Integrated Moist‐Thermoelectric Generator for Efficient Waste Steam Energy Utilization

Abstract Industrial waste steam is one of the major sources of global energy losses. Therefore, the collection and conversion of waste steam energy into electricity have aroused great interest. Here, a “two‐in‐one” strategy is reported that combines thermoelectric and moist‐electric generation mechanisms for a highly efficient flexible moist‐thermoelectric generator (MTEG). The spontaneous adsorption of water molecules and heat in the polyelectrolyte membrane induces the fast dissociation and diffusion of Na+ and H+, resulting in the high electricity generation. Thus, the assembled flexible MTEG generates power with a high open‐circuit voltage (V oc) of 1.81 V (effective area = 1cm2) and a power density of up to 4.75±0.4 µW cm−2. With efficient integration, a 12‐unit MTEG can produce a V oc of 15.97 V, which is superior to most known TEGs and MEGs. The integrated and flexible MTEGs reported herein provide new insights for harvesting energy from industrial waste steam.


Supporting notes for calculation of the energy conversion efficiency
For the MTEG unit (1 cm -2 ), the mass of the polyelectrolyte membrane increased from 0.079 to 0.083 g after one hour of operation under the synergistic system of gradient temperature and humidity (100% RH for the bottom and 40% RH for the top, and 25 °C for the top and 40 °C for the bottom). The change in the mass was due to the adsorption of water during the operation.
In the process of water adsorption induced electricity generation of MTEG, the variation of the chemical potential energy of water molecules, corresponding to the transformation from gaseous water in the air to adsorb water in MTEG, could be reasonably considered as the main energy source. In response to water molecules adsorption of MTEG, oppositely charged ions (i.e., H + and Na + ) will be dissociated. They could diffuse in opposite directions based on the concentration difference effect, thereupon generating electric output on an external circuit. Therefore, the input energy finally is converted into the electric energy of MTEG. For energy conversion efficiency in the electricity generation process, the chemical potential of gaseous water and adsorbed water is µg and µa, respectively. The MTEG enables to spontaneously adsorb gaseous water in the air, and the water adsorption is assumed to be an isothermal and isobaric process. From thermodynamic law, the normal chemical potential µi is calculated as [S1] where , , T, P, R, μ and represents Gibbs free energy, the number of moles, temperature, atmospheric pressure, ideal gas constant, standard chemical potential and activity, respectively. In the process of water adsorption of MTEG, the water molecules will spontaneously change from a free gaseous state to an adsorbed state. The Gibbs free energy variation can be considered as: which reflects the reduction of the chemical potential energy of water molecules. Because there is no additional energy input in this MTEG system (single humid case), the chemical potential variation of water can be considered the sole energy input for electricity generation.
Thus, the maximal energy input could be estimated as: [S2] where 0 and ∆ represents the concentration of water in atmosphere and the concentration variation of water, respectively. The concentration of water in atmosphere and the concentration variation of water could be estimated by relative humidities of two sides. As a result, we could appropriately calculate the maximal energy input of about 0.305 J at 313 K arising from variation in chemical potential of water.
Meanwhile, the temperature gradient of two sides of the polyelectrolyte membrane induces the Na + immigration due to the Soret effect. In the process of thermal migration, the internal energy of the water is reduced, supplying the ions to diffuse and migrate and thus generate further electrical energy. The temperature change of the water (condensed matter), in MTEG, is assumed to be an isobaric and isotropic process.
From thermodynamic law, the change of internal energy of water is calculated as: where ∆ and represent the heat absorbed by the object and the work done on the object, respectively. The calculated maximal energy input under the isobaric and isotropic cooling process was about 0.258 J. In summary, the total energy input during the entire operation is about 0.563 J. In the synergistic system of gradient temperature and humidity, the Pmax is 4.75 μW cm -2 .
The energy of MTEG has been measured by connecting an optimally external resistor. The generated electric power can be calculated as: where U, I, and t are the generated voltage, current, and time of producing electricity, respectively. As a result, the calculated electricity energy is about 0.0171 J in one hour (100% RH for the bottom and 40% RH for the top, and 25 °C for the top and 40 °C for the bottom).
Accordingly, the energy conversion efficiency (W/∆G+∆Q) is estimated to be about 3% for one MTEG unit.
For the integrated MTEGs which are used in the utilization of the waste steam (60% ΔRH and 15 K temperature difference, environment temperature at 70 °C), the output power of the device is about 28.9 μW (effective area = 9 cm -2 ). After one hour of operation, the ∆m of polyelectrolyte is 0.07434 g. Therefore, the input energy and the output energy are about 15.4356 and 0.10404 J, respectively. Accordingly, the energy conversion efficiency (W/∆G+∆Q) is estimated to be about 0.67% for the integrated MTEGs (effective area = 9 cm -2 ) under 60% ΔRH and 15 K temperature difference. The decrease in conversion efficiency of integrated MTEGs is attributed to the increase in internal resistance due to the increased number of integrations.

Supporting notes for the Nyquist plots of the polyelectrolyte
The ionic resistances are the intersection of the line with the x-axis. [S3-5] The Nyquist plots of the polyelectrolyte with different RH under different temperatures are shown in Figure S6.
We measured the L (600 μm), R (shown in Table S1), and A (3.04 cm 2 ) to calculate the ionic conductivity.
S6 Figure S1. ATR-FTIR spectroscopy of AMPS, SSS, and P(AMPS-SSS0.5) membrane.  The integrated MTEG attached to the outside of the mask uses the hot moisture energy of exhaled breath to light up the LED bulb.