Modeling for Ligand-Capped Metallic Nanoparticles in a Gas

Article pubs.acs.org/IECR

Modeling for Ligand-Capped Metallic Nanoparticles in a Gas-Expanded Liquids System: Surface Fraction Model Seong Yun Lee,† Mun Hyeong Lee,† YoonKook Park,‡ and Seong-Sik You†,* †

Department of Applied Chemical Engineering, Korea University of Technology and Education, 307 Gajeon-ri, Byeongcheon-myeon, Cheonan-city, Korea 330-708 ‡ Department of Biological and Chemical Engineering, Hongik University, Sejong, Korea 339-701 ABSTRACT: Gas-expanded liquids (GXLs) are mixtures of gas dissolved in organic solvents and compressed up to pure gas vapor pressure. GXLs are the most commonly used and investigated class in particle separation processes. By employing both CO2-expanded hexane and ethylene-expanded hexane, gold as well as silver nanoparticles were precipitated at 303 K under various gas pressures ranging from 2.07 to 4.82 MPa. The cascaded-vessel apparatus applied in this study allowed fractionation of nanoparticles into a narrow range of fractions in a faster and dependable manner. The mean sizes of metal particles obtained in a GXL system can be adjusted simply by varying the gas pressure. To investigate the effects of ligand length and surface coverage on the production of precipitates, a thermodynamic model developed for the fractionation of ligand-capped nanoparticles in GXLs was applied. Specifically, a surface fraction model with an effective ligand surface area ratio was employed, and the reliability of the modeling results was shown quantitatively. It is worth noting that the results of thermogravimetric analysis led to good estimates of the surface coverage.

1. INTRODUCTION Among all organic compounds, the global production of ethylene (TC = 282 K, PC = 5.0 MPa) is higher than that of any other organic compound.1 In addition to ethylene, CO2 (TC = 304 K, PC = 7.4 MPa) has been considered as an environmentally benign solvent and implemented in many areas. However, the low solvent strength of ethylene and CO2 restricts the use of these gases in many chemical engineering processes. Fortunately, the addition of a cosolvent makes it possible to enhance the solvent property.2 Another way to use ethylene or CO2 as an alternative solvent in chemical processes is as a gas-expanded liquid (GXL). In general, a GXL is a pressurized liquid solution of a compressible gas in an organic solvent. It is well-known that a GXL is an alternate medium for achieving extraction,3 nanorods preparation,4 nanometer-sized particle synthesis,5 and polymer processing.6 With greater amounts of ethylene or CO2, more gaslike fluid properties, such as higher mass transfer, are observed in a GXL system. When an organic liquid solvent is the predominant species in a GXL, the GXL has much more liquidlike properties, such as higher fluid solubility. These above properties can be adjusted simply by varying the amount of gas in the GXL. As a result, a GXL implemented in this way becomes a reliable replacement for traditionally used toxic organic solvents. In parallel with advances on the experimental front, several modeling accomplishments have recently been achieved. Shah et al.7 demonstrated a model that accounts reasonably well for the dependence of nanoparticle size, ligand composition and length, and solvent conditions on the mean size and the polydispersity of the particles. In addition, the method used for estimating the Hamaker constant in a GXL has been corrected to account for the use of another solvent, by taking into consideration a mixed solvent−polymer interaction.8 A total interaction energy model was also developed and showed a reliable result in precipitation of polydisperse nanoparticles; however, it depends heavily on the ligand shell thickness.9 © 2012 American Chemical Society

In the previous model considered, interactions between the entire ligand and solvent molecules by volume fraction the intramolecular interactions are included, conceptually, but rather than the entire ligand, a portion of the ligand surface interacts with solvent molecules. In this study, the surface fraction model (SFM) considering the effective interaction on the surface is derived and used to predict the size of nanoparticles collected by using the GXL process. Korgel et al.10 reported that 1H nuclear magnetic resonance and Fourier-transform infrared spectroscopies could reveal the local molecular environment, enabling one to determine the ligand surface coverage. Saunders and Korgel11 defined the surface coverage as the percentage of nanoparticle surface atoms bound to a ligand molecule. To calculate the ligand surface coverage, thermogravimetric analysis (TGA) has been adapted to determine the surface coverage of silver particles in a GXL.8 Considerable progress has been achieved in producing nanometer-size metal particles under various conditions. In this study, we adapted not only CO2 but also ethylene to deposit both silver and gold nanoparticles. Out of many unsaturated hydrocarbons, we chose ethylene as a compressed gas to form a GXL with hexane because ethylene has a relatively low critical temperature and a moderate critical pressure. We also select several models, derived on the basis of a surface fraction concept, to simulate the effects of process variables on the precipitation of nanoparticles.

2. EXPERIMENTAL SECTION 2.1. Materials. n-Hexane (purity: 99%), ethanol (200 proof), chloroform (99.8%), silver nitrate (99.8%), hydrogen tetrachloroaurate trihydrate (99.9%), tetraoctylammonium bromide (98%), Received: Revised: Accepted: Published: 1705

March 27, 2012 October 23, 2012 December 20, 2012 December 20, 2012 dx.doi.org/10.1021/ie300816t | Ind. Eng. Chem. Res. 2013, 52, 1705−1715

Industrial & Engineering Chemistry Research

Article

Figure 1. The cascaded-vessel apparatus for size fractionation by gas expanded liquids: (a) gas cylinder; (b) pressure regulator; (c) high pressure hand pump; (d) pressure gauge; (e) vent valve; (f) collection vessels 1, 2, 3; (g) circulating pump; (h) drain valve; and (i) air bath.

sodium borohydride (99%), and dodecanethiol (98%) were purchased from Aldrich Chemical Co. Toluene (99%) and deionized water were purchased from Fisher. Supercritical-fluid chromatography (SFC)-grade carbon dioxide and ethylene were supplied by a local gas company (Gongdan Industrial Gas Co., S. Korea). All the chemicals were used as received without further purification. 2.2. Nanoparticle Synthesis. The two-phase liquid−liquid systems proposed by Brust et al.12 were applied to synthesize gold and silver particles, respectively, at room temperature. To synthesize gold particles, an aqueous solution containing 0.965 mmol of hydrogen tetrachloroaurate trihydrate in 36 mL of deionized water was mixed with a solution containing 4.94 mmol of tetraoctylammonium bromide in 24.5 mL of toluene. This two-phase mixture was mixed vigorously for 1 h, the aqueous phase was removed, and 1 × 10−3 mmol of dodecanethiol was then added. A freshly prepared solution containing 0.013 mol of sodium borohydride in 30 mL of deionized water was slowly added as a reducing agent with vigorous stirring for 10 min. After further mixing for 6 h, the aqueous phase was discarded. To synthesize the silver particles, hydrogen tetrachloroaurate trihydrate was replaced with 1.12 mmol of silver nitrate, toluene was replaced with chloroform, and thiol was added after 6 h of mixing. As soon as the metal nanoparticles were dispersed, ethanol was added as an antisolvent. A centrifuge (Union 55R, Hanil Science Industrial Co.) was used to precipitate the metallic nanoparticles out of the solvent/antisolvent mixture. To ensure that any unbound ligands were removed, the washing and centrifuging

steps were carried out at least three times. A sonication method was applied to disperse the nanoparticles initially in hexane. Once the metal nanoparticles were synthesized successfully, the remaining size-selective precipitation of the nanoparticles in hexane in the presence of ethylene was achieved to obtain monodisperse metal nanoparticles, as described in the next section. A similar synthesis was carried out to compare with the literature in the CO2-expanded liquid system. 2.3. Precize-Size-Selective Precipitation Process. The precipitation of polydispersed nanoparticles in hexane was achieved in the presence of an antisolvent (ethylene) by means of a depressurization vessel manufactured in-house and maintained at a constant temperature of 303 K and various pressures from 2.07 through 4.82 MPa. Saunders and Roberts14 made the cascaded-vessel apparatus that is a modification of the spiral tube apparatus proposed by McLeod et al.5 The cascaded-vessel apparatus used in this study is similar but has a high volume capacity (>60 mL) and a circulating pump. The apparatus consists of a circulating pump (magnetic pump), a thermostatic air bath (Wonkwang Eng. Co.), collection vessels (SUS316), a syringe for sample injection, a valve for sampling, and a pressure gauge (Heise dial pressure gauges, model CM, Heise Precision Instruments), as shown in Figure 1. A hand-powered pressure generator (model 50-6-15, HiP Co., Erie, PA, USA) was used to control the pressure in the cell. In this study, pressures between 2.07 and 4.82 MPa were chosen to investigate the effect of ethylene pressure on the nanoparticle precipitation process. Initially, 30 mL of nanoparticles dispersed in hexane was added to the view cell by using the syringe. According to Saunders and 1706

dx.doi.org/10.1021/ie300816t | Ind. Eng. Chem. Res. 2013, 52, 1705−1715


Article

applied, and 3″ represents the hexane. So ϕ̃ 3′ is the ethylene volume fraction in the solvent mixture excluding the ligand, and ϕ̃ 3″ is the volume fraction of the hexane in the GXL solvent excluding the ligand. The Hamaker constants used in this study were 3.1 × 10−19 J for silver7 and 3.5 × 10−19 J for gold.9 Equation 4 was used to calculate the Hamaker constant of each solvent; namely, CO2 and ethylene.9

Roberts,14 it took a long time, ∼90 min, to reach an equilibrium condition at each collection vessel. Initially, the experiments were carried out in the absence of recycling to compare the experimental results obtained to those published.14 To shorten this time, a circulating pump was used for fluid inside the collection vessel 1 to maintain circulation, which allowed reaching an equilibrium within 20 min. We carried out several experiments by reducing the precipitation process time from 90 to 20 min with an interval of 10 min in the presence of recycling. The effect of the precipitation time on the equilibrium revealed that 20 min would be sufficiently long enough to accomplish equilibrium. Several precipitation process experiments were carried out at least twice to obtain the reliability of the experimental results. Each experimental result was in good agreement in terms of reliability within a margin of error. Once equilibrium was accomplished, the valve attached underneath collection vessel 1 was slowly opened to drain to collection vessel 2. It should be noted that the pressure in collection vessel 1 should be maintained at exactly the same pressure as for collection vessel 2. The same recirculating process was applied to collection vessel 2 to drain the fluid to collection vessel 3 by opening the valve attached underneath of collection vessel 3. This cascade vessel apparatus made it possible for the nanoparticles to precipitate on the glass tube (i.d., 11.7 mm; o.d., 15.0 mm) inside the collection vessel. The glass tube containing the nanoparticles was collected and analyzed by ultraviolet− visible (UV−vis) spectroscopy (Varian Cary 500), TEM (JEM2100F, JEOL Ltd., Japan), and TGA (Perkin-Elmer TGA 4000). 2.4. Sample Anaylsis. After the solution was obtained through depressurization, UV−vis spectroscopy was employed to verify the existence of nanoparticles in the solution. Nanoparticles were deposited from hexane onto the TEM sample grids. The size and polydispersity of the particle at each pressure from 2.07 through 4.82 MPa were obtained from the TEM images by means of ImageJ software. In almost all cases, 300 particles were counted to obtain a reliable analysis of the particle size. TGA analysis was carried out at 10 °C/min from 150 to 400 °C in a nitrogen atmosphere.

A(33) ′ =

(4)

Here, kB is Boltzmann’s constant; T, absolute temperature; ε3′ and εvacuum, the dielectric constants for the solvent (ethylene) and vacuum, respectively; h, Planck’s constant; νe, the main electronic UV absorption frequency; and n3′ and nvacuum, the refractive indexes for the solvent (ethylene) and vacuum, respectively. The values of the refractive index and dielectric constant of CO215 required for the Hamaker constant in eq 4 were determined from eqs 5 and 6, respectively, n2 − 1 = 0.07016ρr + (1.412 × 10−4ρr 2 ) n2 + 1 − (3.171 × 10−4ρr 3 )

where ρr is the reduced density. The refractive index and dielectric constant18 of ethylene were calculated from eqs 7 and 8, respectively, n2 − 1 = 10.599ρ + 17.6ρ2 n2 + 2

(7)

ε−1 A = + B + Cρ ε+2 ρ

(8)

where ρ is density and A, B, and C are constants for a given temperature. Several physical properties of the solvents, including the dielectric constant and refractive index, are shown in Table 1. Table 1. Physical Properties of CO2, Ethylene, and Hexane at 303 K and 3.45 MPa

(1)

⎛ d 2 − 4R2 ⎞⎤ A131 ⎡ 2R2 2R2 ⎢ 2 ln + + ⎜ ⎟⎥ 6 ⎣ d − 4R2 ⎝ ⎠⎦ d2 d2

A131 ≈ [ A11 − (ϕ3̃ ′ A(33) ′ + ϕ3̃ ″ A(33) ″ )]

compound

vL (cm3/mol)

δ (MPa/cm3)1/2

dielectric constant

refractive index

CO2 ethylene hexane

65.5 74.5 132

12.3 12.9 14.9

1.483 1.57218 1.89024

1.185 1.257 1.372

3.2. Elastic Repulsive Potential. The elastic repulsive potential is given by (2)

Φelas

Here, A131 is the Hamaker constant; R, the radius of the particles; and d, the center-to-center separation distance between particles. To incorporate the ethylene/hexane GXL system, eq 3 was used to calculate the Hamaker constant. A detail derivation of eq 3 appears elsewhere.8 2

(6) 16,17

where ΦvdW is the van der Waals attractive potential; Φelas, the elastic repulsive potential; and Φosm, the osmotic repulsive potential. 3.1. van der Waals Attractive Potential. The van der Waals attractive potential is approximated by ΦvdW = −

(5)

ε − 1 = 0.2386ρr + 0.02602ρr 2

3. MODELING AND PARAMETER DETERMINATION A soft-sphere model, proposed by Shah et al.,7 was used to depict the stability of dispersions of the metal nanoparticles. The total interaction energy, Φtotal, is given by Φtotal = ΦvdW + Φelas + Φosm

⎛ ε − εvacuum ⎞2 3hνe (n3 ′2 − n vacuum 2)2 3 kBT ⎜ 3 ′ ⎟ + 4 16 2 (n3 ′2 + n vacuum 2)1.5 ⎝ ε3 ′ + εvacuum ⎠

2πRkBTl 2ϕ2ρ2 ⎧ h ⎡ h ⎛ 3 − h/l ⎞2 ⎤ ⎟ ⎥ − 6 ⎨ ln⎢ ⎜ = M2 ⎩l ⎣l⎝ 2 ⎠ ⎦ ⎪

⎪

⎛ 3 − h/l ⎞ ⎛ h ⎞⎫ ⎟ + 3⎜1 − ⎟⎬ × ln⎜ ⎝ 2 ⎠ ⎝ l ⎠⎭ ⎪

⎪

hj

4πRkBT

( ) υM Nav

ϕ2 2

+

4πRkBT

( ) υM Nav

ϕ2 2

(14)

where sj is the ratio of qj to rj of component j; qj, the surface area of component j (1.49 for ethylene and 3.86 for hexane); rj, the segment number of component j (1.57 for ethylene and 4.50 for hexane); and ϕ̃ j, the volume fraction of component j excluding ligand, respectively. The surface area and segment number of the component were obtained from KDB (Korea thermophysical properties Data Bank). 3.4. Parameter Determination. The interchange parameter of the mixture in GXL is calculated by eqs 15 and 16. ⎛ sjϕj + skϕk ⎞ ⎟⎟ Δεjk = χjk ⎜⎜ sjsk ⎝ ⎠

sj =

ref

CO2−hexane ethylene−hexane

0.125 0.029

25 26

0.194 0.574

0.12420

pressure [MPa]

hexane

CO2

hexane

ethylene

0 2.07 2.76 3.45 4.13 4.48 4.82

1 0.758 0.671 0.572 0.462 0.402 0.339

0 0.242 0.329 0.428 0.538 0.598 0.661

1 0.715 0.621 0.521 0.415 0.359 0.300

0 0.285 0.379 0.479 0.585 0.641 0.700

HE = RTx3φ2χ32

(19)

where x3 is the mole fraction of component 3 and ϕ2 is the volume fraction of component 2 in the binary mixture. Yi et al.20 showed a method of applying the heat of mixing that also shows promise in estimating χ for a CO2-containing binary system. In this study, a traditional method involving the use of eq 18 was applied to determine χ. Specifically, as in the study by Goharshadi and Hesabi,21 we used the Peng−Robinson equation of state to predict the solubility parameter of ethylene at various conditions. Table 2 shows the binary interaction parameters used in this study.

(15)

qj(1 − αj) rj

χ

hexane system and the ethylene/hexane GXL system, as calculated using the van der Waals mixing rule at various pressures ranging from 0 to 4.82 MPa. The Flory−Huggins interaction parameter χ of a binary mixture in the presence of ethylene and CO2 plays a critical role in determining the osmotic repulsive potential in many chemical systems, including gas-expanded liquid systems.19 There are several ways to determine the Flory−Huggins interaction parameter. As given by eq 18, χ depends on the Hildebrand solubility parameter of a solvent (component 3), δ3, and that of a ligand (component 2), δ2. v χ32 = 3 (δ3 − δ2)2 (18) RT where v3 is the molar volume of the solvent and R is the ideal gas constant. Another way to determine the Flory−Huggins value is to use the heat of mixing, HE, as shown in eq 19,

⎛ ⎞ Δε s2 2 ⎡ 1 ⎢ + x3 ′r3 ′s3 ′⎜s3 ″ϕ3̃ ″ (3 ′ 3 ″) − Δε(3 ′ 2)⎟ 2⎢ SM SM ⎣ 2 ⎝ ⎠

⎛ h ⎞⎞⎤ ⎛1 ⎞⎤⎡ ⎛ h 1 ⎜ − x3 ″r3 ″s3 ″Δε(3 ″ 2)⎟⎥⎢l 2⎜ − − ln⎜ ⎟⎟⎥ ⎝2 ⎠⎥⎦⎣ ⎝ 2l ⎝ l ⎠⎠⎦ 4

ref

(13)

when h < l, Φosm =

kij

mole fraction

⎡ ⎛ s ϕ ̃ (Δε ) s2 2 ⎢ 1 ⎜⎜ 3 ″ 3 ″ (3 ′ 3 ″) x r s + ′ ′ ′ 3 3 3 2⎢ SM SM ⎣ 2 ⎝

⎤ 2 ⎞ ⎛1 ⎞ ⎛ h⎞ − Δε(3 ′ 2)⎟⎟ + ⎜ − x3 ″r3 ″s3 ″Δε(3 ″ 2)⎟⎥⎜l − ⎟ ⎠⎥⎝ 2⎠ ⎠ ⎝2 ⎦

system

Table 3. Mole Fraction of Each Component in the CO2/ Hexane System and the Ethylene Expanded Hexane System, As Calculated by the Peng-Robinson Equation of State at 303 K

(12)

where qi is the surface area of component i; ni, the number of molecules of component i; θk, the surface fraction of component k; and Δεjk, interchange parameter, respectively. The osmotic repulsion potential8 for GXL is given by the following:When l < h < 2l, Φosm =

Flory−Huggins interaction parameter

molar compositions and molar volumes of the GXL at 303 K. Table 3 shows the mole fraction of each component in the CO2/

(11)

s

δ(ΔGR ) = kBT ∑ ∑ Δεjk δ(qini) θk

(17)

j=1

(10)

j

∑ sjϕj

(16)

As given by eq 16, αj, the effective surface area correction factor, is added with the value of 0.3 in this study. The surface 1708



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Figure 2. TEM micrographs and size distribution of dodecanethiol-coated gold particles precipitated by ethylene pressurization at (a) 2.07, (b) 2.76, (c) 3.45, (d) 4.13, and (e) 4.82 MPa.

4. RESULTS AND DISCUSSION 4.1. TEM analysis. Figures 2 and 3 show an example of the TEM micrographs of nanoparticles in the ethylene/hexane GXL system at various pressures, with size distributions obtained from each TEM image by means of ImageJ software. The particle-size distribution indicates that almost all particles had sizes ranging from

4 to 7 nm; out of these 4−7 nm particles, 20% had sizes ranging from 4 to 5 nm, and 48% had sizes ranging from 6 to 7 nm, as shown in Figure 2. In addition, as the ethylene pressure was increased from 2.07 to 4.82 MPa, the frequency of particles with sizes in the range 4−5 nm increased from 20% to 48%. This result indicates that one can control the mean particle diameter simply by varying the gas 1709



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Figure 3. TEM micrographs and size distribution of dodecanethiol-coated silver particles precipitated by ethylene pressurization at (a) 2.07, (b) 2.76, (c) 3.45, (d) 4.13, and (e) 4.82 MPa.

nanoparticles decreased with an increase in the CO2 pressure in the GXL. The mean particle size at a CO2 pressure of 4.13 MPa is 5.1 nm, and that at 4.48 MPa is 4.8 nm. Interestingly, as the CO2 pressure was increased, a decrease was observed not only in the mean particle size but also in the standard deviation. Similar results were obtained with the ethylene/hexane GXL system. In the silver nanoparticle precipitation experiments that employed the GXL system, as the CO2 pressure was increased from 3.79 to 4.31 MPa,

(ethylene) pressure in the ethylene/hexane GXL system. Similar results were observed for different systems.5,13 Overall, the mean particle size of the gold nanoparticles obtained by means of a CO2-expanded liquid system in this study is in agreement with the particle sizes reported by Anand et al.13 For example, the average diameter obtained by Anand and co-workers at pressures of 3.79−4.13 MPa was 5.5 nm, whereas that obtained in our study was 5.1 nm. As Table 4 shows, the mean size of the gold 1710



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Table 4. Statistical Analysis of Metal Nanoparticles Obtained from the CO2- and Ethylene-Expanded Hexane Systems at 303 K metal gold

system CO2/hexane

ethylene/hexane

silver

CO2/hexane

ethylene/hexane

ΔPd (MPa)

P2me (MPa)

preesure range (MPa)

av diameter (nm)

N/A N/A 0.34 0.18 0.17 N/A N/A N/A 0.69 0.69 0.69 0.69 N/A N/A 0.34 0.34 0.18 0.17 N/A N/A N/A 0.69 0.69 0.69 0.69

N/A N/A 3.96 4.22 4.40 N/A N/A N/A 2.42 3.10 3.79 4.48 N/A N/A 3.62 3.96 4.22 4.40 N/A N/A N/A 2.42 3.10 3.79 4.48

0 0−3.79 3.79−4.13 4.13−4.31 4.31−4.48 4.48+ 0 0−2.07 2.07−2.76 2.76−3.45 3.45−4.13 4.13−4.82 0 0−3.45 3.45−3.79 3.79−4.13 4.13−4.31 4.31−4.48 4.48+ 0 0−2.07 2.07−2.76 2.76−3.45 3.45−4.13 4.13−4.82

5.0 5.7 5.5 (5.1c) 4.8 4.3 (4.8c) 3.4 6.0 7.1 6.8 6.4 5.6 4.8 5.5 6.7 6.6 (6.8c) 5.8 5.3 4.8 (5.6c) 4.1 5.4 6.9 6.6 6.1 5.5 4.3

PDIf

std dev (nm)

rel std dev (%)

1.3 1.3 0.9 0.6 0.5 0.7 1.9 1.9 1.7 1.7 1.8 1.3 1.7 1.4 1.0 1.1 0.5 0.5 0.6 1.8 1.4 1.9 1.0 1.6 1.2

26.0 22.4 15.9 12.5 11.0 20.6 30.9 26.3 25.4 27.4 31.5 26.4 31.9 20.7 15.8 18.9 10.1 11.2 13.7 33.3 20.7 28.1 16.4 28.5 26.5

1.10 1.07 1.06 1.07 1.10 1.07

1.11 1.04 1.08 1.03 1.08 1.07

ref 13a

this work

5b

this work

a The number of particles counted to obtain average diameter was reported to be more than 459. bThe number of particles counted to obtain average diameter was reported to be more than 272. cAverage diameter from this work for comparison with the literature. dThe pressure change of the fractionation process (ΔP = P2 − P1). eThe median pressure of the fractionation process (P2m = (P1 + P2)/2). fPolydispersity index is obtained from the ratio of the diameter-weighted average diameter to the number-average diameter of a nanoparticle sample.

Figure 4. TGA results of dodecanethiol-coated gold nanoparticles fractionated by ethylene-expanded liquids. 1711



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Figure 5. TGA results of dodecanethiol-coated silver nanoparticles fractionated by ethylene-expanded liquids.

Table 5. Comparison of Experimental 1-Dodecanethiol-Stabilized Gold Nanoparticle Diameters and Calculated Diameters from Various Ligand Solvation Models Using the Surface Fraction Model theoretical experimental pressure range (mpa)

a

mean diameter (nm)

P2m a

(MPa)

0−3.79 3.79−4.13 4.13−4.31 4.31−4.48

5.7 5.5 4.8 4.3

1.90 3.96 4.22 4.40

2.07−2.76 2.76−3.45 3.45−4.13 4.13−4.82

6.8 6.4 5.6 4.8

2.42 3.11 3.79 4.48

ELLSM

CPM

diameter (nm)

effective ligand length (nm)

CO2-Expanded Hexane System (CXL)b 10.75 0.50 10.73 0.50 10.71 0.50 10.68 0.50 Ethylene-Expanded Hexane System (EXL) 10.44 0.47 10.37 0.48 10.27 0.48 10.07 0.47

LLLSM diameter (nm)


diameter (nm)

4.80 4.77 4.74 4.68

0.59 0.58 0.50 0.46

5.70 5.50 4.80 4.30

3.93 4.13 4.15 3.94

0.73 0.70 0.62 0.56

6.80 6.40 5.60 4.80

The median pressure of the fraction (P2m = (P1 + P2)/2). bCalculated data from this work for comparison with the literature.13

nanoparticle size. Figures 4 and 5 show the TGA results of dodecanethiol-coated gold and silver particles, respectively. Both dodecanethiol-coated silver and gold nanoparticles reveal the unique thermal decomposition of the dodecanethiol at ∼280 °C. The losses in mass for dodecanethiolcoated silver and the dodecanethiol-coated gold were ∼18 and 22 wt %, respectively. Isaacs et al.23 reported similar results for a series of alkanethiolate-protected gold clusters. The weight percent of the ligand obtained from the TGA, along with the size of the metallic nanoparticles as obtained from the TEM, makes it possible to calculate the surface coverage of the ligand, Γ, as shown in eq 20,8

the mean particle size decreased from 6.6 to 5.3 nm. In terms of the mean particle size, there is a slight difference between the value obtained in this study and that reported by McLeod et al.5 Specifically, the mean particle sizes obtained in this study and that done by McLeod et al.5 were 6.6 and 5.3 nm, respectively. This discrepancy may be attributed to the difference in the precipitation techniques applied. When CO2 was replaced with ethylene to obtain the silver nanoparticles, the mean particle size as well as the standard deviation decreased with increases in the ethylene pressure. This confirms the fact that precise control over the size of the nanoparticles can be achieved simply by varying the pressure in the GXL. 4.2. TGA Analysis. It is well-known that TGA allows one to investigate which temperatures result in a given percentage of weight loss in a given sample. Hostetler et al.22 have determined that the surface coverage of a ligand on a nanoparticle is a function of the

Γ= 1712

number of thiol molecules per nanoparticle number of metal surface atoms per nanoparticle

(20)



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Table 6. Comparison of Experimental 1-Dodecanethiol-Stabilized Silver Nanoparticle Diameters and Calculated Diameters from Various Ligand Solvation Models Using the Surface Fraction Model theoretical experimental

a

pressure range (MPa)

mean diameter (nm)

P2m a (MPa)

3.45−3.79 3.79−4.13 4.13−4.31 4.31−4.48

6.6 5.8 5.3 4.8

3.62 3.96 4.22 4.40

2.07−2.76 2.76−3.45 3.45−4.13 4.13−4.82

6.6 6.1 5.5 4.3

2.42 3.11 3.79 4.48

ELLSM

CPM

diameter (nm)


CO2-Expanded Hexane System (CXL)b 10.61 0.48 10.51 0.48 10.44 0.48 10.36 0.48 Ethylene-Expanded Hexane System (EXL) 10.31 0.43 10.18 0.43 9.98 0.43 9.68 0.43

LLLSM diameter (nm)


diameter (nm)

4.13 4.13 4.12 4.08

0.75 0.67 0.62 0.56

6.60 5.80 5.30 4.80

4.45 4.39 4.30 4.18

0.78 0.73 0.68 0.56

6.60 6.10 5.50 4.30

The median pressure of the fraction (P2m = (P1 + P2)/2). bCalculated data from this work for comparison with the literature.5

Figure 6. Size comparison of fractionated gold nanoparticles with calculation results from various models in ethylene-expanded liquids.

where the number of the ligand molecules per particle, nL is nL =

NAmL MLnNP

effective ligand length plays a key role in determining the threshold particle size.8 In this study, we employed the surface fraction model along with the following models tested by Anand et al.8 to ensure if effective ligand length is such an important model parameter in GXL system: extended ligand length solvation model (ELLSM), collapsed phase model (CPM), and limited ligand length solvation model (LLLSM). In the ELLSM, ligand tails are considered to be extended fully, with the entire length of the tail available to interact with the solvent. It was assumed that 1.2 nm of the dodecanethiol entire length interacts with the solvents. With the LLLSM, only a limited length of the ligand is accessible to the solvent; therefore, an effective ligand length was adjusted by means of a fit to the experimental data. Alternatively, the osmotic repulsion potential for ethylene-expanded hexane can be calculated by applying the SFM in the presence of an effective ligand surface area ratio,8 as shown in eq 23,

(21)

where NA is Avogadro’s number, mL is the mass of ligand obtained by the TGA, ML is the molecular weight of the ligand, and nNP is the number of nanoparticles per TGA sample. Equation 22 was used to determine nNP, mg nNP = ρg VP (22) where mg is the mass of metal analyzed by TGA, ρg is the bulk density of the metal, and VP is the mean particle volume of a sample of metal nanoparticles. The (physical) ligand length used to estimate the mean particle volume, VP, was 1.5 nm. The number of metal surface atoms per nanoparticle was determined from the atomic area using the atomic radius (0.172 nm for silver, 0.166 nm for gold). Equations 20−22 were used to determine Γ for each metal at different conditions. 4.3. Comparison of Models. From the viewpoint of modeling, among many other model parameters, such as particle surface coverage of the ligands and solvent mixture volume,

Φ2 =

3R2 ArΓLext (R + l)3 − R3

(23)

where Ar is the cross-sectional area ratio of ligand tail and metal atom on the surface of the nanoparticle (0.59 for silver, 0.63 for gold). 1713



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Figure 7. Size comparison of fractionated silver nanoparticles with calculation results from various models in ethylene-expanded liquids.

CO2-expanded hexane or ethylene-expanded hexane. However, in general, as the gas pressure was increased, the mean particle size decreased, because the addition of an antisolvent caused a gradual reduction in solubility. In addition, SFM based on the total interaction energy (as determined by the van der Waals attraction force and elastic and osmotic repulsion forces) was used to obtain the mean particle size theoretically. The osmotic repulsion terms considered surface fraction instead of volume fraction were successfully derived. The fully extended ligand length solvation model overestimated the particle size. This overestimation emphasizes the fact that the mean particle sizes depended strongly on the effective ligand length and the surface coverage. The TGA results were used to estimate the surface coverage values employed in the surface fraction model. As a result, it is the surface fraction model that estimated the more effective and reasonable results in GXL system.

With the CPM, because of the poor solvent strength of ethylene, the ligand tails are considered to be collapsed on the particle surface. The effective ligand length available for interaction is determined by using the value of unity for ϕ. Tables 5 and 6 show threshold diameters for gold nanoparticles as calculated by various methods. The ELLSM yielded a much larger particle size than that obtained by experimentation. Consequently, the ELLSM and CPM are not suitable for evaluating the mean particle size. As described earlier, the CPM is based on the assumption that all ligand molecules are collapsed and condensed. The LLLSM successfully simulated the mean particle size. However, at a CO2 pressure of 4.48 MPa, an effective ligand length of 4.6 Å is needed to obtain a vaule of 4.3 nm for gold nanoparticles. This result illuminates the fact that as we varied the effective ligand length to adjust the mean particle diameter, we obtained a much less effective ligand length than the real ligand length. It is noteworthy that the effective ligand length used in this parameter estimation step is far different from the (physical) ligand length used to determine VP in eq 22. As shown in Figure 6, the SFM-based LLLSM model among the three models applied in this study resulted in a reasonable simulation. The surface coverage obtained by TGA was used in the SFM. Similar results were obtained for the precipitation of gold nanoparticles in the presence of ethylene. Table 6 presents threshold diameters for silver nanoparticles as determined by different models based on SFM. As in the case of the gold nanoparticles, the simulation results obtained for silver nanoparticles were in good agreement with the experimental data, as shown in Figure 7. This suggests that the effect of ligand length on nanoparticle precipitation in a GXL plays a certain role in determinig the particle size; however, the effect of ligand length on the particle size in the GXL processs is not quite significant.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +82-41-560-1344. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the Korea Ministry of Commerce, Industry & Energy and the Korea Energy Management Corporation.

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REFERENCES

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5. CONCLUSIONS An ethylene-expanded hexane system was employed to precipitate gold and silver nanoparticles at 303 K under several ethylene pressures. In addition to ethylene-expanded hexane, CO2-expanded hexane was also used to precipitate metal nanoparticles under similar conditions for comparison with the literature. With respect to the size of the metal nanoparticles, almost no significant difference was found between the use of 1714



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Modeling for Ligand-Capped Metallic Nanoparticles in a Gas

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