1. Introduction
Mechanical energy dissipation in friction occurs principally through thermal energy conversion via stick-slip mechanisms, and triboelectric/contact-electric [
1,
2,
3] phenomena arising from interfacial charge transfer during cyclic contact and separation. Contact electrification (CE) is a widespread physical phenomenon with a long-standing history in nature. It essentially involves the transfer of charges and conversion of electric potential energy when two heterogeneous materials with different electronegativities come into contact (or relatively slide), resulting in a potential difference between the materials [
4]. This phenomenon was long regarded as an adverse factor, but with the deepening of research, its positive application [
5,
6,
7,
8] has gradually emerged, providing new ideas for many cutting-edge technological breakthroughs. In addition, triboelectric nanogenerators (TENGs), an emerging technology developed based on contact electrification and electrostatic induction effects, have attracted widespread attention and achieved remarkable progress in fields such as energy harvesting [
9,
10,
11,
12,
13,
14], self-powered sensors [
15,
16,
17,
18], flexible electronics [
19], and the Internet of Things [
20]. To fully exploit the positive application potential of contact electrification, an in-depth investigation into its underlying mechanisms is of critical importance. It should be emphasized that contact electrification is an inherently complex process involving multi-physical field coupling. Therefore, clarifying its intrinsic mechanism will be of great significance to the development of related fields.
With the deepening of research on TENGs, significant progress has been made in the field of solid–solid CE. In particular, extensive studies have been conducted on the CE mechanisms between metals and polymers. Wu et al. [
21] investigated electron transfer at the interfaces of Al/amorphous PET and Al/amorphous Kapton, revealing that only specific molecular functional groups in polymers participate in the CE process and influence charge transfer. Shirakawa et al. [
22,
23] calculated the charge transfer between crystalline polytetrafluoroethylene (PTFE) and Al in both parallel and perpendicular contact configurations, demonstrating the critical role of dangling bonds at the interface in CE. Additionally, Li et al. [
24] experimentally studied the CE effects of seven different polymers in contact with Al, confirming that halogen-containing polymers exhibit stronger electron affinity.
In contrast, research on solid–liquid CE remains in its early stages and is less mature, despite its widespread occurrence in numerous applications. Only in recent years has solid–liquid CE gained increasing attention, with current studies primarily focused on experimental observations. Wang et al. pioneered the use of solid–liquid CE and electrostatic induction effects to develop a triboelectric nanogenerator for harvesting water wave energy [
25]. They also discovered that the energy generated by contact electrification between a single tiny droplet and a polymer film is sufficient to power 100 light-emitting diodes (LEDs) [
26]. In subsequent studies, Wang et al. experimentally investigated the effect of contact area between deionized water and polymers on electrification [
24]. First-principles calculations have revealed significant differences in contact electrification behavior between various polymers and water interfaces [
27]. However, the underlying microscopic mechanisms governing these charge transfer processes remain insufficiently elucidated. Consequently, the quantitative contribution of specific molecular functional groups in polymers to interfacial charge transfer has not been systematically established. This critical knowledge gap severely impedes the rational design of high-performance triboelectric materials.
Furthermore, amorphous polymers typically consist of multiple molecular functional groups. Given the extensive research confirming the strong electronegativity of halogens, halogen modification methods have garnered widespread interest. Examples include the surface treatment of polypropylene (PP) and polyethylene terephthalate (PET) using CF
4 plasma [
28,
29,
30], and atomic-level surface functionalization of PET with halogens and amines [
31,
32,
33]. Therefore, accurately evaluating the contribution level of each molecular functional group during contact electrification is crucial for the targeted chemical modification of triboelectric materials. This holds significant promise for opening new pathways to developing high-performance triboelectric materials. Moreover, the amorphous structure and density of polymer molecules can affect the quantitative estimation of charge transfer. This issue has also been identified in many first-principles calculation studies on contact electrification between single chains and metals [
22,
23]. To overcome the influence of the random spatial distribution of molecular chains on charge transfer calculations, it is necessary to study the CE mechanism with an amorphous structure of polymers composed of multiple chains.
In summary, this work adopts first-principles density functional theory (DFT) calculations, while establishing an intermolecular charge transfer model, to systematically and quantitatively reveal the CE mechanism of the water–amorphous polymer interfaces. Three representative polymers with similar backbones but different halogen-functionalized (F, Cl) side chains (fluorinated ethylene propylene (FEP), polyvinyl chloride (PVC), and polytetrafluoroethylene (PTFE)) are chosen to contact with water. The research first quantitatively analyzes the direction and magnitude of electron transfer between a polymer and water during the CE process. Then, the study delves into the characteristics of electron-accepting and electron-donating atoms. The results indicate that the electron transfer is primarily governed by the polymer’s lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO). Functional groups influence the electrification process by modulating the energy levels of these frontier orbitals, thereby altering the polymer’s electron-donating and electron-accepting capabilities. This study reveals the mechanistic role of different functional groups in contact electrification with water, providing a theoretical foundation for the advancement of TENGs technology.
2. Model and Computational Details
In this subsection, the CE performance between three amorphous polymers (i.e., PVC, PTFE, and FEP) and water is conducted using first-principles calculation methods. Initially, amorphous polymer unit cell models were constructed using molecular dynamics methods, followed by structural optimization via annealing algorithms to obtain stable configurations. Subsequently, the optimized polymer surfaces were coupled with water molecular layers to establish a complete interfacial contact system. Finally, based on density functional theory (DFT) [
34,
35,
36,
37,
38,
39,
40], the CASTEP module is utilized to calculate and analyze the electron transfer behavior and contact electrification mechanism at the amorphous polymer–water interface.
2.1. Molecular Dynamics Modeling of the Amorphous Polymers
This study focuses on halogen-containing materials commonly used in TENGs. PVC, PTFE, and FEP were selected as amorphous polymer study subjects. To further clarify the role of halogen elements in contact electrification, we additionally selected polypropylene (PP) as a complementary sample to investigate its charge transfer characteristics with water. As illustrated in
Figure 1b, all four polymers feature carbon-backbone structures with distinct functional side groups: methyl group (-CH
3) for PP, chloro- (-Cl) for PVC, tetrafluoro- (-CF
2-CF
2-) for PTFE, and trifluoromethyl- (-CF(CF
3)-) for FEP. This functional group disparity provides an ideal model system for studying substituent effects on interfacial charge transfer.
The amorphous polymer models were constructed using the Materials Studio 2020 software program with balanced computational efficiency and structural rationality. The PVC, PTFE, and FEP models each comprise five molecular chains containing seven repeat units. Structural optimization involved (i) 100 annealing cycles (300–800 K) under NVE ensemble, followed by (ii) 1000 ps molecular dynamics relaxation using NPT ensemble. The resulting stable amorphous structures (
Figure 2a) exhibit densities of 0.942 g/cm
3 (PP), 1.46 g/cm
3 (PVC), 2.023 g/cm
3 (PTFE), and 2.128 g/cm
3 (FEP), showing <5% deviation from experimental values, confirming the model’s validity [
41,
42].
2.2. Modeling of the Polymer–Water Contact Interface
The aqueous phase was modeled using ice-like structures to reproduce solid–liquid interfacial molecular orientations [
43,
44]. A three-layer water film was formed through sequential (011) ice plane adsorption on aluminum, with geometric optimization performed on upper layers after fixing the bottom layer to eliminate interfacial stress. The polymer–water contact models incorporated a 50 Å vacuum layer along the
z-axis to mitigate periodic boundary effects, yielding final system dimensions of 18.99 × 16.29 Å
2 (x-y plane,
Figure 2b). Interatomic interactions were described by the COMPASS force field [
45], with van der Waals and Coulombic interactions calculated via atom-based and Ewald methods respectively [
46,
47] (cutoff radius: 18.5 Å).
2.3. First-Principles Simulation on the Charge Transfer in Polymer–Water Contact Interfaces
An interface charge transfer analysis was performed using the CASTEP [
48] module with GGA-PBE [
49] exchange-correlation functional. Given the exclusive presence of light elements (H, C, O, F, Cl), ultrasoft pseudopotentials with Schrödinger relativistic treatment were employed. For the large-scale contact models, the plane-wave cutoff energy was set to 350 eV with Gamma-point only k-space [
21] sampling to balance accuracy and efficiency. Geometry optimization achieved convergence criteria of atomic forces < 0.05 eV/Å and energy tolerance < 1 × 10
−5 eV/atom using the BFGS algorithm.
Subsequently, to elucidate halogen-containing functional group contributions to electron transfer, DMol3 module was utilized for geometry optimization of monomeric and single-chain structures (convergence thresholds: energy change < 1 × 10−5 Ha, displacement < 0.005 Å). Subsequent electronic analyses included density of states (DOS) and partial density of states (PDOS) for band structure resolution; electrostatic potential surface profiling to identify charge transfer active sites; and frontier orbital energy distribution analysis for work function correlation.
To quantify the charge transfer, it is necessary to define the spatial integration range and numerical integration parameters for charge calculations. In this study, with the interface center (Z interface) as the origin, extend along the Z-axis to the polymer phase (Z < Z interface) to z = 0 and to the water phase (Z > Z interface) to the maximum z value, covering the entire configuration thickness. This range is sufficient to include the main influence area of interface charge transfer while avoiding overlap with periodic mirrors; in the X and Y directions, the same periodic boundary conditions as the calculation model are adopted, and the integration range is the entire simulation unit cell (18.99 × 16.29 Å2). In the CASTEP calculation, the Gamma Fine integration grid is used to ensure the accurate description of the spatial variation in charge density. The boundary conditions selected for the calculation are as follows: a free boundary is set in the Z-direction to avoid the influence of artificial constraints on the charge distribution; periodic boundary conditions are maintained in the X and Y directions to simulate an infinite plane.
Notably, in the polymer–water contact system, the interface center is defined as the central position of the transition region between the polymer surface and the water molecular layer, determined by integrating electron density gradient and atomic distribution characteristics. Specifically, the electron density distribution ρ(z) along the Z-direction is calculated to identify the position of maximum gradient (∇ρ(z)max), where the most drastic change in electron density occurs, serving as the preliminary interface center. Concurrently, the Z-directional distribution of polymer and water atoms in the contact configuration is statistically analyzed, with the average Z-coordinates of the nearest neighboring atoms from each phase serving as an additional reference. By synthesizing these electronic structure and atomic distribution features, the interface center is accurately pinpointed. This reference point effectively decouples the charge contributions of the polymer and water phases, eliminating interference from mirror interactions induced by periodic boundary conditions.
Additionally, to verify the reliability of the charge transfer calculation results, the uncertainty analysis is also carried out. Under the same calculation conditions, 5 independent geometric optimizations and charge calculations are performed for each polymer–water interface model. The initial configuration of each optimization is generated by applying random perturbations to the equilibrium structure of molecular dynamics. Then, the average value of the Z-direction charge transfer amounts obtained from 5 samplings is calculated. Finally, the calculation result with the smallest deviation from the average value is selected for a mechanism analysis.
3. Result and Discussion
The simulated charge transfer amount during water-contact electrification for four polymers (PTFE, FEP, PVC, and PP) is shown in
Figure 3. Here, the negative value represents that electron transfer from water to polymer. Simultaneously, this study also reveals that halogen-functionalized polymers (PTFE, FEP, and PVC) exhibit significantly stronger electron-withdrawing capabilities compared to non-halogenated PP, with the following strength hierarchy: FEP > PTFE > PVC. This finding agrees well with observation in Ref. [
50]. Given that these three polymers have the same main chain structure but differ in side-chain functional groups, we attribute the observed differences in charge transfer to the distinctive characteristics of their functional groups. To elucidate the underlying mechanism of halogen functional groups’ influence, we conducted systematic investigations from multiple perspectives including electrostatic potential distribution, frontier molecular orbitals (HOMO/LUMO), and electronic density of states. Our analyses demonstrate that HOMO and LUMO energy levels play a decisive role in the charge transfer process. Building upon these findings, we have further established a quantitative relationship model between HOMO/LUMO energy levels and charge transfer magnitude.
3.1. Charge Transfer Analysis for Polymer–Water Interface
Based on the previously optimized water molecular layer model, we use the CASTEP module to perform first-principles calculations on the electron density distributions at the contact interfaces between four typical amorphous polymers (PP, PVC, PTFE, and FEP) and water. By analyzing the electron density difference (EDD) maps, the spatial redistribution characteristics of the electron cloud density of each atom during the contact electrification process can be clearly observed. In the EDD maps, the yellow iso-surfaces in the interfacial region represent electron-enriched areas, while the green iso-surfaces correspond to electron-depleted areas.
To further quantitatively characterize the interfacial charge transfer characteristics, we calculate the planar average charge density difference (PACDD)
along the direction perpendicular to the interface (z-axis).
can be expressed as follows:
As shown in
Figure 4, the PACDD distribution curve clearly indicates that the charge transfer phenomenon is mainly concentrated within the nanoscale range of the contact interface.
can be mathematically expressed as follows:
represents the differential charge density,
denotes the interfacial charge density of the polymer–water complex, and
and
correspond to the individual charge densities of isolated polymer and water systems, respectively. EDD mapping provides direct visualization of electronic redistribution by quantifying the net variation in electron density before and after contact formation. This analysis enables the determination of charge transfer directionality during electronic coupling processes. As evidenced in
Figure 4, the interfacial analysis reveals the following: distinct electron depletion zones surrounding water atoms at all four interfaces (PP/water, PVC/water, PTFE/water, FEP/water); consistent charge transfer directionality from water to polymer matrices; the electron-accepting behavior of all studied polymers (PVC, PTFE, FEP). The observed charge transfer mechanism serves to equilibrate the orbital energy level disparity between contacting surfaces, with water molecules functioning as electron donors. This computational finding shows excellent agreement with experimental results [
51], validating our theoretical model.
3.2. Influence of Halogen-Containing Functional Groups on Charge Transfer
On the basis of clarifying the direction of charge transfer, the charge transfer amount in the polymer segment along the z-direction was compared with the interface center as the reference. This enabled a further analysis of the differences in contact electrification performance between these four distinct polymers and water. It can be seen from
Figure 3 that PP, FEP, PTFE, and PVC all carry negative charges after contact electrification with the water layer, and their electron capture capabilities follow the order of PP < PVC < PTFE < FEP. Since the main chain elements of these four amorphous polymers are identical, with only differences in the functional groups contained in the side chains, it can be concluded that the presence of different functional groups in amorphous polymers has distinct effects on the charge transfer after contact with the water layer. It can be intuitively observed from
Figure 3 that the electron capture capability of PP without halogen-containing functional groups is far lower than that of PVC, PTFE, and FEP with halogen-containing functional groups. Specifically, the functional group of PVC is Cl, while the functional groups of both FEP and PTFE contain fluorine. It can be thus inferred that polymers with F groups exhibit stronger capture capabilities. An analysis of PTFE and FEP reveals that FEP contains more F groups, which also indicates that a higher content of F groups leads to a stronger charge transfer ability. This conclusion is consistent with the influence of functional groups on contact electrification between amorphous polymers and metals.
3.2.1. Electrostatic Potential Reveals Active Sites for Electron Transfer
Owing to the structural complexity of amorphous polymer unit cells, which consist of five intertwined molecular chains with disordered packing, it is challenging to precisely identify charge transfer sites and elucidate electron transfer mechanisms. To systematically investigate the role of distinct functional groups in contact electrification with water, we subsequently focused our analysis on individual polymer chains. The electrostatic potential of single polymer chains was first calculated, as presented in
Figure 5. In the electrostatic potential mapping, molecular groups with negative potential values exhibit enhanced affinity for attracting negatively charged particles, while those with positive potential values demonstrate a greater tendency for electron donation. The electrostatic potential analysis reveals that chlorine (Cl) functional groups in PVC display negative potential regions, indicating their preferential electron-accepting behavior from water molecules. Similarly, fluorine (F) groups in both PTFE and FEP exhibit pronounced negative potentials, confirming their crucial role as active sites for electron capture during interfacial contact with water.
3.2.2. Frontier Orbital Analysis of Electron Acceptor/Donor Atoms
To elucidate the correlation between electron accumulation/depletion regions and frontier molecular orbitals, as well as to identify the predominant electron acceptor and donor atoms in the three polymers, we performed a frontier orbital analysis on individual polymer chains (
Figure 6). According to Wu et al. [
52], the lowest unoccupied molecular orbital (LUMO) serves as the electron acceptor orbital, while the highest occupied molecular orbital (HOMO) functions as the electron donor orbital. Our computational results reveal distinct orbital distribution patterns: for PVC, the LUMO is mainly concentrated on the Cl group located in the middle front side of the single chain, with partial distribution near the H and C atoms of the monomer connected to the Cl group; the HOMO is mainly concentrated on the Cl group in the middle of the chain. This is because the Cl group has strong electronegativity, causing the electron cloud [
4,
53,
54,
55] to bias toward the Cl group, thereby forming an electron-deficient structure near the C and H atoms. The conclusions of LUMO and HOMO are consistent with the result that the electrostatic potential near the Cl group is negative in the PVC electrostatic potential map. For PTFE, its LUMO is mainly distributed on the C group, and the HOMO is mainly distributed on the F group, which is consistent with the electrostatic potential conclusion. For FEP, the LUMO is mainly distributed on the C group in the middle of the single chain, and the HOMO is mainly distributed on the F group at the chain head. This phenomenon is due to the strong electronegativity of F atoms when forming strong polar covalent C-F bonds, and the electrons captured by F atoms originate from C atoms, which makes C atoms form electron-deficient structures. Electron-deficient structures require external electrons to fill their empty orbitals. Therefore, when polymers containing F groups come into contact with water, a large number of electrons are transferred from the water to the polymers, causing PVC, PTFE, and FEP to exhibit negative charges. The more F groups present in the polymer, the greater the total amount of charge transfer, which is consistent with previous studies [
24].
3.2.3. Density of States Reveals the Composition of Frontier Orbitals
Finally, to gain deeper insights into the electronic structural characteristics of PVC, PTFE, and FEP, this study systematically analyzed the composition of their HOMO and LUMO through DOS and PDOS calculations of molecular monomers. The validity of this analytical approach stems from the inherent charge localization properties of insulating materials, as demonstrated in prior research by Li et al. [
56], which confirmed that similar methodologies can effectively elucidate the electronic structural features of such materials.
The DOS spectra of pristine (before-contact) samples (
Figure 7a,c,e) exhibit sharp, discrete characteristic peaks, reflecting the typical strong electron localization properties of insulating materials. Among these, the first peak above 0 eV corresponds to the LUMO energy level of each material, with the Fermi level defined as 0 eV. A further PDOS analysis (
Figure 7b,d,f), combined with the atomic numbering indicated in the upper-left corner of the DOS plots, enables the precise identification of the atomic orbital contributions to the LUMO.
The integrated DOS/PDOS analysis reveals the energy distribution of electronic states, the atomic composition of frontier orbitals, and charge localization characteristics. This methodology adheres to the computational paradigm for insulating polymers and aligns with previous single-chain analyses, ensuring the comparability of results across different structural hierarchies.
In the case of PTFE, the highly symmetric monomer structure leads to a uniform influence of fluorine atoms on the carbon chain. The PDOS analysis (
Figure 7b) indicates that the p-orbitals of C1 and C2 atoms dominate the LUMO contribution, while the s- and p-orbitals of the F3 atom and the p-orbital of the H8 atom contribute minimally. This suggests that the LUMO is primarily distributed along the carbon backbone, with carbon atoms acting as the main electron-accepting sites. Notably, the electron density of states at the LUMO level is significantly higher than that at the HOMO level, further supporting PTFE’s characteristic as an electron-accepting material.
Figure 7d reveals that the LUMO of PVC is predominantly localized around the C2 atom bonded to the chlorine atom in the repeating unit of the polymer chain. The C2 atom exhibits the most significant contribution to the LUMO, followed by the Cl6 atom. Additionally, the Cl6 atom also plays a crucial role in the formation of the HOMO. These findings are consistent with the previously calculated LUMO and HOMO distributions. As illustrated in
Figure 7f, for FEP, the p-orbitals of the C5 atom in the trifluoromethyl group and the C2 atom in the monomer center are the primary contributors to the LUMO. This observation highlights the substantial influence of the trifluoromethyl group on the electronic structure of carbon atoms, confirming its strong electronegativity.
3.3. Orbital Energy Levels Regulate Charge Transfer Capacity
To dissect the mechanism of how polymer intrinsic properties influence the contact electrification process, this study conducted quantitative calculations on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of PVC, PTFE, and FEP single chains, with the results detailed in
Table 1. The LUMO energy level reflects the electron affinity of molecular orbitals: lower values indicate a stronger tendency for orbitals to capture electrons, facilitating energy level stabilization through electron filling. The HOMO energy level, conversely, correlates with the electron-donating capacity of molecules: higher energy positions signify greater electron delocalization and enhanced electron-release propensity. Materials with positive LUMO energy levels exhibit electron repulsion and cannot effectively couple with external electrons.
The data in
Table 1 demonstrate that PVC, FEP, and PTFE all exhibit electron-accepting capabilities, which reasonably explains that the charge transfer phenomenon during their contact with water–polymer surfaces accumulates electrons to carry a negative charge, while water molecules develop a positive charge due to electron deficiency. Comparing their LUMO energy levels (PVC > PTFE > FEP) reveals that FEP has the strongest electron affinity, followed by PTFE and then PVC. This finding is highly consistent with the theoretical expectation that fluorine-containing groups enhance their electron capture ability, confirming the positive correlation between fluorine content and electron acquisition efficiency. It can thus be inferred that lowering the LUMO energy level optimizes electron transfer kinetics in contact electrification, providing a critical theoretical basis for improving the output performance of TENGs.
Figure 8a illustrates the electron energy level distribution of water and polymer in the non-contact state, where charge transfer does not occur due to the excessive interfacial distance. When in contact, their electron cloud wavefunctions overlap (
Figure 8b), and the interfacial barrier between the polymer and water vanishes, enabling electrons in water molecules to transition into the LUMOs of the polymer. The deep potential well of the polymer’s molecular orbitals effectively traps and stabilizes these transferred electrons, as described in Reference [
57]. Consequently, water molecules become positively charged due to electron loss, while the polymer acquires a negative charge from electron gain (
Figure 8c). A lower LUMO energy level significantly reduces the activation energy for electron transfer during electron cloud overlap. Thus, we conclude that reducing the LUMO energy level facilitates enhanced electron transfer efficiency in the contact electrification process, thereby improving the output performance of TENGs.
4. Conclusions
This study systematically investigates the contact electrification phenomena at the interface between water and three typical halogen-containing amorphous polymers, including PVC, PTFE, and FEP. Using first-principles calculations based on density functional theory (DFT), we first establish separate models of polymeric unit cells and aqueous molecular layers, then combine them into interfacial architectures for computational simulation. By establishing water–polymer interface models, we comprehensively analyze the microscopic mechanisms of contact electrification from multiple perspectives including electron transfer behavior, functional group effects, and electronic structure characteristics. The results demonstrate that fluorinated polymers (PTFE and FEP) exhibit a significantly stronger electron capture capability than chlorinated polymer (PVC), with the fluorine content showing a positive correlation to charge transfer capacity (FEP > PTFE). An electron density difference analysis reveals characteristic electron transfer pathways from water molecules to polymers at the interface, while frontier orbital (i.e., LUMO and HOMO) theory analysis indicates a strong relationship between a material’s electron affinity and its lowest unoccupied molecular orbital (LUMO) energy level (FEP < PTFE < PVC).
The established theoretical model provides reliable insights into contact electrification at amorphous polymer–water interfaces, elucidating the pivotal role of functional groups (particularly fluorine-containing groups) in charge transfer processes. These findings offer fundamental theoretical guidance for designing high-performance TENG materials. The study suggests that optimizing electron capture capacity through the rational selection and proportional control of functional groups or lowering the LUMO energy level in polymers could effectively enhance charge transfer efficiency and consequently improve TENG output performance.
In addition, it should be emphasized that deionized water contains trace ionic components. On the one hand, ions will participate in charge transfer. On the other hand, the adsorption of ions on solid interfaces will play an electrostatic shielding role in the electrification of solid–liquid contact. Therefore, we will further investigate the contact electrification mechanism between ionic solutions and solids. Moreover, working condition factors such as temperature and applied (secondary) electric fields can also affect the contact electrification process. This work only performed simulations at room temperature (298 K), and future work will consider the effects of different temperatures, electric fields, and other factors. Furthermore, this study only investigated three typical polymers with halogen-containing functional groups, and the representativeness of our conclusions needs to be validated through experiments.