Percolation-enabled long-range ion transport to achieve conductivity leap in PVDF-based electrolytes

Abstract

Poly(vinylidene fluoride) (PVDF)-based polymer electrolytes are a focal point in solid-state batteries due to their exceptional ionic conductivity. However, the critical role of residual solvent in the ion transport mechanism remains a long-standing debate. Addressing this critical issue, this work, for the first time, elucidates a percolation mechanism for ion transport in PVDF-based electrolytes that is dependent on residual solvent content. Central to this mechanism, a critical ∼7 wt% N,N-dimethylformamide (DMF) content triggers a two-order-of-magnitude ionic conductivity leap in PVDF-LiTFSI electrolytes from ∼10⁻⁶ S cm⁻¹ to ∼10⁻⁴ S cm⁻¹ at 30 °C. Multi-scale molecular dynamics simulations reveal that this transition is not due to local Li-ion solvation changes but rather due to the establishment of a long-range, continuous transport pathway as the “free-state” Li-ion conductive network reaches its percolation threshold. This work provides crucial insights into the conduction mechanism of PVDF-based electrolytes and contributes a novel conceptual framework, offering valuable design principles for optimizing macroscopic ion transport in polymer-small molecule composite systems via precise microstructural control. These findings pave the way for the development of high-performance, safer, next-generation solid-state batteries.

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1 Introduction

The energy density and safety of lithium-ion batteries are primary objectives in their ongoing development, with the electrolyte being a critical component having a direct impact on these key performance areas.^1–3 While traditional liquid electrolytes provide high ionic conductivity, their flammability and potential for leakage create significant safety concerns, particularly in high-energy-density applications.^4,5 Thus, developing solid-state electrolytes with high ionic conductivity and enhanced safety has become a clear imperative in the field of energy storage.^6–8

Among the various classes of solid-state electrolytes, solid polymer electrolytes (SPEs) have garnered considerable interest due to their inherent flexibility, ease of fabrication, and favorable interfacial properties with electrodes.^9–13 Poly(vinylidene fluoride) (PVDF)-based SPEs, in particular, have emerged as highly promising candidates, capable of achieving substantial room-temperature ionic conductivities in the range of 10⁻⁴–10⁻³ S cm⁻¹, coupled with wide electrochemical stability windows and good mechanical properties through rational design and modification.^14–17 However, PVDF is conventionally regarded as an electrical insulator with extremely low intrinsic ionic conductivity.¹⁸ The often-observed high conductivity in these systems is commonly linked to the presence of residual high-boiling point, high-polarity solvents, such as N,N-dimethylformamide (DMF) or N-methyl-2-pyrrolidone (NMP), which are notoriously difficult to be completely eradicated during material preparation.^19–22 Consequently, significant debate persists in academia, challenging whether these solvated PVDF systems should indeed be classified as solid-state electrolytes and questioning the precise mechanisms by which residual solvents affect ion transport.

Current models for ion transport in PVDF-based electrolytes containing residual solvent suggest that the solvent (e.g., DMF) is largely immobilized, forming Li⁺-solvent complexes within the polymer matrix,^21,23,24 as depicted in region I in Fig. 1. These complexes are thought to facilitate Li⁺ desolvation and migration, thereby lowering transport energy barriers and enhancing ionic conductivity. Beyond this, at high salt concentrations (e.g., >50 wt%), an alternative “salt transport” mechanism through interconnected lithium salt networks has also been proposed,²⁵ as depicted in region II, Fig. 1. This implies that Li⁺ transport likely occurs via intricate pathways, potentially integrating solvent-assisted complex diffusion, inter-salt hopping, and Li⁺ coordination environments involving simultaneous interactions with both solvent and anions, as depicted in region III, Fig. 1. While some early hypotheses considered Li⁺ migration along the PVDF polymer chains themselves,^23,26 accumulating evidence now points to PVDF primarily acting as a mechanical skeleton and a diluent for the ion-conducting phase.^18,27,28 Direct interactions between Li⁺ ions and the fluorinated segments are considered weak, limiting any significant direct contribution of the polymer backbone to ion transport.

Fig. 1 Schematic of the Li-ion transport mechanism in PVDF electrolytes.

While it is widely accepted that residual solvents can act as “plasticizers”, enhancing polymer segment dynamics and promoting ion dissociation to improve ionic conductivity through the mechanisms mentioned above, the precise relationship between residual solvent content and ionic conductivity, particularly regarding any non-linear behavior, remains less understood. Specifically, the existence of a critical solvent concentration that might trigger a substantial leap in ionic conductivity, along with the microscopic mechanisms driving such a transition, has not yet been systematically investigated or clearly elucidated. This knowledge gap significantly hinders the rational design and performance optimization of these electrolytes.

To bridge this critical knowledge gap, this work employs the typical PVDF-LiTFSI-DMF model system to systematically investigate the impact of precisely controlled residual DMF content on ionic conductivity. Combining experimental measurements with multi-scale molecular dynamics simulations, this work aims to provide the first unequivocal elucidation of the percolation-driven transition in ion transport within PVDF-based electrolytes, demonstrating how this evolution from localized ionic interactions to a long-range connected network is critically influenced by the interaction between residual solvent and the lithium salt. Specifically, this research endeavors to quantitatively pinpoint the critical solvent concentration at which PVDF-DMF electrolyte ionic conductivity sharply transitions, and to thoroughly clarify the evolution of Li-ion solvation environments, their dynamic behaviors, and the topology of transport pathways around this critical point. Ultimately, this work seeks to establish the intrinsic relationship between residual solvent content, the microscopic ion transport network, and macroscopic ionic conductivity. It is anticipated that these novel insights will not only deepen the understanding of Li-ion transport mechanisms in polymer-small-molecule systems and inspire the design of continuous, highly efficient ion transport networks using small molecules, but also provide robust theoretical guidance and design principles for developing high-performance, high-safety batteries and other energy storage technologies.

2 Results and discussions

2.1 Critical transition and percolation threshold in ionic conductivity of PVDF-DMF electrolytes

A series of PVDF-LiTFSI (1 : 1, w/w) electrolyte membranes with residual DMF contents precisely controlled between 2 wt% and 85 wt% were prepared precisely by controlling the drying temperature (at 80 °C and 120 °C) and duration. Thermogravimetric analysis (TGA) confirmed these compositions, as detailed in Fig. S1. The impact of DMF content on ionic conductivity is clearly demonstrated in Fig. 2a, which shows a significant enhancement in conductivity across all tested temperatures with increasing DMF. More strikingly, Fig. 2b reveals a sharp, non-linear surge in ionic conductivity around a specific DMF concentration. For example, at 30 °C, increasing the DMF content from just below to slightly above ∼7 wt% results in an approximate two-order-of-magnitude leap in ionic conductivity, from the 10⁻⁶ S cm⁻¹ range to 10⁻⁴ S cm⁻¹. Such an abrupt change in a physical property at a critical component concentration is a hallmark of percolation behavior,²⁹ strongly suggesting that ∼7 wt% DMF represents the percolation threshold in this PVDF-DMF electrolyte system.

Fig. 2 (a) Ionic conductivity of PVDF-DMF electrolytes at different temperatures; (b) ionic conductivity of PVDF-DMF electrolytes with varying DMF contents; (c) FTIR spectra and (d) Raman spectra of PVDF-DMF electrolytes with DMF contents ranging from 5.4% to 21.1%.

To investigate the microscopic origins of this conductivity leap, changes in the local chemical environment within the electrolyte were examined around the percolation threshold. Fourier-transform infrared spectroscopy (FTIR) and Raman spectroscopy were employed to characterize the interactions between LiTFSI and DMF, as well as the solvation structures. As shown in Fig. 2c, the characteristic vibrational peaks of the N–C=O group in DMF (at 659 cm⁻¹ and 675 cm⁻¹)³⁰ exhibit no obvious shifts in position or abrupt changes in intensity as the DMF content crosses the ∼7 wt% threshold, while at much higher DMF contents (e.g., 21.1 wt%), the signal at 675 cm⁻¹ significantly intensifies. Similarly, the Raman spectra in Fig. 2d reveal that the characteristic peaks reflecting Li⁺-TFSI⁻ interactions and solvation structures, such as the coupled –CF₃ bending and S–N–S stretching vibrations³¹ around 745%–750 cm⁻¹, also show no distinct anomalies in the vicinity of 7 wt% DMF. These spectroscopic findings collectively suggest that the sharp transition in ionic conductivity at the percolation threshold is not primarily driven by sudden, drastic changes in the average Li-ion solvation environment or the dominant chemical interaction modes. To assess other potential factors, the possibility of a phase transition within the PVDF polymer matrix was also investigated as a cause of the conductivity leap. The analysis specifically focused on the electrolytes near the critical percolation threshold of ∼7 wt%. Crucially, within the narrow concentration window from 6.2% to 7.6% DMF, where the ionic conductivity exhibits its sharpest increase, the characteristic FTIR and Raman peaks for the PVDF α- and β-phases show no significant changes in position or relative intensity (Fig. S2). This absence of a corresponding structural change in the polymer matrix provides compelling evidence that the abrupt phenomenon is not governed by PVDF phase transformation. Therefore, the underlying mechanism for this phenomenon likely needs to be explored from the perspective of ion transport pathway connectivity.

2.2 Evolution of Li-ion solvation structure and local dynamics

To elucidate the microscopic state of Li⁺ ions around the percolation threshold, classical molecular dynamics (MD) simulations were performed. Fig. 3a and b present the radial distribution functions (RDFs) and corresponding coordination numbers for Li⁺ with TFSI⁻ and DMF, respectively. Additionally, interactions between Li⁺ and PVDF chains were found to be weak (Fig. S3), indicating a limited direct role of the polymer backbone in Li⁺ coordination. As depicted in Fig. 3c, an increase in the total DMF content leads to a gradual rise in the average number of DMF molecules in the first solvation shell of Li⁺, accompanied by a corresponding decrease in the average number of TFSI⁻ anions. This trend is smooth and continuous around the ∼7 wt% DMF content, exhibiting no abrupt or discontinuous changes.

Fig. 3 (a) Radial distribution functions and coordination numbers for Li⁺-O_TFSI⁻; (b) Li⁺-O_DMF in PVDF-DMF electrolytes with varying DMF contents; (c) coordination numbers of O_DMF and O_TFSI⁻ in the first solvation shell of Li⁺ in PVDF-DMF electrolytes; (d) distribution of Li⁺ coordination numbers with oxygen atoms on TFSI⁻ in the first solvation shell for PVDF-DMF electrolytes with different DMF contents; (e) two-dimensional potential energy landscape for Li⁺ dissociation along DMF and TFSI⁻ directions in a typical Li(DMF)₂(TFSI)₂ solvated structure; (f) dissociation energies of Li⁺ from DMF (dashed lines) and TFSI⁻ (solid lines) in various representative solvation structures. Each labeled “path” corresponds to a dissociation energy profile calculated for a different initial solvation configuration, which is shown schematically in Fig. S4.

Fig. 3d further details the Li⁺ solvation environment by illustrating the probability distribution of different configurations. These are classified by the Li⁺-O_TFSI⁻ coordination number, N_Li-Ot, representing coordination with oxygen atoms on TFSI⁻. At lower DMF contents, specifically below 10 wt%, structures with a higher N_Li-Ot value of three or more are dominant. Conversely, as DMF content rises, configurations with lower N_Li-Ot values of two or less, indicative of DMF-rich solvation shells, become increasingly prevalent. However, around the ∼7 wt% DMF threshold, these shifts in population distributions remain gradual, exhibiting no abrupt changes.

Although the types and populations of local solvation structures do not change suddenly near this critical point, the energetic impact of DMF introduction on Li-ion dissociation and migration warrants further investigation. To this end, potential energy surface (PES) analysis was performed for representative solvated structures such as Li(DMF)₂(TFSI)₂ as shown in Fig. 3e. The visual details of the 2D PES provide a clear interpretation: the dissociation of Li⁺ from a DMF molecule, represented by moving vertically away from the stable solvated state at the central energy minimum, traverses a region where the energy contour lines are visibly more spread out compared to the horizontal path for TFSI⁻ dissociation. This wider spacing signifies a smaller potential energy gradient, which directly translates into the lower energy barriers for DMF dissociation, as shown in the 1D energy profiles in Fig. 3f. More specifically, the energies required for Li⁺ to dissociate from DMF molecules and TFSI⁻ anions were calculated across a series of typical solvation configurations, for which schematic dissociation pathways are provided in Fig. S4. As summarized in the calculated dissociation energy curves, the energy barrier for Li⁺ dissociation from a DMF molecule is markedly lower than that for dissociation from a TFSI⁻ anion across all examined structures. This finding confirms that DMF incorporation effectively lowers the Li⁺ dissociation energy barrier, thereby promoting local ionic motion and facilitating “release” from its solvation shell. Nevertheless, while these analyses highlight DMF's role in enhancing local ion dynamics, the smooth evolution of the average Li-ion solvation environment and short-range migration behavior is insufficient to explain the order-of-magnitude leap in macroscopic ionic conductivity observed at ∼7 wt% DMF. This strongly suggests that the answer must be sought in the evolution of larger-scale ion transport network topology, transcending local structural considerations.

2.3 Ionic dynamic transition and local connectivity probability

To describe the actual dynamic states of ions within the electrolyte, the spatial density distribution from MD simulation trajectories was first analyzed, as presented in Fig. 4a. In this map, the color intensity reflects the residence probability of the ions. The clear existence of both deeply colored regions, where Li⁺ ions are localized for prolonged periods, and lightly colored, transient areas visually demonstrates that ions exhibit distinct dynamic behaviors. Based on this observation, the concepts of a “free state” and a “bound state” are adopted to classify the different ionic behaviors, a framework applied in the analysis of ionic liquid systems.³² Ions capable of extensive diffusion are classified as being in a “free state”, while those exhibiting prolonged localized vibrations are considered in a “bound state”. Typical diffusion trajectories for each class are visualized in Fig. 4b (free state) and Fig. 4c (bound state). The mean squared displacement (MSD) curve for an individual ion (Fig. 4d) clearly displays an alternating “trapped-migratory” pattern: the flat plateaus correspond to trapped periods where the ion is in a “bound state”, while the sharp increases are migratory jumps when the ion enters a “free state”. Notably, “free state” ions diffuse approximately two orders of magnitude faster than “bound state” ions, as detailed in Fig. S5 and Table S1. Consequently, the population of “free state” Li⁺ ions and the potential effective transport pathways they constitute are key microscopic factors influencing the macroscopic ionic conductivity of the electrolyte.

Fig. 4 (a) Two-dimensional projection of the Li⁺ trajectory density within the simulation box; (b) typical diffusion trajectory of a “free-state” Li⁺ ion; (c) typical diffusion trajectory of a “bound-state” Li⁺ ion; (d) mean-squared-displacement curve for an individual Li⁺ ion during the simulation; (e) statistical distribution of Li⁺ trajectory densities and their occurrence frequencies; (f) variation in the connection probability with different DMF contents.

Building on the pivotal role of this “free state” population in influencing overall conductivity, a method was developed to quantify their ability to form interconnected networks at any given time or under specific conditions. First, based on the ionic trajectory density, the global median of non-zero density grid cells was used as a baseline criterion to distinguish between ions exhibiting “free state” and “bound state” characteristics, as shown in Fig. 4e. Subsequently, all Li⁺ ions were categorized by their Li⁺-O_TFSI⁻ coordination number, and the probability of ions in different solvation structures being in a “free state” was analyzed (Fig. S6). This analysis reaffirmed that a lower N_Li-Ot correlates with a higher probability of ions being in a “free state”. Based on this identification of “free state” ions, the unit connection probability (P_unit) was further defined. P_unit quantifies the probability that, within a fundamental MD simulation unit at a given moment, ions identified as being in a “free state” form a locally connected network by linking with their nearest “free state” Li⁺ neighbors, according to connectivity criteria detailed in the Experimental methods section. As shown in Fig. 4f, P_unit increases steadily with rising DMF content. This enhanced local-scale connectivity lays a critical foundation for the formation of a macroscopic percolation network capable of spanning the entire system and significantly enhancing the electrolyte's overall ionic conductivity.

2.4 Long-range percolation mechanism for ion transport

The establishment of the P_unit allows for consideration of its role in the formation of a larger-scale, global conductive network, the connectivity of which dictates macroscopic transitions in physical properties. With P_unit serving as the elementary connection probability parameter, a percolation model was constructed based on a 100 × 100 × 100 cubic lattice of these elementary units, representing a micro-nanoscale cube of approximately 500 nm. This framework was subsequently employed to calculate the probability of forming a globally connected, end-to-end ion transport network within this micro-nanoscale cube at varying DMF contents, a value defined as the “percolation probability” (P_perc).

Fig. 5a–f visually demonstrate the formation of the macroscopic percolation network. These figures showcase the largest connected clusters simulated by the percolation model at various DMF contents, which correspond to different P_unit. More quantitatively, Fig. 5g plots the macroscopic P_perc as a function of DMF content. A striking feature is the sharp transition in P_perc, which abruptly increases from near zero to almost one as the DMF content reaches approximately 7 wt%. The inset, which provides a magnified view of this transition region, reveals the underlying mechanism based on percolation theory. The top x-axis of the inset shows the corresponding microscopic P_unit, which serves as the site occupation probability (p) in the model. This view demonstrates that the macroscopic P_perc abruptly transitions from 0 to 1 precisely as the microscopic P_unit crosses the theoretical critical threshold for a simple cubic lattice (p_c ≈ 0.3116). As shown in the inset, this critical crossover point corresponds to a DMF content of approximately 7 wt%.

Fig. 5 (a)–(f) Visualization of the largest ion-connected clusters formed in the extended micro-nanoscale cubic model at different DMF contents (5.4–22.1%). (g) Global percolation probability of the ion-transport network in PVDF-DMF electrolytes as a function of DMF content. (h) Comparison of ionic conductivity values calculated based on the percolation model with experimental measurements.

This percolation threshold at ∼7 wt% delineates two distinct transport states. Below the 7 wt% DMF level, even if localized clusters of “free-state” ions exist within individual units, these units, though rendered conductive by such internal clusters, remain isolated at a macroscopic scale. Consequently, they fail to form an effective, system-spanning conductive pathway. Once the DMF content reaches and exceeds this ∼7 wt% threshold, a point at which a sufficient number of units become conductive, these units, already exhibiting local connectivity in MD simulations, can effectively link together within the macroscopic percolation model. This linkage forms one or more “superhighways” across the entire micro-nanoscale cube, thereby enabling efficient long-range ion migration. The robustness of this critically important 7 wt% threshold was verified through a sensitivity analysis (detailed in Fig. S7), which confirms that the location of the transition is not significantly affected by minor variations in the definition of “free-state” ion. This robust percolation behavior provides a direct mechanistic explanation for the sharp, macroscopic conductivity transition observed experimentally.

To directly correlate percolation theory with macroscopic ionic conductivity, a random resistor network model was employed.³³ The intrinsic conductivity of non-connected regions was taken as the experimental conductivity at near-zero DMF content (∼10⁻⁷ S cm⁻¹), while the conductivity of fully connected regions was assumed to be the saturated conductivity observed at DMF contents well above the percolation threshold (∼5 × 10⁻³ S cm⁻¹). Based on these values and the P_perc, the ionic conductivity of the PVDF-DMF electrolyte was simulated across different DMF contents. As depicted in Fig. 5h, the simulated ionic conductivity curve exhibits excellent agreement with the experimental measurements, particularly in perfectly replicating the sharp conductivity leap around 7 wt% DMF. This provides compelling evidence that the percolation behavior of the ion transport network is the fundamental reason for the abrupt transition in ionic conductivity observed at the critical solvent content in PVDF-DMF electrolytes.

3 Conclusions

In conclusion, this work systematically elucidates the intrinsic mechanism by which residual DMF regulates ion transport in PVDF-based electrolytes, identifying percolation as the governing principle. This study demonstrates that the two-order-of-magnitude leap in ionic conductivity observed at a critical threshold of ∼7 wt% DMF is not driven by abrupt changes in the local chemical environment. Instead, this transition is a direct consequence of the “free-state” Li-ion transport network reaching its percolation point, where a steady increase in local connectivity triggers a sharp jump in global percolation probability from near zero to one. An electrical conductivity model built upon this percolation framework shows excellent agreement with experimental results, providing robust validation for the proposed mechanism. These findings clarify the long-debated role of residual solvents and provide a key theoretical framework for designing the next generation of high-performance solid-state electrolytes by precisely controlling microstructural features to optimize ion transport networks.

4 Experimental section

4.1 Preparation of PVDF-DMF electrolyte membranes

PVDF-DMF electrolyte membranes were prepared via a solution casting method. Poly(vinylidene fluoride) (PVDF, average Mv ∼500 000, Aladdin, Shanghai, China) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI, ≥99.9%, Aladdin, Shanghai, China) were dissolved in N,N-dimethylformamide (DMF, >99.9%, Aladdin, Shanghai, China) at a 1 : 1 mass ratio. The mixture was stirred at room temperature for 1 hour to obtain a homogeneous slurry. This slurry was then cast onto a PTFE mold and dried on a heating plate at 80 °C to yield PVDF-DMF electrolytes with residual DMF contents ranging from 8% to 85%. To achieve lower DMF contents (2–8%), electrolytes previously dried at 80 °C for 24 hours were subjected to further drying at 120 °C for varying durations. All the above procedures were performed in an argon-filled glove box. After drying, the resulting electrolyte membranes could be easily peeled from the PTFE mold.

4.2 Materials characterization and electrochemical measurements

The chemical structures of the electrolytes were characterized using a Nicolet IS50 Fourier-transform infrared (FT-IR) spectrometer and a B&W Tek i-Raman portable Raman spectrometer equipped with a 785 nm laser. Ionic conductivity was evaluated by electrochemical impedance spectroscopy (EIS) using a Gamry Interface 1000 electrochemical workstation. For these measurements, the electrolyte membrane was sandwiched between two stainless steel plates, and tests were conducted at various temperatures.

4.3 Computational method and simulation details

Molecular dynamics (MD) simulations were performed using GROMACS³⁴ to investigate the microscopic ion transport mechanisms. The system, consisting of PVDF, LiTFSI, and varying amounts of DMF, was modeled using the OPLS-AA force field.³⁵ Following equilibration, production runs were analyzed to determine key structural and dynamic properties, including radial distribution functions (RDFs), mean-squared displacement (MSD), and potential energy surfaces (PESs). A custom analysis framework was developed to classify ions into “free” and “bound” states based on their trajectory densities, which then served as the input for a larger-scale percolation model to calculate the macroscopic percolation probability. Full details of the force–field parameters, simulation protocols, and analysis methodologies are provided in the SI.

Author contributions

Lingjie Luo: conceptualization, investigation, formal analysis, visualization, writing – original draft. Han Lin: methodology, investigation, formal analysis, visualization, writing – original draft. Rui Wu: formal analysis, investigation, validation. Zengyao Zhang: investigation, validation. Qiyun Li: resources. Yuxuan Liu: conceptualization, methodology, formal analysis, supervision, project administration, funding acquisition, writing – review & editing. Jun Liu: resources, funding acquisition. Renzong Hu: supervision, funding acquisition, writing – review & editing. Min Zhu: supervision, resources, conceptualization.

Conflicts of interest

There are no conflicts to declare.

Data availability

The supplementary information provides detailed computational methods used for the simulations . It also includes supplementary figures and tables (Fig. S1–S7, Tables S1 and S2) that contain additional thermal analysis (TGA), spectroscopic data (FTIR, Raman), and further results and analysis from the molecular dynamics simulations. See DOI: https://doi.org/10.1039/d5ta05612h.

Acknowledgements

This work was supported by the Guangdong Basic and Applied Basic Research Foundation (2023A1515110448, 2023B1515040011), the Science and Technology Projects in Guangzhou (2024A04J3599), the National Natural Science Foundation of China (52471227, 52231009), Zhongshan Key Research and Development Program (no.2022AJ005), and computational resources from the High-Performance Computing Platform of South China University of Technology.

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Footnote

† These authors contributed equally to this work.

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