Driving Forces for the Triboelectric Charging of Well-Defined Insulating Material Surfaces

Home , Contact electrification, Triboelectric effect

DRIVING FORCES FOR THE TRIBOELECTRIC CHARGING OF WELL-DEFINED INSULATING MATERIAL SURFACES

ANDREW ERIC WANG

Submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Chemical and Biomolecular Engineering Department

CASE WESTERN RESERVE UNIVERSITY

May, 2020 CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

ANDREW ERIC WANG

candidate for the degree of Doctor of Philosophy

Committee Chair

Daniel J. Lacks, PhD

Committee Member

Mohan Sankaran, PhD

Committee Member

John Angus, PhD

Committee Member

Isaac Greber, PhD

Date of Defense

March 16th, 2020

*We also certify that written approval has been obtained

for any proprietary material contained therein. Contents List of Tables ...... 2 List of Chapter 3 Tables ...... 2 List of Chapter 4 Tables ...... 2 List of Chapter 5 Tables ...... 2 List of Figures ...... 3 List of Chapter 3 Figures ...... 3 List of Chapter 4 Figures ...... 3 List of Chapter 5 Figures ...... 4 I Abstract ...... 5 II Introduction ...... 7 2.1. Introduction to triboelectric charging ...... 7 2.2. Select Examples of triboelectric charging ...... 8 2.3. Ongoing progress ...... 9 III First-principles calculation of contact electrification and validation by experiment ...... 11 3.1 Introduction ...... 12 3.2 Methods ...... 14 3.2.1 Calculations ...... 14 3.2.2 Experiments ...... 16 3.3 Results ...... 18 3.4 Discussion and conclusions ...... 24 3.5 Notes ...... 28 3.6 Additional Notes ...... 28 3.7 Acknowledgements ...... 29 IV Dependence of triboelectric charging behavior on material microstructure ...... 30 4.1 Introduction ...... 31 4.2 Methods ...... 32 4.2.1 Experiments ...... 32 4.2.1 Simulations ...... 35 4.3 Results ...... 37 4.3.1 Stress-strain measurements ...... 37 4.3.2 Triboelectric charging experiments ...... 38

4.3.3 Materials characterization ...... 41 4.3.3 Molecular simulations ...... 44 4.4 Discussion and conclusions ...... 47 4.5 Additional Notes ...... 50 4.6 Acknowledgements ...... 50 V Contact Charge Transfer Between Inorganic Dielectric Solids of Different Surface Roughness 51 5.1 Introduction ...... 52 5.2 Experimental ...... 53 5.3 Results ...... 55 5.3.1 Results on Glass Slides ...... 55 5.3.2 Results on N and P-type Silicon...... 60 5.4 Discussion and conclusions ...... 64 5.5 Additional Notes ...... 65 5.6 Acknowledgements ...... 65 VII Conclusions and Future Directions ...... 66 7.1. Conclusions and Future Directions ...... 66 Bibliography ...... 69 Introduction ...... 69 First-principles calculation of contact electrification and validation by experiment ...... 72 Dependence of triboelectric charging behavior on material microstructure ...... 74 Contact Charge Transfer Between Inorganic Dielectric Solids of Different Surface Roughness 80

List of Tables

List of Chapter 3 Tables

[p 22] Table 3.1. Averaged net surface charge density of quartz and sapphire

List of Chapter 4 Tables

List of Chapter 5 Tables

[p 53] Table 5.1. Glass slide roughness categories

[p 58] Table 5.2. Summary of polarity data on glass slides

[p 61] Table 5.3. Summary of polarity data on silicon

List of Figures

List of Chapter 3 Figures

[p 15] 3.1 Modeled [0001] quartz and [0001] sapphire system

[p 19] 3.2 Total energy of quartz-sapphire system as a function of separation distance

[p 20] 3.3 Charge on sapphire and quartz slabs from simulation

[p 21] 3.4 Raw net surface charge densities from contact charging of sapphire against

quartz as a function of humidity

[p 23] 3.5 Averaged XPS spectra of [0001] sapphire and [0001] quartz

[p 24] 3.6 Electrostatic potential energy obtained from DFT calculations of surfaces

[p 28] 3.7 Charge on sapphire slab obtained from calculations

List of Chapter 4 Figures

[p 34] 4.1 Asymmetric and Symmetric contact of PTFE Strips

[p 37] 4.2 Stress-strain measurements for PTFE films

[p 40] 4.3 Summary of contact charging measurements

[p 41] 4.4 XRD and Raman characterization of PTFE samples

[p 42] 4.5 Transmittance of strained and unstrained PTFE

[p 43] 4.6 Optical images of void growth in strained PTFE films

[p 44] 4.7 SEM images of PTFE films strained to fracture

[p 44] 4.8 Simulation results for molecular properties of PTFE

[p 45] 4.9 Simulation results of microstructure of PTFE system

[p 47] 4.10 Quasistatic simulations of void formation

List of Chapter 5 Figures

[p 54] 5.1 Optical comparisons of glass roughness

[p 56] 5.2 Mean net charge transfer densities with and without UV excitation

[p 57] 5.3 Triboelectric series of glass at different surface roughness

[p 62] 5.4 Mean net charge densities of smooth and rough N-type and P-type silicon

wafers

[p 63] 5.5 Charge density of glass slides of varying surface roughness on various other

materials

Driving Forces for the Triboelectric Charging of Well-Defined Insulating Material Surfaces

I Abstract

ANDREW ERIC WANG

I Abstract Triboelectric charging and contact electrification are everyday phenomena that both practical uses and potential hazards. Familiarity with the effects can include shocks when touching other surfaces during a dry day, or as the principal mechanism for laser printers. But the less commonly known effects are the influences on dust and sand saltation, industrial hazards through clogging of feed materials and even dust or grain silo explosions, and lightning occurrences during storms and in volcanic plumes. The process can simply be described as: two surfaces come into contact, transfer charge, and upon separation, have a different electrical charge. However, given two different materials, predicting which material surface charges positive, and which charges negative is not always reliable. And, the common understanding of the phenomena cannot explain why

the contact of two surfaces of chemically identical composition can even produce a net

charge on each other. A fundamental understanding of the mechanisms behind

triboelectric charging is still debated.

In this dissertation, we report mechanisms that drive triboelectric charging on

well-defined insulating surfaces through the use of experiments, simulations, and

modeling. Specifically, the effects of chemical composition, strain, and surface roughness

were explored by carrying out triboelectric charging experiments with single-crystal

surfaces, uniaxially stretched polytetrafluoroethylene (PTFE), and dielectric surfaces of silicon and silica.

II Introduction

2.1. Introduction to triboelectric charging

Triboelectric charging can be defined as the charge transfer that occurs as the result

of contact. It is also known as electrostatic charging and contact electrification. This

common phenomenon occurs when two surfaces come into contact, charge transfers, and

after separation, the surfaces remain electrically charged.

Triboelectric charging is used in many applications today. It is the primary

mechanism behind laser printers, automotive spray painting, and it is also used in

separation processes. In the future, it may be used to harvest energy using triboelectric nanogenerators. However, if unmitigated, triboelectric charging can also be very dangerous. Static discharge can break sensitive computer equipment and serve as the ignition source for grain silo explosions. Triboelectric charging is also the primary mechanism in lighting and volcanic lightning. In manufacturing, it can cause flow processes to clog up and create a non-uniform final product [1]. Terrestrially, knowledge of global transport of sand and dust is important for understanding the redistribution of minerals leading to the degradation of agricultural areas, its impact on air quality, and its precarious role in the global climate [2,3]. In the future, electrostatic charging of dust will have to be controlled as it presents a health hazard and a nuisance for future space missions.

2.2. Select Examples of triboelectric charging

Daily life: Anyone who has experienced a dry winter has also experienced the glow

and crackling of static discharge while taking off a sweater and the pain of getting

“shocked” by touching a metal doorknob. This phenomenon occurs because the human

body and the articles of clothes build up charge when rubbed together. When the semi-

conductive human skin touches a very conductive metal doorknob, the charge built up can

be violently neutralized on the metal surface in the form of static discharge, similar to a

small-scale lightning bolt. A more pleasant example of triboelectric charging would be

rubbing a party balloon on someone’s hair to get the hairs to stick up and repel each other.

Power Generation: Although it is still a developing technology, Triboelectric Nano

Generators (TENGs) work on the principle that bringing two different dielectric materials

into contact, triboelectric charge transfer will occur, and when the materials start to

separate, there will be a voltage potential that can drive electron flow[4]. When compared

to electric-magnetic generators, TENGs can operate more efficiently at lower frequencies

and will be optimal for areas where batteries are not ideal, such as remote sensors and

pacemakers. Another potential scale up opportunity would be in the form of wearable

TENGs to be able to charge a mobile device and harness the power of the impinging rain

[5,6].

Space and Beyond: During the Apollo missions, the tiny particles of lunar dust proved to be dangerous for man and machine. Due to the lack of terrestrial weathering and constant bombardment by ions from the sun, the electrostatically charged, abrasive dust clung to everything causing mechanical failures. This process can also lead to silicosis

“miner’s lung.”[7] Future lunar and Martian missions will deploy electrodynamic screens to clear off solar panels, and electrostatic filters to protect future explorers [8,9].

2.3. Ongoing progress

Surprisingly, for how much we interact with triboelectric charging and know about its potential hazards, the mechanisms driving triboelectric charging are still poorly understood [10-12]. Previously triboelectric experiments were as simple as rubbing two materials against each other and observing which material would charge positively and which material would charge negatively. The results would be recorded on a series, much like the periodic table [13]. But unlike the periodic table, no systematic pattern revealed itself. Materials on the triboelectric series could often switch places depending on conditions, and occasionally, charging loops would occur [14]. A table like this also does not explain how materials of the identical chemical composition would be able to charge one another [15-17]. This drove workers to study the mechanisms behind triboelectric charging and determining the charge carriers, whether they be electrons [15, 16], ions [14,

17], or material transfer [18, 19], or possibly a superposition of all three.

The underlying theme of this dissertation is about symmetry or breaking symmetry and how it drives triboelectric charging. In Chapter 3, given well-characterized surfaces and adequate experimental controls, can we reliably drive charge between two different single perfect crystals of sapphire and quartz, and explain it with simulation techniques with state-of-the-art supercomputers. In Chapter 4, we look into how two samples of chemically identical polytetrafluoroethylene (PTFE) can reliably drive charging if one sample has been strained and the effects of microstructure. Chapter 5, experiments and

mathematical modeling show how surface roughness directs the transfer of charge carriers on doped silicon and glass surfaces.

III First-principles calculation of contact electrification and validation by experiment

[Published: Shen, X., Wang, A. E., Sankaran, R. M., Lacks, D. J., "First-principles calculation of contact electrification and validation by experiment" J. Electrostat., 82 (2016), 11–16. With Corrigendum to “First-Principles Calculation of Contact Electrification and Validation by Experiment”]

Contributions: First-principle calculations and modeling were performed by Xiaozhou

Shen. Experiments were led by Andrew Eric Wang.

Contact electrification is one of the most well-known phenomena in physics and examples arise in almost every industry. However, a scientific basis for contact charging remains unknown. Here, we present a theoretical study of contact electrification, supported by experiments, to calculate for the first time charge transfer between material surfaces from first principles physics. Electronic structure calculations and experiments are performed on single-crystal alumina (sapphire) and silicon oxide (quartz) surfaces, which have well-ordered structures that enable rigorous modeling. Both experiments and calculations show that sapphire charges positively and quartz charges negatively. The calculations cannot determine the magnitude of charge densities remaining on separated surfaces from first principles, as these are non-equilibrium effects, but our analysis is consistent with experimentally obtained charge densities of 10 mC/m2. These results indicate the possibility of quantitatively predicting and explaining contact electrification from only the molecular structure of material surfaces.

3.1 Introduction

When two initially uncharged material surfaces come in contact and then separate,

an exchange of charges can occur such that one surface becomes positively charged and

the other becomes negatively charged. This basic description of “contact electriﬁcation”

is one of the most well-known phenomena in physics, and examples arise in almost every

industry. However, a scientiﬁc basis for contact charging remains unknown [11]. It is

not clear whether the species transferred between surfaces that lead to charging are

electrons, ions, or bits of material [14, 20], how the direction of net charge transfer

depends on material properties [21], or why the charge is heterogeneous both in terms of

polarity and magnitude across the surface [19]. It is possible that various mechanisms may occur, with different species dominating in different situations. For example,

Baytekin et al. [18] recently showed that when polytetraﬂuoroethylene (PTFE) beads are

rolled in a polystyrene dish, the beads charge negatively after a short amount of rolling,

but then become positively charged after a longer amount of rolling. The initial charging

may be due to electrons or ions transferring; however, the shift in the polarity of the

charging at later times was shown to be due to nanoscale patches of material being torn

off and transferred to the other surface. Thus, even in a single experiment, more than one

mechanism can contribute, complicating the charging process.

To fully understand these issues, it will be necessary to model contact charging

with a rigorous approach that draws only on the most fundamental laws of physics, with

no empiricism or experimental input. Experiments alone cannot resolve these issues.

Ideally, the modeling approach should take as input only the molecular description of the

materials involved, and determine the contact charging behavior from this information

alone. Since electron transfer can play a role, the approach must explicitly model the

electron states of the system, which requires quantum mechanical methods. And since

electron states in macroscopic solids are delocalized, the modeling must consider a

system large enough to behave like a macroscopic solid, rather than just a molecular

fragment. Such quantum mechanical calculations on extended systems are

computationally intensive, and to become at all feasible we must consider the simplest

systems possible. Unfortunately, most previous experiments on contact charging

addressed polymers, which are very: (1) complex because they are structurally

heterogeneous, with a distribution of molecular weights and branching; (2) often have

semi-crystalline structures, which are more complicated than either fully crystalline or

fully amorphous structures; (3) are in non-equilibrium states, such that the structures

change with time and are sample-history- dependent; and (4) contain impurities that arise either during processing, such as residuals of catalyst and catalyst support, or from chemical degradation due to oxidation.

Here, we present contact charging results for well-defined materials that can be addressed with both rigorous first- principles calculations and experiments. We examine contact between particular crystallographic surfaces of single-crystal quartz (SiO2) and single-crystal sapphire (Al2O3; we use the term ‘sapphire’ to describe the crystal structure, which is also known as corundum and a-Al2O3). Our calculations and experiments both find sapphire charging positively and quartz charging negatively. To our knowledge, this is the first corroboration of contact charging between rigorous first- principles calculations and experiments. While this study focuses on well-defined

materials that facilitate modeling, our approach may eventually ﬁnd application to other

materials including polymers.

3.2 Methods 3.2.1 Calculations

We addressed contact charging using a ﬁrst-principles approach that takes as input only the molecular description of the component materials involved. We modeled the complete three- dimensional structure of the solid system at the electronic structure level. The electron states were determined, and from the electron states the energy of the system and the forces on the atoms were obtained. Quantum mechanical methods are required to determine the electron states; i.e., the many-body Schrodinger's equation is solved within a set of approximations. The approximations used were based on density functional theory and the use of an atomic orbital basis set. In particular, the Kohn-Sham equations were solved with the PBE functional [22] and the double-zeta with polarization functions basis set. The calculations were carried out with the SIESTA software [23].

The system we modeled is shown in Figure 3. 1. The interface consisted of the

(0001) crystallographic planes of quartz and sapphire oriented parallel to each other.

Periodic boundary conditions were used, and so the surfaces are inﬁnitely wide. It is fortuitous that we can model this system, and we are only able to do so because quartz and sapphire both have monoclinic structures with similar a lattice parameters: a 4.91 Å for quartz [24] and a 4.79 Å for sapphire [25]. Our simulation cell extended two unit cells in the directions parallel to the surface; periodic boundary conditions were applied in these directions with the repeat unit 9.516 Å. In the direction perpendicular to the surfaces, the materials were ﬁnite in thickness, with the layers of quartz and sapphire each being two unit cells thick. The surfaces were hydroxylated, and we began our

simulations with structures previously reported for quartz [26] and sapphire [27] at ambient conditions. The distance between the quartz and sapphire surfaces was varied, and ranged from 1.4 Å to 10 Å. Periodic boundary conditions were also used in the direction perpendicular to the surfaces (these boundary conditions must be applied in all dimensions); however, the repeat distance was chosen to be large enough (50 Å3) to limit interactions to only one quartz-sapphire interface (and not with the periodic image). The simulation cell included 268 atoms, with 132 atoms in the quartz slab and 136 atoms in the sapphire slab.

We ﬁrst obtained the minimum energy structures for the separate quartz and sapphire slab systems; the energy-minimized structures agreed well with previous work for quartz [26] and sapphire [27]. In our calculations of the complete system with both quartz and sapphire slabs, we kept the atom positions ﬁxed at these minimum energy positions.

Figure 3.1. System examined in the calculations. (left) view from the side, with quartz on left and sapphire on right; (middle) quartz [0001] surface; (right) sapphire [0001] surface. In these ﬁgures oxygen is red, silicon is yellow, aluminum is brown, and hydrogen is white. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

3.2.2 Experiments

Contact charging experiments were carried out in a humidity- controlled acrylic

glove box (Electro-Tech Systems Inc.) with feed-throughs for electrical connections and gas fittings. The humidity inside the glove box was controlled with an air stream containing water vapor. The lowest humidity was obtained by flowing only dry air. To increase humidity, a wet air inlet stream was created by bubbling dry air through a heated water bath to reach a desired saturated water vapor concentration. A fan inside the glove box was used to enhance mixing of the inlet air stream with the background air in the glove box. Once the desired steady-state humidity was established in the glove box, the air flow was shut off and experiments were performed in a static (no flow) condition. The humidity and temperature in the glove box were monitored with a digital probe (EQ-RH-

606B). This method was able to achieve desired set points between 5% and 95% ± 0.3%.

We focused on single-crystal oxides for this study. The samples were 1 cm2, 0.5

mm thick, single crystallographic cuts of sapphire [0001] and quartz [0001] (MTI

Corporation), with one side polished; some experiments were also carried out with

MgO periclase (001) (MTI Corporation). Samples were cleaned before contact by the

RCA [28, 29] wafer cleaning recipe, omitting the oxide strip setup. Brieﬂy, the samples

were immersed in a 1:1:5 (v/v/v) mixture of 29% ammonia, 30% hydrogen peroxide, and

distilled water and sonicated at 25 °C for 20 min. The samples were then rinsed and

submerged in distilled water for 1 min. They were then treated in a 1:1:6 (v/v/v) mixture

of 15 M hydrochloric acid, 20% hydrogen peroxide by sonication at 25 °C for 20 min.

The samples were then rinsed and submerged in distilled water for 1 min. Finally, the samples were removed and any residual water was blown off by compressed dry air for 5 s on each face, and placed polished side down in clean polystyrene cells. The cleaned and dried substrates were stored inside the humidiﬁed glove box overnight (>8 h) to equilibrate before the contacting experiments.

Wooden dowels were glued to the unpolished side of each sample (General

Purpose Hot-Melt glue, McMaster-Carr), and act as handles to hold the samples. Our tests showed that the wooden dowels and glue do not affect the charge measurements.

After an experimental trial, the dowels were removed, and the samples were cleaned as described above and reused.

The rubbing of the samples was carried out as follows. The samples were held by the wooden dowels, one in each hand. The samples were brought together, so that the polished sides of the two samples were in planar contact. One sample was held still, and the other sample was translated in the pattern of a circle of radius z3 mm while maintaining planar contact. This motion continued for 30 s. After this contact, each sample was sequentially placed inside a Faraday cup located inside the glove box, connected to an electrometer (Keithley 6517A) located outside of the glove box. The charge was directly measured and recorded by a LabVIEW program. The background drift in our Faraday pail setup was 10-15 to 10-17 C/ s, depending on the humidity inside the glove box (higher drift with higher humidity), and the initial baseline charge was on the order of 10-12 C. Charge measurements above this threshold value were thus considered to be real. For every charging experiment, the initial charge on each sample

was ﬁrst obtained and then the charge after contacting was measured. The surface charge

density was calculated based on the sample surface area of 1 cm2.

X-ray photoelectron spectroscopy (XPS) was performed with a PHI VersaProbe

XPS Microprobe. Spectra were collected from approximately three different spots on three different identically prepared quartz and sapphire samples, either immediately after cleaning or after the contact experiment; the results from these different samples were averaged.

3.3 Results

We ﬁrst describe our modeling results. In Figure 3.2, we show the total energy of

the system as a function of the separation distance between the two surfaces. Beyond a

separation of 4 Å, the surfaces do not interact, due in part to the localized nature of the

atomic orbital basis set. As the surfaces move closer to less than 4 Å, an attractive force

develops between the surfaces, which manifests in Figure 3.2 as the decrease in energy as

the surfaces come closer. At a separation of 2.4 Å, the attraction reaches a maximum, and

the energy begins to increase as the separation between the surfaces decreases. The

minimum energy separation between the surfaces is therefore approximately 2.4 Å; this

separation would correspond to the equilibrium separation, and smaller separations would

only be possible if an external force were applied to push the surfaces closer together.

Figure 3.2. Calculation results for the total energy of the quartz-sapphire system as a function of separation between the quartz and sapphire [0001] surfaces. The energy given is relative to the energy in the limit of large separation.

As the quartz and sapphire surfaces approach one another, the electron states from the two surfaces interact, and the electrons can redistribute between the quartz and sapphire slabs; i.e., electron transfer occurs. We use Mulliken population analysis to assess how the electrons partition to each slab. With Mulliken population analysis, the overlapping electron density between two atomic orbitals is split equally between the two atoms. By summing up electrons in atoms in the quartz slab and atoms in the sapphire slab, we can determine the charge on each slab. This analysis was carried out as a function of separation between the slabs, and the results are shown in Figure 3.3. The simulations show that quartz charges negatively and sapphire charges positively. We address the magnitude of the charge in the Discussion section, but here we note that the charge on the surfaces while in contact does not correspond to the charge on the surfaces that remains after separation.

Figure 3.3. Charge on sapphire and quartz slabs obtained from calculations, using Mullikan Population Analysis.

We now present our experimental results. Figure 3.4 shows cumulative measurements from a total of 91 trials of contact charging carried out between sapphire

(0001) and quartz (0001) surfaces at various humidities. We believe these results correspond to saturated charge, in that further contact would not increase the charge. In all experimental trials, independent of humidity, sapphire was found to charge positively and quartz was found to charge negatively, in agreement with the modeling results. The magnitude of the surface charge density increased with decreasing humidity, which is consistent with the usual inﬂuence of humidity on charging [30]. The mean values for the charge densities as a function of humidity, with the corresponding standard errors (one standard deviation divided by the square root of the number of samples) are summarized in Table 3.1. The mean charges of sapphire and quartz are measured independently, and are found to be the same in magnitude (but opposite in sign) at each value of humidity, which is evidence of the accuracy of the measurements. At the lowest humidity tested

(5% relative humidity) the magnitude of charge on the surfaces is approximately 10

mC/m2.

Figure 3.4. Net surface charge densities from contact charging of sapphire against quartz; open circles (B) represent sapphire trials, open squares (,) represent quartz trials, ﬁlled circles (•) represent sapphire average values, ﬁlled squares (-) represent quartz average values.

To assess the of material transfer mechanisms in our charging results, we carried out XPS measurements. Figure 3.5a shows averaged XPS survey spectra collected from sapphire surfaces before (black) and after (red) contact with quartz. Before contact, the cleaned surface shows peaks corresponding to Al and O with a ratio of ~30:52, which is in agreement with the equilibrium surface composition. Peaks from C and Si are believed to have originated from contamination, either on the surface that could not be removed by the cleaning procedure or from room air during transfer of the samples into the instrument. Importantly, no signiﬁcant differences were observed in the XPS- measured surface compositions before and after contact. Figure 3.5b shows the analogous averaged XPS survey spectra collected from quartz surfaces before (black) and after (red) contact with sapphire. Before contact, the cleaned surface shows peaks corresponding to

Si and O with a ratio of ~27:58, which is in agreement with the equilibrium surface

composition. Again, peaks from C and Al are detected which we attribute to contamination. After contact, there is no significant change in the measured surface compositions. Together, these results indicate that the amount of material transfer upon contact was insignificant, and we can conclude that material transfer did not play a significant role in the charge transfer mechanism.

Table 3.1 Summary of mean charge density for contact charging experiments between sapphire and quartz substrates as a function of relative humidity. The standard error corresponds to the first standard deviation of the experimental trials.

Relative Humidity Sapphire charge density Quartz charge density

(µC/m2) (%) (µC/m2)

5 10.01 ± 1.06 -8.66 ± 0.98

20 7.50 ± 1.00 -6.95 ± 0.98

70 6.07 ± 0.76 -6.13 ± 0.70

95 0.79 ± 0.18 -1.13 ± 0.27

Figure 3.5. Averaged XPS spectra collected from freshly cleaned surfaces (black), and surfaces after contact with one another as described in text (red). (a) [0001] sapphire; (b) [0001] quartz. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

We looked for a simple property to correlate the direction of charge transfer, and carried out further calculations and experiments in this regard. One possible property is the electrostatic potential energy, which represents the amount of work to move a positive charge to a speciﬁc position. The results for the electrostatic potential energy are shown in Figure 3.6. Since sapphire has lower electrostatic potential energy than quartz, it is more likely to attract a positive charge. This result is in agreement with the charging polarity observed experimentally. To test the generality of this correlation, we carried out brief studies with periclase (MgO crystal with the rocksalt structure). Since the periclase crystal structure is cubic, we could not perform calculations of periclase in contact quartz or sapphire (due to the different symmetry of the periodic boundary conditions).

However, we could obtain the average electrostatic potential energy relative to vacuum.

We ﬁnd that the order of the values of the average electrostatic energy relative to vacuum is periclase > sapphire > quartz; thus based on the electrostatic potential energy, we would predict periclase to develop a positive charge when contacted with either sapphire or quartz. To assess this prediction, contact charging experiments involving periclase were carried out at a relative humidity of 1%. For contact between sapphire and periclase we measured average charges of 13 ± 3.0 and -7.6 ± 2.1 mC/m2, respectively; for contact between periclase and quartz, we measured average charges of 14 ± 2.4 mC/m2 and 10 ±

2.8 mC/m2, respectively. These experimental results indicate a triboelectric series ordered from most positive to most negative as sapphire > periclase > quartz, which contradicts the ordering of the electrostatic potential energy. Thus the direction of charging in contact electriﬁcation cannot be simply predicted by the electrostatic potential energy.

Figure 3.6. Electrostatic potential energy obtained from DFT calculations of surfaces separated by 3 Å.

3.4 Discussion and conclusions

Contact charging is a non-equilibrium process that occurs as follows. When the surfaces of two materials are far away from each other, the equilibrium state of the

system corresponds to neutral surfaces. As the material surfaces come very close (within

a few Angstroms) or into contact, the equilibrium state can change such that the two surfaces are no longer neutral (due to electron transfer between the surfaces). As the surfaces move away from one another, the gap between the surfaces creates an energy barrier that inhibits the transfer of charge back to the neutral equilibrium state; the height of this barrier increases as the surfaces move apart. Once the surfaces move more than a few Angstroms apart, the barrier is so large that “electron backﬂow” is effectively zero;

Lowell and Rose-Innes estimated this distance to be approximately 10 Å [10]. In this way, some of the charge that had transferred when the surfaces were in contact becomes

“stuck”, and this “stuck charge” is what we would observe in contact charging experiments. The “stuck charge” is a non-equilibrium situation, which is observed

because the slow kinetics of the electron backﬂow prevents the system from reaching the

equilibrium state with neutral surfaces.

Our calculations are based on the equilibrium (lowest energy) state of the system.

Thus, in the calculations charge is always able to ﬂow back to the other surface during

separation (in contrast to actual contact charging experiments). The process in our

calculations is fully reversible and as the surfaces come together, the charge on the

surfaces follows the curves in Figure 3.3; likewise, as the surfaces move apart, the charge

on the surfaces again follows the curves in Figure 3.3, but in reverse so that the charge on

the surfaces goes to zero as the surfaces move far apart. Our methodology cannot

determine the point at which charge gets “stuck” due to the energy barrier created by

separation. Unfortunately, a non- equilibrium method that addresses the quantum

dynamics of the electrons as the surfaces move apart is far too computationally intensive

to be feasible.

However, we can test the applicability of our calculations to contact charging as

follows. Figure 3.7 shows calculation results for the charge on a sapphire surface

contacted with quartz on a log scale (the charge on the corresponding quartz surface is

equal in magnitude, but opposite in sign). Results at separations greater than 3.2 Å are

dominated by noise (i.e., numerical precision in the calculation) because the charge

values become very small. Therefore, we use an exponential ﬁt to extrapolate our data to

larger separations; an exponential functional dependence is expected because the charge

transfer is due to the overlap of electron wavefunctions, and wavefunctions decay

exponentially with distance [31]. We can assume that the charge on the surfaces will

follow the values given by this extrapolation until a point is reached where electron

backﬂow can no longer occur. We see that this extrapolation reaches the value of the

charge found experimentally (10 mC/m2) at about 8 Å; so if electron backﬂow ceases to

occur for separations greater than 8 Å, the charge of 10 mC/m2 would be “stuck” on the

surfaces as the surfaces move far apart. Thus our modeling results, combined with a

physically reasonable distance for where the electron backﬂow would cease to occur [10], leads to the charge density of 10 mC/m2 that is found in our experiments. Thus, we

conclude that our ﬁrst-principles calculations are consistent with the experimental results.

While our ﬁrst-principles calculations are consistent with the experimental results,

we note a couple of important caveats: (a) the distance taken for where electron backﬂow

ceases (8 Å), while being physically appropriate, is nonetheless arbitrary; other

physically appropriate distances for this parameter would give results that differ

somewhat from experiment; and (b) the extrapolation of charge density data less than 3.2

Å to estimate the value of the charge density at 8 Å will very likely have inaccuracies.

For these reasons we note that our modeling results cannot be considered to be predictive or deﬁnitively in agreement with experiment; rather, our analysis shows that the modeling is consistent with experiment.

The charge transfer results from our ﬁrst-principles calculations, which address only an electron transfer mechanism of charge transfer, can explain our experimental results. Our results suggest that it is an electron transfer mechanism that underlies charge transfer in the quartz-sapphire system. We note that ion transfer and material transfer mechanisms have been shown to play roles in at least some circumstances. The results of our XPS experiments do not show evidence of material transfer, and thus we conclude that the material transfer mechanism is not important for the quartz- sapphire system, perhaps because these materials are both very hard. We cannot rule out an ion transfer mechanism, and of course the possibility exists that the consistency of the calculations with experiment is fortuitous and that an ion transfer mechanism not addressed in our calculations actually dominates. Finally, we note that it is likely that the different charge transfer mechanisms (electron, ion, material) dominate under different conditions and for different materials, and if indeed an electron transfer mechanism dominates for the quartz-sapphire system at low humidity, this will not necessarily apply to other situations and materials.

Figure 3.7. Charge on sapphire slab obtained from calculations. The line is an exponential ﬁt to the data.

3.5 Notes The authors declare no competing ﬁnancial interests.

3.6 Additional Notes The calculations solve the Shrodinger equation, within appropriate approximations, for the electrons for the entire system, including both alumina and silica slabs. The results are the wavefunctions of the electrons and the associated energy of the wavefunction, i.e., Eigenfunction and Eigenvalue of the Shrodinger equations, respectively, and the electron spatial distributions are obtained as the square of the wavefunctions. We were interested in the total electron distribution, which is obtained as the sum of squares of the wavefunctions of all the electrons. To find the band offsets as the alumina and silica slabs are in close proximity, one would want to look at the spatial distributions of particular wavefunctions and their energies. The band offset would then be calculated by comparing the energies of the highest energy occupied wavefunctions on

the two sides of the interface. However, we did not do this analysis, as we were only looking at overall spatial distributions of the electrons.

3.7 Acknowledgements

This material is based upon work supported by the National Science Foundation under grant numbers CBET-1235908 and DMR- 1206480. The calculations were carried out using the computational resources of the Ohio Supercomputing Center.

IV Dependence of triboelectric charging behavior on material microstructure

[Published: Wang, A. E., Gil, P. S., Holonga, M., Yavuz, Z., Baytekin H. T., Sankaran, R. M., Lacks, D. J., "Dependence of triboelectric charging behavior on material microstructure", Phys. Rev. Materials, 1 (2017), 035605. Including supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevMaterials.1.035605 for additional experimental and simulation data.]

Contributions: Simulations done in GROMACS were performed by Phwey Sang Gil.

Experiments and analysis were led by Andrew Eric Wang.

We demonstrate that differences in the microstructure of chemically identical

materials can lead to distinct triboelectric charging behavior. Contact charging

experiments are carried out between strained and unstrained polytetrafluoroethylene

samples. Whereas charge transfer is random between samples of identical strain, when

one of the samples is strained, systematic charge transfer occurs. No significant changes

in the molecular-level structure of the polymer are observed by XRD and micro-Raman spectroscopy after deformation. However, the strained surfaces are found to exhibit void and craze formation spanning the nano to micrometer length scales by molecular dynamics simulations, SEM, UV-vis spectroscopy, and naked-eye observations. This suggests that material microstructure (voids and crazes) can govern the triboelectric charging behavior of materials.

4.1 Introduction

Triboelectric charging describes the process by which two material surfaces

become electrically charged after physical contact and separation [11]. Examples of

triboelectric charging are ubiquitous, from useful technologies such as xerography [32]

and energy harvesting devices [33], to undesired consequences such as damage to

microelectronic device components [34], disruptions to industrial polymer processes [35]

and agglomeration in pharmaceutical powders [36]. Triboelectric charging also appears

in the natural environment, including dust storms and volcanic explosions [37] and has

likely played a key role in the formation of planets [38] and the origin of life [39].

Despite having been a topic of study since antiquity [40], triboelectric charging remains

largely unpredictable, with essentially no scientific understanding of even the most

fundamental aspects [41]. The most basic question in triboelectric charging is what

determines the direction of charge transfer, i.e., which surface will charge negative and

which positive when contacted. The current best approach for addressing this question is

the “triboelectric series”, which refers to an ordering of materials in terms of their

propensity to acquire positive or negative charge when contacted with another. However,

this ordering of materials is completely empirical and cannot be correlated to any

material properties [41–45]; the ordering is not universal and can depend on the nature of

contact [18, 46] and the processing history of the sample [13]; and even two chemically identical materials will transfer charge when contacted [10], which inherently contradicts

the notion of a triboelectric series. There is now growing evidence that triboelectric charging involves subtle material chemistry that cannot be captured with one simple explanation [14, 20, 47, 48]. Here, we introduce a new factor that can govern the

direction of charge transfer resulting from triboelectric charging: the material

microstructure. To demonstrate, we carried out triboelectric charging experiments with

polymer materials of identical chemical composition. When two samples of identical material are contacted symmetrically, the direction of charge transfer is random, as has been previously reported [49]. In contrast, we show that when one of the samples is permanently deformed, this sample behaves triboelectrically like a distinct material; when the permanently deformed material is contacted with an un-deformed material, there is systematic charge transfer in one direction just as would be expected if materials of different chemical composition were contacted. In addition to the triboelectric charging behavior, we examine the changes in microstructure resulting from deformation using a variety of characterization techniques and molecular dynamics simulations. We show that strain leads to the nucleation of voids on the nano and microscale, and we argue that the altered microstructure produces the distinct triboelectric charging behavior.

4.2 Methods 4.2.1 Experiments

We focused our study on polytetrafluoroethylene (PTFE) because it is known to be one of the most electronegative materials (it typically charges negative when contacted with almost any material) and is very hydrophobic (and thus minimally affected by humidity and water adsorption) [50]. The as-purchased PTFE sheets (0.8-mm thickness,

McMaster- Carr) are referred to as unstrained or 0% strain as no additional mechanical deformation was applied. The PTFE sheets were deformed by uniaxial tension using a

MTS Electromechanical Universal Testing System (Criterion Series 43) at a rate of 25 mm/s. Samples were deformed to 100% of the initial length; this deformation is

permanent, as the material does not relax back to the initial state when the stress is released. Both the 0% and 100% strain samples were cut to a final size of 63.5 25.4 mm2 for contacting studies to keep the area the same. Before contacting, samples were cleaned using acetone and methanol and allowed to dry for four minutes in ambient conditions.

A mechanical apparatus was constructed to contact a pair of PTFE samples of varying strain. It is important to contact the two samples in a way that is symmetric, as an asymmetry in contact can lead to systematic charge transfer between the samples. As shown in Figure 4.1, we position the two rectangular samples perpendicular to one another. If we were then to translate one sample linearly back and forth over the other, the motion would be asymmetric in that the area of contact would be smaller on the moving sample than on the stationary sample. However, if we were to translate one sample in a circular trajectory (while maintaining perpendicular orientation) over the stationary sample then the area of contact would be the same on both samples. Thus we constructed a system that automatically contacts the samples in this circular manner, driven by a stepper motor. Contacting experiments were carried out at a rate of 22 cycles per minute for 90 seconds (this rate was the rotation rate of the stepper motor used in the apparatus; we do not think the specific rate would affect the results). The charge on each sample was measured, before and after contact, by placing the samples in a Faraday cup connected to an electrometer (Keithley 6517A). The net charge transferred on each sample was obtained as the difference in charge before and after contact.

Figure 4.1. Comparison of two possible orientations of a pair of substrate samples for contact transfer experiments and resulting contact areas for charge transfer. In both cases, they are arranged one on top of the other, and the bottom sample is stationary while the top sample is moved. The area contacted on the bottom sample is shown in orange, and the area contacted on the top sample is shown in blue. In case I, the top sample is moved linearly back and forth across the bottom sample, leading to an unequal contact area for the two samples (see orange and blue shaded areas). In case II, the top sample is moved in a circular trajectory across the bottom sample, leading to an equal contact area for the two samples (see orange and blue shaded areas).

Changes to optical properties of the samples resulting from strain were measured

by ultraviolet-visible (UV-vis) spectroscopy (Shimadzu 1800) in the transmission mode.

The reference (blank) spectrum was ambient air.

X-ray diffraction (XRD) was performed with a X-Pert Pro diffractometer, Cu Kα1 wavelength (1.5406 Å), at a step size of 0.0131◦ and a scan speed of 0.033667 ◦/s. Micro

Raman spectroscopy was performed with a Witec Model Alpha 300S spectrometer using a 400-mW diode-pumped 532-nm solid state laser. The confocal microscope focused the laser to a spatial resolution of 200 nm. Scanning electron microscopy (SEM) was performed with a FEI Helios Nanolab 650. The system was operated at a low beam voltage of 350 V and images were acquired with multiple frames averaging to increase the signal to noise so that PTFE samples could be directly imaged without any conductive metal coating, in order to preserve the fidelity of the microstructure after straining.

4.2.1 Simulations

Molecular simulations were performed on PTFE. Although PTFE is typically semi-crystalline [51], the molecular simulation of semi-crystalline materials is extremely difficult, and we believe the relevant changes are occurring in the amorphous phase—for these reasons, we carried out our simulations on fully amorphous PTFE. The simulations involved a system of 40 PTFE molecules, with each molecule consisting of 50 monomers. Periodic boundary conditions were used to remove surface effects and thus model a bulk system. The OPLS-AA force field was used to represent the potential energy of the system [52]. Electrostatic interactions were calculated using the particle- mesh-Ewald algorithm with a cutoff distance of 1 nm and a Fourier spacing of 0.4 nm

[53], and Van der Waals interactions were considered up to a cutoff of 2 nm.

The amorphous PTFE system was generated by first inserting PTFE molecules into a large simulation box (15 x 15 x 15 nm3) without allowing them to touch each other.

Molecular dynamics was then used in the NPT ensemble at high temperature (T = 1000

K) and pressure (P = 1 MPa) for 1 ns. To evolve the system to the appropriate density, the pressure was progressively increased in a series of 1-ns simulations until the appropriate density was obtained. The temperature was then reduced to 300 K, and the pressure was reduced to 1 atm, and an additional 40 ns simulation was used to relax the amorphous PTFE configuration at 0% strain. The molecular dynamics simulations were carried out using a leap-frog algorithm with a time step of 2 fs [54], and the temperature and pressure were controlled by a velocity-rescaling couple with a time constant of 10 fs [55], and a Berendsen couple with a time constant of 4 ps [56], respectively.

Axial strain was introduced by incrementally scaling the z coordinate of each

atom by a scaling factor, and then relaxing the system with a molecular dynamics

simulation. These simulations allowed for the transverse dimensions of the material to

contract as the material was strained axially; this is accomplished by NPT ensemble at

atmospheric pressure with the compressibility in the z direction (βz) set to 0 to keep the

axial strain constant. The compressibility in the x and y directions (βx, βy) was set to be

10−4 MPa−1 [57]. Four independent 40 ns simulations were run at each strain. Results were obtained for PTFE at {0%, 5%, 10%, 100%} strains.

We also simulated the straining of PTFE in the quasistatic limit in order to

develop a physical understanding of the changes in structure with strain [58]. The

quasistatic limit corresponds to the limit of zero temperature and zero-strain rate; this limit precludes all thermally induced or inertially induced dynamics, and during the trajectory the system thus remains at the nearest energy minimum. The quasistatic simulations are carried out by elongating the system in tiny increments, with the atom positions varied to minimize the energy after each strain increment. Each strain increment consisted of an axial extension of 0.1% and a perpendicular contraction in the appropriate amount as determined by the strain-dependent Poisson’s ratios from the thermal molecular dynamics simulations described in the previous paragraph. The energy minimizations were carried out using the conjugate-gradient algorithm, to the limits of machine precision.

All simulations were carried out using GROMACS/4.6 [59–62]. AVOGADRO and VISUAL MOLECULAR DYNAMICS software were used for visualization [63, 64].

4.3 Results 4.3.1 Stress-strain measurements

The experimental stress-strain curve of PTFE under tensile strain is shown in

Figure 4.2. For strains up to 2%, the deformation is elastic, such that stress increases linearly with strain; the Young’s modulus, given by the slope, is approximately 460 MPa.

Above 2% strain, yielding occurs which is characterized by a continual decrease in the slope of the stress-strain curve. Above 100% strain, the material enters a strain hardening regime where the slope of the stress-strain curve again increases. The material fractures at about 400% strain. For strains beyond the elastic regime, the strain is irreversible, and the sample permanently remains in a strained state after the applied stress is removed. For our contact charging studies, we used samples deformed to 100% strain, such that the material has maximal inelastic deformation without entering the strain hardening regime.

Figure 4.2. Stress-strain measurements for PTFE films from experiments (open circles) and simulations (red squares). Inset shows a log-log plot of the same data. Deformation of PTFE shows linear elastic (<2%), yielding (2%–100%), and strain hardening regimes (>100%).

Figure 4.2 also shows stress-strain results obtained from simulations at 300 K.

The plastic flow stress observed in simulations is in reasonable agreement with experimental measurements. As the material is stretched axially, it contracts in the transverse dimensions; the magnitude of the contraction corresponds to a Poisson’s ratio of 0.45, which is close to literature values [65]. This agreement between the simulations and experiments supports our hypothesis that the mechanical properties are governed by the amorphous phase of PTFE.

4.3.2 Triboelectric charging experiments

Figure 4.3(a) shows results for 40 contact charging experiments that were conducted between a pair of unstrained (0%) PTFE samples. The measurements show that in each experimental trial, one sample acquires a negative net charge and the complementary sample acquires a nearly equal positive net charge (thus falling on or close to the dashed line with a slope of –1). To assess experimental biases in charging behavior, such as whether the samples were moving or stationary, a statistical analysis of the data was performed. The mean charge was 0.11 ± 0.19 nC for the stationary sample, and 0.13 ± 0.18 nC for the moving sample; both of these mean charges are statistically indistinguishable from zero. Although the mean charges of both the moving and stationary samples were positive, we believe this is not a real effect and just due to noise as these charges were zero within the statistical uncertainty. Overall, the charging behavior is seemingly random, with no clear tendency for a given sample in an individual experiment to predictably charge negatively or positively, irrespective of whether the

sample was moving or stationary. We note that there are some outlier data points with higher magnitudes of charging; these outliers could originate from random impurities on the surfaces, inhomogeneity in surface roughness that could lead to different contact area or different levels of bond breaking and material transfer, as well as other factors.

Results for 40 contact charging experiments between a pair of 100% strain samples are shown in Figure 4.3(b). Again, we find that samples charge negative and positive with approximately equal, but opposite charge in individual experimental trials

(thus again falling on or close to the dashed line with a slope of

–1). Interestingly, the span of charges measured is narrower for the pair of 100% strain than the 0% strain samples. A similar statistical analysis shows that for the stationary samples, the mean charge was 0.048 ± 0.091 nC, and for the moving samples the mean charge was –0.065 ± 0.093 nC; again, both of these mean charges are statistically indistinguishable from zero.

Finally, results for 80 contact charging experiments between 0% strain and 100% strain samples are shown in Figure 4.3(c). In stark contrast to the contacting of equally strained samples, a very clear tendency is observed where the 0% strain sample charges negative and the 100% strain sample charges positive with approximately equal, but opposite charge in each and every experimental trial (thus falling on or close to the dashed line with a slope of –1 but only in the top left quadrant). Importantly, statistical analysis showed that this charge dependency did not change whether the 0% strain or the

100% strain samples were moving or stationary. For the 100% strain samples, the mean charge was 1.2 ± 0.099 nC, and for the unstrained samples the mean charge was –1.2 ±

0.11 nC.

Our results thus show that the 0% and 100% strain PTFE samples have different

triboelectric charging behaviors, such that when contacted, the 0% strain sample tends to

charge negative and the 100% strain sample tends to charge positive. Thus strain appears

to alter the material properties of the PTFE that control triboelectric charging.

6 6

4 4

2 2

0 0

-2 -2

-4 -4

-6 -6 0% Strain PTFE Net Charge [nC] 100% Strain PTFE Net Charge [nC] -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 (a) 0% Strain PTFE Net Charge [nC] (b) 100% Strain PTFE Net Charge [nC]

4 2

-2

-4

-6

100% Strain PTFE Net Charge [nC] -6 -4 -2 0 2 4 6 (c) 0% Strain PTFE Net Charge [nC]

Figure 4.3. Summary of contact charging measurements for the following cases: (a) contact between two samples each at 0% strain; (b) contact between two samples each at 100% strain; and (c) contact between 0% strain sample and 100% strain sample. The net surface charges measured from each sample in the pair, defined as a difference between the surface charge before and after contact, are shown as a scatter plot and frequency histogram in each case.

4.3.3 Materials characterization

X-ray diffraction (XRD) and Raman spectroscopy were used to address potential changes to the chemical structure resulting from permanent deformation. The properties of 0% and 100% strain samples were compared (Figure 4.4). We did not see significant differences in the XRD or Raman spectra, which indicated that the overall chemical structure did not appear to change significantly with strain.

Figure 4.4. (a) XRD and (b) micro Raman characterization of 0% and 100% strain PTFE samples.

The most salient change in the material resulting from strain is the opacity of the sample—the strained sample appears to the naked eye to be visibly whiter. This “strain whitening” is a well-known effect in polymer materials and is attributed to the formation of voids in the material that have sizes comparable to the wavelength of light (hundreds

of nanometers) and thus scatter the light [41]. We quantified this effect spectroscopically.

A comparison of transmission spectra collected for 0% and 100% strain PTFE samples between 350 and 800 nm shown in Figure 4.5(a) confirms that the 0% strain samples have a higher transmittance than 100% strain samples. To illustrate this difference, the transmittance at 400, 550, and 800 nm are plotted as a function of strain in Figure 4.5(b), which more clearly shows that transmittance decreases with increasing percentage of strain.

Figure 4.5. (a) Spectroscopic transmittance of 0% strain (black) and 100% strain (red) PTFE films. (b) Transmission of PTFE samples as a function of percent strain at 400 (blue), 550 (red), and 800 nm (black).

Furthermore, we note that as the material is being strained, a small number of macroscopic holes become visible to the naked eye as the strain exceeds about 150%. As shown by a series of optical images collected from a PTFE sample while being deformed in Figure 4.6, the holes can be seen with the naked eye when they are about 300 μm in diameter [Figure 4.6(a)], and grow in size with increasing strain [Figure 4.6(b)], up to

more than 1000 μm in diameter at strains that fracture occurs [Figure 4.6(c)]. The fracture of the material appears to be initiated from one of these holes.

Figure 4.6. Optical images of void formation and growth in strained PTFE films at (a) 250% strain, where the void is first noticed, (b) 350% strain, and (c) 417% strain, just before the void and film rupture. The diameters of the void are approximately 400, 700, and 1100 μm in (a)–(c), respectively.

Some of the holes that are visible with the naked eye when the material is under tensile stress seem to “close-up” as the tensile stress is released, due to the small elastic contraction that occurs upon release of stress. We examined samples with SEM and found remnants of holes, as shown in Figure 4.7(a), as well as other smaller holes, approximately 50 μm in diameter, that were not visible with the naked eye, as shown in

Figure 4.7(b). The SEM images reveal filamentary structure at the hole (fibrils) characteristic of crazing.

Figure 4.7. Representative SEM images of PTFE films strained to fracture: (a) remnant of a void that was visible to the naked eye when under tension, but closed up when tension was released and (b) a void that was not visible to the naked eye.

4.3.3 Molecular simulations

The molecular simulations show changes occur in the intramolecular structure with strain, in that the polymer chains stretch out and align in the direction of strain

(Figure 4.8). There are also slight shifts in the bond angle and torsion distributions with strain (not shown).

Figure 4.8. Simulation results for molecular properties of PTFE films as a function of strain: (a) average end-to-end distance of polymers and (b) dot product of the end-to-end vector in the direction of strain.

However, we believe the more important changes occur at longer nanometer scales. Above strains of about 50% the volume begins to increase significantly with strain. In comparison, at lower strains, the lateral contractions more closely balance the axial extensions to keep the volume roughly constant. The increase in volume is due to the formation and growth of voids in the material. Figure 4.9 shows snapshots of the system at strain increments of 10%; this is a view from the “top” of the simulation cell, and thus one cannot necessarily see what is happening in the interior (note also that there are periodic boundary conditions in all directions). Voids begin to form at strains of 50%, as evidenced by lighter-colored regions that imply that the top layers of atoms are missing. At 90% strain, a void spans the entire width of the simulation cell (the simulation cell is 4 to 5 nm wide).

Figure 4.9. Simulation results for microstructure of PTFE system as a function of strain.

To investigate the mechanisms of void formation and growth, simulations were

performed for deformation in the quasistatic (zero-temperature and zero-strain-rate) limit.

In this limit, the system always remains in a local energy minimum. Results are shown in

Figure 4.10(a) for the potential energy as a function of strain. Usually, the potential energy increases continuously with increasing strain. However, there are numerous steps where the potential energy drops discontinuously. These changes are due to strain- induced changes in the potential energy landscape. Consider the schematic in Figure

4.10(b). As the system is strained slightly, the potential energy landscape is perturbed, but in the quasistatic limit, the system remains in the same potential energy minimum; such changes correspond to the continuous increases in potential energy with strain in

Figure 4. 10(a). However, as shown in Figure 4.10(b), eventually this potential energy minimum “disappears,” and at this point there are net forces that push the system to a different potential energy minimum; such changes correspond to the discontinuous potential energy drops in Figure 4.10(a). Our previous work has shown that the changes in characteristics of the potential energy landscape (barrier height, normal mode frequencies) follow the mathematical scaling behavior associated with fold catastrophes

[58, 67].

Following a fold catastrophe, the system relaxes to a different energy minimum.

We examined the structural changes associated with these atomic relaxations and find that in some cases these relaxations correspond to the formation and growth of voids

[Figures. 4.10(c) and 4.10(d)]. Thus voids form and grow by sporadic discontinuous events as the system is strained, which correspond to fold catastrophes of the potential energy landscape.

Figure 4.10. Results of quasistatic simulations: (a) potential energy as a function of strain in the inelastic deformation regime. (b) Schematic of changes in the potential energy landscape with strain; note the fold catastrophe where the energy minimum on the left disappears. (c) and (d) The molecular configuration just before (c) and just after (d) the discontinuous drop in potential energy at 83% strain; note the structural change corresponds to the nucleation of a void, see a white circle.

4.4 Discussion and conclusions

Typically, in a pair of chemically identical material surfaces that are contacted

symmetrically, triboelectric charging will occur such that one surface charges positive

and the other charges negative. However, which one of the two surfaces will charge

positive and which negative will appear random [49], as demonstrated here in Figures

4.3(a) and 4.3(b). We show here that when one of these PTFE samples is permanently deformed, there is systematic triboelectric charging such that the strained material almost always charges positive and the unstrained material almost always charges negative. This result is akin to charging behavior between materials with different chemical composition.

Why is the triboelectric charging behavior so dramatically altered when one material is permanently deformed? Previous work has suggested that large strain drives polymer systems into distinct amorphous states [68]. To assess structural changes to

PTFE caused by deformation, we carried out XRD and Raman spectroscopy, but significant differences between the unstrained and strained PTFE were not observed.

These methods probe the material structure at the molecular level, and thus we conclude that the molecular-scale structure of PTFE is not so significantly impacted by permanent deformation.

Instead, we suggest that the relevant structural changes caused by deformation are at a scale larger than the molecular scale, and correspond to the formation of voids. This idea is supported by the following: (1) molecular dynamics simulations which show the formation of voids of nanometer dimensions; (2) spectroscopic characterization which shows decreased transmittance arising from the scattering of light by voids that are the same length scale as the wavelength of visible light (hundreds of nm); (3) SEM analysis which reveals holes on the order of 50 μm diameter and smaller; and (4) the naked- eye observation of holes with diameters of a few hundred μm to over 1 mm. We note that the voids found by these four methods are on very different length scales, ranging from nanometers to a millimeter. We believe these voids are all related, as follows.

Nanometer-sized voids are nucleated by plastic events [69, 70] associated with fold

catastrophes in the energy landscape [71]. These small voids grow and/or merge into larger voids on the order of hundreds of nanometers, which lead to scattering of light and decrease optical transmittance. Likewise, some of these voids in turn grow into the micrometer-sized voids observable by SEM, and some of those grow into macroscopic holes that can be observed by the naked eye.

The distinct triboelectric charging behavior found for permanently deformed

samples could arise from the voids of a wide range of length scales, as well as the

associated fibril structure (crazes). As noted, a correlation between triboelectric charging

and material properties has yet to be established. In fact, it is not known whether charge

transfer is due to the transfer of electrons, mobile ions, or radical moieties generated from

the physical contact. The observed changes in the microstructure of the material could

affect each mechanism of charge transfer: the electronic states near the voids and fibrils

will likely be different from the rest of the material, which could lead to different electron

transfer propensity; the different electronic states would lead to different ion adsorption,

which would in turn affect the transfer of adsorbed ions between surfaces; and the

mechanical strength of the material could be weakened near the voids and fibrils to

enhance ions, radicals, or larger fragments breaking off and transferring during rubbing.

In addition, the presence of voids could lead to a different effective contact area at a

smaller scale than the overall contacting area of the sample surface (see Figure 4.1), and

this asymmetry of contact areas could lead to different charging behavior.

4.5 Additional Notes

Looking closer at Figure 4.10(a), it is shown that the stress imparted on the PTFE material before a discontinuous jump is on the order of 200 kJ/mol which is less than the

C-C bond dissociation energy at 347 kJ/mol. The simulation indicates that the potential energy minimum jumps correlate with structural changes such as void formations, and not just C-C scission. Integration of the real samples' stress-strain curve resulted in approximately 67 kJ of energy added into the system from tensile strain; 9 kJ was returned when the sampled relaxed.

4.6 Acknowledgements

This material is based upon work supported by the National Science Foundation under grant numbers CBET-1235908, CBET-1604909 and DMR-1206480. The calculations were carried out using computational resources through the Ohio

Supercomputing Center. Z.Y. and H.T.B. are grateful for support from The Scientific and

Technological Research Council of Turkey (TUBITAK project No. 214M358). We thank

Richard Pham and Ross Widenor for their work on the early stages of this project.

V Contact Charge Transfer Between Inorganic Dielectric Solids of Different Surface Roughness

[Published: Wang, A. E., Greber, I., Angus, J. C., "Contact charge transfer between inorganic dielectric solids of different surface roughness", Journal of Electrostatics, Vol. 101, pp. 103359, 2019

We measured contact charge transfer between chemically identical, dielectric solids with different surface roughness. Glass of four different roughness levels had its own charge transfer series with the rougher glass negative with respect to the smoother in all combinations. Unpolished N-type silicon wafers became negative to polished N-type wafers; P-type wafers showed the opposite behavior. Rougher glass was more negative than smoother glass after contact with chemically non-identical samples. The results are consistent with modeling studies that show that the concentration of excited electrons is lower in solids in which there is greater access to surface de-excitation.

5.1 Introduction

Charge transfer between nominally identical solids arises in many natural and

industrial processes. Accumulation of charge creates the electric fields found in

thunderstorms, dust clouds, and in volcanic plumes. The buildup of charge in industrial

particulate processes can lead to hazardous process failures and out-of-range product.

Despite its ubiquity and importance, the mechanism underlying the charge transfer,

especially between dielectric objects of identical composition, remains an open question

[11, 19, 49, 72 - 74]. Two of the authors (JCA and IG) have shown through modeling

that differences in size [48] and surface morphology [75] of otherwise identical dielectric

solids can lead to asymmetric charge transfer. The modeling links the asymmetric charge

transfer to differences in the relative accessibility of excited electrons to surface and bulk

de-activation sites. Enhanced access to surface de-excitation sites can lead to lower excited electron concentrations and hence lower quasi-Fermi energies. (In the present

context, “concentration of excited electrons” refers to the concentration of electrons in

the conduction band in excess of the thermal equilibrium value.) The enhanced access to

surface de-excitation sites may arise from either a purely geometric effect or an increase

in the areal concentration of surface de-excitation sites.

This proposed mechanism [8] leads to several testable predictions: 1) otherwise

identical solids with several levels of surface roughness will have their own charge

transfer series with the smoother solid acting as the source of charge carriers for all pairs;

2) otherwise identical solids that conduct by electrons and holes should transfer charge in

opposite directions [75, 76]; 3) the position of a dielectric solid in a contact potential

series should become more negative as the solid is made rougher. In this paper experiments are described that test these predictions.

5.2 Experimental

Uncoated silica glass microscope slides from Corning Glass were abraded in a circular pattern with silicon carbide grit of sizes 120, 320 and 400, which correspond to average grit diameters of 125, 46 and 35 μm. The roughened glass slides were categorized by optical profilometry and UV-visible transmission spectroscopy measurements summarized in Table 1 and Fig. 1. Relative surface areas were characterized by the root mean square asperity height. The current and prior measurements [77] do not give independent assessments of the effect of geometric area and the areal concentration of de-excitation sites.

Table 5.1. Glass Slide Roughness Categories

Measured Asperity Category Abrasive Grit No. Grit Diameter Height, 1 μm

Smoothest − − 0.18 ± 0.01 (as-received)

Smooth 400 35 0.50 ± 0.02

Rough 320 46 1.11 ± 0.45

Roughest 120 125 2.41 ± 0.61

1 Measured with a Nanovea ST400 optical profilometer

Figure 5.1. Optical comparisons of glass slides used in experimental studies. Transmittance measurements were made with a Shimadzu UV-1800 UV-Vis spectrophotometer. Roughness categories are: 1. Smoothest (as-received), 2. Smooth, 3. Rough, 4. Roughest (See Table 1).

The absorption edge at 300 nm in Fig. 1 corresponds to an optical gap of approximately 4.1 eV. The differences in transmission at wavelengths greater than 300 nm arise from light scattering from the surfaces of different roughness.

The roughened slides were cleaned with a DI water, acetone, and methanol rinse sequence, and blown dry with compressed dry air prior to attachment to the ends of wooden rods with hot-melt adhesive. The initial charges on a pair of slides were measured using a Faraday cup connected to a Keithley 6517A electrometer. The two slides being tested were manually contacted while attached to the rods, separated, and the charge on each slide re-measured. The values reported here are the differences in charge

density before and after contact. The contact was performed in ambient room light with

the faces held flush for five seconds. Some sliding motion of the two slides during

contact was unavoidable. The slides were discarded after one measurement. An electron

microscope survey of the surface of selected slides showed no evidence of change after

contact.

Electron excitation can occur thermally from the sliding contact, or by

photons from solar light or fluorescent lamps in the laboratory. To examine the optical

excitation more directly, a set of experiments was conducted with glass wafers

intentionally exposed to the radiation from a Spectroline XX-1NF (254 nm, 15 watts) UV lamp for two minutes at a distance of 15 cm prior to contact. Additional experimental details are given by Wang.

5.3 Results 5.3.1 Results on Glass Slides

Fig. 2 summarizes the results of the charge density measurements on glass slides

with and without supplementary UV excitation. The error bars indicate plus and minus

one standard deviation. In some cases this error range extends into the region of opposite

charge. These large deviations likely arise from transfer of charge by particulate matter

in some of the experiments. The asymmetry of the placement of the error bars arises

from plotting on a logarithmic scale.

The UV excitation increased the average charge transfer and reduced the error

range for all but the Rough/Roughest pair of slides. We note that the mechanisms studied

here [48, 75] are independent of the type of excitation, which could be either photonic or

thermal.

Figure 5.2. Charge densities after contact for all combinations of smoothest, smooth, rough and roughest glass slides; a) no augmented UV excitation, b) with augmented UV excitation. Hatched bars indicate the rougher sample; plain bars indicate the smoother. The root mean square asperity heights for each roughness category are given in Table 1. The error bars show plus and minus one standard deviation.

Control experiments using the same cleaning and experimental procedures were

performed with as-received samples contacting other as-received samples. These experiments showed average charge densities two orders of magnitude lower for the (as- received)/(as-received) pairing than for any other pairing of samples with greater roughness levels.

The observed charge transfer directions shown in Fig. 2 can be summarized by noting that the glass samples with four different roughness levels form their own charge

transfer series, which is illustrated in Fig. 3. The direction of negative charge carrier

transport, in this case presumably by electrons, is from the smoother to the rougher

sample in all cases. A similar result with glass slides of three different roughness was

reported earlier [78] by two of the present authors. We emphasize that the two slides of intermediate roughness act either as electron donors or electron acceptors depending on the relative roughness of the contacting slide.

Figure 5.3. Charge transfer series for glass samples of different roughness taken from data in Fig. 5.2. The arrows show the direction of electron transport between samples. The root mean square asperity heights for each roughness category are shown in the boxes.

The absolute magnitude of the average charge decreased with increase in surface roughness. This decrease is likely caused by the decrease in effective contact area for charge transfer for the rougher samples. Effective fractional contact areas ranging from

10-5 to 10-2 have been reported [79, 80]. While increasing surface roughness decreases

the effective contact area, it increases the difference in Fermi energies between rough and smooth solids.

The experimental results on the final polarity of the glass slides are summarized in Table 2. Outcome r is when the rougher slide became negative; outcome s is the opposite polarity, i.e., the smoother slide became negative. Trials that reported values under the detection limit of the electrometer or that violated charge conservation are reported as “null” results.

Table 5.2. Summary of Polarity Data on Glass Slides

no. of no. of trials no. of trials no. of null trials, n with with results 2 Samples outcome r outcome s

UV UV UV UV

Glass Smoothest / smooth 6 7 6 7 0 0 0 0

Smoothest / rough 6 6 5 5 0 0 1 1

Smoothest / roughest 6 6 6 5 0 0 0 1

Smooth / rough 12 6 10 3 1 0 1 3

Smooth / roughest 12 6 7 4 1 0 4 2

Rough / roughest 9 6 5 3 1 1 3 2

Totals 51 37 39 27 3 1 9 9

Grand Total 88 66 4 18

Outcome r: rougher slide becomes negative.

Outcome s: smoother slide becomes negative.

“Null result:” charge density below detection limit or violation of charge conservation.

2 Root mean square asperity heights for all roughness categories are given in Fig. 1.

Transfer of particulate matter from the rough slide to the surroundings or to the

smoother slide is likely responsible for the s outcomes and the null results. Note that the

number of s outcomes and null results both increased with increasing surface roughness.

The increase in asperity height increases the probability of fracture and transfer of glass

particles. Engineered surfaces with designed specific surface area and surface profile

produced by photolithography and etching should reduce particle transfer, and also

permit the separation of purely surface area effects from the effect of areal density of

defects.

A Chi-squared analysis was performed to estimate the probability that the

observed results (88 trials, 66 r outcomes, 4 s outcomes, 18 null results) could have

occurred by chance, e.g., unbiased coin flip. To give a conservative test, the 18 null

results were counted as s outcomes. The Chi-squared analysis shows that the probability of 66 outcomes of type r in 88 trials occurring by chance is 2.7 x 10-6. The measured

mean charge density of the UV treated samples was 0.028 μC/m2 greater than that of the

non-UV treated samples. A paired Student’s t test showed that the difference in means

was significant at the 95% confidence level (p-value of 0.013).

5.3.2 Results on N and P-type Silicon

Experiments on silicon samples of known conductivity type were performed using

wafers of high resistivity N and P-type silicon with one side polished and one side

unpolished. The wafers were used “as received” from the MTI Corporation with nominal

properties: N-type, resistivity ρe > 1000 ohm cm, carrier concentrations, ne < 5 x 1012

-3 -3 cm ; P-type, ρh > 1000 ohm cm; nh < 1013 cm . The charge carrier type, concentrations

and mobilities were confirmed by independent Hall and resistivity measurements [15]: N-

-3 2 type, ρe = 6170 ohm cm, ne = 6.8 x 1011 cm , μe = 1510 cm /V sec; P-type, ρh = 4950

-3 2 ohm cm, nh = 7.1 x 1012 cm , μh = 190 cm /V sec.

For N-type samples the average final charge state after contact was: unpolished

(negative)/polished (positive). For P-type the final charge state was reversed: unpolished

(positive)/polished (negative). These results are consistent with the model predictions for solids with conduction by electrons and holes respectively.

The results of the polarity measurements on silicon are shown in Table 5.3.

Outcome r is when charge carriers (electrons or holes) transfer from the polished to the unpolished surface; outcome s is when charge carriers transfer from unpolished to polished. As with the experiments on glass slides, we believe that particulate transfer is likely responsible for the outcome s and “null” results.

Table 5.3. Summary of Polarity Data on Silicon

no. of trials no. of trials no. of no. of null with with 3 trials, n results Samples outcome r outcome s

N-type Polished / unpolished 15 11 2 2 silicon

P-type Polished / unpolished 15 13 1 1 silicon

Totals 30 24 3 3

Outcome r: unpolished (rough) silicon surface acquires sign of charge carrier;

Outcome s: polished (smooth) silicon surface acquires sign of charge carrier.

“Null result:” charge density below detection limit or violation of charge conservation.

3 Root mean square asperity heights are given in Fig. 4 caption.

Figure 5.4. Final average charge densities on polished and unpolished N and P-type silicon wafers after contact. In both cases the charge carriers transfer from the polished (smooth) to the unpolished (rough) surface. The root mean square asperity heights for the polished and unpolished samples were 0.25 µm and 2.83 µm respectively. Hatched bars indicate the unpolished sample; plain bars indicate the polished sample. The error bars show plus and minus one standard deviation.

5.3.3 Glass vs. other materials

Results of a series of measurements with glass of different roughness contacted with nylon, polyethylene, polytetrafluoroethylene, and aluminum are shown in Fig. 5.

The final charge density on the glass samples is plotted versus the RMS roughness of the glass. We note that a similar plot has been given by Vladykina et al. [77]. In each series

in Fig. 5 the glass becomes monotonically less positive as the roughness increases. The net sign of the charge on the glass is positive for all pairs except for the roughest glass sample contacted with aluminum. For this pair, the glass shows a net negative charge, i.e., the glass and aluminum have changed places in the charge transfer series. This result is evidence that position in a measured charge transfer series can be influenced by surface treatment as well as the internal electronic structure of the materials.

Figure 5.5. Charge density on glass slides after contact versus RMS roughness of the glass surface. ∇ Nylon,  Polyethylene,  Polytetrafluoroethylene, Δ Aluminum. The roughness categories are summarized in Table 6.1.

5.4 Discussion and conclusions

The experimental results are consistent with the model predictions that the direction of charge carrier transfer is from smoother to rougher surfaces [8]. The results are also consistent with very early measurements of tribo-electric charge transfer between smooth and rough glass samples [13, 82, 83]. Silica glass slides of varying roughness can be placed in their own charge transfer series with rougher more negative than smoother for all combinations. The final charge on silica glass contacted by nylon, polyethylene, polytetrafluoroethylene, and aluminum metal becomes less positive as the glass roughness increases. Silicon wafers with known electron and hole conductivity show behavior consistent with the model: for N-type the rougher surface is negative; for P-type the rougher surface is positive.

All of the present results on the asymmetric direction of charge transfer between nominally identical solids are consistent with charge transfer by electrons (or holes) excited thermally during contact or by photo-excitation from UV light. However, the experiments were done in ambient air so the presence of adsorbed water on the surfaces was highly likely. Adsorbed water films can give rise to surface transfer doping of non- conducting dielectric solids [84, 85] and may facilitate charge transfer by ions [17, 20,

86, 87].

Future experiments using single crystal dielectric solids with well characterized electronic band structure and surfaces in controlled environments would be useful in further understanding contact charge transfer in nominally identical solids. In some situations more than one mechanism may be present.

5.5 Additional Notes

Contacting samples of different surface roughness changes the true contact area,

even if the apparent contact area remains the same. A proposed model that describes the

mechanism of charge transfer in this asymmetric contact is presented in [75]. Parallel

conclusions can be drawn from the work with PTFE. In systems with chemically identical

material surfaces, a singular symmetry breaking component, strain-induced changes in

microstructure, or differences in surface roughness can ultimately drive the direction of

charge transfer.

5.6 Acknowledgements

The authors acknowledge generous access to the laboratory facilities of Dan

Lacks, helpful conversations with Kathleen Kash, laboratory assistance from Anu

Suppiah, and Hall effect and resistivity measurements by Siddarth Joshi and Vidhya

Chakrapani [81]. The support of Case Western Reserve University is gratefully acknowledged.

VII Conclusions and Future Directions

7.1. Conclusions and Future Directions

The main objective of this body of work was to elucidate some of the driving mechanisms that drive triboelectric charging between material surfaces. In the first collaborative project, we are among the first to carry out first-principles calculations to model the contact electrification process. The calculated results were able to predict the direction and magnitude of charge transfer, which was in good agreement to the experimental results performed in a controlled, dry atmosphere. The success of this work was due to choosing single perfect crystals of sapphire and quartz as the experimental substrates as they have well-defined crystalline surfaces, which could limit experimental variability and computational load. The experimental results did implicate that humidity has a crucial role in determining charge transfer magnitude. To summarize, the average charge transfer magnitude decreased with increasing relative humidity. The project can be expanded to run further calculations of the contact electrification of sapphire and quartz with water molecules sandwiched between the two surfaces, which would more closely match the actual contact between the two surfaces in reality. This particular combined experimentation and calculation methodology should also be transferrable to other material systems with similar crystal structures and lattice parameters, like possibly periclase.

In the second project, we tried to understand what can drive seeming two chemically identical samples PTFE to produce reliable charge transfer. We controlled for factors such as asymmetric rubbing, contact area, and humidity through material selection. We managed to demonstrate by straining one sample to 100% strain past the

plastic deformation region; the strained sample tended to charge positively over the as

received strained sample. Through chemical analysis like X-Ray diffraction and Raman spectroscopy, we showed that the two samples were still chemically identical to each other. We discovered and confirmed through simulations, differential transmittance,

SEM, and optical microscopy that as the samples are undergoing strain, nano-size pores

begin to coalesce and grow into larger pores until visible to the naked eye. It is these

difference in microstructures that was driving the triboelectric charging between these

chemically identical surfaces. To further expand upon this work, we would continue to

study this directionality of charge effect with different percent strain to create a series. An

intermediate strain of 50% and excessive strain at 150% can complete the full story. Also,

some minor experimental upgrades would provide more details into the mechanism, such

as running the experiments in a controllable environment an keeping the samples strained

rather than letting them relax after plastic deformation.

In the third project, we were able to show experimentally show how essential a

role surface roughness drives triboelectric charging of identically chemical composition

materials. The experimental results matched model predictions in which the charge

carriers tended to transfer from smooth to rough surfaces. The RMS roughness was

measured through optical profilometry, and the experimental results were able to produce

a mini-triboelectric series with just different roughnesses of glass slides. The surface

roughness effect was strong enough to flip the charge transfer magnitude when contacting

aluminum. To further expand upon this work, we could improve the cleaning and UV-

excitation procedures. We could also use perfect crystals, roughen the surfaces, and then

anneal them back to a smoother state. Preliminary results with smooth and rough sapphire

and quartz showed that the smoother samples tended to charge more positive when rubbed against their coarser counterparts.

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