pH-Controlled Formation Kinetics of Self-Assembled Layers of Thioctic

Oct 3, 2007 - School of Biosciences, University of Exeter, Stocker Road, Exeter EX4 4QD, UK. J. Phys. Chem. C , 2007, 111 (42), pp 15363–15369 ... b...
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J. Phys. Chem. C 2007, 111, 15363-15369

15363

pH-Controlled Formation Kinetics of Self-Assembled Layers of Thioctic Acid on Gold Nanoparticles Maxim Rooth and Andrew M. Shaw* School of Biosciences, UniVersity of Exeter, Stocker Road, Exeter EX4 4QD, UK ReceiVed: June 29, 2007; In Final Form: August 16, 2007

The adsorption kinetics of thioctic acid (ToA) self-assembled monolayer (SAM) formation has been observed by monitoring small changes in the extinction of a gold nanoparticle surface, interrogated by evanescent wave cavity ring-down spectroscopy. A direct measurement of the adsorption kinetics for charged and neutral SAM formation has been made and modeled and shows significant differences in the lateral interactions between surface moieties: the interaction parameter for the charged species is 20 times larger than for the neutral species. Titration of ToA SAMs deposited from basic conditions demonstrate a pH-switchable surface with charge densities varying from 0.1 to 1.0 e nm-2. Similar measurements were performed from SAMs deposited under acidic conditions producing charge densities of 1.8 e nm-2. The surface potential varies between -44 and -198 mV for all SAMs, which produces an interfacial pH 0.8-3.4 units more acidic than the bulk and interfacial capacitances varying from 5.5 to 88 µF cm-2.

Introduction Self-assembled monolayers (SAM) of alkanethiols on both silver and gold surfaces have been used to functionalize the metal-water interface, optimizing the binding for proteins, biosensors, and cells, where the primary aim has been to change the chemical and electrical properties of the interface.1 Selfassembly into an ordered layer structure2,3 on gold surfaces is driven by the specific affinity of a molecular head group such as a thiol for the gold substrate with molecular interactions in the remaining functionality of the molecule controlling the order of the assembly process. SAM formation has been measured as a function of the concentration of the thiol in solution4,5 and, in the case of alkanethiols SAMs, the effect of alkyl chain length.6 It was found that alkyl chains of n > 10 carbon atoms favor greater and more ordered packing density,4 although this is a comparatively weak intermolecular force. The dithiol functionality of thioctic acid [(()-1,2-dithiolane3-pentanoic acid (R-lipoic acid)] (Figure 1) has been studied previously in monolayers on gold specifically as a linker molecule prior to the formation of a biosensor7 layers and Cu layers8 deposited on the -COOH functionality.9 ToA SAMs formed on the Au(111) crystalline surface10 show structural differences in the layer when deposited from ethanol and ethanoic acid solutions, leading to neutral and charged SAMs, respectively. FTIR10 evidence shows the presence of intramolecular hydrogen bonding (1700 cm-1) within the neutrally deposited layer moieties. Studies of the ToA SAM have also been performed on electrochemical surfaces,11-13 although direct comparison of the formation processes within the electric field of the electrochemical cell is not convincing. The potential difference adds a number of complicating factors such as adsorption of the oxidized ToA from solution and degradation of the gold surface below the monolayer. Addition of charge transfer agents such as hexacyanoferrate(II/III)14 causes further degradation of the SAM away from the spontaneous selfassembled process on the gold surface. The redox species * Corresponding author. E-mail: [email protected].

Figure 1. Chemical structure of thioctic acid, (()-1,2-dithiolane-3pentanoic acid (R-lipoic acid).

introduces additional charge into the bilayer forming around the SAM and changes the local relative permittivity of the medium and consequently the formation kinetics. The formation of charged ToA SAMs on uncharged gold surfaces, by assembling thiols with carboxylic acid functionality, is dominated by charge repulsion between the COO- groups in basic conditions. In acidic conditions, the carboxyl group is neutral and the intermolecular forces associated with alkyl group association and intramolecular hydrogen-bonding control the assembly. Neither charged nor neutrally deposited layers have the simple SAM kinetics of long-chain alkanethiol SAMs. The Coulomb interaction between like charges is equal to kT at 300 K when the charges are 56 nm apart in water (depending on the relative permittivity of the solution), although the interaction distance is considerably reduced by the presence of the solvation shells screening ionic charge. The shell may extend several tens of nanometers around the ion providing a two-dimensional “lattice parameter” for the ordering of the charged SAM. The strong lateral interactions may prove a challenge for the conventional theory for the interpretation of self-assembly kinetics derived by Kreuzer.15 The theory was derived for SAM formation of islands of noble gas atoms on metal crystal surfaces where the interactions between the atoms are short range and rather weak. Clearly, the kinetics for charged SAM formation will not be well described by the weak-interaction analysis, and similarly, a Langmuirian adsorption isotherm, which also assumes noninteracting moieties, is unlikely to provide an appropriate description of adsorption. The electrical properties of the charged interface formed by allowing a thiol with -COOH to self-assemble may be

10.1021/jp075083l CCC: $37.00 © 2007 American Chemical Society Published on Web 10/03/2007

15364 J. Phys. Chem. C, Vol. 111, No. 42, 2007

Rooth and Shaw

controlled by the density of the molecules in the SAM and the conditions of deposition. The properties of charged interfaces, notably the silica interface, have been extensively studied by second harmonic generation (SHG) developed by Eisenthal et al.16 and recently using evanescent wave cavity ring-down spectroscopy17 establishing the charge density of ∼2 e nm-2. The charge derives from native SiOH groups on the surface termed Q2 and Q3 groups with a ratio of 4:1 and surface pKa values of 8.5 and 4.5, respectively. Interfacial acidity18 for carboxylic acid-functionalized surfaces has also been measured using the SHG technique from which charge densities have been derived. We recently reported the first measurements of interfacial concentrations19 and the effects of interfacial pH on the concept of surface pKa. The charged interface leads to the concept of interfacial acidity, which we have measured using a tethered indicator molecule.20 The negatively charged surface attracts the positive ions into the interface, producing an interfacial pH two units more acidic than the bulk (for a fully dissociated surface). It has become readily accepted that the pKa of an acid on the surface and within the SAM changes in response to local bonding environments21 and corrugation effects on the surface affect near-neighbor moieties,22 but all of measurements and interpretation of surface pKa require a quantitative treatment of the interfacial pH, which is rarely present. The definition of pKa must be modified for the description at the surface or within the interface to become

Ka )

[ToA-]s[H+]s [ToA]s

(1)

where Ka is the equilibrium constant, [ToA-]s is the interfacial concentration of base, [ToA]s is the interfacial concentration of the acid, and [H+]s is the interfacial acid concentration. The electrical properties of the interface and the nature of the bonding change the relative amounts of protonated and deprotonated species and hence the concentration of counter and co-ions within the interface: all contribute to the “effective” surface pKa reported in the literature. However, pKa is frequently reported as a bulk or interfacial parameter without a quantitative description of the interfacial concentrations. The concentration of positive counterions in the interface balances two negative contributions: the negative surface charge and negative co-ions that are free in solution and attracted into the interface.23 The interfacial concentrations are all moderated by the surface potential and hence surface charge. The interfacial pH has an enhanced value at a negatively charged surface as the surface concentration [H+]s ) [H+] exp(-eΨ0/kT), where Ψ0 is the surface potential.20 A correct determination of surface pKa therefore requires a quantitative description of the interfacial charge and potential properties to determine the interfacial pH before the contributions from of the local bonding environment or surface corrugation to the pKa of the surface carboxylic acid may be considered accurately. A description of the structure of any charged interface, such as the silica-water interface or an electrode, and the effect the charge has on the interfacial pH, surface pKa, and interfacial capacitance are manifest in the titration of the surface.20,23 Titration of the surface by changes in the bulk solution pH produces a hysteresis, so the titration response of the interface from low to high pH is not the same as high to low pH. This is associated with the stability of the interface structure and the stability of the charged layer at the interface once it has formed. The kinetic stability results from the interfacial capacitance

reflecting the energy requirement for removing ions from the charged interface. There are also suggestions that ion condensation occurs at the surface, perhaps a stabilized inner Helmholtz plane.24 However, large changes in pH enable the surface to be switched, suggesting that the interfacial structure is only kinetically stable. In this paper, we have deposited ToA SAMs from both acidic and basic conditions onto a gold nanoparticle surface and followed the adsorption kinetics directly using the change in the small plasmon extinction of gold nanoparticles probed by evanescent wave cavity ring-down spectroscopy (e-CRDS). Gold colloidal nanoparticles are deposited onto the prism surface in the e-CRDS instrument and changes in the optical properties of the nanoparticle are used as a transducer of the binding events at the gold surface, forming a photonic sensor surface. The technique allows for the direct measurement of SAM formation kinetics (rarely seen in the literature) and insight into the formation process and adsorption isotherm for charged and neutral ToA SAMs. The change in the plasmon extinction of the particle is measured quantitatively by e-CRDS and allows the interfacial charge densities to be determined. From this a quantitative description of the interfacial pH is possible and hence an accurate determination of the surface pKa. We have determined the surface pKa for a number of different ToA SAMs deposited both from acid conditions, producing high-density neutral SAM, and from basic conditions with charged acid moieties, producing low-density charged SAM. We have performed titration measurements and determined the interfacial potential, interfacial capacitance, and interfacial pH above the ToA SAM. An analysis of the titration of the resulting SAMs is presented with a model for the interfacial pH, interfacial capacitance, and hence an accurate determination of the surface pKa. The almost unique quantitative description of interfacial pH and surface pKa allows a discussion of the general concept of interfacial acidity as a function of interfacial charge density. Experimental Methods The optical properties of gold nanoparticles are dominated by the localized plasmon resonance and this is finding application in monitoring biological processes25-27 as nanofabricated biophotonic surfaces. The sensitivity of the localized plasmon to the refractive index of the layer above the particle surface can be interrogated by e-CRDS, monitoring the extinction of radiation within an optical cavity. The plasmon field penetrates into the medium above the particle surface with an exponential decay in intensity and a penetration depth on the order of the radius of the particle. The e-CRDS technique has been described in detail elsewhere28 and will only be outlined briefly here. Two high-reflectivity mirrors (99.95%) are placed opposite one another to form a linear optical cavity into which light from a broadband continuous wave (cw) diode laser (830 nm) is introduced. The bandwidth of the laser is sufficiently large to overlap more than one cavity mode in a free-running configuration, so light always enters the cavity, building up intensity determined by the cavity Q-factor. The laser is switched off at a repetition rate of 6 kHz and the radiation intensity in the cavity decays with a ring-down time,τ, determined similarly by the Q-factor. A Dove prism is introduced into the cavity as a total-internalreflection element that generates an evanescent wave at the glass/ water interface. The evanescent wave penetrates 245 nm into the interface above the prism determined by the ratio of the refractive indices of the two media and the angle of incidence of the refracting radiation. Absorption or scatter processes at

Kinetics of Thioctic Acid SAM Formation on Au

Figure 2. Absorption isotherms for ToA deposited onto gold nanoparticle photonic surface: (a) charged ToA SAM deposited at pH 10.57, (b) neutral ToA SAM deposited at pH 1.75.

the laser wavelength from molecules or particles present within the evanescent field remove radiation from the cavity, decreasing the ring-down time, τ. The change in τ is directly related to the extinction of the species and the concentration profile of the species at the interface. The internal calibration of the time scale of the experiment allows an accurate determination of τ and hence the extinction to be determined directly. Gold nanoparticles have been synthesized by following the procedure of Turkevich29 using a simple citrate reduction of HAuCl4. Gold chloride solution (HAuCl4, 100 mL, 1 mM) was heated to 90 °C with rapid stirring. Sodium citrate dihydrate (10 mL, 38 mM) solution was added and then cooled, while being stirred rapidly. This yielded the familiar dark red solution with λmax ) 529 nm. The particle size distribution is 15 ( 3 nm (µ ( σ) and the surface coverage may be estimated from the total extinction on the surface and the measured extinction coefficients,30 830 nm ) (9.8 ( 0.2) × 106 M-1 cm-1, corresponding to a surface coverage of 2.8 layers. The colloid particle concentration in solution is ∼10 nM.30 The nanofabricated surface was washed several times with IPA and water and finally equilibrated with buffer solution of the target pH prior to deposition. The resulting surface has a refractive index sensitivity determined by measuring the change in refractive index (RI) from isopropyl alcohol (IPA) to water, at 25 °C, ∆n ) 4.43 × 10-2 gives a RI sensitivity of typically 5 × 10-4. The variation in extinction with refractive index shows a good linear dependence throughout the RI range investigated. The ToA was dissolved in ethanolic solutions using HCl and NaOH to adjust the pH for each deposition. The neutral SAM deposited from pH 1.75 was deposited from different solutions of ToA over the range 1-20 mM, and the charged SAM was deposited from ethanolic solutions at pH 10.5. Purified water solutions (18 MΩ cm-1) of HCl and NaOH were used for the titration of the SAMs. Results The adsorption isotherms were measured for SAMs deposited from acidic and basic conditions producing neutral and charged ToA SAMs, respectively, and are shown in Figure 2. The isotherm for the neutrally deposited SAM (Figure 2a) shows a nonmonotonic variation of plasmon extinction with concentration for low concentrations of ToA rising to a constant extinction at 7 mM, indicative of a complete monolayer. Higher concentrations of ToA add transiently to the interfacial structure but are washed off with the buffer and are not stable. The adsorption isotherm for the ToA deposited from basic conditions (Figure 2b) (producing a charged SAM) shows an increasing trend throughout the concentration profile and no significant plateau

J. Phys. Chem. C, Vol. 111, No. 42, 2007 15365

Figure 3. Formation kinetics for (a) charged ToA SAM and (b) neutral ToA SAM (concentration 5 mM).

Figure 4. Titrations of two charged-deposited SAMs with pH decreasing from 10 to 1, with the fit to the data: (a) 5 mM higher charge density and (b) 1 mM lower charge density.

for any higher concentrations. There is no significant variation in the observed interfacial RI over a period of hours, suggesting that the SAMs form quickly and only small changes to the initial structure result from incubation. Both isotherms are nonLangmuirian, suggesting significant moiety interaction on the surface. Experiments were performed on two partial SAMs, one neutral and one charged, formed from a ToA deposited from pH 1.75 and 10.75, respectively, at a concentration of 5 mM. The formation kinetics for the neutral and charged SAMS is significantly different, as may be seen in Figure 3. The extinction changed for the neutral SAM is larger and shows more noise on the kinetic trace during deposition. The adsorption kinetics will depend strongly on coverage, subsequent mobility of the species on the surface, and the detailed mechanism of selfassembly. Once formed, the SAMs are stable on the surface and the -COOH group may be titrated. Titration of the 5 mM charged SAM is shown in Figure 4a, with the starting pH of the titration at pH 9.57, and shows a significant drop at pH 3. Titration of a 1 mM SAM (Figure 4b) is also seen showing a considerably smaller change in extinction at the surface and hence change in interfacial RI. Reversing the titration in each case from low pH to high pH does not retrace the titration for these SAMs and shows a nearly constant surface RI: a hysteresis in titration11 of the ToA SAM. Either of the charged SAMs is pH-switchable, however (Figure 5), showing an RI change at the surface of ∆n ) 0.016 when switching the bulk pH from 1. 75 to 11.15, a switch from a fully neutral to fully charged surface. Titration of the neutrally deposited SAM (Figure 6) shows a complicated behavior with pH. The SAM shows a decrease in interfacial RI with increasing pH: the SAM has its highest interfacial RI for low pH (a neutral SAM) and a lower interfacial

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Figure 5. Switch of the charged-deposited 5 mM ToA: (a) pH 1.75, (b) pH 11.15 (∆n ) 0.016).

Figure 6. Titration of the neutral-deposited ToA layer (5 mM): (a) pH 11 f 1.75, (b) pH 1.75 f 11.

Rooth and Shaw photonic surface minimizes the perturbations on the SAM formation kinetics, not requiring the intense electric fields such as are present in SHG measurements or the presence of chromophore or fluorophore markers in the layer. Further, the SAM formation is observed on a particle surface, unlike the previous characterizations of SAM formation in electrochemical cells. The curvature of the particle surface will potentially perturb the formation of the SAM if the curvature is significant over the interaction length between the ToA moieties. Comparison may be made with the monlayer area of perfluoroacetic acid,31 which is 0.3 nm2, suggesting an interaction distance of 0.6 nm. At this separation, the surface of the nanoparticle shows a 0.3% deviation from flat; hence, the interpretation on the surface of the nanoparticles will transfer readily to flat surfaces. The SAM formation kinetics shows the expected sigmoid shape for both the charged and neutral SAMs, although the noise level on the neutral SAM is considerably larger. The charged SAM formation is intrinsically simpler with a large solvation atmosphere around the -COO- group providing a natural lattice parameter for the SAM. However, the neutral SAM requires the deposition of larger numbers of molecules, all of which must undergo rearrangements at the surface to the more subtle neutral-neutral molecule interactions. The local surface rearrangements may, in part, explain the apparent noise level on the adsorption kinetic trace. SAM formation kinetics are described by a kinetic model that accounts for the lateral interaction between the moieties on the surface. The theory was first used to describe the formation of rare gas atoms sticking to clean monocrystalline metal surfaces and was developed by Kreuzer.7 The model has rarely been tested for the assembly of monolayers in solutionphase science, although notably Grunze et al.32 did so using second harmonic generation. The evolution of the surface coverage θ with time is considered to follow the equation

θ)

Figure 7. Switch of the neutral-deposited ToA: (a) pH 1.75, (b) pH 11.15 (∆n ) 0.0235).

RI when the SAM is charged. The SAM interfacial structure can be switched with pH, as seen in Figure 7, with steps in the extinction corresponding to a refractive index change, ∆n ) 0.0235, when switching from pH 1.75 to pH 11.15. The switch shows no particular hysteresis in changing the bulk pH but a large hysteresis is seen in the titration of the SAM (Figure 5). Increasing the pH from 1.75 in Figure 5a causes a decrease in the interfacial RI centered at pH 8, whereas the reverse titration shows an increase at a pH centered at pH 4. The detailed form of the titration curves is, however, complex. Discussion Probing the SAM formation kinetics with e-CRDS on a gold nanoparticle surface allows very small changes in extinction to be observed (1 × 10-5) corresponding to low surface coverages. Hence, the early stages of the SAM formation kinetics may be observed directly, allowing both the adsorption and islandforming phases to be studied. In addition, e-CRDS of the

exp(1 + kE)ckLt - 1 exp(1 + kE)ckLt + kE

(2)

where kE is rate constant describing the sticking probability and adsorption to the islands of molecules forming on the surface, i.e., the lateral interactions; c is the solution concentration of the monomer; t is time; and kL is the sticking rate constant in a Langmuirian sense. The adsorption kinetics seen for the both the charged and neutral ToA SAMs shown in Figure 3 may be fitted to the functional form in eq 2 with the following rate constants: for the neutral SAM, kL ) 0.525 ( 0.050 M-1 s-1 and kE 19.8 ( 2.9, and for the charged SAM, kL ) 0.029 ( 0.002 and kE 394 ( 29. The model assumes negligible desorption of the thiol from the surface (desorption rate, kd ) 0) and a monolayer model with island precursors. The sticking coefficient, or more generally the adsorption rate, depends on the coverage on the surface, initially increasing rapidly as the lateral interaction between groups on the surface increases, perhaps associated with the circumference of the precursor islands and then slowing as monolayer adsorption is approached and the layer becomes more completely packed. The nature of the interactions for the charged-deposited SAM is clearly electrostatic: the interaction between the ionic -COO- groups is controlled by the solvation shell and the ionic strength of the surrounding electrolyte. The layer on the surface must assemble much like a charged ion lattice with a lattice spacing determined by the electrostatic repulsions of the solvation shell around the charged carboxyl group. The lattice spacing for very high surface charge densities (vide infra) may be 0.5-1 nm in diameter.

Kinetics of Thioctic Acid SAM Formation on Au The large lateral interactions are reflected in the magnitude of kE. There are very few values in the literature against which to compare the magnitude of this parameter, but the measurements on the n-alkanethiols reported by SHG23 have a kL value of 3150 M-1 s-1 and kE ) 2.0. The n-alkanethiol SAMs form laterally by the short-range hydrophobic interactions between the alkane chains. The charged SAM, however, shows much larger lateral interactions, reflected in the large value of kE. The ratio kL/kE ) 1575 for the neutral alkanethiol SAM compares with kL/kE ) 2.65 × 10-2 for the neutral ToA SAM and kL/kE ) 7.3 × 10-5 for the charged SAM. There is a clear decreasing trend in kL/kE with increasing lateral interaction. Curiously, the functional form presented in eq 2 and derived for island precursors of noble gas atoms on metal surfaces describes the shape of the kinetic traces rather well, although the fitted parameters are clearly in a different region of parameter space compared with the n-alkane SAM formation. The molecular interpretation of kE has not been developed in the present theory but must be a quantitative description of all of the increasing intermolecular forces with surface coverage. The evolution of the charged SAM is also associated with an evolving charged interfacial structure in the solvent above the SAM surface and affects the formation of the layer or layers. The charge density increases as the SAM moieties adsorb to the surface, which attract a counterion and co-ion concentration to ensure electrical neutrality. The extent of the interfacial structure also evolves from the simplest Gouy-Chapman interface model to an interface with an established Stern layer, perhaps including and inner and outer Helmholtz plane.33,15 The adsorption isotherms onto the surface also reflect an evolving charged interfacial structure; nonmonotonic (non-Langmuirian) adsorption isotherms show cooperative binding (Figure 2). The isotherms are measures of surface coverage as a function of concentration, although the concept of surface coverage is complicated with the current SAMs. For both the neutral and charged SAMs, there are molecular interactions that allow for multilayer formation without completion of the first layers on the surface. Hence, the description of a complete monolayer with θ is not precise. The neutral-deposited SAM does not have the dominating electrostatic interactions of the charged SAM but appears to pass through a number of surface phases, perhaps associated with the dimerization of the carboxylic acids on the surface. The charged SAM has a continually increasing isotherm also associated perhaps with different phases on the surface, cooperative binding adsorption of ToA into the evolving charged surface, and the increase of the interface RI as the counterion and co-ion concentrations increase. The charged layer formed from adsorption of 5 mM SAM under acidic conditions (Figure 2b) is expected to show a low number density on the surface dominated by the interactions from the solvent shells, not complicated by the presence of other moieties. The charge density is a function of the bulk pH, so the structure of the interface depends on the bulk pH. The titration shown in Figure 4 shows an increase in the observed extinction with increasing bulk pH and, hence, an increase in the interfacial RI. The variation of the particle plasmon with RI over the range ∆n ) 4.43 × 10-2 is linear for all experiments. This enables the interfacial RI, averaged over the penetration depth of the plasmon field and the structure of the interface, to be determined as 1.440. More interestingly, the switch of the surface charge with bulk pH (Figure 5) is a measure of the change in interfacial refractive index within the plasmon field when the interface is switched from neutral to charged.

J. Phys. Chem. C, Vol. 111, No. 42, 2007 15367 The charged interface consists of the SiO- charged ions that are native to the silica surface of the prism; positively charged counterions in the interface, which are principally Na+ from the NaOH used to adjust the pH; and some co-ions OH-, which are depleted at the surface. The response of the particle plasmon surface is linear over the refractive index range and only small changes in the extinction are observed. The response of the photonic nanoparticle surface to concentration and hence external refractive index is given by

∆Ext(830) )

∆Ext ∆n ∆c ∆n ∆c

(3)

The change in extinction measured in the experiment, ∆Ext, is a product of the rate of change of extinction with external refractive index, ∆Ext/∆n, and the rate of change of refractive index with concentration, ∆n/∆c. An estimate of the variation of refractive index of an ionic solution with concentration, ∆n/ ∆c, can be made by comparison with NaCl. The refractive index variation is well-known34 from which the interfacial concentrations of Na+ and OH- (and SiO-) are determined at 14.3 M. Similar estimates for determinations may be made from the change in refractive index for switching the neutrally deposited SAM, ∆n ) 1.6 × 10-2, corresponding to an equivalent concentration of Na+ + OH- at the interface of 20.6 M. These extraordinarily large ion concentrations arise from the same origins as the interfacial pH, the surface charge and hence surface potential enhancing the counterion concentration by the Boltzmann equation. The enhanced counterion concentration at a negatively charged surface is derived from the surface charge and hence surface potential. The charged interface may be interpreted as a simple charged surface model20 representing the dissociation of the acid characterized by a dissociation constant, Ka

σ ) Fe

(

)

Ka

(4)

Ka + [H]s

where σ is the layer charge, F is the number density, e is the electronic charge, [H]s is the interfacial pH given by [H]s ) [H+] exp(-eΨ0/kT), and [H+] is the concentration in the bulk. The surface pKa may be derived from eq 1 to give

pKa ) log

(

[ToA]

[ToA-]

)

+ pHs

(5)

Where [ToA-] is the concentration of the dissociated acid at the surface, pHs is the interfacial pH, and [ToA] is the surface concentration. The surface charge is related to the surface potential, Ψ0 (and hence interfacial pH), via the Grahame equation,23 which imposes electrical neutrality at the surface

(

σ2 ) 2r0kT

∑i ni∞ exp

( ) -qeψ0 kT

-

∑i ni∞

)

(6)

where ni∞ is the bulk concentration for each species. Thus, there is a direct relationship between surface charge, interfacial pH, and surface pKa, which must be modeled correctly before the contribution to variations in the surface pKa can be determined. The interfacial pH model was to fit and is shown in Figures 4 and 6. Without varying the pKa of the surface acid but with a correct (if simple) description of the interfacial pH, there is an apparent decrease in the surface pKa when the surface is titrated, and this can be seen in Figure 8a. The effect, however, is masked

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Figure 8. Variation of extinction with surface charge and bulk pH: fixed pKa ) 4.75, surface charge changes σ ) 20, 10, 5, 1, 0.1 e nm-2. (a) Extinction variations showing the increase in the counter ion concentration at the surface associated with the increased charge and (b) normalized extinctions to show the apparent variation of surface pKa

Figure 9. Apparent variation of surface pKa with surface charge.

by the change in the refractive index associated with the larger interfacial ion concentrations and hence interfacial RI. The data may be normalized, as shown in Figure 8b, to reveal the apparent shift in pKa, which in other work has been attributed to a change in the surface pKa at the surface or the structure of the acid group on the surface. Uncertainty in the surface charge and hence the interfacial pH, as is usually the case for surface titration measurements, results in a family of sigmoid curves that may be fitted to the standard titration of a monobasic acid. Without a description of interfacial pH, there is an apparent variation of surface pKa, as shown in Figure 9. The pKa of ToA in solution is reported35 as 4.76-5.3 and is fixed for the simulations at 4.76: the apparent pKa varies from 4.76-3.96, as seen in Figures 8 and 9. The highest charge density simulated, 20 e nm-2 is close to the maximum molecular density on the surface of a SAM and indicates that interfacial pH is responsible for an apparent shift in surface pKa of 0.8. It is clear that without a description of interfacial pH, all experiments leading to the determination of surface pKa are subject to error and produce

Rooth and Shaw misleading values of the surface pKa and hence contributions to possible changes owing to the local bonding environment. The detailed shape of the titration curve for varying interfacial pH shows large changes in the interfacial RI (Figure 4) for the two different SAMS. The increased surface charge density and hence interfacial pH causes the interfacial RI of the SAM to be significantly enhanced, owing to the presence of the counterions. The two curves have been fitted to the simple model (nonlinear Levenberg-Marquart fit) of interfacial pH from which the charge density and pKa can be determined: F ) 1.08 ( 0.05 e nm-2 and a surface pKa ) 5.62 ( 0.14 and F ) 0.105 ( 0.007 e nm-2 with a pKa ) 4.86 ( 0.16 respectively shown as the fitted lines in Figure 4. The charge density derived from the increasing refractive index for the SAM that is switched in Figure 5 suggests a surface concentration of 14.2 M, corresponding to a surface charge density of 0.97 e nm-2, in agreement with the fitted value. The simple model for interfacial pH does not take into account the surface capacitance, the permittivity of the interface, or its detailed structure within the 20 nm of the plasmon field. The fit therefore does not reproduce the detailed shape of the curve correctly. The interfacial capacitance affects the rate of desorption from the interface and hence the position of the equilibrium. For the lowest charge density SAM (F ) 0.105 ( 0.007 e nm-2), shown in Figure 3, the calculated surface potential is -44 mV, giving rise to an interfacial capacitance of 5.5 ( 0.5 µF cm-2. The higher charge density layer (F ) 1.08 ( 0.05 e nm-2) has a surface potential of -173 mV, corresponding to a surface capacitance of 56.6 ( 2.6 µF cm-2, at pH 11. The surface potential produces a Boltzmann distribution of positive counterions at the surface, including the H+, decreasing the interfacial pH by 2.93; hence, the interfacial pH is more acidicsthe bulk pH ) 9.36 and the interface pH ) 6.43 for the highest charged layer. The neutrally deposited SAMs show a larger negative shift in the refractive index of the interface, indicating that the disruption of the SAM by the presence of the incoming Na+ ions reduces the refractive index of the interface. The counterion concentration of 20.6 M indicates a surface charge density of 2.67 e nm-2, which has extreme consequences in the titration of the layer. The simple interfacial pH model only reproduces the trends of the titrations of the high-density SAM (Figure 5), with F ) 1.686 ( 0.047 e nm-2 and a pKa ) 8.90 ( 0.08 for the pH 11 f 1 titration and F ) 1.40 ( 0.04 e nm-2 and a pKa ) 4.53 ( 0.13 for the pH 1 f 11 titration. The up-turn in the data at high pH is consistent with the increasing counterion concentration within the interface causing a rise in the interfacial refractive index. The extreme of pH 11 corresponds to a surface potential of -198 mV and an interface capacitance of 88 µF cm-2, giving rise to an interfacial pH of 7.6 compared with pH 11 in the bulk. The two phases of the titration for the neutrally deposited ToA SAM indicate that, at the low charge density associated with the change in bulk pH from acid (weakly dissociated surface) to base (completely dissociated surface), a pKa ) 4.75 is consistent with the observed response of the layer. However, titration from a highly charged layer to a neutral layer is consistent with a pKa ) 7.5, as reported in the amperometric study using ultramicroelectrodes.7 No estimation of the layer structure, interfacial pH, or interfacial capacitance was made in the study, and importantly, the measurements were made with respect to the standard calomel electrode (SCE) in saturated KCl. The high surface pKa is attributed to hydrogen-bonding stabilization36 of the -COO-/-COOH groups. Indeed, the

Kinetics of Thioctic Acid SAM Formation on Au overpotential or potential bias with the SCE may control the layer response: the SAMs in this study are charged with respect to an absolute zero counter electrode imposed by absolute charge neutrality in the bulk solution. This is an important point: the surface potentials are derived with respect to electrical neutrality in the bulk solution and show no overpotential at the interface, except that derived from the imbalance in the charged distribution within the layer. Electrochemically this is a strange concept but must be true for all charged interfaces at nonconducting surfaces. Interfacial pH hysteresis has been observed previously with a chromophore tethered to the native silica surface (F ∼ 2 e nm-2), with the similar bilayer capacitance resisting the neutralization of the bilayer as the bulk pH is decreased.12 The SAM formed from charged ToA moieties are less densely packed, owing to the solvation shell around the -COO- on deposition. However, the layer may potentially undergo a phase change as the degree of charging influences the packing. Once formed, the SAM is stable until the external pH is titrated. Small variation in pH results in slow kinetic processes and kinetic stability of the layers that is dependent on the bilayer capacitance. However, switching the layer rapidly from low pH to high pH may result in a 1010-fold increase in H+ bulk concentration, and the rates of layer disruption are much faster. Conclusions The sensitivity of the localized particle plasmon to the charged SAM layer structure makes the measurement of the binding of protons to the interfacesthe interfacial pH-possible. The interfacial refractive index response to the charged interface amplifies the proton-binding event and allows the smallest possible ligand binding to be observed by plasmon resonance. This may be compared with the lower-mass limit for conventional surface plasmon resonance (SPR) measurements, which is typically several hundred atomic mass units. The observations presented here show the formation of a low-mass SAM (mass 120 amu) and the addition of a proton to the layer (mass 1 amu), so in the special circumstances of the formation of a charged interface adjacent to a nanoparticle, the localized plasmon shift is sensitive to the ultimate low-mass limit for SPR binding, 1 amu. The concept of layer stability as a function of interfacial pH and capacitance has consequences in a number of fields, such as cell membranes37,38 and the local concentrations around proteins. A local charge density of 2 e nm-2 on the surface of a protein may have a counterion concentration 103 times greater at the interface than in the bulk. Physiological concentrations of Na+ are typically 10 mM, but at the protein surface or along an ion channel or the charged phosphate backbone of DNA, the concentration may be much greater, perhaps as high as 10 M locally. Concepts of electrolyte transport in cells associated with the local charge on a protein surface may be diffusiondriven following a simple protonation event. The role of surface pKa is important in determining the interfacial properties of many systems, from chromatography columns to protein-protein interfaces. However, an understanding of the role of bonding changes to the surface moiety in the local interface environment can only be achieved with a correct quantitative description of the interfacial pH. Surface acidity is conventionally reported as a single parameter that shows a significant departure from the defining equation (eq 1) for pKa. The concepts of interfacial pH, interfacial concentration enhancement, and surface binding variation are collected in one fitted parameter, the surface pKa.

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