Determination of the Concentration and the Average Number of Gold

May 30, 2012 - The concentration of the colloid solution and the average net ion charge number for each gold nanoparticle were determined with the mea...
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Determination of the Concentration and the Average Number of Gold Atoms in a Gold Nanoparticle by Osmotic Pressure Yan Lu,* Lixia Wang, Dejun Chen, and Gongke Wang School of Chemistry and Environmental Science, Henan Normal University, Xinxiang 453007, People’s Republic of China ABSTRACT: For an ideal solution, an analytical expression for the macromolecule concentration, electrolyte concentration, and solution osmotic pressure is obtained on the basis of the van’t Hoff equation and the Donnan equilibrium. The expression was further applied to a colloid solution of about 3 nm glutathionestabilized gold nanoparticles. The concentration of the colloid solution and the average net ion charge number for each gold nanoparticle were determined with the measured osmotic pressure data. Meanwhile, the gold contents of the solutions were analyzed by means of atomic absorption spectrophotometry, and the results were combined with the determined concentration of gold nanoparticle colloids to determine that the average number of gold atoms per 3 nm gold nanoparticle is 479, which is 1/1.7 times the number of atoms in bulk metallic gold of the same size. The same proportion also occurred in the 2 nm 4-mercaptobenzoic acid monolayer-protected gold nanoparticles prepared by Ackerson et al., who utilized the quantitative high-angle annular dark-field scanning transmission electron microscope to determine the average number of gold atoms per nanoparticle (Ackerson, C. J.; Jadzinsky, P. D.; Sexton J. Z.; Bushnell, D. A.; Kornberg, R. D. Synthesis and Bioconjugation of 2 and 3 nm-Diameter Gold Nanoparticles. Bioconjugate Chem. 2010, 21, 214− 218).

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INTRODUCTION Nanoparticles (NPs) have been widely used in various fields. Recently, researchers have attracted attention for using NPs for drug delivery, disease diagnosis and treatment, and in vivo biomedical imaging. However, relatively little is known about the potential biological risks of NP applications in the biomedical field.1 Thus, there has been particular interest in understanding how these materials with size scales comparable to those of biological components interact with biological systems. Presently, a wide range of spectroscopic techniques such as UV−vis absorbance, surface plasmon resonance, circular dichroism, and fluorescence quenching have been used to study the interactions of biomacromolecules and NPs qualitatively.2−4 That is because quantitative research needs an accurate concentration of NP colloids, which has been hard to obtain. Currently, the metal NP colloid concentration is mainly determined by dividing the total number of metal atoms (equivalent to the initial amount of metal salt added to the reaction solution) by the average number of metal atoms per nanoparticle, which is estimated from the particle size and the density of the bulk metallic state. However, the method is based on two assumptions. The first is that the reduction of metallic ions to metallic atoms is 100% complete, and the second is that the structure and density of the metallic nanoparticles are the same as those of the metallic crystal.5 Obviously, this is a simplified model. For gold nanoparticles (Au NPs), there are other ways to determine the concentration. On the basis of the method described above, Khlobystov calculated the concen© 2012 American Chemical Society

trations of Au NPs with various particle sizes and thus used the results to deduce the relationship between the Au NP extinction coefficient and the Au NP size, which could be used to estimate the concentration of the Au NP colloids.6 Given the simplified premise used in this work, the application of the extinction coefficient−core diameter double-logarithm curve would be limited. Haiss has suggested a method to determine both the size and concentration of Au NPs directly from UV−vis spectra.7 However, the formula derived is appropriate only for uncoated, perfectly spherical, monodisperse gold particles larger than 10 nm, not for other situations. Osmotic pressure measurements have been an authentic approach to determining the concentration of macromolecules and have been made primarily for the study of protein solutions.8−10 On the basis of the colligative property principle of the osmotic pressure, the osmotic pressure of the colloid solution is directly related to the concentration of macromolecules that do not permeate membrane. The Donnan effect should be considered for adsorbed macromolecules or dissociated ions in solution.11 As for proteins, the NP colloid is also the dispersion in which the particle size is 1−100 nm; therefore, osmotic pressure can be applied to determine the concentration of the NP colloid. However, there is almost no related work on this topic in the literature. Received: March 1, 2012 Revised: May 30, 2012 Published: May 30, 2012 9282

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Table 1. Measured Osmotic Pressure of Ternary Au NP−Sodium Chloride−Water Solutions at 25 °C c1 (10−4 mol L−1)

π (mmH2O)

c2 (10−5 mol L−1)

5.41 50.0 400 450 500

± ± ± ± ±

4.14 ± 0.04 (eq 5)

16.0 11.5 10.5 10.5 10.5

0.5 0.4 0.5 0.3 0.2

4.15 ± 0.05 (eq 6)

Ra

Z b

5.50 ± 0.14

b

5.24 ± 0.09

0.9941

0.9928

cAu,solution (10−2 mol L−1) 2.00 1.98 1.92 1.97 1.94

± ± ± ± ±

0.02 0.04 0.01 0.03 0.04

cAu,solvent (10−7 mol L−1) 4.6 3.4 4.0 4.2 3.6

± ± ± ± ±

0.3 0.2 0.2 0.1 0.2

Correlation coefficient. bStandard deviation of the fits. The third and fourth columns give assignments to the fitted results from eqs 5 and 6. The last two columns stand for the gold contents of the samples discharged from both the solution cell and the solvent cell. a

Measurement of Osmotic Pressure. The experimental apparatus for osmotic pressure measurements is the same as that reported by our group before. The generated cellulose membrane was rinsed in doubly distilled water for at least 1 h, during which time the water was changed three times, and then in the desired NaCl solution overnight before use. The osmometer cell was assembled by sandwiching the preprepared membrane between two Plexiglas chambers. The Au NP colloid solution and the solvent were then simultaneously injected into the corresponding chambers until the liquid levels in both capillaries reached about two-thirds of their length.14 The osmometer was immersed in a water bath controlled at 25 ± 0.02 °C. As the solvent passed through the membrane from the solvent chamber to the Au NP colloid solution chamber, the pressure exerted on the capillary of the solution chamber was adjusted to keep the liquid levels in the capillaries at same level. If the liquid levels did not change over a period of at least 3 h at a given applied pressure, then this pressure was taken to be the osmotic pressure of the Au NP colloid solution. All measurements were carried out at least three times, and the results are reported as the average. Table 1 shows the measured values of the osmotic pressures of the Au NP colloid solutions at different concentrations of NaCl. Analysis of Gold Content. At the conclusion of each measurement, solvent and solution samples were taken simultaneously using syringes and needles while the solution was still under pressure. Solution and solvent samples discharged from the osmometer were diluted to concentration limits with deionized water and analyzed for gold contents with atomic absorption spectrophotometry (AAS). A Z-5000 flame atomic absorption spectrophotometer (Hitachi) equipped with Zeeman background correction was used for the determination of the gold content of the solution discharged from the solution and solvent cells. Each reported data point is the average of three measurements. A gold hollow cathode lamp operating at 242.8 nm was used as the radiation source. A working standard solution was prepared by serial dilutions of the stock solution of gold (1000 mg L−1) with doubly distilled water immediately before use. The gold contents of the solution samples discharged from both the solution and solvent chambers have also been given in Table 1.

In our work, a 3 nm Au NP colloid solution was prepared, and its concentration was determined with osmotic pressure measurements. According to the concentration of Au NPs, we obtained the average number of gold atoms per nanoparticle, which would provide useful information for the further study of the Au NP structure.

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EXPERIMENTAL SECTION

Reagents. Hydrogen tetrachloroaurate (III) hydrate (HAuCl4·H2O) was purchased from Alfa Aesar. Reduced glutathione (GSH) and sodium borohydride (NaBH4) were purchased from Sigma. Sodium chloride (NaCl) was purchased from Shanghai Sinopharm Chemical Reagent Co. A standard stock solution of gold at a concentration of 1000 mg L−1 was purchased from the National Institute of Standards (Beijing, China). All reagents were used as received without further purification. Ultrafiltration membranes (molecular weight cutoff of 10 000 g/mol) were purchased from Millipore. Preparation of Au NPs Coated with GSH. Au NPs coated with GSH were prepared according to a reported method.12 Briefly, 3.0 mL of a 0.025 M HAuCl4 aqueous solution was mixed with 23.4 mL of a 0.019 M GSH aqueous solution under stirring. The pH of the resulting mixture was adjusted to 8.0 with a 1.0 M NaOH aqueous solution. Then 14.2 mL of a freshly prepared 2 mg mL−1 NaBH4 aqueous solution was added to the former solution drop by drop under vigorous stirring. The mixture was allowed to react overnight at room temperature. Au NPs were washed with two rounds of purification. The mixture was precipitated by the addition of ethanol, the product was collected by centrifugation, the supernatant was removed, and the centrifuged Au NP pellets were dispersed in 50% aqueous ethanol. The procedure of the second round is identical to that of the first round. Then the product was dried in a vacuum oven at room temperature.13 After the solvent was evaporated, the product was immediately redissolved in a certain amount of doubly distilled water. The amount of water is related to the concentration of Au NPs, which will be measured. The more water used, the smaller the concentration of Au NPs. Characterization of Au NPs. UV−vis spectra of the Au NP solutions were recorded on a TU-1810 spectrophotometer (Puxi Analytic Instrument Ltd., China) equipped with 1.0 cm quartz cells. Samples for TEM images (JEOL 2100 JEM) were prepared by placing drops of a Au NP solution onto Cu mesh grids covered with carbon thin films and allowing them to dry at room temperature. The average gold core diameter (D), size distribution, and standard deviation were calculated from measurements of about 300 particles from the TEM images. Preparation of Solvents and Solutions. A stock solution (1.0 mol L−1) of NaCl was prepared by dissolving the appropriate amount of NaCl in doubly distilled water. A NaCl aqueous solution of a certain concentration was prepared by transferring the desired volume of the stock solution of NaCl to a 1000 mL volumetric flask and diluting the solution to the mark with doubly distilled water. The Au NP colloid solution was prepared by placing 8 mL of the preprepared Au NP solution and an appropriate volume of the stock solution of NaCl in a 10 mL volumetric flask. During the addition of NaCl solution to the Au NPs, vigorous stirring was applied to prevent local Au NP aggregation. The pH value of the solution used is 7.05.

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RESULTS AND DISCUSSION Characterization of Prepared Au NPs. UV−vis absorption spectra have been proven to be very sensitive to the formation of gold and silver nanoparticles.15 The UV−vis absorption spectrum of the prepared GSH-stabilized Au NPs is shown in Figure 1a. The surface plasmon resonance band of the freshly synthetized Au NPs was 507.0 nm, which was consistent with the result reported by Brinas.12 After being washed with ethanol, the Au NP solution changed from brick red to deep red and the resonance absorbance peak shifted to 510.4 nm. The shape of the absorbance peak became sharper, which indicates the uniformity and excellent dispersion of gold nanoparticles after centrifugation (Figure 1b). As shown in Figure 1b,c, after the highly concentrated nanoparticles were stored at 4 °C for several days, the resonance absorbance peak was almost invariable and had only slight movement, which indicated that the GSH-stabilized Au NP solution had splendid stability again. Thus, it is clear that because of their high 9283

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Figure 1. UV−vis absorption spectra of (a) the original GSHstabilized Au NPs, (b) the nanoparticles after being precipitated and resuspended, and (c) the resuspended nanoparticles after being stored at 4 °C for several days. The inset shows the magnified surface plasmon resonance band peaks.

stability the nanoparticles will show excellent repeatability when being used in experiments over longer periods of time, which has been verified by the absorbance peak of the solution used to measure the osmotic pressure. To observe the nanoparticles prepared in our experiment directly, we characterized the GSH-stabilized Au NPs with transmission electronic microscopy (TEM). The TEM images show that all of the Au NPs are well-separated from each other and uniform in shape, indicating that the dispersibility of the Au NPs synthetized in our work was very good. One of the images is given in Figure 2A. We have calculated the size distribution with all of the TEM images. As shown in Figure 2B, a narrow size distribution with a standard deviation of 24.90% was observed, indicating the excellent uniformity of the GSHstabilized Au NPs again. Model of Thermodynamics. For the macromolecule dilute solution, the van’t Hoff equation can be expressed as16 π = cRT

Figure 2. (A) Transmission electron micrograph and (B) size distribution of GSH-stabilized Au NPs.

that Au NP dissociated an average of ZNa+ in the solution. In addition, the same concentration, c1, of sodium chloride (NaCl) was separately added to the Au NP colloid solution and the solvent. Therefore, before and after osmotic equilibrium, the concentrations of the related ions are described in Figure 3.

(1)

where π is the osmotic pressure of the solution, c is the concentration of the macromolecules, R is the universal gas constant, and T is the absolute temperature. If the number of monovalent ions dissociated from macromolecules in solution is Z, then the osmotic pressure of the solution can be transformed into π = (Z + 1)cRT

(2)

Because eq 2 involves two unknown quantities, Z and c, they cannot be determined simultaneously through just one osmotic pressure measurement. To achieve our aim, the same concentration of electrolyte should be added to both the macromolecule solution and solvent. One kind of ion of the added electrolyte is identical to that dissociated from the macromolecule. Under such a condition, the effect of Donnan equilibrium on the solution osmotic pressure should be considered. In our work, the macromolecule is the Au NP, of which the concentration is c2. During the preparation, the Au NPs would dissociate sodium ions (Na+),12 thus it was assumed

Figure 3. Related ions' concentrations (A) before osmotic equilibrium and (B) after osmotic equilibrium.

According to the colligative property principle of the osmotic pressure, after osmotic equilibrium, the osmotic pressure can be expressed as π = (c 2 + Zc 2 − 4x)RT 9284

(3)

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On the basis of the Donnan equilibrium, x can be described as follows:

x=

Zc 2c1 Zc 2 + 4c1

various batches of Au NPs were merged together to form the bulk of the Au NP colloid solution, which we used in the experiments. The osmotic pressures of the Au NP colloid solution with different NaCl concentrations were respectively measured by the method described above. The precision of the measured osmotic pressure is ±0.2 mmH2O, which corresponding to the precision of the Au NP concentration of ±8 × 10−7 mol L−1 . The osmotic pressure of the solution is the result of the chemical potential decrease of the solvent with respect to the existence of solutes. The maximum concentration of NaCl in our experiments is 0.05 mol L−1. At this concentration, the activity coefficient of NaCl obviously deviates from 1, but the deviation of the solvent is not obvious. Because the activities of NaCl in the two solutions on both sides of the membrane are the same, their effects on the chemical potential of the solvent and on the osmotic pressure of the two solutions are also the same. Actually, the pressure measured is the osmotic pressure difference for the two solutions, which is still caused by the van’t Hoff effect of the Au NPs and the Donnan effect of NaCl. Therefore, eq 5 can be used to fit the osmotic pressure data (π/ (RT)) to the NaCl concentration (4c1). The obtained concentration of the Au NP colloid solution c2 is (4.14 ± 0.04) × 10−5 mol L−1, and the average net ion charge number Z is 5.50 ± 0.14. The results are given in Table 1 and shown in Figure 5. As shown in the figure, the agreement of the

(4)

Equation 4 is introduced into eq 3: ⎛ 4Zc 2c1 ⎞ π = ⎜c 2 + Zc 2 − ⎟RT Zc 2 + 4c1 ⎠ ⎝ Zc 2 + 4c1c 2 + Z2c 2 2 RT = 2 Zc 2 + 4c1 = c 2RT +

(Zc 2)2 RT (Zc 2) + 4c1

(5)

For a dilute solution, we can assume that it is ideal, thus the first term is the ideal van’t Hoff contribution and the second term accounts for the ideal Donnan effect. As shown in eq 5, in cases where there is no addition of electrolyte (c1= 0), eq 5 is reduced to eq 2. We can also see that if c1 ≫ c2 then eq 5 is reduced to eq 1. Determination of the Concentration of the Au NP Colloid Solution. The osmotic pressure correlates with the concentration of the Au NPs. Thus, to obtain the pressure that can be determined accurately (for instance, 10 mmH2O), the concentration of the Au NPs has a particular requirement. According to eq 1, the concentration of Au NPs should reach 4 × 10−5 mol L−1 to produce an osmotic pressure of 10 mmH2O at 25 °C. From eqs 2 and 3, it is clear from the number of ions dissociated from Au NPs that Z will increase the osmotic pressure whereas the added electrolyte concentration, c1, will reduce it. Given that the number of Au NPs prepared at a time did not suffice to conduct all osmotic pressure measurements, various batches of Au NPs were prepared under the same experimental conditions and are recorded via UV−vis absorption spectra; the results are shown in Figure 4. As indicated in Figure 4, the surface plasmon resonance bands of various batches of Au NPs are almost coincident, indicating the consistency of the particle sizes of various batches. Then,

Figure 5. Au NP reduced osmotic pressure (π/(RT)) as a function of 4 times the sodium chloride concentration (4c1) at 25 °C. The solid curve is fitted to eq 2, and the dashed curve is derived from eq 3.

measured and calculated osmotic pressures was excellent. To verify the reliability of c2 and Z calculated above, we fitted the Au NP osmotic pressure data to the following semiempirical function used in the work of Viker et al.:9 ⎧ ⎫ 2 ⎤1/2 ⎪ ⎡⎛ Zc ⎞ ⎪ π = c 2 + ⎨2⎢⎜ 2 ⎟ + c12 ⎥ − 2c1⎬ ⎪ ⎣⎝ 2 ⎠ ⎪ RT ⎦ ⎭ ⎩

(6)

The results are also given in Table 1 and are rather close to the data obtained from eq 5. Meanwhile, the predicted data fitted to eq 6 is also shown in Figure 5, which coincides with the curve from eq 5. This indicates that the calculated results are reliable. The value of c2 is much higher than the normally used

Figure 4. UV−vis absorption spectra of the solution samples charged to the osmometer. (Inset) Magnified surface plasmon resonance band peaks. 9285

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compared to the average numbers of gold atoms in 2 and 3 nm gold nanoparticles obtained above. The results are 247/144 ≈ 834/479 ≈ 1.72, which indicates that the structure of 2 nm Au NPs prepared by Ackerson19 is probably indentical to that of 3 nm nanoparticles determined by us. Furthermore, the densities of the two kinds of particles are smaller than the density of the metallic gold. The difference between the average number of gold atoms in Au PNs and metallic gold of the same size is probably caused by four factors. The first is the uncertainty in the concentration of Au NPs. The second is the uncertainty in the total gold content. The third is the uncertainty in the radius of the Au NPs. The fourth may be that the ligands have been contained in Au NPs during the preparation procedure. The effects of the first and second factors, comparatively speaking, are smaller than those of the third and fourth. The effect of the third factor is a little larger. If the fourth factor is true, then it will have the greatest effect on the density of Au NPs. As obtained above, the value of Z is quite small, which means that a very small proportion of the ionizable groups are present on the nanoparticle surfaces. This might be support for the fourth factor because the ligands contained in Au NPs should be unionizable.

concentration of Au NPs. However, the solution can be diluted to the concentration needed. Determination of the Average Number of Gold Atoms per Au NP. In the research on the average number of gold atoms in Au NPs, it was usually assumed that the structure and the density of the Au NPs were exactly the same as those of the metallic gold or it was assumed that the structure of the Au NPs was face-centered cubic (fcc).5 However, others claimed that the structure of Au NPs was related to the particle size. As for larger gold particles (>2 to 3 nm), the structure is the crystalline fcc, whereas ultrasmall particles adopt the noncrystalline cluster structure (i.e., no translational symmetry in the metal core).17 However, most of the cluster structures have not been determined.18 Therefore, whether the assumptions above are proper for the ultrasmall particles remains to be seen. To obtain the average number of gold atoms in a 3 nm gold nanoparticle, after each osmotic pressure measurement we recorded the UV−vis absorption spectra and atomic absorption spectrophotometry (AAS) of the solution discharged from the solution cell. Furthmore, we also analyzed the samples discharged from the solvent cell with AAS. The UV−vis absorption spectra coincided with the curves in Figure 2, which indicate that no aggregation of Au NPs took place during the osmotic process measurements. The AAS measurements were used to determine the gold content of the samples from both the solution cell and solvent cell, and the data is summarized in Table 1. As shown in Table 1, there are tiny amounts of free [AuCl4]− in the solvent cell. Because [AuCl4]− could pass through the membrane freely, the small gold content of the discharged solvents verified the existence of tiny amounts of [AuCl4]− in the solution cell. The [AuCl4]− concentrations in both the solvent cell and the solution cell should be equal at osmotic equilibrium. Therefore, we could calculate the average gold atom number per Au NP, N, on the basis of the following expression N=

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CONCLUSIONS In our work, 3 nm Au NPs were prepared, and the concentration of the colloid solution was determined by osmotic pressure measurements. This method is rigorous except that it is assumed that the Au NP colloid solution is ideal and can be used to determine the concentration of small metal nanoparticle colloids. On the basis of the concentration and the total gold content of the Au NP colloid solution, the average number of gold atoms per 3 nm Au NP is calculated and the result is 479. Combining the research by Ackerson et al.19 with ours, we conclude that 2 and 3 nm Au NPs have the same structure.

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cAu,solution − cAu,solvent c2

Corresponding Author

*Tel/Fax: +86-373-3325249. E-mail: [email protected].

(7)

Notes

where cAu,solution and cAu,solvent are respectively the total gold contents of Au NPs in the solution cell and the solvent cell, respectively. According to the values and the uncertainties in c2 and cAu,solution, which are given in Table 1, the value obtained for N is 479 ± 9. Ackerson et al. utilized the quantitative high-angle annular dark-field scanning transmission electron microscope (HAADF-STM) to characterize the prepared 2 nm 4mercaptobenzoic acid (p-MBA) monolayer-protected Au NPs and also to determine that the number of gold atoms per 2 nm nanoparticle was 144.19 If it is assumed that the density of the Au NPs is the same as the density of the metallic state, and the average number of gold atoms in a gold nanoparticle can be calculated according to eq 85 Nc =

πρD3 = 30.89602D3 6M

AUTHOR INFORMATION

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the National Natural Science Foundation of China (grant no. 21173071) and the Research Fund for the Doctoral Program of Higher Education of China (no. 20114104110002) for their financial support.

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REFERENCES

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(8)

where ρ is the density of the fcc gold (19.3 g cm−3), D is the average core diameter of the particles, and M is the atomic weight of gold (197 g mol−1). Thus, we determined that the average numbers of gold atoms in 2 and 3 nm gold nanoparticles were respectively 247 and 834, which were also 9286

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