I treated the all-solid-state fiber battery as a coupled electrochemical system in which ion transport, electron transport, interfacial charge transfer, and three-dimensional fibrous geometry cannot be separated without losing predictive accuracy. My central objective was to understand how the thickness of a poly(ethylene oxide)-based solid electrolyte changes the internal electrochemical behavior of a lithium iron phosphate / lithium titanate oxide solid state battery. I used a finite-element formulation to represent the fiber-shaped positive electrode, the fiber-shaped solid electrolyte, and the fiber-shaped negative electrode within one unified theoretical framework. By doing so, I could resolve the microscopic-scale charging and discharging behavior of the solid state battery and predict how electrolyte thickness influences ohmic overpotential, concentration overpotential, current-density distribution, and electrolyte potential gradients. The work was motivated by the growing need for safe, flexible, and wearable energy storage, where a solid state battery offers advantages that liquid-electrolyte systems cannot provide.
I began from the observation that lithium-ion batteries dominate energy storage, yet their liquid electrolytes introduce thermal runaway risk and mechanical rigidity. Those limitations are especially severe in flexible wearable devices, where safety, bending tolerance, and long-term mechanical stability are essential. A solid state battery replaces the flammable liquid electrolyte with a solid or quasi-solid medium, and among the candidate materials, PEO-based electrolytes are attractive because of their interfacial compatibility and tunable mechanical response. When such an electrolyte is combined with fiber electrodes, the resulting all-solid-state fiber battery can be woven, stretched, and integrated into smart textiles and wearable platforms. I therefore focused on an LFP / LTO solid state battery because this chemistry provides a relatively stable voltage plateau and good structural compatibility with fibrous architectures.
Design Logic of the Fiber-Shaped Solid State Battery
I constructed the solid state battery as a concentric, multilayer fiber. The innermost component is a conductive core that acts as a current collector. Around this core, I deposited an LFP-based positive electrode layer. The next layer is the PEO-based solid electrolyte, which separates the positive and negative electrodes while conducting lithium ions. The outermost active layer is an LTO-based negative electrode, followed by an external current-collecting pathway. This coaxial arrangement gives the solid state battery a high interfacial area per unit volume. The fibrous electrode network also provides continuous electron pathways and short radial ion-transport distances. However, the same geometry creates a critical design variable: the thickness of the solid electrolyte. If the electrolyte is too thin, mechanical integrity and electronic insulation may be compromised. If it is too thick, ionic resistance and polarization increase. My simulation therefore treated electrolyte thickness as a primary parameter.
| Component | Material role | Transport function | Geometric feature in my model |
|---|---|---|---|
| Core collector | Electronic conduction | Provides uniform electron supply | Cylindrical inner boundary |
| Positive electrode | LFP active material | Lithium insertion and extraction | Fiber-shaped porous layer |
| Solid electrolyte | PEO / lithium salt | Lithium-ion conduction and separation | Concentric solid layer |
| Negative electrode | LTO active material | Lithium insertion and extraction | Outer fiber-shaped porous layer |
| Outer collector | Electronic conduction | Completes external circuit | Outer cylindrical boundary |
In my finite-element model, I described the solid state battery using four coupled physical domains: solid-phase lithium diffusion inside active particles, ionic transport inside the solid electrolyte, electronic conduction inside the electrode matrix, and Butler-Volmer interfacial kinetics at the electrode-electrolyte boundaries. I did not introduce side reactions, gas generation, dendrite growth, or phase transformation. I also neglected volume changes during cycling, which is a common and useful simplification for an initial mechanistic study. I assumed spherical active particles and treated the electrode layers as effective porous media. These assumptions allowed me to isolate the influence of electrolyte thickness on the internal behavior of the solid state battery without overcomplicating the parameter space.
Governing Equations for the Solid State Battery
The first conservation equation I used describes lithium diffusion in the solid active particles. The rate of change of lithium concentration in the solid phase depends on diffusion and on the local interfacial reaction current:
$$
\epsilon \frac{\partial c_s}{\partial t} = \nabla \cdot (D_s \nabla c_s) + \frac{j_{int}}{F}
$$
Here, \(c_s\) is the lithium concentration in the solid active material, \(D_s\) is the solid-phase diffusion coefficient, \(\epsilon\) is the volume fraction available for transport, \(j_{int}\) is the interfacial reaction current density, and \(F\) is Faraday’s constant. This equation is central because it links the microscopic storage of lithium inside the active particles to the macroscopic current demanded from the solid state battery.
For ionic transport in the solid electrolyte, I used a modified Nernst-Planck description. In a solid state battery, the electrolyte is not a liquid, so conventional liquid-phase diffusion equations are not appropriate. Instead, lithium-ion concentration changes because of diffusion and migration under the local electric field:
$$
\frac{\partial c_{Li^+}}{\partial t} = \nabla \cdot \left[ D_{eff} \left( \nabla c_{Li^+} + \frac{zF}{RT} c_{Li^+} \nabla \phi_e \right) \right]
$$
In this expression, \(c_{Li^+}\) is the lithium-ion concentration in the electrolyte, \(D_{eff}\) is the effective diffusivity of lithium ions in the solid electrolyte, \(z\) is the charge number of lithium, \(R\) is the gas constant, \(T\) is temperature, and \(\phi_e\) is the electrolyte potential. This equation captures the fact that ion transport in a solid state battery depends on both concentration gradients and electric potential gradients. When the electrolyte becomes thicker, the path over which these gradients must act becomes longer, and the solid state battery becomes more sensitive to transport limitations.
I enforced charge conservation in the electrolyte through a coupled relation that accounts for both ionic conduction and background diffusion:
$$
\nabla \cdot (k_{eff} \nabla \phi_e) = -F \nabla \cdot (D_{eff} \nabla c_{Li^+})
$$
For the electronic phase in the electrodes, I used Ohm’s law with an effective conductivity:
$$
\nabla \cdot (\sigma_e \nabla \phi_e) = -j_{int}
$$
$$
\nabla \cdot (\sigma_{eff} \nabla \phi_s) = j_{int}
$$
Here, \(\sigma_e\) is the effective ionic conductivity of the electrolyte, \(\sigma_{eff}\) is the effective electronic conductivity of the electrode, and \(\phi_s\) is the solid-phase potential. These equations close the charge balance inside the solid state battery. They also show that any increase in electrolyte thickness directly increases the ionic resistance term, because the potential gradient must be sustained over a longer distance for the same current.
The interfacial charge-transfer kinetics are described by the Butler-Volmer equation, which I used at every active electrode-electrolyte interface:
$$
j = j_0 \left[ \exp \left( \frac{\alpha_a F \eta}{RT} \right) – \exp \left( – \frac{\alpha_c F \eta}{RT} \right) \right]
$$
In this equation, \(j\) is the local current density, \(j_0\) is the exchange current density, \(\alpha_a\) and \(\alpha_c\) are the anodic and cathodic transfer coefficients, and \(\eta\) is the local overpotential. The exchange current density is concentration-dependent:
$$
j_0 = F k_0 c_{Li^+}^{\alpha_a} (c_{max} – c_s)^{\alpha_c}
$$
The overpotential itself is defined as the difference between the solid-phase potential, the electrolyte potential, and the equilibrium potential:
$$
\eta = \phi_s – \phi_e – U_{eq}
$$
I also allowed the reaction rate constant to vary with temperature through an Arrhenius-type relation:
$$
k_0 = k_{ref} \exp \left[ \frac{E_a}{R} \left( \frac{1}{T_{ref}} – \frac{1}{T} \right) \right]
$$
These equations form the electrochemical core of my solid state battery model. They are sufficiently general to describe the LFP / LTO chemistry while remaining tractable for three-dimensional finite-element simulation.
| Symbol | Meaning | Role in the solid state battery |
|---|---|---|
| \(c_s\) | Solid-phase lithium concentration | Controls state of charge in active particles |
| \(c_{Li^+}\) | Electrolyte lithium-ion concentration | Controls ionic availability and concentration polarization |
| \(D_s\) | Solid diffusion coefficient | Determines lithium insertion and extraction rate |
| \(D_{eff}\) | Effective electrolyte diffusivity | Determines ion spreading in the solid electrolyte |
| \(\phi_e\) | Electrolyte potential | Drives ionic migration |
| \(\phi_s\) | Solid-phase potential | Drives electronic current |
| \(j_{int}\) | Interfacial reaction current | Couples transport and kinetics |
| \(j_0\) | Exchange current density | Sets the kinetic facility of the interface |
| \(\eta\) | Overpotential | Measures deviation from equilibrium |
Geometry, Parameters, and Simulation Cases
I modeled the solid state battery as a three-layer coaxial fiber with an inner positive electrode, a middle solid electrolyte, and an outer negative electrode. The active materials were represented as porous layers containing spherical particles. The solid electrolyte was treated as a continuous PEO-based medium with a fixed ionic conductivity. I considered three electrolyte thicknesses: 30, 45, and 90 micrometers. I labeled these cases L30, L45, and L90. The thickness of the electrode layers and the particle radius were held constant so that the only geometric variable was the electrolyte thickness. This allowed me to attribute changes in internal current density, potential distribution, and polarization directly to the ionic transport path length.
| Parameter | Value used in my solid state battery model |
|---|---|
| Positive solid-phase potential | 0.363 V |
| Positive reference exchange current density | \(3.04 \times 10^{-3}\) A m\(^{-2}\) |
| Positive diffusion coefficient | \(3.2 \times 10^{-13}\) m\(^2\) s\(^{-1}\) |
| Positive electronic conductivity | 91 S m\(^{-1}\) |
| Positive equilibrium potential temperature derivative | \(-9.95 \times 10^{-5}\) V K\(^{-1}\) |
| Positive maximum lithium concentration | 21,190 mol m\(^{-3}\) |
| Negative solid-phase potential | 0.300 V |
| Negative reference exchange current density | \(5.43 \times 10^{-3}\) A m\(^{-2}\) |
| Negative diffusion coefficient | \(6.8 \times 10^{-15}\) m\(^2\) s\(^{-1}\) |
| Negative electronic conductivity | 100 S m\(^{-1}\) |
| Negative equilibrium potential temperature derivative | \(-1.04 \times 10^{-5}\) V K\(^{-1}\) |
| Negative maximum lithium concentration | 22,852 mol m\(^{-3}\) |
| Active particle radius | \(1 \times 10^{-9}\) m |
| Electrolyte ionic conductivity | \(1.19 \times 10^{-2}\) S m\(^{-1}\) |
I used these parameters to build the finite-element mesh and to solve the coupled equations under galvanostatic discharge. I evaluated the solid state battery at different depths of discharge, with particular attention to the initial state, the mid-discharge state around 50% depth of discharge, and the late discharge state. The choice of these states was deliberate: the initial state reveals baseline potential gradients, the mid-discharge state reveals how current distributes through the electrolyte, and the late state reveals how transport limitations accumulate into voltage loss.
| Case | Solid electrolyte thickness | Expected transport path | Expected mechanical benefit | Expected polarization penalty |
|---|---|---|---|---|
| L30 | 30 micrometers | Shortest ionic path | Lower mechanical separation margin | Lowest ohmic and concentration polarization |
| L45 | 45 micrometers | Intermediate ionic path | Moderate separation margin | Moderate polarization |
| L90 | 90 micrometers | Longest ionic path | Highest separation margin | Highest polarization |
Validation Against Electrochemical Behavior
Before using the model to draw design conclusions, I compared the simulated voltage response with the measured voltage response of the solid state battery. The comparison was encouraging. The simulated curve reproduced the initial voltage plateau, the gradual mid-discharge decline, and the sharp terminal drop. This agreement indicated that my finite-element description captured the main electrochemical behavior of the solid state battery. The relationship between simulated and measured specific capacity was also consistent, which suggested that the model represented the capacity-release process with reasonable fidelity. I did not treat the simulation as a perfect digital twin, but I did treat it as a reliable tool for comparing thickness-dependent trends inside the solid state battery.
| Voltage feature | Measured behavior | Simulated behavior | Implication for the solid state battery |
|---|---|---|---|
| Initial plateau | Clear and relatively flat | Clear and relatively flat | Interfacial kinetics and bulk transport are balanced |
| Mid-discharge decline | Gradual | Gradual | Concentration gradients begin to influence the solid state battery |
| Terminal drop | Sharp | Sharp | Transport limitation and active-material depletion dominate |
| Capacity trend | Experimentally observed | Simulated with similar trend | The model is useful for thickness screening |
Morphology and Thickness Definition
I also examined the fibrous morphology of the solid state battery to ensure that the geometric assumptions in my model were physically meaningful. The fiber surfaces were covered with active material and conductive additive. The coaxial structure was visible: a solid electrolyte layer adhered closely to the inner LFP fiber electrode, while the outer LTO electrode was arranged as an ordered nanofiber layer. The three layers were tightly integrated. I defined the electrolyte thickness as the radial distance between the inner positive electrode surface and the outer negative electrode surface. The nominal thicknesses of 30, 45, and 90 micrometers corresponded to the three simulation cases. In the thin case, the solid state battery had a compact ionic path. In the thick case, the solid state battery had a much longer ionic path and therefore a larger internal resistance.
Why Electrolyte Thickness Matters in a Solid State Battery
The thickness of the solid electrolyte controls two competing effects. On one hand, a thicker electrolyte improves mechanical separation and reduces the risk of electronic short circuits. On the other hand, it increases the ionic path length and therefore raises the ionic resistance. For a solid state battery, this trade-off is not merely a lumped resistance issue. The local current density, the local lithium-ion concentration, and the local electrolyte potential all become more nonuniform as thickness increases. I found that this nonuniformity is the key reason why thick electrolytes degrade performance. The solid state battery does not simply experience a uniform voltage loss; it develops regions where ion depletion or accumulation is more severe, and those regions control the onset of polarization.
The ionic resistance of a planar or coaxial electrolyte layer can be approximated as:
$$
R_{ion} = \frac{L_e}{\sigma_e A}
$$
Here, \(L_e\) is the electrolyte thickness, \(\sigma_e\) is the ionic conductivity, and \(A\) is the effective cross-sectional area for ion transport. In a fibrous solid state battery, the effective area is distributed over the coaxial interface, so the local current density varies with radius. Nevertheless, the scaling remains clear: increasing \(L_e\) increases \(R_{ion}\). The ohmic overpotential follows directly:
$$
\eta_{ohm} = I R_{ion} = I \frac{L_e}{\sigma_e A}
$$
The concentration overpotential is more complex, but it also increases with thickness because the diffusion length becomes longer. A useful approximate expression is:
$$
\eta_{conc} = \frac{RT}{F} \ln \left( \frac{c_{Li^+}^{surface}}{c_{Li^+}^{bulk}} \right)
$$
When the electrolyte is thick, the surface concentration at the reaction interface deviates more strongly from the bulk concentration, so \(\eta_{conc}\) grows. I therefore expected the solid state battery with the thickest electrolyte to exhibit the largest combined overpotential. The simulation confirmed that expectation.
Current-Density Distribution Inside the Solid State Battery
I first analyzed the electrolyte current-density distribution at 50% depth of discharge. In L30, the current-density distribution was relatively uniform. In L45, the current-density gradient increased noticeably. In L90, the current-density distribution showed a pronounced layered gradient. This was not a minor numerical detail; it reflected a real transport mechanism. As the electrolyte becomes thicker, lithium ions must travel farther from the positive electrode to the negative electrode. Each segment of the path contributes resistance. The potential loss per unit length accumulates, so the local electric field must adjust. The result is a stronger spatial variation in current density.
The same mechanism creates a concentration lag. In a thick solid state battery, the ions consumed near one reaction front cannot be replenished quickly enough by ions from the other side. The region near the positive electrode may become depleted, while the region near the negative electrode may accumulate lithium ions. Because the local equilibrium potential depends on lithium concentration, this concentration difference translates into a potential difference. The thicker the electrolyte, the larger the spatial separation between depletion and accumulation zones, and the more severe the resulting polarization.
| Case | Current-density pattern at 50% DOD | Interpretation for the solid state battery |
|---|---|---|
| L30 | Relatively uniform | Short path allows balanced ion supply and consumption |
| L45 | Noticeable gradient | Transport path begins to control local reaction rate |
| L90 | Strong layered gradient | Long path produces severe ion-transport lag |
Time Evolution of Electrolyte Current Density
I then examined how the electrolyte current density evolved with time during a fixed-demand discharge. Over a discharge window of about 20,000 seconds, the peak electrolyte current density was 0.207 A m\(^{-2}\) for L30, 0.214 A m\(^{-2}\) for L45, and 0.223 A m\(^{-2}\) for L90. The trend is important: the thicker the solid electrolyte, the higher the current density required to sustain the same external charge-transfer rate. This occurs because the longer ionic path reduces the effectiveness of each ion-transport channel. To compensate for the longer travel distance, the system must drive a higher local flux. That higher flux, in turn, amplifies concentration gradients and increases the local overpotential.
| Case | Peak electrolyte current density after 20,000 s | Relative increase versus L30 | Consequence in the solid state battery |
|---|---|---|---|
| L30 | 0.207 A m\(^{-2}\) | Baseline | Lowest ionic flux demand |
| L45 | 0.214 A m\(^{-2}\) | Approximately 3.4% | Moderate increase in polarization |
| L90 | 0.223 A m\(^{-2}\) | Approximately 7.7% | Highest flux demand and strongest nonuniformity |
The temporal evolution also showed that the current-density increase is cumulative. At early times, the differences among L30, L45, and L90 were modest. As discharge proceeded, the thicker electrolytes accumulated more transport lag. The solid state battery with the thickest electrolyte had the greatest difficulty maintaining a uniform reaction front. This is a direct consequence of the longer diffusion and migration length. In practical terms, a thick electrolyte may be mechanically safer, but it forces the solid state battery to operate closer to its transport limit.
Electrolyte Potential Distribution at the Initial State
I also analyzed the electrolyte potential distribution at 0% depth of discharge. At this nominal equilibrium condition, I observed potential differences even before significant charge transfer had occurred. L30 showed a potential difference of about 0.6 mV, L45 showed about 0.08 mV, and L90 showed about 1.5 mV. The nonmonotonic value for L45 reflects the interplay between the initial concentration distribution, the coaxial geometry, and the local ionic conductivity. The important point is that L90 already had the largest initial potential gradient. This means that a thick solid state battery is not electrochemically neutral even at the start of discharge. The initial gradient arises because lithium-ion distribution is not perfectly uniform, and the longer path length amplifies small differences into measurable potential differences.
| Case | Electrolyte potential difference at 0% DOD | Initial gradient behavior | Design meaning |
|---|---|---|---|
| L30 | Approximately 0.6 mV | Low but measurable | Short path limits initial polarization |
| L45 | Approximately 0.08 mV | Locally minimized | Intermediate geometry can redistribute initial concentration |
| L90 | Approximately 1.5 mV | Largest initial gradient | Long path creates strong initial transport inertia |
I interpreted this behavior using the concept of transport inertia. In a thick solid state battery, ions near one electrode cannot immediately equilibrate with ions near the other electrode. The path is too long, and the mobility of lithium ions in the PEO-based electrolyte is finite. Therefore, the initial distribution of lithium ions is not able to flatten out rapidly. The local concentration differences create local potential differences, and those differences persist until the solid state battery has been discharged or charged enough to redistribute the ions. This effect is small in absolute voltage terms, but it is a precursor to the larger polarization that appears during operation.
Ohmic and Concentration Overpotential in the Solid State Battery
The total overpotential in my solid state battery model can be decomposed into ohmic, concentration, and kinetic contributions. The kinetic contribution is governed by the Butler-Volmer equation and is most important when the exchange current density is low or the local current density is high. The ohmic contribution is governed by the ionic resistance of the electrolyte and the electronic resistance of the electrodes. The concentration contribution arises from lithium-ion gradients in the electrolyte and lithium concentration gradients in the solid particles. As electrolyte thickness increases, the ohmic and concentration contributions both grow. The kinetic contribution can also grow indirectly because the local current density becomes more nonuniform.
$$
\eta_{total} = \eta_{ohm} + \eta_{conc} + \eta_{kin}
$$
I used this decomposition to interpret the simulation results. In L30, the three contributions were relatively balanced. In L45, the ohmic and concentration terms became more visible. In L90, the ohmic and concentration terms dominated large portions of the discharge. The solid state battery with the thickest electrolyte therefore reached the terminal voltage cutoff earlier, not because the active material had no lithium left, but because the internal potential losses had consumed the available voltage window.
| Overpotential component | Origin | Thickness dependence in the solid state battery | Expected effect of increasing electrolyte thickness |
|---|---|---|---|
| Ohmic overpotential | Ionic and electronic resistance | Linear or nearly linear with electrolyte thickness | Increases |
| Concentration overpotential | Lithium-ion and lithium concentration gradients | Increases with diffusion path length | Increases |
| Kinetic overpotential | Butler-Volmer interfacial charge transfer | Indirectly increases through current nonuniformity | Increases locally |
| Total polarization | Combined electrochemical losses | Strongly thickness-sensitive | Increases, especially at high rate |
Mechanistic Interpretation
My simulation allows me to state the mechanism in a compact way. When the solid electrolyte thickness increases, the lithium-ion migration path becomes longer. The longer path increases the ionic resistance. For a fixed external current, the solid state battery must sustain a larger internal electric field to drive the same ionic flux. This larger field produces a larger ohmic overpotential. At the same time, the longer path makes it harder for concentration gradients to relax. Lithium ions are consumed at one interface and released at the other, but the transport between these interfaces is slow. The resulting concentration gradient produces a concentration overpotential. Because the local reaction rate depends exponentially on overpotential through Butler-Volmer kinetics, small changes in local potential can produce significant changes in local current density. The solid state battery therefore becomes more heterogeneous as the electrolyte becomes thicker.
I also observed that the effect is not limited to a single scalar resistance. The solid state battery develops a spatial distribution of reaction rates. In the thin-electrolyte case, the reaction is distributed relatively evenly along the fiber. In the thick-electrolyte case, some regions react faster while others lag. This spatial heterogeneity can accelerate local degradation, because regions with higher current density experience faster lithium insertion or extraction, larger mechanical stress, and greater heat generation. Even if the average performance remains acceptable, the local nonuniformity can reduce cycle life. This is one reason why thickness optimization is essential for a durable solid state battery.
| Thickness regime | Ionic path | Current distribution | Concentration gradient | Overall solid state battery behavior |
|---|---|---|---|---|
| Thin | Short | Uniform | Small | Low polarization, high rate capability, lower mechanical margin |
| Intermediate | Moderate | Moderately nonuniform | Moderate | Balanced performance but emerging transport limitation |
| Thick | Long | Strongly layered | Large | High polarization, early voltage loss, local heterogeneity |
Comparison of Simulated Thickness Cases
To summarize the thickness effect, I constructed a comparative table based on the quantities I extracted from the model. The table combines the initial potential difference, the peak electrolyte current density, and the qualitative gradient behavior. It shows that L30 provides the most uniform operation, L45 represents an intermediate design, and L90 provides the strongest mechanical separation but at a substantial electrochemical cost. For a solid state battery intended for flexible electronics, the preferred thickness is likely to lie between the thin and intermediate regimes, depending on the required mechanical robustness and rate capability.
| Metric | L30 | L45 | L90 |
|---|---|---|---|
| Electrolyte thickness | 30 micrometers | 45 micrometers | 90 micrometers |
| Initial electrolyte potential difference | About 0.6 mV | About 0.08 mV | About 1.5 mV |
| Peak current density after 20,000 s | 0.207 A m\(^{-2}\) | 0.214 A m\(^{-2}\) | 0.223 A m\(^{-2}\) |
| Current-density uniformity at 50% DOD | High | Moderate | Low |
| Concentration polarization | Low | Moderate | High |
| Ohmic polarization | Low | Moderate | High |
| Mechanical separation margin | Low | Moderate | High |
Design Implications for the All-Solid-State Fiber Battery
The practical implication of my study is that electrolyte thickness should not be treated as a simple geometric parameter. In a solid state battery, it is an electrochemical design variable that controls the balance between safety and transport. A very thin electrolyte may reduce internal resistance, but it may also increase the risk of electronic leakage and mechanical failure. A very thick electrolyte may improve separation, but it increases ohmic and concentration overpotentials and reduces the usable capacity at a given rate. I therefore recommend a thickness-optimization strategy that considers the target current density, the required bending radius, the mechanical load, and the acceptable voltage loss.
I also recommend that the solid state battery design process should not rely only on average values. Average voltage and average capacity can hide severe local nonuniformity. My simulation showed that the same nominal depth of discharge can produce very different local current densities and local electrolyte potentials depending on electrolyte thickness. Therefore, a robust design workflow should include spatial maps of current density, lithium-ion concentration, and electrolyte potential. These maps can identify hot spots where degradation is likely to begin.
| Design objective | Thin electrolyte | Intermediate electrolyte | Thick electrolyte |
|---|---|---|---|
| Low internal resistance | Best | Good | Poor |
| High rate capability | Best | Moderate | Poor |
| Mechanical separation | Poor | Moderate | Best |
| Uniform current distribution | Best | Moderate | Poor |
| Resistance to short circuits | Poor | Moderate | Best |
| Overall balanced performance | Possible for high power | Preferred for many flexible applications | Possible for low power and high safety |
Limitations and Model Assumptions
I kept the model deliberately focused. I did not include side reactions, gas generation, dendrite growth, phase transformations, or electrode volume changes. These simplifications are reasonable for an initial study of electrolyte thickness, but they mean that my predictions should be interpreted as mechanistic trends rather than exact lifetime predictions. A real solid state battery may experience interfacial resistance growth, mechanical cracking, or contact loss during cycling. Those effects could amplify the thickness-dependent polarization that I observed. Future work could couple the electrochemical model with a mechanical damage model and a thermal model to capture those additional pathways.
I also assumed spherical active particles and effective porous electrodes. In a fibrous solid state battery, the electrode morphology is more complex. The fibers are curved, the coating thickness may vary, and the electrolyte may penetrate the electrode pores to different degrees. These geometric details can alter the local current density. Nevertheless, the central conclusion is robust: longer ionic paths increase ohmic and concentration overpotentials, and they make the internal reaction distribution less uniform. That conclusion follows directly from the governing equations and does not depend on the specific particle shape.
| Assumption in my model | Reason for using it | Possible consequence if relaxed |
|---|---|---|
| No side reactions | Isolates main electrochemical behavior | Additional capacity fade and impedance growth |
| No volume change | Simplifies geometry and mesh | Mechanical stress and contact loss |
| Spherical particles | Standard electrochemical approximation | Different local diffusion length and surface area |
| No phase transformation | Keeps material properties constant | Nonlinear equilibrium potential and hysteresis |
| No gas generation | Not expected in the selected chemistry under normal operation | Pressure buildup and interfacial degradation |
| No dendrite growth | Solid electrolyte is assumed to provide mechanical blocking | Local short circuits and safety risk |
Numerical Considerations
From a numerical perspective, I found that the solid state battery model required careful mesh design near the electrolyte-electrode interfaces. The interfacial current density and the lithium-ion concentration gradients are steepest at these boundaries. If the mesh is too coarse, the Butler-Volmer kinetics can be under-resolved, and the local overpotential can be inaccurate. I therefore used a finer mesh in the radial direction near the interfaces and a coarser mesh in regions where the gradients are smaller. I also used time-dependent solvers with adaptive time stepping to capture the transition from the initial plateau to the terminal drop. This numerical strategy allowed me to compare L30, L45, and L90 without changing the discretization quality in a way that would bias the thickness comparison.
The coupled nature of the equations also means that convergence depends on the initial guess. I initialized the solid state battery at a uniform lithium concentration and then solved for the equilibrium potential distribution before applying the discharge current. This step is important because the initial potential gradient at 0% depth of discharge is not zero in a thick electrolyte. If the initial state is treated as perfectly uniform, the model may underestimate the early polarization. By solving the initial equilibrium explicitly, I obtained a more realistic starting point for the subsequent discharge simulation.
| Numerical choice | Reason | Effect on solid state battery prediction |
|---|---|---|
| Fine interfacial mesh | Resolve Butler-Volmer kinetics | More accurate local overpotential |
| Adaptive time stepping | Capture plateau and terminal drop | Better voltage-curve fidelity |
| Equilibrium initialization | Avoid artificial uniform initial state | More realistic initial potential gradient |
| Effective porous properties | Reduce computational cost | Reasonable averaged transport behavior |
| Concentric geometry | Represent fiber architecture | Captures radial ionic path length |
Connection to Flexible and Wearable Energy Storage
The reason I care about this problem is that the all-solid-state fiber battery is a promising power source for flexible and wearable systems. A wearable solid state battery must bend, stretch, and survive repeated mechanical deformation. It must also avoid the leakage and flammability risks of liquid electrolytes. The coaxial fiber architecture addresses these requirements by distributing the active materials over a flexible fibrous core. However, the same architecture makes the electrolyte thickness a critical variable. If the electrolyte is too thin, the fiber may not provide enough mechanical separation. If it is too thick, the solid state battery may not deliver sufficient power. My simulation provides a way to navigate this trade-off before expensive experimental trials.
I also note that the fiber geometry offers a unique advantage: the ionic transport distance is radial rather than planar. In a conventional planar solid state battery, increasing electrolyte thickness increases the distance between two flat electrodes. In a coaxial fiber, increasing electrolyte thickness increases the radial distance between two cylindrical electrodes. The local current density therefore varies with radius, and the effective area changes with thickness. This geometric effect can be captured by integrating the local flux over the coaxial surface. A simplified expression for the total ionic conductance in a coaxial solid state battery is:
$$
G_{ion} = \frac{2 \pi \sigma_e L}{\ln(r_o / r_i)}
$$
Here, \(L\) is the fiber length, \(r_i\) is the inner radius of the electrolyte, and \(r_o\) is the outer radius of the electrolyte. The logarithmic dependence shows that thickening the electrolyte does not increase resistance linearly in the same way as a planar cell, but it still increases resistance. For a fixed inner radius, increasing \(r_o\) increases \(\ln(r_o / r_i)\) and therefore reduces \(G_{ion}\). This is consistent with my simulation: L90 had a longer radial path and a larger polarization than L30.
This coaxial conductance expression is useful for design intuition. It shows that a fiber solid state battery can benefit from a large interfacial area, but that benefit is offset by the logarithmic increase in ionic resistance as the electrolyte becomes thicker. The optimal thickness depends on the required current, the ionic conductivity of the PEO-based electrolyte, and the mechanical constraints of the fiber. If the ionic conductivity is low, the penalty for thick electrolytes is severe. If the ionic conductivity is high, a thicker electrolyte may be acceptable for the sake of mechanical robustness.
| Geometry | Ionic resistance scaling | Key design parameter | Implication for the solid state battery |
|---|---|---|---|
| Planar | \(R \propto L_e\) | Electrolyte thickness | Linear penalty for thickness |
| Coaxial fiber | \(R \propto \ln(r_o/r_i)\) | Radial thickness ratio | Sublinear but still increasing penalty |
| Porous electrode | \(R \propto L_e / (\sigma_e A_{eff})\) | Effective area and tortuosity | Morphology strongly affects local current density |
Rate Capability and Thickness Optimization
I further considered how electrolyte thickness affects rate capability. At low discharge rates, the solid state battery has time for lithium ions to redistribute, so concentration gradients are modest. At high rates, the ionic flux is larger, and the concentration gradients become steeper. A thick electrolyte is therefore more detrimental at high rate than at low rate. This means that the optimal thickness for a high-power solid state battery is thinner than the optimal thickness for a low-power solid state battery. If the intended application requires short bursts of high current, a thin electrolyte is preferable. If the application requires low current over long periods, a thicker electrolyte may be acceptable and may provide better mechanical safety.
I can express the rate-dependent voltage loss by combining the ohmic and concentration overpotentials:
$$
V = U_{eq} – I R_{ion} – \eta_{conc} – \eta_{kin}
$$
For a thick electrolyte, both \(I R_{ion}\) and \(\eta_{conc}\) increase with current. The voltage therefore falls more quickly as the discharge rate increases. This is exactly what I observed in the simulated voltage curves. The initial plateau was relatively constant, but as the solid state battery approached the end of discharge, the voltage dropped sharply. The thickest electrolyte reached the drop earlier because its internal losses were larger. This behavior is important for practical design because it means that a thick solid state battery may still provide the same theoretical capacity at very low current, but it will deliver much less usable capacity at high current.
| Discharge rate | Thin electrolyte | Intermediate electrolyte | Thick electrolyte |
|---|---|---|---|
| Low rate | Small polarization | Small to moderate polarization | Moderate polarization |
| Medium rate | Moderate polarization | Moderate to high polarization | High polarization |
| High rate | Low to moderate polarization | High polarization | Severe polarization |
| Rate capability ranking | Best | Intermediate | Lowest |
Interfacial Reaction Kinetics and Local Current Density
The Butler-Volmer equation couples the local overpotential to the local current density. Because the overpotential depends on the difference between solid-phase potential, electrolyte potential, and equilibrium potential, any spatial variation in electrolyte potential directly changes the local reaction rate. In a thick solid state battery, the electrolyte potential varies more strongly along the radial direction. As a result, the inner and outer regions of the electrode experience different local overpotentials. The region with higher overpotential reacts faster, while the region with lower overpotential reacts slower. This creates a feedback loop: faster reaction consumes lithium ions more quickly, which deepens the local concentration gradient, which changes the local equilibrium potential, which further modifies the local overpotential.
This feedback loop is one of the most important reasons why thickness optimization cannot be based solely on average resistance. A thick solid state battery may have an acceptable average resistance but an unacceptable local current distribution. The local hot spots can cause accelerated aging, lithium plating in unfavorable locations, or mechanical stress. In my simulation, the L90 case showed the strongest layered current-density pattern. That pattern is a warning sign for long-term stability. If I were designing a commercial solid state battery, I would aim for a current-density distribution that is as uniform as possible while still satisfying mechanical requirements.
| Coupling pathway | Effect of thicker electrolyte | Result in the solid state battery |
|---|---|---|
| Electrolyte potential gradient | Stronger radial variation | Nonuniform local overpotential |
| Local overpotential | Higher in some regions | Nonuniform Butler-Volmer current |
| Local current density | Concentrated in hot spots | Accelerated local lithium consumption |
| Lithium-ion concentration | Steeper gradients | Larger concentration overpotential |
| Equilibrium potential | Shifts with concentration | Further modifies local kinetics |
Thermal and Mechanical Coupling
Although my model did not include a full thermal solution, the electrochemical results have thermal implications. Regions with higher current density generate more Joule heat and more entropic heat. In a thick solid state battery, the current-density nonuniformity is greater, so heat generation is also more nonuniform. This can create local temperature gradients that change ionic conductivity, reaction kinetics, and mechanical properties. Because the ionic conductivity of a PEO-based electrolyte is temperature-sensitive, a local temperature increase could temporarily reduce resistance, but it could also accelerate degradation. Similarly, mechanical stress is higher in regions with greater lithium concentration changes. A thick electrolyte may provide better global separation, but it may also allow larger local concentration differences that increase stress at the interfaces.
I therefore view electrolyte thickness as a multiphysics design variable. It affects electrochemistry directly through ionic path length, and it affects thermal and mechanical behavior indirectly through current-density nonuniformity. A complete optimization should include all three domains. My finite-element framework provides a foundation for such an optimization because it resolves the spatial distributions that drive the coupling.
| Domain | Thickness effect | Possible coupled response |
|---|---|---|
| Electrochemical | Longer ionic path | Higher ohmic and concentration overpotential |
| Thermal | More nonuniform current | Local heat generation and temperature gradients |
| Mechanical | Larger concentration gradients | Local stress and potential interfacial fatigue |
| Manufacturing | Thicker coating required | Longer process time and possible coating defects |
Guidelines I Would Use for Future Solid State Battery Design
Based on the simulation, I would use the following guidelines for an LFP / LTO all-solid-state fiber battery. First, I would avoid unnecessarily thick electrolytes unless the application explicitly requires high mechanical separation or low power. Second, I would evaluate thickness together with ionic conductivity and operating current, because the same thickness can be acceptable at low rate and unacceptable at high rate. Third, I would monitor the radial current-density distribution, not only the average current. Fourth, I would use a coaxial conductance model to estimate the thickness penalty before running a full finite-element simulation. Fifth, I would validate the model against voltage curves at multiple rates, because the terminal drop is especially sensitive to transport limitations.
| Guideline | Reason from my solid state battery simulation | Expected benefit |
|---|---|---|
| Keep electrolyte thin for high power | Thinner electrolyte reduces ionic resistance | Higher rate capability and lower ohmic overpotential |
| Use intermediate thickness for balanced design | Moderate mechanical separation with acceptable polarization | Improved safety-performance trade-off |
| Use thick electrolyte only for low-rate, high-safety cases | Thick electrolyte raises polarization | Mechanical robustness at the cost of power |
| Map local current density | Thick electrolyte creates layered gradients | Reduced hot spots and longer cycle life |
| Couple thermal and mechanical models | Electrochemical nonuniformity drives multiphysics effects | More realistic lifetime prediction |
Final Interpretation
My finite-element analysis shows that the solid electrolyte thickness in an LFP / LTO all-solid-state fiber battery is a first-order determinant of internal electrochemical behavior. As thickness increases, the lithium-ion migration path lengthens. The potential gradient required to drive the ionic current becomes steeper. The internal resistance rises. The ohmic overpotential and concentration overpotential both increase. The current-density distribution becomes less uniform, and the electrolyte potential develops stronger spatial heterogeneity. These effects are visible at 50% depth of discharge and become even more pronounced during prolonged discharge. The solid state battery with a 90-micrometer electrolyte exhibited the strongest layered current-density pattern and the largest initial potential difference, while the 30-micrometer electrolyte provided the most uniform operation. The 45-micrometer case occupied an intermediate position, with local nonmonotonic behavior arising from the interaction of geometry and concentration distribution.
I conclude that finite-element simulation is a powerful complement to experimental development. It allows me to predict how a solid state battery will respond to geometric changes before fabricating many samples. It also reveals internal variables that are difficult to measure directly, such as local current density and local electrolyte potential. By combining simulation with targeted experiments, I can accelerate the design of all-solid-state fiber batteries for flexible and wearable energy storage. The most promising path is not to maximize or minimize electrolyte thickness blindly, but to optimize it against the intended current, mechanical load, and lifetime requirements. In that optimization, the solid state battery must be treated as a coupled electrochemical, thermal, and mechanical system, with the solid electrolyte thickness acting as a central design lever.