Thermal Polarization of Water Influences the Thermoelectric

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The Thermal Polarization of Water Influences the Thermoelectric Response of Aqueous Solutions Silvia Di Lecce, and Fernando Bresme J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10960 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 3, 2018

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The Journal of Physical Chemistry

The Thermal Polarization of Water Influences the Thermoelectric Response of Aqueous Solutions Silvia Di Lecce∗,† and Fernando Bresme∗,†,‡ †Department of Chemistry, Imperial College London, SW7 2AZ, UK ‡Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway E-mail: [email protected]; [email protected] Phone: +44 020 7594 5886

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Abstract Aqueous solutions under thermal gradients feature thermodiffusion (Ludwig-Soret) and thermoelectric (Seebeck) effects, whereby the thermal fields build concentration and charge density gradients. Recently, it has been shown that thermal gradients induce polarization fields in water. We use non-equilibrium molecular simulations to quantify the thermoelectric Seebeck coefficient of alkali halide aqueous solutions. We examine the dependence of the coefficient with temperature and salt concentration and show that the thermal polarization of water plays a key role in determining the magnitude of the thermoelectric behavior of the solution.

Introduction When a thermal gradient is applied to a fluid suspension or a fluid mixture, it induces thermodiffusion, i.e. the Ludwig-Soret effect. The heat flux builds concentration gradients 1,2 , and in the case of charged species, the different electric mobility and charge of the ions results in an internal thermoelectric voltage difference across the solution. This thermoelectric response is well known in metals and semiconductors, 3 and it is commonly referred to as the Seebeck effect, 4 although this thermoelectric effect could have been observed by Volta in 1821. 4,5 The Seebeck effect has been used to make thermocouples for temperature measurements and to power spacecrafts, 6 e.g. NASA’s Voyager, which exploits a radioisotope thermoelectric generator to convert the heat produced by a radioactive decay into electricity. The thermoelectric effect is of general interest in the area of energy conversion research, and it is being actively investigated to develop devices that can recover waste heat and convert it to useful electrical energy. 7,8 Biothermal batteries to power heart pacemakers, 9 or the conversion to electricity of the waste heat in automobiles exhaust systems 7 are notable examples. There is a growing interest in the investigation of the Seebeck effect in electrolyte solutions. Theoretical estimates of the Seebeck coefficient are available at infinite dilution con2


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ditions. 10 Although these estimates are of limited use when considering finite concentrations relevant to experimental studies, they provide an idea of the expected order of magnitude of the thermoelectric response. These ideas have been applied to interpret the thermophoretic drift of colloids in solution, and their preference to move towards cold or hot regions was linked to the sign of the estimated Seebeck coefficients. 40 Additional works have highlighted the relevance that thermoelectric effects in aqueous solutions can play in determining the thermophoretic response of colloids and molecules. 11–13 Beyond the role of alkali halide ions on thermophoresis, the Seebeck effect is also being investigated in supercapacitors, 14 thermogalvanic cells, 15 as well as in biology, namely, electro-receptors mechanisms in flies and fishes. 16–18 The discussion above shows that the understanding of the thermoelectric response of ionic solutions is relevant to a wide range of scientific and technological disciplines, and fundamental studies are needed to explain the behavior of the ions and water under thermal fields. Indeed, it was shown recently that thermal gradients induce polarization fields in pure water, which are associated to the polarization of water molecules. 19 The origin of this physical effect has been explained by using non-equilibrium thermodynamics theory, and microscopically, by studying the electrostatic properties of water at different temperature and pressure conditions. 20,21 The thermal polarization effect has been discussed recently in the context of thermal monopoles 22 and the dynamical ordering of quantum fluids. 23 We investigate in this work the importance of the thermal polarization effect in defining the magnitude and sign of the Seebeck coefficient of alkali halide aqueous solutions. We demonstrate that the electrostatic properties of water in the presence of a thermal field and ions is essential to define the thermoelectric response of the solution via the Seebeck coefficient.

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(a)

TC

TH

TC

(b) 400 350

T [K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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300 250 200

0

1

2

3

4

5

6

7

8

9

10

z [nm]

Figure 1: (a) Simulation set up employed in this work. The highlighted molecules represent the thermostatting hot (red) and cold (blue) regions. (b) Representative temperature profile obtained in the stationary state. The shadowed areas indicate the position of the hot and cold thermostats.

Methods We used Non-Equilibrium Molecular Dynamics (NEMD) simulations to set up a thermal gradient across aqueous solutions of different compositions: [Li+ , Na+ , K+ ] Cl− and Na+ [Cl− , I− , F− ]. We performed the NEMD simulations using a modified version of GROMACS v. 4.6.3. 24 , following the algorithm described in reference. 25 The simulation box includes thermostatting regions, where a set of water molecules are thermostatted at predefined hot and cold temperatures (see Figure 1a). The temperature was reset by rescaling the molecule velocities every time step.

26

All the simulations were performed in orthorhombic periodic

cells, with dimensions {Lx , Ly , Lz }/Lx = {1, 1, 3}, with Lx = Ly = 3.55 nm. The trajectories were integrated using the Leap Frog algorithm with a time step δt of 0.002 ps. The temperature gradients were of the order ∇T = 33.43 K nm−1 , corresponding to thermostatting temperatures of 400 K and 200 K for the hot and cold thermostat. In agreement with our previous works, the response of the solutions is found to be in the linear regime. 27,28 4


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A combination of Lennard-Jones (LJ) and Coulombic potentials were used to model the interactions between ions and between ions and water. The LJ interactions were truncated at a cut-off distance rc = 1.5 nm, while the electrostatic interactions were computed in full using the particle-mesh Ewald method (PME) with a mesh width of 0.12 nm and an interpolation order of 4. We used the extended simple point charge (SPC/E) force field 29 to model water and the force field by Dang et al. 30–33 for the ions. The latter force field has been parametrized explicitly for SPC/E water. A typical simulation set up began with an equilibration in the NPT ensemble (1 ns), followed by an additional equilibration in the NVT ensemble (1 ns). We performed the simulations at an average pressure of 600 bar and temperature 300 K. We have shown in previous work that the Soret coefficients do not depend significantly on the pressure for the interval 1-600 bar. 28 Production trajectories spanning 300 ns were used to obtain average properties. The configurations were saved every 10 steps, and we excluded in our analysis the regions within 1 nm from the thermostat. The electric field in the z direction was computed following the approach discussed in references: 20,34 1 E(z) = 0

Z

z

ρq (z 0 )dz 0 ,

(1)

0

where 0 is the vacuum permittivity, ρq (z) is the charge density. For the electrostatic fields, we performed a running average sampling every 20 data points, neglecting 30 data points next to the thermostatted layers. The charge density was also obtained from the sum of monopolar M (z), dipolar Pz (z), quadrupolar Qzz (z) and higher order terms: 19,20,35 " # d dQzz (z) ρq (z) = M (z) − Pz (z) − + ... . dz dz

(2)

We neglected higher order terms, higher than the quadrupole, in the multipolar expansion.

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The monopolar, dipolar and quadrupolar contributions were computed using: 19,20,35 1 M (z) = A

1 Pz (z) = A

*

1 Qzz (z) = A

*

Nm X

*N ions X

+ δ(z − zi )qi ,

δ(z − zi )

" j∈m X

i=1

#+ qj,m zj,m

,

(4)

j=1

i=1 Nm X

(3)

i=1

"

j∈m

1X 2 qj,m zj,m δ(z − zi ) 2 j=1

#+ ,

(5)

where A = Lx × Ly is the cross sectional area of the simulation cell, the sum over i runs over the number of molecules Nm , j is the sub-index for the number of charged sites in each molecule, zi represents the position of the oxygen atom in the water molecule, zj,m is the z-coordinate of the site j (the hydrogen site) in molecule-m in the molecular frame of reference, and qj,m is the charge of site j. The monopolar contribution includes all the ionic charges, i.e., cations and anions. The total electric field of the solution is defined by:

E(z) = EM (z) + EPz (z) + EQzz (z) Z Z Z 1 z dPz (z 0 ) 0 1 z 1 z d2 Qzz (z 0 ) 0 ρq,ion (z)dz − = dz + dz 0 0 ε0 0 dz 0 ε0 0 dz 02

(6) (7)

We fitted the temperature dependence of the Soret coefficients to the empirical equation ∞ proposed by Iacopini et al., 36 sT (T ) = s∞ T [1 − exp ((T0 − T )/τ )], where sT represents the

asymptotic limit of the Soret coefficient, T0 is the inversion temperature and τ a parameter that determines the variation of sT with temperature.

Results and Discussion The simulation set up is represented in Figure 1a. In the NEMD simulations the stationary temperature profile, shown in Figure 1b, is reached in ∼ 500 ps, while the concentration profile takes longer, typically varying with the distance between hot and cold reservoirs, L, 6


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and the diffusion coefficient, D, according to τ∇x ∼ L2 /D. For typical D ∼ 10−9 m2 s−1 and L ∼ 5 nm, τ∇x ∼ 20 ns. Our simulations were much longer, 0.3 µs, hence ensuring the stationary composition gradient was reached. Once the stationary state for both composition and thermal gradients were reached, the Soret coefficient (sT,1 ), which quantifies the thermodiffussion response of the solution, was extracted from an analysis of the gradients via, sT,1 = −1/(x1 x2 ) (∇x1 /∇T )J1 =0 , where xi is the number fraction of salt (1) and solvent (2), ∇x1 and ∇T are the number fraction and temperature gradients, respectively, and J1 = 0 indicates that the computations are performed in absence of a net mass flux of salt. 27,28 To perform the simulations of the solutions we used state of the art force fields (see Methods section for relevant details) and explored different temperatures, 250–350 K; targeting thermophobic and thermophilic states, where the solution concentrates preferentially in the cold and hot region, respectively. The simulations were performed at an average concentration of salt of 1 mol kg−1 . At this concentration the inter-ionic correlations are expected to be important, as shown by the activity coefficients of the salt, obtained both from experiments and simulations. 28 At these conditions computer simulation models become particularly helpful to overcome limitations of mean field theoretical approximations. The quantification of the thermoelectric effect requires the computation of the electrostatic fields generated by the application of the thermal gradient. The fields were computed by integrating the charge densities of all the species in solution, ions and water, and splitting the contributions of salt and water, to address the impact of the latter on the thermoelectric response. In addition we computed the monopole, dipole and quadrupole contributions to the thermoelectric field, to resolve microscopically the dominant contributions defining the magnitude of the Seebeck coefficient, SE = E/∇T , 20,34 which is the ratio between the electric field E and the thermal gradient ∇T . The Soret coefficients for different salt compositions are shown in Figure 2. The coefficients feature a dependence with temperature that is characteristic of that observed in thermodiffusion experiments (see refs. 28,37 and inset in Figure 2). It was found that al-

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kali halide salts are thermophilic at low temperatures (sT,1 < 0) and thermophobic at high temperatures (sT,1 > 0). The temperature dependence of the Soret coefficient can be described accurately using the Iacopini et al. empirical equation 36 (see Methods section for details and Figure 2), and this equation can be used to define the inversion temperature that signals the transition between the thermophilic and thermophobic regimes. The inversion temperature, T0 , varies with salt composition in our simulations, decreasing in the order LiCl > KCl > NaCl, for chloride salts, and NaI ' NaF > NaCl, for sodium salts. The shift in the inversion temperature of NaCl and KCl solutions, ∼ 23 K, is similar to that one reported in experiments, ∼ 10 K, at concentrations of 0.5 mol kg−1 (see inset in Figure 2). The simulated Soret coefficients also reproduce the experimental observation of a crossing in the Soret coefficients of NaCl at KCl at higher temperatures, corresponding to the thermophobic regime. Overall, our results show that the force fields employed in our work reproduce the general thermodifussion response of alkali halide solutions. The calculation of the Soret coefficient was performed by considering the average salt concentration, since the differences in the number fractions of cations and anions are small. Using average values facilitates the comparison with existing data, since the individual ionic contributions to the Soret coefficients have not been resolved before in experimental studies. 37 So far we have characterized the general thermo-phobic/philic response of alkali halide solutions. This shows that our computational models predict thermophilic and thermophobic responses in agreement with experimental observations. The magnitude of the Soret coefficients computed here also agrees well with the experimental data 37 (see inset of Figure 2). We focus now on the polarization of the thermal polarization of the solutions. We performed preliminary simulations of pure water to test our implementation of the NEMD method. We found good agreement between the polarization obtained here and previous simulations results 34 (see Supporting Information). The NEMD method was then applied to compute the thermal polarization of different solutions. Figure 3a shows the electrostatic fields of LiCl aqueous solution obtained from simulations with and without thermal gradi-

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10 5

LiCl KCl NaCl NaI NaF

0

-10

-1

-5

4

3

sT,1 x 10 [K ]

3

-1

sT,1 x10 [K ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

-15

NaCl KCl

0 -2 280

300

320

340

T [K] -20

240

260

280

300

320

340

360

T [K]

Figure 2: Soret coefficient as a function of the temperature for alkali halide solutions ([Li+ , Na+ , K+ ] Cl− , Na+ [Cl− ,F− ]) at 1 mol kg−1 average concentration. (Inset) Experimental Soret coefficients of NaCl and KCl solutions at 0.5 mol kg−1 concentration as a function of temperature (data taken from ref. 37 ).

Figure 3: Thermoelectric analysis of alkali halide solutions at 1.0 mol kg−1 average concentration. (a) Electric fields computed using equation (1) for LiCl aqueous solution in a thermal gradient, ∇T = 33.43 K nm−1 (blue line) and without thermal gradient applied (orange line). (b) Typical electric field of LiCl aqueous solution. The black line are the data obtained from one simulation. The red symbols indicate a running average sampling every 20 data points. The thermostatted regions are indicated by the red (heat source) and blue (heat sink) areas. (c) Seebeck coefficient of alkali halide solutions as a function of the temperature. ent. In absence of thermal gradient the solution does not feature an internal electric field (see orange line in Figure 3a), whereas a significant electric field along the simulation box is observed in the presence of a heat flux (see blue line in Figure 3a). Due to the symmetry of the simulation cell there are two heat fluxes present in the cell, acting in opposite directions. 9



This is reflected in the different signs of the electrostatic fields on both sides of the simulation box. The magnitude of the thermoelectric field is of the order of 1−10 MV m−1 for a thermal gradient of 33 K nm−1 (see Figure 3b), rendering Seebeck coefficients of ∼ 10 − 100 µV K−1 (see Figure 3c). These coefficients are within the range of the ones that can be estimated by analyzing previous simulation studies of NaCl solutions under thermal gradients. 38 Our analysis of the data reported in that work gives Seebeck coefficients of similar magnitude to the ones we obtain here for the same salt. We have included in Figure 3c the thermoelectric fields generated by the gradient for all the solutions investigated in this work. A clear field is present in all cases. The field features difference temperature dependences determined by the salt composition. For KCl the field varies little with temperature while for Na-salts the Seebeck coefficient decreases in general with temperature. The rate of the change of the Seebeck coefficient with temperature decreases in the order, LiCl > NaI > NaCl > NaF > KCl. This trend does not follow the behavior observed in the Soret coefficient (see Figure 2), where LiCl features the lower rate of change of the Soret coefficient with temperature, instead. A smaller thermopolarization field is obtained for KCl in comparison to that for LiCl. Following the observations for LiCl, we find that the Seebeck coefficient of NaF and NaI changes from positive at low temperatures to negative at high temperatures. Changes in the sign of the thermo-polarization field have been reported before in pure water. 20,34 It was found that this change in sign is connected to the temperature dependence of the dipolar and quadrupolar contributions to the total electrostatic field of water. Advancing the discussion below we will show that the microscopic origin of the change in sign in the presence of ions is different. We note that the change in sign of the Seebeck coefficient necessarily implies the existence of a temperature at which SE = 0, i.e. there is a temperature where the thermoelectric effect is cancelled. We examine now the physical origin of the change in sign of the Seebeck coefficient and the observed temperature dependence of the Seebeck coefficient. To tackle these questions we computed the individual contributions of water and the ions to the thermoelectric re-

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(a)

LiCl

300

molecular

200

EM EP

-1

E [MV m ]

100

z

EQ

zz

EP + E

20

z

Qzz

EP + E + EM Q z

0

zz

-20 atomistic

ETOT Ewater ELiCl

-100 -200 -300

1

1.5

2

3

2.5

4

3.5

4.5

z [nm] (b)

-1

E [MV m ]

100 4 2 0

(c)

KCl

200

40 20 0 2

Ewater ETOT EKCl

0 -20

-100 -200

ENaCl

ETOT

Ewater

(e)

NaI

200 100 -1

NaCl

-40 1 1.5 2 2.5 3 3.5 4

1 1.5 2 2.5 3 3.5 4

(d)

E [MV m ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6 3 0

100

Ewater ETOT ENaI

NaF

50

Ewater ETOT ENaF

2 0 -2

-100

-50

-200

-100

1 1.5 2 2.5 3 3.5 4

z [nm]

1 1.5 2 2.5 3 3.5 4

z [nm]

Figure 4: Water and ionic contributions to the total electric field of 1.0 mol kg−1 LiCl (a), KCl (b), NaCl (c), NaI (d) and NaF (e) solutions along the simulated box. The electric fields of the water and of the ions are computed using the equation (1) and equation (7). sponse, so that Etot = Eions + Ewater . We show in Figure 4a these contributions along with the monopole, dipole and quadrupole contributions to the electrostatic field (see Methods section) for LiCl 1.0 mol kg−1 . Our results show clearly that the thermoelectric field is determined both by the ions and water. The total field is the result of a cancellation of two large fields, which are one order of magnitude larger than the total one. The sign of the total thermoelectric field agrees with that of the water contribution at low temperatures, and with that of the ions at higher temperatures. The quadrupolar and dipolar contributions of the water molecules are very different. We find that in ionic solutions the dipolar 11



contribution dominates, unlike what has been observed before in pure water. 34 This result indicates a modification in the thermoelectric response of water when ions are present, which must be connected to the water-ion interactions. We tested that the sum of the dipolar and quadrupolar contribution reproduces well the total thermoelectric field of water (Ewater ) (see Figure 4a). This indicates that the contribution of higher order terms, octupolar and beyond can be neglected to a good approximation. The dipole and quadrupole contributions are connected to the thermal orientation of water in the thermal field and the interactions with the ions. These contributions are not constant, they vary with the local temperature and the local density (see e.g. references 20,34 ). One key conclusion from the results reported in Figure 4a for LiCl is that the Seebeck coefficient cannot be obtained by investigating the charge separation associated to the ions only. Using ELiCl we get Seebeck coefficients that are off by several orders magnitude, 1000 µV K−1 , with respect to the accepted values, 1 − 100 µV K−1 . We conclude that the analysis of the Seebeck effect in aqueous solutions requires the consideration of contributions associated to the polarization fields induced in water as well as in the ions. Figure 4 shows that electrostatic field due to the ions, M (z), is not constant. This indicates that the local number fraction of the cations and anions is different, and there is local charge separation. The analysis of representative number fraction profiles of the ions corroborate this notion (see Supporting Information). We note that charge separation in charged fluids has been observed in models of molten salts when the ion charge is screened significantly. 39 We have analyzed the water/ion contributions for the other salts investigated in this work (see Figure 4). Consistent with LiCl, we find that the polarization field in water plays an important role in defining the thermoelectric response of the solution. For KCl and NaI the magnitude of the fields decreases with temperature, while for LiCl and NaF increases, with NaCl showing an intermediate behavior. This complex behavior highlights the specificity of the Seebeck coefficient regarding salt composition, which is one of the trademarks of thermodiffusion of ionic solutions. Understanding the origin of this specificity will require additional work.

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How do the computed Seebeck coefficients compared with values available in the literature? A number of studies have related the Seebeck coefficient with the ionic heat of transport, Q∗ , of a single ion, 13,40–44 SE,0

Q∗+ − Q∗− = . 2eT

(8)

The heat of transport measures the heat that is absorbed or released by a particle when it is moving between two regions at different temperatures, in order to maintain its temperature constant. 45 Equation (8) is suitable for high diluted solutions and it is expected that deviations will be observed at higher concentrations, such as the ones investigated here since non-ideal effects due to ion-ion interactions and ion solvation will be relevant. In order to compare the order of magnitude of the Seebeck coefficients, we show in Table 1 the estimated Seebeck coefficients using the heats of transport reported by Agar et al. 46 Table 1: Comparison between the Seebeck coefficient of solutions at infinite dilution (SE,0 ) and 1.0 mol kg−1 (SE ) alkali halide solutions, at 298.15 K. SE was obtained from the NEMD simulations performed in this work. Salt NaCl LiCl NaF Kcl NaI

SE,0 [µV K −1 ] 50.92 0.00 -8.17 35.80 87.08

SE [µV K −1 ] 16.5 25.7 14.1 87.0 103.8

The computed values are of the same order as those estimated from equation (8), i.e. µV K−1 , while the sign differs for LiCl and NaF solutions, highlighting the impact of the salt concentration in defining the thermoelectric response. The Seebeck coefficients predicted by the infinite dilution estimate and the simulations follow, however, similar trends. Consistently, we find that NaI has the highest Seebeck coefficient. Table 1 shows that some of the estimates from the infinite dilution approach are reasonable at finite concentrations (1 mol kg−1 ), however the differences for LiCl, NaF and KCl, indicate that the equation should be used with care when considering concentrated solutions.

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-1

SE [10 V K ]

4

-4

3

-4

-1

SE [10 V K ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2

4 270 K 281 K 290 K

2

300 K 310 K 320 K 330 K

0 -2

1

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1

0 1/2

c

2

3

-1 1/2

[mol kg ]

0 -1

1.0 mol kg

-1

-1

2.1 mol kg

-1

3.4 mol kg

-1

4.7 mol kg

-2 250 260 270 280 290 300 310 320 330 340 350

T [K]

Figure 5: Seebeck coefficient of LiCl solutions at different salt concentrations as a function of temperature. (Inset) Seebeck coefficients as a function of the square root of the salt concentration at different temperatures. To address the impact of the salt concentration on the Seebeck coefficient we performed additional simulations for LiCl solutions in the range 2.1 to 4.7 m (see Figure 5). In all cases the Seebeck coefficient decreases with temperature and reverses sign approximately at the same temperature, ∼305 K. Increasing the concentration reduces significantly the magnitude of the Seebeck coefficient at low temperatures, while the changes observed around 300 K are smaller. The dependence of the Seebeck coefficient with concentration was investigated by Helfand and Kirkwood 47 using the Debye-Hückel theory. It was suggested that the Seebeck √ coefficient decreases linearly with the square root of salt concentration, c. Interestingly, our simulation results follow this linear dependence too (see inset in Figure 5). Such agreement is unexpected since as mention above the non-ideal effects are expected to be important for these solutions. Although the Debye-Hückel law is applicable at high dilution, we note that the linear variation of the thermoelectric coefficient predicted by this limiting law has been observed too in previous works dealing with high concentrated solutions. Kang et al. 48 reported a linear decrease of the Seebeck coefficient in going from 0.4 to 6.4 M in potassium ferro/ferricyanide √ redox couples. A linear variation of the thermoelectric coefficient with c was also reported in tetradodecylammonium nitrate in octanol and tetrabutylammonium nitrate in dodecanol

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solutions, for concentrations in the range of 0.1–0.8 mol L−1 . 49 Assuming a linear dependence down to the infinite dilution limit, we extrapolated our vales to estimate the Seebeck coefficient in this limit. At 300 K we find 48 µV K−1 while at a slightly higher temperature, 310 K, we get -38 µV K−1 , indicating a large dependence of the Seebeck coefficient with temperature for this salt, as illustrated in Figure 5. We found that at 307.5 K the Seebeck coefficient would have a value closer to that estimated at infinite dilution at 298 K, being -11.57 µV K−1 and -6.0 µV K−1 , respectively.

Conclusions We list below the general conclusions that can be inferred from our investigation of the thermoelectric response of aqueous solutions: • A key result from our analysis is that both the different mobility of the ions and the polarization of water play a key role determining the thermoelectric response of the solution. This result highlights the important role of solvation and water polarization defining thermoelectric effects in aqueous solutions. We find evidence that the thermal gradient induces local charge separation. Experiments of Seebeck effects have been interpreted in terms of charge separation at electrodes. It is therefore importat to analyze further the charge separation in the bulk region, as we have reported here, and its relevance in defining the Seebeck coefficient. • We find evidence for a reversal of the sign of the Seebeck coefficient for solutions at concentrations relevant to practical situations, 1 M. The Seebeck coefficient changes sign at this temperature, from positive at low temperature to negative at high temperature. This effect is particularly important in LiCl, and it can be explained as a result of the balance of the thermoelectric field contributions of the ions and water, and the dependence of these fields with temperature. Our results show that the Seebeck coefficients can be tuned by varying the temperature. The thermoelectric effect is predicted to cancel at a specific temperature,

15



which depends on the salt composition. This prediction awaits experimental verification. • The thermodiffusion response has been related before to the thermal expansion of water. 50 Such correlation implies that the temperature at which the Soret coefficient (or the Seebeck coefficient) changes sign would coincide with the temperature of the maximum density of water. The SPC/E features a maximum in density at 235 K 51 at 1 bar. Both the Soret and the Seebeck coefficients change sign at higher temperatures (260-320 K, depending on the salt considered). This result indicates there is not an obvious correlation between the thermal expansion of water and the Soret-Seebeck coefficients studied here. • Our results support the linear dependence of the Seebeck coefficient with the square root of concentration, which has been observed experimentally in high concentrated solutions of inorganic ions. Establishing this idea experimentally in aqueous solutions represents an important objective, which might allow a more accurate estimation of Seebeck coefficient at intermediate concentrations, 0.1–0.5 M, where non-equilibrium simulations are challenging, and infinite dilution predictions are expected to become inaccurate due to the increasing relevance of ionic correlations. The present work provides a background to extend the computational studies of Seebeck coefficients to other salts, including those that incorporate more complex ions, which might be relevant in capacitor and low carbon energy conversion applications.

Supporting Information Available The Supporting Information includes data of the thermal orientation of pure SPC/E water and local number fractions of cations and anions. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors thank the EPSRC (EP/J003859/1) and the Research Council of Norway (Project 16


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221675) for financial support, and the Imperial College High Performance Computing Service for providing computational resources. We also thank the anonymous reviewers for valuable comments regarding the charge separation and thermal expansion in solutions.

References (1) Ludwig, C. Diffusion Zwischen Ungleich Erw arten Orten Gleich Zusammengestzter L asungen; Sitz. Ber. Akad. Wiss. Wien Math-Naturw. KI., 1856; p 539. (2) Soret, C. Sur l’ état d’ équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogéne dont deux parties sont portèes á des tempèratures diffèrentes. Arch. Sci. Phys. Nat. 1879, 2, 48–61. (3) Snyder, G. J.; Toberer, E. S. Complex thermoelectric materials. Nature materials 2008, 7, 105–114. (4) Seebeck, T. J. Ueber die magnetische polarisation der metalle und erze durch temperaturdifferenz. Ann. Phys. (Berlin) 1826, 82, 253–286. (5) Anatychuk, L. On the discovery of thermoelectricity by Volta. J. Thermoelectricity 2004, 2, 5. (6) Yang, J.; Caillat, T. Thermoelectric materials for space and automotive power generation. MRS Bulletin 2006, 224. (7) Tritt, T. M. Thermoelectric phenomena, materials, and applications. Annu. Rev. Mater. Res. 2011, 41, 433. (8) Zhang, Q.; Sun, Y.; Xu, W.; Zhu, D. Organic thermoelectric materials: Emerging green energy materials converting heat to electricity directly and efficiently. Adv. Mater. 2014, 26, 6829–6851.

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(9) Bhatia, D.; Bairagi, S.; Goel, S.; Jangra, M. Pacemakers charging using body energy. J. Pharm. Bioall. Sci. 2010, 2, 51. (10) Agar, N.; Lin, J.-l. Single-ion heat of transport in electrolyte solutions. 1989, 3, 2079– 2082. (11) Würger, A. Transport in charged colloids driven by thermoelectricity. Phys. Rev. Lett. 2008, 101, 108302. (12) Reichl, M.; Herzog, M.; Götz, A.; Braun, D. Why charged molecules move across a temperature gradient: The role of electric fields. Phys. Rev. Lett. 2014, 112, 198101. (13) Vigolo, D.; Buzzaccaro, S.; Piazza, R. Thermophoresis and thermoelectricity in surfactant solutions. Langmuir 2010, 26, 7792. (14) Zhao, D.; Wang, H.; Ullah Khan, Z.; Chen, J.; Karlsson, R.; Jonsson, M. P.; Berggren, M.; Crispin, X. Ionic thermoelectric supercapacitor. Energy Environ. Sci. 2016, 9, 1450–1457. (15) Gunawan, A.; Lin, C.-H.; Buttry, D. A.; Mujica, V.; Taylor, R. A.; Prasher, R. S.; Phelan, P. E. Liquid thermoelectrics: Review of recent and limited new data of thermogalvanic cell experiments. Nanoscale and Microscale Thermophys. Eng. 2013, 17, 304–323. (16) Brown, B. R. Neurophysiology: Sensing temperature without ion channels. Nature 2003, 421, 495. (17) Brown, B. R. Temperature response in electrosensors and thermal voltages in electrolytes. J. Biol. Phys. 2010, 36, 121. (18) Fields, R.; Fields, K.; Fields, M. Semiconductor gel in shark sense organs? . Neurosci. Lett. 2007, 426, 166.

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Page 18 of 33

Page 19 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(19) Bresme, F.; Lervik, A.; Bedeaux, D.; Kjelstrup, S. Water polarization under thermal gradients. Phys. Rev. Lett. 2008, 101, 020602. (20) Iriarte-Carretero, I.; Gonzalez, M. A.; Armstrong, J.; Fernandez-Alonso, F.; Bresme, F. The rich phase behavior of the thermopolarization of water: from a reversal in the polarization, to enhancement near criticality conditions. Phys. Chem. Chem. Phys. 2016, 18, 19894. (21) Armstrong, J.; Lervik, A.; Bresme, F. Enhancement of the thermal polarization of water via heat flux and dipole moment dynamic correlations. J. Phys. Chem. B 2013, 117, 14817. (22) Wirnsberger, P.; Fijan, D.; Lightwood, R. A.; Saric, A.; Dellago, C.; Frenkel, D. Numerical evidence for thermally induced monopoles. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 4911–4914. (23) Abe, K.; Hyeon-Deuk, K. Dynamical ordering of hydrogen molecules Induced by heat flux. J. Phys. Chem. Lett. 2017, 8, 3595–3600. (24) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 2008, 4, 435. (25) Römer, F.; Lervik, A.; Bresme, F. Nonequilibrium molecular dynamics simulations of the thermal conductivity of water: A systematic investigation of the SPC/E and TIP4P/2005 models. J. Chem. Phys. 2012, 137, 074503. (26) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101. (27) Di Lecce, S.; Albrecht, T.; Bresme, F. The role of ion-water interactions in determining

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the Soret coefficient of LiCl aqueous solutions. Phys. Chem. Chem. Phys. 2017, 19, 9575–9583. (28) Di Lecce, S.; Albrecht, T.; Bresme, F. A computational approach to calculate the heat of transport of aqueous solutions. Sci. Rep. 2017, 7, 44833. (29) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The missing term in effective pair potentials. J. Phys. Chem. 1987, 91, 6269. (30) Dang, L. Development of nonadditive intermolecular potentials using molecular dynamics: solvation of Li+ and F− ions in polarizable water. J. Chem. Phys. 1992, 96, 6970. (31) Dang, L.; Garrett, B. Photoelectron spectra of the hydrated iodine anion from molecular dynamics simulations. J. Chem. Phys. 1993, 99, 2972. (32) Smith, D.; Dang, L. X. Computer simulations of NaCl association in polarizable water. J. Chem. Phys. 1994, 100, 3757. (33) Dang, L. Mechanism and thermodynamics of ion selectivity in aqueous solutions of 18-Crown-6 Ether: a molecular dynamics study. J. Am. Chem. Soc. 1995, 117, 6954. (34) Armstrong, J.; Bresme, F. Temperature inversion of the thermal polarization of water. Phys. Rev. E 2015, 92, 060103. (35) Glosli, J.; Philpott, M. Molecular dynamics study of interfacial electric fields. Electrochimica Acta 1996, 41, 2145–2158. (36) Iacopini, S.; Rusconi, R.; Piazza, R. The macromolecular "tourist": Universal temperature dependence of thermal diffusion in aqueous colloidal suspensions. Eur. Phys. J. E Soft Matter 2006, 19, 59.

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Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(37) Römer, F.; Wang, Z.; Wiegand, S.; Bresme, F. Alkali halide solutions under thermal gradients: Soret coefficients and heat transfer mechanisms. J. Phys. Chem. B 2013, 117, 8209. (38) Belkin, M.; Chao, S.-H.; Giannetti, G.; Aksimentiev, A. Modeling thermophoretic effects in solid-state nanopores. J. Comput. Electron. 2014, 13, 826. (39) Bresme, F.; Hafskjold, B.; Wold, I. Nonequilibrium molecular dynamics study of heat conduction in ionic systems. J. Phys. Chem. 1996, 100, 1879–1888. (40) Putnam, S. A.; Cahill, D. G. Transport of nanoscale latex spheres in a temperature gradient. Langmuir 2005, 21, 5317. (41) Würger, A. Transport in charged colloids driven by thermoelectricity. Phys. Rev. Lett. 2008, 101, 108302. (42) Majee, A.; Würger, A. Collective thermoelectrophoresis of charged colloids. Phys. Rev. E 2011, 83, 061403. (43) Majee, A.; Würger, A. Charging of heated colloidal particles using the electrolyte Seebeck effect. Phys. Rev. Lett. 2012, 108, 118301. (44) de Groot, S.; Mazur, P. Non-Equilibrium Thermodynamics; Dover Books on Physics Series; Dover Publications, 1984. (45) Eastman, E. D. Theory of the Soret effect. J. Am. Chem. Soc. 1928, 50, 283–291. (46) Agar, J. N.; Mou, C.; Lin, J. Single-ion heat of transport in electrolyte solutions: a hydrodynamic theory. J. Phys. Chem. 1989, 93, 2079. (47) Helfand, E.; Kirkwood, J. G. Theory of the heat of transport of electrolytic solutions. J. Chem. Phys. 1960, 32, 857.

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(48) Kang, T. J.; Fang, S.; Kozlov, M. E.; Haines, C. S.; Li, N.; Kim, Y. H.; Chen, Y.; Baughman, R. H. Electrical power from nanotube and graphene electrochemical thermal energy harvesters. Adv. Funct. Mater. 2012, 22, 477. (49) Bonetti, M.; Nakamae, S.; Roger, M.; Guenoun, P. Huge Seebeck coefficients in nonaqueous electrolytes. J. Chem. Phys. 2011, 134, 114513. (50) Brenner, H. Self-thermophoresis and thermal self-diffusion in liquids and gases. Phys. Rev. E 2010, 82, 036325. (51) Báez, L. A.; Clancy, P. Existence of a density maximum in extended simple point charge water. J. Phys. Chem. 1994, 101, 9837–9840.

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Page 22 of 33

H2O

300 200 100 -1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E [MV m ]

Page 23 of 33

20 0

+

-20

Li Cl

-100 -200 -300 260

280

300

T [K]

TOC Graphic

23


320

340

(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


TC

Page 24 of 33

TH

TC

(b) 400

T [K]

350 300 250 200

0

1

2

3 ACS Paragon 4 Plus Environment 6 5

z [nm]

7

8

9

10

10

Page 25 of 33

5

LiCl KCl NaCl NaI NaF

0

sT,1 x 10 [K ]

-10

-1

-5

4

3

3

-1

sT,1 x10 [K ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44


2

-15

NaCl KCl

0 -2 280

300

320

340

T [K] -20

240

260

280

300


T [K]

320

340

360

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Page 26 of 33

(a)

Page 27 of 33

-1

E [MV m ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LiCl

300

molecular

200

EM EP

100

z

EQ

EP + E

20

z

z

0

atomistic

ETOT Ewater ELiCl

-100 -200 -300

1

1.5

E [MV m ]

2

3

2.5

4

3.5

4.5

z [nm]

100 4 2 0

(c)

KCl

40 20 0 2

Ewater ETOT EKCl

0

NaCl ENaCl

ETOT

Ewater

-100

-20

-200

-40 1 1.5 2 2.5 3 3.5 4

1 1.5 2 2.5 3 3.5 4

(d)

(e)

NaI

200 100

E [MV m ]

zz

-20

200

-1

Qzz

EP + E + EM Q

(b)

-1

zz

6 3 0

100

Ewater ETOT ENaI

NaF

50

Ewater ETOT ENaF

2 0 -2

-100

-50

-200

-100

1 1.5 2 2.5 3 3.5 4


z [nm]

1 1.5 2 2.5 3 3.5 4

z [nm]

4

-4

-1

SE [10 V K ]

-1

SE [10 V K ]

3

-4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43


2

4

270 K 281 K 290 K

2

300 K 310 K 320 K 330 K

0 -2

1

Page 28 of 33

1

0 1/2

c

2

3

-1 1/2

[mol kg ]

0 -1

1.0 mol kg

-1

-1

2.1 mol kg

-1

3.4 mol kg

-1

4.7 mol kg

-2 250 260 270 280 290 300 310 320 330 340 350 ACS Paragon Plus Environment

T [K]

Page 29 ofThe 33 Journal of Physical 300 O HChemistry 2

200 100 -1

E [MV m ]

1 2 3 4 5 6 7

20 0

+

-20

Li Cl

ACS Paragon -200 Plus Environment -100

-300 260

280

300

T [K]

320

340

T [K]

-1

E [MV m ]

-3

ρ [kg m ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

350

∇T = 0 ∇T ≠ 0


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300 250

1000 900

10 0 -10 0

2

4


6

z [nm]

8

10

Page 31 of 33

20 E EP

E [MV m ]

10

EQ

-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43


zz

EP + EQ

zz

0

-10

-20 1

1.5

2

2.5


3

z [nm]

3.5

4

4.5

5

-4

-1

E/∇T [10 V K ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43


Page 32 of 33

RES - 600 bar UNRES - 350 bar

4 3 2 1

~326 K

0 ~320K

-1

240

260

280

300 T [K]


320

340

(a)

Page 33 of 33

n± / (n+ + n-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LiCl 0.52 +

Li Cl

0.51

0.5

0.49

0.48 0.5

1

1.5

2

2.5

3

4

3.5

z [nm]

(b)

(c)

KCl

NaCl

0.52

0.52

n± / (n+ + n-)

+

KCl

0.51

+

0.5

0.49

0.49

0.48

0.48

1

2

3

4

NaCl

0.51

0.5

(d)

1

2

3

4

(e)

NaI

NaF

0.52

0.52 +

n± / (n+ + n-)

4.5

Na I

0.51

+

0.51

0.5

0.5

0.49

0.49

0.48

1

2

3

z [nm]

4

Na F

0.48


1

2

3

z [nm]

4

Thermal Polarization of Water Influences the Thermoelectric

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