I have directed my recent work toward understanding how the thickness of a fiber-shaped solid electrolyte governs the internal electrochemical behavior of a lithium-ion solid electrolyte cell. The motivation is straightforward: flexible and wearable electronic systems require power sources that are simultaneously safe, mechanically compliant, and electrochemically robust. Conventional liquid-electrolyte lithium-ion batteries, despite their high energy density, carry intrinsic risks of thermal runaway and leakage, and their rigid packaging limits integration into textiles and conformable devices. A solid electrolyte cell, especially one constructed from a poly(ethylene oxide)-based fiber-shaped solid electrolyte, offers a promising route to overcome these limitations. In my investigation, I combined finite element simulation with experimental validation to resolve the microscopic transport phenomena inside a lithium iron phosphate / lithium titanate all-solid-state fiber solid electrolyte cell. The central question I asked was: how does the thickness of the solid electrolyte layer alter ion migration, interfacial reaction kinetics, current density distribution, and potential gradients within the solid electrolyte cell?
To answer this question, I constructed a three-dimensional multiphysics model using COMSOL software. The model incorporated the ion-conducting characteristics of the PEO-based fiber-shaped solid electrolyte, the three-dimensional architecture of the fiber electrodes, and the Butler–Volmer interfacial reaction kinetics into a unified theoretical framework. This allowed me to perform a microscopic-scale analysis of the charge and discharge processes in the all-solid-state fiber solid electrolyte cell. I predicted the influence of solid electrolyte thickness on electrochemical performance and compared the simulation results with experimental measurements. The findings reveal that increasing the thickness of the solid electrolyte significantly intensifies the internal potential gradient, raises the internal resistance, and enlarges both ohmic overpotential and concentration overpotential. These effects are rooted in the lengthening of the lithium-ion migration path and the resulting non-linear accumulation of transport resistance.
Before presenting the model and results, I should describe the materials and fabrication route I employed. I prepared the positive electrode spinning dispersion by blending poly(vinylidene fluoride) and poly(ethylene oxide) at a mass ratio of 8:2 to form an 8 wt% polymer matrix. I then combined this matrix with lithium iron phosphate at a mass ratio of 1:2. A conductive agent consisting of carbon black and graphene at a 1:1 mass ratio was added at 10:1 relative to the lithium iron phosphate mass. The mixture was stirred continuously at 55 °C for 12 h to obtain a homogeneous lithium iron phosphate spinning solution. I prepared the lithium titanate spinning solution using the same procedure. For the solid electrolyte spinning solution, I used acetonitrile as the solvent and added lithium bis(trifluoromethanesulfonyl)imide with an ethylene oxide to lithium-ion molar ratio of 32:1. The total solid mass fraction was 6 wt%, and the solution was stirred at 35 °C for 12 h. The resulting PEO-based solution served as the precursor for the fiber-shaped solid electrolyte.
I fabricated the all-solid-state fiber solid electrolyte cell by coaxial electrospinning. First, I injected the lithium iron phosphate spinning solution into two syringes and used a stainless steel strand as the core. Through conjugated electrospinning, I coated lithium iron phosphate nanofibers onto the core, producing a lithium iron phosphate fiber electrode. Then I sequentially spun the solid electrolyte layer and the lithium titanate layer onto the lithium iron phosphate fiber electrode. This yielded a core-shell architecture in which the lithium iron phosphate, solid electrolyte, and lithium titanate layers were tightly integrated. The final structure is a flexible, weavable solid electrolyte cell that can be integrated into smart textiles and wearable devices. I characterized the morphology using scanning electron microscopy, and I evaluated the charge–discharge performance using a battery test system. The solid electrolyte layer thickness was controlled at 30, 45, and 90 µm; I refer to these samples as L30, L45, and L90 throughout this work.
The scanning electron microscopy images confirmed that the fibers were arranged in an orderly manner and that the active materials and conductive agents were uniformly loaded on the fiber surfaces. The cross-sectional views revealed the core-shell structure of the solid electrolyte cell. The solid electrolyte layer, approximately 30 µm thick in the baseline sample, adhered closely to the lithium iron phosphate fiber electrode, forming a continuous intermediate layer. The outer lithium titanate electrode layer consisted of aligned nanofibers. The three layers were tightly bound, constructing a fully integrated solid electrolyte cell. For thicker samples, the solid electrolyte layer expanded accordingly, but the concentric geometry was preserved.
To model the electrochemical behavior of the solid electrolyte cell, I adopted a finite element approach that couples solid-phase diffusion, charge conservation, and interfacial reaction kinetics. I made several basic assumptions: no side reactions occur; volume changes during discharge are negligible; active material particles are spherical; no phase transformation takes place during reaction; gas evolution and dendrite growth are ignored. These assumptions are reasonable for the operating window and materials system I studied. Under these conditions, the solid-phase lithium concentration in the electrode particles evolves according to a diffusion equation with a source term from the interfacial reaction. I used the following governing equation for solid-phase diffusion:
$$ \varepsilon \frac{\partial c_s}{\partial t} = \nabla \cdot (D_s \nabla c_s) + \frac{j_{\mathrm{int}}}{F} $$
Here, \( \varepsilon \) is the porosity or volume fraction available for diffusion, \( c_s \) is the solid-phase lithium concentration, \( D_s \) is the solid-phase diffusion coefficient, \( j_{\mathrm{int}} \) is the interfacial reaction current density, and \( F \) is Faraday’s constant. Because the electrolyte is solid, there is no liquid-phase diffusion equation. Instead, lithium-ion transport in the solid electrolyte is described by a modified Nernst–Planck equation that accounts for both diffusion and migration under the local electric field. The concentration of lithium ions in the solid electrolyte changes according to:
$$ \frac{\partial c_{\mathrm{Li}^+}}{\partial t} = \nabla \cdot \left[ D_{\mathrm{eff}} \left( \nabla c_{\mathrm{Li}^+} + \frac{z F}{R T} c_{\mathrm{Li}^+} \nabla \phi_e \right) \right] $$
In this expression, \( c_{\mathrm{Li}^+} \) is the lithium-ion concentration in the solid electrolyte, \( D_{\mathrm{eff}} \) is the effective diffusivity of lithium ions in the solid electrolyte, \( z \) is the charge number of lithium (which is +1), \( R \) is the gas constant, \( T \) is the absolute temperature, and \( \phi_e \) is the electric potential in the solid electrolyte. The charge conservation in the solid electrolyte is expressed by a modified Poisson-type equation that couples ionic concentration gradients to the potential field:
$$ \nabla \cdot (k_{\mathrm{eff}} \nabla \phi_e) = – F \nabla \cdot (D_{\mathrm{eff}} \nabla c_{\mathrm{Li}^+}) $$
where \( k_{\mathrm{eff}} \) is the effective ionic conductivity of the solid electrolyte. In the electrodes, electronic conduction dominates the potential distribution. I described the electronic potential in the solid electrode phase using Ohm’s law with a source term from the interfacial reaction:
$$ \nabla \cdot (\sigma_{\mathrm{eff}} \nabla \phi_s) = j_{\mathrm{int}} $$
and the ionic potential in the electrolyte phase is governed by:
$$ \nabla \cdot (\sigma_e \nabla \phi_e) = -j_{\mathrm{int}} $$
Here, \( \sigma_{\mathrm{eff}} \) is the effective electronic conductivity of the electrode, \( \sigma_e \) is the effective ionic conductivity of the solid electrolyte, \( \phi_s \) is the electrode potential, and \( \phi_e \) is the electrolyte potential. The interfacial charge-transfer kinetics at the electrode/solid electrolyte interface are described by the Butler–Volmer equation:
$$ j = j_0 \left[ \exp\left( \frac{\alpha_a F \eta}{R T} \right) – \exp\left( -\frac{\alpha_c F \eta}{R T} \right) \right] $$
where \( j \) is the local current density, \( j_0 \) is the exchange current density, \( \alpha_a \) and \( \alpha_c \) are the anodic and cathodic transfer coefficients, respectively, and \( \eta \) is the overpotential. The exchange current density depends on the local lithium-ion concentration and the available sites in the electrode:
$$ j_0 = F k_0 c_{\mathrm{Li}^+}^{\alpha_a} (c_{\mathrm{max}} – c_s)^{\alpha_c} $$
Here, \( k_0 \) is the reaction rate constant, \( c_{\mathrm{max}} \) is the maximum lithium concentration in the electrode, and \( c_s \) is the local solid-phase lithium concentration. The overpotential is defined as the difference between the electrode potential, the electrolyte potential, and the equilibrium potential:
$$ \eta = \phi_s – \phi_e – U_{\mathrm{eq}} $$
The reaction rate constant itself depends on temperature through an Arrhenius-type relation:
$$ k_0 = k_{\mathrm{ref}} \exp\left( \frac{E_a}{R} \left( \frac{1}{T_{\mathrm{ref}}} – \frac{1}{T} \right) \right) $$
In this equation, \( k_{\mathrm{ref}} \) is the reference reaction rate constant, \( E_a \) is the activation energy, \( T_{\mathrm{ref}} \) is the reference temperature, and \( T \) is the operating temperature. I implemented these equations in COMSOL Multiphysics using the finite element method. The model geometry reflected the true fiber architecture: a central lithium iron phosphate fiber electrode, a concentric solid electrolyte layer of controlled thickness, and an outer lithium titanate fiber electrode. I used a time-dependent solver to simulate galvanostatic discharge and charge. The model parameters are summarized in Table 1. These parameters were either taken from literature or extracted from my own electrochemical measurements.
| Parameter | Positive electrode (LFP) | Negative electrode (LTO) | Solid electrolyte |
|---|---|---|---|
| Solid-phase potential (V) | 0.363 | 0.300 | — |
| Reference exchange current density (A/m²) | 0.00304 | 0.00543 | — |
| Diffusion coefficient (m²/s) | 3.2 × 10⁻¹³ | 6.8 × 10⁻¹⁵ | — |
| Electronic conductivity (S/m) | 91 | 100 | — |
| Equilibrium potential temperature derivative (V/K) | −9.95 × 10⁻⁵ | −1.04 × 10⁻⁵ | — |
| Maximum lithium concentration (mol/m³) | 21,190 | 22,852 | — |
| Particle radius (m) | 1 × 10⁻⁹ | 1 × 10⁻⁹ | — |
| Ionic conductivity (S/m) | — | — | 1.19 × 10⁻² |
Table 2 summarizes the governing equations and their physical meanings. I used these equations consistently across all simulations, varying only the thickness of the solid electrolyte layer. The model assumed a uniform initial lithium concentration in both electrodes and a fully wetted interface between the solid electrolyte and the fiber electrodes. Because the solid electrolyte cell operates without liquid electrolyte, the interface between the PEO-based solid electrolyte and the electrode particles is crucial. The contact area and the local ionic conductivity determine the effective exchange current density. In my model, I assumed that the interface was perfectly bonded, which is consistent with the observed core-shell morphology.
| Physical process | Equation | Variables |
|---|---|---|
| Solid-phase diffusion | $$ \varepsilon \frac{\partial c_s}{\partial t} = \nabla \cdot (D_s \nabla c_s) + \frac{j_{\mathrm{int}}}{F} $$ | \( c_s, D_s, j_{\mathrm{int}} \) |
| Ion transport in solid electrolyte | $$ \frac{\partial c_{\mathrm{Li}^+}}{\partial t} = \nabla \cdot \left[ D_{\mathrm{eff}} \left( \nabla c_{\mathrm{Li}^+} + \frac{z F}{R T} c_{\mathrm{Li}^+} \nabla \phi_e \right) \right] $$ | \( c_{\mathrm{Li}^+}, D_{\mathrm{eff}}, \phi_e \) |
| Charge conservation in electrolyte | $$ \nabla \cdot (k_{\mathrm{eff}} \nabla \phi_e) = – F \nabla \cdot (D_{\mathrm{eff}} \nabla c_{\mathrm{Li}^+}) $$ | \( k_{\mathrm{eff}}, \phi_e \) |
| Electronic conduction | $$ \nabla \cdot (\sigma_{\mathrm{eff}} \nabla \phi_s) = j_{\mathrm{int}} $$ | \( \sigma_{\mathrm{eff}}, \phi_s \) |
| Ionic conduction | $$ \nabla \cdot (\sigma_e \nabla \phi_e) = -j_{\mathrm{int}} $$ | \( \sigma_e, \phi_e \) |
| Butler–Volmer kinetics | $$ j = j_0 \left[ \exp\left( \frac{\alpha_a F \eta}{R T} \right) – \exp\left( -\frac{\alpha_c F \eta}{R T} \right) \right] $$ | \( j, j_0, \eta \) |
| Exchange current density | $$ j_0 = F k_0 c_{\mathrm{Li}^+}^{\alpha_a} (c_{\mathrm{max}} – c_s)^{\alpha_c} $$ | \( k_0, c_{\mathrm{max}} \) |
| Overpotential | $$ \eta = \phi_s – \phi_e – U_{\mathrm{eq}} $$ | \( \eta, \phi_s, \phi_e, U_{\mathrm{eq}} \) |
Before analyzing the thickness effect, I validated the finite element model against experimental measurements. I compared the simulated discharge voltage curve with the experimentally measured curve for the baseline solid electrolyte cell. The simulated curve reproduced the initial voltage plateau, the gradual decline during the middle stage, and the sharp drop near the end of discharge. These features are characteristic of a solid electrolyte cell with a well-defined interfacial reaction. The specific capacity obtained from the simulation also matched the experimental value closely. Table 3 lists the key features of the comparison. The agreement confirms that my model captures the essential electrochemical behavior of the all-solid-state fiber solid electrolyte cell, including the interplay between solid-phase diffusion, ionic transport in the solid electrolyte, and interfacial charge transfer.
| Feature | Simulated result | Experimental result | Agreement |
|---|---|---|---|
| Initial voltage plateau | ~1.9 V | ~1.9 V | Excellent |
| Mid-discharge slope | Gradual decline | Gradual decline | Good |
| End-of-discharge drop | Sharp | Sharp | Excellent |
| Specific capacity | ~145 mAh/g | ~148 mAh/g | Within 3% |
| Voltage hysteresis | Small | Small | Consistent |
After validation, I examined the influence of solid electrolyte thickness on the internal current density distribution. I simulated discharge to 50% depth of discharge (DOD) for L30, L45, and L90. The current density distribution became progressively less uniform as the solid electrolyte thickness increased. For L30, the current density was relatively uniform throughout the solid electrolyte. For L45, a clear current density gradient appeared. For L90, the current density exhibited a pronounced layer-by-layer gradient. This behavior arises because a thicker solid electrolyte forces lithium ions to travel a longer path from the positive electrode to the negative electrode. As the migration path lengthens, the cumulative transport resistance increases. The local ionic flux must adjust to maintain the overall charge transfer rate, which leads to spatial variations in current density. Table 4 summarizes the maximum current density and the degree of non-uniformity at 50% DOD. I quantified the non-uniformity as the difference between the maximum and minimum current densities divided by the average current density.
| Sample | Solid electrolyte thickness (µm) | Maximum current density (A/m²) | Minimum current density (A/m²) | Non-uniformity index |
|---|---|---|---|---|
| L30 | 30 | 0.198 | 0.185 | 0.068 |
| L45 | 45 | 0.206 | 0.181 | 0.130 |
| L90 | 90 | 0.219 | 0.168 | 0.265 |
The time evolution of the current density provided further insight. I monitored the maximum current density in the solid electrolyte over a discharge period of 20,000 s. For L30, the maximum current density remained around 0.207 A/m². For L45, it increased to 0.214 A/m². For L90, it reached 0.223 A/m². These values are higher than the steady-state values at 50% DOD because the transient response during the early stages of discharge requires a larger ionic flux to establish the concentration profile. The trend is clear: a thicker solid electrolyte leads to a higher current density for the same external demand. This is a direct consequence of the need to compensate for the longer ion migration path. When the path is long, the system must increase the ionic flux per unit area to deliver the same total charge in the same time. This higher flux, in turn, amplifies concentration polarization and ohmic losses. Table 5 presents the time-averaged and peak current densities for the three samples.
| Sample | Thickness (µm) | Peak current density (A/m²) | Time-averaged current density (A/m²) | Time to reach peak (s) |
|---|---|---|---|---|
| L30 | 30 | 0.207 | 0.192 | 3,200 |
| L45 | 45 | 0.214 | 0.198 | 4,100 |
| L90 | 90 | 0.223 | 0.205 | 6,500 |
I then analyzed the potential distribution in the solid electrolyte. At 0% DOD, before any significant discharge occurs, the potential difference across the solid electrolyte already depends on thickness. For L30, the potential difference was 0.6 mV. For L45, it was 0.08 mV. For L90, it was 1.5 mV. The non-monotonic trend for L45 is likely due to local variations in the initial lithium-ion distribution and the interfacial contact quality. Nevertheless, the L90 sample exhibited a potential difference more than twice that of L30. This indicates that a thicker solid electrolyte creates a larger initial potential gradient even before the cell is discharged. The origin of this gradient is the unequal path length for lithium ions. In a thick solid electrolyte, the lithium ions near the positive electrode have not yet migrated to the negative electrode, while the ions near the negative electrode have a different local environment. This spatial asymmetry in ion distribution translates into a potential difference through the Nernst equation. As discharge proceeds, the potential gradient grows because the continuous consumption of lithium ions at the interfaces and the finite migration speed create concentration gradients along the thickness direction. Table 6 lists the initial potential differences and the potential differences at 50% DOD.
| Sample | Thickness (µm) | Potential difference at 0% DOD (mV) | Potential difference at 50% DOD (mV) | Relative increase |
|---|---|---|---|---|
| L30 | 30 | 0.6 | 4.2 | 7.0× |
| L45 | 45 | 0.08 | 5.9 | 73.8× |
| L90 | 90 | 1.5 | 11.3 | 7.5× |
To interpret these results mechanistically, I decomposed the overpotential into ohmic and concentration contributions. The ohmic overpotential arises from the finite ionic conductivity of the solid electrolyte and the electronic resistance of the electrodes. It scales linearly with the current density and the thickness of the solid electrolyte. The concentration overpotential arises from the accumulation of lithium-ion concentration gradients. It scales with the thickness squared in the diffusion-limited regime, because the characteristic diffusion time is proportional to the square of the path length. In my simulations, both components increased with thickness. Table 7 shows the calculated ohmic and concentration overpotentials at a discharge rate of 0.5 C. The ohmic overpotential for L90 was almost three times that of L30, while the concentration overpotential for L90 was more than four times that of L30. This non-linear increase is a key finding: the penalty for increasing solid electrolyte thickness is not merely proportional but grows faster because of the diffusion length effect.
| Sample | Thickness (µm) | Ohmic overpotential (mV) | Concentration overpotential (mV) | Total overpotential (mV) |
|---|---|---|---|---|
| L30 | 30 | 1.2 | 2.1 | 3.3 |
| L45 | 45 | 1.8 | 3.6 | 5.4 |
| L90 | 90 | 3.5 | 8.9 | 12.4 |
The implications for the solid electrolyte cell are significant. A thicker solid electrolyte improves mechanical robustness and reduces the risk of short circuits, but it also degrades rate capability and increases heat generation. The internal resistance, which I extracted from the slope of the voltage–current relationship, increased from 18 Ω for L30 to 27 Ω for L45 and 48 Ω for L90. This increase in internal resistance directly translates into a larger voltage drop during discharge and a lower energy efficiency. Table 8 summarizes the internal resistance and the corresponding voltage drop at a discharge current of 0.1 mA. The voltage drop for L90 was more than twice that for L30. In a wearable application, this means that a solid electrolyte cell with a thick electrolyte would deliver less usable energy and would be more prone to overheating under high-rate operation.
| Sample | Thickness (µm) | Internal resistance (Ω) | Voltage drop at 0.1 mA (mV) | Relative resistance |
|---|---|---|---|---|
| L30 | 30 | 18 | 1.8 | 1.00 |
| L45 | 45 | 27 | 2.7 | 1.50 |
| L90 | 90 | 48 | 4.8 | 2.67 |
I also investigated the spatial distribution of lithium-ion concentration in the solid electrolyte. At 50% DOD, the concentration gradient along the radial direction was much steeper for L90 than for L30. In L30, the concentration difference between the positive-electrode side and the negative-electrode side was about 120 mol/m³. In L45, it was 210 mol/m³. In L90, it was 480 mol/m³. This concentration gradient is the driving force for diffusion, but it also represents a loss of available energy. According to the Nernst equation, a concentration difference of 480 mol/m³ corresponds to a potential difference of approximately 10 mV at room temperature, which is consistent with the potential differences I computed. The concentration gradient also affects the local exchange current density. Near the positive electrode, the lithium-ion concentration is higher, which increases \( j_0 \) and accelerates the interfacial reaction. Near the negative electrode, the lower concentration reduces \( j_0 \). This spatial variation in reaction kinetics can lead to non-uniform utilization of the electrode material, which over many cycles may cause mechanical stress and capacity fade. Table 9 presents the concentration gradients and the corresponding Nernstian potential differences.
| Sample | Thickness (µm) | Concentration difference at 50% DOD (mol/m³) | Nernstian potential difference (mV) | Local exchange current density variation (%) |
|---|---|---|---|---|
| L30 | 30 | 120 | 3.1 | 8 |
| L45 | 45 | 210 | 5.4 | 15 |
| L90 | 90 | 480 | 12.4 | 32 |
The interfacial reaction kinetics also depend on the local potential. In my model, the Butler–Volmer equation couples the local overpotential to the current density. When the solid electrolyte is thick, the potential distribution is non-uniform, so the overpotential varies along the interface. This means that some regions of the electrode experience a higher driving force for reaction than others. The result is a non-uniform current density at the interface, which can lead to localized degradation. I quantified this effect by computing the standard deviation of the interfacial current density. For L30, the standard deviation was 0.008 A/m². For L45, it was 0.015 A/m². For L90, it was 0.031 A/m². This nearly fourfold increase from L30 to L90 indicates that a thick solid electrolyte promotes heterogeneous electrochemical activity. Table 10 summarizes the interfacial current density statistics.
| Sample | Thickness (µm) | Mean interfacial current density (A/m²) | Standard deviation (A/m²) | Coefficient of variation |
|---|---|---|---|---|
| L30 | 30 | 0.190 | 0.008 | 0.042 |
| L45 | 45 | 0.195 | 0.015 | 0.077 |
| L90 | 90 | 0.201 | 0.031 | 0.154 |
From an optimization perspective, the ideal thickness of the solid electrolyte in a solid electrolyte cell must balance ionic transport and mechanical integrity. A very thin solid electrolyte, such as 10 µm or less, would minimize the ionic path length and reduce ohmic and concentration overpotentials. However, it would also increase the risk of electrical short circuits due to uneven electrode surfaces or dendrite penetration. In my experiments, the 30 µm solid electrolyte layer provided a good compromise: it was thick enough to prevent short circuits and thin enough to maintain uniform current density. The 45 µm layer showed moderate degradation, while the 90 µm layer exhibited severe polarization. Therefore, I recommend that for LFP/LTO all-solid-state fiber solid electrolyte cells operating at moderate rates, the solid electrolyte thickness should be kept below 50 µm, preferably around 30–40 µm. Table 11 lists the trade-offs associated with different thickness ranges.
| Thickness range | Advantages | Disadvantages | Recommended application |
|---|---|---|---|
| < 20 µm | Low ohmic loss, high rate capability | High short-circuit risk, difficult fabrication | Low-voltage, high-power microdevices |
| 20–50 µm | Balanced transport and mechanical strength | Moderate concentration polarization | Wearable solid electrolyte cells, smart textiles |
| 50–100 µm | High mechanical robustness, easy handling | High internal resistance, poor rate performance | Low-rate, safety-critical applications |
| > 100 µm | Very high mechanical strength | Severe polarization, low energy efficiency | Not recommended for fiber cells |
The effect of thickness on the discharge voltage profile is also worth discussing. For L30, the voltage plateau was flat and the end-of-discharge drop was abrupt. For L90, the voltage declined more steeply throughout the discharge, and the end-of-discharge drop occurred earlier. This means that a thick solid electrolyte reduces the accessible capacity at a given cutoff voltage. In my simulations, the delivered capacity at a 1.5 V cutoff was 142 mAh/g for L30, 136 mAh/g for L45, and 118 mAh/g for L90. The capacity loss for L90 was about 17% relative to L30. This loss is attributed to the earlier onset of polarization, which causes the cell voltage to reach the cutoff before the active material is fully utilized. Table 12 shows the discharge capacity and capacity retention for the three samples.
| Sample | Thickness (µm) | Discharge capacity at 1.5 V cutoff (mAh/g) | Capacity retention relative to L30 | Average discharge voltage (V) |
|---|---|---|---|---|
| L30 | 30 | 142 | 100% | 1.82 |
| L45 | 45 | 136 | 95.8% | 1.79 |
| L90 | 90 | 118 | 83.1% | 1.71 |
I also examined the effect of thickness on the lithium-ion concentration at the electrode/solid electrolyte interface. In a solid electrolyte cell, the interfacial lithium-ion concentration determines the local exchange current density and the onset of diffusion limitations. For L30, the interfacial concentration remained above 80% of the maximum concentration throughout discharge. For L90, the interfacial concentration at the negative electrode dropped below 50% of the maximum concentration near the end of discharge. This depletion of lithium ions at the interface is a classic signature of concentration polarization. It increases the local overpotential and reduces the reaction rate, which in turn causes the voltage to drop faster. The interfacial concentration profiles are summarized in Table 13. The data show that a thicker solid electrolyte exacerbates lithium-ion depletion at the negative electrode interface, which is the limiting side for LTO in this system.
| Sample | Thickness (µm) | Interfacial concentration at positive electrode (mol/m³) | Interfacial concentration at negative electrode (mol/m³) | Depletion ratio at negative electrode |
|---|---|---|---|---|
| L30 | 30 | 18,200 | 11,500 | 0.50 |
| L45 | 45 | 17,500 | 9,800 | 0.57 |
| L90 | 90 | 15,100 | 7,200 | 0.68 |
The thermal implications of these findings are also important. A higher internal resistance and larger overpotential mean more heat generation during operation. In a wearable solid electrolyte cell, heat dissipation is limited because the device is in contact with the human body and often encapsulated in textile layers. Therefore, minimizing the solid electrolyte thickness is beneficial not only for electrochemical performance but also for thermal safety. I estimated the volumetric heat generation rate using the product of the current density and the overpotential. For L30, the heat generation rate was 0.6 W/m². For L45, it was 1.1 W/m². For L90, it was 2.8 W/m². The nearly fivefold increase from L30 to L90 underscores the thermal penalty of a thick solid electrolyte. Table 14 lists the heat generation rates and the estimated temperature rise for a typical wearable configuration. These estimates assume natural convection and a small thermal mass, so they should be treated as qualitative trends.
| Sample | Thickness (µm) | Heat generation rate (W/m²) | Estimated temperature rise (°C) | Relative heat generation |
|---|---|---|---|---|
| L30 | 30 | 0.6 | 0.3 | 1.0 |
| L45 | 45 | 1.1 | 0.6 | 1.8 |
| L90 | 90 | 2.8 | 1.5 | 4.7 |
The mechanical benefits of a thicker solid electrolyte cannot be ignored. In a fiber-shaped solid electrolyte cell, the solid electrolyte also serves as a separator and a structural component. If it is too thin, it may not withstand the bending and stretching cycles that occur during weaving and wearing. I performed qualitative bending tests and observed that L30 remained intact after 1,000 bending cycles with a radius of 5 mm. L45 showed no visible damage, while L90 was also robust but exhibited a slight increase in resistance after bending. The trade-off is clear: increasing the solid electrolyte thickness improves mechanical durability but degrades electrochemical performance. For wearable applications, a thickness of 30–45 µm appears to offer the best compromise. Table 15 summarizes the mechanical and electrochemical trade-offs.
| Sample | Thickness (µm) | Bending durability (cycles to failure) | Internal resistance (Ω) | Capacity retention after bending |
|---|---|---|---|---|
| L30 | 30 | > 2,000 | 18 | 97% |
| L45 | 45 | > 2,000 | 27 | 95% |
| L90 | 90 | > 2,000 | 48 | 92% |
To further validate the thickness effect, I performed a sensitivity analysis. I varied the ionic conductivity of the solid electrolyte by ±20% and observed the change in the maximum current density and potential gradient for each thickness. The results showed that the sensitivity to ionic conductivity increased with thickness. For L30, a 20% decrease in ionic conductivity increased the potential gradient by 12%. For L90, the same decrease increased the potential gradient by 31%. This means that thick solid electrolytes are more vulnerable to variations in material properties, which is a concern for manufacturing reproducibility. Table 16 presents the sensitivity coefficients, defined as the fractional change in potential gradient divided by the fractional change in ionic conductivity. A larger absolute value indicates greater sensitivity.
| Sample | Thickness (µm) | Sensitivity coefficient for potential gradient | Sensitivity coefficient for current density |
|---|---|---|---|
| L30 | 30 | −0.60 | 0.35 |
| L45 | 45 | −1.05 | 0.52 |
| L90 | 90 | −1.55 | 0.78 |
The results of my finite element analysis can be summarized by the following scaling relationships. The ohmic resistance of the solid electrolyte is proportional to its thickness \( L \):
$$ R_{\mathrm{ohm}} = \frac{L}{\sigma_e A} $$
where \( A \) is the cross-sectional area. The diffusion time constant for lithium ions in the solid electrolyte scales as:
$$ \tau_{\mathrm{diff}} \propto \frac{L^2}{D_{\mathrm{eff}}} $$
Therefore, the concentration overpotential, which depends on the ratio of the discharge time to the diffusion time, scales approximately with \( L^2 \) when the discharge rate is high. The total overpotential is the sum of the ohmic and concentration contributions:
$$ \eta_{\mathrm{total}} = \eta_{\mathrm{ohm}} + \eta_{\mathrm{conc}} \approx i R_{\mathrm{ohm}} + \frac{R T}{F} \ln\left( \frac{c_{\mathrm{Li}^+, \mathrm{interface}}}{c_{\mathrm{Li}^+, \mathrm{bulk}}} \right) $$
These relationships explain why the performance degradation is non-linear with thickness. They also provide a guideline for designing solid electrolyte cells: to minimize polarization, one should reduce the solid electrolyte thickness while maintaining sufficient mechanical strength and preventing short circuits. For the LFP/LTO system I studied, the optimal thickness window is narrow, roughly 30–40 µm. Table 17 summarizes the scaling laws and their practical implications.
| Quantity | Scaling with thickness \( L \) | Practical implication |
|---|---|---|
| Ohmic resistance | \( R_{\mathrm{ohm}} \propto L \) | Linear increase in ohmic overpotential |
| Diffusion time constant | \( \tau_{\mathrm{diff}} \propto L^2 \) | Quadratic increase in concentration overpotential |
| Maximum current density | \( i_{\mathrm{max}} \propto 1/L \) | Thicker electrolyte requires higher current density for same rate |
| Potential gradient | \( \nabla \phi_e \propto L \) | Larger potential differences in thicker electrolytes |
| Heat generation | \( Q \propto i^2 R \propto L \) | More heat in thicker electrolytes at fixed current |
My simulation results are consistent with the experimental observations. The experimental voltage curves for L30, L45, and L90 showed the same trend: the voltage plateau shortened and the polarization increased with thickness. The measured internal resistance values, obtained from impedance spectroscopy, were 20 Ω, 29 Ω, and 52 Ω for L30, L45, and L90, respectively. These values are slightly higher than the simulated values because the experimental cell includes contact resistance and interfacial resistance that are not fully captured in the model. Nevertheless, the relative trend is identical. The good agreement between simulation and experiment gives me confidence that the finite element model can be used as a predictive tool for designing solid electrolyte cells with optimized thickness. Table 18 compares the simulated and experimental internal resistances.
| Sample | Thickness (µm) | Simulated internal resistance (Ω) | Experimental internal resistance (Ω) | Difference (%) |
|---|---|---|---|---|
| L30 | 30 | 18 | 20 | 10.0 |
| L45 | 45 | 27 | 29 | 6.9 |
| L90 | 90 | 48 | 52 | 7.7 |
The interfacial transport phenomena I have described are central to the operation of any solid electrolyte cell. In a solid electrolyte cell, the absence of a liquid phase means that ion transport relies entirely on the solid electrolyte. This makes the thickness of the solid electrolyte a critical design parameter. My work shows that increasing the thickness of the solid electrolyte in a fiber-shaped solid electrolyte cell leads to a cascade of negative effects: longer ion migration paths, higher internal resistance, larger ohmic and concentration overpotentials, more non-uniform current density, greater heat generation, and reduced capacity. These effects are all rooted in the fundamental transport equations that govern the solid electrolyte cell. By using finite element simulation, I was able to quantify these effects and identify an optimal thickness range. The approach I developed can be extended to other solid electrolyte chemistries and cell architectures.
In conclusion, I have constructed a finite element model of a LFP/LTO all-solid-state fiber solid electrolyte cell and used it to analyze the influence of solid electrolyte thickness on interfacial transport. The model couples solid-phase diffusion, modified Nernst–Planck ion transport, charge conservation, and Butler–Volmer kinetics. I validated the model against experimental discharge curves and found good agreement. My simulations show that as the solid electrolyte thickness increases from 30 to 90 µm, the potential gradient becomes more pronounced, the internal resistance increases, and both ohmic and concentration overpotentials grow. The maximum current density increases from 0.207 to 0.223 A/m², and the initial potential difference at 0% DOD increases from 0.6 to 1.5 mV. The capacity delivered at a 1.5 V cutoff decreases from 142 to 118 mAh/g. These findings demonstrate that the solid electrolyte thickness must be carefully optimized to balance ionic transport, mechanical integrity, and thermal safety. For the LFP/LTO fiber solid electrolyte cell, a thickness of 30–40 µm is recommended. My work provides a theoretical foundation for the design of high-performance solid electrolyte cells for flexible and wearable energy storage.
The broader impact of this research lies in its potential to accelerate the development of safe, flexible, and high-energy-density power sources. By using simulation to predict the effects of design parameters, I can reduce the need for time-consuming and resource-intensive trial-and-error experiments. The finite element framework I have established can be adapted to study other phenomena in solid electrolyte cells, such as interfacial resistance, dendrite growth, and thermal runaway. In future work, I plan to incorporate mechanical deformation and multiphysics coupling to better understand the behavior of solid electrolyte cells under bending and stretching. I also intend to explore composite solid electrolytes with higher ionic conductivity and improved interfacial stability. Ultimately, the goal is to create a solid electrolyte cell that can be seamlessly integrated into smart textiles, wearable sensors, and other flexible electronic systems, providing reliable power without compromising safety or comfort.
To summarize the quantitative findings, Table 19 presents a comprehensive comparison of the three thicknesses across all key performance metrics. The table highlights the trade-offs and supports my recommendation for a 30–40 µm solid electrolyte layer. Table 20 lists the model parameters and their sources, providing transparency and reproducibility. These tables, together with the governing equations and the simulation results, form a complete description of my investigation into interfacial transport in LFP/LTO all-solid-state fiber solid electrolyte cells.
| Metric | L30 (30 µm) | L45 (45 µm) | L90 (90 µm) |
|---|---|---|---|
| Maximum current density at 50% DOD (A/m²) | 0.198 | 0.206 | 0.219 |
| Non-uniformity index | 0.068 | 0.130 | 0.265 |
| Peak current density (A/m²) | 0.207 | 0.214 | 0.223 |
| Initial potential difference (mV) | 0.6 | 0.08 | 1.5 |
| Potential difference at 50% DOD (mV) | 4.2 | 5.9 | 11.3 |
| Ohmic overpotential (mV) | 1.2 | 1.8 | 3.5 |
| Concentration overpotential (mV) | 2.1 | 3.6 | 8.9 |
| Internal resistance (Ω) | 18 | 27 | 48 |
| Discharge capacity (mAh/g) | 142 | 136 | 118 |
| Heat generation rate (W/m²) | 0.6 | 1.1 | 2.8 |
| Parameter | Value | Source |
|---|---|---|
| Positive electrode solid-phase potential | 0.363 V | Experimental measurement |
| Negative electrode solid-phase potential | 0.300 V | Experimental measurement |
| Positive reference exchange current density | 0.00304 A/m² | Fitted from impedance |
| Negative reference exchange current density | 0.00543 A/m² | Fitted from impedance |
| Positive diffusion coefficient | 3.2 × 10⁻¹³ m²/s | Literature and fitting |
| Negative diffusion coefficient | 6.8 × 10⁻¹⁵ m²/s | Literature and fitting |
| Positive electronic conductivity | 91 S/m | Measured |
| Negative electronic conductivity | 100 S/m | Measured |
| Positive equilibrium potential temperature derivative | −9.95 × 10⁻⁵ V/K | Literature |
| Negative equilibrium potential temperature derivative | −1.04 × 10⁻⁵ V/K | Literature |
| Positive maximum lithium concentration | 21,190 mol/m³ | Literature |
| Negative maximum lithium concentration | 22,852 mol/m³ | Literature |
| Particle radius | 1 × 10⁻⁹ m | Estimated from SEM |
| Solid electrolyte ionic conductivity | 1.19 × 10⁻² S/m | Measured |
These results and analyses lead me to conclude that the thickness of the solid electrolyte is a dominant factor in the performance of LFP/LTO all-solid-state fiber solid electrolyte cells. The finite element model I developed accurately captures the coupled electrochemical and transport phenomena and can be used to guide the design of next-generation solid electrolyte cells. By optimizing the solid electrolyte thickness, it is possible to achieve a balance between safety, mechanical flexibility, and electrochemical performance, enabling the widespread adoption of solid electrolyte cells in wearable and flexible electronics.