Thermal Desorption from Heterogeneous Surfaces - The Journal of

Article pubs.acs.org/JPCC

Thermal Desorption from Heterogeneous Surfaces Nayeli Zuniga-Hansen† and M. Mercedes Calbi*,†,‡ †

Department of Physics, Southern Illinois University, Carbondale, Illinois 62901-4401, United States Department of Physics and Astronomy, University of Denver, Denver, Colorado 80208, United States

‡

ABSTRACT: When a given gas can adsorb onto a surface with multiple binding energies, temperature-programmed desorption (TPD) spectra may become relatively more complicated to analyze, making more difficult the extraction of energy and kinetic parameters from the experimental results. Here we present results from kinetic Monte Carlo simulations used to investigate gas desorption from external surfaces of carbon nanotube bundles. By varying the initially adsorbed coverage and keeping track of the particles as they desorb and diffuse across the surface, we identify specific features on the TPD spectra originated by the effects of the surface heterogeneity on the desorption kinetics.

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INTRODUCTION The emergence of carbon nanotubes (and related structures) as potential adsorbents for gas storage and separation applications has motivated a continuous increase in the exploration of their adsorption behavior during the last decades. The first and most extensive investigations explored different aspects of adsorption equilibria such as uptake capacity and binding energies, typically by adsorption isotherms or isosteric heat determination.1,2 Only very recently, the isothermal kinetics of adsorption has been investigated both experimentally3,4 and with the aid of computer simulations.5−8 In this case, the focus has been on the analysis of equilibration times (or adsorption rates) as a function of equilibrium coverage, for both opened- and closed-tubes samples. This kind of study is particularly important when examining adsorption in porous structures such us a nanotube bundle because the large difference in adsorption rates among the various sites may easily affect overall isotherms measurements.7,8 Another traditional technique that has been profusely used in adsorption studies of a broad range of systems is temperatureprogrammed desorption (TPD) (also known as thermal desorption spectroscopy, TDS).9 A typical TPD experiment starts by exposing a surface to a gas until adsorption up to a desired value of the coverage is attained. The sample is then heated by using a controlled temperature ramp that is linearly dependent on time, with characteristic heating rates of 2 to 5 K/s. As the gas desorbs from the surface, the change in the gas pressure due to the increasing concentration of molecules in the gas phase is monitored with a mass spectrometer and then plotted as a function of temperature to obtain the so-called TPD spectra. If the gas is pumped out of the chamber at high © 2012 American Chemical Society

speed, then no readsorption of desorbing particles occurs, and the measured pressure change is proportional to the desorption rate. Using different models to interpret these spectra,9−11 several other quantities can be obtained including binding energies and diffusion coefficients. Desorption of numerous adsorbates12 (including helium,13,14 xenon,15−17 molecular oxygen,17,18 C60,19,20 alkanes,21−23 and CCl424) from carbon nanotube samples has been investigated with TPD experiments. While TPD is a very useful technique to get a quick assessment of overall adsorption properties (such as the total uptake capacity of the adsorbent), the interpretation of the spectra in terms of more detailed parameters such as binding and interaction energies is generally more difficult because it also depends on the knowledge of the specific processes that occur during the desorption experiment, that is, the kinetics of desorption. When the system is characterized by a single binding energy (such as a simple atom adsorbing on a planar surface), TPD spectra appear in the shape of a single peak. The peak temperature Tp is directly associated with the binding energy of the sample through the well-known Polanyi−Wigner equation that relates the rate of change of the coverage dη/dt to the activation energy Edes9 −

dη dη dT =− = νnηne−Edes / kBT dt dT dt

(1)

Received: December 16, 2011 Revised: January 23, 2012 Published: January 24, 2012 5025

dx.doi.org/10.1021/jp212171k | J. Phys. Chem. C 2012, 116, 5025−5032

The Journal of Physical Chemistry C

Article

The index n represents the order of the desorption process that characterizes the coverage dependence of the desorption rate, and νn is the pre-exponential frequency factor that depends on the speed of the reaction; Edes, n, and ν may depend on the coverage or the temperature.9,10 Whereas this approach has been extensively used for the analysis of TPD spectra, it presents serious limitations when there is more than one binding energy present in the system; this energy heterogeneity can arise from different binding sites on the surface25 or from internal degrees of freedom of more complex adsorbates.26 When carbon nanotubes arrange themselves in bundles, the exterior of the structure presents a highly heterogeneous surface: the “grooves” formed between two adjacent tubes are the regions of highest binding due to the proximity of two tubes. The binding energy then decreases laterally to both sides to values closer to the binding on the external surface of a single tube.27 Therefore, the spectra resulting from these surfaces are generally expected to show a series of overlapping peaks, corresponding to different binding sites. The peak overlap would occur as a consequence of particle diffusion taking place between adjacent sites during desorption and would typically prevent the Polanyi−Wigner equation from providing an adequate fit to the resulting spectrum. The elementary processes involved during gas desorption are therefore crucial to understanding the observed spectra. Whereas several methods of analyzing TPD spectra (typically valid under a set of specific conditions) have been developed,10,11 we present here results from kinetic Monte Carlo (KMC) simulations that allow us: (a) to observe directly the evolution of the system through different states while desorption is occurring and (b) to relate the presence of specific features in the spectra to the individual, microscopic processes taking place in the system.

out during the experiments and no significant readsorption takes place. 4) A specific process is selected to occur according to the rule provided by the algorithm, and the system evolves from the state it was on to the state that the selected transition indicates.7 5) The coverage is updated, and the time variable (and corresponding temperature) is increased. Steps 2 to 5 are repeated until the lattice is completely empty. If the system presents more than one binding energy, then several simulations starting with different initial coverages are required to obtain a complete picture of the mechanisms occurring during the desorption process.

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TESTING THE SIMULATION APPROACH: HOMOGENEOUS SURFACE RESULTS With the purpose of testing our simulation approach and for future comparison with more complex systems, we first performed desorption simulations from a homogeneous lattice formed by a single line of sites, which represents a strip along the groove or an edge, characterized by a given binding energy in the range 100 to 600 K. Periodic boundary conditions were assumed to represent the bulk of the material. The simulations were run starting from a full lattice at a low temperature T0. This initial temperature as well as the temperature ramp α have to be adjusted for each system, depending on its binding energy. The upper panel of Figure 1 shows the decrease in coverage with time as the temperature increases. For lower binding

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KINETIC MONTE CARLO SCHEME FOR THERMAL DESORPTION The implemented simulation is based on the same KMC algorithm for the time evolution that we used in our previous studies of kinetics of adsorption.5−8 The main difference is that now the temperature is linked to the time variable, increasing linearly with time as T(t) = T0 + αt, where T0 is the initial temperature and α is the rate of change. The initial temperature of the simulation (and experiment) has to be low enough to sample desorption from the lowest binding energy sites, and α has to be small enough for the process to remain in the quasiequilibrium regime. In our case, this means that we choose the smallest heating rate that allows us to record a change in the coverage, typically 1 K/s. As in our previous studies,6,7 we model the surface as a lattice of sites with binding energies εi. Typically, the simulation proceeds through the following steps: 1) We set up an initial surface coverage and temperature. 2) The energy at the ith site, Ei, is computed, including binding energy to the surface and adsorbate−adsorbate interactions if desired.7 3) The probabilities of transition corresponding to desorption and difussion processes are evaluated.7 The probability of desorption is proportional to the energy of the site that the particle is occupaying while the probabilities of diffusion in the lattice depend on the energy difference of neighboring sites. Adsorption processes are not included because the desorbed particles are pumped

Figure 1. Top panel: Coverage evolution with time during desorption; from left to right, curves correspond to binding energies from 100 to 600 K, with 100 K increments. Lower panel shows the derived TPD spectra for each system.

energies, the process takes place at a faster rate and in a lower temperature range, as expected. Desorption rates can be obtained 5026



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If the TPD experiment or simulation starts from monolayer coverage where all sites are occupied, then we expect desorption from the lower binding sites (edges) to occur relatively earlier in the process, followed by desorption from the groove sites. Our simulations allow us to monitor the individual coverage change in each group of sites as desorption occurs, including the particle exchange across different lines. We anticipate that a fit with P−W equation (for each individual set of sites) will not work because desorption from each line will also involve diffusion or transfer of particles between the lines before they eventually end up in the gas phase. To examine this effect in detail, we perform the simulation for the following systems: 1) Three lines lattice: We consider two systems with different energy gap between the lines: a) εgroove = 300 K, εedge =100 K b) εgroove = 500 K, εedge =100 K 2) Five lines lattice: In this case, εgroove = 500 K, εinner edge = 300 K, εouter edge = 100 K For each case, different values of the initial coverage are to be explored to characterize the dynamics of the desorption process completely. As a first step and to simplify the analysis, we have not included lateral interactions in this work because we have focused primarily on the effect of particle transfer among different sites. However, lateral interactions can be easily included as we did in previous studies7 and its effects are the subject of a study currently in progress.

directly from these curves by numerical differentiation. When we plot these rates as a function of the temperature, singlepeaked TPD spectra are generated as shown in the lower panel of Figure 1. Desorption from lower binding sites leads to taller and narrower peaks, with lower peak temperatures, TP. For systems with higher binding energies, the peaks become shorter, corresponding to slower desorption, and reach their maximum at a higher temperature. The peaks also become wider because the total number of desorbed particles (the area under the curve) is the same for all systems. The presence of these expected features in our results serves to confirm the validity of our approach. Moreover, if we directly compare these results with desorption rates obtained through the Polanyi− Wigner’s equation (assuming first order desorption), then we find

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HETEROGENEOUS SURFACES: THREE-LINES LATTICE RESULTS In this case, we perform several simulations corresponding to various initial coverages, ranging from 10% to full monolayer coverage. The initial distribution of particles among the lines, for a given initial coverage, is determined by the equilibrium distribution η(β, μ) where β = 1/(kBT) and μ is the chemical potential. η (β , μ) =

1 + eβ(εg −μ)

+

2/3 1 + eβ(εe −μ)

(2)

The first term corresponds to the partial coverage on the groove while the other one gives the coverage on the edges. We typically fix the temperature to 100 K to set this initial distribution. A redistribution of particles may occur very early in the process depending on the starting temperature of the simulation; however, this does not affect the resulting spectrum in any considerable way, as we will show later on. The upper panels in Figure 3 show the coverage decrease with time as the temperature increases for the systems with smaller and larger energy gaps, respectively. The different curves correspond to different initial coverages on the lattice. The lower panels are the derived TPD spectra. At relatively low initial coverage (10 and 30%), a single peak is observed at high temperatures and corresponds to desorption of particles initially bound to groove sites. The second peak, at lower temperatures, appears for higher initial coverages, when some of the weaker binding sites on the edges are also initially occupied. These two peaks are present for both systems, but they can be distinguished more easily when the energy gap is larger. The overlap between the peaks at higher initial coverages is also evident for both systems, although it is more notorious for the system with a smaller energy gap. A shift on the location of the peaks with respect to the homogeneous systems (dotted lines) is present in both cases, even for the system where the desorption peaks seem to be relatively decoupled. Indeed, this

Figure 2. Testing the simulation scheme: Full line in the top panel corresponds to simulation results while dotted blue line is derived from P−W equation. Lower panel: Binding energy as function of peak temperature from both simulations and P−W equation.

a close match for all curves. Figure 2 illustrates this match for one of the systems as well as the relationship between the peak temperature and the binding energy corresponding to these simple cases.

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THERMAL DESORPTION FROM HETEROGENEOUS SURFACES

To consider TPD spectra from the outer surfaces of carbon nanotube bundles, we model the surface as three or five lines of adsorption sites.6 The sites in each line share the same binding energy, as follows: the central line, representing the “groove”, has the highest binding energy, whereas the adjacent lines (edges), located symmetrically to both sides of the groove, have weaker binding. 5027



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Figure 3. Coverage evolution (upper panels) and corresponding spectra (lower panels) for three-line lattices with different energy gap (left panels: 100 and 300 K; right panel: 100 and 500 K). Each curve is obtained starting from different initial coverages on the lattice. Dotted lines represent the peak temperatures expected for homogeneous systems characterized by the individual binding energies (Figure 2).

Figure 4. Partial contributions from the groove and edges to the overall coverage evolution (upper panels) and corresponding spectra (lower panels) for three-line lattices with different energy gap (left panels: 100 and 300 K; right panel: 100 and 500 K). Dotted lines represent the peak temperatures expected for homogeneous systems characterized by the individual binding energies (Figure 2).

shift occurs very similarly for both systems, regardless of the

a) The peak corresponding to desorption from the lower binding sites is shifted toward higher temperatures (as if the “effective” binding was higher).

energy gap between the sites: 5028



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distributed on the edge sites. The upper panels in Figure 4 show how desorption from each line contributes to the overall coverage decrease. At the beginning, desorption occurs mostly from the edges (blue, dotted line) while the groove coverage does not change; eventually, the groove’s coverage begins to decrease also. At that time, we observe that edge desorption slows down. This change in the desorption rate from the edges is the evidence that some of the particles leaving the groove sites are being transferred to the edges, before going into the gas phase. This can also be seen in the spectra for both systems; however, in the case of the wider gap system, the particle transfer is not as large and most of the edge particles have been desorbed at the time particles start to leave the groove. The overall spectra exhibit several differences: whereas the presence of desorption from more than one binding site is very clear for the wider gap system, the overall desorption seems to show only a single peak for the other system. Also, it is interesting to note that in this case the contribution from the edges shows a slower rate than the one from the groove, contrary to what would be expected based solely on the energy of the sites. This is another clear manifestation of the particle diffusion across the lines for this system. The spectra for the wider gap system may, however, be somewhat deceiving because it may lead us to believe that desorption happens independently from each group of sites and that we can extract the corresponding binding energies applying the P−W equation to each peak. That is certainly not the case, due again to the particle transfer, as shown by the vertical lines drawn on the spectra: the peak occurs at a temperature more than 30% lower than in the single energy case. Just to emphasize this fact, we show in Table 1 the binding energy values that could be obtained from each peak erroneously using the P−W equation; this would lead to 20− 30% differences with the actual binding energy values, as described above.

b) The peak corresponding to the higher binding site is considerably shifted toward lower temperatures (effectively lower binding). This may be somewhat surprising at first glance because the coverage is low enough to involve desorption from these sites only. c) This temperature-shifting effect is more significant for the higher binding sites. As shown below, we attribute this effect to the role of diffusion across lines during the desorption process. When we examined the kinetics of adsorption in our previous study,6 we observed that most of the occupation of the groove takes place after the particles had been adsorbed on the edge sites. We expect the inverse process, desorption, to occur in a similar manner but in the opposite direction. For example, particles adsorbed on the groove would acquire enough energy to allow them to move to lower binding energy sites in the neighboring edges first and then to the gas phase. To demonstrate this effect, we look in detail at two particular cases, when the initial coverage is 50 and 100% (monolayer), by following how desorption occurs from each of the different lines in the lattice. At 50% initial coverage, the groove sites are at first all occupied (33% of the lattice), and the rest of the particles are Table 1. Binding Energy Values Corresponding to Peak Temperatures on the Spectra Shown in Figure 3 According to P−W Equation (Middle Column) Compared with Actual Values Used in the Simulations (Right Column) peak temperature (K)

P−W “binding energy” (K)

binding energy (K)

∼37 ∼70 ∼100

∼120 ∼240 ∼350

100 300 500

Figure 5. Same as Figure 4 but with a starting coverage of a full monolayer. 5029



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Figure 6. Coverage evolution (upper panel) and corresponding spectra (lower panel) for a five-line lattice with energies 100, 300, and 500 K as described in the text. Dotted lines represent the peak temperatures expected for homogeneous systems characterized by the individual binding energies (Figure 2).

Figure 7. Partial contributions from the groove and edges to the overall coverage evolution (upper panel) and corresponding spectra (lower panel) for a five-line lattice occupied initially up to 30%. Dotted lines represent the peak temperatures expected for homogeneous systems characterized by the individual binding energies (Figure 2).

Figure 5 shows how desorption proceeds when a full monolayer is initially covering the surface, and the partial coverage on each group of sites contributes to the overall, observable coverage. As before, the edges empty first because of its weaker binding. Only a few particles are still on the edges when the groove starts to desorb, although this depends on the magnitude of the gap. The lower panels show the rate of desorption peaks for the whole lattice (black), for the edges (blue), and for the groove (red). The overall peak is the result of the overlapping of the other two individual features; these individual peaks cannot be observed experimentally when they result from the monolayer, but a hint of them can be obtained by varying the initial value of the coverage, as was shown in Figure 3. The lowest energy binding sites show a peak that is narrower, taller, and with a maximum at a lower temperature; on the other hand, desorption from the groove sites leads to a shorter, wider peak with a higher peak T. Even though the features for this particular initial coverage seem to be qualitatively consistent with what would be expected based on results for two independent homogeneous systems (in contrast with the last analyzed case), a noticeable shift on the expected peak temperatures is a clear indication of the inadequacy of the P−W equation to describe desorption from these inhomogeneous surfaces.

extra set of edges is added and hence another binding energy as well. The groove sites have the highest binding strength, followed by its neighboring edges, and the weakest sites belong to the outermost lines. Therefore, the overall TPD spectrum is expected to include features from three overlapping contributions corresponding to the groove sites and each set of edges. In this case, the initial distribution of particles among the lines for a given initial coverage is determined by η(β, μ) =

1/5 1 + eβε(g −μ)

+

2/5 1 + eβε(in.e −μ)

+

2/5 1 + eβε(out.e −μ) (3)

The coverage on the groove is given by the first term, whereas the other two terms represent the coverage on each one of the edge sites. Figure 6 presents the coverage evolution with time starting from different values of the initial coverage (upper panel) and the derived TPD spectrum for the corresponding initial conditions (lower panel). The spectrum appears to be a broad peak that gradually shifts to lower temperatures with increasing initial coverage. A second distinct peak becomes noticeably only for initial coverages closer to a monolayer and corresponds to desorption from the weakest edge sites. Although the individual features have peak temperatures that are representative of the strength of the binding energy of the sites from where the desorption curves come from, it is evidently not obvious to identify how many sites with different

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HETEROGENEOUS SURFACES: FIVE-LINES LATTICE RESULTS For atoms or molecules that adsorb in five lines, the simulation proceeds similarly to the three line case, except that here an 5030



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binding exist or what the binding energies are. Diffusion of particles among sites during desorption clearly affects the rates expected assuming that desorption was occurring independently from each set of sites (see vertical lines). The energy shift is more evident at higher temperatures (stronger sites) when diffusion events toward weaker binding sites are much more likely than direct desorption to the gas phase. We then analyze the contribution to the overall desorption from each group of sites when particles are initially covering 30 (Figure 7) and 90% (Figure 8) of the surface. In the first case, starting from an almost completely filled groove with the remaining particles occupying sites on the inner edges, desorption seems to be occurring simultaneously from both group of sites. A slight increase in the outer edges coverage is

Figure 8. Same as Figure 7 but starting with 90% with the lattice occupied initially. Figure 9. Early redistribution of particles observed at the very beginning of the desorption process. Each panel shows the partial coverage evolution on each line (full black lines), together with the origin of the contributions that make that coverage.

also observed that can be attributed to particles migrating from the groove or inner edges sites. If desorption starts from an almost full monolayer (Figure 8), particles in the outer edges are the first to desorb, followed by the inner edges and the groove. However, there is a considerable overlap between the various contributions to the spectrum that also become noticeably asymmetrical: while the outer edge peak starts with a sharply increasing profile as particles begin to desorb, a much longer tail is a clear evidence of incoming particles from the inner edges and the groove. A similar feature is observed for the inner edges desorption peak (that mostly receives desorbing particles from the groove). Correspondingly, a much broader starting edge present for the groove peak indicates the migration of the particles toward weaker sites much before acquiring enough energy to desorb directly to the gas phase.

As previously mentioned, it is possible that a rearrangement of the initial distribution of particles occurs very early in the process, much before any significant desorption begins. We illustrate this in Figure 9 for the case of 90% initial coverage by keeping track of where particles, initially adsorbed on specific sites, go once the temperature starts to rise. The upper panel shows that the rapidly decreasing coverage of the outer edges is composed of particles that were initially on the outer edges and coming from the inner edges or the groove. The rearrangement of the particles from the initial distribution happens very quickly during the first two time units: particles initially on the outer edges leave the sites to the inner edges, groove, and gas phase, and even though this loss is compensated by particles 5031



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migrating from the other lines to the outer edges, there is a net loss. From then on, the population steadily decreases (regardless of the origin of the particles) due to desorption to the gas phase. Similar processes occur for the inner edge or groove overall coverage, but in these cases, there is not net loss initially. Only after the outer edges are practically empty the overall inner edge coverage starts to decrease, followed by a similar evolution of the groove coverage.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 303-871-3547. Fax: 303-8714405. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support provided by the National Science Foundation through grants CBET-0746029 and DMR0705077.

DISCUSSION AND CONCLUSIONS

We have investigated the kinetics of desorption from a nonuniform surface that represents the external surface of a carbon nanotube bundle. The implemented KMC simulation scheme allowed us to relate the characteristics of the resulting TPD spectra to the elementary processes taking place during the thermal desorption of the adsorbate from that surface. Rather than providing a “data fitting” scheme, we have focused on understanding the origin of some of the observed characteristics of the spectra, based on the elementary processes that occur during desorption. Estimated values of energy parameters and frequency factors can be used to reproduce particular experimental results.7 Several specific features in the TPD spectra have been identified that originate on the energy heterogeneity of the surface. Spectra obtained by starting with progressively increasing initial coverage typically reveal more that one peak (or a single very broad peak if the energies are relatively similar). As explained below, the presence of adsorbate diffusion among different energy sites, which occurs prior to their eventual desorption into the gas phase, affects the spectra in two distinctive ways: 1) In addition to the expected appearance of more than one peak, considerable amount of overlap between them is typically present. Depending on different conditions, this overlap can even lead to a single, broad peak in the spectrum. 2) Even in the case that several individual peaks can still be identified, P−W analysis based on individual peak temperatures does not provide correct binding energies. If the energy gap is large enough, then the multipeak feature becomes evident as long as the initial coverage is high enough to include the occupation of some of the weaker binding sites as expected. However, the shift in the peak temperature is always present, regardless of the number of peaks. This is the case even when the initial coverage is very low, and desorbing particles initially occupying only the strongest binding sites generate a single desorption peak. This occurs because just the presence of empty sites with a different energy allows diffusion to occur, affecting directly the speed of the process. Diffusion makes desorption from weaker binding sites slower (because they are receiving particles from the groove) and desorption from stronger binding sites faster (because they leave the sites at a smaller energy cost to the edges). This effect is in fact larger for the low coverage single peak because desorption to the gas phase is strongly mediated by previous diffusion to available weaker binding sites from where the actual transition to the gas phase typically takes place. The energy difference among the various binding sites has an effect on the observed spectra as well. For a wider gap, the existence of separate features that form the whole system’s peak is more evident and happens for relatively lower coverages. In any case, it is clear the P−W equation cannot not provide accurate results when desorption experiments are performed on energetically heterogeneous systems, not even when the features seem to be separated from each other or a single peak seems to be present.

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REFERENCES

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Thermal Desorption from Heterogeneous Surfaces - The Journal of

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