W.-S Zhang et al: Effects of temperature on loading ratios of H(D) in Pd...

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1 Conference Proceedings Vol. 70 ˆICCF8 F. Scaramuzzi (Ed.) SIF, Bologna, 000 Effects of emperature on Loading Ratios of Hydrogen (Deuterium) in Palladium Cathodes under the Galvanostatic Condition W.-S. Zhang a,, Z.-L. Zhang a and X.-W. Zhang a Institute of Chemistry, Chinese Academy of Sciences, P.O. Box 709, Beijing P.R. China; wszhang@a-1.net.cn; Fax: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009 Beijing , P.R. China Astract On the asis of the thermokinetics of the hydrogen (deuterium) evolution reaction and the thermodynamics of PdH(D) system, we analytically and numerically discuss effects of temperature on the loading ratio of hydrogen (deuterium) asorption into electrodes of β-phase PdH x (PdD x ) under the galvanostatic charging condition. It is found that the change of the loading ratio with temperature depends on the asorption enthalpy, adsorption enthalpy and apparent activation energy of the exchange current density of the afel reaction. Our theoretical predictions fit the availale experimental results well. 1. Introduction It is verified experimentally that the anomalous excess heat production in the Pd D O electrolytic system depends on the D/Pd ratio, the space gradient of deuterium concentration and cell temperature etc. [1-3]. However, ecause not all of these variales are orthogonal, it is necessary to estalish their dependent relation in further research. One of these relations is the loading ratio as a function of temperature [4-8]. Mengoli et al have found that the loading ratio of D in Pd, x D decreases with temperature y a slope of x D / K 1 under the potentiostatic charging condition in the temperature range from 5 C to 90 C [4]. he same group have also found that x H / K 1 under the galvanostatic charging condition and x H / K 1 under the potentiostatic charging condition with the H 3 PO 4 electrolyte from 5 C to 175 C [6]. In addition, Asami et al found that x D / K 1 from 5 C to 80 C [8]. Although these temperature effects can e explained qualitatively y the thermodynamics of PdH(D) system [9] and the kinetics of the hydrogen evolution reaction (HER) [10 13], the quantitative analysis is asent up to now. In this paper, we will deal with this suject in detail.. Model Consider hydrogen asorption into a PdH x electrode in the HER (taken to include D, the same elow). At the outer surface, there are three steps, i.e. the Volmer, afel and penetration reactions taking place at the same time [10,11]. he rate of the Volmer step is the applied current density (CD) and the rate of the afel step is: 05

2 j E Usθ E Usθ = r s F A f (1 θ) A θ (1) Because the penetration reaction is very rapidly, it is in pseudo-equilirium [11] and we have the isotherm: θ Usθ Ss = 1 θ R H s x 1 x U x In Eqs. (1) and (), A and A are the Arrhenius frequency factors of the rate constant for H dissociation and H comination reactions; E and E are the corresponding activation energies; U is the non-ideal interaction energy of H in the ulk of the β-pdh x, U = 44.9 kj mol 1 for oth H and D [9]; U s is the heterogeneity energy of the Frumkin adsorption, its value depends on the additives in the electrolyte and ph value; f is the fugacity of H gas; x is the H/Pd atomic ratio; r is the surface roughness factor; Γ s = mol H cm, is the maximum H molar numer of availale sites per real unit area; θ is the fractional surface coverage of H on Pd. he other symols have their usual meanings. 3. Results 3.1. Equilirium state Prior to detailed discussing the situation of HER, we focused on the equilirium state. o e specific, the electrode reaction is confined to the normal condition of f = 1 atm and 0 C 100 C. he first assumption means that the partial pressure of hydrogen is equal to that of circumstance, this can e realized through carrying out experiment under H gas atmosphere or lowing hydrogen gas from the ottom of cell. Although many experiments are employed without the lowing H gas and the initial state differs from this equilirium state, the hydrogen ules produced in the HER makes the H partial pressure is approximately equal to 1 atm, hence the corresponding equilirium state is the same as that in the hydrogen atmosphere. hese choices of pressure and temperature ensure the PdH system is in the β-phase in equilirium or in the HER. We can otain the exchange CD (per real unit area) of the afel reaction as a function of. Contrary to one s expectation, it is the weak adsorption rather than the strong adsorption dominates the H asorption into the β-pdh x electrode as verified experimentally and theoretically [10 1]. herefore, the Frumkin adsorption reduces to the Langmuir type with U s θ 0 and 1 θ 1. he exchange CD of the afel step is: E j = S FA f H exp (3) with E = H gs E, is the apparent activation energy of j, and it was oserved that E = 7 kj mol 1 in 0.5 M H SO 4 [10]; H gs is the adsorption enthalpy of H on Pd. It is easy to otain the relationship etween the hydrogen pressure and the loading ratio using Eq. () and the equilirium result of Eq. (1): f 1/ Sg Hg x U x = exp (4) R 1 x () 06

3 with S g = S s R/ ln(a / A ) and H g = H s (E E )/. his equation is exactly the isotherm of H asorption into the β-pdh x, it is found that S g = 53.5 and 53.1 J mol 1 K 1, and H g = 50.1 and 47.7 kj mol 1 for H and D, respectively. Although changes of entropy and enthalpy in each step may e influenced y the Pd surface property or solution composition, their sums must e constant values as are indicated y Eq. (4). he loading ratio changing with temperature under a fixed pressure is: x = H g U x 1 U x(1 x) which is K 1 for oth H and D in Fig. 1, the curve j = 0. hese curves are the isoar of H(D) asorption into the β-pdh x (PdD x ) under 1 atm pressure. (5) x H (H/Pd) coupled Volmer-afel mechanism (a) - j/ma cm - = fast Volmerslow afel mechanism temperature / o C x D (D/Pd) 0.90 coupled Volmer-afel () mechanism fast Volmerslow afel mechanism temperature / o C - j/ma cm - = Figure 1. Effects of temperature on the loading ratio for (a) H, and () D asorption into a β-phase Pd H(D) electrode under the galvanostatic charging condition. Current densities are shown esides each curve. he parameters: A = cm atm 1 mol 1 s 1, A = cm mol 1 s 1 ; E = 7, E = 83, U s = 15 kj mol 1 ; H s = and 19.8 kj mol 1 for H and D respectively; S s = J mol 1 K 1 ; r = 1, f = 1 atm. 3.. Fast Volmer slow afel mechanism Because there are two mechanisms of the HER, i.e. the fast Volmer slow afel type at low CD in acidic solution and coupled Volmer afel type in asic solution or at high CD in acidic solution, taking place on the Pd electrode, we will discuss the steady-state asorption in these two situations successively. For the first mechanism, the afel step is irreversile and the Volmer reaction is in pseudo-equilirium, the value of θ is small and the adsorption can e simplified to the Langmuir type as in discussion aout j. Sustituting Eq. () into Eq. (1) gives: 07

4 j = j Ss x Hs U x E = r s FA (6) R 1 x which descries x as a function of j. Hence we otain the loading ratio changing with temperature: x H = g U x E / 1 U x(1 x) which is K 1 for H and K 1 for D in Fig Coupled Volmer afel mechanism Consider the HER is far from equilirium, oth the Volmer and afel steps are completely irreversile. he adsorption is the Frumkin type at intermediate surface coverage, this means the exponent term is prominent in the hydrogen adsorption isotherm. Eliminating the factor exp(u s θ/) etween Eqs. (1) and () gives: j = j S s x Hs U x E = r s Fθ (1 θ) A (8) R 1 x this equation descries the relation etween j and x. We can otain the loading ratio changing with : x Hgs = H g U x E 1 U x(1 x) which is K 1 for H and K 1 for D in Fig. 1. In the deduction, the contriution originated from the term θ(1 θ) is omitted as it is a slowly varying quantity. Fig. 1 shows x changing with ased on Eqs. (1) and () under the galvanostatic charging condition. he related parameters, noted in the caption of Fig.1, result in θ 0 = 0.01 and j = 0.01 ma cm at K. hese choices ensure the adsorption in equilirium is weak; the HER is along the fast Volmer slow afel mechanism while j 1 ma cm or the coupled Volmer afel mechanism while j >> 1 ma cm around the amient temperature. he activation energies are chosen to ensure that E = 7 kj mol 1, H g = 50 kj mol 1 for H and 47.8 kj mol 1 for D as were oserved experimentally [9,10]. All of these parameters are adjusted to simulate the HER in the aqueous acidic solution under the circumstance pressure although our method and conclusion are eyond this confinement. We find the amplitude of x/ increases with increasing CD and/or decreasing temperature. he dependence of x/ on is easy to understand y Eqs. (5), (7) and (9) in which the amplitude of x/ is inversely proportional to. As far as the effect of CD is concerned, we find the HER changes from the equilirium state to the fast Volmer slow afel mechanism and up to the coupled Volmer afel mechanism with increasing CD, and corresponding x/ is expressed y Eqs. (5), (7) and (9), respectively. Because the terms H g U x, H gs and E in the numerators have the same sign (< 0), so the increase of x/ with CD is ovious. (7) (9) 08

5 he change of x with has two origins: one is the thermodynamic contriution as the isoar shown in Fig. 1 or indicated y Eq. (5) and the same term appeared in Eqs. (5), (7) and (9); another is caused y the kinetic process. A crude ut intuitive explanation can understand the reasons of x changing with. Because x is determined y the relative CD, j/j [1], so changes of j/j reflect the change of x in some way. For the galvanostatic charging, j increases with ; this makes j/j decreases with, hence x decreases some more rapidly than in the equilirium case. By comparison our theory with experimental results in Ref. [6,18], we find that x H / K 1 and x D / K 1 under the galvanostatic charging condition lie in the corresponding ranges of our results shown in Fig. 1, although the relevant experimental parameters are not availale. his indicates our theory is appropriate. 4. Discussions In this paper, we specifically discuss the situation of HER in the acidic solution; there is a change of HER mechanism from the fast Volmer slow afel type to the coupled Volmer afel type with increasing CD. But for the asic solution, the valid CD range for the fast Volmer slow afel mechanism is very narrow even disappears; otherwise, the coupled Volmer afel mechanism dominates the HER in a wide CD range due to a small value of j 0V /j and a large heterogeneity energy U s [10]. Of course, our method and results can e applied to this situation with some parameters modified. On the other hand, additives and Pd alloy electrodes are always used to improve the electrode performance for H asorption in experiments. heir effects can e manifested y the same formulae with some parameters adjusted as well. In the paper, we mainly discuss the loading ratio changing with j under the galvanostatic charging condition. However, our theory can e applied to the prolem for the maintenance the loading ratio y increasing the amplitude of j at high temperature. he solution is directly given y Eqs. (6) and (8). It must e pointed out that our theory is more phenomenological than fundamental. A general treatment should e ased on the asolute rate theory and consider sutle effects of temperature on all aspects of the Pd H electrode process, e.g. the temperature dependence of solute activity, the activation free energy of each step and other related issues. Of course, it needs more experiment details as well. However, our results give the most primary effects and there are some experiment evidences supporting our conclusions. Although the systematic experimental study on this suject is asent up to now, we hope our work can stimulate further researches on this issue. Acknowledgements he work is supported y the Natural Science Foundation of China under Grant No , President Innovation Foundation in Chinese Academy of Sciences, Pan-Deng Project of Department of Science and echnology of China under Grant No. 95 YU 41 and Foundation of China Academy of Engineering Physics. References [1] MCKUBRE M.C.H., CROUCH-BAKER S., RILEY A.M., SMEDLEY S.I. AND ANZELLA F.L.: in Frontiers of Cold Fusion, Proc. 3rd Int. Conf. on Cold Fusion, 09

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