Friction 7(1): 2–17 (2019) ISSN 2223-7690 https://doi.org/10.1007/s40544-018-0217-7 CN 10-1237/TH REVIEW ARTICLE Fundamental theories and basic principles of triboelectric effect: A review Shuaihang PAN1,2, Zhinan ZHANG1,* 1 School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 2 School of Mechanical & Aerospace Engineering, University of California Los Angeles, Los Angeles 90095, USA Received: 18 January 2018 / Revised: 14 March 2018 / Accepted: 10 April 2018 © The author(s) 2018. This article is published with open access at Springerlink.com Abstract: Long-term observation of the triboelectric effect has not only proved the feasibility of many novel and useful tribo-devices (e.g., triboelectric nanogenerators), but also constantly motivated the exploration of its mysterious nature. In the pursuit of a comprehensive understanding of how the triboelectric process works, a more accurate description of the triboelectric effect and its related parameters and factors is urgently required. This review critically goes through the fundamental theories and basic principles governing the triboelectric process. By investigating the difference between each charging media, the electron, ion, and material transfer is discussed and the theoretical deduction in the past decades is provided. With the information from the triboelectric series, interesting phenomena including cyclic triboelectric sequence and asymmetric triboelectrification are precisely analyzed. Then, the interaction between the tribo-system and its operational environment is analyzed, and a fundamental description of its effects on the triboelectric process and results is summarized. In brief, this review is expected to provide a strong understanding of the triboelectric effect in a more rigorous mathematical and physical sense. Keywords: triboelectric effect; triboelectrification; triboelectric nanogenerators (TENGs); interface 1 Introduction adds to the complete analyses by decoupling each dominant parameter for modeling the triboelectric The triboelectric effect was the earliest focus in the effect. Considering these esoteric aspects in the tribology study. For over 2000 years, its generality triboelectric effect, many experiments have been and interesting phenomena have attracted significant conducted. Though all these results are appreciable, research interests. In summary, the triboelectric effect their significance suffers greatly, owing to the lack of is interesting but complex mainly due to the more solid theoretical deductions to interpret their following reasons: (1) Even for a highly charged phenomena in the triboelectric process [3]. surface (namely 1 mC·m−2), the charge density can Ironically, with so many tasks to solve and questions only achieve 1 electron unit per 105 surface atoms to answer, triboelectric devices and applications [4–8] [1]. (2) Basic questions including which surface will see a far-reaching success in recent years. For example, be charged positively and which will have negative some previous studies (e.g., into volcanic dusts) have charges when two surfaces are brought into contact revealed a close relation between environmental are still difficult to answer with certainty, and exceptions phenomena and triboelectric effect [9, 10]; manufac- (i.e., cyclic triboelectric series) from different theories turing and processing also face the influence of seem exclusive to each other [2]. (3) Multiple factors triboelectrication [11]. Indeed, these achievements can work on the same triboelectric process, which eagerly need more understanding in theories and * Corresponding author: Zhinan ZHANG, E-mail: [email protected] Friction 7(1): 2–17 (2019) 3 mechanisms in order for a better optimization, a more measurement and assessment of the triboelectric effect efficient design, and a greater development potential. requires suitable models such as charge injection depth Nowadays, newly developed low-band-gap polymers and the evaluation of important parameters such as and hard X-ray generators also urgently require a surface charge density. Given the possible electrical critical review into the triboelectric effect for some novel objects, the charging media can be divided into insights into the applications of these tribo-devices electron, ion, and (nano-)materials. The underlying [12, 13]. Though many simulation and modeling reasoning for the classification has never been methods are being used to help explain the phenomena, explained systematically, and is summarized here, as the insufficient physical laws and mathematical shown in Table 1. From our viewpoint in this review, description add to the difficulty [14, 15]. the most obvious difference for these three media is This review aims at providing and summarizing the unit charge carrying capacity. These are the general the deterministic theories, principles, and mechanisms criteria to decide which media contribute dominantly for the triboelectric effect. Due to the intrinsic to the observed phenomena in the triboelectric effect. characteristics of the triboelectric effect for being system-related and environment-dependent, the review 2.1 General important parameters first analyzes the charging media in the tribo-system 2.1.1 Charge injection depth and summarizes the potential mechanisms for these charging media to transfer (the charging process) in a The triboelectric effect will introduce the charge to more mathematical and physical sense (with some transfer dynamically, be stabilized dynamically, and novel notions). With this understanding, a more be held at the tribological interface. Should the charge complete list of the triboelectric series is summarized be held, the triboelectric interface must have the and the abnormal triboelectric sequence phenomena capacitance characteristics [8, 16, 17]. For example, are discussed with clearer mathematical and physical it has been proved that part of the initial cause of explanations. After all the review into the tribo- tribological electrification depends on the presence system and its related depictions for the triboelectric of the internal electric fields in solid insulators [18]. effect, the important factors influencing the triboelectric Irrespective of the types of triboelectric contact modes performance are systematically studied in the same used, the charge will be effective to a certain depth to analytical manner. In addition, we describe the potential form the capacitance. This depth is called the charge applications for these theories and principles for a injection/penetration depth [19]. more comprehensive integration with the triboelectric For simplicity, the capacitance characteristics in the research and related fields, and how it can be used for triboelectric effect can be depicted with as [4, 16] a rational design of the tribo-system is also included CS / 4π k (1) in each section. where C is the equivalent capacitance, is the 2 Charging media and charging process material’s dielectric constant, and k is the electrostatic constant. The simplest configuration with the capaci- The triboelectric effect is observable through the tance in the triboelectric interface is shown in Fig. 1. measurement of different charging media. An accurate This material-determined capacitance formed by the Table 1 The general difference among electron, ion, and (nano-)material. Tribocharging media Basic unit Mass Unit charge carrying capacity Electron Electron Low (~10–31 kg) 1 (Medium; Constant) Medium (~10–20 – 10–27 kg) Usually 1–10 Ion Ion * No consideration for (Large; Ions may carry multiple charges) macromolecules/ions (Nano-)material Atom & Ion Extremely high (>10–12 kg) <<1 (Small; Some atoms carry no charge) http://friction.tsinghuajournals.com∣www.Springer.com/journal/40544 | Friction 4 Friction 7(1): 2–17 (2019) Fig. 1 The capacitive configuration for triboelectric interface. charge injection depth will possibly interact with can be calculated as [24] interfacial air capacitance, which will influence the dynamical responses of the triboelectric effect (as air Cr4π 0 (0.5ln(/)) Lr (2) has breakdown voltage strength, as stated by Paschen’s where is the Euler constant and L the distance law) [20, 21]. between two identical particles of radius r [24]. Note that this configuration is important in Clearly, the description of particle capacitance is very understanding many more complicated triboelectric different from that of area-unlimited surfaces. systems including triboelectric nanogenerators (TENGs). By manipulating the triboelectrification and electric 2.1.2 Surface charge density induction, there exist four working modes for TENGs, Surface charge density is a parameter for measuring namely vertical contact mode, lateral sliding mode, the final charging effects on both surfaces, and it will single electrode mode, and free-standing triboelectric also significantly determine the triboelectric devices’ layer mode [16, 22]. These configurations are shown efficiency. It serves as the basis for analyzing in Fig. 2. Clearly, the capacitive configuration is parameters such as the current area power density significant in these devices [23]. and volume energy density [25]. Besides, it is a useful If the charge injection depth is larger than the parameter to link and analyze surface capacitance material geometry (i.e., in particle triboelectric characteristics and interface electrical performance, systems), the simplified Eq. (1) may not hold, because as shown in Eq. (3) [26]: the charge distribution will be modified