Modeling of Processes in Fuel Cells Based on Sulfonic Acid Membranes and Platinum Clusters 1

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1 ISSN , Russian Journal of Electrochemistry, 2013, Vol. 49, No. 8, pp Pleiades Publishing, Ltd., Original Russian Text T.S. Zyubina, A.S. Zyubin, Yu.A. Dobrovol skii, V.M. Volokhov, R.V. Pisarev, A.V. Pisareva, L.V. Shmygleva, 2013, published in Elektrokhimiya, 2013, Vol. 49, No. 8, pp Modeling of Processes in Fuel Cells Based on Sulfonic Acid Membranes and Platinum Clusters 1 T. S. Zyubina z, A. S. Zyubin, Yu. A. Dobrovol skii, V. M. Volokhov, R. V. Pisarev, A. V. Pisareva, and L. V. Shmygleva Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Russia Received August 2, 2012 Abstract The density functional theory with account for gradient correction (DFT/PBE) and periodical boundary conditions was used to model the main stages of processes occurring in hydrogen low-temperature fuel cells. Modeling was carried out at the example of calculation of catalytic anodic and cathodic processes occurring on the surface of the Pt 19 catalyst supported on a SnO 2 and water adsorption processes on the surface of a membrane represented by a crystal of metisylene sulfonic acid dihydrate [( CH3) 3C6H2SO 3 HO 5 2 ]. It was shown that the most energy efficient process in the membrane is formation of crystals, in which two stoichiometric water molecules correspond to a single SO 3 H group. Superstoichiometric water is adsorbed on the crystal surface with the adsorption energy of ev; its transition inside the crystal is energy-consuming (2 ev). Barriers of surface proton conductivity are ev. Keywords: mesitylene sulfo acid dihydrate, quantum-chemical calculations, PAW/PBE, proton conductivity, fuel cells, membranes, platinum cluster DOI: /S INTRODUCTION The functioning of polymer fuel cells (PFCs) and sensors is based on electrocatalytic processes. Interest towards such processes has especially increased due to development of resource-conserving and environmentally safe power sources. The understanding at the microlevel of elementary processes and the detailed mechanism of electrocatalysis and transport processes in SPE results in improved control of chemical reactions and makes it possible to design the most effective catalysts. This is one of the ways to cheapen SPE manufacturing due to a decrease in the cost of platinum catalysts, overcome energy losses in the oxygen reduction reaction, and increase the life cycle of electrodes and membranes. In this work, we present results of considering the initial stage of fuel cell operation at the molecular level. CALCULATION TECHNIQUE In the calculation, a quantum-chemical method was used with account for periodic boundary conditions, an approximation based on the local density functional with gradient correction (DFT/GGA = PBE) [1, 2]; the chosen energy limit was 400 ev, the wave function was chosen in the form of a mixture of 1 Published on the basis of the lecture in XI Meeting Fundamental Problems of Solid State Ionics, Chernogolovka, z Corresponding author: zyubin@icp.ac.ru (T.S. Zyubina). components of different multiplicity; their contributions were determined on the basis of the full energy minimum; the VASP software complex was used in the work [3 7]. In the modeling, the projector augmented wave (PAW) basis [7] with the corresponding pseudopotential (a 4 8 layered repetitive units of atoms ((SnO 2 ) 48 (SnO 2 ) 96 ) for the support and a repetitive unit of 257 atoms ({[H 2 C 6 (SO 3 H)(CH 3 ) 3 ](H 2 O) 2 } 8 for the membrane) was used for multiplication in space. Such an approach provides the calculation accuracy of equilibrium distances of Å, of relative energies of ev, and of XPS chemical shifts of ev. The calculation method is described in detail in [8 16]. As seen in the table, crystal parameters and equilibrium distances in the systems under consideration can be obtained with the accuracy of 1 3% in respect to the experimental values. An exclusion is hydrogen bonds that feature a rather great scatter of values both in calculation and in the experiment, due to which the relative error in the description grows to 4 12%. The sublimation heat is described to the accuracy of 6.6%; the adsorption energy of hydrogen and oxygen is described to the accuracy of 0 13%. CALCULATION RESULTS Anode. On the basis of our calculations in [8 13], one can state that barrierless adsorption (and dissociation) of molecular hydrogen on the surface of a platinum cluster supported on SnO 2 on the anode results 788

2 MODELING OF PROCESSES IN FUEL CELLS 789 Parameters of crystals of SnO 2, Pt, and mesitylene sulfonic acid dihydrate, equilibrium distances, sublimation heat, and energy of adsorption obtained in calculation and experiment Crystal parameters* Calculation Experiment** Δ, % SnO 2 [19] a/å b/å c/å S O 1.45, 1.47, , 1.45, Pt [19 ] Pt Pt, Å Sublimation heat D e /n, ev Adsorption energy E a (H 2 ), ev (t) 1.07, Q 0, calorimetry, platinum fiber; [20] 0.98, 0 11 Pt (111) Q 0, calorimetry, platinum fiber, Pt on SiO 2 [21] Adsorption energy E a (O 2 ), ev (t), Pt (111) 2.9 Pt foil, calorimetry; [22] 2.2, Pt(111), Q 0, thermodesorption [23] Mesitylene sulfonic acid dihydrate [17] O w O 2.62, 2.67, , O w O w , H O 1.60, 1.66, , 1.79, HO w O Note: Distances O w O are equilibrium distances between the oxygen atoms in a water molecule (O w ) and SO 3 groups (O), accordingly. The HO w O angle is the angle between hydrogen (H), water oxygen (O w ) and oxygen of the SO3 group (O). ** Powder Diffraction File. Data Cards. Inorganic Section. Sets JCPDS. Swarthmore, Pennsylvania, USA, in transition of atomic hydrogen to the support surface. Adsorption energy of H 2 on the edge of the top surface of a Pt 19 cluster is 1.6 ev (Fig. 1). With low barriers of ev, hydrogen atoms migrate to the support across the edge of the side surface of a platinum cluster. The energy evolved in the course of motion of hydrogen atoms from the upper surface of the Pt 19 cluster to the SnO 2 surface is 1.4 ev (Fig. 1). This energy is sufficient for motion of platinum clusters across the SnO 2 surface. The energy of adhesion of two Pt 19 clusters to each other (9.1 ev) is close to the energy of interaction between the same surfaces and SnO 2 (001) surface, ev. The less active surfaces have still lower energies of interaction of a Pt 19 cluster with the support, e.g., this value for the SnO 2 (110) plane is 8.0 ev. This could explain the experimentally observed motion of platinum atoms across the surface and aggregation of platinum particles in the course of electrocatalysis due to coalescence of finer particles. Cathode. A proton is transported from the anode through the membrane via the relay mechanism (that will be considered in detail below at the example of mesitylene) to the region close to the platinum cluster on the cathode, where it forms a water molecule with the oxygen molecule adsorbed on the cluster (Fig. 1). The oxygen molecule is adsorbed in a barrierless process on the edge of the side surface of a Pt 19 cluster forming various isomers of peroxide type with the energy of ev. Dissociation of an oxygen molecule on the surface of a Pt 19 /SnO 2 cluster is an energetically favorable process (by 0.10 ev) occurring with a barrier of 0.49 ev. This dissociation corresponds to a transition from a peroxide (p) isomer to an isomer (m) with singly coordinated oxygen atoms. The dissociation barrier of an oxygen molecule at the edge of the Pt 19 /SnO 2 cluster decreases at an approach to the SnO 2 (001) support surface: the barrier is 0.5 ev at the level of layers 2 and 3 of platinum atoms from the support surface and 0.3 ev at the level of layers 1 and 2 of platinum atoms. The transition barrier from an isomer with a singly coordinated (m) oxygen atom to the isomer with a doubly coordinated (b) oxygen atom is in the range of ev and the lower its value, the closer the oxygen atom to the SnO 2 surface. Formation of an OH fragment on the tin dioxide surface from an O 2 molecule with participation of a Pt 19 /SnO 2 /H 2 cluster is an energetically favorable process; correspondingly, the energy of 3.29 ev is released. However, two barriers have to be overcome for this process: 0.5 ev for dissociation of an O 2 mole-

3 790 ZYUBINA et al. 0 A M C Pt 19 /SnO 2 H 2 O 2 nh 2 O 1.61 E a = nh 2 O H 3 O Ea = H O Sn 4.74 nh 2 O E a = 0.5 H 3 O E a = Fig. 1. Calculated model of operation of a polymer fuel cell. (A) The anode region, (C) cathode region, (M) membrane region. Energies are given in ev. cule and ev for a transition of the oxygen atom from a platinum atom to a tin atom (that is energetically unfavorable by 0.26 ev). Consequently, it is energetically favorable that an oxygen atom should stay bound to the platinum atom up to formation of water or an OH fragment. But the immediate transition of a hydrogen atom from the SnO 2 support surface to the platinum cluster, as shown above, is also energetically unfavorable; therefore, one should look for another scenario allowing energetically favorable formation of an OH fragment with low barriers. Calculations showed that there is a more energetically favorable path for formation of an OH fragment, apart from direct migration: it is the relay mechanism of motion of a proton via proton-conducting channels. In the presence of a conductivity channel, the proton from the SnO 2 surface passes to the closest water molecule that yields its proton to the neighboring water molecule and, in a chain, the last water molecule acquires a proton from the last but one molecule and yields its proton to oxygen on the platinum cluster for formation of an OH fragment. The calculated reaction of relay migration of a proton with formation of a water molecule is exothermic by 0.3 ev at the first stage (OH formation) and endothermic by 0.3 ev at the second stage (H 2 O formation). This process occurs with the barriers of 0.5 ev (at the O O distances of Å) depending on the distances between the oxygen atoms of water molecules forming protonconducting channels. Let us point out that formation of a Pt H bond as a result of the relay mechanism on the cluster surface is much (by 1.4 ev) less favorable as compared to formation of the OH bond, so that all the arriving protons will interact with oxygen and not platinum. A similar process of the relay transport (but with a high activation barrier) can also be observed for the peroxide isomer. The main difference is observed in the region where the O O peroxide structure is broken and an OH fragment and singly coordinated oxygen atom are formed in the presence of H 3 O (with the barrier of 0.24 ev). Due to endothermicity at the last reaction stage, the formed water molecule must be removed from the cluster. Otherwise, the process on the cathodic platinum cluster can occur in a cycle: water decomposition to two OH fragments in the interaction with atomic oxygen and reverse process of water molecule formation of the two neighboring OH fragments with low energy losses ( ev). On the whole, the process of addition of the oxygen molecule to the Pt 19 /SnO 2 /H 2 cluster and breaking off of the water molecule formed in the interaction (Pt 19 /SnO 2 /H 2 O 2 Pt 19 /SnO 2 /O H 2 O) is energetically favorable by 1.6 ev. Thus, one can state that molecular hydrogen is adsorbed at the initial stage of operation of the polymer fuel cell at the anode on the surface of a platinum cluster supported on SnO 2. Due to the spillover effect, this results in a transition of atomic hydrogen on the support surface, from where it is transported through

4 MODELING OF PROCESSES IN FUEL CELLS 791 the membrane via the relay mechanism to the cathode, where it interacts with oxygen adsorbed on the platinum cluster surface, as a result of which a water molecule is formed on it. The described process is exothermic by 4.64 ev and occurs with barriers determined by the capability of the membrane to form proton-conducting channels. In the case of the membrane providing distances between proton-conducting oxygen atoms close to Å, conductivity barriers via the relay mechanism are ev. On the whole, the process can be represented in the form of a scheme shown in Fig. 1. Membrane. Studies of electrochemical processes of proton transport in polymer membranes represent a topical problem both from the fundamental and applied viewpoint. To understand the structure of proton conducting polymer membranes and the mechanism of proton transport in them, we used a quantum chemical calculation in [14, 15] to model individual aromatic sulfonic acids (SA) in the presence of polyvinyl alcohol (PVA), water, and aldehyde. The crystal of the studied phenolsulfonic acid (PSA), 2,4-PSA 2H 2 O represents a layered structure, in which each of the corrugated layers consists of anions of acid molecules bound through a H 3 O ion (Fig. 1). To estimate the mutual effect of the amount and position of functional groups, various phenolsulfonic acids were calculated. It turned out that acids with 2 or 3 sulfo groups and a single OH fragment are more stable towards breaking off of a water molecule. Studies of sodium and rubidium salts of phenol- 2,4-disulfonic acid and 2-phenolsulfonic acid and their mixed salts showed that motion of hydrogen along the SO 3 group is independent of the presence of a metal cation at the opposite end of an acid molecule. The very metal cations attach several water molecules consistently with the energies of ev. To understand how the proton transport occurs in complexes, which may lead to an increase in conductivity, what combination of components is to be considered more favorable as regards conductivity, and addition of which components and in what amounts should (according to the model) hinder conductivity, we modeled the process of proton transport in a membrane consisting of molecules of phenolsulfonic acid (C 6 H 4 OHSO 3 H, PSA), water ((H 2 O) i, i = 1 4), polyvinyl alcohol (C 5 H 9 (OH) 3, PVA), and dialdehyde (C 3 H 4 O 2 ) in various combinations. According to calculations, the relay mechanism is more favorable for a complex of sulfonic acid and water than rotation of the HSO 3 group or direct proton transport. Physical properties of membranes are noticeably improved when polyvinyl alcohol is added to them. It was shown in calculations that there is at least a single water molecule near each SO 3 group that allows forming a stable complex with a strong hydrogen bond due to formation of Н 3 О ions located between acid molecules. The most favorable structure is an isomer in which PSA and PVA are connected by hydrogen bounds through a water molecule. Under the conditions of water shortage, protons of the OH group of polyvinyl alcohol and acid are also involved in formation of a network of hydrogen bonds. An alcohol molecule is located in a corrugated crystal plane between the acid molecules and strengthens their layered structure. According to calculations, the role of polyvinyl alcohol is reduced to the ordering of positions of acid molecules and participation in the relay mechanism of proton transport. The presence of aldehyde within the membranes results in development of a rigid and rather regular polymer matrix structure. Addition of small amounts of aldehyde to the membrane leads to interaction between the aldehyde and alcohol through OH fragments of polyvinyl alcohol, which, under high humidity, should weakly affect the value of proton conductivity. Membrane crystals connected by hydrogen bonds are unstable towards degradation under the action of water. The strengthening of a crystal by polymers of the type of polyvinyl alcohol with its long molecules extended along the planes of sulfonic acids secures the crystals from degradation up to relative humidity of 95% and increases conductivity by 5 orders of magnitude. Cross-linking by aldehydes improves the physical parameters of membranes. According to calculations, the low degree of cross-linking stabilizes and strengthens the channels of proton conductivity. The interaction between the aldehyde and alcohol occurs with participation of OH fragments of polyvinyl alcohol. According to calculation, a water molecule is added to the acid molecule in a barrierless process. As the barrier is decreased from 0.3 to 0.01 ev at an increase in the amount of water molecules near the HSO 3 group (from one to four), the mechanism of proton transport herewith occurs with participation of not only H 3 O ions, but also of HO 5 2 that are easily converted into one another. Therefore, one could expect improvement of conductivity at an increase in humidity under experimental conditions, which wholly agrees with the experimental data. To find out whether the process of proton conductivity occurs similarly in all sulfonic acids and whether it is a surface or a bulk process, we calculated the structure of a crystallohydrate of phenol-2,4-disulfonic acid 2H 2 O [16] and showed that the positioning of a superstoichiometric water within the crystal is energetically unfavorable by 2.6 ev (but water that by some chance arrived inside cannot any more leave the crystal due to the hindering energy barrier). On the contrary, presence of adsorbed superstoichiometric water on the crystal surface is energetically favorable and improves its proton conductivity. Specific (i.e., per single water molecule) energy of adsorption of supers-

5 792 ZYUBINA et al. S O C H (a) (b) C(9) C(5) O(W(1)) C(6) O(1) O(2) S(1) C(1) O(W(2)) O(3) toichiometric water on the surface of a crystal (phenol-2,4-disulfonic acid 2H 2 O nh 2 O) is ev. As theoretical aspects of the dependence of proton conductivity on humidity and elementary stages of proton transport in polymer sulfonic acids are at present poorly studied, we investigated this process at the example of mesitylene sulfonic acid dihydrate [( CH3) HO 5 2 ], in which the crystal is formed on the basis of the fragment of HO 5 2 (Figs. 2 and 3). According to X-ray diffraction analysis [17] and our calculations [18], the crystal structure of mesitylene sulfonic acid dihydrate [( CH3) HO 5 2 ] includes asymmetric cations HO 5 2 obtained from two molecules of stoichiometric water connected C(7) C(2) C(8) C(4) C(3) Fig. 2. (a) Independent part of the structure and (b) structural fragment of {[H 2 C 6 (SO 3 H)(CH 3 ) 3 ](H 2 O) 2 } 8 multiplied in the space in calculation of a crystal of mesitylene sulfonic acid dihydrate. by a hydrogen bond inside the cation (O O = 2.43 Å, calculation). Presence of a superstoichiometric water molecule within the crystal bulk in energetically unfavorable by 2.1 ev (but water that has arrived into the bulk can no more leave it due to the presence of hindering barriers). Addition of a single superstoichiometric water molecule to the dihydrate crystal surface [( CH3) HO 5 2 ] is energetically favorable by ev. We consistently increased the amount of water molecules and brought it to such a level, at which a single molecule of superstoichiometric water corresponds to a single molecule of stoichiometric water. This allowed us to state that at the sites where the surface is covered by water, barriers of proton migration decrease almost by half and conductivity is significantly improved. One could also expect that formation of proton conducting paths on the surface requires at least a single additional water molecule per each surface stoichiometric water molecule; a lower amount cannot provide sufficiently regular low barriers for proton migration. Therefore, a conductivity channel can be formed on the surface from crystal surface molecules and n superstoichiometric water molecules per stoichiometric surface water molecule. Movement of proton along this channel via the relay mechanism causes the movement of protons in the whole channel. Proton conductivity occurs via the relay mechanism on the crystal surface with the activation energy of ~0.2 ev in the regions where a single surface water molecule corresponds to at least one superstoichiometric water molecule and 0.5 ev at the sites where there is no superstoichiometric water on the surface. At an increase in amount n of superstoichiometric water from zero and above, one could expect the presence of a certain minimum amount n 0, starting from which proton conductivity appears and before which the proton conductivity channels are irregular. Taking into account that hydrogen bridges on the surface formed by superstoichiometric water molecules are geometrically more mobile and fulfill the necessary and sufficient conditions for proton conductivity better than stoichiometric water molecules forming bonds in the crystal, one can state that conductivity in sulfonic acids occurs largely across the crystal surface. Accordingly, the dependence of proton conductivity on humidity can be explained by presence of superstoichiometric water molecules on the surface of a crystal of mesitylene sulfonic acid dihydrate [( CH ) C H SO HO ] ACKNOWLEDGMENTS Calculations were carried out in the Supercomputer Center of Lomonosov Moscow State University.

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