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Effect of the Ligand Shell Composition on the Dispersibility and Transport of Gold Nanocrystals in Near-Critical Solvents Carlos A. Fernandez, Jacky G. Bekhazi, Emily M. Hoppes, Glen E. Fryxell, Chongmin Wang, J. Timothy Bays, Marvin G. Warner, Robert J. Wiacek, and R. Shane Addleman* Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352 Received December 9, 2008. Revised Manuscript Received January 23, 2009 The development of more efficient and environmentally benign methods for the synthesis and manipulation of nanomaterials has been a major focus of research among the scientific community. Supercritical (ScFs) and near-critical fluids (NcFs) offer numerous advantages over conventional solvents for these purposes. Among them, ScFs and NcFs offer dramatic reductions in the volume of organic waste typically generated during advanced material processes with the feasibility of changing a number of physicochemical properties by discrete variations in solvent pressure or temperature. In this work, we study the dispersibility of gold nanocrystals with a 3.7 nm core size stabilized by different ligand shells in NcF ethane and propane over a wide range of densities by fine-tuning the pressure of these fluids. Dispersibility vs density plots are obtained by following the variation in the surface plasmon resonance (SPR) absorption spectra of the nanoparticles. To understand the results obtained in this study, three models are briefly discussed: the total interaction theory, the sedimentation coefficient equation, and the Chrastil method. The dispersibility and behavior of the nanocrystals with variations in fluid density are strongly dependent on the surface chemistry of the nanocrystal and the solvent employed. A correlation between measured dispersibility values and calculated sedimentation coefficients was observed in both compressed solvents. In addition, we successfully applied the Chrastil equation to predict and describe the dispersibility of gold nanocrystals with different shells as a function of density, determining that the reason for the high stabilities of some of the nanocrystal dispersions is the strong solvent-nanocrystal interactions. While NcF propane showed higher nanocrystal dispersibilities, using NcF ethane led to improved tunability of nanoparticle dispersions formed in the pressure range studied. Therefore, with a judicious selection of the fluid, NcFs seem to offer a remarkable advantage over conventional solvents for manipulation of nanomaterials, which could be applied to transport, purification, and separation of nanocrystals.
Introduction During the past decade, there has been a rapid growth in nanotechnology research together with an increasing need for environmentally amenable methods for the manipulation of nanomaterials in various stages of their production. Supercritical (ScFs) and near-critical fluids (NcFs) can offer a number of environmental and commercial advantages over conventional solvents for material and chemical processes.1 One of the main advantages of these fluids is the dramatic reduction in the volume of organic waste typically generated during advanced material processes, making them an environmentally benign solvent system. In addition, the ability to change a number of physicochemical properties such as density, surface tension, viscosity, diffusivity, and solvation strength with only minor changes in pressure or temperature make them an exceedingly versatile solvent system. In particular, the degree of the solvent-nanoparticle interaction can be adjusted, in principle continuously, through the alteration *Corresponding author: e-mail
[email protected], Ph (509) 375-6824, Fax (509) 372-4732. (1) (a) Eckert, C. A.; Knutson, B. L.; Debenedetti, P. G. Nature (London) 1996, 383(6598), 313. (b) Holmes, J. D.; Johnston, K. P.; Doty, R. C.; Korgel, B. A. Science 2000, 287(5457), 1471. (2) Shah, P. S.; Holmes, J. D.; Johnston, K. P.; Korgel, B. A. J. Phys. Chem. B 2002, 106(10), 2545. (3) (a) Saunders, A. E.; Shah, P. S.; Park, E. J.; Lim, K. T.; Johnston, K. P.; Korgel, B. A. J. Phys. Chem. B 2004, 108(41), 15969. (b) Shah, P. S.; Husain, S.; Johnston, K. P.; Korgel, B. A. J. Phys. Chem. B 2001, 105(39), 9433. (c) Shah, P. S.; Hanrath, T.; Johnston, K. P.; Korgel, B. A. J. Phys. Chem. B 2004, 108(28), 9574.
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of fluid density, enabling control of processes such as nanocrystal purification, separation, and assembly.2,3 As a result, theoretical and experimental studies have been devoted to explore the dispersibility of nanocrystals in ScFs and NcFs.4-8 For example, our group has for the first time recently quantified the dispersibility of gold nanocrystals in different ScFs and NcFs and demonstrated that, by continuously adjusting the applied pressure of selected fluids, the dispersibility of nanoparticles can be controlled to obtain different particle fractions from a polydisperse nanocrystal solution.7,8 These findings are significant since the manipulation of nanocrystals is an important area of research that will enable application of nanomaterials to catalysis, optical components, electronic (4) (a) Shah, P. S.; Holmes, J. D.; Doty, R. C.; Johnston, K. P.; Korgel, B. A. J. Am. Chem. Soc. 2000, 122(17), 4245. (b) Ziegler, K. J.; Doty, R. C.; Johnston, K. P.; Korgel, B. A. J. Am. Chem. Soc. 2001, 123(32), 7797. (c) Rabani, E.; Egorov, S. A. J. Phys. Chem. B 2002, 106(26), 6771. (5) (a) Husowitz, B.; Talanquer, V. J. Chem. Phys. 2007, 126(5), 054508. (b) Lal, M.; Plummer, M.; Smith, W. J. Phys. Chem. B 2006, 110(42), 20879. (c) Moisan, S.; Martinez, V.; Weisbecker, P.; Cansell, F.; Mecking, S.; Aymonier, C. J. Am. Chem. Soc. 2007, 129(34), 10602. (d) Anand, M.; Bell, P. W.; Fan, X.; Enick, R. M.; Roberts, C. B. J. Phys. Chem. B 2006, 110(30), 14693. (6) Ghosh, S. K.; Deguchi, S.; Mukai, S.; Tsujii, K. J. Phys. Chem. B 2007, 111(28), 8169. (7) Fernandez, C. A.; Hoppes, E. M.; Bekhazi, J. G.; Wang, C.; Wiacek, R. J.; Warner, M. G.; Fryxell, G. E.; Addleman, R. S. J. Phys. Chem. C 2008, 112, 12947. (8) Fernandez, C. A.; Bekhazi, J. G.; Hoppes, E. M.; Wiacek, R. J.; Fryxell, G. E.; Bays, J. T.; Warner, M. G.; Wang, C.; Hutchison, J. E.; Addleman, R. S. Small 2009, DOI: 10.1002/sm11.200801207.
Published on Web 3/3/2009
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devices, and sensors, among other systems.9,10 In our most recent work we have studied the influence that the core size has in the dispersibility of gold nanocrystals stabilized with an octanethiol ligand shell in NcFs ethane and propane. One of the most significant findings was that the core size largely influences the density of the nanocrystal at sizes smaller than 30 nm and, as a result, the solvent conditions for complete dispersion of the nanoparticles. In this work, we studied the effect of the stabilizing shell on the dispersibility of gold nanocrystals in NcF ethane and NcF propane as a function of solvent conditions. The dispersibility of these nanocrystals is shown to be strongly dependent on the density of the solvent and the surface chemistry of the nanocrystals. Three models; the total interaction theory, the sedimentation coefficient equation, and the Chrastil method;are applied to the data. The models are used to explore and interpret the interactions between the various surface chemistries of the nanoparticles and dynamic solvent systems.
Experimental Section Octanethiol-stabilized gold (C8SH-Au) nanoparticles, 3.7 ( 2.2 nm, were synthesized following a procedure reported by Rowe et al.11 Dodecanethiol- and hexadecanethiol-stabilized gold nanocrystals with a statistically similar core size (3.6 ( 1.5 and 3.9 ( 1.7 nm) were obtained in our laboratory following a procedure reported by Brown and Hutchison12 with some modification, where triphenylphosphine-stabilized gold nanoparticles (also synthesized here with a procedure reported by Weare et al.)13 underwent ligand exchange with dodecanethiol or hexadecanethiol. Gold nanocrystals (4.7 ( 1.1 nm) stabilized with Triton X100 were prepared following a method proposed by Anjali with some modification.14n-Hexane (99%) was obtained from Fisher and used without further purification. Instrument grade liquid propane (99.5%) and chemical grade ethane (99%) were obtained from Oxarc and were also used without further purification. The details of the dispersibility experiments are shown in the Supporting Information.
Results and Discussion Dispersion of Octanethiol-Coated Gold NPs in Ethane and Propane. Samples of gold nanocrystals with statistically equivalent core sizes (3.7 nm) stabilized with a shell composed of octanethiol, dodecanethiol, or hexadecanethiol were employed to prepare unsaturated nanoparticle dispersions in liquid ethane (at 25 °C) and liquid propane (at 65 °C), both at 500 atm. The pressure-temperature conditions for each solvent were chosen based on our previous study, where ethane at 25 °C and propane at 65 °C provided good tunability and dispersibility of 4 nm octanethiol-stabilized gold nanocrystals at lower pressures (less than 500 atm)7 (see Supporting Information). On the other hand, gold (9) (a) Collier, C. P.; Vossmeyer, T.; Heath, J. R. Annu. Rev. Phys. Chem. 1998, 49, 371. (b) Kamat, P. V. J. Phys. Chem. B 2002, 106(32), 7729. cElghanian, R.; Storhoff, J. J.; Mucic, R. C.; Letsinger, R. L.; Mirkin, C. A. Science (Washington, DC, U.S.) 1997, 277 (5329), 1078. (10) (a) Sampaio, J. F.; Beverly, K. C.; Heath, J. R.; J. Phys. Chem. B 2001, 105(37), 8797. (b) Wang, L. Y.; Shi, X.; Kariuki, N. N.; Schadt, M.; Wang, G. R.; Rendeng, Q.; Choi, J.; Luo, J.; Lu, S.; Zhong, C.-J. J. Am. Chem. Soc. 2007, 129(7), 2161. (c) Chan, G. H.; Zhao, J.; Hicks, E. M.; Schatz, G. C.; Van Duyne, R. P. Nano Lett. 2007, 7(7), 1947. (11) Rowe, M. P.; Plass, K. E.; Kim, K.; Kurdak, C. E.; Zellers, T.; Matzger, A. J. Chem. Mater. 2004, 16(18), 3513. (12) Brown, L. O.; Hutchison, J. E. J. Am. Chem. Soc. 1997, 119(50), 12384. (13) Weare, W. W.; Reed, S. M.; Warner, M. G.; Hutchison, J. E. J. Am. Chem. Soc. 2000, 122(51), 12890. (14) Anjali, P. Talanta 1998, 46, 583.
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nanocrystals with similar core diameters and triphenylphosphine (TPP) or Triton X100 (a nonionic surfactant which has a hydrophilic poly(ethylene oxide) group and a hydrocarbon hydrophobic group) as ligand shells were unable to be dispersed in either solvent under identical conditions. As detailed in the Supporting Information, the pressure of the alkanethiol-stabilized gold nanoparticle dispersions was subsequently lowered from 500 atm by discrete pressure variations. A spectrum between 200 and 900 nm showing the surface plasmon resonance (SPR) peak at ∼510 nm was recorded every 20 atm after equilibrium (of a saturated solution) was reached. The experiments were concluded at the pressure at which the system became biphasic (approximately 10 atm for propane and 40 atm for ethane). The density-normalized spectra of 3.7 nm gold nanocrystals with an octanethiol shell are shown in Figure 1A for different (decreasing) pressures in ethane at 25 °C. Figure 1A clearly shows the reduction in the core size-dependent SPR absorption peak with decreasing pressure as the larger nanoparticles began to precipitate, leaving in solution the fraction containing smaller nanocrystals (davg < ∼2.0 nm) that no longer exhibit a distinct absorbance peak in this spectral region.2,7 Figure 1B shows a representative transmission electron micrograph (TEM) of 3.7 ( 2.2 nm core size gold nanocrystals with an octanethiol ligand shell. TEM micrographs of nanocrystals with dodecanethiol and hexadecanethiol shells were similar to those shown in Figure 1B since only the metallic core of the particle is visible in TEM. The concentration of nanocrystals in the dispersions at each pressure value was calculated from the values of absortivity (in mL mg-1 cm-1) for each particle, which are known and constant in the entire density range (see Supporting Information). The concentrations of gold nanocrystals with statistically equivalent core diameters having octanethiol, dodecanethiol, or hexadecanethiol shells are shown as a function of ethane pressure (Figure 2A) and density (Figure 2B) at 25 °C. In the pressure range between 500 and 420 atm (or density range 0.478-0.467 g/mL), the concentration of gold nanocrystals with octanethiol and dodecanethiol shells show no variation with pressure. Gold nanocrystals stabilized with a hexadecanethiol shell remain insensitive to pressure variations to as low as 340 atm (a density of 0.454 g/mL). Below these pressures, the fraction of larger particles in each sample begins to precipitate as a consequence of the continuing reduction in the solvation strength of the fluid,15 leaving behind the fractions of smaller nanocrystals remaining in solution. The concentration values in the region where the nanocrystals begin to precipitate correspond to the concentration of a saturated dispersion and an actual measure of the dispersibility (equivalent to solubility for molecular species) of the nanocrystals. Since the absorption signal is densitynormalized, the concentration profile in Figure 2A,B would remain constant across the pressure range if the analyte was not precipitating. It is important to notice from Figure 2B that small variations in the pressure/density of the solvent cause considerably larger variations in the dispersibility of the nanocrystals. In addition, Figure 2 clearly shows that at any given density or pressure (in the saturated region where the nanoparticles are precipitating) the dispersibility of the nanoparticles increases as the length of the stabilizing ligand (e.g., hexadecanethiol) increases. These results are directly (15) Kumar, S. K.; Johnston, K. P. J. Supercrit. Fluids 1988, 1(1), 15.
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Figure 1. (A) Variation of the surface plasmon resonance (SPR) absorption peak by a stepwise pressure reduction of a liquid ethane solution of octanethiol-stabilized gold nanoparticles (core diameter 3.7 nm) at 25 °C. (B) Representative transmission electron micrograph of the gold nanoparticles stabilized by an octanethiol ligand shell. Scale bar corresponds to 20 nm.
Figure 2. Density-normalized concentrations of octanethiol, dodecanethiol, and hexadecanethiol-passivated gold nanocrystals with statistically equivalent core diameters (3.7 nm) in compressed ethane at 25 °C as a function of the solvent pressure (A) and density (B). At higher pressures or densities, constant concentrations represent unsaturated solutions. related to the influence of the shell on the density of the nanoparticle as well as to a stronger interaction between the ligand shell and the solvent as the ligand becomes longer. The results obtained by performing dispersibility measurements in NcF propane at 65 °C are shown in Figure 3. As in the case of the dispersions prepared in liquid ethane, the nanoparticle concentration vs pressure (Figure 3A) or density (Figure 3B) plots in NcF propane shows two principal regions: the region corresponding to an unsaturated dispersion at larger pressure/density regimes (∼430-500 atm, 0.525-0.537 g/mL) and the region where an equilibrium precipitate dispersion was present (pressure j 430 atm, density j 0.525 g/mL). An exception was observed for the case of the hexadecanethiol-passivated gold nanocrystals, which were completely dispersed in the entire pressure (or density) range, except near the solvent vapor-liquid phase transition at 10 atm. As with ethane, propane shows that the longer the stabilizer alkyl chain in the nanocrystal shell, the greater the dispersibility measured at a given pressure or density. Under identical pressure-temperature conditions, propane shows higher dispersibility values than ethane for equivalent alkanethiol-stabilized gold nanocrystals.7 These results show that the length of the solvent hydrocarbon chain plays an important role in the dispersion of these 4902
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nanocrystals by providing access to higher solvent densities and more stable dispersion forces as the length of the alkane chain in the solvent increases. Total Interaction Theory. In order to describe the stability of nanocrystals in conventional as well as in ScFs and NcFs, a number of theoretical and semiempirical models have been proposed.5,16-19 For example, in the mid-1980s, Vincent et al.16 offered the total interaction theory as a model to describe and predict the dispersibility of sterically stabilized nanocrystals (treated as soft spheres) in conventional solvents. This model was later employed by Shah et al. to describe the stability of nanocrystal dispersions in ScFs.2 The total interaction theory describes the stability of nanocrystal dispersions as a balance of the van der Waals attraction forces (ΦvdW) between the nanocrystal cores (which in the case of metallic nanocrystals is large due to extremely high polarizabilities of the nanocrystal cores) and steric (16) Vincent, B.; Edwards, J.; Emmett, S.; Jones, A. Colloids Surf. 1986, 18 (2-4), 261. (17) Romero-Cano, M. S.; Puertas, A. M.; De las Nieves, F. J. J. Chem. Phys. 2000, 112(19), 8654. (18) Gibb, S. E.; Hunter, R. J. J. Colloid Interface Sci. 2000, 224(1), 99. (19) Lal, M.; Plummer, M.; Richmond, N. J.; Smith, W. J. Phys. Chem. B 2004, 108(19), 6052.
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Figure 3. Density-normalized concentration of octanethiol, dodecanethiol, and hexadecanethiol-passivated gold nanocrystals with statistically equivalent core diameters (3.7 nm) in compressed propane at 65 °C as a function of the solvent pressure (A) and density (B). At higher pressures or densities, constant concentrations represent unsaturated solutions. repulsive forces (Φosm + Φelas) provided by the ligand shell. The sum of each of these energy contributions accounts for the total interaction energy (Φtotal) as follows: Φtotal ¼ ΦvdW þ Φosm þ Φelas ð1Þ The energy term related to the van der Waals attraction (ΦvdW) between two nanocrystals increases with larger particles.16,17 This theory also proposes two repulsive energy contributions to the total interaction between nanocrystals: the elastic repulsive energy component (Φelas) and the osmotic repulsive energy component (Φosm). The former contribution originates from the entropy loss that occurs upon the compression of the stabilizing ligands, which is important only at interparticle separations shorter than the ligand length. Because of the fairly low concentration of the nanoparticle dispersions employed herein (ppm range), this repulsive energy contribution may be negligible.2,7 On the other hand, the osmotic repulsive energy component resulting from the energetic balance between solvent-ligand tail and tail-tail interactions has a predominant role in the total interaction energy. The solvent conditions and the stabilizing ligand length largely control the osmotic repulsion energy. As a result, the total interaction energy will depend mainly on the nanoparticle core size, solvent condition, and the surface chemistry.16 Figures 2B and 3B show two relevant trends: one that corresponds to the clear decrease in the nanoparticles dispersibility as the density of the solvent decreases and another that is related to a decrease in the dispersibility of the nanocrystals as the length of the ligand shell decreases (for a constant density). Both trends can be explained by the total interaction theory.2,16 This model predicts a smaller steric repulsion among the nanoparticles ligand shell at lower solvent densities as a result of decreased ligand solvation. Additionally, an increase in the van der Waals core-core attraction forces occurs as the solvation strength of the fluid decreases. Consequently, as the density of the fluid decreases, the larger nanoparticles precipitate fractionally faster than the smaller nanoparticles, decreasing the concentration (and hence, dispersibility) of nanoparticles in solution.2,7 The reduction in nanocrystal dispersibility at constant density for nanoparticles with shorter stabilizing ligands can be explained by the change in the osmotic repulsive energy term. This energy term, associated with the repulsion between nanocrystal shells in solution, Langmuir 2009, 25(9), 4900–4906
decreases with the reduction of the stabilizer length.2,16,17 In addition, nanoparticle density increases with shorter ligand shells. These two effects together with a stronger interaction between longer ligand shells and the solvent (see Chrastil Model section) seem to explain the larger dispersibility values observed for nanoparticles stabilized with a longer alkanethiol shell. Sedimentation Theory. Another useful and well-known equation that semiempirically describes the dispersibility and transport properties of particulate material (including nanoparticles) is the sedimentation equation.20 This equation relates a parameter known as sedimentation coefficient (Sa) to physical properties of the particle and the solvent, including the nanoparticle hydrodynamic radius (RH), the nanoparticle density (δparticle), the solvent density (δsolvent), and solvent viscosity (η). In the absence of centrifugal force, the sedimentation equation predicts a quadratic relationship between Sa and RH, assuming spherical particles in dilute suspensions (where g is the gravitational constant): Sa ¼ 2gRH 2 ðδparticle -δsolvent Þ=9η
ð2Þ
A large Sa implies a large sedimentation rate for a given solvent condition (viscosity, temperature, density, etc.).20 In the case of a nanocrystal, RH can be approximated to a spherical inorganic core with radius R and an organic shell with thickness t (RH = R + t). By using the empirical equation shown below, it is possible to estimate the length (l) of the stabilizer in the shell based in the number of methylene groups (k) in the hydrocarbon chain.21 l ðnmÞ ¼ 0:25 þ 0:127k
ð3Þ
For gold nanocrystals with octanethiol, dodecanethiol, and hexadecanethiol as the stabilizer, the ligand shell thickness is estimated from eq 3 to be approximately 1.27, 1.77, and 2.28 nm, respectively. For nanocrystals having these shell thicknesses and diameters smaller than ∼40 nm, using the bulk density of the inorganic core (19.3 g/mL) to approximate the nanoparticle density is no longer a valid (20) Hiemenz, P. C., Rajagopalan, R., Eds. In Principles of Colloid and Surface Chemistry; Marcel Dekker: New York, 1997; p 62. (21) Fernandez, C. A.; Wai, C. M. J. Nanosci. Nanotechnol. 2006, 6(6), 669.
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Fernandez et al. Table 1. Average Dimensions and Density for Alkanethiol-Coated Gold Nanocrystals with Different Stabilizer Lengthsa
stabilizer shell
stabilizer thickness (nm)
hydrodynamic diameter (nm)b
density (g/mL)c
nanoparticle mass (10-19 g)c
octanethiol 1.27 6.3 4.84 6.4 dodecanethiol 1.77 7.3 3.40 7.1 hexadecanethiol 2.28 8.4 2.58 7.9 a Note: a gold nanocrystal with a core diameter of 3.7 nm has a core mass of 6.0 10-19 g. b Based on a spherical core with statistically equivalent core diameters (3.7 nm). c Based on hydrodynamic diameter of particle and eq 4.
Figure 4. Sedimentation coefficients of 3.7 ( 2.2 nm octanethiol-stabilized gold nanocrystals, 3.6 ( 1.5 nm dodecanethiol-stabilized gold nanocrystals, and 4.0 ( 1.7 nm hexadecanethiol-passivated gold nanocrystals, calculated employing eq 2, as a function of fluid density in compressed ethane at 25 °C (A) and compressed propane at 65 °C (B).
assumption since the ligand shell contributes substantially to the nanocrystal density (see Supporting Information). This contribution increases dramatically as the nanoparticle core size approaches the length of the stabilizing ligands. For that reason, Jamison et al.22 derived the anticipated density of the functionalized nanocrystal and arrived at the following equation: δparticle ¼ δshell þ ½ðRH -tÞ3 =RH 3 ðδcore -δshell Þ
ð4Þ
where δshell and δcore are the density of the organic shell and the core, respectively, and the other parameters are defined above. For the small particle sizes of interest in this work, dynamic light scattering is not suitable for measuring RH; therefore, we estimated this parameter by adding the shell thickness to the measured core radius from TEM. By making use of eq 4, we calculated the approximate mass and density of the gold nanoparticles with different ligand shells. Table 1 shows the average nanoparticle core size, the corresponding hydrodynamic diameter, and the calculated nanocrystal mass and density employing eq 4. The density of bulk gold was employed as the density of the core, and the density of liquid octanethiol, dodecanethiol, and hexadecanethiol (0.843, 0.845, and 0.84 g/mL, respectively) was used for the densities of the shell. Even though this is an approximation, it has been proven that the density of the organic ligand has only a small effect on the predicted nanoparticle densities (see Supporting Information). Table 1 also shows the relatively large decrease in density as compared to the slight increase in the nanoparticle mass as the thickness of the ligand shell increases. The decrease in nanoparticle density (with nearly constant mass) with the thickness of (22) Jamison, J. A.; Krueger, K. M.; Yavuz, C. T.; Mayo, J. T.; LeCrone, D.; Redden, J. J.; Colvin, V. L. ACS Nano 2008, 2(2), 311.
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the nanoparticle shell might explain the observed higher dispersibility values. By introducing the density values from Table 1 into eq 2, it was also possible to calculate the corresponding sedimentation coefficients for any given solvent density and viscosity in ethane and propane NcFs. Figure 4 shows a plot of Sa for nanoparticles stabilized with different ligand lengths as a function of the fluid density in compressed ethane at 25 °C (Figure 4A) and in compressed propane at 65 °C (Figure 4B). These Sa values were calculated by introducing the correction of the size-dependent nanoparticle density (from (4)) to the sedimentation equation (2). It is important to note that the calculated sedimentation coefficients shown in Figure 4 were obtained using average core diameters and do not represent the actual Sa values of each fraction of nanoparticles in the polydisperse samples. In addition, the model does not account for the nonuniformity of the ligand shells or for nanocrystal shape effects. However, the Sa values provide an approximate average of the sedimentation coefficient of each sample as a function of solvent density and, with the calculated average mass and density of the nanocrystals, allowed us to interpret the nanoparticle dispersibility results qualitatively. From Figure 4, it is clear that the model predicts a decrease in the sedimentation coefficient with increasing fluid densities for all three samples and in both solvents. At a given density, ethane showed smaller sedimentation coefficients than propane for the three nanoparticle shells studied (see Supporting Information). We believe this effect reveals a difference in the number of solvent molecules in the solvation sphere under similar densities. Another significant result emerged when comparing the sedimentation coefficients where smaller Sa values were obtained as the length of the stabilizer increased (for a given solvent at constant density). This is probably due to the relative contributions of the ligand shell to the total density Langmuir 2009, 25(9), 4900–4906
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Figure 5. Density-normalized dispersibility plots of 3.7 ( 2.2 nm octanethiol-stabilized gold nanocrystals, 3.6 ( 1.5 nm dodecanethiol-stabilized gold nanocrystals, and 4.0 ( 1.7 nm hexadecanethiol-passivated gold nanocrystals as a function of the solvent density in a (natural) log-log form in compressed ethane at 25 °C (A) and propane at 65 °C (B). Solids lines represent the calculated linear regressions.
of the alkanethiol-stabilized nanocrystal. As shown in Table 1, the thicker the ligand shell, the lower the nanocrystal density, resulting in a smaller Sa. The reduction in nanoparticle density along with the expected larger interaction between the solvent and the ligand shell for larger ligands (see next section) clearly explains the higher dispersibility values observed on nanoparticles with thicker shells at any given solvent density in either NcF ethane or propane. As a result, the sedimentation equation likely correlates with the dispersibility measurements obtained in this study. A more accurate analysis where the nonuniformity of the ligand shell, nanocrystal shape effects, and sedimentation coefficients are calculated as a function of solvent density for each nanoparticle size fraction in the polydisperse samples should enable a more quantitative correlation of the sedimentation values with the dispersibility measurements (but is beyond the scope of this study). Chrastil Model. An important method employed to predict the solubility of numerous organic and organometallic compounds in near-critical and supercritical solvents was introduced by Chrastil et al.23 This model relates the solubility of molecular species to the density of the solvent without the need of complex equations of state and unavailable thermodynamic data that other models require.24,25 For this reason, we made use of the Chrastil approach to obtain more information from the dispersibility plots of gold nanocrystals with different ligand shells in NcF ethane and propane. The Chrastil expression relates the solubility of any solute C with the density δ of the solvent:25 ln C ¼ n ln δ þ m
ð5Þ
where n is the number of solvent molecules associated with the solvated complex (association number) and m is related to the enthalpy of solvation and the solute volatility as follows: m ¼ ΔHtotal =RT þ lnðMA þ nMB Þ þ q -n ln MB
ð6Þ
(23) Chrastil, J.. J. Phys. Chem. 1982, 86 (15), 3016. (24) Lagalante, A. F.; Hansen, B. N.; Bruno, T. J.; Sievers, R. E. Inorg. Chem. 1995, 34(23), 5781. (25) Cross, W.; Akgerman, A.; Erkey, C. Ind. Eng. Chem. Res. 1996, 35(5), 1765.
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In eq 6, MA and MB are the molecular weights of solute and solvent, respectively, q is a constant, and ΔHtotal is the sum of the enthalpy of solvation and the enthalpy of solute vaporization (ΔHtotal = ΔHsolv + ΔHvapor). The parameter m is usually negative for soluble species.7,23,26 Equation 5 predicts a linear relationship from a natural log-log plot between the solubility and the solvent density. The parameters m and n are functions of the solution temperature and the specific solute/solvent system. Therefore, by simply knowing these two parameters, the solubility of a material can be predicted for a wide range of densities. The Chrastil model has been applied to predict and interpret solubility data for a wide variety of chemical species, including metal chelates in liquid and supercritical solvents.23,26 In addition, it has been recently employed successfully to describe the dispersibility of nanocrystals in near-critical and supercritical solvents.7 Figure 5A,B shows the Chrastil plots obtained in compressed ethane at 25 °C and propane at 65 °C for gold nanocrystals with statistically equivalent core sizes (∼3.7 nm) and different ligand shells. Under the pressure-temperature conditions employed here, the (natural) log-log plots of the nanocrystal dispersibility as a function of fluid density are a linear function as predicted by the Chrastil equation. Table 2 displays the Chrastil fit parameters (n and m) for the gold nanocrystals stabilized with different alkanethiol shells in NcF ethane and propane. The values of the association number n that express the number of solvent molecules associated with the nanocrystal are not integers for these systems, as shown in Table 2. These nonstoichiometric values are attributed to the presence of several solvated association complexes in the solution as it has been also observed for numerous chemical species, including metal chelates.23,26 In the case of solutions of nanocrystals with a size distribution such as the ones employed here, these nonstoichiometric values should be expected due to the nanocrystal size distribution for any particular sample set.7,27 Table 2 shows that compressed ethane at 25 °C has higher n values than compressed propane at 65 °C, clearly implying that more ethane molecules are directly interacting with the nanoparticle ligand shell. (26) Smart, N. G.; Carleson, T.; Kast, T.; Clifford, A. A.; Burford, M. D.; Wai, C. M. Talanta 1997, 44(2), 137. (27) Addleman, R. S.; Carrott, M. J.; Wai, C. M. Anal. Chem. 2000, 72(17), 4015.
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Table 2. Chrastil Parameters for Gold Nanocrystals Stabilized with Alkanethiols of Different Lengths in Compressed Propane (65 °C) and Ethane (25 °C) ethane
propane
stabilizer
n
m
n
m
octanethiol dodecanethiol hexadecanethiol
8.12 8.57 10.6
-53.7 -56.1 -67.8
3.42 4.29 5.53
-25.2 -30.3 -37.7
The larger number of ethane solvent molecules associated with the nanoparticles (relative to propane) may explain why ethane provides higher nanocrystal dispersibility than propane for equivalent densities (Figures 2B and 3B, density range 0.43-0.48 g/mL). It is also noted that the values of n increase as the length of the ligand shell increases for both solvents. This observation can be attributed to an increase in the average number of solvent molecules interacting with the nanocrystal as the ligand shell extends further away from the nanocrystal core. The values for the zero intercept parameter m, related to the heat of solvation and the solute volatility (6),23,26 are also shown in Table 2 for both solvents. Similar values of m have also been observed on metal chelates, such as copper acetylacetonate (Cu (Acac)2), ferrocene, and uranyl nitrate tributyl phosphate under comparable temperature-pressure conditions in supercritical carbon dioxide (ScF CO2).26,27 The similarities in Chrastil values between nanocrystals and metal chelates indicate the existence of strong solvent-nanocrystal interactions, which might be surprising given the difference in molecular weights.26 Since nanocrystals show negligible vapor pressures under the temperaturepressure conditions, the main factor determining the values of m for nanocrystals (as well as for metal chelates) is the heat of solvation.7,26,27 As in the case of the association number n, Table 2 shows that an increase in the length of the stabilizer in the nanocrystal produces an increase in the absolute value of m (becoming more negative) in both solvents. This increase in the absolute value of m can be related to a higher heat of solvation when dispersing nanocrystals. A thicker ligand shell allows a larger number of solvent molecules (n) to associate with the longer alkanes on the surface of the nanoparticles. Finally, for both solvent systems, there is a correlation between the larger number of solvent molecules associated with the solute (n) and the greater (negative) values for m (associated primarily to the heat of solvation) supporting the concept that strong solutesolvent interactions are the driving force for the dispersibility of the nanoparticles.
Conclusion The surface chemistry is a key factor for determining the dispersibility of gold nanoparticles. Gold nanoparticles stabilized with a ligand shell consisting of TPP or Triton X-100, two molecules with a relatively higher dielectric constant and polarity compared to alkanethiols, were not soluble in NcF
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DOI: 10.1021/la804058x
ethane or propane but formed stable dispersions in more polar solvents such as acetone or chloroform. On the other hand, alkanethiol-stabilized gold nanocrystals with different shell thickness formed stable dispersions in NcF ethane and propane, and their dispersibility values as a function of fluid density and pressure were reported. As predicted by the total interaction theory, as the density of the solvent (hence the solvation strength) decreases, the van der Waals core-core attraction increases and the steric repulsion between the ligand shells decreases, resulting in precipitation of the nanocrystals. Dispersibility versus density plots of the nanocrystals are strongly dependent on the length of the stabilizer and the length of the alkane solvent. Shorter ligands in the nanocrystal shell generated lower dispersibility values and higher sedimentation coefficients at every solvent density. In addition, the reduction in nanocrystal dispersibility with decreasing solvent density was more pronounced on dispersions of nanocrystals with a shorter stabilizing ligand shell. Further, we successfully applied the Chrastil equation to predict and describe the dispersibility of these gold nanocrystals. The Chrastil model trends and fit parameters for the alkanethiol-passivated gold nanocrystals in ethane and propane were comparable to those observed over similar pressure and temperature ranges for a number of metal chelates in ScF CO2. Larger dispersibility variations were observed in compressed ethane at 25 °C compared to compressed propane at 65 °C due to the lower fluid densities and comparative larger density variations found in ethane (for the conditions studied). The tunable dispersibility of NcFs together with the dramatic reduction of organic waste volumes when utilizing the aforementioned fluids offer dynamic, environmentally benign, and readily controllable solvent systems for nanoparticle manipulation. Consequently, ScFs and NcFs may offer substantial advantages over conventional solvents for nanomaterials processes, including transport, separation, and purification. Acknowledgment. Funding for this work was provided by the Safer Nanomaterials Nanomanufacturing Initiative (SNNI) of Oregon Nanoscience and Microtechnologies Institute (ONAMI) and Pacific Northwest National Laboratory (PNNL). A portion of the research was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at Pacific Northwest National Laboratory. PNNL is operated for the U.S. Department of Energy by Battelle under Contract DEAC06-67RLO 1830. Supporting Information Available: Additional information on nanoparticles used as well as the near-critical fluid handling and equipment; additional analysis on nanoparticle density and sedimentation coefficients. This material is available free of charge via the Internet at http://pubs. acs.org.
Langmuir 2009, 25(9), 4900–4906
