Role of Hydrogen Bonding in the pH-Dependent ... - ACS Publications

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J. Phys. Chem. C 2009, 113, 14236–14244

Role of Hydrogen Bonding in the pH-Dependent Aggregation of Colloidal Gold Particles Bearing Solution-Facing Carboxylic Acid Groups Thomas C. Preston,†,‡ Mohammad Nuruzzaman,‡ Nathan D. Jones,*,† and Silvia Mittler*,† Department of Physics and Astronomy, The UniVersity of Western Ontario, London, Ontario, Canada N6A 3K7, and Department of Chemistry, The UniVersity of Western Ontario, London, Ontario, Canada N6A 5B7 ReceiVed: April 9, 2009; ReVised Manuscript ReceiVed: June 8, 2009

The kinetic stability of aqueous gold colloids containing particles of 11 nm diameter and bearing solutionfacing carboxylic acid groups has been analyzed by experiment and theory. Three different types of particles were made whose surfaces were modified by three different thiolate-tethered acids of varying chain-length and pKa: 6-mercaptohexanoic and 12-mercaptododecanoic acids (pKa 4.80 in H2O/EtOH, 80:20 by volume), and N-(2-(S)-methylacetic acid)-6-mercaptohexamide (pKa 3.85). As measured by a combination of UV-visible absorption spectroscopy and dynamic light scattering, the particles were reversibly aggregated and dispersed by cycling the pH of solution between low (pKa), or the ionic strength between high and low values, respectively. Conditions of aggregation were satisfactorily and quantitatively explained using a model incorporating a superposition of a repulsive electric double layer and van der Waals attraction. That is, colloidal kinetic stability was predicted accurately using the classical theory of Deraguin, Landau, Verwey, and Overbeek (DLVO), without resorting to the addition of ad hoc forces such as hydrogen bonding. Introduction The hydrogen bond is arguably the most significant, ubiquitous, and studied interaction in all of chemistry. Since the earliest speculations by Latimer and Rodebush on the structure of liquid water in 1920,1 followed by mainstream acceptance with the publication of Pauling’s seminal treatise The Nature of the Chemical Bond in 1939,2 and the development of a broad, working definition in 1960 by Pimentel and McClellan,3 our understanding and appreciation of the hydrogen bond have evolved to a high degree of sophistication. It is therefore no surprise that D-H · · · A interactions have also been implicated as a driving force for the aggregation of nanoparticles,4-8 which themselves have been the focus of intense recent scrutiny.9-11 An intimate description of the forces driving the aggregation of nanoparticles is at the foundation of understanding the stability of colloids. This has far reaching ramifications for fields as diverse as food preparations,12 environmental pollution,13 and materials science.14 Over the past decade, sensitive and selective (bio)sensing applications have been developed on the basis of this understanding.15-24 These rely on visible changes in the localized surface plasmon resonance (LSPR)25 of, particularly, colloidal gold that results from specific aggregation events. The classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) explains the kinetic stability of colloids by positing an energy barrier that two approaching particles must overcome to form a cluster.26,27 This barrier is assumed to result from the superposition of repulsive electric double layer and attractive van der Waals potentials (Figure 1). In this theory, the barrier height and, therefore, the kinetic stability of a * To whom correspondence should be addressed. E-mail: [email protected] (S.M.); [email protected] (N.D.J.). † Department of Physics and Astronomy. ‡ Department of Chemistry.

Figure 1. Two potentials considered by classical DLVO theory and their resulting superposition. The separation distance refers to the surface-to-surface distance between two particles. In this example, it can be seen that a small energy barrier must be overcome for these particles to form an aggregate.

colloidal suspension are governed by the relative magnitudes of these two potentials. Given its conceptual simplicity, DLVO theory has successfully provided quantitative or, at the very least, qualitative insight into the behavior of a wide range of systems. Nevertheless, it does have limitations, some of which arise from the negligence of other interactions present between colloidal particles.28,29 For instance, short-range repulsion that results from surface structure is now well-known to be critical in colloidal particles of silica.30-33 With these sols, it has been found that some surface morphologies may provide stability under conditions of pre-

10.1021/jp903284h CCC: $40.75  2009 American Chemical Society Published on Web 07/17/2009

Aggregation of Colloidal Gold Particles

Figure 2. Previously proposed forces between nanoparticles bearing solution-facing carboxylic acid groups: (a) electric double layer overlap, (b) van der Waals attraction, and (c) interparticle hydrogen bonding.

dicted aggregation. The converse is also possible, and it is not unreasonable to expect that if an additional attractive force were present, but ignored in calculations, situations of predicted stability would in fact result in aggregation. Nanoparticles elaborated with solution-facing carboxylic acid groups have attracted a great deal of recent attention because they exhibit reversible color changes as the pH of solution is cycled between high and low values.4-8,34 While the solution color unequivocally results from the presence or absence of interparticle LSPR coupling modes (these emerge when aggregation takes place),35-38 there is inconsistency in the reported mechanisms for aggregation, and theoretical treatments potentially suffer from over- or underestimating colloidal stability by the omission or inclusion of ad hoc potentials. Shiraishi et al.34 explained the pH-dependent color changes of 3-mercaptopropionic acid-coated nanoparticles by reasoning that at high pH negatively charged carboxylate groups cause the formation of an electric double layer that stabilizes the dispersed state (Figure 2a), while at low pH, when these groups are substantially protonated and their charge is neutralized, van der Waals attraction dominates and drives aggregation (Figure 2b). While there is no dispute concerning the stabilization of the dispersed state, it has either been proposed or implied by several groups4-8 that aggregation is not the result of van der Waals attraction, but rather of interparticle hydrogen bonding between protonated carboxylic acid groups (Figure 2c). Although there is no doubt that hydrogen bonds form once a cluster is assembled,6 one cannot claim a priori that they driVe aggregation because the bonds may result simply from the proximity into which opposing carboxylic acid groups are forced once aggregation has occurred. However, if hydrogen bonding were a significant driving force for assembly, one would expect marked deviations from straightforward DLVO theory. Specif-

J. Phys. Chem. C, Vol. 113, No. 32, 2009 14237 ically, aggregation would occur under conditions of predicted stability. If this were not the case and aggregation could be explained satisfactorily by classical DLVO theory, which assumes only electrostatic and van der Waals forces, then hydrogen bonding would be eliminated as a driving force for aggregation process. In the approach to this work, we surmised that hydrogen bonding should not act as a significant driving force for aggregation because of the following arguments: 1. The particles are dispersed in water. While there are numerous examples of hydrogen bonding in water, it is generally recognized that an entropy gain must accompany the formation of the bonds (i.e., a previously solvent-exposed hydrophilic group becomes hidden).38,39 It is not obvious how such a gain could occur in these systems, especially if one considers that entropy is believed to decrease as two hydrophilic surfaces approach closely in water.40 2. At least one other aqueous, monolayer-coated, and charged-stabilized gold nanoparticle system exhibits behavior similar to that of the carboxylic acid-coated nanoparticles reported herein. Chen has reported 4-hydroxythiophenol-coated nanoparticles that aggregate at pH values of less than 10 (in the range of the pKa of the alcohol).41 3. There is nothing unique, insofar as morphology is concerned, that would differentiate these gold particles from a wide range of previously studied systems that possess pHsensitive surface groups. Specifically, the aggregation of carboxylic acid-coated latex particles as a function of pH has been satisfactorily explained using classical DLVO theory.42,43 To the best of our knowledge, a quantitative treatment of gold nanoparticles elaborated with solution-facing carboxylic acid groups using DLVO theory has not yet been reported, and therefore a full understanding of the stability of this important class of pH-sensitive colloids is lacking. In this paper, we measure using both UV-visible extinction spectroscopy and dynamic light scattering the responses to changes in pH and ionic strength of three aqueous gold colloids in a thorough quantitative comparison of predicted and experimentally determined stabilities. The nanoparticles were 11 nm in diameter in each case but were coated with three different mercapto-acids with varying chain lengths and pKa values. We unequivocally demonstrate that classical DLVO theory adequately predicts the conditions of stability and aggregation without the need to resort to additional attractions proVided by hydrogen bonding. Theory Central to DLVO theory is an interaction energy that is defined as the sum of the electric double layer repulsion and the van der Waals attraction that exists between two colloidal particles. When this function is calculated for all distances that separate two particles, the resulting curve can be used to analyze the stability of the dispersion that the model is designed to represent. However, this process is by no means straightforward, as both the surface charge and potential, which are parameters used to compute the electrostatic term, vary on approach. The mathematical difficulties introduced by this variation are often circumvented by assuming that either the charge or the potential remains constant on approach. However, as has been shown by Behrens and Borkovec,42 this type of approximation can introduce large errors, especially at small distances. Therefore, for our system (Figure 4), we resorted to neither assumption and instead used the so-called charge regulation model in which both charge and potential are allowed to vary with the distance between the particles.

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Preston et al. medium, and I is the ionic strength of the bulk solution. Using this model and the boundary conditions at x ) 0 of dψ/dx ) 0 and at x ) -h/2, h/2 of dψ/dx ) -σ/εm, both σ and ψo can be solved as a function of the midpoint potential, ψm.38 Specifically,

σ)

εmκ exp(2βeψm) - 1 sn(V|m) βe exp(βeψm /2) cn(V|m)dn(V|m)

(5)

and

ψo ) ψm +

Figure 3. Potential between two charged surfaces separated by a distance h.

2 ln(cd(V|m)) βe

(6)

Where sn(V|m), cn(V|m), dn(V|m), and cd(V|m) are Jacobian elliptic functions44 whose arguments V and m are κh/4 exp(βeψm) and exp(2βeψm), respectively. By solving eqs 3, 5, and 6 simultaneously it is possible to obtain values for ψo, ψm, and σ at any separation h. The utility of the previous discussion is that the osmotic pressure, Π, can be described as a function of the midpoint potential at a given separation (here we specify that cations have a valency of one):45 Figure 4. Model system used for DLVO calculations. Two particles with identical radii, r, and coating thickness, δ, that are separated by a surface-to-surface distance, h.

A. Electrostatic Interaction. For a particle coated with a homogeneous layer of molecules containing solvent facing carboxyl groups, the surface charge density, σ, will be determined by the equilibrium:

-COOH T -COO- + H+

(1)

Π(h) )

) aH exp(-βeψo)

(2)

Where β-1 ) kbT, e is the elementary charge, and ψo is the potential at the carboxyl-solution interface. Therefore, for an acid with a uniform coating density of Γ, the surface charge can be expressed as:

σ)

-eΓ 1 + exp(-βeψo)10pKa-pH

(3)

In the charge regulation model, both σ and ψo vary approach of a second surface. This relationship can understood by considering two identical plates separated a distance h (Figure 3). For such a system, the counterion distribution can described by the Poisson-Boltzmann equation:

d2ψ κ2 ) sinh(βeψ) 2 βe dx

on be by be

(4)

Vel(h) ) π(r + δ)

κ being the inverse Debye length, defined as κ ) 2ej NAβI/εm where NA is Avogadro’s number, εm is the permittivity of the

∫h∞ ∫y∞ Π(x) dx dy

(8)

Where h is the distance of closest approach between the two spheres and x and y are dummy variables. Equation 8 has been thoroughly studied and is recognized to be valid when considering interactions that take place between large particles (κr > 10)46 or over short distances (κh < 2).28 B. van der Waals Attraction. To describe the van der Waals potential for the system shown in Figure 4, three main interparticle attractions need to be consideredscore-to-core, coating-to-coating, and core-to-coating. Labeling the core with the subscript j and the coating with k, the total van der Waals energy in Figure 4 will be

VvdW(h) ) Vjj(h) + Vkk(h) + 2Vjk(h)

(9)

For two coated spheres (Figure 4), the functions referred to by eq 9 have been derived elsewhere47 and can be expressed as follows

Vjj(h) )

(

(

-Ajj × 6

1 1 + (h + 2δ)(h + 4r + 2δ) (h + 2(r + δ))2 (h + 2δ)(h + 4r + 2δ) + ln (h + 2(r + δ))2

2r2

2

(7)

As should be obvious from the arguments that preceded it, eq 7 is valid only for flat surfaces. However, by building two spheres from a series of flat, parallel rings, the Derjaguin approximation overcomes this limitation and the energy for two spheres of equal radii, r, and coating thickness, δ, is46

If we first consider a flat interface, the proton activity, aHs, at the surface will be related to that of the bulk solution, aH, described by the Boltzmann distribution:

aHs

2NAI [cosh(βeψm(h)) - 1] β

[

]

)

)

(10)


(

Vjk(h) )

Ajk × 6

2r2 2r(r + δ) (h + 2δ)(h + 4r + 2δ) (h + δ)(h + 4r + 3δ) 2r2 2r(r + δ) + 2 2 (h + 2(r + δ)) (h + δ) + 4r(r + δ) +

[

+ ln

Vkk(h) ) -

]

2(h + δ)(2r + δ) (h + 2δ)(h + 4r + 2δ)(h2 + 4r2 + 8rδ + 3δ2 + 4h(r + δ)) (h + δ)(h + 4r + 3δ)(h + 2(r + δ))2

Akk(r + δ) 1 2 1 + 12 h + 2δ h+δ h Akk h(h + 2δ) ln 6 (h + δ)2

(

[

)

]

)

(11)

(13)

(14)

D. Kinetics. Having defined the potential energy of the two approaching particles in Figure 4, it is now necessary to establish its relationship to the rate of aggregation because in the DLVO model dispersed particles are only kinetically stable. This is accomplished by introducing the stability ratio, W, which may be conceptually defined as the “productivity” of collisions, and is given by the ratio:46

W)

Number of collisions between particles Number of collisions that result in dimer formation (15)

and the solution to the diffusion equation in a potential47 with the correction factor of Honig, Roebersen, and Wiersema,49 eqs 14 and 15 can be combined to yield

W ) 2r

exp(βVT(x)) dx ∫0∞ 2xB(x) +h

(16)

Where x is a dummy variable and the function B(x) is the correction factor:

B(x) )

6(x/r)2 + 13(x/r) + 2 6(x/r)2 + 4(x/r)

3Wβη 4co

(18)

(12)

C. Total energy of interaction. The total energy of interaction, VT(h), can now be written as the sum of eqs 8 and 9:

VT(h) ) Vel(h) + VvdW(h)

This quantity, W, which approaches unity in the diffusioncontrolled limit, is not something that may be measured experimentally, but it may be calculated according to eq 16. It depends upon the total energy of interaction, which in turn, among many other variables, such as the radius of the particles, coating thickness, coating density, pKa of the acid groups, temperature, etc., depends upon pH and ionic strength. These last two parameters are important for our purposes in testing the DLVO theory in this system (see Figure 12). Finally, as the relationship between slow and rapid coagulation is linear when W is chosen as the scale factor, we can extend the expression for the so-called rapid coagulation time, τ ) 3βη/ 4co,46 to the situation where an energy barrier exists between particles:

τ)

Where Ajj, Ajk, and Akk are the Hamaker constants for the respective attractions. The value for Ajj (the Au Hamaker constant) was taken from ref 28 and set equal to 31.3 × 10-20 J. The value for Akk (the coating Hamaker constant) was set equal to either 0.360 × 10-20 J for 11-H (the C ) 6 value in ref 42 or 0.502 × 10-20 J for 11-A and 11-D (the C ) 12 value in ref 46). The core-to-coating constant can be approximated using46

Ajk ≈ √AjjAkk

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(17)

Where η is the viscosity of solution (for water η ) 0.891 mPa · s at 25 °C) and co is the concentration of the colloidal particles in units of particles/cm3. This value, τ, is defined as the time at which half the particles in solution will have clustered into a dimer. In this paper, it is used to connect experiment and theory. In studying carboxylic acid-coated nanoparticles, our primary interest is to observe how the pH of aggregation varies with several adjustable parameters of the system. It is against these data that we test the predictions made by classical DLVO theory, i.e., without resorting to hydrogen bonding potentials. Aggregation is most easily monitored by observing the wellknown color differences17 between the dispersed and aggregated states of gold nanoparticles by visual inspection and/or UV-vis extinction spectroscopy. Experimental Section A. Instrumentation. Hydrodynamic diameters were determined by dynamic light scattering (DLS) using a Malvern Nano-S type Zetasizer equipped with a 532 nm laser for solutions of nanoparticles dispersed in H2O (refractive index ) 1.33); analyses were performed at 298 K using 1 cm pathlength optical glass cuvettes. Transmission electron microscopy (TEM) images were recorded using a Philips CM10 transmission electron microscope. Ultraviolet-visible (UV-vis) extinction data were recorded using a Perkin-Elmer Lambda 850 spectrometer. Spectra were recorded at 298 K using 1 cm pathlength optical glass cuvettes. Prior to this analysis, all stock nanoparticle solutions were first diluted by a factor of either 20 or 60 in Milli-Q water. At these concentrations, the color of the solution was still easily detected both by the naked eye and spectrometer, and when comparing results for solutions prepared at either dilution, it was found that there was no noticeable difference in the pH at which a color change occurred so long as all other factors remained constant. B. Syntheses of Colloidal Gold Solutions. Gold nanoparticles were made by reduction of HAuCl4 with sodium citrate using the method described by Grabar et al.50 Thus, HAuCl4 (178 mg, 0.500 mmol) was dissolved in Milli-Q water (500 mL) and brought to a rolling boil. A solution of sodium citrate in Milli-Q water (38.8 mM, 50 mL) was added quickly. Stirring and boiling were continued for 10 min after which the heat source was removed and stirring was continued for an additional 1 h. Electron microscopy gave the diameter of these nanoparticles to be 11 ( 1 nm (100 particle count, Figure 5). Optical spectroscopy gave a single LSPR peak at λmax ) 521 nm.

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Figure 5. TEM image of prepared particles.

Nanoparticles were stored in the dark and used within a month of preparation, and their concentrations were not altered from this “stock” value in onward reactions. On the basis of the assumption that all of the gold was incorporated into the colloids, the concentration was ∼22 nM. C. Syntheses of Mercapto Acids Used to Coat the Gold Nanoparticles. 1. Synthesis of Compound 1. To a solution of alanine methylester hydrochloride salt (2.30 g, 16.47 mmol) in dry CH2Cl2 (40 mL), Et3N (5.74 mL, 48.19 mmol) and DMAP (0.40 g, 3.29 mmol) were added at 0 °C. A solution of 6-bromohexanoyl chloride (5.28 g, 24.71 mmol) in CH2Cl2 (10 mL) was added dropwise, and the reaction mixture was stirred at room temperature overnight. It was then quenched with H2O, extracted with CH2Cl2, and washed with 1 M HCl, H2O, and brine. The organic fraction was dried over MgSO4. Removal of solvent gave the crude product, which was purified by crystallization from EtOAc. Yield: 4.48 g (97%). 1H NMR (CDCl3): δ 1.24 (d, J ) 7.2, 3H), 1.29-1.36 (m, 2H), 1.52 (q, J ) 7.6, 2H), 1.73 (q, J ) 7.2, 2H), 2.11 (t, J ) 7.2, 2H), 3.27 (t, J ) 7.2, 2H) 3.59 (s, 3H), 4.42 (dt, J ) 7.2, 1H), 6.59 (d, J ) 7.6, 1H). 13C{1H} NMR (CDCl3): δ 18.25, 24.78, 27.77, 32.55, 33.84, 36.02, 48.04, 52.52, 172.76, 173.74. Mass (m/z) 280 (M + H)+, 220, 145. HRMS calcd for C10H18BrNO3 (M + H)+: 280.1588; found: 280.0540. 2. Synthesis of Compound 2. To a solution of ester 1 (2.8 g, 9.99 mmol) in THF/H2O (4:1, 75 mL), LiOH (0.50 g, 11.99 mmol) was added at 0 °C and the resulting mixture was stirred at the same temperature for about 4.5 h before 1 M HCl was added. Following extraction with EtOAc, the organic fraction was dried over MgSO4. Evaporation to dryness gave the crude product which, was purified by crystallization from Et2O. Yield: 2.50 g (94%).1H NMR (CDCl3): δ 1.44-1.50 (m, 5H), 1.66 (q, J ) 7.6, 2H), 1.86 (q, J ) 7.6, 2H), 2.26 (t, J ) 7.2, 2H), 3.39 (t, J ) 7.2, 2H), 4.57 (dt, J ) 7.2, 1H), 6.33 (d, J ) 7.2, 1H), 9.85 (br s, 1H). 13C{1H} NMR (CDCl3): δ 18.29, 24.84, 27.81, 32.55, 33.76, 36.29, 173.80, 176.29. Mass (m/z) 266 (M + H)+, 131. HRMS calcd for C9H17BrNO3 (M + H)+: 266.0314; found: 266.0395. 3. Synthesis of N-(2-(S)-Methylacetic acid)-6-mercaptohexamide (A). To a stirred solution of 2 in THF (70 mL), a mixture of nBu4NF (3.19 g, 12.19 mmol) and hexamethyldisilathiane (2.95 mL, 14.07 mmol) in THF (30 mL) were added. The mixture was stirred at 0 °C for 30 min before being allowed to warm to room temperature. After 12 h, 1 M HCl was added. The mixture was diluted with CH2Cl2, washed with saturated NH4Cl solution, H2O, and brine, dried over Na2SO4, and concentrated under reduced pressure. Purification by column chromatography (90% EtOAc/hexanes) gave the title compound in 60% yield. 1H NMR (CDCl3): δ 1.42-1.49 (m, 6H),

Preston et al. 1.60-1.78 (m, 4H), 2.27 (t, J ) 7.2, 2H), 2.50 (q, J ) 7.2, 2H), 4.95 (dt, J ) 7.2, 1H), 6.33 (d, J ) 7.2, 1H), 8.45 (br s, 1H). 13C NMR: δ 18.32, 24.57, 25.18, 27.93, 33.79, 36.34, 48.48, 174.20, 176.17. Mass (m/z) 219 (M)+, 186, 131. HRMS calcd for C9H17NO3S: 219.0929; found: 219.0929. D. Coating Acids. Figure 7 shows the three different acids used to coat the Au particles. The pKa’s of these were measured in H2O/EtOH solution (80:20 v/v) by tritration against KOH. They were found to be 3.85 for A, and 4.80 for both 12-mercaptododecanoic acid (D) and 6-mercaptohexanoic acid (H). Coating acid A was made in three steps from commercially available starting materials in ∼55% overall yield. Acids D51-53 and H54 are known compounds and were purchased from commercial suppliers. E. Coating Reactions. Three solutions of coated nanoparticles were prepared from the stock solution of 11 nm gold nanoparticles and the acids shown in Figure 7; these were named 11-A, 11-D, and 11-H. Thus, the appropriate acid (5 mg) was dissolved in CH2Cl2 (10 mL) and added to the stock solution (50 mL) whose pH had been adjusted to ∼10.5 using 3 M NaOH. This biphasic solution was stirred at room temperature for 24 h. Excess acid was then removed through a series of liquid-liquid extractions with CH2Cl2 (10 × 50 mL). The aqueous fraction was separated and used in subsequent experiments. Aqueous solutions containing 11-A, 11-D, and 11-H featured LSPR absorption maxima at 521 nm, which indicated that the particles were stable under the conditions of the coating reactions. The coating density, Γ, of the acids was taken to be the same as that of an alkanethiolate monolayer on a flat Au(111) surface, i.e., 4.67 molecules/nm.2,55 This assumption was based on reported coverage of various thiols on 36 nm citrate-stabilized gold nanoparticles, which was found to be approximately the same as that of a thiol monolayer on a planar Au substrate.56 Results and Discussion A. Establishing Criteria for Aggregation. As the pH of the 11-NP solutions are lowered, a color change occurs concomitant with aggregation. The electronic spectra of these solutions (Figure 8) show the emergence of a peak at longer wavelengths (vide infra). By plotting the extinction of this peak as a function of pH (Figure 9), it is clear that an end-point can be defined for these nanoparticle solutions. Furthermore, this region of change is also easily identified by visual inspection. For gold nanoparticle solutions, this has been referred to as a kinetic end-point57 but it is really just the critical coagulation concentration for the colloid. It is important to note that, as an equilibrium between the disperse and aggregated particles will not be established during the titration, the time scale over which the actual titration takes place can affect the location of this end-point; even if all other parameters are held constant. In parallel, pH-dependent DLS data were obtained (not shown here). They confirm the data depicted in Figure 9. The hydrodynamic diameter of 11-A, 11-D, and 11-H samples falls abruptly at a particular pH during an increasing pH-value titration. In order to establish a more precise relationship between aggregation and color change, DLS was used to monitor particle size changes directly. For all three solutions, the pH at which a significant change of size (from ∼11 to >100 nm) begins to take place is in reasonable agreement with its corresponding end-point in Figure 9. Therefore, the terms pH of aggregation and pH of color change are used interchangeably in this paper and should be taken as equivalent.



Figure 6. Synthesis of coating acid A.

Figure 7. Mercapto acids used to coat the gold nanoparticles.

B. Coating Thickness and Degree of Color Change. One of the values necessary to complete a DLVO calculation using the model shown in Figure 4 is the thickness of the coating layer, δ. For the carboxylic acid-coated nanoparticles chosen in our experiments, the value of δ is ∼0.8 nm for 11-H, 1.15 nm for 11-A, and 1.35 nm for the 11-D. These values assume that the coating molecules form monolayers similar to those made by packed alkane thiolate chains on Au and, therefore, stand at angles of ∼30° to the normal of the nanoparticle surface.56 Not only should these differences in monolayer thickness affect the pH of color change, but they should also influence the degree of color change itself. It is possible that the free energies of solvation of the tethered carboxylic acids may dictate changes in their conformations, and therefore in δ, as a function of pH or ionic strength. However, these changes will necessarily be very small in our system whose ligands are relatively short.57 For the 11-NP group, a lower energy peak appeared at 585, 595, and 640 nm for 11-D, 11-A, and 11-H, respectively, as pH was lowered. If these results are considered within the context of the well-established theory that surrounds the optical properties of conducting spheres35-37 the following explanation can be proposedsbecause all three solutions contain particles of similar radii, it must be the case that the distance of separation between metallic centers for clusters of 11-H is less than it is for clusters of 11-A and 11-D. Furthermore, the gold cores of 11-A should be more closely spaced than those of 11-D. This conclusion is based on the observed and predicted correlation between the extinction modes in conducting nanoparticle couples and the distance separating the nanoparticles that form such a couple. In essence, when all other factors are equal, the shorter the distance between two metallic particles, the lower the energy of the longer wavelength extinction peak. That the metallic centers of clustered 11-H are more closely spaced than those

Figure 8. Extinction spectra for (a) 11-H, (b) 11-D, and (c) 11-A at various pH values (indicated on traces). All solutions were diluted by a factor of 20 in Milli-Q water prior to titration.

of 11-A or 11-D is also consistent with what should be expected given the chain lengths of the molecules that form the respective coatings.

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Figure 9. Extinction of the lower energy peak, λlow, as a function of pH for 11-D (λlow ) 585 nm), 11-H (λlow ) 640 nm), and 11-A (λlow ) 595 nm). All solutions were diluted by a factor of 20 in Milli-Q water prior to titration. Lines are added to guide the eye.

Figure 10. pH of color change as a function of NaCl concentration for 11-H, 11-D, and 11-A. Each point is determined with a unique titration using a freshly prepared sample diluted by a factor of 60 with Milli-Q water. The asterisk (*) indicates concentrations of NaCl at which pH-independent aggregation occurs. Lines are added to guide the eye.

C. Effect of Ionic Strength. If the dispersed nanoparticles are stabilized through an electrical double layer, decreasing the size, or Debye length, of this double layer should result in a higher pH of aggregation. This can be accomplished by increasing the ionic strength of the bulk solution. Figure 10 shows the variation of the pH of color change with concentrations of NaCl ranging from 0 to 100 mM. These plots exhibit three distinct domains: (i) at low [NaCl], the pH of color change is clearly very sensitive to [NaCl]; (ii) at intermediate [NaCl] (e.g., in the 55-80 mM region of the 11-D plot), the pH of color change reaches a maximum and becomes unresponsive to [NaCl]; and (iii) at even greater [NaCl], a point is reached where color change occurs immediately regardless of pH. While this final region is observed in only one of the plots shown in Figure 10 (denoted by the asterisk), titrations of 1 M NaCl into colloidal solutions at pH 8 (Figure 11) indicated that conditions of pH-independent aggregation were possible for all members of the 11-NP group. Furthermore, this salt-induced color change was found to be reversible by lowering the concentration of NaCl through a subsequent dilution in Milli-Q water. This behavior was similar to the reversible, pH-dependent aggregation that is characteristic of these nanoparticles, the

Preston et al.

Figure 11. Extinction at the emerging, lower energy peak as a function of [NaCl] for 11-H, 11-D, and 11-A. All solutions were initially diluted by a factor of 20 in Milli-Q water from their stock concentration. The pH of the solution was adjusted to 8 and remained constant over the course of the titration. Lines are added to guide the eye.

difference being that in this case, the carboxylic acid groups are essentially completely deprotonated. The reversibility would also seem to preclude the likelihood that aggregation is somehow caused by destabilization of the colloid through the destruction or alteration of the monolayer coating by Cl-. Therefore, for all 11-NP, it is possible to have reversible aggregation under conditions where no protonated carboxylic acid groups/hydrogen bond donors are present. This observation alone places serious doubt on the claim that hydrogen bonding drives aggregation forward in these systems. Prior to turning to an analysis of these results using DLVO theory, there is one final issue relating to Figure 11 that must be addressed. Given that 11-A possesses similar surface charge density but a smaller coating thickness than 11-D, it may seem unusual that the former requires concentrations of NaCl larger than the latter to achieve pH-independent aggregation. We believe this difference can be accounted for through consideration of well-known “steric stabilization forces” that are often exploited in polymer-stabilized colloidal particles.59 Because the coating layers of 11-A are composed of molecules with a greater hydrophilicity than those that make up the layer in 11-D, further stability can be imparted to the dispersed state through a more favorable solvent-coating interaction. While it is typical to invoke these forces when dealing with coatings of much larger molecules, there seems to be little doubt that they apply to this scale as well. For instance, Hu et al.60 have successfully dispersed gold nanoparticles coated with 1-mercapto-3,6,9trioxodecane in water. Such a coating layer, which is comparable in size to ours, possesses no solvent-facing charged groups. As a consequence, no electric double layer can form around these particles and their stability must arise from steric stabilization. D. DLVO Analysis. Figure 12 shows the same data presented in Figure 10, only in this case four different stability ratios (W ) 100, 1000, 10 000, 100 000) have been superimposed on each of the data sets. The pH at which W is equal to these values was calculated (beginning from eq 16) as a function of ionic strength over the interval of 1-100 mM. Also shown in Figure 12 are the approximate times, τ, at which half of the colloidal particles in solution will have aggregated. These values were calculated from the chosen values of W using eq 5 and range from 74 s to 20 h. The region in which τ is on the order of minutes is chosen to represent the predicted pH of aggregation/color change because the pH at which color change occurs is approached within this time frame during a typical titration.



Figure 13. DLVO-predicted potential energy curves for 11-H colloids at two different ionic strengths. The pH discrepancy is intentionally set to ensure very similar barriers.

Figure 12. Experimental (open circles) and predicted (hatched region) pH of color change as a function of [NaCl] for (a) 11-H, (b) 11-D, and (c) 11-A.

For clarity, this region has been emphasized with hatched lines in the plots shown in Figure 12. There is reasonable agreement between the observed and predicted pH of color change for 11-NP (Figure 12) below the boundary of pH-independent aggregation (not shown in Figure 12b and c). Beyond this, DLVO theory fails to predict correctly the onset of aggregation in this region. The discrepancy, however, is not uncommon when matching DLVO predictions to experimental results and can be explained through the analysis of energy curves that are used to calculate W. Figure 13 shows the potential energy as a function of surfaceto-surface separation for 11-H at two different ionic strengths (I ) 5 and 50 mM) and at pH values where the maxima of these functions, or the barriers that two particles must overcome to dimerize, are very nearly equal (pH 4.10 and 4.83, respectively). Examination of these two curves reveals that the location

of the energy maximum is found at larger separations for I ) 5 mM (ca. 1 nm) than for I ) 50 mM (ca. 0.3 nm). While only two cases are shown here, the location of this maximum will in general shift toward smaller separations as the ionic strength of the solution is increased. This position is important because short-range, non-DLVO forces play a significant role in the subnanometer scale61 and can greatly influence the height of the barrier maximum if it falls into this regime. By not accounting for this change, significant error is introduced into the calculation of the stability ratio (as the function eβVT(x) ensures that eq 16 will be determined largely by the maximum value of VT(x)), and, as has been argued by others, this leads to the discrepancy between observation and theory.43 Although it is possible that hydrogen bonding is one of these non-DLVO forces, the pHindependent nature of this aggregation makes this highly unlikely. Therefore, below their respective limits of pH-independent aggregation, the pH-dependent aggregation of 11-H, 11-A, and 11-D are satisfactorily described by DLVO theory without any consideration of hydrogen bonding. Our analysis here has been restricted to particles with only one core size. For this diameter (11 nm) the preparation of gold particles that are well-defined by a spherical morphology and possess a small size dispersity is straightforward. While the consideration of particles with larger diameters would validate the theory further, the practical aspect of particle preparation complicates this. It is well known that the preparation of Au particles with diameters larger than 20 nm leads to particles with substantial size dispersities and nonspherical morphologies. Given that the model used in the calculations assumes the approach of two spheres of identical radii (Figure 4), a good relation between experiment and theory should not be expected if only a small fraction of the prepared particles fit these parameters. This type of substantial deviation has been reported previously for other colloidal systems that are poorly described both by a spherical model and a narrow size dispersity.62-64 Conclusions Small, spherical gold particles with narrow size distribution and solution-facing carboxylic acid groups are not driven to aggregate in water by hydrogen bonding. Below ionic strengths of pH-independent aggregation, their kinetic stability is adequately described by classical DLVO theory, which considers only electrostatic and van der Waals interactions. Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada (NSERC), the Cana-

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dian Foundation of Innovation (CFI), The Ontario Innovation Trust and the University of Western Ontario for financial support of this work. S.M. acknowledges the support of the Canada Research Chair program. Note Added after Print Publication. Figures 9 and 12 have been switched in this paper. The article was published on the Web on July 17, 2009 and in the August 13, 2009 (Vol. 113, No. 32, pp 14236-14244) print edition. The corrected electronic version was posted on August 19, 2009. References and Notes (1) Latimer, W. M.; Rodebush, W. H. J. Am. Chem. Soc. 1920, 42, 1419. (2) Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry; Cornell University Press: Ithaca, NY, 1939. (3) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; W. H. Freeman and Co.: San Francisco, 1960. (4) Han, L.; Luo, J.; Kariuki, N. N.; Maye, M. M.; Jones, V. W.; Zhong, C. J. Chem. Mater. 2003, 15, 29. (5) Li, G.; Wang, T.; Bhosale, S.; Zhang, Y.; Fuhrhop, J. Colloid Polym. Sci. 2003, 281, 1099. (6) Mandal, T. K.; Si, S. Langmuir 2007, 23, 190. (7) Simard, J.; Briggs, C.; Boal, A. K.; Rotello, V. M. Chem. Commun. 2000, 1943. (8) Su, C.; Wu, P.; Yeh, C. Bull. Chem. Soc. Jpn. 2004, 77, 189. (9) Nanoparticles: From Theory to Application; Schmid, G. , Ed.; Wiley-VCH: Weinheim, 2004. (10) Metal Nanoparticles: Synthesis, Characterization, and Applications; Feldheim, D. L., Foss Jr., C. A., Eds.; Marcel Dekker: New York, 2002. (11) Colloidal Nanoparticles in Biotechnology; Elaissari, A., Ed.; WileyInterscience: Hoboken, NJ, 2008. (12) Food Colloids: Self Assembly and Material Science; Dickinson, E., Leser, M. E., Eds.; Royal Society of Chemistry: Cambridge, 2007. (13) Saiers, J. E.; Ryan, J. N. Water Resour. Res. 2006, 42. (14) Rosenholm, J. B.; Peiponen, K.-E.; Gornov, E. AdV. Colloid Interfac. 2008, 141, 48. (15) Choi, Y.; Ho, N.-H.; Tung, C.-H. Angew. Chem., Int. Ed. 2007, 46, 707. (16) Dai, Z.; Kawde, A.-N.; Xiang, Y.; La Belle, J. T.; Gerlach, J.; Bhavanandan, V. P.; Joshi, L.; Wang, J. J. Am. Chem. Soc. 2006, 128, 10018. (17) Daniel, M.-C.; Astruc, D. Chem. ReV. 2004, 104, 293. (18) Hone, D. C.; Haines, A. H.; Russell, D. A. Langmuir 2003, 19, 7141. (19) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. Nature 1996, 382, 607. (20) Otsuka, H.; Akiyama, Y.; Nagasaki, Y.; Kataoka, K. J. Am. Chem. Soc. 2001, 123, 8226. (21) Reynolds, R. A.; Mirkin, C. A.; Letsinger, R. L. J. Am. Chem. Soc. 2000, 122, 3795. (22) Schofield, C. L.; Haines, A. H.; Field, R. A.; Russell, D. A. Langmuir 2006, 22, 6707. (23) Storhoff, J. J.; Elghanian, R.; Mucic, R. C.; Mirkin, C. A.; Letsinger, R. L. J. Am. Chem. Soc. 1998, 120, 1959. (24) Thanh, N. T. K.; Rosenzweig, Z. Anal. Chem. 2002, 74, 1624. (25) Moores, A.; Goettmann, F. New J. Chem. 2006, 30, 1121. (26) Derjaguin, B. V.; Landau, L. Acta Physiochim. USSR 1941, 14, 633. (27) Verwey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.

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