Tuning and Quantifying the Dispersibility of Gold Nanocrystals in

J. Phys. Chem. C 2008, 112, 13947–13957

13947

Tuning and Quantifying the Dispersibility of Gold Nanocrystals in Liquid and Supercritical Solvents Carlos A. Fernandez, Emily M. Hoppes, Jacky G. Bekhazi, Chongmin Wang, Robert J. Wiacek, Marvin G. Warner, Glen E. Fryxell, John T. Bays, and R. Shane Addleman* Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352 ReceiVed: April 30, 2008

The application of nanomaterials relies on the ability to synthesize, purify, transport, and deposit them in a controllable fashion. The capacity to adjust the density, and thus the solvent strength, of a supercritical or near-critical fluid can be used to tune reaction and separation processes as well as to assemble nanomaterials in a controllable fashion. Herein we demonstrate and quantify density-tunable and reversible size-dependent dispersibility of octanethiol-stabilized gold nanocrystals with a size of 3.7 ( 2.2 nm in near-critical and supercritical solvents as a way to show the significant potential of these fluids for nanomaterials processing. This study introduced discrete variations on the pressure of nanocrystal dispersions in compressed ethane and propane at temperatures of 25, 45, and 65 °C until they reached a saturation region, at which point actual measurements of nanocrystal dispersibility were obtained using UV-vis absorption spectroscopy. Transmission electron microscopy (TEM) was employed to correlate the dispersibility results with the actual size of the nanoparticle fractions at different densities. The results showed that stable dispersions of nanocrystals could be obtained at pressures as low as 50 atm in both solvents. Compressed ethane in its liquid or supercritical state was found to provide better dynamic tunability, whereas propane provided higher dispersibility of these nanocrystals under the studied pressure-temperature conditions. Two theoretical models, the total interaction theory and Chrastil equation, are briefly presented as a means of interpreting the experimental observations. It was determined that dispersibility depends strongly on the nanocrystal size, solvent density, and carbon chain length of the solvent. These results clearly show that selected supercritical fluids can be remarkably effective for the manipulation of nanoparticles. Introduction The ability to understand, quantify, and control the dispersibility of nanoparticles into solvent systems is of central importance for efficient and effective nanomaterials synthesis, purification, transport, deposition, and ultimately, utilization. Supercritical fluids (ScFs) can provide significant advantages over conventional solvents, since manipulation of the density, and thus the solvent strength, can be easily used to tune reaction and separation processes as well as to assemble nanomaterials to grow functional superstructures.1-12 ScFs, such as ethane, propane, and carbon dioxide, can offer a number of environmental and commercial advantages over conventional solvents. For example, they offer dramatic reductions in the volume of organic waste typically generated during advanced material processes and are fairly inexpensive. ScFs are particularly well-suited for particle deposition and assembly on surfaces13 and within porous materials due to their unique wetting properties.6-12,14,15 The intermediate transport properties of ScFs allow for faster rates in diffusion-limited reactions compared to liquid systems.16 The higher densities provide enhanced solvation, and thus increased reactant loadings, relative to gas-phase systems.17,18 The single-phase fluids do not exhibit a liquid-vapor interface, thereby eliminating surface tension driven Laplace pressures, which might otherwise collapse porous structures during solvent removal. Even subcritical fluids can * Corresponding author. E-mail: [email protected]. Phone: (509) 375-6824. Fax: (509) 372-4732.

provide interfacial tensions which are much lower than those of conventional solvents. Furthermore, ScF solvents can also provide access to higher temperature regimes (350-600 °C), which are well above the boiling points of conventional solvents (at ambient pressures), a key characteristic that enables access to synthetic temperatures needed to crystallize highly covalent nanocrystals, such as Si19 and Ge,20 and for the general application of metal particle-seeded vapor-liquid-solid (VLS)type growth of nanowires in solution.21-24 It is no wonder why numerous research groups have explored the use of heated and pressurized solvents near or above their critical points for synthesis, stabilization, and processing of numerous nanomaterials, including nanocrystals,3,4,6-12,25-28 nanowires,29,30 and nanorods31,32 during the past decade. Particularly, the stability of organic ligand-coated nanocrystals has been the focus of research for years due to the advantages that these fluids offer over conventional solvents.13,33-39 To mention just a few, theoretical studies concerning the interactions between passivated nanocrystals in ScFs have been presented, making use of the integral equation theory.40,41 These studies, based on a continuum model for the nanocrystal core and the passivation layer (if any) combined with a molecular model for the solvent, showed that the solvation strength increased as the density of the fluid increased and that the solute dispersibility is a decreasing function of solute size. This proved in agreement with the experimental results revealed by Johnston and co-workers33,36 who instead used the colloidal theory42 as a theoretical model to describe the observed dispersibility change

10.1021/jp8038237 CCC: $40.75  2008 American Chemical Society Published on Web 08/16/2008

13948 J. Phys. Chem. C, Vol. 112, No. 36, 2008

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Figure 1. High-pressure system for dispersibility determinations of nanoparticles in compressed solvents.

of nanocrystals with the pressure and temperature of ScFs.33 Johnston attributed these observations to a balance between van der Waals attraction between nanocrystal cores and steric repulsive forces provided by the adsorbed ligands.33,36 Molecular dynamics simulations of especially small (8 and 38 atoms) passivated and bare gold nanoparticles immersed in ethane have been performed in the proximities above and below the critical region, showing quite surprisingly that the presence of the passivating layer reduces the solvation capacity of the particle.43,44 In supercritical carbon dioxide (ScF CO2), the dispersibility of alkanethiol-coated nanocrystals has been shown to be very limited, even with large percentages of cosolvent. This is due to the lack of solvation of the hydrocarbon capping ligands by the weak van der Waals forces between CO2 molecules for preventing flocculation between particles. To enhance dispersibility, several fluorinated stabilizing ligands or ligands such as isostearic acid or dendritic polyamines have been developed. They have proven not only to be soluble in CO2 but also to disperse nanoparticles stabilized with the ligand due to their weak van der Waals forces, which are consistent with those of CO2.33,36,45,46 Conversely, even at high solvent densities where ligand stabilization is most effective, a significant amount of interparticle interaction and clustering has been observed in ScF CO2.37 Ghosh et al.47 studied the dispersibility of silica nanocrystals in supercritical ethanol and showed that silica nanoparticles are highly stable in this solvent over a wide range of temperatures (24-335 °C). These findings proved that these nanomaterials are an excellent probe with which to investigate the colloidal transport phenomenon in these fluids. Copper nanocrystals can be dissolved in supercritical water, revealing that pH and the interfacial stabilization are important considerations during their synthesis and stabilization.39 Shah et al.33 have shown that the dispersibility of gold and silver nanocrystals can be adjusted in supercritical ethane (ScF ethane) by varying either the temperature or the pressure of the fluid. In addition, they reported the nanocrystals absorbance at different pressures and temperatures together with particle size analysis as direct evidence of the material dispersed in solution.33 Although several theoretical as well as experimental studies have been devoted to explore the dispersibility of nanocrystals in ScFs, to our knowledge no one has been able to quantify this parameter. Our study will show for the first time the actual values of nanocrystal dispersibility in compressed ethane and propane and how this parameter can be adjusted by fine-tuning the density of these fluids. Size analysis of nanoparticles collected at different fluid densities in liquid ethane will be reported to associate the dispersibility values to the actual average size and size distribution of the fractions of nanoparticles remaining in solution. Two theoretical models (the total interaction theory and the function proposed by Chrastil) are briefly discussed to interpret the experimental observations. We will also show that this process of size-selective dispersion is

reproducible and totally reversible. In this manner, precise control of nanomaterials separation, purification, and assembly can be readily achieved. Experimental Section The octanethiol-stabilized gold nanoparticles (C8SH-Au), 3.7 ( 2.2 nm, used in this study were synthesized in our laboratory following the procedure reported by Rowe et al.48 with some modification. n-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. Figure 1 is a schematic of the high-pressure system used for the dispersibility experiments. Compressed propane or ethane at various temperatures was used as the solvent in this system. These fluids were metered with an ISCO syringe pump (model 260 D) and a pump controller (series D) and introduced to the high-pressure view vessel via stainless steel tubing (1/16 in. o.d., 0.03 in. i.d.). The pumps and high-pressure vessel were heated with a recirculating bath (Fisher Scientific, model Isotemp 3006P), and the temperature was controlled and kept constant ((0.1 °C) with a K-type sensor and a Digi-Sense temperature controller. The rest of the system was isolated to keep the temperature constant. The 0.8 mL vessel was equipped with two sapphire windows (7 mm optical path length) and placed inside a double-beam UV-vis spectrometer (Varian Instruments, model Cary 3E, deuterium and tungsten dual source, photomultiplier detector) that is capable of recording a full spectrum from 200 to 900 nm in 7 s. The windows were functionalized with a tridecafluoro-1,1,2,2-tetrahydrooctylsilane monolayer to eliminate nonspecific adsorption of nanocrystals to their surface by a method previously described.49 The other output of the high-pressure vessel was connected to a second pump via 1/16 in. stainless steel tubing. Each system was isolated from the others by an HIP high-pressure valve. A 2 m stainless steel equilibration coil (1/16 in. o.d., 0.03 in. i.d.) was immersed in the same temperature-controlled bath as the optical cell to ensure that the liquid or supercritical solution was at the correct temperature prior to entering the cell. With the system sealed, liquid propane or ethane was loaded into one of the pumps and pressurized before introducing it into the rest of the system. A blank measurement was taken at every pressure to provide a spectroscopic baseline using pure propane or ethane. Subsequently, 400 µL of a solution of gold nanoparticles in n-hexane (1 mg/mL) was then loaded into the vessel and the solvent was evaporated. The final concentration of nanoparticles in the highpressure system was 20 µg/mL. This concentration is below the maximum amount of material that can be dispersed in either of these solvents in the pressure range of 450-500 atm at the temperatures used in this study.

Gold Nanocrystals in Supercritical Solvents

J. Phys. Chem. C, Vol. 112, No. 36, 2008 13949

Figure 2. (A) Variation of the density-normalized surface plasmon resonance (SPR) absorption peak by a stepwise pressure reduction of a solution of octanethiol-stabilized gold nanoparticles (3.7 ( 2.2 nm) in liquid ethane at 25 °C. (B) Density-normalized concentration of the nanoparticles in the fluid as a function of its pressure.

While maintaining the pressure constant with one pump, the piston of the second pump was moved backward and forward in order to mix and homogenize the reaction mixture within the reactor. This was confirmed by following the absorbance of the surface plasmon resonance (SPR) peak at 510 nm33 until it reached a maximum (and constant) value. This first spectrum, corresponding to the maximum allowable pressure in our system (500 atm), was followed by a series of spectra taken at lower pressures. The UV-vis absorption spectra of the dispersions were recorded as the pressure was reduced stepwise in intervals of only 5 atm. The absorbance was found to be constant in less than 2 min; therefore, a 5 min period was found to be satisfactory for data collection at each pressure. After that time, the flow rate was stabilized and lowered to a rate of 0.01 mL/ min. This pressure-reduction process was repeated until the liquid-gas or supercritical-gas region was reached. Following each sequence of dispersibility measurements, the system was cleaned by flushing with hexanes, followed by supercritical ethane or liquid propane, without disassembling the cell. This washing procedure was used to eliminate any nanoparticle contamination from the entire system. In order to get transmission electron micrographs (TEM) of the nanocrystals at different stages of the experiment, a sixport injection valve with a 500 µL collection loop (Rheodyne, model 7725) was utilized. The valve was attached next to the view cell and immersed in the same bath, keeping it isothermal with the rest of the system (valve not shown in Figure 1). The collection loop was opened at the desired pressure allowing the supernatant to flow into the loop. The pressure was kept constant at all times by the computer-controlled syringe pump. Once the system was equilibrated, the loop was isolated and its pressure dropped to 1 atm causing the nanoparticles to precipitate inside the loop. The nanoparticles were then collected by flushing the loop with n-hexane. An additional 30 mL of n-hexane was then used to further clean the loop. This process was then repeated for other pressures. TEM images were obtained with a JEOL 1200 EX II high-resolution transmission electron microscope (HRTEM) at an accelerating voltage of 120 kV. Results and Discussion 1. Nanocrystals Dispersibility: Effect of Pressure, Temperature, and Density. Figure 2A shows a representative density-normalized absorption spectrum of 3.7 nm gold nanocrystals as a function of pressure in liquid ethane at 25 °C. In order to obtain these series of spectra, the pressure of the fluid was sequentially lowered from 500 to 40 atm, at which point

the liquid-vapor equilibrium of the fluid was reached. Note that the solvent strength (directly related to density) of liquid and supercritical ethane (or liquid propane) does not vary significantly in the pressure range of 150-500 atm since pressure changes result in only small changes in density, particularly in compressed propane (Figure 3). However, as will be shown, the dispersibility of the nanocrystals was highly sensitive to small density changes (hence, solvation strength), especially when ethane was used as a solvent. As a result, subsequent spectra were recorded as the pressure was reduced stepwise in intervals of only 5 atm as described in the Experimental Section. The system was allowed to equilibrate at each pressure before a new spectrum was taken. Gold nanoparticles display a clear SPR absorption spectrum that correlates with particle size.33 Figure 2A illustrates the sizedependent SPR of gold nanocrystals showing its reduction with pressure as the larger nanoparticles started to precipitate, leaving only the smaller (davg < ∼2.0 nm) ones in solution which do not exhibit a distinct absorbance peak at ∼510 nm.33 As mentioned before, one of the most useful properties of supercritical (and even subcritical) fluids is the tunability of the solvation strength by manipulation of the fluid density. However, it has also been shown that changes in the density of these solvents can cause shifts in the position of the absorption maximums, as well as significantly affect the molar absorptivity.50 For anthracene and pyrene, the molar absorptivity was found to increase from 30% to 170% as the carbon dioxide density was increased from 0.3 to 0.9 g/mL. If such an effect were observed for the passivated nanoparticles, it could introduce serious errors into any dispersibility measurement made using UV-vis absorption spectroscopy. No changes in the wavelength of the SPR absorption maximum have been reported for silver and gold nanoparticles in compressed ethane, and none were observed here in either ethane or propane.33 The effect of pressure/density on the absorptivity of octanethiolstabilized gold nanoparticles was determined using the same high-pressure system described in the Experimental Section but with a 3.8 cm path length view cell, having an internal volume of 9 mL. Aliquots of nanoparticles solution in n-hexane (1 mg/ mL) were introduced to the cell, and the solvent was allowed to evaporate. Liquid ethane or propane was then added to the desired pressure, the solution was mixed for 60 min to ensure complete dispersion, and the UV-vis spectra were recorded. Spectra were obtained at pressures of 50, 80, 160, 300, and 500 atm, at the three temperatures of the study, for several solute concentrations. By plotting density-normalized absorbance as


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Figure 3. Variation in the density of compressed ethane (left) and propane (right) with the fluid pressure at different experimental temperatures (ref 51).

Figure 4. Density-normalized concentration of octanethiol-passivated gold nanoparticles (3.7 ( 2.2 nm) in liquid (25 °C) and supercritical (45 and 65 °C) ethane as a function of the solvent pressure (A) and density (B). Invariable data at higher pressures or densities correspond to concentrations of a nonsaturated solution.

a function of concentration, below the saturation limit of the nanoparticles, a linear calibration curve was obtained for each pressure/density value. The absorptivity was calculated from the slope of each plot and found to be independent of density (5.5 ( 0.4 mL · mg-1 · cm-1, density range of 0.478-0.192 g/mL). Statistically equivalent results were obtained in liquid propane. Figure 2B represents the nanoparticle concentration in liquid ethane at 25 °C as a function of pressure. As the pressure is reduced, the solvent density and strength of the fluid decreases52 and the larger nanoparticles begin to precipitate until the system reaches saturation, with a corresponding decrease in the absorption spectrum. Due to the fact that the absorptivity is known and constant for the entire pressure range, it is possible to estimate the concentration of nanocrystals in solution at each pressure by normalizing the absorbance at 510 nm with respect to density. The concentrations measured in the precipitation region (below 400-450 atm depending on the temperature) correspond to a saturated system and hence a measurement of dispersibility that is free from the questions concerning the dissolution equilibrium. Since the absorption signal is densitynormalized, the concentration profile in Figure 2B would be invariant across the pressure range if the analyte was not precipitating. As the fluid pressure was reduced, the small amount of precipitated material did not affect the dispersibility measurements. Although analyte material was assumed to

precipitate upon all internal surfaces, the majority of material probably precipitated within the 2 m equilibration coil that precedes the optical cell. In addition to the primary precipitation occurring outside of the cell, the fluid solutions utilized were fairly low (parts-per-million range). Consequently, the amount of material deposited upon the interior surfaces was minimized. Finally, the precipitation of nanoparticles on the windows of the vessel itself was prevented by functionalizing the sapphire surface with a tridecafluoro-1,1,2,2-tetrahydrooctylsilane monolayer to eliminate the nonspecific adsorption of nanocrystals to this surface.49 All the dispersibility curves obtained here were reproducible within a tolerance of 3-5% in both solvents. Errors due to spectral analysis, ScF solution mixing, and ScF flow fluctuations might be among the sources of these signal variations. Similar dispersibility experiments were also performed in supercritical ethane (critical pressure, Pc ) 48.2 atm, critical temperature, Tc ) 32.5 °C). Figure 4, parts A and B, compares the nanoparticle concentration measured for liquid and supercritical ethane at temperatures of 25, 45, and 65 °C as a function of pressure and density, respectively. As in the case of liquid ethane, the nanoparticle concentration decreased with decreasing ethane pressure or density, as an increasing proportion of nanocrystals precipitate from the solution resulting from the decrease in the solvation strength.52 In general terms, as its density decreases (either due to variations in temperature or



Figure 5. Density-normalized concentration of octanethiol-passivated gold nanoparticles (3.7 ( 2.2 nm) in liquid propane at 25, 45, and 65 °C as a function of the solvent pressure (A) and density (B). Solids lines represent phase transition boundaries. Invariable data at higher pressures or densities correspond to concentrations of a nonsaturated solution.

pressure), the fluid tends to leave the solute to increase its volume and entropy. At constant density, the dispersibility of nanoparticles was shown to increase notably as the temperature of the solvent increased (Figure 4B). This dispersibility difference becomes larger as the density of the solution approximates the liquid-gas or supercritical-gas region. These results are comparable to the solubility studies performed on metal chelates, such as copper acetylacetonate (Cu(acac)2) in ScF CO2 at higher temperatures (>150 °C) where an increase in their solubility with temperature was attributed to an increase in the vapor pressure of the solute.53 Furthermore, naphthalene in ScF CO2 showed increasing solubility values as the temperature increased at constant density; these observations are attributed to a positive heat of dissolution, which is usually the case in conventional solvents and ScFs at constant density.54 A cosolvent effect, coming from some desorption of the ligand shell at higher temperatures, could also be the cause of the increase in dispersibility of the octanethiol-stabilized gold nanocrystals studied here with temperature and will be explored later.33 Liquid propane (Pc ) 41.9 atm, Tc ) 96.7 °C) at different temperatures and pressures was also used as a solvent for this study of the dispersibility of 3.7 nm gold nanoparticles. Figure 5 shows the variation of the nanoparticle concentration with pressure and density at three different temperatures, 25, 45, and 65 °C. It is evident that, in this solvent, the nanocrystals formed a stable unsaturated dispersion in the entire pressure or density range at 25 °C. As the temperature increased, dispersion tunability by liquid propane was beginning to manifest at pressures near 150 atm at 45 °C and 300 atm at 65 °C (Figure 5A). Once again, this is due to the fact that an increase in temperature brings the solvation strength (and density) to values where the nanoparticles, particularly the larger-sized fraction, begin to precipitate from solution. In this region the nanoparticle concentration corresponds to the measure of the actual dispersibility of the studied nanocrystals. By plotting the concentration of gold nanoparticles as a function of density, it can be seen that there is no obvious dependence of the concentration of nanoparticles on temperature at constant density, in contrast to what it was observed in liquid and supercritical ethane where an increase in temperature at constant density increased the nanocrystal dispersibility. Consequently, unlike ethane, at constant pressure a temperature increase resulted in a decrease in the dispersibility of the particles, due to the reduction in solvent density, similar to what it was observed for silver nanoparticles in compressed ethane.33 The reason for this

dissimilar behavior in liquid propane could be due to the fact that, in ethane (particularly at the temperatures of 45 and 65 °C), the solvent is in its supercritical state (at pressures larger than the critical pressure, Pc ) 48.2 atm). ScFs, unlike liquids, may be considered macroscopically homogeneous but microscopically inhomogeneous, consisting of clusters of solvent molecules and free volumes. As a consequence, extremely wide variations in the solvent properties should be observed.55 An example is shown in Figure 3 where compressed ethane (particularly ScF ethane at 45 and 65 °C) shows significantly larger variations in the fluid density with pressure and temperature compared to propane. Also, in an ScF solution it is believed that the local solvent density about the solute is greater than the bulk solvent density.55 Therefore, the dispersibility changes with density and temperature in near-critical and ScF dispersions will be greater than those observed in more microscopically homogeneous liquid dispersions (compare Figures 4B and 5B). Furthermore, the effect of temperature on the solubility of chemical species in ScFs has also been shown to be solute-solvent system dependent, as manifested in solubility studies on different metal chelates in ScF CO2 where a solubility increase with temperature was observed for copper acetylacetonate (Cu(acac)2), whereas a reduction of the solubility with temperature was noticed for yttrium acetylacetonate (Y(acac)3).53 Other significant observations can be found in comparing relative dispersibility in ethane and propane as a function of solvent density. The higher densities provided by propane (for equivalent temperatures and pressures) generally provided higher dispersibilities. Furthermore, the density range at which the nanoparticles begin to precipitate in propane (saturation region: 0.501-0.418 g/mL) has some overlap with the density values where precipitation was observed in ethane (0.482-0.266 g/mL). In propane above 0.501 g/mL, the nanoparticles were completely dispersed at all three temperatures studied. For this reason, in compressed propane at 25 °C (density range ) 0.497-0.570 g/mL), nanoparticles are soluble at nearly all densities, except in the lower density values approaching the liquid-gas transition (0.493 g/mL). This is consistent data from other higher molecular weight alkanes. The size of the solvent hydrocarbon chain clearly plays a key role in the stabilization of these nanocrystals by providing, at identical pressure-temperature conditions, both a higher solvent density (hence solvation strength) and more stable dispersion forces as the alkane chain length of the solvent increases. For example, in n-hexane,


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density ) 0.660 g/mL, we were able to disperse the octanethiolstabilized gold nanoparticles with concentrations up to 1 mg/ mL at 25 °C, a much higher concentration than the observed for either propane or ethane at any density. In summary, we have found that the dispersibility of nanocrystals in liquid and ScFs seems to be a function of the solute size and the solvent density, as demonstrated in both solvents. Gold nanocrystals showed higher dispersibility values in propane than in ethane under identical pressure-temperature conditions. In other words, high-pressure propane provides better nanocrystal dispersibility than ethane but does not provide the dynamic dispersion tunability that ethane revealed (for the temperature and pressures ranges explored). It was also noted that for equivalent densities, ethane surprisingly provided significantly higher dispersibilities than propane, particularly in its ScF state. The reason for this behavior may be due to a larger number of fluid molecules solvating the nanocrystals in ethane with respect to propane. This particular argument will be extended later. Finally, it was observed that although liquid and ScF CO2 are common and effective solvents for many chemical systems they were found to be completely ineffective for the dispersion of octanethiol-passivated gold nanocrystals. 2. Total Interaction Theory. Several theoretical studies56-59,33 have been performed to investigate the stability of nanoparticle dispersions in various compressed solvents, such as ethane and CO2, and although a detailed theoretical examination is outside the scope of this paper, we will briefly compare our results with the theoretical and qualitative experimental work performed by Johnston’s group on metallic nanoparticles in compressed ethane.33 They employed the total interaction theory developed by Vincent et al.58,59 to explain their UV-vis spectral observations obtained from solutions of silver and gold nanoparticles in compressed ethane. This approach describes the stability of nanocrystal dispersions as a balance of the van der Waals attraction forces between the nanocrystal cores (which in the case of metallic nanocrystals is large due to their extremely high polarizabilities) and the steric repulsive forces provided by the ligand shell. The total interaction energy (Φtotal) was expressed as a sum of two repulsive terms, the osmotic repulsive energy (Φosm) and the elastic repulsive energy (Φelas), and a van der Waals attraction term (ΦvdW):33,58,59

Φtotal ) ΦvdW + Φosm + Φelas

(1)

The van der Waals attraction, ΦvdW, between two nanocrystals increases with larger particles and decreased center-to-center separation. The elastic repulsive energy, Φelas, originates from the entropy loss that occurs upon compression of the stabilizing ligands, which is only important at interparticle separations shorter than the ligand length. The osmotic term, Φosm, results from the energetic balance between solvent-ligand tail and tail-tail interactions. The solvent conditions and ligand length largely control Φosm. A very important parameter in this equation (specifically in the Φosm term) is the Flory-Huggins interaction parameter (χ) that differentiates a good solvent (χ < 0.5) from a poor solvent (χ > 0.5). Good solvents for alkanethiol-stabilized nanocrystals such as hexane and chloroform would have χ values close to zero. The parameter χ is related to the difference between the cohesive energy density3 of the solvent and the cohesive energy density of the ligand shell.3,33,58,59 The more comparable these two values are to each other, the closer the fluid is able to reach a good solvent regime at a given density. In other words, a decrease in solvent density can lead to phase separation, due to a growth in the asymmetry of the solute and solvent cohesive energy densities. As a result, the total interac-

tion energy (Φtotal) is defined to depend on the solvent condition, nanoparticle size, and ligand shell density on nanocrystal surface, composition, and length. By applying these concepts to a system composed of dodecanethiol-stabilized silver nanocrystals with a core diameter of 9 nm, Johnston’s group calculated that, in ScF ethane at 35 °C, a minimum pressure of 272 atm (density ) 0.428 g/mL) was needed in order to have a stable dispersion of the nanoparticles.33 Their calculations also indicated that, under these solvent conditions, dispersions of nanoparticles larger than 12 nm were unstable, due to the fact that the magnitude of the core-core attraction between nanoparticles brings the total interaction energy to (negative) values larger than the energy provided by Brownian motion. They performed dispersibility experiments on both 5.3 nm dodecanethiolpassivated silver nanocrystals and a bimodal mixture of 1.8 and 4.2 nm dodecanethiol-coated gold nanoparticles. Their experiments with dodecanethiol-stabilized silver nanocrystals showed agreement with the calculations, where a minimum density value of 0.428 g/mL was needed to disperse these nanoparticles in solution as confirmed by UV-vis absorption spectra. In contrast, in the case of their experiments on bimodal dodecanethiolstabilized gold nanoparticles, they were able to resuspend the nanocrystals in liquid ethane at 25 °C and 136 atm (density ) 0.404 g/mL), conditions that their calculations described as poor solvent conditions (density < 0.428 g/mL). Our experiments with 3.7 nm gold nanoparticles stabilized with an octanethiol ligand shell also showed stable dispersions at lower pressures and higher temperatures (density < 0.428 g/mL) than those obtained from the calculations on 9 nm silver nanocrystals (see Figure 4).33 It is important to mention that these dispersions would correspond to nanoparticles in the small end of the size distribution, due to the absence of the SPR peak at 510 nm under these pressure-temperature conditions (Figure 2A). The reason for the discrepancy between Johnston’s calculations using the total interaction theory and the experimental results obtained with gold nanoparticles by both his33 and our group is simple. Their calculations were performed based on 9 nm silver nanoparticles with a dodecanethiol shell. Calculations to find good solvent regimes on smaller nanoparticles, such as the 3.7 nm octanethiol-stabilized gold nanocrystals employed here or the 4.2 and 1.5 nm dodecanethiol-stabilized gold particles used by Johnston’s group, should result in lower density values. (In our case, we should also correct for the difference in chain length of the stabilizer ligand shell.) In addition, the concentration of nanocrystals in the fluid does not seem to be considered in the theory. Although the concentration in Johnston’s publication is not mentioned, we performed our experiments with fairly low concentrations (on the order of parts-per-million), although the solution became saturated as the density of the fluid was decreased during the experiment. Furthermore, the total interaction theory does not take into account the nanocrystals size dispersion, which might be also the reason why the experimental results on dodecanethiol-stabilized silver nanocrystals (5.3 ( 1.9 nm) employed by Johnston behaved differently to his dodecanethiol-stabilized gold nanocrystals (bimodal mixture of 1.8 ( 0.5 nm and 4.2 ( 1.0 nm particles). Another reason for the difference between the experimental results obtained by this group with silver nanocrystals and the ones obtained with gold nanocrystals might be the discrepancy in the particles’ polarizability values that account for the van der Waals attraction between the cores, hence the stability of the nanocrystal dispersion. Nevertheless, in general terms, our results and Johnston’s calculations and experimental results all agree in that the



Figure 6. Density-normalized dispersibility plots of octanethiol-passivated gold nanoparticles (3.7 ( 2.2 nm) at 25, 45, and 65 °C as a function of the solvent density in a log-log form in compressed ethane (A) and propane (B). Solids lines were obtained by linear regression.

dispersibility of the nanocrystals depends on the nanocrystals size and on the fluid density. Larger nanoparticles require higher densities for their stabilization in solution. As the density of the solvent decreases, the steric repulsion between the nanoparticles ligand shell weakens as a result of decreased ligand solvation. At the same time, an increased van der Waals core-core attraction leads to precipitation of the larger nanoparticles as the smaller ones remain in solution under the same solvent conditions. 3. Chrastil Model. An important semiempirical model that has been employed for dispersibility calculations of numerous molecular species in near-critical and ScFs was developed by Chrastil.60 This model represents a direct semiquantitative approach which relates the solubility of molecules to the density of the fluid and does not need unavailable thermodynamic values that some methods require.61,62 Chrastil assumed a reaction equilibrium between the solute (A), n molecules of a solvent (B), and a solvate complex (AB) as follows:60

A + nB ) ABn

(2)

K)[ABn]/([A][B]n)

(3)

ln K + ln [A] + n ln[B] ) ln[ABn]

(4)

or

where K is the equilibrium constant, [A] is the molar vapor concentration of the solute, [B] is the molar concentration of the fluid, and [ABn] is the molar concentration of the solute in the fluid. By combining these expressions and making use of simple equations that associate the heat of vaporization of the solute (∆Hvapor) and the heat of solvation (∆Hsolv) with the equilibrium constant K, Chrastil arrived to a final expression that relates the solubility of the solute (C) in the fluid with the density of the fluid (δ):60

ln C ) n ln δ + m

(5)

where n is the number of solvent molecules associated with the solvated complex (association number) and m is related to the enthalpy of solvation as well as the solute volatility and is usually negative for soluble species.60,63 It is important to clarify here that the enthalpy of solvation and enthalpy of dissolution are two different terms. Enthalpy of solvation refers to the energy released when solute molecules associate with molecules of the solvent, whereas enthalpy of dissolution is the sum of mainly three terms. These are the enthalpy to break solute-solute

TABLE 1: Chrastil Parameters of Octanethiol-Stabilized Gold Nanocrystals ethane

propane

temp, °C

n

m

n

m

25 45 65

7.81 4.79 2.99

-51.9 -33.0 -21.9

4.94 3.98 3.20

-34.6 -28.7 -23.7

attractions (in our case this would be enthalpy of solute vaporization), enthalpy to break solvent-solvent interactions, and the enthalpy of solvation. Equation 5 predicts a linear relationship between ln δ and ln C where the values of the slope (n) and intercept (m) are functions of temperature and the specific solute/solvent system. Knowledge of the two constants (n and m) for a specific solute/solvent system enables solubility data (which can be very difficult to experimentally obtain) to be calculated over a wide range of densities. The Chrastil model has shown to be valid for a wide variety of solid and liquid chemical species, including metal chelates in near-critical and supercritical solvents.60,63 To our knowledge this is the first application of the Chrastil model for interpretation of the dispersibility of nanoparticles into supercritical and near-critical fluids. Figure 6 shows a graph of the concentration of the nanoparticles, utilizing the values obtained in the saturation region, as a function of density in a (natural) log-log plot at three different temperatures for both ethane and propane. Clearly, the excellent linearity of the data in Figure 6 shows that nanoparticle dispersibility follows the linear Chrastil relationship given in eq 5 (at least under these pressuretemperature conditions). Table 1 gives the Chrastil fit parameters (n and m) for octanethiol-stabilized gold nanocrystals at three different temperatures in ethane and propane. The dynamic tunable dispersibility of octanethiol-stabilized gold nanocrystals observed (Figure 4B) results in wellseparated lines on the Chrastil plot for ethane (Figure 6A). However, in propane the Chrastil plot has overlapping dispersiblity functions (Figure 6B) due to the very small changes in the density-dependent dispersibility as a function of temperature. The reasons for the more uniform behavior of nanoparticle dispersibility with propane when compared to ethane have been previously discussed in section 1. From Table 1 it can be noted that increasing temperature produces a decrease in n, the variable in the Chrastil equation that describes the number of solvent molecules associated with the


Fernandez et al.

solvated complex. This decrease in n with temperature is consistent with other low volatile species, such as large metal chelates (ferrocene, Cu(acac)2), in compressible fluid solvents at these temperature ranges and can be attributed to reduction of the solvation sphere density as solvent temperature rises.53,60,63,64 With a complexing organic ligand shell and a metal core, the metal chelates are the closest molecular analogues available for comparative discussions. Part of this reduction in n may be due to the introduction of cosolvent molecules in the solvating sphere coming from some nanocrystal ligand desorption originated as the temperature of the dispersion is raised.33,65 These free octanethiol ligands would replace solvent molecules associated with the nanocrystals, decreasing their average number per particle, hence n. However, it should be pointed out that the nanoparticle concentration is very low and the gold-thiol bond between the ligand shell and the core is very strong.66 It can also be noted in Table 1, and in literature for chemical species,63 that n is not typically an integer indicating that the number of solvent molecules associated with the solute is variable. These nonstoichiometric values are attributed to the fact that there are often several, more or less stable, solvated association complexes present. We believe this is especially true for polydisperse nanocrystals because a different solvated complex should be formed for each nanocrystal size. For comparative purposes it is interesting to note that in ScF CO2 in the 40-70 °C temperature range ferrocene, transition metal betadiketones, and many other metal chelates have n values ranging from 2.5 to 8, which are very similar to those observed for the octanethiol-stabilized gold nanoparticles in ethane and propane.63 Although the solvents being compared are different, this agreement in Chrastil model fit values is surprising given the much larger size and mass of the nanoparticles when compared to the metal chelates. When comparing Chrastil n values in Table 1 between ethane and propane it can be seen that the ethane values change substantially more than the propane values (over the experimental temperature range), which is consistent since ethane undergoes a much larger change in solvent density than propane over the pressure and temperature range studied. It is also interesting to note that ethane can achieve higher n values (specifically at 25 and 45 °C) than propane clearly suggesting more ethane molecules are interacting with the nanoparticle ligand sphere for a given temperature. The reason for this behavior might be due to the fact that in supercritical and near-supercritical solutions the local solvent density about the solute is greater than the bulk solvent density54 as opposed to the more microscopically homogeneous liquid dispersions. The enhanced number of ethane solvent molecules (relative to propane) associated with nanoparticle may explain why for equiValent densities ethane provides much higher nanocrystal dispersibility than propane. From Table 1 it can be seen that increasing temperature increases the Chrastil parameter m in both propane and ethane. Similar m values have been observed on metal chelates such as ferrocene, uranyl nitrate tributyl phosphate, and Cu(acac)2 in ScF CO2 under comparable temperature ranges.63,64 For these molecular species, m was also shown to increase (i.e., become less negative) with temperature.63,64 As previously noted, m is related to the enthalpy of solvation as well as the solute volatility and specifically is given by60

m ) ∆Htotal/RT + ln (MA + nMB) + q - n ln MB

(6)

where ∆H is the total heat of reaction (∆Htotal ) ∆Hsolv + ∆Hvapor), MA and MB are the molecular weight of solute and solvent, respectively, and q is a constant. (Please note that ∆Htotal is not the enthalpy of dissolution because it is missing the enthalpy term to break solvent-solvent interactions.) For

nanoparticles, as well as many metal chelates, the vapor pressures are negligible at the temperatures employed here. Therefore, the main factor determining the values of m is the heat of solvation (∆Hsolv). The general trends observed in m with temperature are due to its reciprocal (1/T) relationship. It is interesting to note that, for the nanoparticles studied, m has similar values as the metal chelates ferrocene and Cu(acac)2 in ScF CO2. However, it has a remarkably larger degree of change over the temperature range compared to the metal chelates, particularly in ethane.53,63,64 The reason for this difference between nanocrystals and metal chelates seems to be related to a greater enthalpy of solvation of the nanocrystals dispersions coming from a stronger interaction between the alkyl chains of the solvent (ethane and propane) and the nanocrystal shell (octane) as compared to the one between CO2 molecules and the corresponding coordinating ligand in the metal chelates being considered. In addition, given the difference in molecular weight between metal chelates and nanoparticles, their similar parameter values in the Chrastil plots clearly indicate very strong solvation interactions and very good shielding and surface charge neutralization of the metal core by these solvents. Larger changes in m were observed in ethane, particularly when going from 25 to 45 °C, compared to propane. This is the region in temperature where ethane undergoes the transition from liquid state to the ScF state (Tc ) 32.5 °C). As mentioned earlier, the variation in physicochemical properties in near-critical and ScFs is greater than in liquid solvents and is the reason why the larger differences are observed on the parameter m with temperature in ethane as compared to propane. From the values of m in ethane and propane, the enthalpy of reaction (∆Htotal ) ∆Hsolv + ∆Hvapor) is negative in both solvents. Moreover, from a simple m versus 1/T plot the relative ∆Htotal for ethane showed to be 3 times larger than for propane. This is consistent since ethane undergoes a much larger change in solvation strength than propane over the pressure and temperature range studied (Figure 3). Moreover, there is a correlation (particularly at 25 and 45 °C) 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) when comparing ethane with respect to propane. In addition, as described earlier, some desorption of the nanoparticles ligand shell might be occurring with increasing temperature.33,65 These free ligands may introduce a cosolvent effect in the immediate solvent shell and, as a result, a decrease in the absolute value of m. Further experiments introducing increasing percentages of a cosolvent at constant temperature should be performed in order to validate this last speculation. Finally, although enthalpy variations appear to have a dominant role on the nanocrystals dispersibility, the entropic effects of the solvent seem to begin to dominate as the temperature rises. This can be seen from the results in Table 1 where an increase in temperature reduces the number of solvent molecules associated to the solute as the absolute values of m (related primarily to the heat of solvation) decline. In summary, these results confirm that the Chrastil model is applicable, under the given conditions, to describing and predicting the dispersibility of nanoparticles in liquid and supercritical solvents. The Chrastil model trends and fit parameters for the octanethiol gold nanoparticles in ethane and propane are similar to those observed over similar temperature ranges for a number of metal chelates in ScF CO2. 4. Selective Dispersion and Reversibility. Figure 7 shows representative TEM obtained at different stages of an experiment performed with a solution of octanethiol-stabilized gold nanocrystals in liquid ethane at 25 °C. An amount of 500 µL of



Figure 7. Representative TEM of octanethiol-stabilized gold nanocrystals dispersed in liquid ethane (25 °C) at (A) 500, (B) 250, and (C) 50 atm. The average size and size dispersion of the nanocrystals collected at each pressure were 3.7 ( 2.2, 2.5 ( 1.1, and 1.7 ( 0.3 nm, respectively. The average size and size dispersion were calculated by measuring over 300 nanoparticles per sample. Micrograph C is a combination of two micrographs with exactly the same magnification due to the very dilute concentration of nanocrystals in this sample. Scale bars correspond to 20 nm.

Figure 8. Nanoparticle size as a function of fluid density for a dispersion of octanethiol-stabilized gold nanocrystals, 3.7 ( 2.2 nm, in liquid ethane at 25 °C. The average size as well as the size dispersion (bars) decreases when the density of the solvent is reduced at constant temperature.

nanocrystals solution was collected at each pressure (starting at 500 atm) by allowing the system to equilibrate after each pressure reduction, as described in the Experimental Section. For collection of the second aliquot, the pressure was reduced by intervals of 5 atm until reaching 350 atm. The process was repeated until a final pressure of 50 atm was reached. It is evident from the micrographs in Figure 7 that the nanoparticle size and size distribution decreased as the pressure (hence, the density) of the solvent was reduced. We began with a polydisperse (3.7 ( 2.2 nm) sample at the initial pressure of 500 atm (δ ) 0.48 g/mL) and ended with a solution of monodisperse (1.7 ( 0.3 nm) and smaller nanocrystals at a final pressure of 50 atm (δ ) 0.34 g/mL). The average size and size distribution were calculated, measuring over 300 particles per sample, for a total of five samples collected at 500, 350, 250, 250, and 50 atm. It is important to mention that the average size and size distribution obtained for the as-synthesized nanocrystals dispersion and the one obtained for the aliquot collected at 500 atm were statistically equivalent, confirming that the as-synthesized nanocrystals are completely soluble at the upper pressure range. The numeric results of nanoparticle size and size distribution are plotted as a function of the fluid density in Figure 8. It can be clearly observed that the average particle size, the upper limit of observed particles sizes, and the range of particle sizes all decrease dramatically with the density/pressure of ethane. The

data shown in Figure 8 correlate with observations from the pressure-dependent absorption spectra. It can be seen in Figure 2A that the SPR absorption peak at 510 nm decreases with pressure as would be expected if the larger nanoparticles were precipitating and the smaller nanoparticles were remaining in solution. Figure 8 also compares with the results shown on Figures 4B and 5B. The dispersibility of the nanocrystals along with their size and size distribution decreases as the density of the fluid is reduced. These results demonstrate the tunable properties of selected near-critical and ScFs and the potential applications they have for use in purification and size-selective separation processes of nanoparticles. It should be noted that this tunability can be achieved in ethane at readily available temperatures and pressures. Finally, we explored the reversibility of the precipitation of these materials in both solvents. To this end, at the completion of selected dispersibility determination experiments, the system was repressurized to its initial high-density (pressure) conditions. The nanocrystals were then remixed, as described in the Experimental Section, in order to homogenize the dispersion within the reactor. Once the dispersion was homogeneous, a second series of pressure reductions was performed. Determination of a new set of dispersibility values was then obtained. In all cases the process of precipitation and redispersion was reversible bringing the initial concentration of material back into solution and exhibiting a dispersibility plot similar to that obtained with the original solution. Figure 2B shows the dispersibility measurements obtained in liquid ethane at 25 °C on the initial sample and on the sample after redispersion at its original pressure. It is evident that the curves are equivalent within 3-5%. Conclusions This study shows for the first time the quantitative values for the dispersibility of gold nanocrystals in compressed ethane and propane by measuring the absorption spectra of the nanoparticles as a function of pressure and density at three working temperatures. Transmission electron microscopy was employed as a complementary technique to successfully demonstrate how discrete variations in the solvation conditions affected the average size and size distribution of these nanomaterials. We have shown that high-pressure ethane, in its liquid or supercritical states, is an excellent solvent for tunable sizeselective dispersion of octanethiol-stabilized gold nanocrystals of up to 6 nm in diameter. For equivalent densities ethane is a

13956 J. Phys. Chem. C, Vol. 112, No. 36, 2008 significantly better solvent for octanethiol-stabilized gold nanocrystals than propane. However, high-pressure propane provides higher dispersibility of the nanocrystals than ethane due to the higher solution densities achievable under similar pressuretemperature conditions. Although liquid and ScF CO2 is a common and effective solvent for many chemical systems it was found to be completely ineffective for dispersion of these octanethiol-stabilized gold nanocrystals. Two previously reported ScF solvation models, the total energy interaction theory58,59 and the approach proposed by Chrastil,60 were explored as means to interpret the dispersibility results obtained for these nanocrystals. In particular, the parameters obtained from the Chrastil dispersibility plots (which are related to the number of solvent molecules associated to the nanocrystals and to the heat of solvation) capture the essential thermodynamic of density tuning of the size of the dispersed nanocrystals. Although the basis and assumptions of each model are different, they both agreed that the dispersibility of these nanomaterials can be fine-tuned through slight variations in the density of these fluids. The deposition and solvation process was demonstrated to be completely reversible and reproducible. In summary, we have shown that through the manipulation of the density of supercritical and near-critical fluids it should be possible to precisely control nanomaterials processes, including separation, transport, and purification of nanocrystals. Acknowledgment. Funding for this work was provided by the Safer Nanomaterials Nanomanufacturing Initiative (SNNI) of the Oregon Nanoscience and Microtechnologies Institute (ONAMI) and Pacific Northwest National Laboratory. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle under contract DE-AC06-67RLO 1830. A portion of this 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. References and Notes (1) Eckert, C. A.; Knutson, B. L.; Debenedetti, P. G. Nature 1996, 383, 313. (2) Holmes, J. D.; Johnston, K. P.; Doty, R. C.; Korgel, B. A. Science 2000, 287, 1471. (3) Fernandez, C. A.; Wai, C. M. Small 2006, 2, 11–1266. (4) Fernandez, C. A.; Wai, C. M. Chem. Eur. J. 2007, 13 (20), 5838. (5) Puniredd, S. R.; Srinivasan, M. P. Ind. Eng. Chem. Res. 2007, 46, 464. (6) Fulton, J. L.; Matson, D. W.; Pecher, K. H.; Amonette, J. E.; Linehan, J. C. J. Nanosci. Nanotechnol. 2006, 6 (2), 562. (7) Fulton, J. L.; Deverman, G. S.; Yonker, C. R.; Grate, J. W.; De Young, J.; McClain, J. B. Polymer 2003, 44 (13), 3627. (8) Koga, T.; Zhou, S.; Chu, B.; Fulton, J. L.; Yang, S.; Ober, C. K.; Erman, B. ReV. Sci. Instrum. 2001, 72 (6), 2679. (9) Ji, M.; Chen, X.; Wai, C. M.; Fulton, J. L. J. Am. Chem. Soc. 1999, 121 (11), 2631. (10) Ye, W. J.; Keiper, J. S.; DeSimone, J. M. Chin. J. Polym. Sci 2006, 24 (1), 95. (11) Siripurapu, S.; DeSimone, J. M.; Khan, S. A.; Spontak, R. J. Macromolecules 2005, 38 (6), 2271. (12) Lacroix-Desmazes, P.; Andre, P.; Desimone, J. M.; Ruzette, A. V.; Boutevin, B. J. Polym. Sci., Part A: Polym. Chem. 2004, 42 (14), 3537. (13) Shah, P. S.; Novick, B. J.; Hwang, H. S.; Lim, K. T.; Carbonell, R. G.; Johnston, K. P.; Korgel, B. A. Nano Lett. 2003, 3, 1671. (14) Fukushima, Y.; Wakayama, H. J. Chem. Phys. B 1999, 103, 3062. (15) Blackburn, J. M.; Long, D. P.; Caban˜as, A.; Watkins, J. J. Science 2001, 294, 141. (16) Brennecke, J. F.; Chateauneuf, J. E. Chem. ReV. 1999, 99, 433. (17) Meredith, J. C.; Johnston, K. P. In Supercritical Fluids Fundamentals and Applications; Kiran, E., Peters, C., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000; p 211.

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