Article pubs.acs.org/JPCC
First-Principles Study of the Charge Distributions in Water Confined between Dissimilar Surfaces and Implications in Regard to Contact Electrification Rui Fu, Xiaozhou Shen, and Daniel J. Lacks* Department of Chemical and Biomolecular Engineering, Case Western Reserve University, Cleveland, Ohio 44106, United States ABSTRACT: The role of humidity in contact electrification is complex and multifaceted. With the aim of elucidating this role, we carry out first-principles molecular dynamics simulations of water confined between dissimilar surfaces. We address water confined between the (0001) surfaces of quartz and sapphire, as these surfaces have simple structures that allow for rigorous simulation while also being amenable to experimental investigation. The water takes on a layered structure, with the molecules somewhat oriented by the electric fields that arise in the system. The simulations find that the quartz charges negatively with respect to the sapphire, which concurs with previous experimental results. Yet interestingly we find that the water phase obtains a significant positive charge; we believe that this effect can have consequences in the contact electrification process, and also elucidate several experimental results for changes in electrostatic charge due to changes in relative humidity or pressure.
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INTRODUCTION Contact electrification is a well-known phenomenon that occurs when the surfaces of materials are brought into contact and then separated. Everyday examples include children rubbing balloons on their hair, or a person walking across a rug and getting a shock as they touch a doorknob. Technologies have exploited intentional contact electrification for beneficial purposes, such as digital printing. Yet inadvertent contact electrification leads to serious problems in a wide range of industries, including the damage of microelectronic components, disruptions of granular solids processing operations such as fluidized beds, and the ignition of combustible solvents and dusts. Our scientific understanding of contact electrification is surprisingly quite limited, and the most basic aspects are still being debated.1−5 For example, the direction of charge transfer, that is, which surface charges positive and which charges negative, cannot be predicted or correlated with any material properties. It is not known if the charge carriers that are transferred between surfaces are electrons, ions, or nanoscopic bits of material. The role of rubbing during surface contact is not known: Does the energy imparted by the rubbing play a role in the charge transfer process, or does rubbing simply increase the areas of the surface actual in contact? Also, the role of humidity is not fully understood. We are all familiar with the decrease in contact electrification at high humidity, but (at least in some cases) contact electrification actually increases with increasing humidity at very low humidity.6,7 Why is it that contact electrification remains so poorly understood, while computational chemistry has become such a powerful tool for studying other material properties? The © 2017 American Chemical Society
answer is that contact electrification is very difficult to model because it is an inherently nonequilibrium quantum-mechanical process. It is clearly a quantum mechanical process due to the role of electrons and bonding. Regarding the nonequilibrium nature of the process, this can be understood as follows.8 The equilibrium state of all isolated materials is neutral (uncharged). However, when two materials are in contact or at very close proximity, a state with oppositely charged surfaces may be the equilibrium state; in this case, the Coulombic attraction of the oppositely charged surfaces provides the stabilization. As the surfaces separate after contact, the system will want to relax from the state with charged surfaces to the state with neutral surfaces. However, the kinetics of this charge “backflow” decreases exponentially with increasing separation between the surfaces. Beyond some critical separation, perhaps about a nanometer, the kinetics of charge transfer become effectively zero, and the system remains trapped in a nonequilibrium state with charged surfaces; this charged state is the final state observed in contact electrification processes. It is beyond the capabilities of the current state-of-the-art to carry out rigorous simulations of this nonequilibrium quantum-mechanical process. While it is not feasible to model the complete contact charging process described above, we can use first-principles molecular dynamics simulations to address the first step of this process, the charge distribution at equilibrium of two surfaces in contact. This step provides the driving force for contact Received: April 28, 2017 Revised: May 19, 2017 Published: May 19, 2017 12345
DOI: 10.1021/acs.jpcc.7b04044 J. Phys. Chem. C 2017, 121, 12345−12349
Article
The Journal of Physical Chemistry C electrification, and thus can address the question of how to predict the direction of charge transfer and correlate this direction to material properties. In our previous work, we addressed two surfaces in contact in dry conditions.9 To enable the rigorous application of firstprinciples methods and validation by comparison with experiment, we chose a simple system that could be studied both with simulations and with experiments: the (0001) surfaces of SiO2 quartz and Al2O3 alumina. We carried out firstprinciples calculations of the charge distribution of surfaces in contact and at small separations, and also experimental studies of the contact charging of these surfaces. Our calculation and experimental results were in agreement, in that both showed that quartz develops a negative charge while sapphire develops a positive charge. Yet surfaces generally have water adsorbed on their surfaces under ambient conditions, and this adsorbed water may play a key role in contact electrification. For this reason, we now examine the charge distribution of two surfaces where their contact is mediated by water. We study the case of water sandwiched between the (0001) surfaces of quartz and alumina; these surfaces have been well studied both experimentally and with simulations, including their interactions with water.10,11
Figure 1. Structure of the system being simulated. (a) View perpendicular to the xy plane. The simulation cell is hexagonal with sides of 9.52 Å and an angle of 120°. (b) View perpendicular to the yz plane. The simulation cell contains two slabs of materials, which are quartz and sapphire, respectively. The length of the box is 48.24 Å. Atoms are presented using colored spheres (white for H, red for O, yellow for Si, and pink for Al). Water molecules are positioned between the slabs.
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METHODOLOGY The contact charging between quartz and sapphire is investigated using first-principles molecular dynamic (MD) simulations. The energy and force on each nucleus are calculated using the electron states obtained by solution of the many-body Schrodinger’s equation in the density functional approximation using standard norm-conserving pseudopotentials.12 The generalized gradient approximation with the PBE functional13 is used to account for the exchange-correlation energy. The double-ζ polarized (DZP) basis set is used, which meets the requirements of computational speed and accuracy. We carry out simulations with thin slabs of quartz and sapphire oriented such that their (0001) crystallographic faces are perpendicular to the z-axis. Periodic boundary conditions are used in all directions. We note that these calculations are possible only due to the fortuitous similarity of the crystal structures of quartz and sapphire, which are hexagonal structures with lattice parameters a = 4.91 Å for quartz9 and a = 4.79 Å for sapphire.9 In the z dimension, the length of the repeat unit is c = 48.27 Å, which allows for gaps of approximately 10 Å between the quartz and sapphire slabs. The surfaces were hydroxylated following previous work,9 and an energy minimization was initially carried out to find the stable structure with which to begin the simulations. The simulation cell is shown in Figure 1. Water molecules were placed into one of the gaps between the quartz and sapphire slabs (the other gap remains as a vacuum). Three systems were studied, with either 18, 20, or 21 water molecules; these numbers of water molecules lead to water densities in the gap near the value for bulk water. The initial positions of water molecules were chosen randomly in the gap between quartz and sapphire, using the Packmol software package to avoid overlap of molecules.14 The molecular dynamics simulations were carried out in the NVT ensemble at a temperature of 500 K; this high temperature was used to increase the amount of dynamics occurring in the short simulation time. A time step of 1 fs was used for molecular dynamics simulation. Equilibration runs are carried out for 1 ps, and then data to be used for further
analysis are recorded after this equilibration time for up to 5 ps. The net charge on each atom is approximated by Hirshfeld net atomic population analysis, which distributes the electrons among bonded atoms in proportion to their free-atom densities at the corresponding distances from the nuclei.15 The SIESTA16 software package is used to carry out the simulations.
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RESULTS The density distributions obtained from our simulations are shown in Figure 2, where they are compared to the experimental density values for bulk quartz,17 sapphire,17 and water.18 The simulation densities for these thin slabs of quartz, sapphire, and water are close to the experimental values for the bulk phases (note the variations in the density of quartz and
Figure 2. Average density as a function of position. The experimental results for the density of water, quartz, and sapphire are shown in the graph with blue, green, and red lines, respectively. (a) Model with 18 water molecules. (b) Model with 20 water molecules. (c) Model with 21 water molecules. 12346
DOI: 10.1021/acs.jpcc.7b04044 J. Phys. Chem. C 2017, 121, 12345−12349
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The Journal of Physical Chemistry C
be understood in terms of the net charge of the quartz and sapphire surfaces, described below. The charge distribution in the system was determined with the Hirshfeld population analysis method. The average charge distribution is obtained over the course of the simulation, and the results are shown in Figure 5. In the absence of water
sapphire are due to the positions of crystal planes relative to the arbitrary bin positions of the histogram). It is evident from Figure 2 that the water density near the sapphire surface is lower than that near the quartz surface. Thus, the water molecules are more attracted to quartz than to sapphire. This conclusion concurs with the experimental result that water wets quartz more fully than sapphire; the water contact angle of quartz (28°) is lower than that of sapphire (64°).19 The water structure is analyzed in more detail. Figure 3a shows a snapshot of the system, and Figure 3b shows the
Figure 5. Total net charge on water (black), quartz (red), and sapphire (blue) phases.
molecules inside the gap, the quartz and sapphire slabs are both neutral; our previous work showed that the dry surfaces must be closer than about 4 Å for charge transfer to occur.9 However, when water molecules fill the gap between the surfaces, significant charge transfer occurs such that quartz has a large negative charge, sapphire has a slight negative charge, and the water has a positive charge to balance. The charge on each water molecule depends on its position in the system. As shown in Figure 6, the water molecules in the layer closest to quartz have the highest net charge. The water molecules closest to quartz also have a lower dipole moment; that is, the atomic charges on their oxygen and hydrogen atoms are smallest in magnitude, even though their net charge is highest. Note that the large negative charge of quartz causes the water molecules near quartz to be strongly oriented with their hydrogen atoms pointing toward the quartz surface, and the slight negative charge of sapphire causes the water molecules near sapphire to be weakly oriented with their hydrogen atoms pointing toward the sapphire surface.
Figure 3. Structural results for the system with 21 water molecules. (a) Snapshot of the system, focusing on the water phase. Note the layered structure of the water phase. Atoms are presented using colored spheres (white for H, red for O, yellow for Si, and pink for Al). (b) Probability distribution of water molecules as a function of position, where the position of a water molecule is defined as the position of the O atom.
probability density for the water molecules as a function of position. These results show that the water molecules exist in a layered structure. There are three layers of water, and in the case of 21 water molecules each layer has approximately 7 molecules. For the case of 18 water molecules, the numbers of molecules in the three layers are 7, 7, and 4 (the layer with fewer molecules is the one nearest to sapphire). The orientation of the water molecules is shown in Figure 4. In the layer closest to quartz, water molecules are strongly
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DISCUSSION AND CONCLUSIONS It is well-known that high humidity decreases the magnitude of contact electrification. For example, when the humidity is low, one is more likely to get a shock upon touching a doorknob after walking across a rug. The reason for lower electrostatic charging at high relative humidity is that the water layer that forms on the surface can provide a conductive path to enable charge on an object to leak to ground.20 However, the role of humidity in triboelectric charging may be more complicated. Several studies have shown that for some systems, at low humidity, the magnitude of contact charging increases with increasing humidity.6,7,21 It was proposed that interfacial water could form a water bridge between two surfaces that enables ion transfer between the surfaces.6 Our results demonstrate a new effect that interfacial water can have in regard to contact electrification, in that the interfacial water accumulates charge by electron transfer. This charge redistribution occurs due to the modification of electron states at the surfaces and in the water due to the presence of the other components. The consequences of this charge accumulation by the water would then depend on the nonequilibrium
Figure 4. Orientation of water molecules in each layer. (a) Definition of the vector used to describe the orientation of the water molecule. (b) Dot product of the normalized orientation vector with the z-axis vector. Note layer 1 is closest to the quartz surface, and layer 3 is closest to the sapphire surface.
oriented with the hydrogen atoms pointed toward the quartz surface. In the middle layer, the water molecules are randomly oriented. In the layer closest to sapphire, the water molecules show some small orientation with the hydrogen atoms pointed to the sapphire surface. The reason for these orientations can 12347
DOI: 10.1021/acs.jpcc.7b04044 J. Phys. Chem. C 2017, 121, 12345−12349
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Figure 6. (a) Average net charge per water molecule in each layer. (b) Absolute value of average net charge on O atom (red) and the two H atoms (blue) of each water molecule in each layer. Note layer 1 is closest to the quartz surface, and layer 3 is closest to the sapphire surface.
Notes
processes that occur as the surfaces are separated. As the surfaces move apart, (i) the charge will redistribute in the direction of neutralization of the surface, but this redistribution toward neutralization will not be complete for kinetic reasons, as discussed in the Introduction; and (ii) the water molecules will redistribute onto one of the two surfaces or desorb into the atmosphere. For these two reasons, the accumulation of charge in the water can lead to net charges on the separated surfaces, that is, contact electrification. The present simulation results find that quartz charges more negatively than sapphire. This simulation result concurs with our experimental results that show that contact electrification between (0001) surfaces of quartz and sapphire leads to quartz charging negatively and sapphire charging positively.9 Thus, there is some validation of the simulations in regard to contact electrification. These ideas may also elucidate some puzzling experimental results. Experiments have shown that changing humidity leads to changes in the electrostatic charge on a surface,22,23 and that decreasing pressure leads to discontinuous changes in the electrostatic charge on a surface at certain values of pressure.24,25 Previously, these phenomena have been interpreted as being due to the desorption of ions from the surface. However, the present results suggest that the phenomena could also be due to the desorption of adsorbed water molecules with partial charges that they could “take with them” when they desorb. Of course, electrons are discrete, and a single molecule cannot desorb with a partial charge, but rather there would be a quantum mechanical probability that the molecule desorbs with a unit electron charge. Finally, we looked into whether water dissociation occurs because previous investigators proposed that the resulting ions might be involved in charge transfer.26 We saw dissociation and recombination occur at the beginning of the simulations, but we believe this was an artifact of the initial configurations in the simulations. We did not see any water dissociation after the simulations had equilibrated. However, the absence of dissociation is not meaningful because of the small system size and short simulation time. For these reasons, our present simulations are not able to effectively address the question of water dissociation and its role in charge transfer.
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under grant number DMR-120648. The calculations were carried out using computational resources through the Ohio Supercomputing Center.
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Daniel J. Lacks: 0000-0002-9381-6804 12348
DOI: 10.1021/acs.jpcc.7b04044 J. Phys. Chem. C 2017, 121, 12345−12349
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