Oscillatory Rates of Heat Evolution during Sorption of Hydrogen in

J. Phys. Chem. C 2008, 112, 18483–18492

18483

Oscillatory Rates of Heat Evolution during Sorption of Hydrogen in Palladium Erwin Lalik,*,† Jerzy Haber,† and Aleksander J. Groszek†,‡ Institute of Catalysis and Surface Chemistry, Polish Academy of Science, ul. Niezapominajek 8, Krakow 30-239, Poland, and Microscal Limited, 79 Southern Row, London W10 5AL, U.K. ReceiVed: June 19, 2008; ReVised Manuscript ReceiVed: September 25, 2008

The oscillatory character of sorption of H2 in Pd has been observed for the first time by measuring the oscillating rate of heat evolution accompanying the reaction. The process was investigated by using isothermal flowthrough microcalorimetry with in situ calibration to monitor the sorption of gaseous hydrogen in palladium powder at 105 °C from a mixture of H2/N2 at various H2 molar fractions and flow rates. The microcalorimetric measurements made it possible to determine the conditions at which the well-known reaction of H2 and Pd reaches the oscillatory regime. One of these conditions is that the total pressure of the gas phase within the system needs to be lowered initially to ∼600 hPa before admitting the reaction mixture. The oscillatory behavior occurs then at the molar fraction of H2 ranging from 0.83 to 0.92 and the flow rate of the reaction mixture between 1.2 and 2.2 cm3/min. The oscillations are nonsinusoidal, periodic, or quasiperiodic with the period length varying from 50 to 30 s. The frequency was found to be a strong function of the flow rate. The oscillatory dynamics appears to be very sensitive to even slight variations of certain parameters; nevertheless, no chaotic behavior was observed under the conditions investigated. Provided that all important reaction conditions were kept constant, the oscillatory behavior shows remarkable short-term reproducibility; that is, nearly identical series of oscillations could be recorded for a pair of consecutive experiments. An effect of sample aging was also noted, however, in the form of a marked tendency to quasiperiodicity increasing for samples over their repeated exposure to hydrogen. The total heat of sorption was found invariant, irrespective of the oscillations changing character. It has been confirmed by a statistically significant number of experiments that when the oscillatory behavior occurs during the sorption, it does not affect the total amount of heat produced upon the reaction. 1. Introduction Palladium metal is unique in at least two different ways: as a material for membranes and as a catalyst. Its ability to dissolve gaseous hydrogen reversibly is a prerequisite for its application as a membrane material for hydrogen separation.1,2 As a catalyst in heterogeneous oxidation, palladium is one of few metals that have long been associated with the unusual phenomena of oscillatory kinetics.3,4 The reaction of hydrogen with palladium seems to be unique in the sense that palladium hydride is being formed directly and under mild conditions by simply contacting gaseous H2 with metallic Pd. Its thermal effect is relatively low for a chemical reaction, being only around 40 kJ/molH2.5-10 The palladium hydride appears to be an example of a solid of which one component remains in equilibrium (presumably a dynamic one) with its gaseous form, which means that its stability and composition are a function of the component’s molar fraction in the gas phase.11 Indeed, palladium hydride can decompose nearly as easily as it is formed. Desorption of hydrogen from palladium can be initiated simply by removal of hydrogen from the gas phase, but at ambient pressure and temperature, it takes ∼20 h for the process to be completed.12 It proceeds much faster in vacuum, where a 15 min period is enough for total evacuation at RT, or at pressures about normal and a temperature around 100 °C, where the desorption takes less than 2 h. Both the sorption and the desorption have a * Phone: +48126395189. Fax: +48124251923. E-mail: nclalik@ cyf-kr.edu.pl. † Polish Academy of Science. ‡ Microscal Limited.

complicated kinetics, also showing hysteresis phenomena.13 The latter influence the behavior of palladium catalysts in hydrogenation reactions so that the catalytic performance appears to be as much a function of the actual reaction conditions as it is a function of a way that a given set of the reaction conditions has been reached. Oscillatory behavior has been noted in the hydrogenations of CO14 and acetylene,15 but considering the notoriously complex kinetics of Pd-catalyzed hydrogenations, the cases are surprisingly few. In the oxidative processes, on the other hand, the cases of Pd-catalyzed oscillations are ample. The metallic palladium catalyst is well-known for being a subject of several early studies in which the oscillatory behavior in heterogeneous catalysis has been observed. These include the now classic case of oxidation of CO to CO2 with oxygen,3,4,16-18 as well as the oxidation of hydrocarbons with oxygen19,20 and the oxidation of hydrogen to water by oxygen.21 There are two groups of variables that can be monitored to assess the periodicity of the reactions, and accordingly, two different experimental approaches can be distinguished. The first consists of using various techniques for measuring the concentrations of products or transient species that can be used to evaluate the oscillating reaction rate. The second approach consists of monitoring variations of reaction temperature, the so-called thermokinetic oscillations. Here again, the metallic palladium features prominently as a catalyst in several thermokinetically oscillating processes, such as the oxidation of alcohols,22-24 formic acid,25 and CO26 over supported Pd. Experimentally, the thermokinetic oscillations depend on detecting a periodicity in changes of the temperature difference,

10.1021/jp805414a CCC: $40.75  2008 American Chemical Society Published on Web 10/31/2008

18484 J. Phys. Chem. C, Vol. 112, No. 47, 2008 ∆T, between the catalytic bed and the gas phase above it, arising from reaction thermal effects. The results are presented as a calorimetric profile of oscillatory ∆T recorded and plotted against time. Such a profile can be considered a measure of the reaction periodicity, provided the thermal changes it represents can be related to the variations in reaction rate. Expectedly, the changes of reaction temperature reflect the variations in reaction energetics, which in turn are a function of the reaction rate. The reaction energetics can be evaluated by measuring calorimetrically the rate of heat evolution during the process. One may therefore propose to measure variations in the rate of heat evolution, expected to be used as a measure of reaction periodicity, instead of the “raw” ∆T. However, to evaluate the rate of heat evolution while measuring the ∆T, there is a need to determine the heat transfer coefficient, often denoted as k (W/m2K). Together with ∆T, they appear in the Newton formula for the convective heat transfer Q ) kF∆T where Q (W) is the rate of heat evolution, and F (m2) is the geometric area of the surface (say, of a reactor wall) through which the heat is flowing (not to be confused with the surface area of the catalyst). The heat transfer coefficient is a complicated function of a number of parameters, including the shape of the catalytic bed, and its calculation may be very difficult in practice. One way to solve this difficulty is to use a calorimeter with a built-in in situ calibration procedure. The calibration makes it possible to apply the obtained ∆T data for calculation of the rate of heat evolution during reaction. In this paper, we report the finding of an oscillatory behavior in the sorption of hydrogen in metallic palladium powder, monitored using the Microscal gas flow-through microcalorimeter with a heat sink and the in situ calibrator. With this instrument, it was possible for the first time to evaluate the oscillations of energy for this process; that is, to calculate the oscillating rate of the heat evolution during the reaction of H2 with Pd. It was also possible to record certain nonlinear phenomena characteristic for chemical oscillations, including the periodic-to-quasiperiodic transitions. The oscillations are nonsinusoidal and have mostly a periodic character, with the period varying from around 50 to 30 s. To the authors’ best knowledge, any periodic or quasiperiodic oscillations in the H2/ Pd system have not yet been reported, despite a considerable body of data available for this system. An irregularly periodic behavior in the electrode concentration has been reported for palladium loaded electrochemically with hydrogen,27 but with a periodicity of ∼3 days, only two full periods have been shown. We believe our findings may be of interest to at least three different communities of researchers. Those studying the heterogeneous catalysis, in particular the hydrogenations over metallic Pd, may find them insightful in explaining the notoriously hysteretic behavior of these reactions. Another potentially interested group is the researchers looking into the hydrogen storage materials. On its own merit, the periodicity of the Pd hydride formation represents a new oscillatory reaction, and as such, it may expectedly be of interest from the point of view of the science of nonlinear dynamics. It should also be noted that altough palladium is by no means a stranger to oscillatory chemistry, the oscillating reactions it catalyzes are largely oxidations and, therefore, seem to be confined to the catalyst surface, whereas the sorption of hydrogen is essentially a bulk phenomenon. Understanding these oscillations, hopefully following their current recognition, may therefore help to further understand the relations between the surface-induced phenomena and the bulk-induced, structure-driven properties of palladium and possibly other materials.

Lalik et al. 2. Experimental Materials. Palladium powder (purity 99.999%) was supplied by Aldrich Co.; nitrogen (99.999%) and hydrogen (99.999%) were provided by Linde Gas Poland S.A. The surface area of the Pd powder measured by low-temperature adsorption of nitrogen and calculated from BET was ∼0.1 m2/g. Equipment. A Microscal flow-through microcalorimeter, model FMC-4110 designed for use in isothermal mode at temperatures up to 240 °C and pressures up to 5 MPa, was employed. The design and operation of this microcalorimeter was recently described in detail in ref 28, and its use was reviewed in refs 29 and 30, so its operation principle will be sketched here only briefly. The instrument measures the rate of heat evolution accompanying a solid-gas interaction. A sample of sorbent is placed in a small microcalorimetric cell (7 mm in diameter), and the measurement is carried out in flow-through mode. The cell is placed centrally within a much larger, metal block acting as a heat sink, which ensures a steady removal of total evolving heat, thus preventing its accumulation within the cell. The heat sink has to be large enough for its outer edge to be sufficiently far away from the cell so as not to sense the rising temperature. Hence, as a reaction is occurring within the cell, a minute difference of temperatures between the close vicinity of the cell and the outermost edge of the heat sink can be measured continuously by a system of thermistors appropriately located within the block. This signal can be used for a calculation of rates of heat evolution with application of a calibration factor. For the latter to be extracted, each experiment (or a group of experiments) needs to be preceded by an in situ calibration pulse of controlled power and duration. The pulse is being produced by a small electric coil sealed in the calibrator, which is located axially within the calorimetric cell and totally surrounded by powdered sample. An area under the peak recorded on such a calibrating pulse is then used as a standard to calculate the calibration factor for individual experiments. A gas analyzer, model UMS, provided by Prevac, and thermoconductivity detector (Gow-Mac) were used as downstream detectors. The gas analyzer contains a mass spectrometer (SRS model RGA 200) and a vacuum system combining a diaphragm pump (Vacuumbrand, MD1, 1.5 hPa) and a turbomolecular pump (Leybold Vacuum, Turbovac TW 70 H). The flow rate of the gases was controlled by two Bronkhorst mass flow controllers. Procedures. All measurements were performed in a continuous sorption mode. The temperature was kept at ∼105 °C. The same sample was used for a succession of days and a daily sequence consisted of up to five sorption/desorption cycles. A sample of around 0.2 g of palladium powder was required to fill the calorimetric cell of 0.15 cm3. The sample was then thermally equilibrated in a flow of nitrogen after sealing the cell with a top and bottom gas inlet and outlet, the latter connected to a termoconductivity detector (TCD) and, subsequently, via a stainless steel capillary tube (1 m long, 0.12 mm in diameter) to a mass spectrometer (MS) equipped with a diaphragm pump and turbomolecular pump. The supply of gases to the inlet was controlled by two mass flow controllers and a system of valves, making it possible to form a reaction mixture of H2 and N2 at various proportions and to set up flow rates of both the mixture and the inert N2. During the periods of nitrogen’s passing, when no reaction takes place in the cell, this arrangement makes it possible for the system pressure to be effectively controlled by setting up the N2 flow rate while the system is continuously pumped out. During the sorption,

Heat Evolution during Sorption of H in Pd

J. Phys. Chem. C, Vol. 112, No. 47, 2008 18485

Figure 1. An overview of thermal effects accompanying the reactions of hydrogen and palladium powder, recorded with the Microscal microcalorimeter for a typical sequence of sorption/desorption cycles at 105 °C.

however, when a substantial fraction of hydrogen is being removed from the gas phase as it passes through the Pd sorbent, the total pressure is no longer tunable, and in fact, it is more a function of the reaction rate rather than a function of the flow rate. In some of the experiments, the pressures within the system as well as the volumetric flow rate were measured with a mercurial manometer and rothameter, both located between the TCD and MS. Calorimetric calibration has been made in situ prior to each daily sequence of sorption/desorption cycles according to the calibration procedure described in the above paragraph. A usual experimental routine was as follows: After reaching thermal equilibrium with the N2 gas and following a calibration pulse, the sample is ready for a sorption measurement. At this point, the flow of N2 may be lowered to decrease the system pressure to around 600 hPa, which takes around 20 min. The flow of N2 is than replaced by the flow of the H2/N2 reaction mixture, which marks the beginning of sorption. Upon admission of the reaction mixture, the H2 molar fraction is usually being increased gradually by accelerating the flow rate in the mass flow controller supplying hydrogen, which takes ∼25 s. This gradual adjustment is a measure taken to compensate for a pressure drop that may appear when the stream of reaction mixture hitherto under ambient pressure enters the system in which pressure is lowered to 600 hPa. Alternatively, a reaction mixture in appropriate proportions may be admitted instantaneously. We have noticed that the gradual adjustment leads to a higher amplitude and more regular oscillations, and hence, all the time series presented in this paper have been obtained in this manner, except for three experiments used for testing the aging effect (see below), where the instantaneous admission was used for better standardization of the admission procedure. Having the reaction mixture admitted, an exotherm is recorded by the microcalorimeter, and the changes in H2 concentration in the effluent from the cell are measured by TCD and MS. The end of the process is signaled by cessation of heat evolution, as well as by a plateau being reached in the curve of the TCD downstream detector, indicating no more uptake of hydrogen by the sample from the reaction mixture. At this point, returning to the pure nitrogen flow initiates desorption from the sample, during which an endothermic peak that concludes a sorption/ desorption cycle is being recorded. The end of the desorption is again signaled by cessation of heat evolution and by readings from the TCD and MS. With the desorption completed, the system is ready for the next cycle. It takes around 25-40 min

for an average sorption to saturate the Pd sample with hydrogen and, afterward, around 1.5-2 h for desorption in the flow of pure N2. 3. Results and Discussion An Overview. Figure 1 shows the typical sequence of sorption-desorption cycles in which each sorption of hydrogen from a mixture of H2/N2 flowing through the palladium powder was followed by a desorption in the flow of pure N2. The temperature was kept constant at ∼105 °C throughout the experiment, while the pressure varied from 600 to 730 hPa as a result of reaction in Pd. The calorimetric curve in Figure 1 depicts the rate of heat evolution during the sorption or desorption as a function of time, showing, respectively, exothermic or endothermic peaks, the areas of which represent the total heats evolving in either of the processes. The oscillatory character of heat evolution accompanying the sorption is evident in all three cases shown in Figure 1. The oscillations start immediately after the H2/N2 mixture reaches Pd and continue unabated until the Pd sample is saturated with hydrogen, at which point the heat evolution ceases. They appear only during sorption; in fact, we never observed any oscillation upon desorption of hydrogen with pure N2. The latter must also have a complex kinetics, indicated by the shape of its endotherms in which two stages of clearly different heat evolution rate can be distinguished. Such two-staged desorption was observed in virtually all sorption-desorption sequences performed with our microcalorimeter, but no oscillatory behavior was ever noted in either of these desorptive stages. Invariance of the Heats of Sorption/Desorption. Integration of the peaks present in Figure 1 yields the total heats evolved during sorption or desorption. It can be noted that within a single cycle, the thermal effects match each other; that is, absolute values of the heat of sorption equals the heat of desorption. This indicates that sorption of H2 in Pd is reversible at 105 °C. Remarkably, apart from their matching within a single cycle, the heats also remain practically invariant from one cycle to another. Both the long-term near-invariance, and the sorption/ desorption matching that are visible in Figure 1 appear to be parts of a typical behavior of the system, in a sense that they have been confirmed in virtually all the microcalorimetric experiments. Table 1 lists the absolute values of thermal effects for 65 sorption/desorption cycles, corrected for Pd sample mass. The heats of sorption and the heats of desorption have been

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TABLE 1: Thermal Effects of 65 Sorption/Desorption Cycles of Hydrogen in Palladiuma no.

oscillation character

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 61 62 63 64 65 mean median std dev

periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic periodic no oscillations periodic periodic periodic periodic no oscillations periodic periodic no oscillations no oscillations very weak quasiperiodic quasiperiodic quasiperiodic quasiperiodic quasiperiodic quasiperiodic quasiperiodic no oscillations no oscillations quasiperiodic quasiperiodic quasiperiodic quasiperiodic quasiperiodic no oscillations no oscillations no oscillations no oscillations no oscillations no oscillations no oscillations no oscillations irregular, not sustained

median difference sum of positive ranks sum of negative ranks P value (from normal aproximation)

0.000 394 538 873 1080 0.4702

sorption thermal desorption thermal sample heat of heat of flow rate, H2 molar effect, mJ effect, mJ mass, g sorption, kJ/gPd desorption, kJ/gPd cm3/min fraction 29 534 26 087 27 263 27 885 29 756 30 226 29 726 30 915 31 414 30 935 30 649 31 247 31 803 31 212 31 742 31 546 30 861 31 475 31 226 31 238 30 946 30 678 31 582 31 019 27 228 27 940 27 313 26 956 31 313 30 955 28 225 28 953 28 240 27 731 28 795 28 446 27 179 28 448 28 158 28 335 28 238 28 868 30 351 31 358 30 888 31 564 31 422 30 971 31 404 30 863 30 924 30 721 31 257 31 157 31 013 31 134 31 846 31 905 32 027 31 665 31 370 28 444 31 526 31 016 30 351

29 612 26 523 27 405 27 846 29 276 29 765 29 624 30 540 31 261 30 816 30 715 31 164 31 313 31 187 31 479 31 582 30 809 31 209 31 354 31 220 30 892 30 488 31 278 31 243 27 884 28 020 27 775 27 280 31 338 31 158 28 942 29 017 28 599 28 000 29 000 28 810 27 485 28 363 28 471 28 452 28 500 28 840 30 694 31 056 30 736 31 209 31 040 31 099 30 944 30 900 31 275 30 977 31 206 31 161 31 606 31 565 32 001 31 593 28 618 31 246 30 810 30 694

0.2470 0.2470 0.2470 0.2470 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2244 0.2244 0.2244 0.2244 0.2636 0.2636 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2244 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.2636 0.1192 0.1190 0.00454

0.1196 0.1056 0.1104 0.1129 0.1129 0.1147 0.1128 0.1173 0.1192 0.1174 0.1163 0.1185 0.1206 0.1184 0.1204 0.1197 0.1171 0.1194 0.1185 0.1185 0.1174 0.1164 0.1198 0.1177 0.1213 0.1245 0.1217 0.1201 0.1188 0.1174 0.1258 0.1290 0.1258 0.1236 0.1283 0.1268 0.1211 0.1268 0.1255 0.1263 0.1258 0.1286 0.1151 0.1190 0.1172 0.1197 0.1192 0.1175 0.1191 0.1171 0.1173 0.1165 0.1186 0.1182 0.1177 0.1181 0.1208 0.1210 0.1215 0.1201 0.1190 0.1079 0.1196 0.1177 0.1151 0.1194 0.1185 0.00497

0.1199 0.1074 0.1110 0.1127 0.1111 0.1129 0.1124 0.1159 0.1186 0.1169 0.1165 0.1182 0.1188 0.1183 0.1194 0.1198 0.1169 0.1184 0.1189 0.1184 0.1172 0.1157 0.1187 0.1185 0.1243 0.1249 0.1238 0.1216 0.1189 0.1182 0.1290 0.1293 0.1274 0.1248 0.1292 0.1284 0.1225 0.1264 0.1269 0.1268 0.1270 0.1285 0.1164 0.1178 0.1166 0.1184 0.1178 0.1180 0.1174 0.1172 0.1186 0.1175 0.1184 0.1182 0.1199 0.1197 0.1214 0.1199 0.1086 0.1185 0.1169 0.1164

1.2 1.2 1.2 1.2 1.4 1.4 1.4 1.4 1.6 1.6 1.6 1.7 1.7 1.8 1.8 1.8 1.8 1.8 2.0 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.4 2.2 2.2 2.2 2.2 2.2 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8

0.83 0.83 0.83 0.83 0.86 0.86 0.86 0.86 0.87 0.87 0.87 0.92 0.92 0.89 0.89 0.89 0.89 0.89 0.88 0.89 0.89 0.89 0.89 0.89 0.92 0.90 0.87 0.84 0.90 0.89 0.91 0.91 0.91 0.91 0.91 0.91 0.90 0.92 0.92 0.92 0.92 0.92 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.84 0.86 0.89 0.89

2.0 2.0 2.0 2.0 2.0 2.0 1.4 1.2 1.8

0.90 0.90 0.91 1.0 1.0 0.91 0.86 1.0 1.0

Wilcoxon Signed-Rank Test for Paired Data

a The heats of sorption and the heats of desorption have been compared using the Wilcoxon signed-rank test, and no significantly differences (P ) 0.4702) were found.

compared using the Wilcoxon signed-rank test for paired data and no significant differences (P ) 0.4702) were found. This means that in each of the experiments listed in Table 1, the heats of sorption and desorption are statistically the same, and

therefore, the test confirms the reversible character of sorption of H2 in Pd at the reaction temperature. Table 1 also attests to the long-term practical invariance of the heats of both sorption and desorption, although a very mild


Figure 2. Dependence of the heats of sorption and desorption on the molar fraction of H2.

increase (∼5%) of both heats with an increase in the molar fraction of H2 can also be noted.31 This is illustrated in Figure 2, showing the heats of sorption and desorption plotted against the entire range of molar fractions of H2, from 0.83 to 1.0. The actual amount of hydrogen absorption could not be directly determined in our experiments because both the total pressure within the system and the flow rate of the reaction mixture were changing upon oscillations, making it impossible to calculate reliably the total uptake of H2 absorbed or released during a sorption/desorption cycle. The amount of absorption can be approximated using a relation between the heat of sorption expressed per gram of Pd and the H2/Pd ratio.5 The values of heats of sorption per gram of Pd, which are listed in Table 1 (on average ∼0.12 kJ/g Pd), are comparable to those quoted in ref 5 as obtained for the H/Pd of around 0.6 (0.110 53 kJ/g Pd for H/Pd 0.6365),5 which is close to saturation.6 We have previously obtained similar saturation values of H/Pd for absorption in the same kind of Pd powder material used in our previous microcalorimetric (nonoscillatory) and gravimetric experiments.12 It seems safe to conclude that the heats of sorption listed in Table 1 correspond to uptakes of H2 close to the saturation of the palladium sample. The crucial conclusion, therefore, which is supported by the data in Table 1, is the practical invariance of heats of sorption; that is, the notion that the thermal effect of sorption is independent of the dynamics of the oscillations. The experiments presented in Table 1 include the periodic and the quasiperiodic oscillations, as well as a few cycles that do not show oscillatory behavior. Clearly, the heats of sorption remain invariant, regardless of the character of the oscillations or weather the reaction reaches an oscillatory regime. The oscillations therefore do not affect the amount of heat evolving upon reaction of H2 in Pd, but rather, only an instantaneous rate of heat evolution. They appear to be a kinetic phenomenon that does not influence directly the thermodynamics effects of sorption. Dynamics of Oscillations. With the total of the thermal effects invariant, dynamics of the heat evolution during sorption of H2 in Pd appears to be very sensitive to certain reaction conditions; in particular, the flow rate of the H2/N2 mixture and the molar fraction of H2. Table 1 shows the values of these parameters for each sorption/desorption experiment listed, in addition to their heat effects. The ranges of values of the flow rates and H2 molar fractions under which the oscillatory behavior occurs are relatively narrow. Both have to be carefully selected,

J. Phys. Chem. C, Vol. 112, No. 47, 2008 18487 and their ability to support oscillations is also affected by the overall system volume. Generally, it was possible to observe sustainable oscillations for the H2 molar fractions ranging from 0.83 to 0.92 and for the flow rates of N2/H2 from 1.2 to 2.2 cm3/min; however, not all combinations of these parameters turned out to be equally successful. The impact of the combined action of the H2 molar fraction and the flow rate is illustrated in Figure 3 a-c, which shows more detailed representations of the sorption experiments depicted in Figure 1. The sensitivity of sorption dynamics to even minute variations in reaction conditions is illustrated in Figure 3a, which shows a comparison of two oscillatory time series recorded for the two cycles denoted as 2 and 3 in Figure 1. Their markedly different behavior was brought about by relatively minor alterations of the flow rate and molar fraction of H2, lowered from 1.8 to 1.4 cm3/min, and from 0.89 to 0.86, respectively, before beginning cycle 3. The most conspicuously different are the duration and amplitude, but also the power spectra (Figure 3c) reveal altered frequencies and, by the same token, a significant difference in periods of the two series of oscillations (respectively, 38.3 and 44.8 s). The areas under the two oscillatory curves are, however, practically the same, both yielding heats of sorption of ∼31 J (0.117 kJ/g Pd). On the other hand, keeping the flow rate and H2 molar fraction constant (1.8 cm3/min and 0.89) throughout the first two cycles (1 and 2 in Figure 1) resulted in nearly identical series of nonsinusoidal oscillations. Nevertheless, under closer examination (Figure 3b) the two series reveal slightly different period lengths (38.9 and 38.3 s for cycles 1 and 2, respectively). In terms of frequencies, this difference, however minor, can be confirmed by a slight shift in the respective power spectra for cycles 1 and 2 presented in Figure 3c. For all three cycles, the oscillations appear nonsinusoidal (anharmonic), which can be confirmed by their first and second derivatives (not shown). Inspection of the power spectra in Figure 3c reveals that all three time series are periodic; that is, each one has only a single frequency. Total Pressure in the System. A preeminent condition for the oscillations to start seems to be that the pressure in the system has to be lowered to around 600 hPa prior to the beginning of sorption. After admission of the reaction mixture, the pressure may change as a result of sorption reaction, but for the oscillation to be sustained until the saturation of palladium with hydrogen is completed, the pressure within the system should not rise more than by ∼130 hPa during the process; that is, it should remain lower than ambient by ∼260 hPa. We will refer to the pressure of the nitrogen carrier in the calorimetric cell immediately before the beginning of sorption as the initial pressure, p0, and to the pressure of the H2/N2 mixture during sorption as the maximal pressure, pmax, meaning that it is a pressure showed by manometer at the stage of maximum amplitude of oscillations being attained. The three sorption experiments presented in Figure 4a-c were performed with the same flow rate of 1.6 cm3/min and hydrogen molar fraction of 0.87 (except for a short initial stage in Figure 4a), but differ in both the initial and the maximal pressures. The first two experiments, shown in Figure 4a and b, were carried out with p0 580 and 620 hPa, respectively, and they both developed a series of full fledged oscillations, both reaching an amplitude of ∼40 mW. In the third experiment presented in Figure 4c, however, sorption was started at a p0 as high as 960 hPa, and the system responded with an array of irregular, lowamplitude oscillations which only began to develop into a more


Lalik et al.

Figure 3. Dynamics of heat evolution during the sorption reaction of H2 gas in Pd powder influenced by reaction conditions: the flow rate of H2/N2 mixture and the molar fraction of H2, xh. The cycles are the same as those shown in Figure 1. (a) Very different types of oscillations have developed during the sorptions in the cycles 2 and 3, respectively, as a result of relatively small variations of the flow rate and the H2 molar fraction. (b) Nearly identical oscillations appeared when the flow rate and molar fraction were kept constant in cycles 1 and 2; nevertheless, over the initial 600 s, both time series developed slightly different frequencies at the same amplitude. (c) The power spectra for all three cycles show very similar, single frequencies (and their harmonics) for cycles 1 and 2, and a more different single frequency for cycle 3. (p0, pressure in the system prior to beginning of sorption; pmax, pressure in the system when a maximum amplitude of oscillations is being attended.)

fully grown series when the pressure in the cell dropped of its own accord to around 680 hPa. This point has been marked with arrow in Figure 4c. Since the onset of the regular oscillations came already after 600 s from the start of sorption, there was not enough time left for an amplitude to develop as high as those in Figure 4 a and b before the saturation of the sample was reached. This is an example of the system’s spontaneous switching from irregular to regular oscillations within the same sorption run. On the other hand, in the experiment in Figure 4a, the delayed onset of regular oscillations is not spontaneous; instead, it was induced by increasing the flow rate from 1.2 to 1.6 cm3/min and the hydrogen concentration from 0.83 to 0.87 after ∼400s since the start of sorption. As in the previous experiments, the areas under the three oscillatory curves and, by the same token, the total amounts of heat generated by the three sorptions remains practically constant (∼31 J or 0.117 kJ/gPd for the sample mass of 0.2636 g). The periods of oscillations determined from power spectra (not showed) are similar for all three sorptions in Figure 4a-c, and they are, respectively: 42.9, 41.8, and 42.9 s.

Figure 4d shows a similar effect of the initial pressure for another combination of the H2 molar fraction and flow rate; namely 0.92 and 2.2 cm3/min. The solid line represents the sorption experiment performed without the initial lowering of total pressure in the system. Although the reaction is oscillating very slightly, the amplitude is never higher than 5 mW. In vivid contrast, the dotted line represents the large oscillations with amplitude reaching 30 mW, which appeared when the initial pressure was lowered by ∼400 hPa. The areas under both curves are basically equal, showing the heat of sorption in both cases to be ∼28 J (0.125 kJ/gPd). In general, the total pressure in the system does not, on its own, show a significant oscillatory behavior. After the reaction passes the stage of maximum amplitude, the total pressure increases gradually, reaching around 950 hPa upon full saturation of the sample with hydrogen. Hence, the pressure can change along the process by a total of ∼350 hPa. Although these changes are gradual, occasionally, a certain mild but regular oscillation of the total pressure could also be observed (with the mercurial manometer), but only



Figure 4. A lowering of the initial total pressure in the cell is necessary for the oscillations to develop. (a) The initial pressure lowered sufficiently, but needed to increase both the H2 molar fraction, xh and flow rate after an initial 450 s for high amplitude to grow. (b) The initial pressure lowered slightly less, but the H2 molar fraction and flow rate “correct”: full-grown oscillations develop. (c) The initial pressure not lowered sufficiently: the sorption proceeds initially with low amplitude; however, after ∼550 s (see arrow mark), the total pressure in the cell decreases enough for the higher amplitude to start developing. (d) The same effect of lowering of the initial total pressure confirmed at altered conditions. The dotted line shows oscillations with a high amplitude; the solid line represents the sorption carried out under the same conditions but without the initial pressure lowered. (p0, pressure in the system prior to beginning of sorption; pmax, pressure in the system when maximum amplitude of oscillations is being attained.)

during the thermal oscillations’ attaining their highest amplitudes. However, amplitude of these pressure oscillations was always very low, not more than 15 hPa, which is only a fraction of the total pressure change that occurs gradually during the oscillatory sorption. The Effect of H2 Molar Fraction. The molar fraction of H2 (xh) was the only parameter that was varied (from xh ) 0.84 to xh ) 0.92) in the series of experiments presented in Figure 5. It is clear that with the other parameters and conditions constant, the oscillation amplitude is a strongly increasing function of xh. Thus, the highest amplitude of ∼25 mW is being reached for the xh of 0.84 (Figure 5a), 20 mW for xh 0.90 (Figure 5b), and ∼15 mW for xh 0.87 (Figure 5c). For the lowest xh of 0.84, the oscillations are no longer sustainable because they cease after an initial 400 s without ever reaching an amplitude higher than 5 mW (Figure 5d). The oscillation frequencies are practically not affected by changes of xh. As can be seen from the power spectra shown in Figure 5e, nearly the same single frequency (and its harmonics) can be observed for all four experiments, yielding oscillation periods of 33.8, 34.1, 34.4,

and 34.5 s, respectively. The total heat of sorption was ∼27 J for all four sorption experiments, as well as for desorption (not shown), which for the sample mass of 0.2244 g yields 0.120 kJ/gPd. Aging Effect and Short-Term Reproducibility. Studies of palladium as a membrane material have revealed a strong deterioration effect on its mechanical properties resulting from the repeated exposures to hydrogen.2 In our experiments, the same samples were repeatedly subjected to a number of saturations with H2, and so it may be expected that this multiple exposure should be reflected as changes in oscillatory characteristics. To test this possibility, a comparison was made between a certain earlier experiment, on one hand, and the experiments performed after 10 sorption/desorption cycles later, on the other hand. Great care has been taken for the two later experiments to be performed under precisely the conditions and with the procedure applied for the first one. The results are represented in Figure 6a, showing the first experiment, and in Figure 6b, representing the two later sorptions performed in two consecutive cycles. Comparison of the oscillatory series depicted in


Lalik et al.

Figure 5. (a-d) Changes in amplitude of oscillations resulting from variations of molar fraction of H2, xh, from 0.84 to 0.92, with flow rate and other conditions being kept constant. (e) The corresponding power spectra.

Figure 6a with any one of the two profiles represented in Figure 6b suggests that an effect of sample aging exists. In Figure 6b, the amplitude is distinctively lower, and the oscillations are visibly less regular than those in Figure 6a. Indeed, the power spectra represented in Figure 6c show two incommensurate frequencies, indicating quasiperiodicity of the oscillations for the two later sorptions (dotted and dashed lines in Figure 6c),

in contrast to a single frequency dominating the oscillations of the earlier experiment (solid line in Figure 6c). It can be suggested that aging of the sample decreases the amplitude of oscillations, causing at the same time their less regular, quasiperiodic character. The aging effect that appears over a 10-cycle-long series of experiments needs to be seen against a backdrop of short-term



Figure 6. Aging effect vs short-term reproducibility. Comparing the oscillations in a certain earlier experiment (a) to those recorded after 10 cycles later under the same conditions (b) reveals that the latter amplitudes are clearly lower and that they are also showing a quasiperiodicity, not detectable yet in the earlier experiment (a), which may be indicative of sample aging. On the other hand, the extensive overlap of the two series of oscillations shown in part b, which have been recorded over a pair of consecutive cycles, demonstrates very good short-term reproducibility. This can be further confirmed by a near identity of their power spectra which are depicted in part c, together with the spectrum for cycle a, also shown for comparison. (p0, pressure in the system prior to beginning of sorption; pmax, pressure in the system when maximum amplitude of oscillations is being attended; xh, molar fraction of H2.)

reproducibility from cycle to cycle. The latter may be apprised from nearly a perfect overlap of the time series shown in Figure 6b, which, as stated above, were recorded in two consecutive experiments at the same conditions (but not on the same day). Clearly, no aging effect can be noticed from cycle to cycle; in fact, both the oscillatory time series in Figure 6b are practically identical, despite their rather significant complexity. Moreover, they also have the same power spectra, depicted as the dotted and dashed lines in Figure 6c, respectively. In conclusion, the aging of the Pd sample can be noticed long-term, whereas there is a remarkably good short-term reproducibility. We note that the short-term reproducibility in Figure 6b is revealed for the samples already aged; that is, already subjected to multiple exposures to hydrogen. A short-term reproducibility from cycle to cycle for relatively fresh samples can be seen in Figures 1 and 3b by comparing cycles 1 and 2, which are consecutive and performed under the same conditions during the same daily sequence. This comparison has already been discussed in detail in the subsection on oscillation dynamics. Frequency-Flow Rate Dependence. Figure 7 presents the frequencies calculated for 28 sorption experiments in which

regular and sustained oscillations were observed. The data are plotted solely as a function of the flow rate of the reaction mixture H2/N2 through the cell. Within the range of flow rates from 1.2 to 2.2 cm3/min, the oscillation frequencies increase nearly linearly with the flow rate. These 28 sorption experiments were preformed at different molar fractions of H2 and different sample masses, but even without a correction for the two variables, it is clear that the oscillation frequency is a very strong function of the flow rate. 4. Conclusions The sorption of hydrogen in palladium powder is totally reversible at 105 °C, as indicated by the identical absolute values of both the heat of sorption and the heat of desorption. The sorption process may proceed in an oscillatory manner under certain conditions. The most eminent conditions with this respect are the initial pressure and the molar fraction of hydrogen in the gas phase; selected properly, these parameters determine the occurrence of oscillations during sorption. The oscillations are sustainable throughout the whole sorption period and


Lalik et al. Acknowledgment. This work was financed from funds for science in years 2006-2008 as a research project. References and Notes

Figure 7. Dependence of oscillation frequencies on the flow rate of a H2/N2 reaction mixture.

disappear only upon saturation of the Pd sample with hydrogen. The oscillation’s amplitude and frequency are very sensitive to the conditions of the process, such as H2 molar fraction, initial pressure, and flow rate. The amplitude depends strongly on the H2 molar fraction. The frequency is nearly a linear function of the flow rate of the H2/N2 reaction mixture through the sample. The total of the measured thermal effect of sorption is, however, invariant and not affected by any varying characteristics of the oscillations. Hence, the occurring oscillations never affect the thermodynamic amount of heat produced upon sorption, but only an instantaneous rate of heat evolution. Aging effects of Pd samples over their repeated exposure to hydrogen can be observed in the long run. Nevertheless, the reaction shows remarkable reproducibility from one experiment to the next. Indeed, despite sometimes very complicated shapes of oscillations, it is possible to obtain nearly identical time series in two consecutive experiments. This reproducibility seems to point to advantages of recording the oscillatory rates of heat evolution during the reaction and using them as a measure of the reaction periodicity. The use of a microcalorimeter with in situ calibration makes it possible to avoid ambiguity arising out of the heat transfer coefficient changing from one experimental setup to the other. Using the in situ calibrator yields the data that facilitate relevant comparisons between oscillatory experiments performed under various conditions.

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Oscillatory Rates of Heat Evolution during Sorption of Hydrogen in

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