Langmuir 1993,9, 3067-3076
3067
Effects of Heterogeneous Surface Geometry on Adsorption Alon Seri-Levy and David Avnir* Department of Organic Chemistry and the F. Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Received January 5, 1993. In Final Form: April 6, 1993
We demonstrate through simulations that surface geometry heterogeneity is sufficient to induce an adsorption/desorption hysteresisloop. The simulationsshow that the hysteresis originatesfrom the quasiequilibrium nature of the adsorption branch. Different shapes of hystereses were obtained (parallel, widening,and unclosed at low relative pressure),accordingto the geometryof the surface (lowmicroporosity, high microporosity, and mesoporosity). A unique population of permanently trapped gas phase molecules was identified and the dynamic nature of this population, termed “latent adsorbed” molecules, was demonstrated. The behavior of the BET equation in the presence of geometrical surface heterogeneity and lateral interactions was examined. It was found that the error in calculating the BET surface area, for the same surface-adsorbate and adsorbate-adsorbate interactions, is greater for irregular surfaces than for smooth surfaces. This observation is attributed to the effect of surface heterogeneity on higher adsorbed layers, which in turn increases the influence of adsorbate-adsorbate interactions. For weak lateral interactions the BET surface area estimation was within 10% of the theoretical prediction. The effects of surface heterogeneity on the thermodynamic functions of the adsorption/desorption process were calculated. The important role of the entropy of adsorption in the generation of the hysteresis loop was identified. 1. Introduction
A major difficulty in surface science and catalysis is that of analyzing physical and chemical adsorption processes carrried out on geometrically heterogeneous solids. In this report, we simulate adsorptionldesorption processes in order to explore the effects of heterogeneous surface geometry on the structure of adsorption isotherms and their hysteresis loops, on the thermodynamic parameters of the adsorption process, and on the accuracy of the BET equation in calculating surface areas. For a detailed simulative analysis of the BET isotherm on smooth surfaces, see our previous rep0rt.l The complexity of reaching an analytical description of multilayer localized adsorption of gases on heterogeneous solids is extensively addressed in refs 2 and 3. It has been observed that most proposed models do not fully mimic reality and that quite often the resultant equations are rather complex. In the same vein, Young and Crowel14 write “reductioad absurdum,the prefect adsorption theory which takes all factors into account would lead to an isotherm equation of such complexity that it could not fail to describe any isotherm shape”. A modern scientific tool which helps to overcome, at least partially, these difficulties is Monte Carlo simulat i o n ~ . ~Although *~ these do not provide analytical formulations for adsorption on heterogeneous solids, they do enable the observer to look into the reaction system a t molecular resolution and, hence, to qualitatively examine the effect of heterogeneity (and lateral interactions) on the adsorption isotherm. As will be shown below, this technique not only has provided an indication that surface geometric heterogeneity alone may result in the formation (1) Seri-Levy, A.; Avnir, D. Langmuir 1993, 9, 2523. (2) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (3) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: London, 1992. (4) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworths: London, 1962; p 157. ( 5 ) Nakagawa, T. Kolloid 2.2.Polym. 1967,221,40. Patrykiejew, A.; Binder, K. Surf. Sci. 1992, 273, 413. Nicholson, D.; Parsonage, N. G.
Computer Simulation and Statistical Mechanics of Adsorption; Academic Press: London, 1982.
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Figure 1. Irregular curves. Curve c is similar to b but with a larger minimal pore area.
of a hysteresis loop but also demonstrates the existance of a unique molecular population, to which we refer as “latent adsorbed molecules”.6 (6) (a) Seri-Levy, A.; Avnir, D. Proceedings of the 4th International Conference on Fundamentals of Adsorption; Suzuki, M., Ed.; in press. (b) Seri-Levy, A. Ph.D. Thesis, The Hebrew University of Jerusalem, Jerusalem, December 1992.
1993 American Chemical Society
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Figure 3. Adsorption isotherms for curve c in Figure 1: (a) for QJRT = 3.25 and QdRT = 0.325, (b) for QIIRT= 6.5 and QdRT = 0.65;0,adsorption;0 ,desorption. The dotted horizontal line
indicates the monolayer.
surface (Figure 1) straight line curve a curve b curve c
coastline length (pixel) 100 486 1142 2284
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The origin of the hysteresis loop anomaly has been attributed to several factors: For example, Zsigmondy' assumed that hysteresis is due to a difference in the wetting angle during adsorption and desorption processes; Cohans has proposed that cylindrical pores are filled from their walls inward, forming a cylindrical meniscus, while desorption occurs from a hemispherical meniscus; McBaing suggested that hysteresis is caused by the presence of bottleneck pores, such that during adsorption the wider inner pore section is filled at high relative pressure and emptied during desorption only after the pore neck is emptied of adsorbates at low relative pressure. It seems that no single mechanism is responsible for the hysteresis phenomenon, but we show below that the combination of simple adsorption rules and surface geometric heterogeneity is sufficient to result in hystereses of the type described by McBain, which in turn is the result of the finite observation time, i.e. of the establishment of a quasiequilibrium state.
Attempts to extend the BET equation to simple energetically heterogeneous systems were made by, e.g., McMillan,'O Walker and Zettlemoyer,ll and Joy,12 who considered heterogeneous surfaces with two different types of adsorption sites only. Their resultant equations, and those of other researchers such as Aston et al.,13Levin,14 and Honig,15who assumed a wider variety of adsorption sites, led to complex multiparameter equations. As Gorter and Frederikse16 have noted, "the kinetical BET theory gives a simple and valuable first picture of the phenomenon of adsorption, but it seems difficult to correct its obvious shortcomings without destroying the simplicity which perhaps constitutes ita chief attraction". This convenience is probably what has made the classical BET equation so popular among experimentalists, who favored ita simplicity even at the price of its inaccuracy. For this reason, evaluating the error obtained in the application of the classical BET equation to heterogeneous systems is of vital importance. The Monte Carlo simulations conducted in this work enable this estimation. (10)McMillan, W. G. J. Chem. Phys. 1947,15,390. (11) Walker, W. C.;Zettlemoyer, A. C. J. Phys. Chem. 1948,52,47. Zettlemoyer, A. C.; Walker, W. C. J. Phys. Chem. 1948,52,68. (12)Joy,A.S.Proeeedingsofthe2ndZnterMtionaZ CongressofSurface Activity;Schulman,J.H.,Ed.;Butterworths London,1967;Vol. 11,Solid/ Gas Interface, p 54. (13) Aston, J. G.; Tykodi,R.J.;Steele, W. A.J.Phys. Chem. 1966,59, 1nxi.
(7) Zeigmondy, A. Z . Anorg. Chem. 1911, 71, 366. (8) Cohan, L. H. J. Am. Chem. SOC.1938,60,433. (9) McBain, V. W. J. Am. Chem. SOC.1936,57, 699.
(14)Levin, V. I. 2.Fiz.Khim. 1961,25, 463. (15)Honig, 3. M. J. Phys. Chem. 1963,57, 349. (16) Gorter, C. J.; Frederikse, H. P.R. Physica 1949, 15, 891.
Effects of Surface Geometry on Adsorption
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b
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Figure 4. Two points on the adsorption branch of the isotherm in Figure 2a: top, PIP0 = 0.15; bottom, P/Po = 0.62; red circles, adsorbed molecules; blue circles, unadsorbed molecules.
Figure 5. Two points on the desorption branch of the isotherm in Figure 2a: top, PIP0 = 0.15; bottom, P/Po = 0.62.
2. Simulation Details Three irregular lines (Figure 1)and a straight line were compared in this study. All lines are portions of fractal lines and were chosen because of the growing evidence that natural irregularity is well described in that way. Yet this choice was a matter of convenience and we do not use the fractal dimension below. The construction of the curves is detailed in ref 17. Curves a and b contain pores of minimal area equal to the adsorbate size (micropores). Curve c is similar to curve b but with a minimal pore area, equal to that of three adsorbates (mesopores). Above each line, a reservoir envelope was built by positioning onepixel layers one on top of the other. Table I summarizes the surface and reservoir details. For each set of simulations, two interaction heats are defined. The first, Q1, is defined as the heat of adsorption to the surface, and the second, Q2, is defined as the heat of interaction between two adjacent adsorbed molecules. In thermodynamic terms, the probability of desorption from the first layer is exp(-Ql/RT) and the probability of detachment from higher layers is exp(-Q2/RZ'). Hence, by adding lateral interactions of van der Waals type, the desorption probability, either from the first layer or from any higher layer, D,is (17)Seri-Levy, A.; Avnir, D. Surf. Sei. 1991,248, 258.
where 21 is the number of nearest neighboring surface sites (21 = 1 in the case of smooth line) and 2 2 is the number of nearest neighboring adsorbed molecules. (exp(-22&2/RT> is the desorption probability from layers higher than one.) The temperature, T,is also an input parameter of the simulation. Since the surfaces are geometrically heterogeneous,adsorbed molecules desorb from the surface with different probabilities, according to the number of adjacent surface sites. The geometric heterogeneity is the source of the surface energetic heterogeneity. The adsorption/desorption simulation rules were carried out as fo1lows.l An initial number of adsorptives (gasphase molecules) is homogeneously distributed in the reservoir, each adsorptive occupying an area of one pixel. No interactions are allowed between the adsorptives. At each time step, all molecules are treated consecutively in random order, according to the following rules: If the chosen molecule neighbors a surface site or an adsorbed molecule, this neighboring molecule becomes adsorbed. If the chosen molecule is adsorbed desorption is attempted with probability D. After all the molecules have been treated, all gas-phase molecules are mixed and redistributed randomly and homogeneously, and the next time step begins. This procedure is repeated until equilibrium is reached, i.e.
3070 Langmuir, Vol. 9, No. 11, 1993
Seri-Levy and Avnir a
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Figure 6. Two points on the adsorption branch of the isotherm in Figure 2b: top, PIP0 = 0.13; bottom; PIP,-, = 0.62.
Figure 7. Two points on the desorption branch of the isotherm in Figure 2b: top, PIP0 = 0.13; bottom, P/Po = 0.61.
until the amount of adsorbed molecules remains constant for at least 1000 time steps. To ascertain equilibrium, sample simulations were run for an additional 50 000 time steps or more without any significant difference, neither in the amount adsorbed nor in the pores filling. This was done for both adsorption and desorption branches. For a full adsorption isotherm, the whole procedure is repeated for various initial gas-phase concentrations. While the adsorption branch of the adsorption/desorption isotherm is calculated from an initially exposed surface, the desorption branch was obtained by initially filling all the surface pores with adsorbed molecules,in accordance with the Gurvitsch rule.ls The P/Po value for each adsorption/ desorption isotherm point is calculated from the ratio of the equilibrium concentration at that point and the "saturation" concentration, i.e. the concentration were the adsorption isotherm climbs up sharply. The simulations were carried out with Ql/RT = 3.25 and &2/RT = 0.325. The probability of adsorption to an already adsorbed molecule was chosen to be relatively low in order to avoid masking the effect of the surface heterogeneity with lateral interactions.
3. Results and Interpretations
(18) Gurvitsch, L.J . Phys. Chem. SOC. Russ. 1915, 47,805.
3.1. The Adsorption/Desorption Isotherms. The isotherms obtained are shown in Figure 2a (for curve a), Figure 2b (for curve b), and Figure 3a (for curve c). For reasons of comparison, we doubled, for one set of simulations on curve c, the values of Q1 and Q2, which resulted in the isotherm shown in Figure 3b. Due to the high heat of adsorption to the surface, the obtained isotherms are of type 11, with different types of hystereses according to the minimal pore area, as explained below. We begin the hysteresis analysis from a case in which it is barely evident, namely Figure 2a. The reason for the similarity of the adsorption and desorption branches becomes evident by comparing Figure 4 (adsorption) and Figure 5 (desorption). Figure 4 top (P/Po = 0.15) shows that the adsorbed molecules obstruct the entrances to the smallest pores and prevent additional adsorption in these pores even at the low relative pressure. Increasing the relative pressure to P/Po = 0.62 (Figure 4 bottom) does not affect this picture of blocked pores, and the same pores that were empty at the low relative pressure remain empty at the high relative pressure with no further blocking. On the other hand, on the desorption branch (Figure 5), the pores are filled with adsorbed molecules at both relative
Effects of Surface Geometry on Adsorption
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Figure 8. Equilibrium point on adsorption branch: QdRT = 6.5; Q$RT = 0.65; P/& = 0.28. The turquoise filled circles are latent adsorbed molecules (observation time = 2000 time steps at equilibrium). The green circles are temporarily trapped molecules. The black circles mark pore entrances.
pressures, and therefore the total difference between adsorption and desorption (for the same P/Po) remains almost constant; hence the similarity in shape of the two branches. The very narrow gap between the two is due the very small number of the blocked pore entrances and to their small size. In the surface described by curve b (Figure l), there are narrow pores of varying sizes such that the degree of obstruction of these pores changes with the relative pressures. Hence the obtained hysteresis shown in Figure 2b widens as the relative pressure increases and the desorption branch meets the adsorption branch only at liquefaction. A comparison between Figure 6 top (PIP0 = 0.13)and Figure 6 bottom (P/Po = 0.62) indeed shows that at high relative pressure, additional pores become obstructed. At similar pressures on the desorption branch
(Figure 7 top and Figure 7 bottom, respectively), the blocked pores are filled with adsorbed molecules which causes the resultant hysteresis to widen. The desorption branch fails to merge with the adsorption branch at low relative pressure due to the microporosity: all molecules are adsorbed and no equilibrium is reached. This phenomenon of an open hysteresis is observed experimentally in microporous material^.^^^^^ And indeed, when the smallest pores are 3 times wider than the adsorbate size (Figure 1curve c), obstruction of these pores occurs at a higher pressure (PIP0 = 0.25), and the hysteresis bifurcation is observed. Finally, when the surface heat of (19) Burgess, C. G. V.; Everett, D. H.; Nuttall, S. Pure Appl. Chem. 1989,61, 1845.
(20)Gregg, S . J.; Sing,K.S . W .Adsorption, Surface Area and Porosity; Academic Press: London, 1982; pp 228-242.
3072 Langmuir, VoZ. 9, No. 11,1993
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Figure 9. Equilibrium point on adsorption branch: QlIRT = 6.5; QJRT = 0.65;P/Po= 0.3. The turquoise filled circles are latent adsorbed molecules (observation time = 2000 time stem at eauilibrium). The green circles are temporarily trapped molecules. The black circles mark pore entrances.
adsorption for the isotherm in Figure 3b is significantly increased Figure 3b vs Figure 3a), then a shaper rise to the monolayer is observed at lower P/Po, and the isotherm is more characteristic of type 11. The adsorption/desorption hysteresis is explained below by showing the quasi-equilibrium nature of the adsorption branch. 3.2. Latent Adsorption. We draw the reader’s attention to a unique population of trapped gas phase molecules evident in Figures 8 and 9 (turquoise filled circles). These are molecules which are entrapped in bottleneck pores or in narrow pores and thus disconnected from the adsorptive bulk during the observation time (2000 time steps at equilibrium for Figures 8 and 9). To an experimenter, they may appear not as part of the adsorptives but as part of the adsorbed molecules; hence we term this phenomenon “latent adsorption”. Furthermore, a distinction can be made between two populations of trapped molecules. The first is a population of latent adsorbed molecules, trapped inside the smallest pores and “never” (very long observation time) released to the bulk (37 particles for Figure 8 and 47 particles for Figure 9). The second population is of those molecules temporarily trapped during the observation time period. Their amount (green hollow circles in Figures 8 and 9) depends on the rate of opening and closure of pore entrances and on the
observation time window. Notice that the latent adsorbed molecules can equilibrate with the adsorbed molecules within the closed pores but “never” with the bulk adsorptives. The discrete pore size distribution on the surface described in Figure 8results in a clear distinction between the latent adsorbed molecules and the temporarily trapped molecule population, as shown in Figure loa. Opening and closing of the two pores marked by circles in Figure 8 produces two subgroups of temporarily trapped molecules (uppermost on the graph), while the latent adsorbed molecules are the main component of the lowest subgroup on the graph. In Figure lob, no such distinct subgroups can be identified, since the surface pore size distribution is almost continuous. Parts a and b of Figure 10 highlight the dynamic nature of the trapped molecule population and emphasize the importance of the lifetime of the plugs that block the pore entrances. This lifetime, in turn, is a reflection of the relative pressure, the heats of adsorption, and the details of the surface structure. Notice the significantly longer periods of pore obstruction in Figure lob. (Following a conference presentation of this result,& suggestions were made as to how to evaluate the amount of latent adsorbed molecules experimentally. We encourage readers interested in that question to correspond with us on possible experiments.)
Effects of Surface Geometry on Adsorption
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It is therefore evident now that the adsorption/desorption hysteresis originates from the quasi-equilibrium nature of the adsorption branch. Eventually, if sufficient time is allowed, all blocked pores will open and be filled by adsorbates. We suggest that in many real microporous systems, this is the main cause of hysteresis. 3.3. BET Analysis of Adsorptionon Geometrically HeterogeneousSurfaces. Simulations carried out on a smoothline with Q1/RT = 3.25 and QdRT = 0.325 indicate that although the BET constant is relatively low, C = 30, the surface area is determined with an error of only 1% (Table 11),indicating that the effect of lateral interactions is very weak. (cf. also our BET study in ref 1.) The BET analysis results of adsorption simulations on all curves are summarized in Table 11. For curves a and c, and QdRTand QdRTvalues identical to those used for the smooth line, the calculated BET surface areas were found to be only 10% below the actual surface area. This remarkable robustness of the BET equation, which was not tailored for these conditions, was already commented on in ref 1. Even so, a significant improvement in the estimation of the surface area of curve c is obtained by reducing the P/Po interval (see Table 11). A high C value isotherm for curve c is shown in Figure 3b, for conditions of Q1/RT = 6.5 and Q2/RT = 0.65. High C value isotherms are characterized by a very sharp knee at a very low P/Povalue, and thus the B-point indicates the exact monolayer (shown by the horizontal dotted line). This being so, the B-point of the high C value isotherm in Figure 3b indicates the exact monolayer value, while
Figure 11. Top: 2041 adsorbed particles on the adsorption branch of the isotherm in Figure 3b. Bottom: 2026 adsorbed particles on the adsorption branch of the isotherm in Figure 3a.
the isotherm in Figure 3a, for the same curve c but a low BET constant, yields an underestimated monolayer. Examining the surface distribution of the adsorbed molecules at monolayer coverage, as taken from the adsorption branch of these two isotherms, reveals the almost uniform monolayer coverage for the Figure 3b isotherm (Figure 11bottom). This is in contrast to the nonhomogeneous and uneven coverage for the Figure 3a isotherm (Figure 11,top), indicating the presence of strong lateral interactions between adsorbed molecules, which impede accurate surface area estimation. For the microporous surface described by curve a, only a small improvement in the monolayer estimation is achieved by increasing C and lowering the P/Po interval. The failure of this manipulation can be attributed to the blocking of the surface pores. As shown above in Figure 4, part of the surface is totally inaccessible to adsorption and is not measured. (These unmeasured blocked zones, however, can be active in other physical and chemical reactions not involving adsorption.)
3074 Langmuir, Vol. 9, No. 11, 1993 ~
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Seri-Levy and Avnir
Table 11. BET Analysis Results for Irregular Surfaces BET analysis QdRT QdRT isotherm PIP0 min. P/Po max. N, 0.08 0.28 99 0.325 3.25 0.28 294 0.05 0.325 Figure 2a 3.25 293 0.05 0.28 0.325 6.5 0.005 0.05 299 0.325 6.5 0.29 477 0.06 0.325 Figure 2b 3.25 0.27 1868 0.05 0.325 Figure 3a 3.25 1804 0.05 0.30 0.325 6.5 0.003 0.05 2064 0.325 6.5 0.25 1793 0.05 0.65 Figure 3b 6.5 0.05 2025 0.003 0.65 6.5
corr coeff 0.9996 0.9999 0.9998 0.9999 0.9991 0.9990 0.9988 0.9993 0.9990 0.9997
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Figure 13. Thermodynamic parameters for the isotherm in Figure 2a: 0,adsorption; @, desorption.
A significant portion of the surface described by curve b is within micropores, which become blocked at relatively low PiPo. This significant portion of the surface is hence inaccessible to further adsorption and attempts to measure
the surface area by adsorption processes will lead to a false estimation. It followsthat surface area measurements from adsorption branches should only be carried out if the hysteresis commences after the B-point.
Effects of Surface Geometry on Adsorption
Langmuir, Vol. 9, No.11,1993 3075
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The simulation results show that, for the same heats of adsorption, adsorption on the smooth line was unaffected by lateral interactions and the monolayer BET was accurately measured, while for the irregular a and c curves, an underestimationof 10% was obtained. Our explanation of this observation is that the influence of surface geometry heterogeneity does not terminate at the first adsorbed layer but rather is reflected on to higher adsorbed layers. The first (and subsequent) adsorbed layers on curves a and c are therefore more irregular than the first (and subsequent) adsorbed layers on the smooth line. A molecule adsorbed on curves a and c has more neighboring adsorbed molecules, and lateral adsorbate-adsorbate interactions are more dominant than for the smooth line. In summary, although surface heterogeneity contributes to an increase in lateral interactions and hence to the error in the BET surface area estimation, for relatively weak adsorbate-adsorbate lateral interactionsthe BET area was
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found to be accurate to within 10%. To understand why the BET equation is so robust, we recall that Brunauer21 pointed out that up to monolayer coverage, surface heterogeneity and lateral interactions compensate each other. This is so since high-energy surface sites are occupied at lower relative pressure where lateral interactions are relatively weak, and low energy surface sites are occupied at higher relative pressure where lateral interactions are dominant. We therefore propose to lower the PIP0 range below the B-point, if the BET equation is selected for estimation of surfaceareas of heterogeneouslygeometric materials. 3.4. Thermodynamic Functions of the Adsorption Process. The net free energy change, AG,accompanying ~~
(21) Brunauer,S.SolidSwfaeesand theGas-SolidZnterface;Advancea in Chemistry Series, No. 33; American Chemical Society Wmhingbn,
DC,1961.
3076 Langmuir, Vol. 9, No. 11, 1993 the condensation of vapor in a pore during adsorption, is given by RT ln(P/Po),22 and the net free energy of the adsorption and desorption branches can therefore be calculated from the adsorption/desorption isotherms (cf. also refs 23 and 24). The net enthalpy of adsorption, AH, can be independently calculated in our simulations from the difference between the average heat of adsorption of a molecule at equilibrium with bulk at pressure P and the average heat of adsorption of a molecule at equilibrium with bulk liquid at pressure PO. The net entropy of adsorption, AS, is then calculated from AG = AH - TAS. The resultant thermodynamic parameters for the smooth surface and the isotherms shown in Figures 2a,b and 3a are presented (in units of R T ) in Figures 12-15, respectively. It is seen that the enthalpy profiles of both the adsorption and desorption branches rapidly coincide.This similarity of the enthalpy profiles, for the same amount of adsorbed molecules, is a consequenceof a similar degree of geometrical irregularity of the hull contour of adsorbed molecules which is the actual surface the adsorption process *sees” on both branches. Thus, the main factor (22) Lowell,S.; Shields,J. E. Powder Surfaces and Porosity; Chapman and Hall:London, 1987; p 68. (23) Pfeifer, P.;Cole,M. W.New J. Chem. 1990, 14, 221. (24) Jaroniec, M.; Lu,R.; Mndey, R.; Avnir, D. J. Chem. Phys. 1990, 92, 7689.
Seri-Levy and Avnir
contributing to the gap between the branches of the net free energy of adsorption is the net entropy of adsorption. This is also evident in the similarity between the isotherm hystereses shapes and the net entropy of adsorption hystereses: A wide gap in the adsorption isotherm hysteresis results in a wide gap between the branches of the net entropy of adsorption. The identification of entropic effects as the major ones in the opening of the adsorption/desorption hysteresis loop is a main result of this study. The knee in the net entropy curves observed inFigures 12and 15is a sensitive indicator of the transition from surface adsorption to higher layer adsorption. However, for the net entropy curves of the microporous surfaces (Figures 13and 141,no noticeable knee is observed since the smallpores are immediately blocked and a higher layer liquefaction process commences. Finally notice that the net entropy of adsorption is always positive since a bulk molecule at pressure P has more degrees of freedom than a bulk liquid molecule (at PO).
Acknowledgment. We thank A. Ben-Shad and J. Samuel for their help in the thermodynamic aspects of this report. This work was supported by the US.-Israel Binational Foundation. D.A. is a member of the Farkas Center for Light Energy Conversion.
