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Lei Miao, Sijing Zhu, Chengyan Liu, Jie Gao, Zhongwei Zhang, Ying Peng, Jun-Liang Chen, Yangfan Gao, Jisheng Liang, [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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Comfortable wearable thermoelectric generator with high output powerArticle https://doi.org/10.1038/s41467-024-52841-1Comfortable wearable thermoelectricgenerator with high output powerLei Miao 1,7 , Sijing Zhu 1,2,7, Chengyan Liu 3, Jie Gao 3,Zhongwei Zhang 1, Ying Peng 4, Jun-Liang Chen3, Yangfan Gao 3,Jisheng Liang1 & Takao Mori 5,6Wearable thermoelectric generators provide a reliable power generationmethod for self-powered wearable electronic devices. However, there hasbeen a lack of research regarding the comfort of wearable thermoelectricgenerators. Here we propose a design for a comfortable wearable thermo-electric generators system with high output power based on sandwichedthermoelectric model. This model paves the way for simultaneously optimiz-ing comfort (skin temperature and pressure perception) and output power bysystematically considering a variety of thermal resistive environments andbending states, the properties of the thermoelectric and encapsulationmaterials, and the device structure. To verify this strategy, we fabricatewearable thermoelectric generators usingMg-based thermoelectric materials.These materials have great potential for replacing traditional Bi2Te3-basedmaterials and enable our wearable thermoelectric generators with a powerdensity of 18.4 μWcm−2 under a wearing pressure of 0.8 kPa and with a skintemperature of 33 °C, ensuring the wearer’s comfort.Rapid progress in personalization propelled by remarkableadvancements in wearable and implantable electronics is revolu-tionizing the field of healthcare1,2. An uninterrupted power supplyis indispensable for such bioelectronics, particularly for life-critical applications like artificial cardiac pacemakers. Wearablethermoelectric generators (w-TEGs) can provide continuouselectrical energy by harnessing human body heat through theSeebeck effect3–5. Their numerous advantages, including highreliability, the absence of moving parts and noise, and environ-mental friendliness, make them an ideal potential solution forensuring uninterrupted power6–10. Despite these benefits, how-ever, research into achieving high-output and comfortablew-TEGs is still in its infancy.To ensure wearability, w-TEGs must be comfortable, includingmaintaining appropriate skin temperature, limiting perceived pres-sure, and being mechanically flexible (including bending, stretching,and folding) to accommodate the body’s dynamicmovement11,12. Whilesignificant progress has been achieved in elevating the output powerof w-TEGs at extreme conditions13–18, their comfort, unfortunately,remains consistently overlooked, even though this is indeed a neces-sary consideration for applications since it affects the stability of theheat source and the wearability of the device, like for other wearableelectronics19,20.Optimizing both wearability and device output presents a sig-nificant challenge. Wearability (the device’s bending stiffness andbending radius, the body’s perceived temperature, etc.) and outputReceived: 12 March 2024Accepted: 23 September 2024Check for updates1Guangxi Key Laboratory for Relativity Astrophysics, Guangxi Novel Battery Materials Research Center of Engineering Technology, State Key Laboratory ofFeatured Metal Materials and Life-cycle Safety for Composite Structures, School of Physical Science and Technology, Guangxi University, Nanning, P. R.China. 2School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, P. R. China. 3Guangxi Key Laboratory of Infor-mation Materials, Engineering Research Center of Electronic Information Materials and Devices, Ministry of Education, Guilin University of Electronic Tech-nology,Guilin, P. R.China. 4GuilinUniversity of ElectronicTechnology,Guilin, P. R.China. 5ResearchCenter forMaterials Nanoarchitectonics (MANA), NationalInstitute forMaterials Science (NIMS), Tsukuba, Japan. 6Graduate School of Pure andApplied Sciences, University of Tsukuba, Tsukuba, Ibaraki, Japan. 7Theseauthors contributed equally: Lei Miao, Sijing Zhu. e-mail: miaolei@gxu.edu.cn; mori.takao@nims.go.jpNature Communications |         (2024) 15:8516 11234567890():,;1234567890():,;http://orcid.org/0000-0002-2281-2689http://orcid.org/0000-0002-2281-2689http://orcid.org/0000-0002-2281-2689http://orcid.org/0000-0002-2281-2689http://orcid.org/0000-0002-2281-2689http://orcid.org/0009-0005-6195-1322http://orcid.org/0009-0005-6195-1322http://orcid.org/0009-0005-6195-1322http://orcid.org/0009-0005-6195-1322http://orcid.org/0009-0005-6195-1322http://orcid.org/0000-0001-7411-8069http://orcid.org/0000-0001-7411-8069http://orcid.org/0000-0001-7411-8069http://orcid.org/0000-0001-7411-8069http://orcid.org/0000-0001-7411-8069http://orcid.org/0009-0002-2995-955Xhttp://orcid.org/0009-0002-2995-955Xhttp://orcid.org/0009-0002-2995-955Xhttp://orcid.org/0009-0002-2995-955Xhttp://orcid.org/0009-0002-2995-955Xhttp://orcid.org/0009-0000-3469-3018http://orcid.org/0009-0000-3469-3018http://orcid.org/0009-0000-3469-3018http://orcid.org/0009-0000-3469-3018http://orcid.org/0009-0000-3469-3018http://orcid.org/0000-0001-6548-207Xhttp://orcid.org/0000-0001-6548-207Xhttp://orcid.org/0000-0001-6548-207Xhttp://orcid.org/0000-0001-6548-207Xhttp://orcid.org/0000-0001-6548-207Xhttp://orcid.org/0009-0002-5044-4032http://orcid.org/0009-0002-5044-4032http://orcid.org/0009-0002-5044-4032http://orcid.org/0009-0002-5044-4032http://orcid.org/0009-0002-5044-4032http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52841-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52841-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52841-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52841-1&domain=pdfmailto:miaolei@gxu.edu.cnmailto:mori.takao@nims.go.jpwww.nature.com/naturecommunicationsperformance (power density:Pd , load resistance:Rl , voltage density:Vd ,etc.) are intricately coupled through the device structure, the prop-erties of the thermoelectric (TE) material, and the environment21–23.Hence, achieving comfort and high output simultaneously is notstraightforward. In essence, maximizing output does not rely only onoptimizing TE material performance, but also requires meticulousdesign of the w-TEG’s structure and thermal management at the sys-tem level. However, no general analytical formula for system efficiencyand wearability of w-TEGs has been reported to date.In this study, we establish a model for w-TEGs utilizing a sand-wiched structure, themost representative of TE devices. By integratingmechanical and TE analyses, we derive explicit formulas to quantita-tively analyze the optimization of multidimensional parameters forboth comfort and power output while worn on a human body in real-world environments. We establish a direct link between the system’soutput and its wearing comfort by considering the interconnectionsamong the structural parameters of the device, the performanceof theTE materials, and the external environment. We identify the optimalstructural matching range for maximizing system efficiency andwearability and predict the maximum output power of w-TEGs posi-tioned at various locations on or near the human body. Moreover,experimental validation is conducted on actual human subjects usingw-TEGs that employ n-type Mg3Bi2 and p-type MgAgSb-based TEmaterials (n-type: Mg3.2Bi1.49Sb0.5Se0.01; p-type: MgAg0.95Sb0.99; the TEperformance of each is shown in Supplementary Fig. S1). Recently,these materials have been intensively studied for use in non-wearableTEGs due to their cost effectiveness and high TE performance nearroom temperature24,25. The outcomes here closely approximate thosefor state-of-the-art Bi2Te3-based w-TEGs, highlighting the potential ofour fabricated w-TEGs. Our work provides a comprehensive strategyfor the design of w-TEG systems, incorporating a multidimensionalquantification analysis to maximize device output power whileensuring wearing comfort.ResultDesign process for w-TEGsCoupled interactions among the thermal networks in w-TEGs and theirlow in-plane thermal conductivity resulting from the use of flexiblesubstrates give rise to additional thermal leakage in these devices15,26.Finite element analysis (FEA), inwhich all influencing factors, includinglateral heat transfer analysis and parameters related to TE leg shape,are encompassed within a unifiedmodel, has proven to be an effectiveapproach for addressing such intricate issues27–29. Nevertheless, itscomputational cost is notably high, and it cannot offer concise andprofound guidance similar to that from analytical formulas, making itchallenging to analyze coupling mechanisms and quantify parametersfrom a macroscopic perspective. One-dimensional (1D) numericalanalysis is straightforward and efficient30,31. It is often employed forgeneral, macroscopic mechanism quantification, aiding in parameterguidance for w-TEG design.Here we have proposed a complete design strategy based on the1D coupling mechanism. Figure 1 illustrates the logical framework forthe full parameter optimization of a wearable TE power generationmodule based on the coupled field equations of TE and mechanicalmodels. Our design strategy takes into account various applicationscenarios by considering environmental temperature (Ta), bendingradius (r), body temperature (Tb), and parameters of the TE andencapsulation materials, including Young’s modulus (E) and thermalconductivity (κE) values for the encapsulation materials. Here theencapsulation materials are defined as the filler and substrates of thew-TEG. For a given environment and set of materials, the output andwearability of the system are highly dependent on the TE leg geometryand the heat dissipation design32–34. We first established the connec-tion between the wearability parameters for the system, including skinpressure (Pr) and skin temperature (Ts), and those for its structure,including length (L)/width (w) of the TE leg, the fill factor (F), the p-/n-type material area ratio (Fp=n), the ambient and total heat transfercoefficient (ha,h), and obtained the ranges of values for the structuralparameters. Then, on the base of ensuring wearability, the optimalgeometric parameters of the TE leg were obtained by combiningmultiple parameters and optimizing the output efficiency of the sys-tem. When determining optimal geometric parameters that meet thedesign requirements, the properties of the TE and encapsulationmaterialsmust also be properly considered since, on the one hand, theTE materials directly determine the electrical and thermal perfor-mance of the w-TEG system under ideal conditions, while on the otherhand, its mechanical performance mainly depends on the physicalproperties of the encapsulation materials. For example, using low-Efilling materials for the TE legs or the absence of filling materials cangreatly improve the flexibility of the device but reduce its reliability.The device design should thus be based on the application environ-ment and incorporate matching encapsulation materials. After theoptimal geometric parameters were obtained, FEA was used for moreprecise adjustment to maximize the power output while meeting thewearing resistance requirements for any given material and environ-mental conditions and the device was finally prepared for experi-mental verification.Couplingmechanismbetween output performance andwearingcomfortTo assess the various aspects of w-TEG system performance, we haveseparately constructed thermal-electric and mechanical models of thedevice when worn on a human body as ideally simulated (no dis-placement between the two materials, without considering the cen-terline stretching and without considering Poisson’s ratio, etc.). Thethermal-electric model primarily focuses on investigating the w-TEG’soutput performance and Ts, while the mechanical model is employedto study the flexibility of the w-TEG and determine the minimumpressure exerted on the skin when worn. The mechanical model isshown in Fig. 2a, b and assumes a cylindrical shape for the body part onwhich the w-TEG is worn. According to static equilibrium principles,given its three-layer structure, the bending stiffness (EiTEG) of thesystem should satisfy the following expression (see SupplementaryNote S1):EiTEG = E�bib + E�i+ E�t it ð1ÞIn this context, E�b, E�, and E�t represent the effective Young’smodulus of the bottom substrate (hot side of TEG), the filler layer, andthe top substrate (cold side of TEG), respectively, and are functions ofthematerial’s Young’smodulus and F . ib, i, and it denote the respectivearea moments of inertia of the bottom substrate, the filler layer, andthe top substrate with respect to the neutral axis and are functions ofthe material’s style modulus and L (see Supplementary Notes S1, S2).E�bib, E�i, and E�t it represent the effective bending stiffness of thebottom substrate, the filler layer, and the top substrate, respectively.Thus, given Young’s modulus and height of the material, the device’sEiTEG with respect to the F and L can be computed. Furthermore, asshown in Fig. 2b, it is possible to derive the pressure (Pr) exerted on theskin as a result of the device bending against a body part (assumed tobe an ideal cylinder), and this can be expressed as (see SupplementaryNotes S1, S2):Pr =12EiTEGWTEG3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 � 0:25WTEG22q+ r2 � 0:25WTEG2r� � , ð2Þwhere WTEG is the width of the TEG and r is the bending radius.Equation (2) is based on the encapsulation material being a linearArticle https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 2www.nature.com/naturecommunicationselastomer. For the hyperelastomer material, we also give the deriva-tion process (Mooney_Rivlin model, see Supplementary Note S3), butthe result is more complicated. For general applications, we canapproximate the linear elastomer to simplify the analysis (It adapts tothe application environment when the bending radius exceeds 5 cm.).The thermal-electric model, the parameters for which are depic-ted in Fig. 2c, integrates corebody temperature, the thermal resistanceof the skin layers (Ks), contact thermal resistance between the deviceand the skin (Kcon), the TEmodule, and heat sink elements to evaluatedevice output and Ts . Generally, human skin is a complex, multi-layered system. Skin temperature varies depending on the ambienttemperature or different points of the body (Supplementary Table S1).To simplify the calculations, the core body temperature was set withinthe range of 36.5 °C to 37.5 °C, which is according to balancing theenergy produced through metabolism with the heat dissipated to theenvironment through convection, radiation and evaporationprocesses, and is typically independent of the environment9,35. SinceTsexhibits relatively minor variations within a small range around roomtemperature36,37, we model it using an equivalent heat transfer coeffi-cient (Supplementary Table S2). In accordance with non-equilibriumthermodynamics, under 1D current and energy flow conditions, thedifferential equations describing the temperature distribution T(x) inthe presence of electric current density Je are:∇ κ � ∇Tð Þ+ Je2σ� τ � Je � ∇T=0 ð3ÞQ= S � T � Je � κ � ∇T ð4Þwhere S, σ, κ, T, τ, and Q represent the Seebeck coefficient, electricalconductivity, thermal conductivity, temperature, Thomson coeffi-cient, and heat flux, respectively. In practical w-TEG systems, the fillerFig. 1 | Logical framework for the full-parameter optimizationof aw-TEG.The target parameters (Vd , Pd , Pr , Ts , Rl) are determinedby the application environment, theoptimized process, and optimal geometric parameters for w-TEG preparation and performance verification.Fig. 2 | w-TEGmodels. a Schematic illustration of the internal structure of the w-TEG. bMechanical model of the w-TEG during bending. c Thermal network of the w-TEGsystem.Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 3www.nature.com/naturecommunicationsmaterial significantly impacts both heat transfer and output. There-fore, we incorporate the study of filler thermal conductivity into ourthermodynamic model. For simplicity, we naturally assume that thecontribution of the filler material to heat conduction within the TEsystem is uniform. Under this assumption, and by disregarding theThomson effect and the contact resistance and thermal resistance ofthe substrate (see Supplementary Note S4), the governing equationsand boundary conditions for a single-leg TE system under steady-stateconditions are as follows:κ� d2Tdx2 +RTEGI2LAF=0, ð5Þ�κ�AdTdx+ SThI =Qh =Tb � ThKh, x = L, ð6Þand�κ�AdTdx+ STcI =Qc =Tc � TaKc, x =0, ð7Þwhere I, A, and RTEG are the electric current, cross-sectional area, andresistance, respectively, of the TE leg; Ta and Tb are ambienttemperature and body temperature, respectively; Tc and Th are thetemperature at the cold and hot sides, respectively, of the TEG;Qc andQh are the heat flow values at the cold and hot sides, respectively, ofthe TEG; and Kc and Kh are the thermal resistance values at the coldand hot sides, respectively, of the TEG. κ� represents the thermalconductivity of the TEG, encompassing that for both the TE legs andthe filler material. It can be expressed by the following formula:κ� = κF + κf 1� Fð Þ, ð8Þwhere κ and κf are the thermal conductivity values for the TEmaterialsand the filler materials, respectively. The derived expressions for thesimplified generator’s maximum power density (Pd) and the effectivetemperature difference shown below are presented in detail in Sup-plementary Note S4:Pd =ΔT24×Z1 + κ�hL� �2 � LFκ + ðκ�Lh + 1Þ � ZTavghð9Þand1h=1hc+1hcon+1hs, ð10Þwhere Z = S2σ=κ; ZTavg is the average TE figure of merit determiningthe efficiency of TEG38,39. hc, hs, and hcon are the heat transfer coeffi-cients for the cold side of the TEG, the skin, and the contact betweenthe TEG and the skin, respectively. Through analysis of the Pd , it can bededuced that attaining high Pd requires a multifaceted approach. Onone hand, it involves enhancing the ΔT, h, and ZT while decreasing κf .On the other hand, achieving optimal structural design, which includesoptimizing L and F along with κ, is essential for achieving maximumpower output.While the pursuit of high Pd is undoubtedly a primary objectivefor real-world applications of w-TEGs, it comes with the trade-off ofincreased L, which could impact wearing comfort. Here we alsofocused on Ts as a quantitative reference for wearing comfort.Assuming that the w-TEG operates at the optimal current, andconsidering the heat transfer equation, the expression of Ts is:Ts =Tb �KsKΔT =Tb �ΔThsh + hsLκF + κf 1�Fð Þ, ð11Þwhere K is the total thermal resistance of the system and can beexpressed as: K =Kc +Kh +KTEG. KTEG is the total thermal resistance ofthe TEG. The above analysis is based on a single-leg model (i.e., the TEproperties of the p- and n-type materials are identical), and we alsoanalyzed a two-leg model (Supplementary Note S5). Once the TEmaterials are identified, the optimal cross-sectional area ratio (Fp/n, opt)for the p- and n-type materials can be obtained by inserting thestructural parameters into Supplementary Eq. (S57). Notably, underconditions where the temperature difference is not significant and theTE performance of thematerials remains stable, the optimal Fp/n, opt forachieving the highest Pd does not change with variations in devicestructure or heat dissipation (Supplementary Fig. S5a–c). Theequivalent ZT and effective thermal conductivity can then be derived[Supplementary Eqs. (S61) and (S63) and Fig. S5d]. Once the equivalentZT (ZTpn) and effective thermal conductivity (κpn) are determined,they can be incorporated into the single-leg model for analysis.Multi-parameter w-TEG optimizationBased on the study of the above model, the object-oriented w-TEGdesign is determined by the usable temperature difference, bendingradius, equivalent skin thermal resistance, area, target power, andvoltage density of w-TEGs by considering the application environmentof the target use. In addition, the appropriate TE materials need to beselected according to the temperature range, and flexible, low-thermal-conductivity fillers and high-thermal-conductivity substratesneed to be selected according to the application. Here we chose Mg-based TE materials for our study. Compared to the state-of-the-artroom-temperature Bi2Te3 and Ag2Se alloys, Mg-based materials aremuchmore cost-effective since they contain no expensive elements andthey are less toxic, making them better suited for wearable devices, aswell as the most promising candidates to replace Bi2Te3 for room-temperature applications15,24,40–43. In addition, to ensure uniform heatdissipation and mechanical performance during bending when thedevice is worn, we employed a high-thermal-conductivity and stretch-able liquid metal (LM)-metal-encapsulated polydimethylsiloxane(PDMS/LM/Copper, Eb&Et =820 kPa, κ1 = 2.1Wm−1K−1) for the substrate.The intermediate fill material comprises a soft and low-thermal-conductivity polyurethane foam (E =270 kPa, κf = 0.025Wm−1K−1). Wefirst considered the mechanical properties as the optimization para-meters for the w-TEG. Figure 3a shows Pr as a function of devicestructure on the arm (r= 5 cm). Evidently, the Pr of the w-TEG increaseswith increasing L and F . The black line represents the critical Pr (0.5 to0.8 kPa) associated with wearing tight-fitting clothing on the body44.Beyond this Pr, the skin perceives tightness. Results for the Ts of thearm were determined based on Eq. (11) and are shown as a function ofstructure at room temperature in Fig. 3b. Here, we set the operativeenvironment to the arm, with an equivalent skin heat transfer coeffi-cient of 30Wm−2K−1 and a contact heat transfer coefficient of80Wm−2K−1 between the device and the skin. These values are used asreferences and are based on previous studies, although they will vary inpractical applications due to the presence of sweat discharge45,46. Inaddition, the heat transfer coefficient of the cold end is set to30Wm−2K−1. Clearly, as F increases or L decreases, the Ts decreasesaccordingly. We defined four temperature ranges to represent theperception of warmth or coldness on the skin. For instance, tempera-tures exceeding 34 °C are perceived as hot, and those between 32 and34 °C are perceived as warm, which is considered ideal for comfort.Temperatures between 32 and 30 °C and below 30 °C are perceived ascold and very cold, respectively. It is worth noting that temperatureperception varies among individuals and body parts. For example,Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 4www.nature.com/naturecommunicationslower-temperatures objects are perceived differently on the headand feet. Our definition of warmth and coldness perception isbased on the examples of the torso and the arms for reference.After the w-TEG wearing comfort was optimized, to maximize Pd ,it was determined as a function of the structure using Eq. (9), andthe results are shown in Fig. 3c. On one hand, increasing L canimprove the output, and on the other hand, when L is fixed, thefilling factor needs to meet certain conditions to maximize theFig. 3 | Structural design workflow for a w-TEG system. a–c Pr, Ts , and Pd ,respectively, as functions of F and L for a device designed for the arm at roomtemperature. d, Relationship among the w-TEG’s Pd and Ts and Pr based on (a–c).e Voltage density and maximum stress as functions of w. f Final refinement andoptimization through FEA.Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 5www.nature.com/naturecommunicationspower output. Generally, given the selection of TE materials, thethermal conductivity remains constant. Thus, Eq. (9) can bereformulated to obtain the optimal expression for F :Fopt =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðκ � κf Þ � ðκ � κf +Z �Tavg � κÞ2qðκ � κf Þ2 + ðκ2 � κ � κf Þ � Z � Tavg× ðh � L+ κf Þ ð12ÞFor ease of analysis, mapping the structural parameters yields thecoupled results for Pr, Ts , and output Pd when the w-TEG is worn onthe arm, as illustrated in Fig. 3d.While higher temperature differences,TE leg performance, and heat transfer coefficients lead to elevatedoutput, it is essential to maintain them within a reasonable range toensure long-term wearing comfort, a criterion to which wearabledevices should adhere. High Pd is undoubtedly appealing. However, asdevice flexibility diminishes, it subjects the skin to increased pressure.In this case, a TE leg height greater than 3mmwould result in reducedflexibility or excessively high Ts. Conversely, reducing the deviceheight too much to enhance flexibility would be inappropriate as wellsince the resulting increased F may lead to a sensation of coldness onthe skin. For long-term wear, prioritizing wearing comfort over deviceoutput enhancement is the design objective we aspire to achieve. Asshown in Supplementary Fig. S6, achieving comfort-centric structuraldevice design becomes particularly stringent under low-temperatureconditions with high heat transfer.In addition to Pd , output voltage density (Vd) is another crucialindicator that should be considered throughout the comprehensivedesign process. The expression for output voltage density undermaximumpoweroutput conditions dependsnot only on the structuralparameters discussed above but also significantly on the TE leg width(w, Supplementary Note S6):Vd =12ΔTSFoptLhw2 Lh+ κFopt + κf ð1� Fopt Þ� � ð13ÞThe derived Vd results are displayed in Fig. 3e, which shows thatthe voltage density can reach high values when the w is very small. Inregard to the w, a comprehensive balance among factors such asmanufacturing precision, material mechanical strength, and weldingstrength should be considered for device design. For example, FEA(see Supplementary Fig. S7 for details) shows that thinner TE legs aresubjected to greater shear stress than thicker TE legs (Fig. 3e) and are,therefore, more likely to break. It should be noted that the aboveanalysis disregards secondary thermal effects within the TEG system,including the thermal diffusion resistance within the substrate and thecontact thermal resistance between the filler and the TE leg, which arechallenging to incorporate into 1D numerical analysis. Furthermore,wdoes not contribute to the Pd in the 1D numerical analysis, but in real-world applications, the influence of secondary thermal effects will alsoimpact the Pd . A smallerw leads to amore even distribution of thermalconduction, reducing the impact of secondary thermal effects andaligning more closely with the estimations from the 1D numericalanalysis, which was validated through more accurate FEA (see Sup-plementary Fig. S8 for details). Based on the research discussed above,certain parameter margins should be reserved (Supplementary Fig. S9showsPdbasedondifferentmodels as a function of F, h,w. Themargincan be reserved according to the related parameters.). When finalizingthe design structure, allow for minor adjustments using FEA, as illu-strated in Fig. 3f, and in turn, for greater precision among theseparameters.Furthermore, at F = Fopt , Pd increases with increasing L and h(Supplementary Fig. S12a, b). For given target Pd and ambient tem-perature values, the range of heat transfer and L values satisfying thetarget power can be determined by using Eqs. (8–10, 12). The devicestructure can then be optimized to satisfy the target power asmuch aspossible while simultaneously improving the wearability of the deviceusing Eqs. (2, 8–13) (the detailed design process is shown in Supple-mentary Fig. S12–S14). Whether under low or high heat dissipationconditions, the optimal L exceeds 8mm (Supplementary Fig. S15a, b).While reducing the κ of the TE material contributes slightly toincreasing Pd and decreasing the optimal L (Supplementary Fig.S15c, d), its effect is rather minor. This finding differs from the con-clusions of Suarez et al., primarily due to the absence of an optimizedstructural design in their studies35,47. In our study, for w-TEG based oninorganic bulk TE materials (usually the thermal conductivity of TEmaterials exceeds 0.1Wm−1K−1), assuming that ZT is unchanged,reducing κ of TEmaterials (while the power factor is also reduced) haslittle impact on improving the Pd of the device, but the Fopt will beincreased (Supplementary Fig. S16), increasing the cost of the device.Through further optimization calculations, we can subsequentlyderive an expression for the maximum Pd at various parts of thehuman body under the assumption of ideal structural parameters andby neglecting interface thermal resistance (Kc & Kcon = 0):Pd =Z � Tb � Ta� �2 � hs4 � ð2 +ZTavg +2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 + ZTavgqÞð14Þwhere hs represents the equivalent skin thermal resistance. Forinstance, the equivalent skin thermal resistance is relatively low forbody parts like the forehead (25–40Wm−2K−1). When Kc & Kcon = 0 andat room temperature, the maximum achievable Pd by a Mg-based w-TEG with a ZT of approximately 0.75 is 67μWcm−2. Conversely, forbody parts with relatively large equivalent skin thermal resistance,such as the foot (7–25Wm−2K−1), the maximum achievable Pd is about33μWcm−2 (Supplementary Table S4).Device preparation and mechanical propertiesThe materials and device structures were chosen based on the resultsin the previous section. The TE legs are Mg-based materials withouttellurium (n-type: Mg3.2Bi1.49Sb0.5Se0.01; p-type: MgAg0.95Sb0.99). Thefiller material is polyurethane and the substrate materials are PDMSfilled with liquid metal (LM) and copper composites. The fabricationsteps are illustrated in the method part. Both the substrate and thefiller have excellent stretchability, which can effectively reduce thehcon, which is very important for enhancing the performance ofwearable heat collection (Supplementary Fig. S17). The stress-strainresults of the substrate and the filler are shown in Supplementary Fig.S10. The solid-liquid blend substrate with high thermal conductivity(2.1Wm−1K−1) and low thermal conductivity filler (0.025Wm−1K−1) canreduce the secondary thermal effect, establish a higher temperaturedifference and improve the output performance of w-TEG (Supple-mentary Fig. S18). As shown in Fig. 4a, the TE legs of the TEG areconnected by S-type copper electrodes, and due to the stretchableencapsulation and electrodes, the prepared device has good flexibilityand stretchability (Fig. 4b–d). It can be installed on non-deployablespherical surfaces with a radius of 30mm or on complex human skinsurfaces. The mechanical reliability of w-TEG was demonstrated bymeasuring the properties under different bending and tensile condi-tions. Figure 4e illustrates the variation in the w-TEG’s resistance overmultiple bending cycles, and the results show that the bending radiusof the w-TEG can reach 5mm.When the device was placed on a testingplatform with a target bending radius of 10mm, its internal resistancechange rate (RTEG 0/RTEG) and output remained relatively stablethroughout more than 500 bending cycles (Fig. 4f, g). In addition, ourw-TEG showed up to 30% stretchability, and the RTEG 0/RTEG and out-put performance of the device remained unchanged after more than200 repetitions at 20% strain (Fig. 4h–j).Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 6www.nature.com/naturecommunicationsModel verificationTo validate the accuracy of the model discussed above, we fabricatedw-TEGs with different structures and conducted several verificationtests on the fabricated devices to confirm the reliability of the model.We set up a test system for TE performance (Fig. 5a) and a test systemfor mechanical performance (Fig. 5b). First of all, w-TEGs with legheights of 2.5–4mm and F values of 3–17% were separately placed onan arm and subjected to three different heat transfer conditions(natural convection, moderate convective heat transfer, and higherconvective heat transfer). Results from 1D numerical analysis, FEA, andexperimental characterization are shown in Fig. 5c–e. The experi-mental results are in good agreement with the predicted results butslightly deviate under the conditions of low F or high convection. Thereasons could be accounted for w-TEGs with low F have a greaterinfluence on secondary thermal effects (FEA also proves this result).The results under high convection conditions were higher thanexpected because the device not only collects heat from the skin itcovers, but the surrounding skin also supplements heat to the hot endof the device, and the skin slightly alters its metabolism (heat pro-duction) as the environment becomes cold/hot. The second set ofverification tests focused on Ts . Similar to the first set of tests, deviceswere separately placed on an arm under the same three heat dissipa-tion conditions, and the experimentally obtained Ts values on the armwere found to align closely with those anticipated from the model, asshown in Fig. 5f. The third set of verification tests addressedmechanical performance. Deviceswith optimized F and three differentL values were each placed beneath a cylindrical object to exert pres-sure. The applied pressure and the bending radius of the w-TEG on thecylinder were recorded, from which experimental EiTEG results werederived for comparison with the numerical model (Fig. 5g). The highlevel of conformity between the expected values and the experimentalresults highlights the reliability and sophistication of our model.w-TEG performance during operation on a human bodyAMg-basedw-TEGwith anareaof4.5 cm×4.5 cmwas fabricatedbasedon the design criteria discussed above to validate the efficiency andreliability of our model and design procedure for practical applica-tions. First, a composite SiO2/TiO2/PMDS (STP) radiative cooling (RC)film was applied to the device (Fig. 6a) to enhance the heat exchangebetween the device and the environment48. The ultraviolet (UV)reflectance and infrared emissivity characteristics of the compositefilm are presented in Supplementary Fig. S19, which shows that itexhibits both high UV reflectance and high infrared emissivity to meetthe heat exchange requirements. We subsequently evaluated thedevice’s voltage on a human wrist (Fig. 6b) and thigh (Fig. 6c). Com-pared to the wrist, the open circuit voltage of the thigh is lower, andFig. 4 | Photographs andmechanical properties of w-TEG. a–d Photographs of afabricated w-TEG and its bending performance, respectively. Variation inRTEG0=RTEG of the w-TEG as a function of (e), Bending radius, and (f), Bendingcycles. g Voltage and output power of the w-TEG as a function of bending cycleswhenΔT = 10K. Variation inRTEG0=RTEG of thew-TEGas a functionof (h), Strain and(i), Strain cycles. j Voltage and output power of the w-TEG as a function of straincycles when ΔT = 10K.Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 7www.nature.com/naturecommunicationsthe voltage of the device reaches thermal equilibrium and becomesstable after 5mins, at which time the output power of the device wornon the arm was obtained. The results (Fig. 6d) revealed that at roomtemperature, the w-TEG exhibited an output power of up to 126μWwhen the person wearing the device stood still, while its output powerreached 367μW (Pd = 18.4μWcm−2) when the wearer engaged in slowwalking (walking speed = 1ms-1). Furthermore, when a temperaturedifference of 40K was applied, the device achieved a maximum Pd of0.9mWcm−2 (Supplementary Fig. S20). This Mg-based w-TEG withmeticulously optimized geometry thus exhibited output and flexibilitycomparable to those of Bi2Te3-baseddevices.Demonstrations of body-heat harvesting showed that our w-TEG can be widely employed forsustainably powering microwatt-scale wearable electronic devices(Fig. 6e). Figure 6f provides a comprehensive comparison between ourMg-based w-TEG and state-of-the-art Bi2Te3-based devices in terms ofPd , ZT of the TE materials, Bending curvature (r−1), flexibility (EiTEG−1),and Ts. It is evident that our work (indicated by the red pentagon andstars) excels in all these aspects13,21,22,26,49–54, indicating the exceptionaloverall performance of our device. Finally, this design strategy is alsosuitable for other TE materials, such as Bi2Te3, or low-temperatureindustrial applications that do not need to consider wearability. Forexample, we used this design strategy to collect the heat from hotwater at 50 °C (or industrial wastewater) and successfully drive aBluetooth thermometer to remotelymonitor the ambient temperature(Supplementary note S7). Thedesignprocessof object-orientedw-TEGis summarized in SupplementaryNote S8. In thiswork, a systemdesignstrategy proposed by us will have a positive effect on the field ofthermoelectric devices.DiscussionIn conclusion, for practical applications, an ideal wearable thermo-electric generator (w-TEG) should not only fulfill power generationrequirements but its wearability should also be comprehensivelyconsidered. We calculated the output performance of the w-TEG sys-tem, including power and voltage, as well as aspects of wearing com-fort such as bending radius, bending pressure, skin temperature, andother multidimensional parameters, providing a connection betweenthe device and the humanbody based on an analyticalmodel. Throughdecoupled analysis, we proposed a set of system-level design strate-gies for the rapid assessment of maximum output power and optimalFig. 5 | Model verification. Testing platform (a), For determining simulated Pd , Tsat different L, F , ha values for experimental validation of the model, and (b), Fordetermining simulated EiTEG at different L values for experimental validation of themodel. Simulation-based (c–e),Pd and (f) Ts under different ha for experimentalvalidation of the model. g Comparison of experimental EiTEG results with thosefrom calculations.Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 8www.nature.com/naturecommunicationswearability for w-TEGs. Following this approach, we developed a high-power-density Mg-based w-TEG that exhibits excellent flexibility andwearer comfort. The research findings underscore the effectiveness ofour w-TEG in harvesting body heat for energy, with potential applica-tions extending to self-powered wearable electronic devices and sen-sors. This work provides an in-depth perspective on the system-leveldesign of wearable thermoelectric systems and low-temperature-difference thermoelectric cogeneration systems.MethodsSynthesis and preparation of n-type Mg3Bi2-based TE materialMagnesium (Mg) powder (99.5%, Aladdin), bismuth (Bi) powder(99.99%, Aladdin), antimony (Sb) powder (99.5%, Aladdin), andselenium (Se) powder (99.5%, Aladdin) were weighed inside a glovebox according to the nominal composition Mg3.2Bi1.49Sb0.5Se0.01. Theraw materials were then loaded into a stainless steel can and con-tinuously ball-milled at 550 rpm (SPEX 8000M) for 20 h in an argon(Ar) environment. The ball-to-powder weight ratio was approximately30:1. After the ball-milling process was complete, the powderedmaterial obtained was removed from the glove box and placed in anagate mortar for further grinding. The ground powder was thencompacted uniformly and sandwiched between two layers of 304stainless steel powder inside a graphite mold with a diameter of12.7mm (the upper and lower barrier layers were approximately0.5mm each, and the TE material had a height of ~ 2.5mm). Sparkplasma sintering (SPS)was performedunder pressure of 60MPawith aFig. 6 | Design and application of a Mg-based w-TEG. a Schematic illustration ofthe Mg-based w-TEG structure enhanced with radiative cooling for improved heatexchange. Measured open-circuit voltages of the w-TEG (b) When worn on the armand (c) When worn on the thigh. d Testing of the w-TEG’s power generation per-formance [load voltage (dashed curves) and output power (solid curves) asfunctions of current] when worn on the wrist. e Photograph of a w-TEG driven bybody heat collection powering a light-emitting diode (LED) through a voltageconverter. f Comprehensive comparison between this study and previouslyreported state-of-the-art Bi2Te3-based w-TEGs.Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 9www.nature.com/naturecommunicationsheating rate of 100Kmin−1 to reach 773 K, which was maintained for5min, followed by additional heating at a rate of 100Kmin−1 to reach1073 K for sintering for 5mins.Synthesis and preparation of p-type MgAgSb-based TE materialMg powder (99.5%, Aladdin), silver (Ag) powder (99.9%, Macklin), andSbpowder (99.5%,Aladdin)wereweighed inside a glove box accordingto the nominal compositionMgAg0.95Sb0.99 and placed in a ballmillingcan. Themixture was then ball-milled for 18 h under an Ar atmosphereat a rotational speed of 600 rpm. The obtained powder was com-pacted between two layers of Ag powder and placed into a graphitemold with a diameter of 12.7mm (the upper and lower barrier layerswere ~ 0.75mm each, and the TEmaterial had a height of ~ 2.5mm) forSPS. Sintering was carried out under pressure of 60MPa, and thetemperature was raised to 523 K at a rate of 150 Kmin−1, followed byslow heating at a rate of 50Kmin−1 to reach 573 K, which was main-tained for 10mins. The sintered samples were then subjected to a heattreatment at 573 K for 10 days in a tubular furnace with a mixed gasatmosphere containing 5% H2 and 95% Ar.Substrate precursorThe stretchable substrate precursor was prepared bymixing PDMS (10wt%-diluent, used to reduce viscosity), GaIn (75.5 wt% Ga and 24.5wt%In), and copper (10μm, Aladdin) in a ratio of 35 vol%: 50 vol%: 15 vol%.After adding LM and stirring for 30mins (oxidizing LM to preventcopper corrosion), add copper and stir for 30mins.Synthesis of radiative cooling filmTo prepare the composite SiO2/TiO2/PMDS (STP) radiative cooling(RC) film, inorganic particles of SiO2 (5 µm, Aladdin) and TiO2 (150 nm,Aladdin) were first added to a reagent bottle containing ethyl acetate(99.9%, Aladdin) and sealed. The mixture was stirred using a magneticstirrer at roomtemperaturewith a rotational speed of 1000 rpm for 1 hto obtain a well-dispersed SiO2/TiO2 suspension. PDMS (Sylgard 184,Dow Corning) was then added in a mass ratio of 10:1 to the preparedSiO2/TiO2 suspension. Themixture was stirred using amagnetic stirrerat room temperature with a rotational speed of 1000 rpm for anadditional hour. Ultrasonic dispersion was subsequently performedfor 20mins. After completion of the ultrasonic treatment, a curingagent was added to the PDMS mixture in a mass ratio of 10:1, and themixture wasmixed at room temperature for 10mins to obtain the STPcomposite solution. The prepared STP coating solution was degassedfor 3mins in a 100% ultrasonic cleaner to obtain the coating solution,which was poured onto an aluminum foil fixed reflector surface andspread into a film using a film coater. Finally, the coated sample wasplaced in an oven for heating with a staged profile. The temperaturewas initially maintained at 40 °C for 30mins and then gradually raisedto 60 °C, which was maintained for 2 h to obtain an RC composite filmwith a smooth and uniform surface without bubbles. For practicalhuman body energy harvesting applications, the RC film is attached tothe top of the device to enhance heat exchange between the deviceand the environment.w-TEG fabrication stepsStep 1: The bulk TE materials prepared as described above were cutinto n-type Mg3Bi2-based TE legs with dimensions of 1.5 mm× 1.5mm× 3.5mm and p-type MgAgSb-based TE legs with dimensions of2 mm× 2 mm×3.5mm.Step 2: Copper electrodes were prepared using the transferetching method and then coated with a 0.2mm-thick layer of solderpaste using screen printing. Theprepared TE legswere placed onto thesolder-paste-coated copper electrodes and placed on a heating stage.The temperature was raised to 240 °C and maintained for 30 s.Step 3: In a mold, the substrate precursor prepared as describedabove was poured to a thickness of about 1–1.5mm and preheated at80 °C for 10mins. At this point, the surface of this hard substrate layerhad not yet solidified. The device prepared in Step 2 was then placedon this preheated layer, and an additional layer of PDMS with athickness of about 0.2mmwas poured. The assembly was then placedon the heating stage and heated to 80 °C for 1 h. The same procedurewas used to encapsulate the top electrode using the top substrateprepared as described above.Step 4: A polyurethane precursor (1076a) and a catalyst (1076b)were mixed in a weight ratio of 2.5:1 and stirred for about 10 s. Themixture was quickly drawn into a syringe and injected between the TElegs. The polyurethane subsequently foamed in the air and naturallysolidified to form the structure.The w-TEG fabrication steps are schematically illustrated in Sup-plementary Fig. S25.Material characterizationThe electrical conductivity (σ) and Seebeck coefficient (α) of allmaterials were measured using the ZEM-3 apparatus (ULVAC, Japan).The tested samples were cut and polished to form rectangular speci-mens with dimensions of 3 mm×3 mm× 12.5mm. The testing tem-perature ranged from 323 K to 523 K, with a temperature gradientset at 50 K.The thermal conductivity (κ) of the TE materials was calculatedusing the formula: κ =DTECPd, where DTE represents the thermal dif-fusivity of TE material, CP is the specific heat capacity of the material,and d is the material density. Given that measuring CP introduces sig-nificantmeasurement error, previously reported values were adopted.In this study, previously reportedCP values for n-typeMg3Bi2-based TEmaterials41,55, determined using the Archimedes drainage method,were used.DTE wasmeasured using the LFA 457 laser thermal analyzer(NETZSCH, Germany). The κ values of the filling and substrate mate-rials were measured using a thermal conductivity analyzer (TCi,C-Therm Technologies Ltd.)Contact resistance testing was conducted using a homemadefour-probe measurement apparatus. The testing current was set at100mA. As the probes moved from the contact metal layer throughthe contact interface to the TE material, a series of voltage readingswere recorded to calculate the contact resistance.Thermoelectric and mechanical performance characterizationof w-TEGsThe Pd of each device was characterized using a digital multimeter(Victor, VC8246A) to measure the load voltage (Vl) of the w-TEG. ThePd was deduced using the formula Pd =V2lRl�A, where Rl is the resistanceof the load resistor andA denotes thedevice area. During testingunderwalking conditions, a fan was placed at the top of the device tosimulate an airspeed of 1.5ms−1. The airflow speedwasmeasured usingan airflow velocity sensor (SMART SENSOR, AS836). The internalresistance of the w-TEG after bending was determined by calculatingthe slope of the I-V curve, which was established by subjecting thew-TEG to a range of currents from − 30mA to 30mA using a sourcemeter (Tektronix Keithley 6220) while simultaneously measuring thevoltage difference.Three-dimensional finite element analysis of w-TEGperformanceWe employed COMSOL Multiphysics (COMSOL Inc.) coupled with theHeat Transfer and Electric Current modules to assess the thermo-electric performance of our w-TEG. Within the TE module, the π-shapedTE legswere envelopedby thefillingmaterial and connected tocopper foil electrodes. These electrodes were further encapsulated bythe thermal conductive substrates. The model dimensions andboundary conditions for the specific w-TEG configuration used in thesimulation are illustrated in Supplementary Fig. S8c. Simulation para-meters included the material properties provided in SupplementaryArticle https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 10www.nature.com/naturecommunicationsTable S3, as well as default values available within the COMSOL Mul-tiphysics software package.Reporting SummaryFurther information on research design is available in the NaturePortfolio Reporting Summary linked to this article.Data availabilityThe data supporting the plots in this paper and the other findings ofthis study are available from the corresponding author upon reason-able request.References1. Gao, W., Ota, H., Kiriya, D., Takei, K. & Javey, A. Flexible electronicstoward wearable sensing. Acc. Chem. Res. 52, 523–533 (2019).2. 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High thermoelectric performance at room temperatureof n-typeMg3Bi2-basedmaterials bySedoping. J.Magnes. Alloy. 10,1024–1032 (2022).AcknowledgementsL.M., J.G., and P.Y. gratefully acknowledge financial support from theNational Natural Science Foundation of China (Grant No. U21A2054 and52273285), J.G. gratefully acknowledgesfinancial support fromNationalNatural Science Foundation ofChina (GrantNo.51961011), Y. P. gratefullyacknowledges financial support from National Natural Science Foun-dation of China (Grant No.52262032). T.M. acknowledges support fromJST Mirai JPMJMI19A1.Author contributionsL.M. and S.Z. conceived the idea, prepared the devices, and wrote thedraft. Y.G., J.C., and Z.Z. assisted inmeasuring the properties of devices.J. L. assisted in TEmaterials synthesis and simulation analysis. J. G., Y. P.,andC. L. assisted in editing themanuscript. L.M. and T.M. supervised thisresearch and revised the manuscript as corresponding authors. Allauthors contributed to the interpretation of the data and to thewriting ofthe manuscript.Competing interestsL. Miao, S. Zhu, C. Liu, J. Gao, and Y. Gao have applied for two Chinesepatents (ZL202010977167.9, 202211728686.7) on the main parts ofw-TEG described here. The remaining authors declare no competinginterests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-52841-1.Correspondence and requests for materials should be addressed toLei Miao or Takao Mori.Peer review information Nature Communications thanks Yuanwen Gao,Jian-Wei Liu, and the other anonymous reviewer(s) for their contributionto the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-52841-1Nature Communications |         (2024) 15:8516 12https://doi.org/10.1038/s41467-024-52841-1http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Comfortable wearable thermoelectric generator with high output power Result Design process for w-TEGs Coupling mechanism between output performance and wearing comfort Multi-parameter w-TEG optimization Device preparation and mechanical properties Model verification w-TEG performance during operation on a human body Discussion Methods Synthesis and preparation of n-type Mg3Bi2-based TE material Synthesis and preparation of p-type MgAgSb-based TE material Substrate precursor Synthesis of radiative cooling film w-TEG fabrication steps Material characterization Thermoelectric and mechanical performance characterization of w-TEGs Three-dimensional finite element analysis of w-TEG performance Reporting Summary Data availability References Acknowledgements Author contributions Competing interests Additional information