Multiscale Investigation of Triboelectric Nanogenerator: An Expanded DFT Calculation Based on Machine Learning

Abstract

Various types of triboelectric nanogenerators (TENGs) have been proposed, which rely on the details of electron transfer, ion migration, and mechanochemistry, but their largely different scales complicate the quantitative analysis of their contributions. In this study, we first investigate the electron transfer behavior at the nanoscale using density functional theory (DFT) calculations for the contact of two typical insulating materials, poly­(vinyl chloride) (PVC) and poly­(vinyl alcohol) (PVA), with an adsorbed water layer in between. The DFT results are then used to construct machine learning (ML) potentials, which enable us to execute larger-scale classical molecular dynamics (MD) simulations. The results demonstrate that electron transfer contributes to the generation of an electrostatic potential difference among materials, while ion migration compensates for part of the potential, leading to a reduced power output. This approach with ML establishes a multiscale simulation framework that links quantum-level mechanisms based on DFT to the investigation of mesoscale behaviors using classical MD simulations, providing insights into the interplay of charge transfer processes and offering guidance for the design of efficient TENG materials.

1. Introduction

Since the concept of triboelectric nanogenerators (TENGs) was first proposed in 2012 by Wang et al., , it has emerged as a promising technology for harvesting mechanical energy from the environment. Due to their advantages of low cost, lightweight, material diversity, and structural flexibility, TENGs have attracted significant attention in various applications, such as self-powered sensors, wearable electronic devices, and the Internet of Things (IoT).

At the macroscale level, TENGs operate through the periodic contact and separation, or relative motion, of two materials with different triboelectric polarities, as schematically shown in Figure . When two surfaces come into contact, charge transfer occurs at the interface due to triboelectrification. Subsequent mechanical motions, such as vertical contact–separation or lateral sliding, lead to charge redistribution and induce an electrostatic potential difference between the electrodes. This potential difference drives electrons through an external circuit, thereby generating an electric current. In addition to the classical contact–separation and sliding modes, other configurations such as the single-electrode and freestanding triboelectric-layer modes have been developed to adapt TENGs for diverse applications and geometrical constraints. Regardless of its specific design, the essential working mechanism is based on a combination of interfacial charge transfer and electrostatic potential induction, making the mechanical motion of surfaces a key for the device performance.

1.

Typical cycle of a TENG with two electrodes.

Experimental studies have provided valuable insights into TENG device architectures, material selection, ,, and performance optimization. However, directly resolving charge transfer processes and interfacial charge dynamics at the atomic scale remains challenging through experimental approaches alone.

Recent advances have further demonstrated the importance of interfacial regulation and material engineering in enhancing TENG performance. For example, ionic components and interfacial chemical environments have been introduced to regulate triboelectric charge generation, highlighting the potential influence of molecular-level interactions on TENG output. , In addition, advanced material designs have been developed to improve the environmental stability and practical applicability of the TENG devices. These studies indicate that, beyond macroscopic device optimization, a deeper understanding of interfacial charge dynamics is essential for further improving the TENG performance.

Theoretical investigations on the mechanism have been reported at various spatial scales. At the atomic or nanoscale, density functional theory (DFT) and other first-principles quantum mechanics approaches have been employed to probe electron transfer processes at material interfaces with high accuracy; however, such methods are restricted to relatively small systems and fast processes. In contrast, classical molecular dynamics (MD) simulations − can capture larger-scale structural evolution and ion migration, but they essentially neglect the quantum nature of electron dynamics. As a result, any single-scale approaches cannot fully cover the multiscale nature of TENGs, where interfacial electron transfer and long-range ion transport are inherently coupled. Therefore, it becomes essential to develop computational strategies that combine quantum-level accuracy with large-scale dynamical descriptions.

In this work, we aim to fill this gap by employing a classical MD simulation with a machine-learning (ML) potential, which is developed based on DFT calculations. This combined approach enables reasonably accurate and scalable simulations of the contact and separation processes among polymeric materials.

As a test target of this approach, we chose a simple system of poly­(vinyl alcohol) (PVA) and poly­(vinyl chloride) (PVC) films in aqueous environments. We first employed density functional tight-binding calculations using the DFTB+ package to verify the electron transfer behavior between PVC and PVA in a small-scale model. By adopting a similar DFT approach, a training data set is constructed for ML. Using this data set, a model was developed with the DeepMD-kit tool, , and the potential data were generated for large-scale MD simulations on LAMMPS package. Considering the importance of the capillary bridge formed by adsorbed water, we extend the system illustrated in Figure to include water layer, which enables us to investigate the synergistic contributions of both electron and ion transport to the TENG performance.

The multiscale quantum-classical MD simulation scheme proposed in this study not only provides a deeper understanding of the elementary process with combined effects of electronic and ionic contributions in TENGs, but also offers theoretical guidance for optimizing device performance under varying humidity conditions.

2. Systems and Methods

2.1. Material Selection

Triboelectric tendency series have been given in several studies, which list various materials according to their tendency to have positive/negative charges when contacted. A typical example provided by Gooding and Kaufman , describes that, among various polymeric materials, PVC has a strong tendency to be negatively charged, next to the widely used poly­(tetrafluoroethylene) (PTFE), while PVA exhibits a tendency to be positively charged, close to mica. PVA and PVC are also favorable because of their low production cost. For these reasons, we explore in this work the PVA/PVC combination, which is less discussed in the literature. The structural formulas of PVA and PVC are shown in Figure .

2.

Structural formulas of PVA and PVC.

We are also interested in capillary bridges in insulator systems, where water vapor spontaneously condenses on material surfaces (especially on a highly hydrophilic PVA surface) to form water bridges, which should have significant effects on the charging process. Based on this picture, we investigate the role of a thin water film between PVA and PVC as the medium to facilitate ion transport. In this study, we focus solely on water molecules and a small amount of H⁺ and OH^– ions, which are spontaneously produced during the DFT calculation. The presence of other types of ions, such as Na⁺ and Cl^–, might have a significant effect, which is left for future study.

2.2. Quantum Simulation with DFT

2.2.1. Geometry Optimization

To construct the molecular models of the polymer systems, we first prepared single polymer chains of PVA and PVC using the molecular editor Avogadro. We suppose that the local electronic structure is not much affected by the molecular size for these insulating polymers, so we limit the degree of polymerization to n = 5 for both polymers to save computational resources. Thus, each PVA: (C₂H₄O)₅ and PVC: (C₂H₃Cl)₅ “chain” is composed of 37 and 32 atoms, respectively.

Four chains were then placed on a plane with some spacing to form a slab, as shown in Figure . To suppress unphysical atomic interactions during the subsequent structural relaxation and optimization, the spacing between adjacent chains was set to 3.5 Å, which is a typical Lennard-Jones (LJ) diameter of carbon atoms. ,

3.

Initial arrangement of PVC slab before geometry optimization.

As for the water film, 40 water molecules with atomic configurations of the TIP3P model were placed on the lattice points of a 4 × 5 × 2 simple cubic configuration with intermolecular separations of 3.188 Å, corresponding to the LJ diameter of oxygen atoms. ,

We carried out geometry optimization for each of the generated molecular systems (PVA, PVC, and water) with a DFT quantum calculation, for which we utilized the software DFTB+. As the Slater–Koster parameter set, we employed the 3ob-3–1 family, , which is being optimized for bio-organic molecules. Table shows the atomic Hubbard derivatives for the third-order correction, which were chosen from refs , , and the orbitals of maximum angular momentum to be considered. These settings ensure an appropriate balance between computational efficiency and accuracy for describing the electronic structures of the polymer–water systems under investigation.

1. Relevant Parameters for DFTB Calculations.

atom	Hubbard derivatives [eV]	orbital of maximum angular momentum
O	–0.1575	p
H	–0.1857	s
C	–0.1492	p
Cl	–0.0697	d

2.2.2. Charge Transfer through Surface Contact

Next, the optimized three slabs, PVA, water, and PVC, were combined and placed into a cuboid simulation box of 22 Å × 15 Å × 40 Å, which provides sufficient space to accommodate the molecular slabs while avoiding artificial interactions under periodic boundary conditions. The three slabs were initially arranged along the z-direction with an approximate separation of 10 Å. Prior to the main simulation of surface contact and separation, thermal equilibration for 5000 steps with a 0.1 fs time step was performed under the NVT ensemble at 300 K using the Nosé–Hoover chain thermostat.

After the equilibration, the contact–separation simulation was carried out with the following two steps.

• Step 1 (slab collision): A velocity shift of Δv _z = ±15 Å/ps is added to each atom in the PVA and PVC slabs to make the film collide, as shown in Figure . A subsequent 1 ps NVT simulation is carried out, during which the two polymer slabs move toward the water layer and collide.

• Step 2 (separation): After the collision, an opposite velocity shift of Δv _z = ∓15 Å/ps is added to each atom in the PVA and PVC slabs to drive them apart. This process is monitored for another 1 ps.

4.

Quantum simulation of slab collision; initial setting after the geometry optimization and equilibration.

The detailed parameters used in the DFT calculations are summarized in Table .

2. Relevant Conditions for Quantum Simulation of Slab Collision.

molecule type	number of molecules	number of atoms	total number of atoms	total number of electrons
PVA	4	148	396	1056
H2O	40	120
PVC	4	128

box size	L x  × L y  × L z  = 22 Å × 15 Å × 40 Å
Boundary condition	Periodic for all directions
Controlled temperature	300 K
Time step	0.1 fs
Total simulated time	2 ps

2.3. Building ML Potential

To construct a machine learning (ML) potential for the classical MD simulations, we employed the open-source package DeepMD-kit.

The Deep Potential (DP) model represents the total potential energy of a molecular system as a sum of atomic energy contributions, each of which depends on the local chemical environment of the corresponding atom

$$E_{\mathrm{total}}=\sum _{i=1}^N{E}_i({\mathbf{R}}_i)$$ 1

where E _i is the energy associated with atom i and R _i denotes the set of relative positions of neighboring atoms within a cutoff radius r _c . The descriptors are constructed to satisfy translational, rotational, and permutational invariance, ensuring that the resulting force field is physically consistent and independent of the choice of coordinate system or atomic indexing. The force acting on each atom is obtained as the gradient of the total energy with respect to atomic positions

$${\mathbf{F}}_i=-\frac{\partial E_{\mathrm{total}}}{\partial {\mathbf{R}}_i}$$ 2

Since the atomic energy functions E _i (R _i ) are represented by deep neural networks, the corresponding atomic forces are computed through automatic differentiation of the network outputs. This approach guarantees that the forces are conservative and fully consistent with the potential energy surface learned from the ab initio reference data. During training, the network parameters are optimized by minimizing a loss function $\mathcal{L}$ , which balances the contributions from energies and forces

$$\mathcal{L}={\omega }_E\sum _k{(E_k^{\mathrm{pred}}-E_k^{\mathrm{ref}})}^2+{\omega }_F\sum _k\sum _i{\parallel {\mathbf{F}}_{i,k}^{\mathrm{pred}}-{\mathbf{F}}_{i,k}^{\mathrm{ref}}\parallel }^2$$ 3

where E _k and F _i,k denote the reference energy and atomic forces of frame k, respectively, while E _k and F _i,k are the corresponding model predictions. The prefactors ω _E and ω _F control the relative importance of the energy and force terms in the loss function and are dynamically adjusted during the training to ensure an accurate reproduction of both quantities.

As the DFT reference model described in the previous section contains many atoms and a large vacuum region, it is not suitable to be used as the training data set due to its high computational cost and poor sampling efficiency. Instead, we newly generated smaller systems for the training data sets using Packmol. Five data sets were prepared, the atomic compositions of which are summarized in Table .

3. Atomic Compositions of the Training Datasets Used for Building the ML Potential Model.

	number of atoms
data set	H	O	C	Cl	total
Data set-1	18	3	5	9	35
Data set-2	20	3	6	9	38
Data set-3	22	3	6	10	41
Data set-4	22	5	7	10	44
Data set-5	23	5	7	11	46

For efficient sampling of the condensed phase, all data sets were placed in a cubic box of 8.16 Å × 8.16 Å × 8.16 Å, which gives the mass density close to 1 g/cm³. MD simulations with DFTB+ were carried out at a rather high temperature of 1000 K for 10 ps with a time step of 0.5 fs to generate the training data, to ensure sufficient sampling of diverse atomic configurations. For each of the five data sets listed in Table , we extracted configurations every 50 fs, resulting in 200 frames for each data set. Among these samples, 90% of the frames were used for training, while the remaining 10% were reserved for validation. In total, the training set consists of 900 frames, and validation was done on the remaining 100 frames.

The data of box size, atomic species, atomic coordinates, system energy, and atomic forces generated by DFTB+ were subsequently converted into binary NumPy (.npy) format using a Python script, which are the input data to DeepMD-kit. The input configurations for training the DeepMD model are summarized as follows:

• 1.The type map includes four atomic species, H, O, C, and Cl, to generate a potential model for the multicomponent systems.
• 2.For the descriptor, we employed the se_e2_a type, with an automatically selected neighbor list.
• 3.The embedding network consists of three layers with neuron sizes of [25, 50, and 100], while the number of axis neurons is set to 16. The fitting network was defined with three hidden layers of 240 neurons each, incorporating residual connections to enhance training stability.
• 4.The learning rate follows an exponential decay schedule, decreasing from an initial value of 1 × 10^–2 to 1 × 10^–8 with a decay step of 50.
• 5.The loss function consists of energies and forces, with the energy prefactor ω _E gradually increasing from 0.02 to 1, while decreasing the force prefactor ω _F from 1000 to 1; the virial contribution was excluded.

These settings allow the training procedure to be dominated by the force term at the beginning and by the energy term at the end of the training.

2.4. Classical MD Simulations with ML Potential

Finally, we carried out classical MD simulations with LAMMPS , by employing the obtained DP model, which provides access to longer time scales than those of direct DFT calculations.

We adopted a model structure consistent with the DFT setup, i.e., a three-layer slab configuration consisting of PVA, water, and PVC, as shown in Figure . To fairly compare the results of DFT and DeepMD simulations, the same size of polymerization n = 5 was used, and the number of polymer chains was increased to eight. The number of water molecules was also increased accordingly, with the detailed atomic compositions summarized in Table . The simulation box was also enlarged to 30 Å × 30 Å × 50 Å, which ensures an appropriate density and sufficient separation between periodic images.

5.

Classical MD simulation of slab collision with DeepMD potential; initial setting.

4. Relevant Conditions for Classical MD Simulation with DeepMD Potential.

molecule type	number of molecules	mumber of atoms	total number of atoms
PVA	8	296	882
H2O	100	300
H3O+	5	20
OH–	5	10
PVC	8	256

box size	L x  × L y  × L z  = 30 Å × 30 Å × 50 Å
Boundary condition	Periodic for all directions
Controlled temperature	300 K
Time step	0.1 fs
Total simulated time	15 ps

The overall MD procedure is similar to that of the DFT simulations. The main difference exists in the method to drive slabs; while initial velocity shifts Δv _z were directly added to each atom in the molecular slabs in the DFT simulation, the slab motion along the z-direction was indirectly controlled by confining each slab (PVA, PVC and water) in moving external fields,

$$U^{\mathrm{ext}}(z)=\{\begin{array}{ll}\frac{k}{2}{(z-z_b)}^2& \mathrm{for}z\le z_b\\ \frac{k}{2}{(z-z_t)}^2& \mathrm{for}z\ge z_t\end{array}$$ 4

with an appropriate harmonic spring constant k, which confines molecules between moving boundaries z _b (t) and z _t (t) when z _b < z _t . This driving field was realized with the fix_indent command in LAMMPS. This confinement prevents structural collapse of the molecular slabs and enables the slabs to be driven at a slower speed, thereby allowing a longer equilibration/relaxation during the MD runs.

The contact/separation was traced in the following two steps:

• Step 1 (slab collision): The confining field is moved toward the water slab with a velocity of v _z = ±5 Å/ps for 2 ps, followed by an equilibration run of 8 ps. The total simulation time for this step is 10 ps.

• Step 2 (separation): The direction of the confining field is inverted, and the slabs are driven apart to their initial positions over 2 ps, followed by an equilibration run for 3 ps. The total simulation time for this step was 5 ps.

The initial z _b (t) and z _t (t) of each component are shown in Table

5. Initial Bottom and Top Positions of the External Field for PVA, H₂O, and PVC.

	PVA	H2O	PVC
Z b (t = 0) [Å]	10.0	24.0	39.8
Z t (t = 0) [Å]	14.2	30.0	44.0

The simulation was performed under the canonical (NVT) ensemble conditions at 300 K. Since we assign “deepmd” to the setting pair_style in the LAMMPS simulation, no further specification of interaction parameters was required, which greatly simplifies the simulation setup when compared with conventional empirical force fields.

3. Results and Discussion

3.1. Density of States

First, the electronic density of states (DOS) was calculated for each slab equilibrated at T = 300 K to investigate its electronic properties. The results are shown in Figure with the Fermi levels,

• PVA: ε_F = 0.021 eV

• PVC: ε_F = −4.232 eV

• Water: ε_F = 0.873 eV

The order of the Fermi level, ε_F ≪ ε_F < ε_F , suggests that electrons tend to transfer from water and PVA to PVC.

6.

Density of states (DOS) of thermally equilibrated slabs. The arrows indicate the Fermi level.

3.2. Charge Transfer Dynamics

Typical configurations during the MD simulation with DFT are depicted in Figure . Initially, at 0 ps, the PVA and PVC slabs are positioned in parallel, with a uniform thin layer of water molecules in between. The polymer slabs approached the water layer and collided with a rather high speed |v _z | ≃ 15 Å/ps (=1500 m/s). Figure (c) shows the configuration at the closest contact, where significant structural distortion of the polymer slabs as well as the water layer is observed. The hydrogen-bonding network within the water layer undergoes rearrangement, while local density fluctuations emerge near the interfaces. The v _z values of all atoms in the polymer slabs were inverted at 1 ps, after which the separation process was traced. By 2 ps, the slabs completely separated again; however, the water molecules did not fully reestablish their original interfacial liquid-film structure. Instead, a fraction of the water molecules are dragged by the PVA or PVC slab, while the remaining fractions are dispersed in the central region.

7.

Snapshots of the system obtained from DFT-based MD simulation: (a) Initial state at 0 ps, (b) first contact at 0.8 ps, (c) closest contact at 1 ps, and (d) completely separated state at 2 ps. Red sphere: oxygen atom, cyan: carbon, white: hydrogen, brown: chlorine.

During the simulation with DFTB+, orbital-resolved charge data were stored, from which we evaluated atomic charges using the Mulliken population analysis as implemented in DFTB+. The Mulliken electron population N _i for each atom was recorded during the simulation, and the atomic charge q _i was defined as the difference between N _i and nuclear charge Z _i . Changes of the slab charge, defined as the sum of atomic charges within each slab, are illustrated in Figure .

8.

Change of total electric charge during DFT simulation.

Both PVC and H₂O exhibit a pronounced charge transfer, which reaches its peak of −0.557 e (PVC) and +0.507 e (H₂O) around 0.95 ps, where e = 1.602 × 10^–19C is the elementary charge. In contrast, PVA shows only a moderate electron loss of +0.226 e at ∼0.8 ps, slightly earlier than PVC and water. As seen in Figure , each polymer slab starts to get in contact with the water layer around 0.8 ps, and a significant number of electrons are transferred from the water to PVC, establishing a dominant pathway that facilitates charge redistribution between the polymer slabs. This suggests that the role of water on polymer slab surfaces is not passive; water molecules actively govern the charge dynamics at the interface, leading to an asymmetric electronic response of PVA and PVC. Although Mulliken charges are known to be basis-dependent, they are sufficient for capturing the relative trends of charge transfer discussed in this work.

It is noticeable that a negative charge of about −0.2 e (corresponding to one electron per 16 nm²) remains in the PVC slab after separation, confirming the PVC’s strong tendency to become negatively charged in the triboelectric series.

3.3. Electric Field Analysis

To gain a deeper insight into the electronic response of the system during the dynamic process, we further analyzed the spatial distribution of electrostatic potential. The whole system is divided into three-dimensional cubic grids, and the electrostatic potential ϕ­(r⃗) is determined by the Poisson equation

$$\mathrm{\Delta }\varphi =-\frac{\rho }{{ϵ}_0}$$ 5

where ϵ₀ = 8.854 × 10^–12 F/m is the electric constant and ρ­(r⃗) is the local atomic charge density, with the boundary conditions

$$\begin{array}{ll}\mathrm{a}\mathrm{long}x,y:& \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{c}\\ \mathrm{a}\mathrm{long}z& \frac{\partial \varphi }{\partial z}=0\mathrm{at}z=z_{\min }=0\AA \mathrm{and}{z}_{\max }=40\AA \end{array}$$

We use a small grid size of 0.2 Å to have an atomistic resolution.

The Poisson equation is discretized using a second-order central finite-difference scheme. At each grid point, the electrostatic potential is updated according to

$${\varphi }_{i,j,k}=\frac{1}{6}({\varphi }_{i+1,j,k}+{\varphi }_{i-1,j,k}+{\varphi }_{i,j+1,k}+{\varphi }_{i,j-1,k}+{\varphi }_{i,j,k+1}+{\varphi }_{i,j,k-1}+\frac{\mathrm{\Delta }{x}^2}{{ϵ}_0}{\rho }_{i,j,k})$$ 6

which corresponds to the standard six-point stencil of the Laplacian operator. The resulting linear system is solved iteratively using the successive over-relaxation (SOR) method.

The convergence of the iterative procedure is monitored by the maximum change in potential ϕ _i,j,k between successive iterations, and the calculation is considered to be converged when the absolute error falls below 10^–6 V. Since the electrostatic potential is defined up to an arbitrary constant, the spatial average of the potential is subtracted during each iteration step to remove the gauge freedom and to ensure numerical stability.

Examples are shown in Figure , which indicate cross-sectional views of ϕ on the y = 7.5 Å plane. Initially at 0 ps, the PVA slab exhibits a bright yellow region corresponding to relatively high electrostatic potential, whereas the PVC slab appears green, indicating lower potential. This pronounced initial potential difference is likely caused by the polar configuration of the PVC surface, where negatively charged chlorine atoms are preferentially oriented toward the vacuum side. The PVA slab and water layer show comparatively smoother potential distributions due to their less ordered atomic structures. Around 1 ps, the two slabs collide and the maximum charge transfer is reached. A significant redistribution of the potential is observed in the interfacial region, consistent with the charge dynamics shown in Figure . After the collision, the initially ordered polar arrangement is largely disrupted, and the electrostatic potential in the vacuum region becomes nearly zero. The slabs are completely separated by 2 ps, after which the remaining potential distribution mainly reflects the residual surface charges generated during contact electrification.

9.

Spatial distribution of the electrostatic potential on the xz plane at y = 7.5 Å at different stages of the DFT simulation: (a) Initial state at 0 ps, (b) approaching/contact stage at 0.8 ps, (c) closest contact at 1.0 ps, and (d) separated state at 2.0 ps.

The electrostatic potential profile ϕ­(z) averaged over an xy plane is defined as

$$\varphi (z)=\frac{1}{L_x{L}_y}\int \varphi (\mathrm{r⃗})\mathrm{d}x\mathrm{d}y$$ 7

and examples are shown in Figure . To evaluate the generated electrostatic potential difference, we define the potential of each material at its center-of-mass (com) position, as

$$\{\begin{array}{l}{\varphi }_{\mathrm{PVA}}\equiv \varphi (z=z_{\mathrm{com}}^{\mathrm{PVA}})\\ {\varphi }_{{\mathrm{H}}_2\mathrm{O}}\equiv \varphi (z=z_{\mathrm{com}}^{{\mathrm{H}}_2\mathrm{O}})\\ {\varphi }_{\mathrm{PVC}}\equiv \varphi (z=z_{\mathrm{com}}^{\mathrm{PVC}})\end{array}$$ 8

The potential difference is then defined as

$$\mathrm{\Delta }\varphi \equiv {\varphi }_{\mathrm{PVA}}-{\varphi }_{\mathrm{PVC}}$$ 9

The change of z _com for each material and Δϕ are shown in Figure .

10.

Electrostatic potential along the z-direction at different stages of the simulation: (a) Initial state at 0 ps, (b) approaching/contact stage at 0.8 ps, (c) closest contact at 1.0 ps, and (d) separated state at 2.0 ps.

11.

Time evolution of (a) the center-of-mass (COM) position for each material and (b) the electrostatic potential difference Δϕ ≡ ϕ_PVA – ϕ_PVC.

Initially, a positive electrostatic potential difference of ∼1.1 V exists between the PVA and PVC slabs, reflecting their intrinsic electronic asymmetry. As the simulation proceeds and the two slabs approach each other, the potential difference increases rapidly, reaching nearly twice its initial value. This indicates interfacial polarization enhancement and charge redistribution driven by the reduced separation and increased interaction between the slabs, mediated by the confined water layer.

As the system undergoes further equilibration near the contact state, the potential difference gradually relaxes back toward its initial level, suggesting a transient nature of enhanced charge separation. Once the separation process begins (around 1 ps), the potential difference decreases sharply and even temporarily becomes negative, indicating a reversal of the interfacial electric field due to the dynamic redistribution of the charges.

After the separation process is completed, the system continues to equilibrate, and the potential difference recovers to a value close to the initial state. This behavior demonstrates that the electrostatic response of the system is largely reversible under the present simulation conditions, although transient charge transfer and polarization effects are clearly observed during the contact–separation cycle.

3.4. Classical MD Simulations with ML Potential

Using the developed machine-learning (ML) potential, we carried out classical MD simulations for a much larger system. Typical snapshots are shown in Figure . As we made positional restrictions separately on the PVA, PVC, and water layers, the system successfully preserved its overall slab morphology throughout the simulation, in clear contrast to the DFT simulations. However, certain limitations of the DeepMD-generated potentials are observed. The backbone carbon chains in the polymers exhibit partial cleavage into shorter fragments during the simulation, suggesting that the trained ML potential may not fully capture the polymer’s structure and stability. Further optimization of the ML potential, such as incorporating additional training configurations involving polymer deformation and bond-breaking processes, would be necessary to improve the description of polymer stability in future simulations.

12.

Snapshots of the system obtained from classical molecular dynamics (MD) simulations using the Deep Potential (DeepMD) model at different time steps: (a) initial configuration at 0 ps, (b) intermediate state at 10 ps, and (c) postcontact/separation state at 15 ps.

Unlike the conventional potentials, the atomic interactions in the DeepMD scheme do not separately consider the long-range Coulombic terms and other short-range ones. Thus, we cannot directly obtain the atomic charge data with the DeepMD model. Instead, we evaluate the charges separately with atomic configurations by utilizing a charge equilibrium (Qeq) method. Among several schemes, we adopt the qeq/shielded method, which is often used in MD simulations of chemical reactions, such as ReaxFF schemes.

Change of the evaluated total charge for each material is plotted in Figure . Unlike the DFT calculations, this classical MD simulation produces nonzero initial charges because Qeq schemes generally give an equilibrium charge distribution, even when atoms are far apart. Upon collision at about2 ps, PVA quickly stabilizes at a nearly constant positive charge, while PVC and water continue to exchange electrons during equilibration.

13.

Change of total electric charge during MD calculation with ML potential.

From 0 ps to the closest contact at 10 ps, the change in the relative charge separation between PVA and H₂O remains small, |Q _PVA – Q _H2O|_10 ps – |Q _PVA – Q _H2O|_0 ps ≈ 0.807 e, whereas a much larger increase is observed for the PVC–H₂O pair, |Q _PVC – Q _H2O|_10 ps – |Q _PVC – Q _H2O|_0 ps ≈ 6.560 e. At 10 ps, PVA carries a charge of +2.715 e, PVC of −4.642 e, and water +1.918 e relative to their initial states.

These results suggest that charge transfer is dominated by PVC–H₂O interactions, whereas PVA remains largely unaffected after the initial exchange, in qualitative agreement with the DFT simulation.

In addition to electron transfer between polymer interfaces, the aqueous layer may also influence the interfacial electrostatic response through ionic redistribution. In the present model, the water layer contains 100 H₂O molecules together with 5 H₃O⁺ and 5 OH^– ions, allowing the contribution of water dissociation to the interfacial ionic response to be considered. Under the interfacial electric field generated by charge transfer, these dissociated ions may undergo redistribution and partially screen the local electrostatic potential. Such electrostatic screening behavior is consistent with the electric double layer (EDL) effect commonly observed at charged aqueous interfaces, where interfacial charges induce ionic rearrangement and modify the local electrostatic environment.

Besides, the surface density of the maximum stored charge is 2–5 times larger than that obtained from the DFT simulation. We suppose that this difference partly stems from limitations of the developed DeepMD potential; unrealistic fragmentation of polymers can enhance charge transfer.

3.5. Implications for Material Design

The multiscale framework developed in this work provides practical guidance for the rational design of triboelectric nanogenerators (TENGs). By combining DFT calculations with machine-learning-assisted molecular dynamics simulations, the present approach links atomistic electronic structures to interfacial dynamics, providing a computational route for evaluating candidate triboelectric materials before experimental device fabrication.

The DFT calculations demonstrate that the relative Fermi-level positions of contacting materials provide a reliable indicator of the electron transfer direction. Therefore, electronic descriptors such as the work function, Fermi level, and density of states can serve as useful screening parameters during material selection. In addition, surface modification methods, including chemical functionalization and plasma treatment, can alter these electronic properties and thereby influence the charge transfer behavior. Similar correlations between DFT-predicted electronic properties and experimentally measured work function variations have been demonstrated using Kelvin probe force microscopy (KPFM).

Beyond electronic properties, the present simulations reveal that interfacial water also plays a critical role in the triboelectric charge generation. While electron transfer establishes the initial potential difference, ion migration within the water layer partially compensates for the accumulated charges. These results suggest that optimizing TENG performance should consider both the electronic structure and interfacial ion transport rather than maximizing electron transfer alone. Recent reviews have likewise highlighted the growing importance of DFT calculations in understanding contact electrification and guiding material selection for TENGs. The present work extends these studies by integrating first-principles calculations with machine learning-based molecular dynamics, providing a practical multiscale framework for evaluating triboelectric material systems and interface designs before experimental implementation.

4. Conclusion

We investigated fundamental charge transfer processes in triboelectric nanogenerator (TENG) systems by DFT-based quantum simulations and by classical molecular dynamics (MD) simulations with a machine-learning (ML) potential.

We chose a simple PVA/water/PVC layer structure as the target and found that

• 1.The difference in the Fermi level explains the direction of charge transfer between insulating materials, providing guidance for material selection.
• 2.The presence of capillary bridges by water layers between insulator surfaces greatly affects the charge transfer, often suppressing the net charge separation. Thus, in practical applications, environmental humidity and water adsorption should be carefully controlled.
• 3.While PVC proves to be a reasonable choice as the anode material in TENGs, PVA appears to compete unfavorably with water in electron depletion, which requires further investigation.
• 4.ML potential models, such as those developed with the DeepMD-kit in this study, offer a powerful bridge between quantum and classical MD simulations. However, their applicability to triboelectric processes still remains limited because chain fragmentation sometimes occurs with artificial enhancement in charge separation.

Triboelectric processes essentially require multiscale investigations, from local electron transfer in atomistic scales to surface states, such as surface roughness, distortions, and adsorptions at the sub-μm scale. In some situations, the generation of electric double layers at much larger scales can have relevant effects. As the spatial and temporal scales in quantum calculations are very much limited and charge variation is hard to treat in conventional atomistic potential models, classical MD simulations with ML potential models proposed in this study seem to provide a promising tool for such multiscale investigations. Further improvements are underway.

The authors declare no competing financial interest.