- Email: [email protected]
Separation of chiral molecules by temperature programmed desorption
Applied Surface Science 256 (2010) 5503–5507
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Separation of chiral molecules by temperature programmed desorption Paweł Szabelski * Department of Theoretical Chemistry, Maria Curie-Skłodowska University, pl. M.C. Skłodowskiej 3, 20-031 Lublin, Poland
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 28 December 2009
The Monte Carlo simulation method was used to model thermal desorption of a pair of enantiomers from a solid surface with a chiral periodic pattern of active sites. The main objective of the study was to determine the optimal number of the active sites and their spatial distribution within the unit cell of the surface to achieve the most efficient separation of the enantiomers. For that purpose we tested the series of chiral patterns which were found previously for the equilibrium adsorption. Temperature programmed desorption spectra were calculated using a square lattice of adsorption sites in which the active sites were distributed spatially according to the candidate patterns. Additionally, influence of relaxation of the adsorbed layer on the relative shift of the TPD peaks of the enantiomers was assessed and the key factors affecting the chiral separation were identified. ß 2009 Elsevier B.V. All rights reserved.
PACS: 68.43.h 68.43.De 68.03.Hj 68.43.Vx Keywords: Chiral molecules Thermal desorption Monte Carlo simulation Enantioseparation
1. Introduction Adsorptive separation of chiral molecules has been long recognized as a powerful method that is frequently used in pharmaceutical, drug, cosmetic and agricultural industries. The effectiveness of the enantioseparation process is particularly important because in the vast majority of practical applications only one enantiomer is usually needed either for the fabrication of a final product or for further processing. For example, it is often observed that while one enantiomer can have desired (e.g. therapeutic) effect, the other can be neutral or even harmful in the worst case, leading to poisoning of a patient. For that reason substantial effort has been made to develop and improve methods of fabrication of extremely pure enantiomeric substances [1,2]. Liquid chromatography, which uses chiral stationary phases (CSPs) composed of a silica support with chiral ligands capable of selective recognition of the complementary enantiomer, holds a leading position in this field [3]. Recently there has been growing interest in alternative methods of separation of enantiomers. One promising avenue in this area is adsorption of chiral molecules on nanostructured solid surfaces which are created using single crystal planes [4,5]. The chiral nanostructured surfaces are obtained, for example, by cleavage of achiral bulk materials such as metals [6,7], templating
* Tel.: +48 81 537 5518; fax: +48 81 537 5658. E-mail address: [email protected]. 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.12.124
surfaces with organic modifiers [8,9] or exposing of surfaces of naturally chiral crystals [10,11]. The above techniques allow fabrication of a crystalline surface which has a unique structure not superimposable with its mirror image and thus it is chiral. Temperature programmed desorption has been used to examine binding of chiral adsorbates to naturally chiral metallic surfaces [12,13] as well as to metallic surfaces templated with organic molecules [14,15]. An interesting application of this technique has been proposed by Gellman and coworkers who have used TPD to demonstrate the potential of naturally chiral surfaces to differentiate between enantiomers of chiral alcohols [16]. To explore further enantiospecific desorption of chiral molecules from naturally chiral surfaces MC simulations of thermal desorption of small chiral hydrocarbons from the series of chiral platinum single crystal faces have been performed [17]. In this case the largest difference in desorption energy, 2 kJ/mol, was predicted for the enantiomers of dimethylcyclopropane desorbing from the Pt(643)S surface. These simulations have demonstrated the importance of local atomic order which is responsible for the preservation of individual enantiospecific adsorption properties of the surface. Recently, we have started systematic investigations of a model chiral surface which provides a new mechanism of selective differentiation between enantiomers under equilibrium conditions [18–21]. We demonstrated that the one-to-one correspondence between a chiral selector and the complementary enantiomer is not a necessary condition for the selective adsorption of that enantio-
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mer. The proposed surface, apart from conventional adsorption experiments, can be also used in ultra high vacuum conditions, providing for example, enantioselective environment for thermal desorption of chiral molecules. The main purpose of this study is to examine the possibility of manipulating structural properties of the model chiral surface to achieve efficient separation of enantiomers by temperature programmed desorption. Moreover, we examine the influence of mobility of adsorbed chiral molecules on the extent of separation. 2. Simulation We consider thermal desorption of model chiral molecules from a solid surface represented by a square lattice of binding sites with well-defined binding energies. The chiral molecules are modelled as rigid S-shaped chain structures composed of four identical segments. A molecular segment can be an atom or a functional group occupying one binding site. In the simplified approach adopted here only that part of the molecule which directly contacts the surface is considered. The remaining part of the molecule which is not involved in the adsorption is disregarded and assumed to be responsible only for preservation of chirality in the bulk phase. According to this assumption, the only important structural property of the molecule is the footprint it leaves on the surface. One example is trans-1,2-dimethylcyclopropane (DMCP) whose enantiomers are shown schematically in the top part of Fig. 1. This figure shows also the chiral footprints of enantiomers S and R of DMCP consisting of four adsorption sites, each occupied by one segment of the adsorbed enantiomer.
The adsorbing surface was built using two types of sites whose strength of interaction with a single segment of the chiral molecule was markedly different. The energy of interaction between an active site and a segment of the molecule was characterized by ea while that between an inert site and the segment by ei. In order to construct a surface selective towards one of the enantiomers the active sites were distributed on the lattice in such a way that the chosen enantiomer can adsorb more strongly than the other one, as assumed in our previous works [18–21]. An example of the distribution meeting this requirement is shown in the bottom part of Fig. 1 for the S-selective surface. The main origin of selectivity of this surface is the larger number of active sites which can be occupied by a single molecule of S (maximally two sites) compared to enantiomer R (maximally one site), as shown in the bottom part. The simulations were performed on a square L L lattice of adsorption sites with L = 100. The adsorbing surface consisted of active and inactive sites whose energy of interaction with a single molecular segment was ea = 20 kJ/mol and ei = 10 kJ/mol, respectively. To model the TPD spectra we used the conventional algorithm of thermal desorption whose details can be found elsewhere [22–24]. When the adsorbed layer was allowed to relax via very fast diffusion [22] we assumed that a molecule can jump either vertically or horizontally by one lattice site to the next position. In the simulations described here we used N = 200 molecules (100 S + 100 R) so that the total surface coverage, u = 4 N/L2 was equal to 0.08. The MC desorption rate was defined as Du/DT, where Du is the change in the surface coverage induced by increasing the temperature from T to T + DT. Analogous definitions refer to pure enantiomers R and S. The pre-exponential frequency factor and the heating rate used in the simulations were 1013 s 1 and 1 K/s, respectively. The values of the parameters used in our virtual TPD experiment do not correspond to any real system and they were chosen just to illustrate basic properties of the proposed model. In particular, one has to remember that the assumption of the same pre-exponential factor for different configurations of a molecule on the nanostructured surface does not have to be valid in real systems. Similarly, the small difference between the desorption energies ea and ei can be insufficient to produce visible changes in the rate of desorption. These issues are, however, beyond the scope of the present paper whose main objective is to find optimal topography of the chiral surface. The results of the simulations described here are averages over 50 independent starting configurations of the adsorbed enantiomers. For each of these configurations the temperature scan was repeated 200 times and the resulting spectra were subsequently averaged. 3. Results and discussion Below we present the results of the MC simulations of thermal desorption of the racemic mixture (S + R) from a few surfaces which differ in both spatial distribution and number of actives sites within the unit cell. These results were obtained for localized as well as mobile adsorption of the enantiomers and they are compared in the following sections. 3.1. Effect of surface topography and molecular diffusion
Fig. 1. Method of construction of the model chiral molecules from the backbone of 1,2-dimethylcyclopropane and projection of the enantiomers onto a square lattice (top). An example of the S-selective surface with a periodic chiral distribution of active sites. The thick dashed line delimits the unit cell of the surface. The examples of possible adsorbed configurations differing by the number of occupied active sites are also shown for each enantiomer (bottom).
Figs. 2–4 show the examples of TPD spectra calculated for different spatial distributions of the active sites on the chiral surface. These distributions were found using the Monte Carlo search technique which was based on maximization of the ratio of the Henry constants calculated for enantiomer S and for enantiomer R, that is on maximization of the selectivity of the surface towards enantiomer S. A detailed description of this procedure can be found elsewhere [20]. Note that the unit cells
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Fig. 2. An example of TPD spectra of the racemate S&R from the nanostructured surface A with a different distributions of five active sites within the (5 5) unit cell (see the top panel). The results presented in the top part correspond to localized adsorption while those from the bottom part were obtained assuming relaxation of the adsorbed molecules.
Fig. 3. One more example of TPD spectra of the racemate S&R from the nanostructured surface B with a different distribution of five active sites within the (5 5) unit cell (see the top panel). The results presented in the top part correspond to localized adsorption while those from the bottom part were obtained assuming relaxation of the adsorbed molecules.
shown in the three figures are identical with respect to the size of the cell (5 5) as well as to the number of active sites they contain (5). The only difference between the unit cells from Figs. 2–4 is the way in which the active sites are arranged spatially. As it follows from the comparison of Figs. 2–4 redistribution of the active sites within the unit cell leads to significant qualitative changes in the shape of the corresponding TPD spectra. This can be easily noticed and explained for the curves obtained assuming a lack of relaxation of the adsorbed layer (top parts). Namely, the number of composite peaks on the total TPD curve is equal to 5, 4 and 3 for patterns A–C, respectively. This originates mainly form a different number of energy modes associated with possible adsorbed configurations of enantiomers S and R. For example, in the case of pattern C shown in the bottom part of Fig. 1 we can observe that a molecule of S can have three energetically different configurations while for enantiomer R the number of configurations is equal to two. The energies of these configurations are strongly correlated with the number of active sites occupied by a molecule of a given enantiomer. For enantiomer S adsorbed on the surface from Fig. 1 there are three values of desorption energy equal to 2ea + 2ei, ea + 3ei and 4ei, corresponding to two, one and no active sites occupied by the molecule, respectively. For enantiomer
R the desorption energy is equal to ea + 3ei or to 4ei which gives only two energy modes. For this simple reason the total TPD spectrum, which is a linear combination of the TPD curves calculated for pure enantiomers consists of three peaks. The peaks at 150 and 185 K come from simultaneous desorption of both enantiomers while the high-temperature peak at 220 K corresponds to desorption of S alone. Analogous analysis can be performed in the case of systems A and B and the composite peaks shown in Figs. 3 and 4 (top parts) can be assigned to the corresponding adsorbed configurations of each enantiomer. Furthermore, peak temperatures for immobile enantiomers in systems A–C can be calculated using the Redhead’s formula based on the desorption energies associated with each molecular configuration [22]. Regarding the effect of fast surface diffusion, we can observe that the shape of the TPD spectra shown in the top parts of Figs. 2– 4 changes markedly when the adlayer is allowed to relax (see the bottom parts). In particular, switching on the relaxation leads to a reduction in the number of composite peaks on the total TPD spectrum calculated for each system. Moreover, it can be also noticed that the low-temperature peaks disappear which leads to a substantial growth of the peaks centered at higher temperatures.
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effect is the possibility of separation of the enantiomers by collecting desorbed fractions, that is just by cutting-off the lowtemperature part of the spectrum. 3.2. Enantioseparation
Fig. 4. TPD spectra of the racemate of enantiomers S and R from the nanostructured surface C whose (5 5) unit cell is shown in the top panel. The results presented in the top part correspond to the localized adsorption while those from the bottom part were obtained assuming relaxation of the adsorbed molecules.
This can be easily noticed while looking at the peaks marked with rectangular frames in both parts of Figs. 2–4. The main source of the observed effect is migration of adsorbed molecules to energetically favourable clusters of adsorption sites (supersites). For example, in the simplest case C, molecules of S which are adsorbed on supersites containing 0 or 1 active site jump to supersites with two active sites from which they next desorb. This leads to disappearance of the peaks at 140 and 180 K and to simultaneous growth of the peak at 220 K. For enantiomer R the highest desorption energy corresponds to supersites with one active site. Thus, molecules of R adsorbed on the clusters of four inactive sites tend to move and occupy supersites with one active site. In consequence, the peak at 140 K decreases and the peak at 180 K increases when the molecules are allowed to take equilibrium positions. The effect of fast diffusion described above refers not just to system C but it occurs in all of the systems described here, including A and B. As we can easily notice, the relaxation is responsible for enhanced migration of the target enantiomer to the most energetically favourable supersites. In consequence, the TPD peaks of pure enantiomer S become much more pronounced, as it is indicated by the frames in Figs. 2–4. A direct consequence of this
According to the results obtained assuming relaxation of the adsorbed layer, it is straightforward to obtain pure enantiomer S by collecting molecules which are desorbed at a sufficiently high temperature. More precisely, to achieve this it is enough to collect the molecules within the temperature range which is delimited by the frames shown in Figs. 2–4. Obviously, the collected molecules of S are only a part of the total amount of this enantiomer adsorbed initially on the surface. To quantify this part we introduced recovery of enantiomer S defined as a ratio of the area of the peak within the frame to the area under the entire TPD curve of S. The resulting values are shown in Fig. 5 for both localized and mobile adsorption of the enantiomers. Additionally, in Fig. 5 we displayed recovery calculated for the (5 5) unit cell containing lower (D) and higher numbers of active sites (E), that is 4 and 7, respectively. As it follows from this figure, pattern C gives the largest recovery among all of the systems studied. This refers to localized as well as mobile adsorption of the enantiomers and makes pattern C the optimal distribution. For example, the recovery of enantiomer S which can be reached in a single TPD run in system C is equal to about 93% when the adsorbed layer is allowed to relax. This quantity is about three times smaller in the case of the two surfaces with the unit cell containing the same number of active sites (A and B). Note also that, changing the number of active sites within the unit cell (patterns D and E) does not cause visible increase in the recovery compared to systems A and B. The results obtained for systems A, B, D, and E indicate that the corresponding surfaces are rather poor enantioselective adsorbents and their use in the TPD-driven enantioseparation is impractical. Note, however that, despite this drawback it is still possible to achieve 100% recovery of S but this task requires multiple TPD runs. For example, in the case of system C it is enough to collect the mixed fraction which desorbs below 202 K and repeats the TPD run. This involves low-temperature adsorption of the fraction on a clean surface C and subsequent heating of the system. Additional amount of pure enantiomer S can be then collected again at temperatures higher than 202 K. To illustrate
Fig. 5. Recovery of pure enantiomer S obtained in a single TPD run for the surfaces with different spatial distributions of the active sites shown in the figure. The black and grey bars correspond to the localized and mobile adsorption of the enantiomers, respectively.
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distribution of active sites. It was demonstrated that a suitable arrangement of the active sites on the surface can lead to a substantial growth in the extent of separation. Additionally, our Monte Carlo simulations revealed that fast surface diffusion of enantiomers is an important factor which promotes the separation. For example, it was observed that the recovery of the target enantiomer can be up to 20 times larger when the molecules are allowed to reach equilibrium configuration by fast surface diffusion. For the nanostructured chiral surfaces which are less effective enantiospecific adsorbents, the use of multiple or cyclic TPD runs revealed to be a useful way to achieve complete separation of the enantiomers. Acknowledgement This work was supported by the Polish Ministry of Education and Science research grant: 1 T09A 103 30. References
Fig. 6. Cumulative recovery of pure enantiomer S as a function of the number of TPD runs simulated for the surfaces with different spatial distributions of active sites.
this in Fig. 6 we plotted the cumulative recovery of S as a function of the number of TPD runs calculated for the unit cells with 5 active sites. The cumulative recovery was defined as the percent of the total amount of enantiomer S adsorbed initially on the surface (first run) that was obtained in a given number of TPD runs. As it follows from Fig. 6, five-fold repetition of the TPD run in systems A and B is sufficient to recover about 90% of pure enantiomer S. Note also that, the curves plotted in Fig. 6 for systems A and B overlap, indicating very similar performance of the two surfaces. Obviously, in the case of the optimal distribution of active sites almost 100% recovery is achieved yet in the second run. 4. Conclusions The results of this work show that an efficient separation of enantiomers can be achieved using thermal desorption of their racemate from a nanostructured chiral surface with a special
[1] N.M. Maier, P. Franco, W.J. Lindner, J. Chromatogr. A 906 (2001) 3. [2] S.C. Stinson, Chem. Eng. News 79 (2001) 45. [3] S. Ahuja, Chiral Separations by Chromatography, Oxford University Press, Washington, 2000, pp. 3–13. [4] D. Rampulla, A.J. Gellman, in: J.A. Schwarz, C.I. Contescu, K. Putyera (Eds.), Dekker Encyclopedia of Nanoscience and Nanotechnology, Marcel Dekker, Inc, New York, 2004, pp. 1113–1123. [5] Q. Chen, N.V. Richardson, Annu. Rep. Prog. Chem., Sect. C 100 (2004) 313. [6] C.F. McFadden, P.S. Cremer, A.J. Gellman, Langmuir 12 (1996) 2483. [7] J.D. Horvath, A.J. Gellman, J. Am. Chem. Soc. 124 (2002) 2384. [8] D. Stacchiola, L. Burkholder, W.T. Tysoe, J. Am. Chem. Soc. 124 (2002) 8984. [9] I. Lee, F. Zaera, J. Am. Chem. Soc. 128 (2006) 8890. [10] W.A. Bonner, P.R. Kavasmaneck, F.S. Martin, J.J. Flores, Science 186 (1974) 143. [11] R. Hazen, D.S. Sholl, Nat. Mat. 2 (2003) 367. [12] J.D. Horvath, A.J. Gellman, J. Am. Chem. Soc. 123 (2001) 7953. [13] A.J. Gellman, J.D. Horvath, M.T. Buelow, J. Mol. Catal. A 167 (2001) 3. [14] D. Stacchiola, L. Burkholder, T. Zheng, M. Weinert, W.T. Tysoe, J. Phys. Chem. B 109 (2005) 851. [15] I. Lee, F. Zaera, J. Phys. Chem. B 109 (2005) 12920. [16] J.D. Horvath, A. Koritnik, P. Kamakoti, D.S. Sholl, A.J. Gellman, J. Am. Chem. Soc. 126 (2004) 14988. [17] T.D. Power, A. Asthagiri, D.S. Sholl, Langmuir 18 (2002) 3737. [18] P. Szabelski, Appl. Surf. Sci. 253 (2007) 5387. [19] P. Szabelski, D.S. Sholl, J. Chem. Phys. 126 (2007) 144709. [20] P. Szabelski, D.S. Sholl, J. Phys. Chem. C 111 (2007) 11936. [21] P. Szabelski, J. Chem. Phys. 128 (2008) 184702. [22] P. Szabelski, T. Warzocha, T. Pan´czyk, Thermochim. Acta 497 (2010) 77. [23] J.L. Sales, G. Zgrablich, Phys. Rev. B 35 (1987) 9520. [24] J.L. Sales, G. Zgrablich, Surf. Sci. 187 (1987) 1.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Separation of chiral molecules by temperature programmed desorption Paweł Szabelski * Department of Theoretical Chemistry, Maria Curie-Skłodowska University, pl. M.C. Skłodowskiej 3, 20-031 Lublin, Poland
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 28 December 2009
The Monte Carlo simulation method was used to model thermal desorption of a pair of enantiomers from a solid surface with a chiral periodic pattern of active sites. The main objective of the study was to determine the optimal number of the active sites and their spatial distribution within the unit cell of the surface to achieve the most efficient separation of the enantiomers. For that purpose we tested the series of chiral patterns which were found previously for the equilibrium adsorption. Temperature programmed desorption spectra were calculated using a square lattice of adsorption sites in which the active sites were distributed spatially according to the candidate patterns. Additionally, influence of relaxation of the adsorbed layer on the relative shift of the TPD peaks of the enantiomers was assessed and the key factors affecting the chiral separation were identified. ß 2009 Elsevier B.V. All rights reserved.
PACS: 68.43.h 68.43.De 68.03.Hj 68.43.Vx Keywords: Chiral molecules Thermal desorption Monte Carlo simulation Enantioseparation
1. Introduction Adsorptive separation of chiral molecules has been long recognized as a powerful method that is frequently used in pharmaceutical, drug, cosmetic and agricultural industries. The effectiveness of the enantioseparation process is particularly important because in the vast majority of practical applications only one enantiomer is usually needed either for the fabrication of a final product or for further processing. For example, it is often observed that while one enantiomer can have desired (e.g. therapeutic) effect, the other can be neutral or even harmful in the worst case, leading to poisoning of a patient. For that reason substantial effort has been made to develop and improve methods of fabrication of extremely pure enantiomeric substances [1,2]. Liquid chromatography, which uses chiral stationary phases (CSPs) composed of a silica support with chiral ligands capable of selective recognition of the complementary enantiomer, holds a leading position in this field [3]. Recently there has been growing interest in alternative methods of separation of enantiomers. One promising avenue in this area is adsorption of chiral molecules on nanostructured solid surfaces which are created using single crystal planes [4,5]. The chiral nanostructured surfaces are obtained, for example, by cleavage of achiral bulk materials such as metals [6,7], templating
* Tel.: +48 81 537 5518; fax: +48 81 537 5658. E-mail address: [email protected]. 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.12.124
surfaces with organic modifiers [8,9] or exposing of surfaces of naturally chiral crystals [10,11]. The above techniques allow fabrication of a crystalline surface which has a unique structure not superimposable with its mirror image and thus it is chiral. Temperature programmed desorption has been used to examine binding of chiral adsorbates to naturally chiral metallic surfaces [12,13] as well as to metallic surfaces templated with organic molecules [14,15]. An interesting application of this technique has been proposed by Gellman and coworkers who have used TPD to demonstrate the potential of naturally chiral surfaces to differentiate between enantiomers of chiral alcohols [16]. To explore further enantiospecific desorption of chiral molecules from naturally chiral surfaces MC simulations of thermal desorption of small chiral hydrocarbons from the series of chiral platinum single crystal faces have been performed [17]. In this case the largest difference in desorption energy, 2 kJ/mol, was predicted for the enantiomers of dimethylcyclopropane desorbing from the Pt(643)S surface. These simulations have demonstrated the importance of local atomic order which is responsible for the preservation of individual enantiospecific adsorption properties of the surface. Recently, we have started systematic investigations of a model chiral surface which provides a new mechanism of selective differentiation between enantiomers under equilibrium conditions [18–21]. We demonstrated that the one-to-one correspondence between a chiral selector and the complementary enantiomer is not a necessary condition for the selective adsorption of that enantio-
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mer. The proposed surface, apart from conventional adsorption experiments, can be also used in ultra high vacuum conditions, providing for example, enantioselective environment for thermal desorption of chiral molecules. The main purpose of this study is to examine the possibility of manipulating structural properties of the model chiral surface to achieve efficient separation of enantiomers by temperature programmed desorption. Moreover, we examine the influence of mobility of adsorbed chiral molecules on the extent of separation. 2. Simulation We consider thermal desorption of model chiral molecules from a solid surface represented by a square lattice of binding sites with well-defined binding energies. The chiral molecules are modelled as rigid S-shaped chain structures composed of four identical segments. A molecular segment can be an atom or a functional group occupying one binding site. In the simplified approach adopted here only that part of the molecule which directly contacts the surface is considered. The remaining part of the molecule which is not involved in the adsorption is disregarded and assumed to be responsible only for preservation of chirality in the bulk phase. According to this assumption, the only important structural property of the molecule is the footprint it leaves on the surface. One example is trans-1,2-dimethylcyclopropane (DMCP) whose enantiomers are shown schematically in the top part of Fig. 1. This figure shows also the chiral footprints of enantiomers S and R of DMCP consisting of four adsorption sites, each occupied by one segment of the adsorbed enantiomer.
The adsorbing surface was built using two types of sites whose strength of interaction with a single segment of the chiral molecule was markedly different. The energy of interaction between an active site and a segment of the molecule was characterized by ea while that between an inert site and the segment by ei. In order to construct a surface selective towards one of the enantiomers the active sites were distributed on the lattice in such a way that the chosen enantiomer can adsorb more strongly than the other one, as assumed in our previous works [18–21]. An example of the distribution meeting this requirement is shown in the bottom part of Fig. 1 for the S-selective surface. The main origin of selectivity of this surface is the larger number of active sites which can be occupied by a single molecule of S (maximally two sites) compared to enantiomer R (maximally one site), as shown in the bottom part. The simulations were performed on a square L L lattice of adsorption sites with L = 100. The adsorbing surface consisted of active and inactive sites whose energy of interaction with a single molecular segment was ea = 20 kJ/mol and ei = 10 kJ/mol, respectively. To model the TPD spectra we used the conventional algorithm of thermal desorption whose details can be found elsewhere [22–24]. When the adsorbed layer was allowed to relax via very fast diffusion [22] we assumed that a molecule can jump either vertically or horizontally by one lattice site to the next position. In the simulations described here we used N = 200 molecules (100 S + 100 R) so that the total surface coverage, u = 4 N/L2 was equal to 0.08. The MC desorption rate was defined as Du/DT, where Du is the change in the surface coverage induced by increasing the temperature from T to T + DT. Analogous definitions refer to pure enantiomers R and S. The pre-exponential frequency factor and the heating rate used in the simulations were 1013 s 1 and 1 K/s, respectively. The values of the parameters used in our virtual TPD experiment do not correspond to any real system and they were chosen just to illustrate basic properties of the proposed model. In particular, one has to remember that the assumption of the same pre-exponential factor for different configurations of a molecule on the nanostructured surface does not have to be valid in real systems. Similarly, the small difference between the desorption energies ea and ei can be insufficient to produce visible changes in the rate of desorption. These issues are, however, beyond the scope of the present paper whose main objective is to find optimal topography of the chiral surface. The results of the simulations described here are averages over 50 independent starting configurations of the adsorbed enantiomers. For each of these configurations the temperature scan was repeated 200 times and the resulting spectra were subsequently averaged. 3. Results and discussion Below we present the results of the MC simulations of thermal desorption of the racemic mixture (S + R) from a few surfaces which differ in both spatial distribution and number of actives sites within the unit cell. These results were obtained for localized as well as mobile adsorption of the enantiomers and they are compared in the following sections. 3.1. Effect of surface topography and molecular diffusion
Fig. 1. Method of construction of the model chiral molecules from the backbone of 1,2-dimethylcyclopropane and projection of the enantiomers onto a square lattice (top). An example of the S-selective surface with a periodic chiral distribution of active sites. The thick dashed line delimits the unit cell of the surface. The examples of possible adsorbed configurations differing by the number of occupied active sites are also shown for each enantiomer (bottom).
Figs. 2–4 show the examples of TPD spectra calculated for different spatial distributions of the active sites on the chiral surface. These distributions were found using the Monte Carlo search technique which was based on maximization of the ratio of the Henry constants calculated for enantiomer S and for enantiomer R, that is on maximization of the selectivity of the surface towards enantiomer S. A detailed description of this procedure can be found elsewhere [20]. Note that the unit cells
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Fig. 2. An example of TPD spectra of the racemate S&R from the nanostructured surface A with a different distributions of five active sites within the (5 5) unit cell (see the top panel). The results presented in the top part correspond to localized adsorption while those from the bottom part were obtained assuming relaxation of the adsorbed molecules.
Fig. 3. One more example of TPD spectra of the racemate S&R from the nanostructured surface B with a different distribution of five active sites within the (5 5) unit cell (see the top panel). The results presented in the top part correspond to localized adsorption while those from the bottom part were obtained assuming relaxation of the adsorbed molecules.
shown in the three figures are identical with respect to the size of the cell (5 5) as well as to the number of active sites they contain (5). The only difference between the unit cells from Figs. 2–4 is the way in which the active sites are arranged spatially. As it follows from the comparison of Figs. 2–4 redistribution of the active sites within the unit cell leads to significant qualitative changes in the shape of the corresponding TPD spectra. This can be easily noticed and explained for the curves obtained assuming a lack of relaxation of the adsorbed layer (top parts). Namely, the number of composite peaks on the total TPD curve is equal to 5, 4 and 3 for patterns A–C, respectively. This originates mainly form a different number of energy modes associated with possible adsorbed configurations of enantiomers S and R. For example, in the case of pattern C shown in the bottom part of Fig. 1 we can observe that a molecule of S can have three energetically different configurations while for enantiomer R the number of configurations is equal to two. The energies of these configurations are strongly correlated with the number of active sites occupied by a molecule of a given enantiomer. For enantiomer S adsorbed on the surface from Fig. 1 there are three values of desorption energy equal to 2ea + 2ei, ea + 3ei and 4ei, corresponding to two, one and no active sites occupied by the molecule, respectively. For enantiomer
R the desorption energy is equal to ea + 3ei or to 4ei which gives only two energy modes. For this simple reason the total TPD spectrum, which is a linear combination of the TPD curves calculated for pure enantiomers consists of three peaks. The peaks at 150 and 185 K come from simultaneous desorption of both enantiomers while the high-temperature peak at 220 K corresponds to desorption of S alone. Analogous analysis can be performed in the case of systems A and B and the composite peaks shown in Figs. 3 and 4 (top parts) can be assigned to the corresponding adsorbed configurations of each enantiomer. Furthermore, peak temperatures for immobile enantiomers in systems A–C can be calculated using the Redhead’s formula based on the desorption energies associated with each molecular configuration [22]. Regarding the effect of fast surface diffusion, we can observe that the shape of the TPD spectra shown in the top parts of Figs. 2– 4 changes markedly when the adlayer is allowed to relax (see the bottom parts). In particular, switching on the relaxation leads to a reduction in the number of composite peaks on the total TPD spectrum calculated for each system. Moreover, it can be also noticed that the low-temperature peaks disappear which leads to a substantial growth of the peaks centered at higher temperatures.
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effect is the possibility of separation of the enantiomers by collecting desorbed fractions, that is just by cutting-off the lowtemperature part of the spectrum. 3.2. Enantioseparation
Fig. 4. TPD spectra of the racemate of enantiomers S and R from the nanostructured surface C whose (5 5) unit cell is shown in the top panel. The results presented in the top part correspond to the localized adsorption while those from the bottom part were obtained assuming relaxation of the adsorbed molecules.
This can be easily noticed while looking at the peaks marked with rectangular frames in both parts of Figs. 2–4. The main source of the observed effect is migration of adsorbed molecules to energetically favourable clusters of adsorption sites (supersites). For example, in the simplest case C, molecules of S which are adsorbed on supersites containing 0 or 1 active site jump to supersites with two active sites from which they next desorb. This leads to disappearance of the peaks at 140 and 180 K and to simultaneous growth of the peak at 220 K. For enantiomer R the highest desorption energy corresponds to supersites with one active site. Thus, molecules of R adsorbed on the clusters of four inactive sites tend to move and occupy supersites with one active site. In consequence, the peak at 140 K decreases and the peak at 180 K increases when the molecules are allowed to take equilibrium positions. The effect of fast diffusion described above refers not just to system C but it occurs in all of the systems described here, including A and B. As we can easily notice, the relaxation is responsible for enhanced migration of the target enantiomer to the most energetically favourable supersites. In consequence, the TPD peaks of pure enantiomer S become much more pronounced, as it is indicated by the frames in Figs. 2–4. A direct consequence of this
According to the results obtained assuming relaxation of the adsorbed layer, it is straightforward to obtain pure enantiomer S by collecting molecules which are desorbed at a sufficiently high temperature. More precisely, to achieve this it is enough to collect the molecules within the temperature range which is delimited by the frames shown in Figs. 2–4. Obviously, the collected molecules of S are only a part of the total amount of this enantiomer adsorbed initially on the surface. To quantify this part we introduced recovery of enantiomer S defined as a ratio of the area of the peak within the frame to the area under the entire TPD curve of S. The resulting values are shown in Fig. 5 for both localized and mobile adsorption of the enantiomers. Additionally, in Fig. 5 we displayed recovery calculated for the (5 5) unit cell containing lower (D) and higher numbers of active sites (E), that is 4 and 7, respectively. As it follows from this figure, pattern C gives the largest recovery among all of the systems studied. This refers to localized as well as mobile adsorption of the enantiomers and makes pattern C the optimal distribution. For example, the recovery of enantiomer S which can be reached in a single TPD run in system C is equal to about 93% when the adsorbed layer is allowed to relax. This quantity is about three times smaller in the case of the two surfaces with the unit cell containing the same number of active sites (A and B). Note also that, changing the number of active sites within the unit cell (patterns D and E) does not cause visible increase in the recovery compared to systems A and B. The results obtained for systems A, B, D, and E indicate that the corresponding surfaces are rather poor enantioselective adsorbents and their use in the TPD-driven enantioseparation is impractical. Note, however that, despite this drawback it is still possible to achieve 100% recovery of S but this task requires multiple TPD runs. For example, in the case of system C it is enough to collect the mixed fraction which desorbs below 202 K and repeats the TPD run. This involves low-temperature adsorption of the fraction on a clean surface C and subsequent heating of the system. Additional amount of pure enantiomer S can be then collected again at temperatures higher than 202 K. To illustrate
Fig. 5. Recovery of pure enantiomer S obtained in a single TPD run for the surfaces with different spatial distributions of the active sites shown in the figure. The black and grey bars correspond to the localized and mobile adsorption of the enantiomers, respectively.
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distribution of active sites. It was demonstrated that a suitable arrangement of the active sites on the surface can lead to a substantial growth in the extent of separation. Additionally, our Monte Carlo simulations revealed that fast surface diffusion of enantiomers is an important factor which promotes the separation. For example, it was observed that the recovery of the target enantiomer can be up to 20 times larger when the molecules are allowed to reach equilibrium configuration by fast surface diffusion. For the nanostructured chiral surfaces which are less effective enantiospecific adsorbents, the use of multiple or cyclic TPD runs revealed to be a useful way to achieve complete separation of the enantiomers. Acknowledgement This work was supported by the Polish Ministry of Education and Science research grant: 1 T09A 103 30. References
Fig. 6. Cumulative recovery of pure enantiomer S as a function of the number of TPD runs simulated for the surfaces with different spatial distributions of active sites.
this in Fig. 6 we plotted the cumulative recovery of S as a function of the number of TPD runs calculated for the unit cells with 5 active sites. The cumulative recovery was defined as the percent of the total amount of enantiomer S adsorbed initially on the surface (first run) that was obtained in a given number of TPD runs. As it follows from Fig. 6, five-fold repetition of the TPD run in systems A and B is sufficient to recover about 90% of pure enantiomer S. Note also that, the curves plotted in Fig. 6 for systems A and B overlap, indicating very similar performance of the two surfaces. Obviously, in the case of the optimal distribution of active sites almost 100% recovery is achieved yet in the second run. 4. Conclusions The results of this work show that an efficient separation of enantiomers can be achieved using thermal desorption of their racemate from a nanostructured chiral surface with a special
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