Nanoparticle separation and deposition processing using gas expanded liquid technology

Nanoparticle separation and deposition processing using gas expanded liquid technology

Available online at www.sciencedirect.com Nanoparticle separation and deposition processing using gas expanded liquid technology Steven R Saunders1 a...

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Available online at www.sciencedirect.com

Nanoparticle separation and deposition processing using gas expanded liquid technology Steven R Saunders1 and Christopher B Roberts2 Most currently employed nanoparticle post-synthesis processing techniques are solvent intensive and time consuming. This article reviews the development of highly tunable CO2 gas-expanded liquid (GXL) systems to process nanoparticles in a sustainable and efficient manner. The highly adjustable physico-chemical properties of these GXLs provide unique opportunities to control nanoparticle dispersability and precipitation through simple variations in applied CO2 pressure. This article illustrates that these tunable solvent systems can be used to create high quality, wide-area nanoparticle thin films and can also be used for the size-selective fractionation of ligand stabilized metallic nanoparticles. Recent advancements in the development of models that accurately predict nanoparticle dispersability in these tunable solvent systems are also described. Addresses 1 311 Ferst Drive NW, School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States 2 212 Ross Hall, Department of Chemical Engineering, Auburn University, AL 36849, United States Corresponding author: Roberts, Christopher B ([email protected])

Current Opinion in Chemical Engineering 2012, 1:91–101 This review comes from a themed issue on Nanotechnology Edited by Hua Chun Zeng Available online 3rd January 2012 2211-3398/$ – see front matter # 2011 Elsevier Ltd. All rights reserved. DOI 10.1016/j.coche.2011.12.004

Introduction While the vast majority of research dealing with nanoparticles over the past several decades has been synthesisbased and application-based, developments in post-synthesis nanoparticle processing has been more limited. Nanoparticles with diameters less than 20 nm are of particular interest since these materials demonstrate significantly novel and highly size-dependent properties. Large-scale nanoparticle synthesis methods are often solution-based and the products must typically undergo significant post-synthesis processing (e.g. size-selective fractionation to finely tune the size distribution) in order to prepare them for their intended application. Traditional nanoparticle post-synthesis processing is both time consuming and solvent intensive such that relatively www.sciencedirect.com

large quantities of organic waste are created for modest nanoparticle yields. Through the use of tunable solvent systems, specifically CO2 gas-expanded liquids (GXLs), it is possible to process nanoparticles in a green, sustainable and efficient manner that provides complete solvent recycle. The highly adjustable physico-chemical properties of GXLs provide unique opportunities to control nanoparticle dispersability and deposition through simple variations in applied CO2 pressure. This review focuses on the use of the tunable properties of CO2 GXLs for the purposes of nanoparticle processing.

Gas-expanded liquids GXLs are mixtures of an organic solvent and a compressed gas, where the gas partitions (i.e. dissolves) into the liquid phase at applied pressures less than the vapor pressure of the gas. These GXLs possess highly tunable physico-chemical properties at moderate temperatures and pressures. Through simple adjustments in the applied gas pressure, the properties of the mixed solvent media can be tuned between those of the liquid organic solvent and those of the gas [1]. The use of GXLs provides several processing advantages over traditional solvent media including solvent recovery through simple depressurization, enhanced gas solubility compared to the neat solvent, and lower operating pressures than those required for supercritical operation. A more detailed review of GXL properties and applications is available in Jessop and Subramanium’s review [1]. CO2-expanded liquids are the most widely utilized GXL due in part to safety and economic reasons. CO2-expanded hexane has been a widely used GXL for nanoparticle applications since hexane is a good solvent for the aliphatic stabilizing ligands (e.g. thiols or carboxylic acids) that are commonly used to passivate the surface of nanoparticles during synthesis as a means of maintaining a stable dispersion of nanoparticles in a solvent. The vapor–liquid equilibrium of CO2-expanded solvents, including CO2expanded hexane, has been demonstrated to be predicted well by the Peng–Robinson equation of state (PR-EOS) [2–4]. Figure 1a demonstrates the volume change of hexane when pressurized with CO2. As the applied CO2 pressure increases, the solubility of CO2 in the organic solvent (in this case, hexane) increases leading to a volume increase and a significant change in the properties of the liquid mixture. Density and molar volume, as demonstrated in Figure 1b, can be tuned between those of the organic solvent and those of liquid CO2. This also implies that other solvent properties, such as solvent strength [5], Current Opinion in Chemical Engineering 2012, 1:91–101

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Gas-expanded liquid properties or hexane expanded with CO2 at 258C as predicted by the Peng–Robinson equation of state: (a) volume expansion (i.e. change in volume with respect to the initial volume) of the liquid phase as a function of the applied CO2 pressure and (b) solvent mixture density and molar volume as a function of the applied CO2 pressure.

viscosity [6], and mass diffusion through the solvent [7,8] can be tuned by simply varying the applied CO2 pressure.

Nanoparticle precipitation The ability to controllably precipitate nanoparticles from a dispersion is required for most post-processing methods, including cleaning [9,10], thin film deposition [11,12], and size-selective fractionation [9,13]. This is typically accomplished through a liquid solvent–antisolvent (LSAS) precipitation [9,10,14]. For example, nanoparticles can be stabilized with dodecanethiol or any other type of aliphatic ligand (e.g. hexanethiol, octanethiol, and dodecyl acid) and these nanoparticles can be dispersed in any number of nonpolar solvents (defined here as the primary solvent). LSAS precipitation is typically performed by adding an antisolvent (e.g. ethanol, methanol, and acetone) to the primary solvent (e.g. hexane, pentane, toluene, and chloroform) where the antisolvent is a poor solvent for the stabilizing ligand. The addition of the antisolvent will destabilize the nanoparticle dispersion causing reversible flocculation of the nanoparticles leading to precipitation. In the LSAS method, the solvent mixture is comprised of two components (i.e. liquid solvent and the liquid antisolvent), Current Opinion in Chemical Engineering 2012, 1:91–101

each with relatively high viscosities and low nanoparticle diffusivities, as such, precipitation must be aided with centrifugation. The supernatant, containing the mixture of the solvent and the antisolvent, is then disposed of and the precipitated nanoparticles can be redispersed in a neat solvent. In order to, for example, size-selectively fractionate nanoparticles, an amount of the antisolvent is added to precipitate only the largest nanoparticles while the smallest nanoparticles remain dispersed in the supernatant. The largest nanoparticles are recovered by simply decanting the supernatant (containing the smallest nanoparticles) and redispersing the precipitated nanoparticles in the neat primary solvent. This process is repeated several times in order to narrow the size distribution of a polydisperse sample of nanoparticles. This precipitation process produces large amounts of solvent waste which must be either disposed of or separated requiring large amounts of energy. These drawbacks combined with the intensive manual labor involved in these precipitations makes this LSAS precipitation method costly, nonsustainable and environmentally hazardous. Several of these problems with the LSAS precipitation may be remedied through the use of GXLs, specifically CO2-expanded hexane, rather than the mixed liquid solvents [11,15,16,17,18,19,20]. When a thermodynamically stable dispersion of nanoparticles is pressurized with CO2, the CO2 partitions into the liquid phase reducing the solvent strength of the mixture due to CO2 being a non-solvent for the aliphatic stabilizing ligands. At sufficiently large concentrations of CO2 (i.e. applied CO2 pressure), the solvent strength of the mixture is reduced to the point of no longer being capable of stabilizing the nanoparticles and the nanoparticles begin to flocculate and precipitate. CO2 gas-expanded solvents have been shown to reduce the viscosity of the mixture by a factor of five [6] when compared to the neat solvent, while also enhancing the diffusivity of compounds through the GXL mixture [7,8]. Due to the decreased viscosities and increased diffusivities of compounds through the GXL, the nanoparticles can be precipitated from a stable dispersion without the need for centrifugation, thereby making the process less energy and time intensive. This GXL precipitation process provides for the ability to recover the CO2 and the hexane through simple adjustments in pressure and temperature thus virtually eliminating any waste from the process while significantly improving the sustainability and environmental safety. The relative amount (number density) of nanoparticles that are dispersed in a solvent can be quantified by tracking the surface plasmon resonance (SPR) band of the nanoparticle material using UV–vis spectroscopy [15, 16, 21, 22, 20]. SPR is a delocalized dipole created on the surface of nanometer-sized particulates due to propagating surface electromagnetic waves induced via incident www.sciencedirect.com

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Conformal nanoparticle thin-films Some of the more interesting nanoparticle applications involve depositing nanoparticles into thin monolayer or multilayer films [24,25]. Traditionally this has been accomplished through solvent evaporation on the surface (i.e. drop-casting) to which the thin film should be deposited [25,26]. The capillary forces created at the interface as the solvent evaporates can help induce self-assembly [27,28] or to target the location of the thin film [29]. While these capillary forces may be useful, they can also cause dewetting effects which can create islands, rings and highly uneven nanoparticle structures [30–32] and may also destroy desired surface features [33]. An example of the uneven films that are cast by simple solvent evaporation is shown in Figure 3a. One method to overcome the detrimental solvent dewetting effects is to use liquid CO2 as the solvent for nanoparticle dispersions [35] since CO2 does not experience the dewetting instabilities due to its extremely low surface tension [36]. In this case, nanoparticles must be stabilized with fluorinated ligands [37–42] or other CO2philic ligands [42–46], such that they will disperse in the CO2 prior to dropcasting. www.sciencedirect.com

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light [23]. Using high pressure UV–vis spectroscopy [15,16,21,22,20], the precipitation of dodecanethiolstabilized gold nanoparticles dispersed in neat hexane due to the addition of CO2 can be monitored. A typical set of UV–vis spectra at varying applied CO2 pressures is shown in Figure 2a. The decrease in absorbance at approximately 520 nm is due to the combination of two effects: firstly, dilution of the nanoparticles due to the volume expansion of the solvent mixture and secondly, precipitation of nanoparticles from the liquid dispersion thereby reducing the number density of dispersed nanoparticles. After correcting for the volume expansion (where the volumes are calculated from PR-EOS and the correction term is determined from the Beer–Lambert Law), a clear trend of nanoparticle precipitation as a function of applied CO2 pressure arises which can be seen in Figure 2b. On the basis of this, the nanoparticles remain completely dispersed up to an applied CO2 pressure of approximately 35 bar whereupon a significant decrease in absorbance occurs with further pressurization, signifying precipitation of the nanoparticles. In the case of dodecanethiol-stabilized gold nanoparticles dispersed in hexane, nanoparticles precipitate in the range of approximately 35–48 bar at room temperature [15,16,21,22,20]. At an applied CO2 pressure of 48 bar the nanoparticles are completely precipitated from the dispersion, and it should be noted that this pressure is still slightly less than the vapor pressure of pure CO2. This GXL precipitation is completely reversible. Depressurization of the GXL mixture decreases the amount of CO2 in the solvent mixture, thereby increasing the solvent strength and thus, redispersing the nanoparticles.

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(a) UV–vis spectra of GXL precipitation of dodecanethiol-stabilized gold nanoparticles from hexane at various applied CO2 pressures (arrow signifies increasing applied CO2 pressure from 0 bar to 48.3 bar). (b) Absorbance at the surface plasmon resonance band (approximately 520 nm) after correction for volume expansion and normalization as function of applied CO2 pressure. Adapted with permission from [15]. Copyright 2005 American Chemical Society.

CO2 GXLs can be used to provide improved solubilities compared to neat CO2 while still providing the desirable low interfacial properties. The controlled reduction in solvent strength of CO2 GXLs by CO2 pressurization to nearly its vapor pressure allows nanoparticles to be controllably precipitated from an expanded liquid dispersion and deposited directly onto a surface [11]. With all of the previously dispersed nanoparticles now deposited onto the surface, the CO2-expanded solvent can be removed via a supercritical CO2 drying process, thereby avoiding the detrimental dewetting effects and interfacial tensions that exist in conventional solvent-evaporation techniques [11,12,34]. This process ensures that the nanoparticle thin film surface never contacts a liquid– vapor interface that can negatively affect the quality of the nanoparticle thin films and surface features. Current Opinion in Chemical Engineering 2012, 1:91–101

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Figure 3b is an example of a gold nanoparticle thin film deposited from neat hexane using this CO2 GXL nanoparticle deposition process. This deposition process has been found to create a high quality, uniform, wide-area conformal thin film of the substrate surface (i.e. all surfaces exposed to the CO2 GXL solvent media are uniformally coated with nanoparticles)[12]. This can be seen when nanoparticles have been deposited onto a microelectromechanical system (MEMS) device, as seen in Figure 3c [12]. By controlling the concentration of nanoparticles in the neat solvent, the number of nanoparticle layers (monolayer versus multilayer) can be tuned [34]. The rate of pressurization from the neat primary solvent to near-vapor pressure conditions can affect the quality of the thin film. For example, the thin film of nanoparticles created when the precipitation is performed over the course of five hours tends to show more order than those created when the precipitation occurs over 0.5 hours. The faster precipitation causes particles to flocculate and deposit on the surface in small groups whereas the slower precipitation allow the nanoparticles to self-assemble on the surface creating higher quality thin films [11].

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Comparison of dodecanethiol-stabilized gold nanoparticles deposited from hexane: (a) deposited via drop-casting onto a transmission electron microscope grid, (b) deposited via GXL precipitation onto a transmission electron grid, and (c) deposited via GXL precipitation onto a microelectromechanical system (MEMS) device.Adapted with permission from [34] and [12]. Copyright 2006 American Chemical Society and 2009 Institute of Physics.

Current Opinion in Chemical Engineering 2012, 1:91–101

It has been shown that the precipitation of nanoparticles in a poor organic solvent (as is the case in LSAS precipitation) is due to the inability of the solvent to provide sufficient steric stabilization (repulsive interactions) to overcome the inherent van der Waals attractive forces between nanoparticles in a dispersion [22,19,47,17]. The magnitude of the van der Waals potential scales with the nanoparticle size [48–50], as such, the nanoparticles with the largest van der Waals potential (i.e. the largest nanoparticles) will precipitate first upon worsening solvent conditions. When only a portion of nanoparticles are precipitated from a stable dispersion, these nanoparticles will be the largest fraction of nanoparticles from the original dispersion. In traditional LSAS fractionations, the supernatant containing the still dispersed smaller nanoparticles can be recovered for additional fractionations and the precipitated nanoparticles can be redispersed in addition neat solvent. This process is repeated several times in order to produce a monodisperse sample of nanoparticles. However, the repetition produces large quantities of organic solvent waste and occupies large amounts of time due to the necessary centrifugation step. This LSAS fractionation process is typically capable of rendering 30% of the nanoparticles within 5% of the mean diameter [14]. Using CO2 GXLs, it has been demonstrated that nanoparticles can be controllably, and quickly, precipitated through simple adjustments in applied CO2 pressure without producing any organic waste or requiring centrifugation [11,15,16,18]. Knowing that the largest particles precipitate first upon worsening conditions, if some portion of the nanoparticles are precipitated and the www.sciencedirect.com

Nanoparticle Processing Using Gas-Expanded Liquids Saunders and Roberts 95

remaining dispersed nanoparticles are moved away from the precipitated nanoparticles, an effective size-selective fractionation of nanoparticles should be achieved. To size-selectively fractionate small quantities (<1 mL) of a nanoparticle dispersion, an apparatus was designed [21] which consists of a glass tube with a spiral indentation along its length within a high pressure vessel. Rotation of the spiral tube about its axis allows a small drop of a nanoparticle dispersion to be translated along the interior surface of the tube, much like an Archimedes screw [16,21]. This open ended glass tube contains a small droplet of the nanoparticle dispersion on a specific location of the interior of the glass tube and is placed within a high pressure vessel. The pressure of the entire system is then raised to a desired level by adding CO2 gas whereupon a fraction of the nanoparticles within the droplet (the largest nanoparticles) will precipitate onto a small portion of the interior surface of the glass tube. The tube can then be rotated causing the droplet containing the still dispersed smaller nanoparticles to move away from the precipitated larger nanoparticles and the process can then be repeated. The vessel is then depressurized, and precipitated fractions recovered with a simple solvent washing at each precipitation location. CO2 gas-expanded hexane fractionations can be performed in as little as 20 min for each pressurization stage such that multiple monodisperse fractions can be collected in less than two hours [15] as opposed to several hours for an LSAS fractionation. The CO2 GXL fractionation also produces negligible waste, as all of the solvent and CO2 can be recovered at the end of the process [15,21]. An example of a polydisperse dodecanethiolstabilized gold nanoparticle sample that has been fractionated into five monodisperse fractions using this GXL fractionation technique is shown in Figure 4 [15]. The small-scale apparatus was initially designed as a proof-of-concept device to demonstrate that nanoparticle size-selective fractionation was possible using CO2 GXLs. The geometry of the device is not amenable to being scaled to handle larger dispersion quantities. An apparatus that is capable of fractionating larger quantities (gram-scale quantities of nanoparticle material) of nanoparticles was designed [18]. This apparatus maintains the concept of controlling the location of nanoparticle precipitation in order to achieve an effective fractionation. This apparatus consists of sequential vertically mounted high pressure vessels connected with high pressure valves such that each vessel can be isolated from the others. Each individual vessel can be scaled to handle any volume required. Additional vessels can be added to increase the number of fractions that the original dispersion can be divided into by arranging them into a contiguous series of fractionation stages at increasing levels of applied CO2 pressure. It is noted that at these www.sciencedirect.com

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TEM micrographs of dodecanethiol-stabilized gold nanoparticles fractionated from hexane using the GXL fractionation technique in the small-scale spiral tube apparatus. The nanoparticle fractions were collected at applied CO2 pressures of (i) 0–37.9 bar, (ii) 37.9–41.4, (iii) 41.4–43.1, (vi) 43.5–44.8, (v) 44.8–48.3. Reproduced with permission from [15]. Copyright 2005 American Chemical Society.

larger volumes the rate determining step for the fractionation process is the diffusion of the vapor CO2 into the liquid phase [18]. Therefore, the system is infinitely scalable if the timescales for CO2 diffusion is acceptable or if the mass transport of CO2 into the liquid phase can be enhanced (e.g. bubbling the CO2 directly into the liquid). Fractionations using this apparatus are initiated by introducing the original, polydisperse dispersion of nanoparticles into the first high pressure vessel (i.e. top of the cascade). The entire system is then pressurized with CO2 to a desired pressure thereby decreasing the solvent strength of the liquid mixture to the point where a fraction of the original dispersion is destabilized and precipitated onto the walls of the high pressure vessel. In order to separate the smaller sized nanoparticles that remain dispersed in the solvent mixture from the larger sized nanoparticles that have adhered to the vessel walls, the isolation valve separating the high pressure vessels is slowly opened to allow the solvent mixture containing the smaller, still dispersed nanoparticles to drain (via gravity) away from the larger precipitated nanoparticles. The drainage step is performed slowly and at constant pressure to ensure that the precipitated nanoparticles are not sheared from the vessel wall nor inadvertently redispersed due to a change in the solvent strength of the GXL mixture. This pressurization–precipitation– drainage cycle is then repeated. The fractions can be Current Opinion in Chemical Engineering 2012, 1:91–101

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recovered from the vessel walls through simple washing with neat hexane (assuming aliphatic ligand stabilized nanoparticles) with the largest sized fraction of nanoparticles recovered from the first vessel and the smallest sized fraction recovered from the last vessel [18]. An example of fractionated dodecanethiol-stabilized gold nanoparticles precipitated from a 20 mL (approximately 300 mg of gold) hexane dispersion using this GXL fractionation apparatus is shown in Figure 5 [18].

the solubility parameters for the solvent and ligand, respectively. If a stronger solvent is used to disperse the nanoparticles prior to pressurization with CO2, larger applied CO2 pressures will be required to induce nanoparticle precipitation. Using longer hydrocarbons as the primary solvent will provide a stronger stabilization than shorter hydrocarbons but will require larger applied CO2 pressures to induce precipitation [15], as seen in Figure 6b.

This CO2 GXL fractionation technique has been effective in size-selectively separating silver [15,21], gold [15,18], and CdSe/ZnS [16] nanoparticles efficiently at different scales. The CO2 GXL fractionation technique should be applicable to any material provided that the nanoparticles can be stabilized with an aliphatic ligand tail such as dodecanethiol or tri-n-octylphosphine oxide (TOPO). Compared to the LSAS fractionations method which is capable of rendering 30% of the nanoparticles within 5% of the mean diameter after several fractionation stages [14], the CO2 GXL precipitation method has been shown to be capable of producing approximately 40% of the nanoparticles within 5% of the mean diameter within a single fractionation [18]. It is possible to control the size distributions of the recovered fractions by judiciously selecting the precipitation pressures [18]. Lower pressures correspond to larger mean diameters at a given precipitation stage and vice versa, while the magnitude of the change in pressure from one stage to the next dictates the broadness of the size distribution of the nanoparticles collected [15,18].

A second method of adjusting the effect of solvent would involve changing the strength of the primary solvent by adding a secondary liquid antisolvent [20]. This is essentially the goal of LSAS precipitations however, rather than adding sufficient liquid antisolvent to induce precipitation, the quantity of antisolvent added is only that needed to bring the dispersion to the verge of precipitation while still remaining stabilized [20]. For example, a mixed solvent of hexane and acetone (55 mol% and 45 mol%, respectively) can maintain and stabilize a dispersion of sub-10 nm dodecanethiol-stabilized gold nanoparticles. Starting with a mixture of hexane and acetone, rather than neat hexane, the applied CO2 pressure necessary to induce precipitation can be reduced by approximately 15 bar, as seen in Figure 6b.

Effect of temperature, ligand, solvent, and solvent composition Precipitation of dodecanethiol-stabilized gold nanoparticles from hexane begins at an applied CO2 pressure of 35 bar and continues through approximately 48 bar. While 35 bar may not be considered high pressure, any adjustments to the system that can reduce the onset of precipitation or increase the pressure range over which nanoparticles precipitate will reduce operating costs and increase control over the fractionation process, respectively. Process variables that can be adjusted include, but are not limited to: operating temperature, choice of solvent, and choice of capping ligand [15,20] as shown in Figure 6.

Similar to the effect of hydrocarbon solvent length, increasing the length of the hydrocarbon ligand can increase the stability of nanoparticle dipersions [15]. Ligands of shorter length have weaker interactions with the solvent compared to ligands of a longer length. This trend holds true for ligand lengths up to tertdecanethiol where the pressure needed to induce precipitiation is less than that of dodecanethiol implying that tertdecanethiol does not stabilize the nanoparticles as well as dodecanethiol. This effect can be seen by high pressure UV–vis spectroscopy as seen in Figure 6c. When precipitation is induced at very low applied CO2 pressure (e.g. hexanethiol-stabilized nanoparticles dispersed in a mixture of hexane and acetone), the time required for precipitation is drastically increased due to higher liquid viscosities and lower diffusivities [20].

Modeling nanoparticle precipitation in GXLs It has been demonstrated that the length of the hydrocarbon solvent can have a significant impact on the stability of sterically stabilized nanoparticles [37,47]. The solvation of a sterically stabilized nanoparticle depends on the solvent–ligand interaction parameter [37,17, 51, 52, 53], x, such that n ðd1  d2 Þ1=2 (1) RT where n is the molar density of the solvent, R is the gas constant, T is the operating temperature and d1 and d2 are x¼

Current Opinion in Chemical Engineering 2012, 1:91–101

To further aid nanoparticle precipitation and fractionation process development, it is necessary to be able to predict the size of nanoparticles that can be dispersed in a CO2 GXL at a given set of conditions. Current methods of predicting nanoparticle dispersability, including DLVO theory, are not directly applicable to organic solvent systems [54]. A theoretical model based on the total interaction energy between two interacting nanoparticles of the same size, is capable of predicting the maximum nanoparticle size that can be dispersed in solvent media at a given set of conditions in conventional liquid solvents www.sciencedirect.com

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TEM micrographs and size distributions of CO2 gas-expanded liquid fractionated dodecanethiol-stabilized gold nanoparticles using CO2-expanded hexane. (a) Original sample prior to fractionation, (b) nanoparticles precipitated between 0 and 42.7 bar of applied CO2 pressure, (c) nanoparticles precipitated between 42.7 and 45.5 bar, and (d) nanoparticles recovered from the last vessel. Scale bars are 20 nm. Reproduced with permission from [18]. Copyright 2009 Institute of Physics.

[47], compressed liquids [55], supercritical fluids [37,53], and CO2 GXLs [17,19]. These models followed a ‘softsphere’ modeling approach where the total interaction energy is the sum of the attractive and repulsive potentials which act upon a nanoparticle in a dispersion. The total interaction energy depends, in part, on nanoparticle size, distance between nanoparticles, ligand length, ligand surface coverage, and solvent properties. GXL nanoparticle dispersions involve a ternary system where www.sciencedirect.com

two solvent components interact with the stabilizing ligand and should be modeled accordingly. The van der Waals attractive potential [48], the only attractive contribution in this total interaction energy model, increases with an increase in nanoparticle radius or with a decrease in center-to-center separation distance between nanoparticles. An expression for the Hamaker constant (a proportionality factor that accounts for the Current Opinion in Chemical Engineering 2012, 1:91–101

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Effect of various factors on nanoparticle dispersion (as determined by high pressure UV–vis spectroscopy) as a function of applied CO pressure. (a) Effect of temperature on dodecanethiol-stabilized gold nanoparticles dispersed in hexane, (b) effect of solvent on dodecanethiol-stabilized gold nanoparticles at room temperature, (c) effect of ligand on gold nanoparticles dispersed in hexane at room temperature. Adapted with permission from [15] and [20]. Copyright 2005 and 2009 American Chemical Society.

interaction between two nanoparticles of the same material through a solvent medium) which accounts for the two components of the GXL (the organic solvent and the gas) was developed for a more rigorous modeling approach [17]. Current Opinion in Chemical Engineering 2012, 1:91–101

Two repulsive contributions, osmotic and elastic contributions [51,52], oppose the van der Waals attractive contribution. The osmotic potential depends on the free energy of the solvent–ligand interactions arising from the free energy increase due to a solvent exclusion between the ligands as the nanoparticles approach each other. The elastic potential arises from the entropic loss due to the compression of ligand tails between two metal cores. These repulsive contributions depend largely on the ligand length, solvent parameters, nanoparticle radius and center-to-center distance. As with the Hamaker expression discussed above, an expression for the ligand–solvent interaction parameter was developed [17] which accounts for the two solvent components in the GXL system. The van der Waals, osmotic, and elastic contributions to the total interaction energy are calculated for two identically sized nanoparticles as a function of the separation distance for CO2-expanded hexane at various pressures (below the vapor pressure of CO2, 57.2 bar at 208C) [17,19]. If the minimum of the total interaction energy curve is greater than or equal to the Boltzmann threshold stabilization energy required for Brownian motion, 3/ 2kBT, the nanoparticle pair has enough energy to maintain normal Brownian motion and remain dispersed. However, if the minimum of the total interaction energy curve is less than the Boltzmann threshold stabilization energy, the nanoparticle pair does not have enough energy to remain dispersed and will precipitate. The largest nanoparticles that can be dispersed at the given set of conditions can be determined by equating the minimum of the total interaction energy curve with 3/2kBT and solving for the corresponding nanoparticle diameter. A detailed explanation of this model for certain CO2 GXL systems has been described elsewhere [17], including different phenomenological models to account for the nature of the solvent–ligand interaction. Investigations involving this theoretical model indicated that only a portion of the stabilizing ligand could be solvated by the GXL mixture in order for this model to accurately predict the results from GXL size-selective fractionation experiments [17]. As such a more detailed understanding of the physical nature of the solvent–ligand interaction was needed. Determining the physical nature of the solvent–ligand interaction (i.e. what physically occurs when the solvent mixture interacts with the ligand as the solvent strength of the mixture decreases) can be accomplished through small angle neutron scattering (SANS). SANS is a unique technique to monitor the solvent–ligand interaction based on the accessible length scales measurable by SANS. Neutron scattering techniques are sensitive to isotopic substitution, particularly the difference between hydrogen and deuterium [56–58]. Metal nanoparticles stabilized with hydrogenated alkanethiol ligands can be dispersed in a www.sciencedirect.com

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Comparison between model predicted size distributions and experimental findings for three recovered fractions from a GXL sizeselective fractionation of dodecanethiol-stabilized gold nanoparticle initially dispersed in hexane. Line — model prediction. Histogram — experimental findings. Reproduced with permission from [19]. Copyright 2011 American Chemical Society.

sizes interacting to indicate all of the size combinations which yield a dispersable pair and all of the size combinations which yield a pair that would precipitate. Then, combining this knowledge with simple probabilities that describe how often the interactions between differing sized nanoparticles occur, size distributions for precipitated and dispersed fractions can be calculated. This model has been shown to be capable of predicting the average size of a nanoparticle fraction that could be recovered from a GXL size-selective fractionation within 10% of what is found experimentally, as shown in Figure 7.

Conclusions This review illustrates the utility of CO2 GXLs for a number of post-synthesis nanoparticle processing operations. The tunable physico-chemical properties of these GXLs, specifically CO2-expanded solvents, afford opportunities to affect nanoparticle dispersability through reversible changes in solvent strength via simple adjustments in applied CO2 pressure. This allows for the creation of high quality thin films and precise control over nanoparticle deposition for size-selective fractionation. These systems make it possible to utilize nontoxic carbon dioxide as an alternative antisolvent in simple organic nanoparticle dispersion systems. Moreover, the tunable solvent properties of the CO2 GXLs allow for the complete recycle and reuse of the organic solvent and the CO2 antisolvent through simple adjustments in temperature and pressure thereby reducing organic solvent consumption. This paper also reviews recent developments in modeling nanoparticle dispersability in these complex tunable solvent systems.

References and recommended reading deuterated solvent (e.g. n-hexane d-14) in order to provide contrast between the ligand and solvent [59]. Details on measurement and analysis techniques are available in [60]. Using SANS, it is possible to measure the length of the ligand shell as a function of applied CO2 pressure (or CO2 solvent composition) [60]. SANS studies have shown that the length of the ligand shell gradually decreases with increasing CO2 antisolvent. At the point of nanoparticle precipitation, dodecanethiol ligands have collapsed to approximately 50% of their original, fully extended length [60] confirming the prediction of the previously discussed total interaction energy model. Incorporating the details of the physical nature of the ligand as the solvent strength of the GXL is reduced, a more rigorous total interaction energy model was developed [19]. Accounting for not only the collapsing of the ligand, but also how the ligand surface coverage changes as a function of nanoparticle size [61], allows for a very detailed and realistic total interaction energy model to be created [19]. With these modifications to the total interaction energy model previously discussed, calculations were performed for two nanoparticles of different www.sciencedirect.com

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