Comfortable wearable thermoelectric generator with high output power

The proliferation of wearable and implantable electronics demands continuous, reliable power. Wearable thermoelectric generators (w-TEGs) can harvest body heat via the Seebeck effect and offer advantages such as reliability, lack of moving parts, and environmental friendliness. Despite progress improving w-TEG power under extreme conditions, wearer comfort—skin temperature, perceived pressure, and mechanical flexibility—has been largely overlooked, though it is crucial for practical, long-term use. Optimizing both comfort (wearability) and electrical output is challenging due to tight coupling among device structure, thermoelectric (TE) material properties, and environmental heat transfer. Moreover, a general analytical framework linking system efficiency and wearability has been lacking. This study addresses these gaps by establishing a sandwiched-structure model that quantitatively connects output power and comfort, enabling co-optimization under realistic wearing conditions.

Prior work has highlighted the promise of w-TEGs for self-powered systems and explored flexible/stretchable device architectures and heat management strategies. Many studies focus on maximizing output power under strong thermal gradients or with efficient heat sinks, often using Bi2Te3 or Ag2Se materials, but typically neglect wearer comfort metrics (skin temperature ranges perceived as hot/warm/cold, and pressure thresholds associated with clothing tightness). Modeling approaches include computationally intensive 3D finite element analysis to capture lateral heat spreading and complex geometries, and simpler 1D models used for macroscopic parameter guidance. However, a concise analytical treatment that simultaneously integrates TE performance, structural parameters, and comfort constraints for w-TEGs has not been reported. Mg-based materials (n-type Mg3Bi2-based and p-type MgAgSb) have recently emerged as cost-effective, less toxic alternatives to Bi2Te3 for near-room-temperature applications, achieving competitive ZT and module efficiencies in non-wearable TEGs.

The authors developed coupled analytical mechanical and thermal-electric models for a sandwiched w-TEG worn on the body. Mechanical model: The device is treated as a three-layer structure (bottom substrate, filler with embedded TE legs and electrodes, top substrate) conforming to a cylindrical body segment. An effective bending stiffness E_ITEG is derived as the sum of contributions from bottom substrate, filler, and top substrate, each dependent on material Young’s modulus, fill factor (F), and geometry (leg length/height L, width, area moments of inertia). From static equilibrium, an expression for the skin pressure Pr as a function of E_ITEG, device width W_TEG, filler thickness tf, and bending radius r is derived (linear elastomer approximation; a Mooney–Rivlin hyperelastic derivation is provided in supplementary notes). Thermal-electric model: A 1D steady-state model integrates core body temperature, skin thermal resistance (Ks), contact thermal resistance between device and skin (Kcon), the TE module (including filler contribution), and cold-side heat transfer (Kh, Kc). Under simplifying assumptions (uniform filler contribution, neglecting Thomson effect and some contact resistances), the temperature distribution equation and boundary conditions yield closed-form expressions for maximum power density Pd and skin temperature Ts at optimal current. Effective thermal properties incorporate the filler via an effective conductivity term. The model also determines the optimal p/n cross-sectional area ratio Fp/n,opt and equivalent ZT for two-leg modules, reducing to an effective single-leg description for system-level optimization. Design workflow: Given an application scenario (ambient temperature Ta, bending radius r, body temperature Tb), encapsulation properties (Young’s modulus E and thermal conductivity κ of fillers and substrates), and TE material properties (Seebeck S, electrical conductivity σ, thermal conductivity κ), the authors: (1) constrain structural parameters (L, TE-leg width w, fill factor F, p/n area ratio Fp/n) to satisfy comfort bounds on skin pressure (Pr) and skin temperature (Ts); (2) maximize output metrics (Pd, voltage density Vd) within those comfort-constrained ranges using analytic expressions; (3) perform 3D finite element analysis (FEA) for refinement, capturing secondary thermal effects (lateral spreading, interfacial resistances) not included in 1D analysis. Materials and device fabrication: n-type Mg3.2Bi1.49Sb0.5Se0.01 and p-type MgAg0.95Sb0.99 bulk legs were synthesized via ball milling and spark plasma sintering with metallic barrier layers. Stretchable, thermally conductive substrates were made from PDMS with liquid metal (Ga–In) and copper (E ≈ 820 kPa, κ ≈ 2.1 W m−1 K−1); the filler was soft, low-κ polyurethane foam (E ≈ 270 kPa, κ ≈ 0.025 W m−1 K−1). Copper S-type interconnects and screen-printed solder were used for assembly, followed by encapsulation with the stretchable substrates and foam injection. A radiative cooling (RC) SiO2/TiO2/PDMS film was applied to enhance cold-side heat exchange. Model verification and testing: Multiple devices (L = 2.5–4 mm, F = 3–17%) were tested on the arm under three convective conditions (natural, moderate, higher convection). Output power Pd and skin temperature Ts were compared among 1D analysis, FEA, and experiments. Mechanical characterization measured E_ITEG and durability under bending (r ≥ 5 mm) and tensile strain (up to 30%), tracking resistance and electrical output over repeated cycles. On-body performance was evaluated on wrist and thigh in sitting and walking (≈1 m s−1) conditions; I–V curves, load power, and open-circuit voltage were recorded after thermal equilibration (~5 min).

- Analytical coupling of comfort and performance: Closed-form relations quantify how TE-leg geometry (L, w, F), encapsulation properties (E, κ), and environmental heat transfer (hc, hs, hcon) jointly determine maximum power density Pd, skin temperature Ts, and skin pressure Pr. - Comfort constraints and design ranges: Skin pressure perceived as tightness occurs near 0.5–0.8 kPa; comfortable skin temperature range is ~32–34 °C (hot >34 °C; cold 30–32 °C; very cold <30 °C). Increasing L and F raises Pr; increasing F or decreasing L lowers Ts. - Optimal geometries: For comfort-centric design on the arm (r ≈ 5 cm, representative hc ≈ 30 W m−2 K−1, hcon ≈ 80 W m−2 K−1), excessive TE-leg height (>3 mm) reduces flexibility or yields high Ts, whereas too small L requires higher F, risking cold sensation. Voltage density Vd increases as TE-leg width w decreases, but mechanical stress rises in thinner legs, posing breakage risk; FEA confirms trade-offs. - Material system: Mg-based legs (n-type Mg3.2Bi1.49Sb0.5Se0.01; p-type MgAg0.95Sb0.99) with stretchable, thermally conductive PDMS/LM/Cu substrates (κ ≈ 2.1 W m−1 K−1) and low-κ polyurethane foam filler (κ ≈ 0.025 W m−1 K−1) reduce secondary thermal losses and improve flexibility. - Model validation: Experimental Pd and Ts on the arm across convection conditions agree with 1D analysis and FEA, with slight deviations at low F (greater secondary effects) and at high convection (additional heat replenishment from surrounding skin and metabolic adjustment). - On-body performance: A 4.5 × 4.5 cm2 Mg-based w-TEG produced up to 126 µW at room temperature during sitting and 367 µW during slow walking (~1 m s−1), corresponding to Pd ≈ 18.4 µW cm−2, with comfortable Ts ≈ 33 °C and Pr ≈ 0.8 kPa. - High ΔT operation: With an applied ΔT of 40 K, maximum Pd ≈ 0.9 mW cm−2 was achieved. - Theoretical upper bounds by body location: For ZT ≈ 0.75 and ideal interfaces (Ki = Kcon = 0), predicted maximum Pd ≈ 67 µW cm−2 at locations with low equivalent skin thermal resistance (e.g., forehead, 25–40 W m−2 K−1) and ≈ 33 µW cm−2 at higher-resistance locations (e.g., foot, 7–25 W m−2 K−1). - Mechanical reliability: Stable internal resistance and output over >500 bending cycles at r ≈ 10 mm and after >200 tensile cycles at 20% strain; bending radius capability down to ~5 mm; stretchability up to ~30% without performance degradation. - Benchmarking: The Mg-based w-TEG attains output and flexibility comparable to state-of-the-art Bi2Te3-based devices, while leveraging lower-cost, less-toxic materials.

The study establishes an analytical framework that directly links wearable comfort metrics (skin pressure, perceived temperature) with w-TEG output. By integrating mechanical and thermo-electric models, the authors identify structural and material parameter windows that meet comfort thresholds while maximizing power and voltage density. Experimental results on human subjects validate the model’s predictions, confirming that comfort-aware optimization can still deliver high output, especially under realistic on-body convection (e.g., walking). The findings demonstrate that Mg-based materials, combined with stretchable, thermally tuned encapsulation and radiative cooling films, can match or approach the performance of Bi2Te3-based w-TEGs while enhancing wearability. The approach generalizes to different body sites via equivalent skin thermal resistance and to other TE materials or applications where comfort is secondary (e.g., low-temperature industrial harvesting).

This work presents a system-level, comfort-aware design strategy for wearable thermoelectric generators that unifies mechanical and thermoelectric analyses into tractable formulas for co-optimizing output and wearability. Guided by this framework and refined with FEA, the authors fabricated Mg-based w-TEGs that achieve high power density (up to ~18.4 µW cm−2 on-body during walking) with comfortable skin temperature (~33 °C) and low perceived pressure (~0.8 kPa), alongside excellent mechanical durability. The strategy extends to other TE materials and non-wearable, low-temperature energy harvesting scenarios, as demonstrated by driving electronics from warm-water heat. Future research could further incorporate complex skin-device interface phenomena (sweat, dynamic contact resistance), long-term on-body variability, and additional secondary thermal pathways to refine predictive accuracy and broaden application domains.

- Modeling simplifications: 1D steady-state thermal-electric model neglects the Thomson effect, some contact/electrode resistances, and thermal resistance within substrates; filler contribution is assumed uniform. Mechanical model uses a linear elastomer approximation (with separate hyperelastic derivation) and neglects Poisson’s effects and centerline stretching in the primary analysis. - Secondary thermal effects: Lateral heat spreading, interfacial thermal/contact resistances (filler–leg, leg–electrode), and diffusion within substrates are not fully captured in the analytical model; these effects contribute to deviations at low fill factors and high convection. - Environmental and physiological variability: Equivalent skin heat transfer coefficients and contact resistances vary with sweat, motion, and local anatomy; metabolism may adjust with ambient conditions, affecting heat supply. - Generalizability of comfort thresholds: Perception of skin temperature and pressure varies across individuals and body sites; chosen ranges (e.g., 32–34 °C as comfortable; 0.5–0.8 kPa pressure threshold) are representative but not universal.