Aggregation Kinetics of SERS-Active Nanoparticles in Thermally

Article pubs.acs.org/Langmuir

Aggregation Kinetics of SERS-Active Nanoparticles in Thermally Stirred Sessile Droplets Meysam R. Barmi,† Chrysafis Andreou,‡ Mehran R. Hoonejani,† Martin Moskovits,§ and Carl D. Meinhart*,† †

Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, United States Department of Biomolecular Science and Engineering, University of California Santa Barbara, Santa Barbara, California 93106, United States § Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States ‡

S Supporting Information *

ABSTRACT: The aggregation kinetics of silver nanoparticles in sessile droplets were investigated both experimentally and through numerical simulations as a function of temperature gradient and evaporation rate, in order to determine the hydrodynamic and aggregation parameters that lead to optimal surface-enhanced Raman spectroscopic (SERS) detection. Thermal gradients promote effective stirring within the droplet. The aggregation reaction ceases when the solvent evaporates forming a circular stain consisting of a high concentration of silver nanoparticle aggregates, which can be interrogated by SERS leading to analyte detection and identification. We introduce the aggregation parameter, Γa  τevap/τa, which is the ratio of the evaporation to the aggregation time scales. For a well-stirred droplet, the optimal condition for SERS detection was found to be Γa,opt = kcNPτevap ≈ 0.3, which is a product of the dimerization rate constant (k), the concentration of nanoparticles (cNP), and the droplet evaporation time (τevap). Near maximal signal (over 50% of maximum value) is observed over a wide range of aggregation parameters 0.05 < Γa < 1.25, which also defines the time window during which trace analytes can be easily measured. The results of the simulation were in very good agreement with experimentally acquired SERS spectra using gas-phase 1,4-benzenedithiol as a model analyte.

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tures which possess surface plasmon resonances,22−25 often at, or near interstices, crevices or junctions between silver nanoparticles.26−32 One simple but effective way to use SERS is to probe the mixture of nanoparticles and analyte resulting from a droplet that has dried on a substrate. Much stronger SERS signals are obtained from the ring-shaped dry nanoparticle deposits than from the nanoparticles in the colloidal solution.33−37 Since the degree of nanoparticle aggregation is the key to the enhancement,38 controlling the aggregation process could lead to optimal SERS detection. Aggregation occurring in solution is induced by analyte adsorption onto the nanoparticles displacing the charged, surface species that stabilize the colloid. The overall reaction rate depends on the concentration of analyte, as well as the initial concentration of nanoparticles. A sessile droplet of colloidal silver in contact with the surrounding atmosphere can absorb and concentrate airborne analytes that partition into the aqueous phase. The Marangoni

INTRODUCTION Evaporating droplets are used in biological and chemical applications such as DNA deposition,1 protein analysis,2,3 and carbon nanotube formation.4 When evaporation occurs on moderately hydrophobic surfaces, the contact-line of the droplet is pinned, inducing convective flow within the droplet toward the contact-line. In a colloid droplet, this flow deposits the suspended particles onto the substrate forming a so-called ‘coffee ring stain’.5−9 In this context one needs to pay attention to Marangoni-induced fluid motion resulting from temperature gradients, promoting efficient mixing and thereby hindering particle deposition during evaporation.10 Various experimental approaches and mathematical formulations have been proposed for modeling convective flows in droplets, both for Marangoni flow and for the flow toward the pinned contact-line due to evaporation.11−19 In this study, we investigate evaporating sessile silver colloid droplets as a platform for chemical detection using surfaceenhanced Raman spectroscopy (SERS), yielding moleculespecific (vibrational) Raman spectra.20,21 The most intense SERS signals arise from molecules residing in hot spots associated with strongly interacting silver or gold nanostruc© 2013 American Chemical Society

Received: March 15, 2013 Revised: October 1, 2013 Published: October 1, 2013 13614

dx.doi.org/10.1021/la400949x | Langmuir 2013, 29, 13614−13623

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Figure 1. Schematic of sessile droplet of SERS-active colloidal suspension of silver nanoparticles on substrate: (a) Silver nanoparticle colloidal droplet on a surface and gas phase analyte in surrounding, (b) absorption of gas phase analyte from surrounding and aggregation, (c) stirring due to Marangoni stress and evaporation increase the aggregation rate, and (d) interrogation of the deposited aggregates with a Raman spectrometer to detect adsorbed analyte.

flow mixes the analyte and the silver nanoparticles, accelerating their aggregation. Aggregation stops when the droplet dries out, so that the degree of aggregation depends on the evaporation time. If evaporation occurs too quickly, there is insufficient time for analyte absorption by the droplet and subsequent nanoparticle aggregation to occur, and a large fraction of the nanoparticles remain as ineffectual monomers. For long evaporation times, many very large aggregates are formed, which produce non-optimal signals. By controlling the evaporation rate, one can tune the analyte interaction and nanoparticle aggregation to obtain optimal SERS signals. In this report, we use COMSOL Multiphysics v3.5 to carry out numerical simulations modeling the aggregation kinetics during the droplet evaporation to discover the optimal conditions for producing large SERS intensities and, specifically, the range in evaporation times leading to maximal SERS signals. The results are validated experimentally using 1,4-benzenedithiol (1,4BDT) as a model analyte.

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THEORY AND NUMERICAL SIMULATIONS Overview. The model system is illustrated schematically in Figure 1. The droplet is exposed to the environment at room temperature to absorb analyte. As the droplet evaporates, its volume decreases, thereby concentrating the analyte and the nanoparticles. Heating the droplet from below creates a temperature gradient that imposes Marangoni stresses at the air/water interface and induces internal flow. Fluid flow, heat transfer, and evaporation are modeled, together with the related aggregation kinetics covering all the relevant physics. The numerical simulation results were compared to experimental results. Droplet Evaporation and Stirring Simulations. Numerical simulations were carried out using COMSOL Multiphysics v3.5 (COMSOL, Inc. Stockholm, Se). The governing equations and associated boundary conditions are illustrated in Figure 2, where an axisymmetric droplet of aqueous silver colloid suspension is surrounded by air with a specified humidity. The droplet volume is 2 μL with initial contact angle of 65°. The radius of the contact-line is nominally a = 1.2 mm and the

Figure 2. Computational domain: The axisymmetric droplet on silicon substrate in ambient conditions. The evaporative flux Je and Marangoni stress τM are applied on the air/water interface. The volume of the droplet is 2 μL and the initial contact angle is θi = 65°. The computational domain is 100 times larger than the droplet size so that the numerical results are independent of the domain size.

height of the droplet is h = 0.77 mm. In the surrounding atmosphere, the partial pressure of water vapor is pv,∞ and the temperature is T∞. An evaporation flux, Je, and a Marangoni stress, τM, are applied on the air/water interface. These equations are solved simultaneously assuming temperaturedependent physical and thermodynamic properties of water and air 39,40 to calculate the fluid velocity u and species concentration ci within the droplet. Triangular mesh elements with first order discretization were utilized. Various mesh sizes were assessed for mesh independency. The results reported were based on calculations with 4 × 104 mesh elements, corresponding to a physical spatial resolution of 10 μm inside of the droplet. 13615


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The Marangoni stress is τM = −(dσ/dT)∇sT, where for water dσ/dT = −0.1657 × 10−3 N m−1 K−1. The Marangoni stress becomes the prominent driving force within the droplet when the Marangoni number, Mg = −(dσ/dT)(aΔT/μα) > 10−2. The characteristic velocity in the droplet is defined in terms of the Marangoni number as, UMg = (dσ/dT)(ΔT/μ) = (Mgα/a). The Rayleigh number, Ra = gβΔTa3/αν, is in the range of 10−2 < Ra < 100, implying that the buoyancy force does not have a significant effect on the fluid flow. The Reynolds number, Re = Ua/ν, is in the range 10−2 < Re < 100, indicating that flow is dominated by viscous forces. The Péclet number, Pe = (Ua/D) ≫ 1 for all species within the droplet indicating the importance of convection relative to diffusion. Analyte-Induced Aggregation. The dimerization rate constant41 was assumed to be of the following form: k = e−Vmax / kBT , k0

Vmax =

Relevant Time Scales and Aggregation Regimes. Four important time scales define the regime of the aggregation kinetics in evaporating sessile droplets. These are • Analyte-induced aggregation time scale: τa =

The aggregation rate depends on the initial concentration of nanoparticles within the droplet, cNP and dimerization rate constant, k. For typical applications, k = 106 ∼ 109 M−1s−1 and cNP = 102 ∼ 103 pM, there is a range for analyte-induced aggregation time scale as τa = 100 ∼ 104 s. • Evaporation time scale: τevap =

V0 (1 + βca)12/5

(2)

where i indicates the species as follows: i = a for analyte, i = 1 for colloid monomers, i = 2 for dimers, and so on up to tetramers. The diffusion coefficient, Di, of each species is estimated using the Stokes−Einstein equation, D = kBT/6πμRs, where Rs is the radius of the species, yielding diffusion coefficients of Da ≈ 10−10 m2 s−1 for the analyte, and Di ≈ 10−11 m2 s−1 for colloid monomers and higher order aggregates. The initial concentration of the analyte was assumed to be ca = c0 at the interface and ca = 0 in the interior side of the droplet, c1 = cNP and c2 = c3 = c4 = 0 for the aggregates. The total number of nanoparticles in the droplet is cNP. We also assumed zero nanoparticle flux through the interface. The reaction terms, Ri, are calculated using the rate equation and the concentration of the first four orders of the aggregates as

where Di = 10−11 ∼ 10−10 m2 s−1 is the diffusivity of species in solution. A typical range of diffusion time scale is τdiff = 103 ∼ 104 s, which makes it insignificant for mixing within the droplet during most of the evaporation process. As droplet size decreases, diffusion becomes increasingly more important. • Convection time scale: τconv =

a = UMg

a dσ ΔT dT μ

=

a2 Mgα

Here, UMg is the characteristic velocity within the droplet based on Marangoni number, and thermal diffusivity of water, α = 1.43 × 10−5 m2 s−1. The convection time scale corresponds to the characteristic time that it takes for a particle to travel one turn inside of the droplet, which is an indication the degree of stirring within the droplet. For a typical droplet a = 1 ∼ 3 mm and Mg = 10−3 ∼ 101, the range for convection time scale becomes τconv = 10−2 ∼ 102 s. Using these time scales, we define two non-dimensional parameters, based upon the ratio of two time scales, which correspond to the degree of stirring within the droplet and degree of analyte-induced aggregation kinetics. • Stirring parameter:

R1 = −2kc1c1 − kc 2c1 , R 2 = kc1c1 − kc 2c1 − 2kc 2c 2 − kc3c1 , R 4 = kc3c1 + kc 2c 2 (3)

The surface temperature and initial concentration of nanoparticles significantly influence the nanoparticle aggregation. The surface temperature governs the evaporation time, which is also the maximum available time for analyte-induced nanoparticle aggregation. The number of formed aggregates during evaporation is calculated by integrating the concentration over the droplet volume as ni = ∫ ci dV. We assumed the formation of first four V aggregates during evaporation; therefore, the total number of nanoparticles is conserved and equal to

∫V (c1 + 2c2 + 3c3 + 4c4) = nNP

a2 Di

τdiff =

Ra = 0

R3 = kc 2c1 − kc3c1

ρRTa 2 2πMDΔpv

where M = 18 × 10−3 kg mol−1 is the molecular weight of water, D = 2.46 × 10−5 m2 s−1 is the diffusion of water vapor in air, ρ = 998 kg m−3 is water density, R is gas constant, T is surrounding temperature, a = 1 ∼ 3 mm is the droplet contactline radius, and Δpν = 103 ∼ 104 Pa is the gradient of vapor pressure. The total evaporation time determines the total available time for mixing of the analyte, and analyte adsorption on to the nanoparticles. For the parameters considered here, the characteristic range for evaporation time scale is τevap = 101 ∼ 104 s. • Diffusion time scale:

(1)

where the maximum dimerization rate constant k0 and the potential barrier V0 are constant, the factor β depends on temperature, and ca is the concentration of the analyte in solution. The convection-diffusion equations of the analyte and colloidal aggregates are summarized as ∂ci + u·∇ci = ∇·(Di∇ci) + R i ∂t

1 kc NP

Γstir ≡

min(τa , τevap) τconv

• Analyte aggregation parameter: τevap Γa ≡ τa

(4) 13616


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Figure 3 shows the simulation results for velocity within the droplet during the evaporation of a 2 μL droplet. Figure 3a corresponds to the well-stirred case Γstir >1, while Figure 3b corresponds to the weakly stirred case Γstir ∼1, where the Marangoni number is reduced from Mg = 10−1(UMg = 1.6 × 10−3m s−1) in Figure 3a to Mg = 10−3(UMg = 1.6 × 10−5m s−1) in Figure 3b. In the well-stirred example (Figure 3a), the Marangoni stresses and subsequent convective flows created along the interface, result in circulating flow with velocities of order 1.6 mm/s, compared to velocities of order 16 um/s for the weakly stirred case (Figure 3b). The mass loss from the interface generates an additional evaporation-driven flow from the apex to the contact-line, which is negligible for (t/τevap) 0.8, the evaporation-driven flow dominates the Marangoni-driven flow, and creates a jet-like flow, which is responsible for depositing aggregates at the contact line. Figure 4 illustrates the concentration of dimers formed during evaporation for the four regimes depicted in Table 1. For the regimes that are well-stirred, the Marangoni number is Mg = 10−1 corresponding to Γstir >1 and for the regimes with weakly stirred condition the Marangoni number is Mg = 10−3, resulting in Γstir ∼ 1. For the evaporation-induced aggregation regime, Γa = 0.05 < 1, and for the analyte-induced aggregation regime, Γa = 2.5 > 1. In the weakly stirred droplet in Regimes 1 and 2, there is a gradient of concentration of formed aggregates toward the contact-line throughout the evaporation which leads to accumulation of particles at the contact-line. However, in the well-stirred droplet in Regimes 3 and 4, the concentration of aggregates is uniform during evaporation when the stirring effect due to Marangoni is dominant. At the end of evaporation when (t/τevap) > 0.8, the flow toward the contact-line

Two limiting cases can be defined for the stirring parameter: 1. Well-stirred (Γstir >1): When convective time scale is much less than the analyte-induced time scale or the evaporation time scale, the analyte can be regarded as very well mixed within the droplet resulting in the uniform formation of aggregates. 2. Weakly stirred (Γstir 1): During the evaporation of the droplet, aggregation occurs in solution, and is induced by analyte adsorption onto the nanoparticles displacing adsorbed species that stabilize the colloid. The four limiting regimes for aggregation kinetics in an evaporating droplet are shown in Table 1. Table 1. Aggregation Regimes Resulting from the Stirring Parameter, Γstir, and Analyte Aggregation Parameter, Γa

evaporation-induced aggregation: Γa < 1 analyte-induced aggregation: Γa > 1

weakly stirred: Γstir < 1

well-stirred: Γa > 1

Regime 1 Regime 2

Regime 3 Regime 4

Figure 3. Simulation results for an evaporating sessile droplet with pinned contact-line at Tw − TD = 34 °C. The velocity field on the left half, and velocity vectors and streamlines within the droplet on the right half. (a) Well-stirred condition at Mg = 10−1 (Γstir > 1) Marangoni flow dominates during the evaporation and flow toward contact-line dominates at the end of evaporation. (b) Weakly stirred condition at Mg = 10−3 (Γstir ∼ 1). 13617


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Figure 4. Simulation results for an evaporating sessile droplet with pinned contact-line for different aggregation regimes. In the Regimes 1 and 2, the concentration dimers increases locally near the contact-line. In Regimes 3 and 4, the concentration of dimers is uniform throughout the droplet during evaporation, and they are carried toward the contact-line at the end of evaporation and deposited on the surface.

Figure 5. Evaporation-induced aggregation regime (Γa = 0.05) in a 2 μL droplet at Tw −TD = 34 °C, cNP = 100pM, and k0 = 3.6 × 107 M−1s−1 in a well-stirred droplet (Γstir = 288). (a) Concentration of aggregates within the droplet during the evaporation, (b) Number of formed aggregates during the evaporation, where the final number of dimers is denoted by the red circle.

dominates the Marangoni flow leading to accumulation of

formed when the droplet is well-stirred and they are carried toward the contact-line at the end of evaporation. In the weakly stirred cases Γstir ∼ 1 (Figure 4a,b), the evaporation-driven flow toward the pinned contact-line concentrates nanoparticles at the meniscus. Whereas in the

formed aggregates at the contact-line. Around this time, the contact angle of the droplet becomes very small leading to breakage of the contact-line. Therefore, all the aggregates are 13618


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Figure 6. Analyte-induced aggregation regime (Γa = 2.5) in a 2 μL droplet at Tw −TD = 34 °C, cNP = 100pM, and k0 = 1.8 × 109 M−1s−1 in a wellstirred droplet (Γstir = 112). (a) Concentration of the aggregates within the droplet during the evaporation. (b) Number of formed aggregates during the evaporation, where the final number of dimers is denoted by the red circle.

well-stirred condition, Γstir >1 (Figure 4c,d), the dimer concentration is nearly uniform throughout the droplet at each time step, due to the circulating Marangoni flow. The effects of analyte-induced aggregation, Γa = 2.5, shown in Figure 4b,d, are compared to the effects of evaporationinduced aggregation Γa = 0.05, shown in Figure 4a,c. The results indicate that when analyte induces aggregation, the aggregation occurs throughout the volume of the droplet during the entire evaporation process. When the analyte does not induce aggregation, the aggregation is induced due to the effects of evaporation, which increases the nanoparticle concentration leading to aggregation. In all cases, the combinations of Marangoni flow, diffusion and evaporation lead to significant aggregation, regardless of analyte/nanoparticle affinity. This result explains why sessile droplets make a good platform for SERS detection. The remaining analysis is focused only on the well-stirred cases. The concentration and number of formed aggregates are depicted for evaporation-induced aggregation in Figure 5 (Γa = 0.05), and analyte-induced aggregation in Figure 6 (Γa = 2.5). Figure 5a and Figure 6a show that the concentration of the species increases during evaporation as a result of volume reduction while the total number of nanoparticles in the solution is constant (see Figure 5b and Figure 6b). At higher concentrations, the interaction between nanoparticles and consequently the reaction rate is higher leading to more aggregation of nanoparticles. Figure 5 corresponds to Regime 3, with Γstir = 288 and Γa = 0.05, where the aggregation process is slow and there is not enough time for formation of higher aggregates during evaporation. Therefore, the aggregation process is dominated by formation of dimers. If the aggregation parameter increases, the rate of dimer production increases as well and can reach the maximum point. At higher aggregation rate, the formed dimers are consumed to produce higher aggregates. As shown in Figure 6 in Regime 4 with Γstir = 112 and Γa = 2.5, higher order aggregates are created as a result of the high reaction rate. At the beginning of evaporation, monomers are used to create dimers. However, after a certain point, the rate of formation of dimers becomes less than the rate of consumption of dimers to produce higher aggregates.

Therefore, there is an optimal point in time where the number of formed dimers is maximal. All formed aggregates including dimers are deposited at the contact-line at the end of evaporation. The total number of dimers, at the final stage of evaporation just before breakage of the contact-line, is denoted by the red circles in Figure 5b and Figure 6b. We performed simulations for different aggregation parameters and found the total number of formed dimers at the end of evaporation process similar to the red circle in Figure 5b and Figure 6b. Figure 7 shows the number of dimers formed at the

Figure 7. Simulation results for the total number of dimers after evaporation of the droplet. The arrow indicates the point of maximum dimer concentration at Γa,opt = kcNPτevap ≈ 0.3, which is expected to give the optimum SERS signal. The simulations assume a 2 uL droplet with 100 pM nanoparticle concentration, at temperature difference Tw − TD = 30 °C with different aggregation rates from k0 = 1.8 × 106 M−1 s−1 to k0 = 4.3 × 109 M−1 s−1.

end of droplet evaporation, t = τevap, for a range of 0.01 < Γa < 2. The number of dimers increases and reaches the maximum at Γa,pot = τevap/τa = kcNPτevap ≈ 0.3. This time point occurs when the rate of dimer generation equals the rate of dimer depletion. It is also clear from the results that the dimer concentration remains within 10% of its maximum value over a range of analyte aggregation parameters, 0.16 < Γa < 0.55, and within 13619


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Figure 8. (a) Evaporation time of 2 μL sessile droplet for different surface temperatures. (b) Formation of the stain at the final stage of evaporation for Tw − TD = 34 °C. (c) Schematics of the convective flow from the apex to the pinned contact-line at the end of the evaporation depositing aggregates on the surface and breakage of the contact-line after formation of the stain at contact angle between 2° and 4°.

Figure 9. Interrogation of the stain with spectrometer to detect adsorbed 1,4-BDT. (a) Stain of aggregates on the surface, (b) the intensity map of the SERS signal over the stain showing detection of the 1,4-BDT spectrum, (c) 1,4-BDT spectrum, and (d) intensity profile of the 1560 cm−1 peak across the stain edge.

50% of its maximum value over the range 0.05 < Γa < 1.25. This provides a reasonably large time window in which high-quality signals can be obtained. It is clear, however, that erring on the side of too large an evaporation time, is preferable to using too short a value of τevap.

pM) was placed on the substrate and introduced into an environmental chamber containing equilibrated vapor of the airborne model analyte 1,4-BDT (partial pressure ∼7 Pa44) at temperature of 21 °C and relative humidity 45% for 1 min. The substrate was removed from the chamber and placed on a temperature-controlled hot plate. The experiments were performed at various temperatures of the hot plate between 30 and 70 °C. The evaporation time, τevap, depends on the surface temperature, Tw, and the dew point, TD, as shown in Figure 8a. The temperature and, therefore, the evaporation rate is locally a maximum at the contact-line. The Marangoni-induced flow dominates evaporation-induced flow during the major portion of the evaporation process. At the end of the evaporation process, the flow due to evaporation becomes dominant carrying formed aggregates to the contact-line and depositing them on the substrate. At a contact angle between 2°

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EXPERIMENTAL METHODS AND RESULTS The aggregation kinetics were analyzed experimentally in a sessile droplet with a colloidal suspension of ∼20 nm diameter silver nanoparticles on a clean 500 μm thick silicon substrate. The silicon wafer substrate was prepared by performing a 10 min Nanostrip cleaning at 70 °C, followed by a one minute HF etch. The initial contact angle of an aqueous droplet on the Si surface was measured to be 65° ± 2°. A 2 μL droplet of colloidal suspension of silver nanoparticles (Ted Pella, Inc., BioPure 20 nm, 1 mg/mL in citrate buffer, diluted in DI water for a final nanoparticle concentration of 100 13620


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and 4°, the pinned contact-line breaks and the droplet evaporates while the contact-line recedes rapidly. The formation of the stain before unpinning of the contact-line is clearly visible in Figure 8b,c. Therefore, our original assumption that the species are not deposited on the substrate during the evaporation as well as neglecting aggregation after the breakage of the contact-line are justified from experimental observation. The resulting stains, composed of aggregated nanoparticles, were interrogated at multiple locations in a Raman spectrometer (labRAM Aramis, Horiba Ltd., excitation: 633 nm, 7.9 mW). The acquisition time of each measurement was 100 ms, and averaged at least 15 times for each location. Background subtraction using a polynomial curve fitting42,43 was applied to all spectra prior to spectral analysis. The coffee ring stain and the area of interrogation are shown in Figure 9a, together with the collected Raman mapping for cNP = 100 pM and temperature Tw − TD = 34 °C (see Figure 9b). A typical SER spectrum is shown for 1,4-BDT in Figure 9c. The spatial distribution of the dominant 1560 cm−1 peak is shown as a function of spatial position in Figure 9d. This signal peaks at the x = 5 μm location, which corresponds to the location of the coffee stain. The intensity of SER spectra depends on the evaporation time of the droplet as illustrated for the prominent peak of 1,4BDT (υ̃ = 1560 cm−1) in Figure 10a. The optimum point occurs at τevap ≈ 390 s, which corresponds in the current experiments to Tw −TD = 29 °C. Therefore, the reaction rate is approximated according to the simulation results for the optimum point as

k≈

Γa,opt cNPτevap

≈

0.3 ≈ 7.7 × 106 M−1 s−1 100 × 10−12 × 390 (5)

The dimerization rate constant, k of the analyte can be measured using the method described in the Supporting Information. At low concentration of 1,4-BDT, the dimerization rate constant becomes ⎛ 0.08 eV ⎞ k ≈ exp⎜ − ⎟ k0 kBT ⎠ ⎝

(6)

As a result, we can estimate the maximum dimerization rate constant as k0 ≈ 7.7 × 106 exp[(1.2817 × 10−20)/(1.3807 × 10−23 × 310)] ≈ 1.5 × 108 M−1 s−1 Using this value, we compare the results of the numerical simulations of the dimers formed during the evaporation with the intensity of the acquired SER spectra from the deposited stain. Figure 10 compares the experimental intensity measurements with numerically simulated dimer concentrations. The experimental and numerical results show good agreement, using a single fitting parameter, k0. Therefore, according to the reaction rate equation, the optimum point that exhibits maximum SERS intensity can be achieved by controlling the initial concentration of nanoparticles and the evaporation time of the droplet.

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CONCLUSION Nanoparticle aggregation kinetics and aggregation regimes were investigated numerically and experimentally for sessile silver colloid droplets. Marangoni stresses and evaporation combine with the pinned contact-line induce fluid motion to enhance analyte mixing within the droplet. The stirring process together with the increase in the analyte concentration due to droplet evaporation promote nanoparticle aggregation. When evaporation ceases, the nanoparticle aggregates are deposited as a ‘coffee ring stain’ near the original location of the pinned interface of the droplet. The stain consists of SERS-active nanoparticle aggregates with adsorbed analyte, which can be interrogated by Raman spectroscopy using of 1,4-BDT, used as analyte. Numerical simulations were carried out using COMSOL Multiphysics v3.5 to model the evaporation, internal droplet fluid motion, and aggregation kinetics. The simulated results are in excellent agreement with the experimental measurements. The initial concentration of nanoparticles and the evaporation temperature significantly affect the number of dimers (and hence higher aggregates) and consequently the intensity of SERS signal. In a well-stirred droplet, the optimum nanoparticle aggregation occurs when the analyte aggregation parameter, Γa,opt = kcNPτevap ≈ 0.3, which also approximately corresponds to the condition of near maximal SERS intensity. Nanoparticle aggregation is within 50% of its optimum value over a relatively large range of aggregation parameter 0.05 < Γa < 1.25. This result demonstrates that sessile droplet evaporation is effective and reproducible platform for SERS detection. The parameters in the dimerization rate constant, k/k0 = exp{−V0/[kBT(1 + βca)12/5]}, were determined using resonance absorption measurements to be V0 ≈ 3.21 kBT = 0.08 eV and β ≈ 2.82 × 10−4 M−1. The value of k0 was determined from the SERS measurements to be ∼108 M−1 s−1.

Figure 10. The number of dimers formed during the evaporation and acquired SERS signal from the stain at υ̃ = 1560 cm−1 (a) as a function of the evaporation time and (b) as a function of nondimensional time. There is an optimum point at Γa,opt = kcNPτevap ≈ 0.3 where number of dimers and the intensity of SERS signal are maxima. 13621


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ASSOCIATED CONTENT

S Supporting Information *

Article

SUBSCRIPTS AND SUPERSCRIPTS Analyte Buoyancy Convection Diffusion Evaporation Order of aggregates Nanoparticle Saturation Surrounding Vapor Wall

Notes

a B conv dif f evap i NP sat ∞ v w

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CONSTANTS kB Boltzmann constant g Gravity acceleration

The governing equations for fluid flow, heat transfer and evaporation as well as experimental method for determination of dimerization rate constant of the model analyte are presented in this section. 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].

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The authors declare no competing financial interest.

ACKNOWLEDGMENTS Fabrication was done at the University of California, Santa Barbara, nanofabrication facility, which is part of NINN. This work was supported by the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the U.S. Army Research Office. The content of the information does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred.

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U c ρ D k h a V μ Je F R α θi ν τM M n pv V0 p Rs RH R σ T β τ u

NOMENCLATURE: VARIABLE UNIT NAME (m s−1) Characteristic velocity (J kg−1 K−1) Concentration (kg m−3) Density (m2 s−1) Diffusion coefficient (M−1 s−1) Dimerization rate constant (m) Droplet height (m) Droplet radius of contact-line (m3) Droplet volume (Pa s) Dynamic viscosity (kg s−1) Evaporation rate (N) Force (J mol−1 K−1) Gas constant (m2 s−1) Heat diffusivity (rad) Initial contact angle (m2 s−1) Kinematic viscosity (Pa) Marangoni stress (kg mol−1) Molecular weight (#) Number of aggregates (Pa) Partial pressure of water vapor (eV) Potential barrier (Pa) Pressure (m) Radius of species (%) Relative humidity (M s−1) Reaction rate (N m−1) Surface tension (K) Temperature (K−1) Thermal expansion (s) Time scale (m s−1) Velocity field

Γa Bo Mg Pe Re Ra Γstir

NON-DIMENSIONAL NUMBERS Aggregation parameter Bond number Marangoni number Péclet number Reynolds number Rayleigh number Stirring parameter

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REFERENCES

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Aggregation Kinetics of SERS-Active Nanoparticles in Thermally

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