The Role of Heating in the Electrochemical Response of Plasmonic

Subscriber access provided by UNIV AUTONOMA DE COAHUILA UADEC

C: Plasmonics; Optical, Magnetic, and Hybrid Materials

The Role of Heating in the Electrochemical Response of Plasmonic Nanostructures under Illumination Marquis Maley, Joshua W. Hill, Partha Saha, Joshua D. Walmsley, and Caleb M. Hill J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01479 • Publication Date (Web): 18 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

The Role of Heating in the Electrochemical Response of Plasmonic Nanostructures under Illumination Marquis Maley, Joshua W. Hill, Partha Saha, Joshua D. Walmsley, and Caleb M. Hill* 1000 E. University Ave., Laramie, WY, University of Wyoming

ABSTRACT: The role played by heating in the electrochemical behavior of plasmonic nanostructures under illumination was examined through a combination of theoretical modeling and experimental investigations. A theoretical treatment of heating in plasmonic electrochemical systems was developed which treats heat flow from arrays of nanoparticles attached to an electrode as a heat source delocalized across the electrode-solution interface. Within this framework, simple analytical expressions for the temperature profile in the vicinity of illuminated electrodes are presented for a 1D model treating heat transfer via conduction. Results from more detailed finite element simulations treating heat transfer via both conduction and convection in realistic cell geometries are also provided. Both approaches predict significant increases in the mass transfer of dissolved redox species which can readily explain the current enhancements observed with electrodes decorated with plasmonic nanostructures under illumination. These predictions were tested experimentally by employing conventional, mm-sized electrodes decorated with Au nanoparticles in potential step experiments under intermittent illumination. Experiments with both

ACS Paragon Plus Environment

1

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 31

outer sphere (ferrocene methanol) and inner sphere (hydrazine) redox couples displayed significant current enhancements due to illumination which agreed well with theoretical predictions. Experiments at individual nanoparticles were also carried out using probe-based techniques. These measurements displayed no significant effects due to heating, attributable to efficient heat transfer away from nanoparticles in this experimental geometry. Implications of these results on research into the effects of hot charge carriers in electrochemical experiments are discussed.

INTRODUCTION Plasmonic nanostructures, which possess strong, tunable optical resonances, are of great interest in a variety of light-harvesting and sensing applications. In particular, there is growing interest in the effects of illumination on the catalytic properties of plasmonic structures. Nonequilibrium carrier distributions resulting from excitations, “hot” electrons lying well above the Fermi level and holes well below the Fermi level, have been hypothesized to drive photocatalytic transformations.1,2,11,12,3–10 While hot carrier effects in electrochemical systems have been reported for some time,13,14 researchers are beginning to investigate hot carrier effects in these systems with increasing frequency, reporting rate enhancements at plasmonic nanostructures under illumination for electrocatalytic reactions,15,16 kinetically fast, “outer sphere” electrochemical reactions,17,18 and nanoparticle dissolution.19 A common concern in the interpretation of these experiments is the role of local heating. As plasmonic nanostructures absorb light efficiently, often possessing optical cross-sections several times larger than their physical dimensions, a significant amount of heat is dissipated into their surroundings under illumination. In electrochemical experiments, any resulting temperature increases could result in rate enhancements through increasing local heterogeneous electron transfer rates (kinetic effects) or the mass transfer of redox active species. Thus, evaluating the


2

Page 3 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


possible unique role of hot carriers on the electrochemical properties of plasmonic nanostructures must properly account for any possible thermal effects. This remains a matter of debate, as some authors report thermal effects play a significant role in the electrochemical responses observed at plasmonic nanostructures17,18 and others do not.15,16,19 It is commonly argued that the efficient dissipation of heat via conduction from small nanostructures makes thermal effects negligible in these systems, even under intense illumination. Such arguments are often based on the consideration of isolated nanostructures, in which heat is dissipated efficiently via spherical conduction.20 Such arguments, however, do not properly reflect the most relevant experimental geometry of a planar electrode randomly decorated with plasmonic structures. In this geometry, light absorption by a random array of nanostructures (and any absorption by the substrate itself) would effectively constitute a uniform heat source delocalized across the electrode-solution interface. Such a source would result in the dissipation of heat in a linear geometry, a situation which involves more significant temperature changes which increase over time. While theoretical investigations into local heating at arrays of plasmonic nanostructures under illumination have been investigated previously, these analyses have only considered the steady-state properties of small, finite arrays (or infinite arrays under highly localized excitation).21,22 Thus, a more careful analysis of the time dependent behavior of electrochemically relevant systems is necessary. Presented in this report is a theoretical analysis of the role thermal effects play in the electrochemical response of electrodes decorated with plasmonic nanostructures under illumination and corresponding experimental investigations into these effects at the bulk and single nanoparticle level. The time dependent temperature profiles in the vicinity of illuminated electrodes are evaluated in a straightforward manner which treats heat flow via conduction away


3


Page 4 of 31

from a planar electrode-solution interface, yielding analytical expressions for the temperature profile in the system and subsequent electrochemical rate increases due to enhanced diffusion. This analytical treatment is compared to explicit finite element simulations which also include effects due to convection. Experimental results are presented which tested these predictions at two drastically different scales: through bulk studies on films of plasmonic nanoparticles adsorbed to conventionally sized electrodes and measurements at single nanoparticles obtained using probebased methods. Implications from these studies on the possible role of hot carriers in plasmonic electrochemical systems are then discussed. EXPERIMENTAL METHODS Nanoparticle Synthesis, Characterization, and Electrode Functionalization. Spherical, citratecapped Au nanoparticles were synthesized according to the method of Frens.23 Au nanorods were synthesized following the method of El-Sayed and coworkers.24 Before use, the synthesized nanorod dispersion was cleaned via centrifugation twice, replacing the supernatant with deionized water. All synthesized nanoparticles were characterized via transmission electron microscopy (FEI Technai G2 F20). The total Au(0) content in the resulting dispersions was evaluated from the UVVisible absorption of the dispersions at 400 nm as described by Liz-Marzan.25,26 Glassy carbon electrodes employed in bulk measurements (3 mm diameter, CH Instruments) were functionalized by dropcoating 15 μL of the as-synthesized stock of spherical Au particles (determined to have an average diameter of 17 nm and a concentration of 1.7 nM) onto the electrode and allowing the solution to dry in air. The indium tin oxide electrodes employed in the single nanoparticle studies were functionalized by contacting 5 μL of the synthesized nanorod dispersion with an indium tin oxide (ITO)-coated coverglass substrate for 5 min and rinsing with copious amounts of deionized water.


4

Page 5 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Bulk Electrochemical Measurements. All bulk electrochemical measurements were carried out in a three-electrode configuration using a potentiostat (Gamry Reference 600). A Pt coil served as the counter electrode and a homemade Ag/AgCl (3 M KCl) electrode served as the reference. The Au nanoparticle-decorated glassy carbon electrodes described above were employed as the working electrode. Potential step experiments were carried out while irradiating the electrode surface with a 532 nm laser (Crystalaser) at a maximum intensity of 1.1 W cm-2. The intensity at the electrode surface was varied through the use of neutral density filters (ThorLabs). During the power dependence studies described in Figure 5, powers were altered randomly within the depicted range in order to ensure any observed trends were not attributable to stability effects. The illumination was made intermittent via manual chopping. Single Nanoparticle Electrochemical Measurements. Electrochemical measurements at individual Au nanorods were carried out using a recently described methodology.27 Briefly, samples consisting of Au nanorods (average size of 22 nm x 55 nm as determined via TEM) dispersed on an indium tin oxide-coated coverglass slide were mounted on an inverted optical microscope. Scattering from the sample was excited using intense broadband illumination (Energetiq EQ-99, ~50 W cm-2 at the sample plane). Scattered light was collected by a long working distance objective and directed onto the slit of a spectrometer/CCD combo (Andor Newton DU970-P/Shamrock SR-303i). Nanorods were imaged through a hyperspectral imaging protocol, and the locations of isolated nanorods were generated through the analysis of these images. Electrochemical measurements were then made by bringing an electrolyte-filled pipette into contact with the sample over the located nanorods, forming a “trapped nanoparticle” configuration. Measurements were made using a patch-clamp style electrometer (Dagan CHEMCLAMP), with the indium tix oxide substrate serving as the working electrode and a AgCl-coated


5


Page 6 of 31

Ag wire inserted in the pipette serving as a counter/reference electrode. Pipettes were prepared from borosilicate capillaries (1 mm OD, 0.5 mm ID, Sutter) using a pipette puller (Sutter P-2000, HEAT = 350, FIL = 4, VEL = 30, DEL = 200, Pull = 0), and were found to have an average pore radius of 0.3 μm and a half-angle of 7°. RESULTS AND DISCUSSION Temperature Increases in the Vicinity of Illuminated Electrodes. Temperature changes due to heat flow in a continuous medium can be described by the following general equation:28 ∂𝑇 1 + ∇ ⋅𝑞=01 ∂𝑡 𝜌𝐶𝑝 where 𝑇 is the temperature, 𝜌 is the density of the medium, 𝐶𝑝 is the specific heat of the medium, and 𝑞 is the heat flow within the medium. In a liquid, 𝑞 can be described as a combination of two terms corresponding to conduction and convection: ∂𝑇 1 + ∇ ⋅ [ ―𝜅∇𝑇 + 𝜌𝐶𝑝𝑇𝑣] = 02 ∂𝑡 𝜌𝐶𝑝 Here, 𝜅 is the thermal conductivity of the medium and 𝑣 is the flow velocity within the medium. When convection can be ignored, this simplifies to a diffusion equation: ∂𝑇 ― 𝛼∇2𝑇 = 03 ∂𝑡 where 𝛼 = 𝜅/𝜌𝐶𝑝 is referred to as the thermal diffusivity of the medium. Temperature increases in the vicinity of illuminated nanostructures can be evaluated by solving these equations with boundary conditions which reflect the heat being input into the system. Consider first the case of an individual spherical nanoparticle, a case which has been treated previously.20 A nanoparticle will continuously absorb incident radiation and covert it to heat with a power of: 𝑃𝑎𝑏𝑠 = 𝐼0𝜎𝑎𝑏𝑠 = 𝐼0(𝐴𝑐𝑠𝑄𝑎𝑏𝑠)#4


6

Page 7 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where 𝑃𝑎𝑏𝑠 is the absorbed power, 𝐼0 is the intensity of the incident radiation, and 𝜎𝑎𝑏𝑠 is the absorption cross-section of the nanoparticle, which can be expressed as a product of the crosssectional area of the nanoparticle (𝐴𝑐𝑠) and an efficiency factor for absorption (𝑄𝑎𝑏𝑠). If heat flow into the nanoparticle is neglected (i.e., a trivial amount of energy is required to raise the temperature of the nanoparticle), the heat flow into the surrounding medium at the surface of the nanoparticle can be expressed as: 𝑞(𝑟 = 𝑟0) =

𝑃𝑎𝑏𝑠 𝐴𝑁𝑃

𝑟=

𝐼0𝑄𝑎𝑏𝑠 4

𝑟#5

Here, 𝑟0 is the radius of the nanoparticle, 𝐴𝑁𝑃 is the surface area of the nanoparticle and 𝑟 is the radial unit vector normal to nanoparticle surface. Using this boundary condition, the following steady-state expression for the temperature in the vicinity of the nanoparticle can be found: 𝐼0𝑄𝑎𝑏𝑠𝑟20 𝑇(𝑟) = 𝑇 + #6 4𝜅𝑟 ∗

where 𝑇 ∗ is the bulk temperature. Using typical values for 𝑄𝑎𝑏𝑠 (1), 𝜅 (0.6 W m-1 K-1 for H2O), and 𝑟0 (10 nm), this equation would predict intensities upwards of 25 kW cm-2 to be necessary to generate a temperature increase of just 1 K at the surface of a nanoparticle. This logic is often used to support the assertion that heating effects are insignificant in experiments at illuminated plasmonic nanoparticles. This argument is only valid, however, when the following conditions are met: (1) heat flows from the particles in question solely via spherical conduction and (2) no radiation is absorbed by the substrate or surrounding medium. While the latter condition is straightforward, condition (1) is subtler, and depends critically on the interparticle spacing of the particles. Individual particles serving as heat sources will change the temperature of the surrounding medium over a finite distance, which changes with time and can be estimated as 𝛿𝑞 = 𝛼𝑡. For an array of particles


7


Page 8 of 31

on a substrate, when this thickness becomes comparable to the interparticle spacing, 𝑑, the geometry of heat transfer shifts from spherical to linear, making Eq. 6 invalid. A time limit is thus put on condition (1), becoming invalid when 𝑡 ≈ 𝑑2/𝛼. For an experiment involving heating for 5 s in an aqueous solution, a large interparticle spacing of ~1 mm would be required for the assumption of spherical diffusion to hold. This situation is directly analogous to the electrochemical problem of mass transfer to an array of active sites on a substrate, which has been treated extensively,29–31 but the relevant diffusion constants differ greatly in magnitude (e.g., 𝛼 for H2O is 1.5 × 10-3 cm2 s-1, over two orders of magnitude larger than typical diffusion coefficients for small molecules in solution). When these conditions are not met, it is necessary to treat heat transfer in a linear, rather than spherical, fashion. To do so, we will consider an array of nanoparticles at the interface of two dissimilar phases representing a substrate electrode and a solvent medium. The flow of heat in each phase can be described by the following differential equations: ∂𝑇𝐸 ∂𝑡 ∂𝑇𝑊 ∂𝑡

∂2𝑇𝐸

― 𝛼𝐸

∂𝑥2

= 0#7

∂2𝑇𝑊

― 𝛼𝑊

∂𝑥2

= 0#8

Subscripts of 𝐸 and 𝑊 refer to the electrode and solvent medium, respectively. The heat input at the interface, 𝑞𝑖𝑛, can be assumed to be homogeneous: 𝑞𝑖𝑛 = 𝐼0[𝜒𝑠𝑢𝑏 + Π𝑁𝑃𝜎𝑎𝑏𝑠]#9 Here, 𝜒𝑠𝑢𝑏 represents the fraction of light absorbed by the substrate at the interface (e.g., by a film such as indium tin oxide) and Π𝑁𝑃 represents the density of nanoparticles on the sample surface. Assuming 𝑞𝑖𝑛 is constant, the following expressions can be derived describing the temperature profile of the solvent phase (see SI for details and corresponding expressions for the substrate):


8

Page 9 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(

𝑇𝑊 ≈ 𝑇 ∗ + Δ𝑇0 1 ―

𝑥

)

𝛿𝑞𝑊

#10

1 2𝛿𝑞𝑊𝑞𝑖𝑛 Δ𝑇0 = #11 1 + 𝜉 𝜅𝑊

( )

𝛿𝑞𝑊 = 𝜉=

2 𝛼𝑊𝑡 #12 𝜋

𝜅𝐸𝜌𝐸𝐶𝑝𝐸

#13 𝜅𝑊𝜌𝑊𝐶𝑝𝑊

These equations describe a linear approximation for 𝑇 which is valid near the electrode surface (exact, though unattractive, solutions are provided in the SI). Δ𝑇0 represents the temperature increase at the electrode surface and 𝛿𝑞𝑊 represents the effective diffusion layer thickness discussed earlier. This temperature increase is expected to be directly proportional to the heat input, 𝑞𝑖𝑛, and grows larger over time with a 𝑡1/2 dependence. 𝜉 is a parameter which represents the ratio of the input heat which flows into the substrate vs. the solvent medium. Example calculations using the above equations for an isolated 10 nm radius nanoparticle in H2O and a square array (100 nm particle-to-particle spacing) of the same nanoparticles at the interface of a glassy carbon electrode and H2O are given in Figure 1. The relevant physical constants used in this calculation are provided in Table 1. An isolated nanoparticle is expected to quickly reach a steady-state after illumination is initiated, and the temperature increases at the nanoparticle surface are expected to be very small, on the order of 4 × 10-5 K under an illumination intensity of 1 W cm-2. Heating is highly localized at the nanoparticle surface, within a distance of a few nanoparticle radii. In the case of an array adsorbed at the surface of an electrode, temperature increases are expected to be much more significant. At a typical experimental timescale of 5 s, the same illumination intensity of 1 W cm-2 is expected to result in temperature increases of ~2 K, a difference of roughly 5 orders of magnitude. Additionally, effects are expected


9


Page 10 of 31

to extend spatially over mm-scale distances. Considering many experiments in the field often employ intensities of several 10’s of W cm-2, thermal effects should be expected to be significant and cannot be immediately dismissed using arguments based on heat flow from isolated nanostructures. The above discussion is correct for perfect 1D systems in the absence of convection. I.e., the velocity, 𝑣, of the solution is everywhere equal to zero. In realistic electrochemical systems, this will not hold true due to the formation of solution flows via natural convection. In such cases, the solution velocity should be treated through the Navier-Stokes equation:32

[

]

∂𝑣 𝜂 1 + 𝑣 ⋅ ∇𝑣 ― ∇2𝑣 + ∇𝑃 ― 𝑔 = 0#14 ∂𝑡 𝜌 𝜌 which is given here for an incompressible fluid. Here, 𝜂 is the dynamic viscosity of the solution, 𝑃 is the pressure, 𝑔 is the acceleration due to external forces (here assumed to be gravity), and 𝜌 is again the density of the solution. Eq. 14 dictates that the solution velocity can vary locally due to convection, viscous dissipation of momentum, pressure gradients, and external forces, respectively. Most interesting to the present case are the last two terms, which allow for accelerations of an initially quiescent solution upon heating. Sudden changes in temperature can lead to alterations of 𝜌 and therefore a nonzero acceleration, leading to the phenomenon commonly referred to as natural convection. In general, finding solutions for 𝑣 is a difficult task, as 𝜂, 𝜌, and 𝑃 will all vary spatially and can exhibit significant variations with temperature. Axisymmetric 2D finite element simulations in COMSOL Multiphysics were employed to find solutions for the prototypical system depicted in Figure 2. The experimental geometry consists of a cylindrical, glassy carbon electrode surrounded by an insulating sheath, immersed in a cylindrical electrochemical cell containing an aqueous electrolyte. Differential equations for the solution velocity and temperature (Eqs. 2 and


10

Page 11 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


14) were solved simultaneously, employing a uniform heat input at the electrode surface as described above and no-slip boundary conditions for 𝑣 at all solid-liquid interfaces. Example results are given in Figure 2, which gives the velocity and temperature distribution in the system resulting from a heat input of 10 W cm-2 over a time of 10 s. The local input of heat at the electrode surface results in significant solution flows, which initially run vertically from the edge of the electrode, dissipating and changing direction further into solution. These convective flows have the effect of lowering the temperature increases at the electrode surface by a factor of ~2 compared to the 1D case, as it serves as an additional means of heat flow away from the electrode surface. Effects of Heating on Mass Transfer in Electrochemical Systems. The local temperature increases described above would be expected to impact electrochemical reaction rates through mass transfer enhancements, increases in heterogeneous electron transfer rates, and shifts in reduction potentials. Here, we will consider the effects on mass transfer, showing that these effects are substantial and can alone account for enhancements on par with those observed experimentally. A discussion of the magnitude of potential shifts resulting from heating is provided in the SI. The mass transfer of a redox active species to an electrode is described by the following general expression: ∂𝐶 + ∇ ⋅ 𝐽 = 0#15 ∂𝑡 where 𝐶 is the concentration of the species in solution and 𝐽 is the corresponding flux. Neglecting migration (which is justified when a significant concentration of supporting electrolyte is employed), the flux, 𝐽, can be described as: ∂𝐶 + ∇ ⋅ [ ―𝐷∇𝐶 + 𝐶𝑣] = 0#16 ∂𝑡


11


Page 12 of 31

where 𝐷 is the diffusion coefficient for the redox active species and 𝑣 is the solution velocity as before. Once 𝐶 and 𝑣 are found for a given experiment, the corresponding current, 𝑖, can be calculated as:

∫𝐽 𝑑𝐴#17

𝑖 = 𝑛𝐹

𝑛

where 𝑛 is the number of electrons involved in the reaction, 𝐹 is the Faraday, 𝐽𝑛 is the flux magnitude normal to the electrode surface, and the integration is taken over the entire electrode surface. Heating will alter the mass transfer-limited current observed in an electrochemical experiment in two ways: by altering 𝐷 for the redox active species and by creating significant solution velocities via natural convection. A rough estimate of the current enhancement in these systems can be made by ignoring convection for the moment and noting that the diffusion coefficient relevant to heat transfer (𝛼) is much larger than that for mass transfer (𝐷). As a result, the temperature over electrochemically relevant length scales can be assumed to be equal to temperature at the electrode surface, 𝑇 ≈ 𝑇 ∗ + Δ𝑇0. For small molecules in solution, 𝐷 can be assumed to follow the Stokes-Einstein relationship: 𝐷=

𝑘𝑏𝑇

#18 6𝜋𝜂𝑎

Here, 𝑘𝑏 is Boltzmann’s constant and 𝑎 is the molecular radius. 𝜂 carries a strong temperature dependence which can typically be well described by a sum of exponentials (corresponding parameters for H2O are given in Table 1): 𝜂=

∑𝜂𝑒 𝑖

𝜖𝑖 𝑘𝑏𝑇

#19

𝑖

Current enhancements can then be rationalized based on the change in 𝐷 resulting from the local temperature increase in the system. For most common electrochemical situations where mass


12

Page 13 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


transfer occurs via linear diffusion, currents are expected to scale with 𝐷1/2. Current increases due to heating could then be calculated as: 1 2

( )

𝑖 𝐷 = 𝑖0 𝐷0

=

(

𝑇𝜂0 𝜖𝑖

𝑇 ∗ ∑𝑖𝜂𝑖𝑒𝑘𝑏𝑇

)

1 2

#20

where 𝑖0, 𝐷0, 𝑇 ∗ , and 𝜂0 are the current, diffusion coefficient, temperature, and viscosity in the absence of heating. For electrochemical experiments in aqueous electrolytes, a 10 K increase in temperature at the electrode surface would be predicted to result in enhancement factors of ~1.8. It should be emphasized that this is only a rough value, as Eq. 20 ignores convection effects and cannot account for experiments involving dynamic changes in 𝑇 over the course of the electrochemical experiment. Finding solutions to Eq. 16 which take these effects into account requires more detailed numerical simulations. Results from such simulations for a basic potential step experiment involving heating at an electrode surface are provided in Figure 3, where heating is initiated 10 s after the application of a large amplitude potential step. Simulations are provided both for a 1D simulation neglecting convection and an axisymmetric 2D simulation treating convection. Upon the onset of heating, transient increases are observed in both the current and temperature at the electrode surface, both scaling roughly with 𝑡1/2. This results in a quasi-steady state, as the increase in mass transfer offsets the usual 𝑡 ―1/2 behavior of a potential step experiment under linear diffusion control.33 There is a distinct difference in the transient behavior in the 1D and 2D cases, which is illustrated in Figure 4a. The predicted transients agree well for the first ~1 s of heating, showing that effects on this timescale do not carry significant contributions from convection. After ~1 s, additional increases are observed in the 2D case, demonstrating that solution flows due to natural convection take an experimentally significant amount of time to be established.


13


Page 14 of 31

The magnitudes of the predicted current increases in the 2D case treating convection are roughly twice that of the 1D case, while the inverse is true for the temperature increases at the electrode surface. These simulations show that while convection has the effect of lowering temperature increases at electrode surfaces due to local heating, the resulting flows significantly increase mass transfer, having a significant net positive effect on the measured currents. Though, since these quantities only differ by a factor of ~2, the analytical expressions given above for a 1D case neglecting convection should provide a good first estimate of heating effects in plasmonic electrochemical systems. The dependence of these effects on the magnitude of the heat source (i.e., illumination intensity) are provided in Figure 4b. In the 1D case, the current increases scale linearly with the power of the heat source. In the 2D case, a more complicated dependence on the power is observed, scaling with 𝑞0.8 𝑖𝑛 . It can thus be concluded that effects due to conduction scale linearly with the incident power, while effects due to convection show a lower order dependence which should be more dominant at lower intensities. Bulk Experimental Investigations. Bulk electrochemical experiments were carried out with glassy carbon electrodes decorated with spherical Au nanoparticles, the prototypical plasmonic nanostructure. In order to enable quantitative comparisons to the simulations provided above, potential step voltammetry (chronoamperometry) was employed. Since local temperature increases could be expected to play a significant role in modifying the kinetics of an electrode process in addition to the mass transfer considerations presented above, the properties of both an outer sphere redox couple with fast heterogeneous electron transfer kinetics (ferrocene methanol, FcMeOH) and an inner sphere redox couple with slow kinetics (hydrazine, N2H4) were investigated separately. The fast inherent kinetics of the outer sphere couple (which has standard


14

Page 15 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


rate constant, 𝑘0, greater than 0.1 cm s-1)34 would prevent further kinetic enhancements due to heating from influencing the observed electrochemical response. Current-time data displaying the typical response observed for FcMeOH are given in Figure 5c. The reaction being probed in this case is the simple one-electron oxidation of FcMeOH: 𝐹𝑐𝑀𝑒𝑂𝐻→𝐹𝑐𝑀𝑒𝑂𝐻 + + 𝑒 ― . Before heating is initiated, the current transients display the typical 𝑡 ―1/2 behavior expected for a potential step experiment. Upon illumination, a distinct transient behavior is observed which is very similar to the theoretical predictions discussed above. There is an essentially immediate increase followed by a more gradual increase which is initiated after several seconds. The magnitudes of these responses were found to increase linearly with the intensity of the incident radiation, which is illustrated in Figure 5d. These increases were normalized to the concentration of redox species employed and number of electrons involved in the reaction. The heat input 𝑞𝑖𝑛 was estimated as: 𝑞𝑖𝑛 = 𝐼0Π𝑁𝑃𝜎𝑁𝑃 =

𝜋𝑟20𝐼0𝐶𝑁𝑃𝑉𝑁𝑃𝑄𝑎𝑏𝑠 𝐴𝑒

#21

where 𝑟0 is the nanoparticle radius, 𝐼0 is the incident intensity, 𝐶𝑁𝑃 and 𝑉𝑁𝑃 are the concentration and volume of nanoparticle stock solution employed in functionalizing the electrode, and 𝐴𝑒 is the area of the electrode. This expression assumes the total heat absorbed is that which one would expect if the nanoparticles were distributed randomly across the electrode surface. 𝐶𝑁𝑃 was evaluated through a combination of visible absorption spectroscopy and TEM, as described in the experimental section. 𝑄𝑎𝑏𝑠 was taken from finite element simulations described in the SI, and was found to have a value of ~1. The resulting power dependence data in Figure 5d, which depicts a response of ~2.5 μA per mM redox species per W cm-2, is in very good agreement with the theoretical predictions provided in Figure 4. The results obtained with this kinetically facile outer


15


Page 16 of 31

sphere redox couple strongly support the existence of significant local temperature increases in these systems. Data for experiments involving N2H4 are provided in Figure 5e and 5f. Here, the reaction being probed is the electrocatalytic oxidation of hydrazine: 𝑁2𝐻5+ →𝑁2 +5𝐻 + +4𝑒 ― . Despite the significantly more complicated nature of this reaction, similar responses are observed overall. The transients resulting from illumination show the same two stage behavior which follows the predictions given in Figure 4a. After normalizing the observed increases to the concentration of redox species employed (0.5 mM vs. 2 mM) and number of electrons involved in their respective redox reactions (1 vs. 4), the magnitudes of the observed current increases are very comparable, yielding values of ~1.5 μA per mM redox species per W cm-2. The slightly lower enhancements observed for this reaction is likely attributable to kinetic limitations preventing the reaction from proceeding at the mass transfer limit. The similar response to illumination displayed by outer sphere and inner sphere redox couples, together with the good quantitative agreement between the observed enhancements and the theoretical predictions given above, strongly suggest that thermal mass transfer enhancements play a dominant role in the electrochemical response of illuminated plasmonic nanostructures. It should be noted that the degree of local heating which would be implicated in these mass transfer enhancements would certainly accelerate the kinetics of reactions at the electrode surface, as well. However, this would be attributable to traditional thermal enhancements, not unique effects resulting from the excitation of plasmons. Single Nanoparticle Investigations. In order to provide further evidence into the origin of current enhancements resulting from illumination in these systems, experiments on individual plasmonic nanostructures were carried out using a pipette-based method recently described by our


16

Page 17 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


laboratory.27 In this method, which employs the Scanning ElectroChemical Cell Microscopy detection scheme developed by Unwin and coworkers,35–39 individual nanostructures are located on a substrate optically and trapped within the meniscus of an electrolyte filled pipette, resulting in the experimental geometry depicted in Figure 6a. Hemispherically-capped Au nanorods with ~20 nm x ~50 nm dimensions were employed for these studies, due to the ease of optically locating these particles on a substrate. The electrochemical properties of the nanorods towards hydrazine oxidation were investigated via linear sweep voltammetry under intermittent broadband illumination. Intense, broadband illumination was employed (~50 W cm-2) in order to ensure both interband and intraband transitions were driven in nanorods as a result of light absorption.19,40 Thus, the “temperature” of any excited carriers should be comparable to those generated in the bulk experiments described above. This pipette-based experimental geometry ensures minimal local temperature increases at the nanoparticle/substrate surface due to efficient heat transfer away from the sample. Assuming heat flow occurs solely via conduction in a spherical segment defined by the pipette employed, the temperature increase at the nanoparticle surface can be estimated as: ∗

𝑇≈𝑇 +

𝐼0𝑄𝑎𝑏𝑠𝑟20

#22 2(1 ― cos 𝜃𝑝)𝜅𝑟

where 𝜃𝑝 is the half cone angle of the pipette. For the pipettes employed, with 𝜃𝑝 ≈ 7𝑜, the predicted temperature increases would be 2-3 orders of magnitude larger than the completely spherical case depicted in Figure 1a, which are still negligibly small. Eq. 22 would be an overestimation of the temperature increase, as well, since this expression neglects heat transfer through the underlying substrate or air surrounding the solution. Due to the negligible temperature increases present in this experimental geometry, it could be safely assumed that any observed rate


17


Page 18 of 31

enhancements would not be due to thermal effects, but to kinetic effects resulting from the nonequilibrium electron distributions created immediately after excitation. Results from these experiments are given in Figure 6b. Clear hydrazine oxidation currents could be measured at individual nanorods, consistent with our previous investigations. However, illumination had no significant effects on these currents across any of the individual nanorods investigated (n = 31). The lack of effects observed in these experiments, even under the large excitation intensities employed (~50 W cm-2), suggests that kinetic effects resulting from nonequilibrium carrier distributions in these structures do not play a significant role in the model electrocatalytic reaction employed. Implications for “Hot Carrier” Electrochemistry and Photocatalysis. Taken together, the presented simulations and experiments call into question the proposed role of hot carrier effects in electrochemical systems. The straightforward theoretical analyses of these systems presented above, which are based only on fundamental equations governing heat transfer via conduction and convection, predict that light absorption at electrode surfaces results in significant local temperature increases and solution flows. These thermal effects are predicted to alter observed electrochemical currents in a number of ways, including the enhancements of mass transfer presented here, shifting of the equilibrium redox potential,18 or increasing the kinetic rate of an electrode process in a conventional manner with temperature. In particular, the presented analysis predicts that mass transfer enhancements alone would result in sizable current increases, and these enhancements would apply to any electrochemical reaction involving dissolved reactants and/or products. The presented experiments, which display similar effects with both outer sphere and inner sphere reactants, support this assertion.


18

Page 19 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


It should be noted that the analyses presented above treat the heat source in a rather agnostic manner, and particular attention should be paid to the influence of substrate absorption, some degree of which will always be present even when employing “transparent” electrodes such as ITO. As an example, consider an ITO substrate which absorbs 1% an incident 1 kW cm-2 beam of light. Following Eq. 9, substrate absorption alone would constitute an effective heat source at the electrode surface of ~10 W cm-2, which would locally raise temperatures by 10’s of K according to the analysis presented above. It is thus not sufficient to merely treat absorption by the structure in question when intense excitation sources are employed. Future investigations into the possible influence of nonequilibrium carrier distributions on the electrochemical properties of plasmonic nanostructures should carefully analyze these systems in the manner presented here to ensure thermal effects are truly negligible. CONCLUSIONS A straightforward theoretical framework was developed for treating temperature gradients near electrodes decorated with absorbing nanostructures. This framework treats light absorption by the nanostructures and the substrate as an essentially homogeneous heat source located at the electrode-solution interface, which is valid when the spacing between adjacent structures is smaller than the thermal diffusion length. Analytical expressions for the temperature profile in the vicinity of the interface neglecting convection were presented, as well as results from finite element simulations treating convection explicitly. Both approaches predict significant local temperature increases under commonly employed experimental illumination conditions and significant subsequent enhancements on electrochemical signals due to increases in mass transfer via diffusion and convection. Potential step voltammetry experiments under intermittent illumination employing electrodes decorated with plasmonic nanostructures displayed significant current


19


Page 20 of 31

responses which were consistent with these theoretical predictions for both outer sphere and inner sphere electrochemical reactions, demonstrating that thermal effects are significant in experiments employing electrodes decorated with a high density of absorbing nanostructures. No effects were observed in experiments at individual nanostructures, where efficient thermal transport is expected to minimize local temperature variations. Taken together, this work demonstrates the significant role thermal effects play in the electrochemical rate enhancements observed at illuminated plasmonic nanostructures. ASSOCIATED CONTENT Supporting Information. The following files are available free of charge. Mathematical derivations, details on finite element simulations, and bulk cyclic voltammetry (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENTS Support for this work from the University of Wyoming, Wyoming NASA Space Grant Consortium (NASA Grant #NNX15AI08H), NIH Wyoming INBRE (2P20GM103432), the


20

Page 21 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


University of Wyoming Science Initiative’s Wyoming Research Scholars Program, and the National Science Foundation (CHE 1358498) is gratefully acknowledged. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

Mukherjee, S.; Libisch, F.; Large, N.; Neumann, O.; Brown, L. V; Cheng, J.; Lassiter, J. B.; Carter, E. A.; Nordlander, P.; Halas, N. J. Hot Electrons Do the Impossible: PlasmonInduced Dissociation of H2 on Au. Nano Lett. 2013, 13, 240–247. Schlather, A. E.; Manjavacas, A.; Lauchner, A.; Marangoni, V. S.; DeSantis, C. J.; Nordlander, P.; Halas, N. J. Hot Hole Photoelectrochemistry on Au@SiO 2 @Au Nanoparticles. J. Phys. Chem. Lett. 2017, 8, 2060–2067. Robatjazi, H.; Bahauddin, S. M.; Doiron, C.; Thomann, I. Direct Plasmon-Driven Photoelectrocatalysis. Nano Lett. 2015, 15, 6155–6161. Reineck, P.; Brick, D.; Mulvaney, P.; Bach, U. Plasmonic Hot Electron Solar Cells: The Effect of Nanoparticle Size on Quantum Efficiency. J. Phys. Chem. Lett. 2016, 7, 4137– 4141. Yan, L.; Xu, J.; Wang, F.; Meng, S. Plasmon-Induced Ultrafast Hydrogen Production in Liquid Water. J. Phys. Chem. Lett. 2018, 9, 63–69. Shaik, F.; Peer, I.; Jain, P. K.; Amirav, L. Plasmon-Enhanced Multicarrier Photocatalysis. Nano Lett. 2018, 18, 4370–4376. Linic, S.; Christopher, P.; Xin, H.; Marimuthu, A. Catalytic and Photocatalytic Transformations on Metal Nanoparticles with Targeted Geometric and Plasmonic Properties. Acc. Chem. Res. 2013, 46, 1890–1899. Christopher, P.; Xin, H.; Linic, S. Visible-Light-Enhanced Catalytic Oxidation Reactions on Plasmonic Silver Nanostructures. Nat. Chem. 2011, 3, 467–472. Li, K.; Hogan, N. J.; Kale, M. J.; Halas, N. J.; Nordlander, P.; Christopher, P. Balancing Near-Field Enhancement, Absorption, and Scattering for Effective Antenna–Reactor Plasmonic Photocatalysis. Nano Lett. 2017, 17, 3710–3717. Yu, S.; Wilson, A. J.; Heo, J.; Jain, P. K. Plasmonic Control of Multi-Electron Transfer and C–C Coupling in Visible-Light-Driven CO2 Reduction on Au Nanoparticles. Nano Lett. 2018, 18, 2189–2194. Kim, Y.; Dumett Torres, D.; Jain, P. K. Activation Energies of Plasmonic Catalysts. Nano Lett. 2016, 16, 3399–3407. Brongersma, M. L.; Halas, N. J.; Nordlander, P. Plasmon-Induced Hot Carrier Science and Technology. Nat. Nanotechnol. 2015, 10, 25–34. Redmond, P. L.; Brus, L. E. “Hot Electron” Photo-Charging and Electrochemical Discharge Kinetics of Silver Nanocrystals. J. Phys. Chem. C 2007, 111, 14849–14854. Redmond, P. L.; Wu, X.; Brus, L. Photovoltage and Photocatalyzed Growth in CitrateStabilized Colloidal Silver Nanocrystals †. J. Phys. Chem. C 2007, 111, 8942–8947. Shi, F.; He, J.; Zhang, B.; Peng, J.; Ma, Y.; Chen, W.; Li, F.; Qin, Y.; Liu, Y.; Shang, W.; et al. Plasmonic-Enhanced Oxygen Reduction Reaction of Silver/Graphene Electrocatalysts. Nano Lett. 2019, acs.nanolett.8b05053. Wang, C.; Nie, X.-G.; Shi, Y.; Zhou, Y.; Xu, J.-J.; Xia, X.-H.; Chen, H.-Y. Direct PlasmonAccelerated Electrochemical Reaction on Gold Nanoparticles. ACS Nano 2017, 11, 5897– 5905.


21


(17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35)

Page 22 of 31

Yu, Y.; Williams, J. D.; Willets, K. Quantifying Photothermal Heating at Plasmonic Nanoparticles by Scanning Electrochemical Microscopy. Faraday Discuss. 2018, 00, 1–3. Yu, Y.; Sundaresan, V.; Willets, K. A. Hot Carriers versus Thermal Effects: Resolving the Enhancement Mechanisms for Plasmon-Mediated Photoelectrochemical Reactions. J. Phys. Chem. C 2018, 122, 5040–5048. Al-Zubeidi, A.; Hoener, B. S.; Collins, S. S. E.; Wang, W.; Kirchner, S. R.; Hosseini Jebeli, S. A.; Joplin, A.; Chang, W.-S.; Link, S.; Landes, C. F. Hot Holes Assist Plasmonic Nanoelectrode Dissolution. Nano Lett. 2019, acs.nanolett.8b04894. Richardson, H. H.; Carlson, M. T.; Tandler, P. J.; Hernandez, P.; Govorov, A. O. Experimental and Theoretical Studies of Light-to-Heat Conversion and Collective Heating Effects in Metal Nanoparticle Solutions. Nano Lett. 2009, 9, 1139–1146. Baffou, G.; Quidant, R.; García de Abajo, F. J. Nanoscale Control of Optical Heating in Complex Plasmonic Systems. ACS Nano 2010, 4, 709–716. Baffou, G.; Berto, P.; Bermúdez Ureña, E.; Quidant, R.; Monneret, S.; Polleux, J.; Rigneault, H. Photoinduced Heating of Nanoparticle Arrays. ACS Nano 2013, 7, 6478– 6488. FRENS, G. Controlled Nucleation for the Regulation of the Particle Size in Monodisperse Gold Suspensions. Nat. Phys. Sci. 1973, 241, 20–22. Nikoobakht, B.; El-Sayed, M. A. Preparation and Growth Mechanism of Gold Nanorods (NRs) Using Seed-Mediated Growth Method. Chem. Mater. 2003, 15, 1957–1962. Scarabelli, L.; Sánchez-Iglesias, A.; Pérez-Juste, J.; Liz-Marzán, L. M. A “Tips and Tricks” Practical Guide to the Synthesis of Gold Nanorods. J. Phys. Chem. Lett. 2015, 6, 4270– 4279. Scarabelli, L.; Grzelczak, M.; Liz-Marzán, L. M. Tuning Gold Nanorod Synthesis Through Prereduction with Salicylic Acid. Chem. Mater. 2013, 25, 4232–4238. Saha, P.; Hill, J. W.; Walmsley, J. D.; Hill, C. M. Probing Electrocatalysis at Individual Au Nanorods via Correlated Optical and Electrochemical Measurements. Anal. Chem. 2018, 90, 12832–12839. Hahn, D. W.; Ozisik, M. N. Heat Conduction, 3rd Ed.; Wiley, 2012. Gueshi, T.; Tokuda, K.; Matsuda, H. Voltammetry at Partially Covered Electrodes Part I. Chronopotentiometry and Chronoamperometry at Model Electrodes. J. Electroanal. Chem. 1978, 89, 247–260. Peerce, P. J.; Bard, A. J. Polymer Films on Electrodes. Part II. Film Structure and Mechanism of Electron Transfer with Electrodeposited Poly(Vinylferrocene). J. Electroanal. Chem. 1980, 112, 97–115. Leddy, J.; Bard, A. J. Polymer Films on Electrodes. Part XII. Chronoamperometric and Rotating Disk Electrode Determination of the Mechanism of Mass Transport Through Poly(Vinyl Ferrocene) Films. J. Electroanal. Chem. 1983, 153, 223–242. Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1962. Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; 2001. Bourdillon, C.; Demaille, C.; Moiroux, J.; Saveant, J.-M. Catalysis and Mass Transport in Spatially Ordered Enzyme Assemblies on Electrodes. J. Am. Chem. Soc. 1995, 117, 11499– 11506. Bentley, C. L.; Kang, M.; Unwin, P. R. Nanoscale Structure Dynamics within Electrocatalytic Materials. J. Am. Chem. Soc. 2017, 139, 16813–16821.


22

Page 23 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(36)

(37) (38) (39) (40) (41) (42)

(43) (44) (45)

Snowden, M. E.; Güell, A. G.; Lai, S. C. S.; McKelvey, K.; Ebejer, N.; O’Connell, M. A.; Colburn, A. W.; Unwin, P. R. Scanning Electrochemical Cell Microscopy: Theory and Experiment for Quantitative High Resolution Spatially-Resolved Voltammetry and Simultaneous Ion-Conductance Measurements. Anal. Chem. 2012, 84, 2483–2491. Bentley, C. L.; Edmondson, J.; Meloni, G. N.; Perry, D.; Shkirskiy, V.; Unwin, P. R. Nanoscale Electrochemical Mapping. Anal. Chem. 2018, acs.analchem.8b05235. Kang, M.; Perry, D.; Bentley, C. L.; West, G.; Page, A.; Unwin, P. R. Simultaneous Topography and Reaction Flux Mapping at and Around Electrocatalytic Nanoparticles. ACS Nano 2017, 11, 9525–9535. Bentley, C. L.; Kang, M.; Unwin, P. R. Nanoscale Surface Structure–Activity in Electrochemistry and Electrocatalysis. J. Am. Chem. Soc. 2018, jacs.8b09828. Cai, Y.-Y.; Liu, J. G.; Tauzin, L. J.; Huang, D.; Sung, E.; Zhang, H.; Joplin, A.; Chang, W.S.; Nordlander, P.; Link, S. Photoluminescence of Gold Nanorods: Purcell Effect Enhanced Emission from Hot Carriers. ACS Nano 2018, 12, 976–985. CRC Handbook of Chemistry and Physics, 89th ed.; Lide, D. R., Ed.; CRC Press, 2008. Ferrer-Argemi, L.; Cisquella-Serra, A.; Madou, M.; Lee, J. Temperature-Dependent Electrical and Thermal Conductivity of Glassy Carbon Wires. In 2018 17th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm); IEEE, 2018; Vol. 6, pp 1280–1288. Shinzato, K.; Baba, T. A Laser Flash Apparatus for Thermal Diffusivity and Specific Heat Capacity Measurements. J. Therm. Anal. Calorim. 2001, 64, 413–422. Glassy Carbon Product Information https://www.2spi.com/catalog/documents/GlassyVitreous-Carbon-Info.pdf (accessed Feb 5, 2019). Cappelletti, R. L.; Udovic, T. J.; Li, H.; Paul, R. L. Glassy Carbon, NIST Standard Reference Material (SRM 3600): Hydrogen Content, Neutron Vibrational Density of States and Heat Capacity. J. Appl. Crystallogr. 2018, 51, 1323–1328.


23


Page 24 of 31

Figure 1: Predicted temperature increases in the vicinity of absorbing nanoparticles and nanoparticle arrays considering only conduction. (a) Calculated temperature increase per unit intensity at the surface of an isolated nanoparticle as a function of time (top) and the temperature profile in the vicinity of the nanoparticle during heating (bottom). (b) Calculated temperature increase per unit intensity at the surface of a glassy carbon electrode decorated with a square array of nanoparticles as a function of time (top) and the calculated temperature increase along the axis perpendicular to the interface after 5 s of heating. Calculations were carried out using the equations given in the text, assuming a nanoparticle radius of 10 nm, 𝑄𝑎𝑏𝑠 = 1, and an interparticle spacing of 100 nm for the array. The black and red lines in the bottom panel of (b) show an exact solution to the temperature profile (given in the SI) and the linear approximation provided in the main text, respectively. Note the drastically different scales in panels (a) and (b).


24

Page 25 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2: Example velocity (left) and temperature (right) profiles in an electrochemical cell with a heat source at the electrode surface. Results from finite element simulations of heat transfer which includes contributions from both conduction and convection for a 1.5 mm radius glassy carbon electrode in water with a heat input at the surface, 𝑞𝑖𝑛, of 10 W cm-2. Velocity magnitude and temperature data are encoded via the indicated colormaps, and values are given 10 s after the initiation of heating. The bottom panels give the vertical profile of the z-component of the solution velocity, 𝑣𝑧, and the temperature. The red curve in the bottom-right panel gives the corresponding temperature profile calculated via the 1-D equations which neglect convection.


25


Page 26 of 31

Figure 3: Results from finite element simulations of a large-amplitude potential step experiment with intermittent heating at the interface of a glassy carbon electrode and an aqueous electrolyte. Calculations were carried out for a 1.5 mm radius electrode in an aqueous solution containing 1 mM of a redox species with a diffusion coefficient of 1 × 10-5 cm2 s-1 initially at 300 K. Results are given for an axisymmetric 2-D model treating convection (left) and a linear model neglecting convection (right).


26

Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4: Power dependence of transient current increases resulting from an intermittent heat source at the surface of a 1.5 mm radius glassy carbon electrode in an aqueous electrolyte. (a) Current increases calculated as the difference between the 4 W cm-2 current transients given in Figure 3 and the corresponding ideal Cottrell response. (b) Maximum current increase (e.g., at point of dashed line in (a)) observed as a function of the heat input, 𝑞𝑖𝑛. The dashed lines give fits of the functions to a generic power law, Δ𝑖𝑚𝑎𝑥 = 𝐴𝑞𝑝𝑖𝑛.


27


Page 28 of 31

Figure 5: Experimental results from potential step experiments under intermittent illumination employing electrodes decorated with plasmonic nanoparticles. (a) Experimental schematic depicting an electrode decorated with a large number of nanoparticles (not to scale) and the applied potential/illumination waveforms. (b) Aqueous phase visible absorption spectrum of the spherical (17 nm diameter) Au nanoparticles employed in these studies. The dashed line denotes the 532 nm excitation wavelength, and the inset gives a 200 nm x 200 nm TEM image of the nanoparticles. (c) Current-time curve recorded in an aqueous solution of 0.5 mM FcMeOH, 100 mM LiClO4 after stepping from open circuit to 0.8 V vs. Ag/AgCl showing transient behavior resulting from illumination. (d) Maximum current increases above baseline (Δ𝑖) as a function of the estimated heat input, 𝑞𝑖𝑛. The data provided in panel (c) was obtained with the highest employed intensity ( 𝑞𝑖𝑛 ≈ 0.56 W cm-2). Panels (e) and (f) give similar data for an aqueous solution containing 2 mM N2H4, 25 mM trisodium citrate, and 25 mM citric acid, stepping the potential from open circuit to 1.3 V vs. Ag/AgCl. All electrochemical data was obtained with a 1.5 mm radius glassy carbon electrode, and the current values given in (d) and (f) are normalized to the concentration of redox species employed and number of electrons involved in the respective reaction. See text for estimation of 𝑞𝑖𝑛. Corresponding cyclic voltammograms of these systems are provided in the SI.


28

Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6: Hydrazine oxidation at an individual Au nanorod under intermittent excitation. (a) Experimental schematic for electrochemical measurements at individual nanostructures. Individual Au nanorods were located optically and interrogated with pipette-based probes are described in a previous report.27 (b) Cyclic voltammograms recorded in the depicted geometry at an individual Au nanorod and a bare section of ITO under 50 W cm-2 broadband illumination chopped at 25 Hz. 1000 mV s-1 sweep rate. The corresponding scattering spectrum for the nanorod is also given (black points show raw data, the red line depicts a Lorentzian fit to the data).


29


Page 30 of 31

Table 1: Relevant physical constants Watera

Glassy Carbonb

𝜅 / W m-1 K-1

0.61

5

𝜌 / g cm-3

0.997

1.5

𝐶𝑝 / J g-1 K-1

4.18

0.7

𝛼 / cm2 s-1

0.0015

0.05

𝜂1 / Pa s

6.3 × 10-6

--

𝜖1 / eV

0.12

--

𝜂2 / Pa s

1.1 × 10-10

--

𝜖2 / eV

0.37

--

a. Quantities given are standard reference values at 300 K, except for the viscosity parameters, which were obtained from fitting viscosity data between 273 K and 373 K.41 b. Quantities given are representative values from various literature sources.42–45


30

Page 31 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


31

The Role of Heating in the Electrochemical Response of Plasmonic

Recommend Documents