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Harvesting energy from low-grade heat based on nanofluids

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journal homepage: www.elsevier.com/locate/nanoenergy Available online at www.sciencedirect.com RAPID COMMUNICATION Harvesting energy from low-grade heat based on nanofluids Baoxing Xu a , Ling Liu a , Hyuck Lim b , Yu Qiao b,c , Xi Chen a,d,e,n a Columbia Nanomechanics Research Center, Department of Earth and Environmental Engineering, Columbia University, New York, NY 10027, USA b Program of Materials Science & Engineering, University of California, San Diego, La Jolla, CA 92093
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   journal homepage: www.elsevier.com/locate/nanoenergy  Available online at www.sciencedirect.com RAPID COMMUNICATION Harvesting energy from low-grade heatbased on nanofluids Baoxing Xu a , Ling Liu a , Hyuck Lim b , Yu Qiao b,c , Xi Chen a,d,e, n a Columbia Nanomechanics Research Center, Department of Earth and Environmental Engineering,Columbia University, New York, NY 10027, USA b Program of Materials Science & Engineering, University of California, San Diego, La Jolla, CA 92093, USA c Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093-0085, USA d International Center for Applied Mechanics, SV Lab, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China e Department of Civil & Environmental Engineering, Hanyang University, Seoul, 133-791, South Korea Received 20 April 2012; received in revised form 12 July 2012; accepted 13 July 2012Available online 22 July 2012 KEYWORDS Energy harvesting;Electrical potential;Low-grade heat;Conversion efficiency;Nanofluids Abstract Conventional thermoelectric materials have limited capability of scavenging electrical energy fromlow-grade heat (LGH). Based on the capacitive effect of liquid–solid interface in a nanoconfine-ment, we investigate a novel energy harvesting mechanism which is based on the thermallysensitive ion/charge distribution of electrolytes confined in nanopores. The mechanism iselucidated using comprehensive molecular dynamics (MD) simulations. The effective thermalsensitivity, effective figure of merit, and thermal-to-electric energy conversion efficiency of thenanofluidic system compare favorably with respect to the conventional thermoelectric materials.The result of a preliminary thermal-to-electrical energy conversion experiment on a nanoporouscarbon is presented, to qualitatively show the feasibility of the approach. &  2012 Elsevier Ltd. All rights reserved. Introduction Harvesting low-grade heat (LGH) from ambient environmentalsources, such as waste heat from power plants, automobileengines, and solar panel substrates, has attracted significantinterests in addressing the challenge of energy and sustain-ability. Conventional direct energy conversion methods focuson utilizing thermoelectric materials and structures [1–3], which convert a temperature gradient to an electrical poten-tial based on the Seebeck effect and work well at highertemperatures (usually  4 350  1 C); however, their conversionefficiency is rather small for low-grade heat (temperaturebelow 130  1 C), because a comparatively large amount of heatis conducted due to the thermal shortening effect [4,5]. Despite the progresses over the past decades on usingnanowires and superlattices as advanced thermoelectric 2211-2855/$-see front matter  &  2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.nanoen.2012.07.013 n Corresponding author at: Columbia University Columbia Nanome-chanics Research Center, Department of Earth and EnvironmentalEngineering New York, NY 10027, USA E-mail address:  xichen@columbia.edu (X. Chen).Nano Energy (2012)  1 , 805–811  materials and structures (which takes advantages of thequantum size effect, band structure modification, electron/photon scattering, etc.), for LGH with  D T  o 100  1 C the effi-ciency is typically below 1% [4,6–8]. To develop high efficiency and low-cost LGH harvesting systems, a new mechanism needsto be discovered.In contrast to the single phase solid-state thermoelectricmaterials, when a liquid phase is confined in a nanochannel (ora nanoporous material), the ‘‘composite’’ material under-pinned by the unique and strong liquid–solid interactioncharacteristics has shown significant promise in energy con-version, including energy absorption [9] and actuation [10,11] with high efficiency. A number of theoretical and experimentalstudies have demonstrated that the flow of water or electro-lyte solution over one-dimensional nanostructures (such ascarbon nanotubes [12–14] and graphene [15]) can induce a voltage along the flow direction. This voltage generation isgenerally attributed to the streaming flow, and has a lowenergy conversion efficiency due to the limit of the liquid sliplength near the solid wall of nanopores [16,17], although pressure-driven flow may somewhat improve is efficiency[18,19]. More importantly, such an approach is difficult to harvest LGH, since the pressure gradient of LGH-driven liquidflow is fairly small [20,21], and thus the energy conversion efficiency would be quite low.In this study, we investigate a novel thermal-to-electricalenergy conversion approach through which an electricalpotential can be generated along the radial direction of nanopores with a decent efficiency. When an electrolytesolution is confined in a nanopore, near the solid–liquidinterface the solvated ions are under the influence of differentforce fields from the solid and liquid phases, and thus theyexhibit anisotropic structures [10,22], leading to a net inter- face potential difference. Since the ion structure and behaviorin the interfacial double layer are thermally dependent[23–25], if two liquid–solid interfaces with different tempera- tures form a circuit, their distinct surface charge densitieswould cause an output voltage. Thanks to the ultralargespecific surface area [26] and the prevention of thermalshortening, the harvesting efficiency is expected to beprominent upon a small temperature difference (e.g., in theLGH range, below 100  1 C). Model and computational method To validate this concept, molecular dynamics (MD) simula-tions are performed in a NVTensemble with LAMMPS [27]. Asmooth segment of armchair (20, 20) CNTwith the diameterof   D =2.712 nm is employed to model a nanopore and is keptfixed during the simulation. The axial length of CNT,  l , ischosen to be 10.7 nm and has been verified to be longenough for robust data collection. For a desired electrolyteconcentration, the numbers of water molecules and ions(Na + and Cl  ) are chosen such that the density of liquidphase inside the CNT is close to that of bulk at 300 K and0.1 MPa. Periodical boundary condition is imposed in theaxial direction of the computational cell so as to mimic aninfinite long pore. The extended Simple Point Charge(SPC/E) potential is used to model water molecules [28].The 12–6 pairwise  L –  J   potential and Coulomb interaction areemployed for interactions among ions and atoms, and the L –  J   parameters are taken from Ref. [29], which have beenconfirmed to reproduce the experimental information suchas contact angle of water droplet on a graphite surface [30]and the binding energies of ion-water interactions [31]. AllMD simulations are carried out for 2.0 ns with the integralstep of 1.0 fs, and the positions of ions and atoms areobtained via their averaged configurations within 0.5 nsafter equilibrium. The system temperature is maintainedwith a Nose/Hoover thermostat. Results and discussion Fundamental distribution of molecules/ions andthermal dependence Fig. 1a shows the averaged radial density profiles (RDPs) of O and H atoms and Na + and Cl  ions in the nanoconfined1.5 mol/l aqueous solution of sodium chloride (NaCl), wherea significant amount of H and O atoms are within aperipheral annular region (the first solvation shell, FSS)owing to the strong interactions with carbon wall. A closerlook at RDPs finds that H atom is closer to the CNTwall than Fig. 1  (a) Average radial density profiles (RDPs) for differentatoms and ions across a (20,20) CNT at 300 K; (b) Thecorresponding net radial charge distribution  r ne ( r  ) at differenttemperatures. In both figures the left and right axis are alignedwith the tube axis and wall of CNT, respectively. B. Xu et al.806  the O atom, and the Na + ion can approach the CNT wallmore closely than the Cl  ion. The latter is primarily due tothe bar radius difference between Na + and Cl  (0.095 nmand 0.181 nm [32], respectively): the smaller Na + ionsubjects to stronger attractive force from the H atom andweaker repulsive force from the O atom (compare with thelarger Cl  ion), in part owing to the smaller repulsive forcebetween the H atom and CNTwall (compare with that of theO atom). The similar behavior has been noted by Cazadeet al. [33] and Qiao and Aluru [34] in their studies on NaCl solution confined in CNTs. The difference in distribution bythe cations and anions near the CNT wall leads to a netcharge. Meanwhile, the associated difference in the radialdensity distribution between O and H atoms forms apreferential dipole orientation [35,36], which is usually regarded as a connection between an O shell and aneighboring H shell pointing from the H shell to the O shell,and that leads to a net charge distribution near the CNTwall. In essence, the mechanism is due to the Coulomb andVan der Waals interaction of the dipoles and inhomogeneousion distribution in the radial direction.The overall net charge distribution can be determined by r ne ð r  Þ¼ P ni ¼ 1 r i ð r  Þ c i , where  n  represents the total number of particles in the solution and  c i  represents the partial charge of the  i th ion/atom specie. Fig. 1b shows the calculated netcharge distribution across the CNT at different temperatures,where  r ne ( r  ) varies with a stronger fluctuation near the CNTwall due to a stronger inhomogeneous distribution of ions andatoms (Fig. 1a). As temperature varies, the ions are moremobile and become easier for them to overcome the energywell and move away from the interface. Thus  r ne ( r  ) changesaccordingly with ion redistribution: the higher temperature ( T  )is the lower  r ne ( r  ) near the CNTwall. A conceptual LGH energy harvesting system Given the radial distribution of net charge,  r ne ( r  ), the radialvariation of the electrical potential  f ( r  ) can be calculatedthrough the Poisson equation  r  2 f ( r  )=  r ne ( r  )/( e 0 e ) (where e 0  and  e  are the vacuum permittivity and the dielectricconstant of liquid medium, respectively;  e  is 52.87 for1.5 mol/l NaCl solution [37]), and is plotted in Fig. 2a, where  f ( r  ) also shows an oscillation with respect to  r  . Theliquid-CNT interfacial electrical potential difference can bededuced as  U  = f ( r  ) 9 r  = D  /2  f ( r  ) 9 r  =0 , which apparentlyincreases with temperature. The sign of   U   qualitativelyreflects the net charge in FSS (which is also poresize-dependent). Following the similar procedure, the ana-lysis is performed on a smaller nanotube, (12, 12) CNT, witha diameter of 1.627 nm and enclosing 1.5 mol/l NaCl solu-tion, Fig. 2b. The smaller tube shows fewer numbers of oscillation peaks of   f ( r  ) (due to smaller confinement) yetwith larger peak magnitude (due to the stronger interactionamong water, ions and carbon wall). More importantly, theeffect of temperature on  f ( r  ) is more obvious for thesmaller tube, indicating the stronger size effect.Based on the thermally-dependent interface ion densityand associated potential difference, when two nanoporeinterfaces of different temperatures form a circuit (schema-tically shown in Fig. 3a, with the same  D ), an instantaneousnet voltage will be generated until a new equilibrium isestablished, effectively converting thermal energy to elec-trical energy. Fig. 3b shows that such an output electricaldifference  D U  ð¼ 9 U  T  L þ D T   U  T  L 9 Þ  increases with temperaturedifference,  D T   (where the low temperature end,  T  L , isassumed to maintain 300 K). Besides, the energy harvestingcapability shows an obvious size effect from both Fig. 3b and c.For LGH of   D T  =20 K, 40 K and 60 K, the induced  D U   can be ashigh as several tens of mV, and the optimum pore size seems tobe around 2.2 nm for the current range of parameters. More-over,  D U   depends on electrolyte concentration, illustrated for(20,20) CNTs in Fig. 3d (in these computations the dielectricconstant  e  changes with respect to the concentration of NaClsolution [37]). With the increase of ion concentration,  D U  arises, indicating an enhanced thermal sensitivity for the sameLGH source.Following the conventional approaches for thermoelectricmaterials, one may estimate the effective thermal sensitivityin a way similar to that of the Seebeck coefficient, and isdefined as the output electrical difference per Kelvin changein temperature. For instance, for a pair of (16,16) CNTsenclosing 1.5 mol/l NaCl solution and subjecting to D T   in LGHrange, the effective thermal sensitivity is  ~ a ¼ 0 : 32 mV = K. Fig. 2  Distribution of the electrical potential,  f ( r  ), across (a)a larger tube (20,20) CNT, and (b) a smaller tube (12, 12) CNT;both with 1.5 mol/l NaCl solution under different tempera-tures. The left axis is aligned with the tube axis. Harvesting energy from low-grade heat based on nanofluids 807  The effective figure of merit  ~ z   depends on thermalconductivity of NaCl solution and electric resistance of counter electrodes (here assumed to be copper), whichmay be taken from a somewhat similar experimental systemas  l E 0.6 W/ (mK) , and  k E 1.68  10  8 O m [38], respec-tively, and hence we estimate  ~ z  ¼  ~ a 2 = ð kl Þ¼ 10 : 2 for thesystem under consideration. These performance indices holdadvantage over conventional thermoelectric materialsincluding superlattices and nanowires [7,8,39], although it is reminded that the present system is based on thethermally dependent surface electrification effect, whosemechanism is distinct from the Seebeck effect in conven-tional thermoelectrics. Estimation of thermal-to-electric energyconversion efficiency As the voltage is being generated, the excess charges wouldmove from the low-temperature (high ion density) end to thehigh-temperature (low ion density) end, until a new equilibriumis established. The thermal-to-electrical energy conversion atthe liquid-CNT interface can be regarded the discharge processof capacitor, with the initial electrical potential of   U   and themotion of maximum charge of   D q  . Thus, the output electricenergy can be evaluated as  W  output = D qU  /2, and  U  = q  / C , where q   is the total net charge of ions inside the FSS, as illustrated inFig. 4a,  C =2 pe l /ln( D /( D  2 a )) is the system capacitanceaccording to the theoretical analysis by Huang et al. [40],and  a  is the inner radius of FSS region. The total inputthermal energy is  W  input ¼ P ni ¼ 1 C i D T  , where  C i  are the molarspecific heat of atom or ion specie, which equals to 74.539 J/mol, 8.52 J/mol, 27.6 J/mol, and 33.949 J/mol for watermolecule, carbon atom, Na + and Cl  ions, respectively. Thus,the conversion efficiency is estimated as  Z c ¼ W  output = W  input ¼ D q   q  =  ð 2 C P ni ¼ 1 C i D T  Þ . Based on the MD calculations of  D q  , for (12,12) CNTs with 1.5 mol/l NaCl solution, and (20,20)CNTs with 1.5 mol/l NaCl solution, the computed conversionefficiency of the present system,  Z , can be deduced in Fig. 4bfor different  D T  with the ambient temperature of   T  L =300 K.By comparison, the calculated the efficiency of (12, 12) CNTswith 3 mol/l NaCl solution is also included. The resultsindicate that the conversion efficiency has an obvious poresize and concentration effect.The efficiency can also be improved by combining nano-pores/liquids of different characteristics; for instance, if the low-temperature cell uses (12,12) CNT whereas thehigh-temperature cell contains (20, 20) CNT with the sameconcentration of 1.5 mol/l NaCl, the effective thermalsensitivity will increase, leading to a higher efficiency, asshown in Fig. 4b. It is noteworthy that in the present model,the liquid/nanopore environment is closed and there is no Fig. 3  (a) Schematic of the potential difference generated between two liquid-nannopore interfaces under a heat grade. (b)Variation of the net output voltage, D U  , with heat grade; (c) Effect of pore size and (d) Effect of electrolyte concentration on D U   atdifferent heat grades. In these simulations the ambient temperature (low temperature end) is set at  T  L =300 K; note that for thesame thermal difference ( D T  ), the results have some (although not significant) dependence on  T  L . B. Xu et al.808

Molecular Dynamics

Jul 23, 2017
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