equation describing the changes in the particle coverage with the adsorption time is as follows:where B(θ) is the surface blocking function, and K _a is the equilibrium adsorption constant.

For spherical particles, the RSA blocking function can be approximated by the expression:where \(\overline{\theta } = \theta /\theta_{\text{mx}}\) is the normalized coverage of particles; θ _mx is the maximum coverage of particles equal to 0.547 for hard (non-interacting) particles (Adamczyk 2006), and a ₁–a ₃ are the dimensionless coefficients equal to 0.812, 0.426, and 0.0717, respectively.

In the general case, for arbitrary initial coverage, Eq. (10) can be evaluated by numerical integration. Using such solutions to fit experimental data, one can calculate the equilibrium adsorption constants K _a for various particle sizes. The adsorption constants are collected in Tables 3 and 4.

Knowing the equilibrium adsorption constants one can determine the energy minima depth using the equation previously derived (Oćwieja et al. 2012a):where δ _m is the characteristic thickness of the energy minima between the particle and the interface.

Equation (12) can be iteratively solved, which results in the approximate expression:

Assuming a typical value of the energy minimum δ _m = 0.5 nm = 5 × 10⁻⁷ cm, one obtains, from Eq. (13), the following energy minima depths: ϕ _m = −20 kT for 10⁻⁴ M, ϕ _m = −19 kT for 10⁻² M, and ϕ _m = −18 kT for 0.1 M. Similar results were obtained for ex situ measurements, see Table 3. It is worth mentioning that the energy minima depth increases slightly with ionic strength. However, the difference between ionic strength of 10⁻⁴ and 10⁻² M is only −1 kT for in situ and ex situ measurements.

Analogous results were obtained in experiments performed for various pH and fixed ionic strength of 10⁻² M where ϕ _m varies between −18 kT for pH 3.5 and −19 kT for pH 9.0. In this case, the agreement between the streaming potential and the ex situ method was even better than before (see Table 4).

It should be mentioned that the minor changes in the energy minima depths with the ionic strength and pH determined in our work agree with the discrete charge interaction model previously proposed in Adamczyk (2006). According to this concept, the electrostatic interactions are governed by the finite number of ion pairs, N _i, formed between the PAH molecules and silver particles (see Fig. 9), strictly related to the number of charges on the silver particle. It is assumed (Adamczyk 2006) that these interactions can be described by the unscreened Coulomb potential, i.e.,

where N _i is the number of ion pairs in the interaction zone, and d _im is the minimum distance charges in the between ion pairs.

It is interesting to observe that the interaction energy expressed by Eq. (14) is independent of the particle size and the ionic strength.

Using this ion pair interaction model, one can reasonably reflect the experimentally determined interaction energy depths. Thus, for I = 10⁻⁴ M, T = 298 K, assuming N _i  = 16 (the number of the available charges on the silver particles in the interaction zone) and d _im = 0.5 nm, one can calculate from Eq. (16) ϕ _m = −22 kT, which is close to the experimental value of −20 kT. Analogously, for I = 10⁻² M, assuming N _i  = 10, one obtains from Eq. (16) ϕ _m = −16 kT, which is also close to the experimental value of −19 kT. Analogous results were observed for I = 10⁻² M and different pH. In the case of pH 3.5, the value of energy minima depth calculated from the ion pair model was ϕ _m = −17 kT (experimental value −18 kT), and for pH 9.0, ϕ _m = −18 kT (experimental value −19 kT).

As can be deduced, the ion pair model well reflects the basic features observed in the silver particle release kinetics measurements, i.e., the negligible dependence of the depth of energy minima on ionic strength and pH.