On the Mechanism of Metal Nanoparticle Synthesis in the Brust

Article pubs.acs.org/Langmuir

On the Mechanism of Metal Nanoparticle Synthesis in the Brust− Schiffrin Method Siva Rama Krishna Perala and Sanjeev Kumar* Department of Chemical Engineering, Indian Institute of Science, Bangalore, India S Supporting Information *

ABSTRACT: Brust−Schiffrin synthesis (BSS) of metal nanoparticles has emerged as a major breakthrough in the field for its ability to produce highly stable thiol functionalized nanoparticles. In this work, we use a detailed population balance model to conclude that particle formation in BSS is controlled by a new synthesis route: continuous nucleation, growth, and capping of particles throughout the synthesis process. The new mechanism, quite different from the others known in the literature (classical LaMer mechanism, sequential nucleation−growth-capping, and thermodynamic mechanism), successfully explains key features of BSS, including size tuning by varying the amount of capping agent instead of the widely used approach of varying the amount of reducing agent. The new mechanism captures a large body of experimental observations quantitatively, including size tuning and only a marginal effect of the parameters otherwise known to affect particle synthesis sensitively. The new mechanism predicts that, in a constant synthesis environment, continuous nucleation−growth-capping mechanism leads to complete capping of particles (no more growth) at the same size, while the new ones are born continuously, in principle leading to synthesis of more monodisperse particles. This prediction is validated through new experimental measurements.

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INTRODUCTION Gold nanoparticles find applications in a number of fields, such as nanoelectronics, nonlinear optics, biophysics, theranostics, and so forth.1,2 Their unique properties and synthesis methods are extensively reviewed in the literature.3−8 The synthesis methods differ from one another in the use of reducing agent, synthesis temperature, and their ability to produce watersoluble vs organic phase soluble, relatively monodispersed vs polydispersed, and tunable vs fixed mean size particles. Citrate reduction9,10 and citrate-tannic acid reduction11,12 of chloroauric acid are in wide use to produce relatively monodispersed, water-soluble, spherical gold nanoparticles, with mean size in the range of 4 to ∼150 nm. The mean particle size is tuned by controlling the amount of reducing agent added to the metal precursor solution, in agreement with the LaMer13 mechanism. The Brust−Schiffrin method14 (BSM) facilitated room temperature synthesis of highly stable functionalized nanoparticles of small sizes (2−2.5 nm), with 10 times larger particle loading. The method has impacted the pace of the subsequent developments quite substantially.15 A great variety of functionalized nanoparticles of noble metals have been synthesized over the years16,17 using this method. The extraordinary stability of the synthesized particles is attributed to alkanethiols which form a strong bond with the particle surface14,18−20 and passivate it. Instead of following the widely used approach of adding different amount of reducing agent, the mean particle © XXXX American Chemical Society

size in BSM is tuned by adding different amounts of alkanethiol18,19,21−23 to the solution. Figure 1 brings together

Figure 1. Experimentally measured mean particle size for various values of thiol to gold ratio [*, data of Brust et al.14 and #, data of Brust et al.30].

the data available in the literature. The mean particle size decreases from 8 nm at 0:1 mol ratio of alkanethiol to gold precursors to about 2 nm at a ratio of 2:1, and a marginal decrease thereafter. Although BSM is in extensive use and is studied widely,18,19,22,24−28 the synthesis process and the features it Received: April 27, 2013 Revised: July 13, 2013

A

dx.doi.org/10.1021/la401604q | Langmuir XXXX, XXX, XXX−XXX

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Figure 2. Overview of the synthesis of thiol capped gold nanoparticles by the method of Brust et al.14

manifests are poorly understood. For example, the reasons for the addition of alkanethiols instead of the reducing agent for size control, high polydispersity19 even though the alkanethiols are quite effective at preventing coagulation, and less than the expected effect of variables such as temperature and the rate of addition, etc are not clear. The absence of a mechanistic understanding of the synthesis process is the main impediment.29 The present work aims to probe the mechanism of particle synthesis in BSM using a mathematical model. The synthesis mechanism should not only explain size tuning and the various features of BSM, but also rationalize observations such as the presence of a shallow maximum in time variation of the mean particle size.24 The improved understanding will hopefully lead to modification of BSM for large scale synthesis of relatively monodispersed nanoparticles. In the next section, we put together the findings of a large body experimental investigations reported in the literature, some of them apparently quite unrelated, and develop a general model of the synthesis process. The framework of population balances31 is used next to quantify it. The model is then used to explore the mechanism of the synthesis process and to develop an understanding of its many unexpected features. One model prompted variation of BSM is tried experimentally for its impact on the synthesis of gold nanoparticles.

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(R 8)4 N + AuX4 − + 3RSH → − (AuSR)n − + RSSR + (R 8)4 N + + 4X − + 3H+ (2)

The organic phase at this stage thus consisted of TOAB, dialkyl disulfide (RSSR), Au1+ in the form of −(AuSR)n− polymer, and either AuX4− complexed with TOA ion or excess RSH. The reduction of Au3+ and Au1+ to Au0 by sodium borohydride was considered to occur through the following reaction:22,25 k2

−(AuSR)n − + BH4 − + RSH + RSSR → Aux (SR)y k3

(R 8)4 N + AuX4 − + BH4 − + RSH + RSSR → Aux (SR)y (4)

These reactions for the biphasic BSM were initially considered14,32 to occur at the organic−aqueous interface. The robust nature of the protocol14,18,19,24 and a number of variables that can influence interfacial area, such as the intensity of mixing, vessel size, and so forth, suggesting that either the above reactions do not occur on the interface or they have no effect on particle synthesis. Corbierre and Lennox26 eventually contacted toluene containing −(AuSR)n− polymer with sodium borohydride solution. The overnight stirring of the two phases did not produce any reaction. The addition of PTC brought about a rapid formation of particles, though. The PTC thus facilitates particle synthesis in the bulk of the organic phase, in the presence of alkanethiols or dialkyl disulfide. Since the aqueous phase remains colorless throughout the synthesis, the nucleation and the growth of the particles must be confined to the organic phase. The role of −(AuSR)n− polymer in BSM has interested investigators from the beginning itself. Porter et al.33 substituted octadecanethiols by dioctadecyl disulfides to eliminate the formation of −(AuSR)n− polymer while maintaining capping agents in the system. Their measurements showed that the mean particle size and the breadth of the size distribution remained unaffected for both gold and silver nanoparticles, provided the ratio of the concentration of S group to metal precursor was kept constant. Shon et al.22 substituted dodecanethiol by didodecyl disulfide, and found that both the synthesis routes lead to formation of particles of nearly similar sizes and distributions. The experimental data is shown in Figure 1 through entries marked RSH and RSSR (1 mol of RSSR is equivalent to 2 mol of RSH in the plot). The authors also formed mixed gold(I) thiolate polymers of three different compositions and found that their reduction led to the synthesis of identical size particles. A complete breakup of −(AuSR)n− polymer upon the addition of sodium borohydride was proposed to explain the observation. A number of changes designed to influence the kinetic steps of the synthesis had only limited influence on the end results.

CURRENT UNDERSTANDING OF BRUST−SCHIFFRIN SYNTHESIS

Briefly, the Brust−Schiffrin protocol is as follows. First, chloroauric acid (Au3+) is phase transferred into toluene from an aqueous phase using a phase transfer catalyst. This is followed by the separation of the two phases and the addition of a desired amount of dodecanethiol to the separated organic phase, which reduces Au3+ to Au1+. Another aqueous solution containing sodium borohydride, the main reducing agent, is contacted with the organic phase next. The particle formation is indicated by the change of color of the organic phase. An overview of the protocol is presented in Figure 2. The phase transfer of chloroauric acid into toluene using tetraoctylammonium bromide (TOAB), a phase transfer catalyst (PTC), occurs through the following reaction:14 H+AuCl4 −(aq) + (R 8)4 N +Br −(org) → (R 8)4 N + AuX4 −(org) + HX (aq)

(3)

(1)

Here, X stands for both Cl and Br as the extent of substitution of Cl− by Br− is not known. The reduction of Au3+ to Au1+ state by alkanethiol (RSH) in BSM was believed to occur through the following reaction14,22,25 B


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form clusters by aging43 and digestive ripening at high temperature involve long synthesis times,42 we consider that Brust−Schiffrin synthesis carried out over 1−3 h time scale at room temperature in tolune, a nonpolar medium, is not significantly influenced by the above-mentioned processes. Tong and co-workers28,44 have recently concluded, based on their NMR studies, that tetraoctylammonium bromide with four octyl chains forms inverse micelles with water core in them. They propose that the ions are transferred from the aqueous to the organic phase by their incorporation into inverse micelles. The water cores are suggested as reaction sites. Particle formation through the fusion of inverse micelles45,46 containing precursors in them however brings up a number of unexplainable situations. The alkanethiols must reduce Au3+ to Au1+ inside the water core of the inverse micelles. We contacted toluene containing alkanethiol with an aqueous solution containing Au3+ and found no reduction. Further, the particles confined in water cores of inverse micelles should equilibrate with the external aqueous phase and get partitioned between the two aqueous phases. The aqueous phase however remains colorless all through, indicating that nanoparticles do not partition between the two phases. The capping of a nanoparticle present in an aqueous phase by organic phase soluble thiol is known to require solvating agents such as ethanol or acetone47 which are not present in BSM. Given these unresolved issues, we carried out a detailed investigations48 into the presence of inverse micelles using SAXS, light scattering, and variation of interfacial tension, viscosity, and water content at equilibrium as a function of PTC concentration. All the measurements point to the absence of any structure in the organic phase. These results and the NMR studies are consistently explained through water of hydration around polar groups of PTCs.49 In this work, we have therefore considered, similar to the earlier investigators,14,19,27 that ions are transferred from the aqueous phase into the organic phase through complexation with the phase transfer catalyst. Liu et al.24 have measured the time variation of mean size of gold nanoparticles stabilized by butanethiolate in place of dodecanethiol in BSM. The experimental data interestingly show the presence of a weak maximum in particle size with time. The authors have assumed the number of particles to remain constant during their growth. The nucleation phase is thus assumed to be complete in a short burst. The number of particles born is obtained by dividing the total gold in the system with the experimentally measured mean particle size. The growth rate was considered to be proportional to (i) the rate of reduction of gold ions and (ii) the product of the rate of reduction of gold ions and the surface area of the particles. The agreement of the fitted growth kinetics with the experimental data for the two cases is not conclusive. The presence of a weak maximum in the particles size is attributed to the etching of the particles. A mechanism that facilitates the gold atoms to first deposit on the particles to grow them and then overcome the lattice energy to leave them on the time scale of particle synthesis is not apparent. The mechanisms proposed in the literature are thus quite different. To summarize, Brust et al.14 proposed that the particle size is controlled by surface coverage by alkanethiols. Murray and co-workers16 developed it further into a sequential nucleation−growth−passivation model; the particles stop growing after their surface is fully passivated. Shimmin et al.50 have shown that the competition between growth and passivation of particles fails to explain the size tuning observed

This pointed to the possibility of thermodynamic control of particle size.18,22 Leff et al.18 considered surface excess energy of gold atoms, energy of adsorption of thiol molecules on gold particles, and the entropy of mixing of thiol molecules and gold nanoparticles, and proposed that particle size corresponds to the minimum in free energy at equilibrium. Their predictions are in reasonable agreement with the experimental data at thiol to gold ratios larger than 1/3. The model predicts a steep increase in particle size to infinity as the thiol concentration approaches zero. The experimental measurements on the other hand show a gradual increase in particle size to 8 nm in the absence of thiols19,30 (Figure 1). Hostetler et al.19 conducted initial reaction at different temperatures, followed by mixing the contents at room temperature for about 3 h. The final particle size in all the cases depended on the path taken. The main advantage of the thiol capped nanoparticles is that they can be stored as a powder and resuspended in an organic solvent with zero amount of thiol in it. This cannot be realized if the particles were to be in thermodynamic equilibrium. Murray and co-workers,16,19,35 who studied BSM most extensively, have proposed particle formation to be kinetically controlled through nucleation−growth−passivation sequence. The larger the concentration of alkanethiols, the faster the passivation of growing particles and therefore the smaller the particle size. The sequential mechanism indicates16 that a faster rate of addition of reducing agent should produce smaller particles, through a burst of nuclei formation in the beginning. The experimental observations34 suggest that both the mean particle size and the breadth of size distribution are affected only marginally. The recent studies of Goulet and Lennox27 and Li et al.28 show that gold(I) thiolate polymer −(AuSR)n− is not formed in the original BSM. This finding reconciles a number of earlier conjectures related to the role of −(AuSR)n− in BSM. The reduction of AuX4− by alkanethiol is instead found to produce a new intermediate, AuX2− through (R 8)4 N + AuX4 − + 2RSH k1

→ (R 8)4 N + AuX 2− + RSSR + 2HX

(5) 3+

1+

Two moles of RSH reduce one mole of Au to Au . For thiol to gold ratios smaller than 2, the gold precursor is present as Au3+ and Au1+ before the addition of sodium borohydride. Goulet and Lennox27 suggest that the ratio of precursors, along with the ratio of thiol to gold, affects the kinetics of particle formation. The size tuning known for BSM can thus be explained through different rates of reduction of Au3+ and Au1+ to Au0. This mechanism is similar to the classical mechanism due to LaMer and Dinegar13 in which the reactivity of precursors determines the number of nuclei born. Goulet and Lennox27 and Li et al.28 show that −(AuSR)n− is formed when water is not removed before the addition of thiol. The formation of −(AuSR)n− as an intermediate precursor36−38 also plays a critical role in single phase syntheses of gold nanoparticles in polar media such as tetrahydrofuran and alcohols, a method that has recently gained importance to make thermodynamically stable magic clusters with less than 150 gold atoms.39,40 The etching of large size particles in this method to make small size clusters during the aging process is known to be influenced by Br−, H+, O2, TOA+, and so forth in interesting ways.39,41 The formation of AuSR from gold nanoparticles in the presence of alkanethiols under reflux conditions is implicated in digestive ripening.42 Given that size focusing to C


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Figure 3. Schematic representation of the over all model.

reactivity effected by the ratio of Au3+ and Au1+, and/or by (ii) the capping of the growing particles by alkanethiols and dialkyl disulfides. Reduction of Au3+ to Gold Atoms. As discussed before, AuX4− can also be directly reduced by phase transferred BH4− to produce gold atoms through

for BSM for the initial burst of nucleation to be independent of the concentration of alkanethiols, and also when alkanethiol is replaced by polymeric thiol. Leff et al.18 proposed a thermodynamic model which drew its support from the insensitivity of BSM to a number of parameters that are normally known to influence particle synthesis. Goulet and Lennox,27 based on their finding that the reduction of the main precursor Au3+ by alkanethiols produces another reactive precursor Au1+, suggested that the ratio of precursors Au3+ and Au1+ may affect the kinetics of formation of nanoparticles. The observed size tuning may be explained through the classical approachprecursor reactivity controlled nuclei formation as per the LaMer mechanism. The steep decrease in mean particle size for alkanethiol to gold ratio from 0:1 to 2:1 over which the composition dependent reactivity changes lends support to this mechanism. Liu et al.24 considered nucleation−growth mechanism (LaMer mechanism), with nucleation and particle growth to occur at separate time scales, to fit the variation of mean particle size with time. Clearly, the formation of nanoparticles in BSM is not well understood. In the next section, we take up development of a comprehensive model that encompasses various kinetic pathways for the synthesis of gold nanoparticles, and is consistent with the experimental findings discussed above. We then use it to explore the synthesis mechanism and the other related findings quantitatively.

k3

AuX4 − + 3BH4 − → Au 0

(6)

AuX4−

−

can be reduced by alkanethiol to produce AuX2 , which is further reduced by BH4− to produce gold atoms through k2

AuX 2− + BH4 − → Au 0

(7)

These reactions (eqs 5−7) can be concisely written in terms of Au3+, Au1+, Au0, RSH, RSSR, and BH−4 as k1

Au 3 + + 2RSH → Au1 + + RSSR

(8)

k2

Au1 + + BH4 − → Au 0 + ···

(9)

k3

Au 3 + + 3BH4 − → Au 0 + ···

(10)

The disproportionation of Au ions (3Au → 2Au + Au3+) leading to the formation of gold atoms, which occurs at high temperatures,9,31 is not considered in this room temperature, organic phase synthesis. The notation A for Au3+, B for Au1+, C for Au0, L for RSH, L′ for RSSR, and R for BH4− is used in the following model equations. Nucleation. The nucleation of metal nanoparticles with close to zero solubility of metal atoms continues to challenge researchers.51−56 The birth of similar size particles from AuX4− and gold(I) thiolate polymer22 as precursors made the nucleation process even more perplexing. The identification of AuX2− as a new intermediate has bypassed the need for any direct role of alkanethiols in nucleation in BSM. Abécassis et al.57 have recently investigated nanoparticles synthesis in toluene in the presence of slightly different PTC and stabilizing agents using X-ray absorption near edge spectroscopy (XANES) and small-angle X-ray scattering (SAXS). Their measurements reveal significant concentration of Au0 over a short time, coinciding with a burst of nuclei formation. The results of Saunders et al.32 are shown to be similar to those obtained for systems obeying classical homogeneous nucleation 1+

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MODEL The general kinetic model considers (i) PTC to transfer watersoluble precursors by complexing with them, (ii) all the reactions to occur in the organic phase, and (iii) the reduction of Au3+ to Au1+ by alkanethiols to go to completion before the addition of the main reductant. We assume ripening and etching to have negligible effect on this room temperature synthesis. Since TOAB and alkanethiols can stabilize particles individually, we assume that the particles do not coagulate during the synthesis. The starting point for the model is the addition of sodium borohydride solution which produces Au0. At some stage, the nuclei are born. The nuclei offer surface area for simultaneous assimilation of Au0 atoms and capping. Figure 3 shows a schematic of the synthesis process. With the dominance of one process over the others, the general model can lead to size control through (i) change in precursor D

0


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theory.13 Both these findings point to a burst of nuclei formation through homogeneous nucleation like mechanism. We have assumed the mechanism to represent nucleation in the presence of thiols also. The synthesis of particles forming a near continuum of sizes18,19,24 has led us to ignore the formation of particles with close shells (magic clusters) in BSM. The rate of particle formation for homogeneous nucleation mechanism is given by58 ⎛ k n2 ⎞ ⎟ Ṅ = kn1[C ]A v exp⎜ − 2 ⎝ (log S) ⎠

estimate of ams provided by Leff et al.18 is used in the present model. The values of rate constants kg, kL, and kL′ are discussed in a later section. Number Density. A particle needs its volume v and capped surface area a to be specified for its identification. Such a collection of particles is best characterized using a bivariate number density p(v,a,t); p(v,a,t) dv da represents the number of particles in size range v to v + dv with thiol covered surface area in range a to a + da at time t per unit volume of the reaction mixture. The time evolution of number density p in the framework of population balances31,59,60 is given by

(11)

∂p(v , a) ∂ ∂ + [Gp(v , a) p(v , a)] + [Lp(v , a) p(v , a)] ∂t ∂v ∂a = Ṅ (t ) δ(v − vc) δ(a − ac) (15)

where kn2 =

16πγ 3vg 2 3(kBT )3

,

S=

[C ] [Cs]

(12)

where Ṅ (t) is the nucleation rate, and vc and ac are the volume and capped surface area of a nucleus, respectively. As the process of capping begins after a nucleus is born, ac = 0. Equation 15 can be integrated after multiplying with viaj to obtain time variation of a general moment Mi,j. The latter is defined as

Here, kB is the Boltzmann’s constant, T is temperature, kn1 and kn2 are nucleation rate constants, [C] is concentration of gold atoms, Av is Avogadro number, vg is atomic volume of gold, γ is specific surface energy, [Cs] is the solubility of gold atoms in the solution, and S is the extent of supersaturation (Table 1). Table 1. Values of Constants and Parameters for Nucleation parameter γ kB T vg m

M i , j (t ) =

value 2

0.25 J/m 1.38 × 10−23 J/K 300 K 1.7 × 10−29 m3 10

dv = kgvmg(a ̃ − a)[C ] dt

dv

∫0

∞

v i a j p(v , a , t ) d a

(16)

d[A] = −k1[A][L] − k 3[A][R ] dt

(17)

d[B] = k1[A][L] − k 2[B][R ] dt

(18)

mṄ d[C ] = k 2[B][R ] + k 3[A][R ] − Av dt ∞

− kg[C ]

∫0 ∫0

∞

(a ̃ − a)p(v , a) dv da ̇ Nm Av

= k 2[B][R ] + k 3[A][R ] −

− kg[C ][(36π )1/3 M 2/3,0 − M 0,1] d[R ] = −k 2[B][R ] − 3k 3[A][R ] dt d[L] = − 2k1[A][L] − kL[L] dt

∞

∫0 ∫0

d[L′] = k1[A][L] − kL ′[L′] dt (14)

Here, (ã − a) is the free surface area of a particle of volume v with capped surface area a. The total surface area ã is equal to (36π)1/3v2/3. [C], [L], and [L′] represent concentrations of gold atoms, alkanethiols, and dialkyl disulfides, respectively. The surface areas covered by one mole of L and L′, denoted by ams and 2ams, respectively, are taken to be independent of the particle size in the absence of more precise information. The

M1,0 dt

M 0,1 dt

∞

∫0 ∫0

(19)

(20) ∞

(a ̃ − a)p(v , a) dv da

= 2k1[A][L] − kL[L][(36π )1/3 M 2/3,0 − M 0,1]

(13)

and da L p (v , a ) = = (kL[L]ams + kL ′[L′]2ams)(a ̃ − a) dt

∞

Model Equations. The model equations for the reactions proposed in eqs 8−10 can be written as

The nucleus is assumed to consist of 10 gold atoms (the value of m), similar to the smallest size particle synthesized by BSM.20 The values of S and m are similar to those considered earlier by Abécassis et al.57 Growth and Capping. The particle growth and the corresponding increase in free surface area occur through assimilation of new gold atoms. The simultaneous adsorption of sulfur group containing molecules increases the capped (passivated) surface area. Saunders et al.32 earlier found that while the mean particle size increased with time, the breadth of the size distribution did not change, which suggests surface process controlled assimilation of new gold atoms. We assume here the same mechanism for the adsorption of larger size alkanethiols and dialkyl disulfides.22 The particles are assumed to be spherical at all times. Since the diffusion is not the rate controlling step, the species concentrations are the same everywhere. Thus, Gp(v , a) =

∫0

(21)

∞

(a ̃ − a)p(v , a) dv da

= k1[A][L] − kL ′[L′][(36π )1/3 M 2/3,0 − M 0,1]

(22)

= Nv̇ c + kgvmg[(36π )1/3 M 2/3,0 − M 0,1][C ]

(23)

= (kLams[L] + 2kL ′ams[L′])[(36π )1/3 M 2/3,0 − M 0,1] (24)

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Table 2. Model Constants and Initial Conditions for Thiol/ Gold::1:1 for Experiments of Hostetler et al.19b

= Nv̇ c 2/3 + kgvmg[C]

∫0

∞

da

∫0

∞⎡

1/3 1/3

⎢⎣(36π )

v

−

a v

2/3

⎤ · v1/3⎥p(v , a) dv ⎦ (25)

In order to keep the model equations simple so as to solve them using the standard ODE integrators, we introduce a closure by assuming that a/(36π)1/3v2/3, the ratio of capped area of a particle to its surface area, is equal to fraction f that evolves with time. Thus, M 2/3,0 dt

= Nv̇ c 2/3 + kgvmg[C ](36π )1/3

∫0

∞

∞⎡

M 0,0 dt

1 = Nv̇ c1/3 + (36π )1/3 kgvmg[C ](1 − f )M 0,0 3

= Ṅ

(27)

(28)

Here, f is taken to be equal to the average fractional surface coverage, defined as f=

M 0,1(t ) (36π )1/3 M 2/3,0

(29)

The above simplified system of model equations is complete. The model equations were solved using LSODE solver of GNU Octave, version 3.2.4 and ODE15S solver of MATALB 7.7.0.471 (R2008b).

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1.02 × 10−5 m3 mol−1 1.2887 × 105 m2 mol−1 0.333 0.667 1

(30)

Parameter Estimation/Values. The parameter values need to be specified in order to test a synthesis mechanism for its ability to capture the size tuning and the other aspects of the synthesis protocol. The experiments show that the solution changes its color almost immediately after the reducing agent is added. The particle formation must therefore commence over a time scale of seconds. Saunders et al.32 synthesized gold nanoparticles in the absence of thiols. They added the reducing agent slowly and found that color of the solution changes after conversion of a significant fraction of gold ions into gold atoms. These observations together suggest that the reduction of the gold ions and the formation of nuclei occur on time scales of seconds. The values of reduction rate constants (k2 and k3) and nucleation rate constants (kn1 and Cs) were fitted accordingly. The rate constant kn2 can be calculated using the physical properties alone. The rate constant k1 for reduction of Au3+ by alkanethiols, completed before the addition of sodium borohydride, does not play a role in the synthesis. The rate constant for particle growth, kg, is fitted based on the experiments carried out by Brust et al.30 and Li et al.28 in the absence of alkanethiols. Finally, the value of kL is fitted to correctly predict the experimental data of Hostetler et al.19 who used thiol for capping. The rate constants k2, and k3 correspond to AuXn− precursors, and may vary to some extent if the precursor composition (X in terms of actual Cl and Br) is varied. Reactivity Controlled Particle Size. We test in this section the hypothesis that different reactivities of AuX−4 and AuX−2 can explain the size tuning obtained by varying thiol to gold ratio. We set the rate constants kL and kL′ close to zero so that thiols and disulfides do not cap the growth of particles, but get adsorbed on them slowly to provide long-term stability. The simulations were carried out for thiol to gold ratio ranging from 0 to 5 for the reducing agent addition time of 10 s.19 Figure 4 shows the model predictions for the parameter values presented in Table 3. The rate constant k2 for reduction of AuX−2 to Au0 is required to be 2 orders of magnitude larger than the rate constant for reduction of AuX−4 to Au0 to fit the experimental data of Hostetler et al.19 The experimental data of Leff et al.18 shows much larger sensitivity of particle size to thiol to gold ratio and the synthesis of larger size particles in the presence of thiol than in its absence,19,30 as shown in Figure 1. The X-ray induced aggregation of particles during the measurement is held responsible for these observations.19 We have therefore not compared the model predictions with their experimental data.

Further, dt

vmg ams B*(0)a A*(0)a R*(0)a

⎡⎛ 6 ⎞1/3 M1/3,0 ⎤ ⎥ Dp = ⎢⎜ ⎟ ⎢⎣⎝ π ⎠ M 0,0 ⎥⎦

da

(26)

M1/3,0

value

a Asterisk (∗) denotes nondimensionalized variable. bAll the remaining initial conditions not mentioned here are equal to zero. [C0 = 0.00983 M, R0 = 0.0244 M, L0 =0.00983 M.]

⎤ a ⎢v1/3 − v1/3⎥p(v , a) dv 1/3 2/3 ⎦ ⎣ (36π ) v 2 = Nv̇ c 2/3 + (36π )1/3 kgvmg[C ](1 − f )M1/3,0 3

∫0

constants and initial conditions

RESULTS

Simulation Approach and Initial Conditions. The simulations are started with the addition of the reducing agent. The initial concentrations of Au3+, Au1+, Au, BH4−, RSH, and RSSR are specified accordingly, depending on the amount of alkanethiols added. As there are no particles present initially, all the moments Mi,j and fraction f are set to zero. The PTC remaining after transferring Au+3 transports BH4− to the organic phase. When BH4− is added at a finite rate, it is transported to the organic phase at the same rate until the maximum amount of BH4− that can be transported by the remaining PTC is reached. If BH4− is added instantaneously and is stoichiometrically larger than what the remaining PTC can transport, then PTC transports BH4− to the organic phase at the maximum level and maintains it at this level. The governing equations are nondimensionalized using the appropriate maximum values. The model parameters and initial conditions for room temperature synthesis for thiol to gold molar ratio of 1:1 are presented in nondimensionalized form in Table 2. As the TEM measurements report average value of particle diameter, the number average diameter (Dp) defined below is considered to be the equivalent mean diameter. F


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Capping Rate Controlled Particle Size. Brust et al.14 suggested that the particle size in their protocol is controlled by the surface coverage, not by the reduction kinetics of precursors. We test this proposal by increasing kL and kL′ to larger value to enable surface coverage to compete with particle growth, for similar levels of reactivity for the two precursors. The parameter values leading to the predictions shown in Figure 5 are presented in Table 4. The figure shows that the

Figure 4. Comparison of model predictions for “reactivity based control” mechanism with the experimental data.

Table 3. Model Parameters of Reactivity Modela

a

parameter

value

Cs k2 k3 kn1 kg

1.0 × 10−7 M 6.10 × 10−3 dm3 mol−1 s−1 7.20 × 10−5 dm3 mol−1 s−1 7.0016 × 103 s−1 4.80 × 10−5 m s−1

Figure 5. Comparison of model predictions for “capping based control” mechanism with the experimental data. *, Brust et al.;14 #, Brust et al.30

All other values are same as in Table 2.

Figure 4 clearly shows that the “reactivity based control” mechanism captures the experimental observations quite well. An increase in the thiol concentration increases the proportion of AuX−2 , which, due to its high reactivity, leads to more intense burst of nucleation, hence a decrease in the mean particle size. For the thiol to gold ratio in excess of two, the initial composition of the reactive precursors becomes independent, hence the prediction for the mean particle size also becomes independent of the thiol to gold ratio. While, the experimental data of Hostetler et al.19 (Figure 4) is in agreement with this prediction, Shon et al.22 who later used the same protocol for slightly different conditions (HAuCl4: 0.8 mM vs 0.9 mM; tetraoctylammonium bromide: 3 mM vs 4 mM; sodium borohydride: 8 mM vs 10 mM) reported the decrease in mean particle size to continue to high thiol concentration range as well, separately for both dodecanethiol and dodecyl disulfide as the capping agents. If the more recent measurements of the same group are more accurate, clearly the reactivity based control cannot explain them. The predicted monotonic increase in mean particle size with time for this mechanism also does not offer any explanation for the weak maximum reported in the literature.24 We next simulated the experiments of Porter et al.33 and Shon et al.22 in which they substituted alkanethiols by dialkyl disulfides while keeping the concentration of sulfur groups the same. The model predictions, indicated by the dotted line in Figure 4, show that the particle size should increase by several times. The experimental data, as pointed out earlier, show no change in particle size. The reason why the “reactivity based control” mechanism fails to capture these findings is that it requires reduction of AuX−2 to proceed at a 2 orders of magnitude faster rate than the reduction of AuX−4 . Setting the initial concentration of AuX−2 to zero, because of the direct addition of dialkyl disulfide, decreases the intensity of the nucleation burst, hence a substantial increase in the mean particle size. We next evaluate the “capping/passivation based control” mechanism.

Table 4. Model Parameters Used Only in the Capping Model parameter

value

Cs k2 k3 kn1 kg kL

4.226 × 10−8 M 4.0022 × 10−1 dm3 mol−1 s−1 1.0006 × 10−1 dm3 mol−1 s−1 1.147 × 104 s−1 1.062 × 10−4 m s−1 1.9337 × 10−7 m s−1

“capping based control” can capture the experimental data in the entire range of thiol to gold ratio: rapid decrease in particle size at low values and a slow decrease at larger values. We also use the model to test if the kinetics of reduction indeed has no effect on the synthesis process, as conjectured above. The effect of 5-fold increase and decrease in the values of rate constants for the reduction reactions is shown by the dotted and the dashed lines in the same figure. The predicted particle sizes at very low thiol to gold ratios are quite different. The differences vanish as the thiol to gold ratio is increased. Also, the effect is in opposite direction in the two concentration ranges. The model predictions thus validate the insightful claim of Brust et al.14 that reduction kinetics of precursor does not play a controlling role. The particle size is determined by the competition between the capping and the growth of a particle. Larger the rate of capping, smaller is the particle size to which it can grow before its growth is capped. For thiol to gold ratios smaller than 1/4, the thiol available is less than that required to cap the particles. The predicted increase in particle size in this range and its dependence on the reduction kinetics is largely on account of the precursor reactivity, discussed earlier in the context of Figure 4. The “capping based control” mechanism is activated at thiol to gold ratios larger than 1/4. It is still intriguing why an increase in the concentration of the reduced gold atoms, led by an increase in the reactivity of the precursors, should not favor particle growth over capping and thereby produce larger size particles. A slight under-prediction at high thiol concentrations is attributed to the inability of the G


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time variation of only Au3+ is shown for case (a) (Figure 6A) as Au1+ is not formed for this case. For case (b), the concentration of Au1+ approaches zero faster than that of Au3+ because of the slightly higher reactivity of the former (k2 = 4k3). Figure 6B shows time variation of the concentration of gold atoms. The concentration of Au0 rises rapidly for case (a), goes through a maximum, and rapidly decreases to zero (the time is plotted on log scale). The concentration of Au0 for case (b) rises at a faster rate (due to the higher rate of reduction of Au1+), goes through a maximum, rapidly decreases like for case (a), but instead of decreasing to extremely low values and remaining low, rises again and maintains significant levels over a prolonged time interval. Figure 6C compares the nucleation rate profiles for the two cases. The figure shows, that for case (a), as expected, a single short burst of nucleation is realized. The rate of nucleation drops to zero as the growing particles consume gold atoms. The rate of nucleation for case (b) shows quite an interesting behavior. After an initial burst of nucleation, the rate of nucleation rises again and the new nuclei continue to form over a prolonged time, almost until the end of synthesis process. This is more clearly shown in Figure 6D; most of the nuclei for case (a) are formed quite early whereas for case (b) they continue to be formed throughout the synthesis. The continued nucleation after an initial burst finds its imprint on time variation of the mean particle size. Figure 7

measurement technique to pickup the small size particles continuously introduced into the system (addressed in the next section). We now revert back to the experiments of Porter et al.33 and Shon et al.22 The effect of substitution of alkanethiols by dialkyl disulfides, for the marginal role of precursor reactivity in the presence of thiols, impacts particle size through the kinetics of adsorption of capping agents. Shon et al.22 show that particle size for sulfur in dodecanethiol to gold ratio of 4:1 and sulfur in didodecyl disulfides to gold ratio of 4:1 produces mean particle sizes of 2.0 and 2.1 nm. The former, before the addition of sodium borohydride, has an equimolar mixture of sulfur groups in dodecanethiol and didodecyl disulfides while the latter has all the sulfur groups present in didodecyl disulfides. The formation of similar size particles for the two synthesis routes points to similar rates of capping for alkanethiols and dialkyl disulfides. The latter requires the respective rate constants kL and kL′ to be similar. Li et al.61 recently carried out similar experiments for sulfur to gold ratio of 3:1, and found slightly different particle sizes (1.70 ± 0.22 and 2.24 ± 0.26 nm), which might require the use of slightly different values for kL and kL′. Zhang et al.62 used BSM to synthesize AuNP in the presence of n-tetradecanethioacetate (C14SAc) as the capping agent. C14SAc does not reduce Au3+ to produce disulfides during the synthesis. The reducing agent was added over a period of 5 min. The synthesis at Au:C14SAc ratio of 1:1 yielded particles of mean size of 4.93 nm, much larger than those obtained with alkanethiols at similar ratio. The increase in size was attributed62 to thioacetate being a weak ligating agent. The model predicts the same value for the mean particle size when the rate constant kL is reduced by 12 times while keeping all the other constants shown in Table 4 unchanged. The model predicts for Au:C14SAc ratio of 1/3:1 a mean size of 9.07 nm, which is in good agreement with the measured value of 7.23 nm. Dynamics of Gold Nanoparticle Synthesis. The dynamics of particle synthesis is discussed for the absence of thiol [case (a)] and thiol to gold ratio of 1:1 [case (b)]. Figure 6 shows time variation of the concentration of gold ions, gold atoms, the rate of nucleation, and the number of particles. The

Figure 7. Comparison of time evolution of mean particle size for particle synthesis in the absence (thiol/gold = 0:1) and presence (thiol/gold = 1:1) of thiol.

shows a characteristic increase in particle size in the absence of thiol: rapid increase in particle size as the nuclei consume the supersaturation available at their birth, followed by a slow and sustained increase matched with the rate of formation of gold atoms. The increase in particle size in the presence of thiols follows a different path. The increase at short time is similar to that in the absence of thiol, but it soon gives way to a slower increase due to the capping of particles. The supersaturation begins to build up again and so does the rate of nucleation. The continued birth of new particles brings the average particle size slightly down as time proceeds. The “capping based control” mechanism thus predicts a shallow maximum on account of sustained nucleation and depleting levels of gold precursors. It is noteworthy that Liu et al.,24 who followed a similar protocol with butanethiol as the capping agent, indeed found the particle size to go through a weak maximum in time. While the authors attributed it to the etching of particles, continued nucleation predicted by the present model offers an alternative interpretation.

Figure 6. Dynamics of nanoparticle synthesis in the absence of thiol (thiol/gold = 0:1) and presence of thiol (thiol/gold = 1:1). In panel C, the rate of nucleation is in the nondimensionalized form. [Subscript a denotes case (a) where thiol is absent and b denotes case (b) where the ratio of thiol to gold is 1:1.] H


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Figure 8. Comparison of size distributions obtained by the modified and the original BSM for total thiol to gold precursor ratio of 3:1. Panels A and B are the TEM micrographs of BSM and the modified BSM, respectively. Histograms C and E are plotted by analyzing 181 particles from TEM micrographs of BSM and the modified BSM, respectively. Panel D presents the UV−visible spectroscopy of both the samples.

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DISCUSSION Figures S2−S4 in the Supporting Information show the individual effect of 2-fold increase and decrease in rate constants k2, k3, and kn1. The figures show negligible effect of these parameters on particle size for thiol to gold ratios larger than 1/4. The effect of similar changes in the solubility of gold atoms, growth rate constant kg, adsorption rate constant kL, and the number of atoms in the nuclei m is shown in Figures S5− S8. The figures suggest marginal to significant effect of these parameters for all the values of thiol to gold ratios. Figure S9 in the Supporting Information shows the effect of adding reducing agent over 10, 120, and 900 s. For thiol to gold ratios larger than 1/4, the rate of addition does not impact particle size. Clearly, the capping based control mechanism appears as a far more robust way to control particle size than the reactivity based mechanism. If the concentration of gold atoms and the capping agents is kept constant with time, the “capping based control” mechanism predicts (through eqs 13 and 14) that the particles whose growth has been arrested by capping (a = ã) should all be of the same size. The continued nucleation under these conditions produces monodispersed particles. One of the reasons for the observed polydispersity in BSM must be attributed to the falling concentrations of the reduced gold atoms and thiols as the gold precursor is exhausted and capping agent is utilized to arrest particle growth. Synthesis of Monodisperse Particles Using Modified BSM. The classical LaMer mechanism is invoked universally to explain particle formation. According to this mechanism, the synthesis of monodispersed particles requires a burst of nuclei formation followed by the pure growth of particles. Continued nucleation is considered as the main reason for poor control on particle size distributions. The continuous nucleation−growth− capping mechanism unraveled in the present work on the other hand suggests that if the conditions in the reaction system are maintained constant, the particles born at different times through continued nucleation will grow to the same size before getting fully capped. We can use this alternative route to attempt synthesis of more uniform size particles. In the modified strategy, detailed in the Supporting Information, we use the same precursors as in BSM, in the

same quantities. The precursors are only contacted differently to realize constant reaction conditions. The experiments were carried out for total thiol to gold ratio of 3:1. Instead of adding aqueous solution of reducing agent to the organic phase containing gold precursors and alkanethiols in 10 s,19 we added phase transferred gold precursor in toluene containing 2/3 of the total 1-dodecanethiol to another toluene phase containing phase transferred sodium borohydride and the remaining 1dodecanethiol. The former was added slowly over a total time of 17 min to maintain the concentration of reduced gold atoms at a low level but constant over a period that almost covers the entire synthesis process. The capping agent is added to both the phases to minimize the effect of finite rate of mixing. The particles synthesized using both the protocols were analyzed using spectroscopy and TEM. Figure 8 shows a comparison of the TEM images (panels A and B), size distributions (panels C and E), and absorption spectra (panels D) for the modified and the original BSM. It is clear that the modified BSM has resulted in the formation of far more monodispersed particles than the original BSM. A slight decrease in particle size with a decrease in addition rate, supported by both TEM images and absorption spectra with a weaker shoulder, is consistent with the earlier findings,19 and is irreconcilable with LaMer type mechanisms for particle synthesis or its variations.

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CONCLUSIONS We have brought together in this work a large body of earlier investigations on Brust−Schiffrin method (BSM) to show that the mechanism of particle synthesis and size tuning is not well understood. After concluding that a thermodynamic mechanism is untenable, two competing mechanisms for size control, variation in precursors reactivity and by arresting growth of particles at different stages, are tested using a population balance based mathematical model. The model establishes that the reactivity based control mechanism with a short burst of nuclei formation, similar to the classical mechanism, does not explain all the experimental findings when taken together. The continuous nucleation−growth−passivation based mechanism explains (i) the size tuning obtained with BSM, (ii) no significant change in particle size with substitution of I


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(6) Cushing, B. L.; Kolesnichenko, V. L.; O Connor, C. J. Recent advances in the liquid-phase syntheses of inorganic nanoparticles. Chem. Rev. 2004, 104, 3893−3946. (7) Park, J.; Joo, J.; Kwon, S. G.; Jang, Y.; Hyeon, T. Synthesis of monodisperse spherical nanocrystals. Angew. Chem., Int. Ed. 2007, 46, 4630−4660. (8) Zhao, P.; Li, N.; Astruc, D. State of the art in gold nanoparticle synthesis. Coord. Chem. Rev. 2013, 257, 638−665. (9) Turkevich, J.; Stevenson, P. C.; Hiller, J. A study of the nucleation and growth processes in the synthesis of colloidal gold. Discuss. Faraday Soc. 1951, 11, 55−75. (10) Frens, G. Controlled nucleation for the regulation of the particle size in monodisperse gold suspensions. Nature, Phys. Sci. 1973, 241, 20−22. (11) Mühlpfordt, H. The preparation of colloidal gold particles using tannic acid as an additional reducing agent. Cell. Mol. Life Sci. 1982, 38, 1127−1128. (12) Slot, J.; Geuze, H. A new method of preparing gold probes for multiple-labeling cytochemistry. Eur. J. Cell Biol. 1985, 38, 87−93. (13) LaMer, V.; Dinegar, R. Theory, production and mechanism of formation of monodispersed hydrosols. J. Am. Chem. Soc. 1950, 72, 4847−4854. (14) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. Synthesis of Thiol-derivatised Gold Nanoparticles in a two-phase liquid-liquid system. J. Chem. Soc., Chem. Commun. 1994, 0, 801−802. (15) Liz-Marzán, L. M. Gold nanoparticle research before and after the Brust−Schiffrin method. Chem. Commun. 2013, 49, 16−18. (16) Templeton, A.; Wuelfing, W.; Murray, R. Monolayer-Protected Cluster Molecules. Acc. Chem. Res. 2000, 33, 27−36. (17) Love, J. C.; Estroff, L. A.; Kriebel, J. K.; Nuzzo, R. G.; Whitesides, G. M. Self-assembled monolayers of thiolates on metals as a form of nanotechnology. Chem. Rev. 2005, 105, 1103−1170. (18) Leff, D. V.; Ohara, P. C.; Heath, J. R.; Gelbart, W. M. Thermodynamic Control of Gold Nanocrystal Size: Experiment and Theory. J. Phys. Chem. 1995, 99, 7036−7041. (19) Hostetler, M.; Wingate, J.; Zhong, C.; Harris, J.; Vachet, R.; Clark, M.; Londono, J.; Green, S.; Stokes, J.; Wignall, G.; et al. Alkanethiolate Gold cluster molecules with core diameters from 1.5 to 5.2 nm: Core and monolayer properties as a function of core size. Langmuir 1998, 14, 17−30. (20) Negishi, Y.; Takasugi, Y.; Sato, S.; Yao, H.; Kimura, K.; Tsukuda, T. Kinetic Stabilization of Growing Gold Clusters by Passivation with Thiolates. J. Chem. Phys. B 2006, 110, 12218−12221. (21) Alvarez, M. M.; Khoury, J. T.; Schaaff, T. G.; Shafigullin, M.; Vezmar, I.; Whetten, R. L. Critical sizes in the growth of Au clusters. Chem. Phys. Lett. 1997, 266, 91−98. (22) Shon, Y. S.; Mazzitelli, C.; Murray, R. W. Unsymmetrical disulfides and thiol mixtures produce different mixed monolayerprotected gold clusters. Langmuir 2001, 17, 7735−7741. (23) Robert, G. S.; Andrew, B. S.; Paul, V. B. Polymer Size and Concentration Effects on the Size of Gold Nanoparticles capped by Polymer Thiols. Langmuir 2004, 20, 5613−5620. (24) Liu, X.; Warden, J. G.; Huo, Q.; Brennan, J. P. Kinetic study of gold nanoparticle growth in solution by Brust-Schiffrin Reaction. J. Nanosci. Nanotechnol. 2006, 6, 1054−1059. (25) Chen, S.; Templeton, A. C.; Murray, R. W. MonolayerProtected Cluster Growth Dynamics. Langmuir 2000, 16, 3543−3548. (26) Corbierre, M. K.; Lennox, R. B. Preparation of thiol-capped gold nanoparticles by chemical reduction of soluble Au(I)-thiolates. Chem. Mater. 2005, 17, 5691−5696. (27) Goulet, P.; Lennox, R. New Insights into Brust−Schiffrin Metal Nanoparticle Synthesis. J. Am. Chem. Soc. 2010, 132, 9582−9584. (28) Li, Y.; Zaluzhna, O.; Xu, B.; Gao, Y.; Modest, J.; Tong, Y. Mechanistic Insights into the Brust- Schiffrin Two-Phase Synthesis of Organo-chalcogenate-Protected Metal Nanoparticles. J. Am. Chem. Soc. 2011, 133, 2092−2095. (29) Lu, Y.; Chen, W. Sub-nanometre sized metal clusters: from synthetic challenges to the unique property discoveries. Chem. Soc. Rev. 2012, 41, 3594−3623.

alkanethiols by dialkyl disulfides, (iii) the presence of a weak maximum in time variation of mean particle size, (iv) insensitivity of particle size to the rate of addition of reducing agent, and most importantly (v) the need to use thiol to gold ratio to tune the particle size instead of the conventional approach of varying the amount of reducing agent. Based on the model driven insights, a modified protocol is tested experimentally for the synthesis of more monodispersed particles. The TEM measurements show significant improvement in size distribution in comparison with the original protocol. From the viewpoint of the theory of colloids, the continuous nucleation−growth−passivation based mechanism is quite interesting. It does away with the notion that formation of monodispersed particles requires a short and an intense burst of nucleation. The new mechanism shows for the first time that slow and sustained nucleation with particle growth contained by capping of particle surface can also leads to the synthesis of uniform size particles, in a far more robust way than is possible with the other mechanisms.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental section covering gold nanoparticle synthesis using the original and the modified Brust−Schiffrin synthesis along with the representative TEM images. Results showing (i) the sensitivity of model predictions to the parameter values and (ii) the effect of rate of addition of reducing agent on particle size. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. K S Gandhi and Dr. S Venugopal of the Indian Institute of Science (IISc), Bangalore, and Prof. G U Kulkarni of Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore, for their intriguing discussions during the model development. We also thank Intensification of Research in High Priority Areas-Department of Science and Technology (DST-IRHPA), India for extending financial support to carry out this work.

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REFERENCES

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On the Mechanism of Metal Nanoparticle Synthesis in the Brust

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