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Contact Potentials, Fermi Level Equilibration, and Surface Charging Pekka Peljo,*,† Joséa

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Contact Potentials, Fermi Level Equilibration, and Surface Charging Pekka Peljo,*,† Joséa Article pubs.acs.org/Langmuir Contact Potentials, Fermi Level Equilibration, and Surface Charging Pekka Peljo,*,† JoséA. Manzanares,‡ and Hubert H. Girault† † Laboratoire d’Electrochimie Physique et Analytique, École Polytechnique Fedéralé de Lausanne, EPFL Valais Wallis, Rue de l’Industrie 17, Case Postale 440, CH-1951 Sion, Switzerland ‡ Department of Thermodynamics, Faculty of Physics, University of Valencia, c/Dr. Moliner, 50, E-46100 Burjasot, Spain *S Supporting Information ABSTRACT: This article focuses on contact electrification from thermodynamic equilibration of the electrochemical potential of the electrons of two conductors upon contact. The contact potential difference generated in bimetallic macro- and nanosystems, the Fermi level after the contact, and the amount and location of the charge transferred from one metal to the other are discussed. The three geometries considered are spheres in contact, Janus particles, and core−shell particles. In addition, the force between the two spheres in contact with each other is calculated and is found to be attractive. A simple electrostatic model for calculating charge distribution and potential profiles in both vacuum and an aqueous electrolyte solution is described. Immersion of these bimetallic systems into an electrolyte solution leads to the formation of an electric double layer at the metal−electrolyte interface. This Fermi level equilibration and the associated charge transfer can at least partly explain experimentally observed different electrocatalytic, catalytic, and optical properties of multimetallic nanosystems in comparison to systems composed of pure metals. For example, the shifts in the surface plasmon resonance peaks in bimetallic core−shell particles seem to result at least partly from contact charging. ■ INTRODUCTION of an electric double layer around the particles. In addition, the forces between two spheres in contact are described. Although observation of potential differences when two metals To understand what happens upon metal−metal contact and are placed in contact dates back from the late 18th century how this phenomenon affects, for example, electrocatalytic, “electricians” and of course to the seminal work of Alessandro ff fi catalytic, and optical properties of bimetallic nanosystems, we Volta, the actual e ects of the contact electri cation are often must understand the governing principles. However, electro- neglected. Although bimetallic nanoparticles have recently chemists use different terms than solid state and semiconductor received increasing attention because of their promising 1−3 4−8 4,9 physicists, giving rise to additional confusion. In this article, we electrocatalytic, catalytic, and optical properties, it is describe the thermodynamics of the contact electrification from fi equally important to understand how contact electri cation can the point of view of an electrochemist. change and contribute to enhance these properties. The The history of the contact electrification until year 1900 has interaction of nanoparticles with their environment can, been comprehensively reviewed by Hong.11 The accurate sometimes drastically, shift the Fermi level of electrons in the measurement of the contact potential difference dates back to nanoparticles and influence their chemical and electrochemical the works of Hankel, Pellat, and Kelvin.12 Hankel studied an 10 properties as highlighted in a review by Scanlon et al. Contact apparatus based on a capacitor with two plates of different electrification can also significantly shift the Fermi level of materials, charging itself upon contact. When one plate was electrons in bi- or multimetallic structures in comparison with grounded and the other was insulated, the potential difference pure materials. This is important because these shifts in the increased with an increase in the separation distance between Fermi level can have a drastic effect on the properties of plates, enabling the measurement of the contact potential. multimetallic systems. For example, shifts observed in surface Pellat improved this method by connecting the first plate to a plasmon resonance of core−shell nanoparticles seem to result potentiometer to allow compensation of the contact potential. from contact electrification, as described vide infra. This so-called null method is very accurate, because even small, The aim of this article is to clarify the position of the Fermi uncompensated potentials resulted in measurable forces level after contact charging, to understand how much charge is between the capacitor plates, and this method was named transferred and where this charge is located, to give some idea about how these effects influence properties of these systems, Received: April 4, 2016 and to illustrate what happens when these particles are Revised: May 9, 2016 immersed in an electrolyte solution, leading to the formation Published: May 13, 2016 © 2016 American Chemical Society 5765 DOI: 10.1021/acs.langmuir.6b01282 Langmuir 2016, 32, 5765−5775 Langmuir Article after Kelvin. The sensitivity of the Kelvin probe was further electron at rest in a field-free vacuum. Then, the electronic increased by Zisman13 using vibrating plates coupled with energies in a metal have negative values. The work to bring this headphones as the detecting instrument. The state-of-the-art electron from the reference point to just outside of the metal is − ψ 20 ff system is now the Kelvin probe force microscope, allowing the e . The work function Φ=−eψμ − ẽ− is the di erence in measurement of the local contact potential difference between a the energies of the electron just outside of the metal (−eψ) and conducting atom force microscopy tip and the sample. This fi inside of the metal (μẽ−). The ionization energy (IE) is de ned technique allows the mapping of the surface topography and as the work to remove one electron from a particle. When the local work function with high spatial resolution. For further fi ff 14 state of charge is not signi cantly a ected by the removal of an details, the reader is directed to the review by Lee et al. electron, the IE can be approximated by The triboelectric electrostatic charging by friction has also 15 been covered in a review by Lacks and Sankaran, and is out of IE =−μẽ− =Φ+eψ (1) scope of this article focusing on the thermodynamics of the ψ ffi contact electrification. In 1951, Harper16 studied contact The electrostatic term e indicates that it is more di cult to electrification of different metal spheres. He demonstrated extract electrons from a particle that is positively charged. The that the amount of charge transferred upon contact of two basic concepts are further reviewed in the Supporting different metal spheres showed almost a linear relationship with Information. Electrons tend to flow in the direction that decreases the the contact potential difference between the two metals. To gradient of their electrochemical potential until it vanishes. This eliminate the effects of the triboelectric charging, the contact fl − process is known as Fermi level equilibration. In the case of two was achieved by a oating sphere apparatus, and the Volta A B 20 μ −−μ Helmholtz hypothesis that “the charge obtained on separating conductors A and B, the equilibrium condition is ẽ = ẽ. two bodies must have been present as a double layer when they This equilibrium is achieved through charge redistribution, and were in contact” was corroborated.16 These results clearly show hence it involves the electrostatic energy of the electrons. Thus, that when the separation between two spheres is increased, the the equilibrated Fermi level should be understood as the 21,24 fi − capacitance of the system changes: rst, the charge transfer electrochemical potential of the electrons, EF = μẽ; this is occurs to keep the Fermi levels of both spheres equal, and then also the highest occupied energy level at 0 K provided that at a certain threshold value, the tunneling of electrons is no these levels include the electrostatic potential energy. longer possible between the two spheres, and the charge When two conductors of different metals A and B carry remains constant.16 Because the capacitance of the system charges qA and qB, their energy is varies as a function of the separation, the electrostatic 1 1 interactions between the two equal spheres redistribute the W =Φ+Φ+()qqAA BB() qq AAψψ + BB surface charge, so that they can effectively be considered as e 2 (2) large dipoles.17 These large dipoles attract each other unless In the capacitance matrix formalism, the charges on the they have exactly the same charge (in this case they repel each conductors are expressed in terms of their (outer) electrostatic other).17 potentials and the self- and mutual capacitances as17 fi This article focuses on the contact electri cation from ⎛ ⎞ ⎛ ⎞ qA ⎛CC⎞ ψ A thermodynamic equilibration of the electrochemical potential ⎜ ⎟ ⎜ AA AB ⎟⎜ ⎟ of the electrons of two conductors upon contact. We have ⎜ ⎟ = ⎜ ⎟⎜ ⎟ ⎝ B ⎠ ⎝CC⎠⎝ B ⎠ recently proposed that the contact electrification in bimetallic q AB BB ψ (3) segregated systems can be quantitatively understood by simply ≡ A B fi At constant total charge qT q + q and xed spatial considering the system as a nanocapacitor, where a thin vacuum configuration of the conductors, the equilibrium condition layer separates the two metals. The potential difference (∂∂Wq/)A = 0with respect to the exchange of charge is between the two metals is directly given by the work function qCT, ij difference, and the amount of transferred charge can be achieved when the Volta potential difference is calculated simply from electrostatics.18 Comparison between ΔB ψψψ≡−()()//BA =−Φ−Φ≡−ΔΦBAe B e numerical simulations of the electrostatics and more A eq eq A comprehensive density functional theory (DFT) calculations (4) showed that the continuum calculations can satisfactorily From eq 1, this is equivalent to the Fermi level equilibration describe the general charge transfer behavior, but DFT A B μẽ−−= μẽ. Thus, the outer potentials of two conductors in calculations are required to accurately describe the atomic ff ff scale charge transfer at the metal−vacuum interface and to equilibrium di er in a quantity proportional to the di erence in fi − their work functions.
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