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Dynamics and structure of self-assembled organic molecules at the solid-liquid interface
Surface and Coatings Technology, 67 (1994) 201—211
201
Dynamics and structure of self-assembled organic molecules at the solid—liquid interface J. F. Jørgensena, N. Schmeissera, J. Garnaesa, L. L. Madsena,b, K. Schaumburg”, L. Hansen, P. Sommer~Larsenc ~DanishInstitute of Fundamental Metrology, Building 307, Lundtoftevej 100, DK-2800 Lyngby, Denmark bCentrefor Interdisciplinary Studies of Molecular Interactions, Department of Chemistry, University of Copenhagen, Fruebjerguej 3, DK-2100 Copenhagen, Denmark The Engineering Academy of Denmark, Department of Chemistry (DIA-K), Building 375, DK-2800 Lyngby, Denmark
Abstract We have analysed scanning tunnelling microscope (STM) images of self-assembled didodecylbenzene (DDB) molecules physisorbed on graphite from a DDB solution using octylbenzene as solvent. The DDB images were obtained alternating with images of the graphite substrate using two different bias voltages. The well-known lattice constant of the graphite substrate was used for an accurate determination of the calibration factors and drift of the STM. The DDB unit cells were detected and measured in the Fourier domain and corrected by the calibration data. The commensurability between the graphite lattice and the DDB lattice was analysed. Although the graphite lattice and the DDB lattice planes are parallel, incommensurability was observed as superstructures in the Fourier pattern. The molecules dioctadecyldiselenide and dioctadecyldisulphide also form well-ordered monolayers when adsorbed on graphite from solution. Dioctadecyldiselenide and dioctadecyldisulphide form ideal mixtures. It is therefore of interest to determine to what extent the molecules form mixed structures when physisorbed on the graphite substrate. Theoretical and experimental observations show that S and Se atoms yield markedly different contrasts in the STM images. When imaging mixed surface layers, the dynamic adsorption and dissolution of individual molecules can be followed. A time scale ofaround 1 s was found for this process. The ratio between fractions of adsorbed molecules of different species was found to be very similar to the ratio in solution, indicating a small difference in bonding energy.
1. Introduction Regular patterns of self-assembled molecules have been observed in a number of cases at the interface between organic solutions and solids [1—3]. Most studies have been performed on highly oriented pyrolytic graphite (HOPG). Long-chain aliphatic compounds appear to have a strong affinity for graphite. To illustrate this, we analyse the commensurability between selfassembled didodecylbenzene (DDB, H25 C12(C6H4) C12H25) molecules and an HOPG substrate. Such commensurability analysis done qualitatively in the spatial domain has been reported by other groups [4,5]. Here we apply a subpixel Fourier technique for quantitative measurements. In compounds where functional groups have been inserted, the self-assembled layers still exist, but the stability is found to be reduced depending on the functional group inserted. Self-assembled layers have been suggested as starting materials for performing in situ chemical modifications locally on the surface layer. This technique might lead to nanometre patterns on the surface. In order to evaluate the feasibility of this
SSDI 0257-8972(94)002304-9
approach, it is necessary first to determine the mean residence time of molecules in the surface layer, i.e. the mean time from adsorption to desorption. Molecular dynamics at domain boundaries has been studied before [4,5] and also dynamics observed at different temperatures has been reported [6]. Here we report quantitative measurements of the mean residence time for the individual molecules in ordered layers far from the domain boundaries. The problem is that exchange of identical molecules in the surface layer will not be visible, save the infrequent situations where an exchange leads to fractional occupancy of a lattice site. The problem may be overcome by use of a binary mixture. The requirement will be that the two molecular species should form ideal mixtures in solution and should form mixed surface layers including both molecules. The molecules should be sufficiently different that the scanning tunnelling microscopy (STM) technique can distinguish the species in the surface layer. The above considerations have led us to use dioctadecyldisuiphide (DODS, H37C18SSC18H37) and dioctadecyldiselenide (DODSe, H37C18SeSeC18H37) as a pair of analogous molecules for these experiments.
Elsevier Science S.A.
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Self-assembled organic molecules at the solid/liquid interface
Sulphur and selenium belong to the same group in the periodic table and their chemical properties are very similar, The long-chain aliphatic compounds in question show perfect miscibility in solution. Initial studies showed that DUDS forms stable surface layers with a packing consistent with space-filling molecular models. The expectation based on this finding is that DUDS and DODSe will form mixed surface layers of the same packing structure, Compared with sulphur, selenium is more metallic in character and more polarizable. As a result, the electron tunnel current is larger through selenium than through sulphur. Consequently, we expect the apparent height measured by STM for the two molecules to appear distinguishable. We confirm this by theoretical calculations and from STM measurements. 2. Preparation and scanning technique Samples were prepared by dissolving the molecules of interest in octylbenzene as dilute solutions. Binary mixlures were prepared by mixing known quantities of the single-component solutions. A drop of the solution is placed on the HOPG substrate and scanning of the surface is performed during the period where the droplet slowly evaporates, thereby increasing the concentration of the molecular species of interest in the drop. For a certain concentration interval the molecules form a monolayer on the graphite. The instrument used comprised a self-made scanning tunnelling microscope (STM) [7,8] and a Rasterscope 3000 with an STM 9 ~.tmscanning tube and with the scanning tip facing downwards. Cut PtIr tips were used. The scanned regions were 10—40 nm square with a resolution of 256 x 256 or 128 x 128 pixels; the scan rate was typically one image per 7 ~ 3. Didodecylbenzene We have shown [3] that self-assembled DDB molecules can be imaged by STM using a bias voltage of about I V. At lower bias voltages of about 0.1 V the tunnelling mechanism is different and the STM images show the contrast of the HUPG substrate. We will demonstrate that the well-known lattice of HOPG is useful for calibration and subsequent measurements of the adsorbed surface layer unit cell. 3.1. Image processing and analysis For the DDB molecules, where we want an accurate measurement of the unit cell, we apply a novel calibration and drift elimination technique based on Fourier analysis. The calibration factors are calculated from low voltage STM images showing the graphite substrate. The detection and measurement of the DDB unit cell are also done in Fourier space and carried out on the
images recorded with a high bias voltage. The measured DDB unit cells were corrected by using the calibration values calculated from the graphite images, which were recorded within 44 s before or after. 3.2. Calibration For the calculation of the calibration factors a novel technique [3,9] has been utilized. The advantage of this technique is that it is automatic and can estimate the drift in the fast-scanning direction, which makes it more reliable. The technique is based on the detection and measurement of the position of Fourier peaks associated with the graphite lattice. The determination of calibration factors and the subsequent restoration are illustrated in Fig. 1. The fact that we can measure the drift in the fastscanning direction (dr) makes it possible to perform a perfect restoration of the distorted image. As will be demonstrated, the calibration factor for the fast-scanning direction (cr) can be determined with a standard deviation less than 0.02%. However, it is not possible from a single image to tell how much of the scan range in the slow-scanning direction is caused by the calibration factor (cv) and how much is caused by the drift (dr) in this direction. This is not important when correcting the DDB unit cells, but it is crucial to have up-to-date c~values. 3.3. DDB unit cell measurements The DDB oblique unit cell was calculated by measuring the position of the associated peaks in the Fourier domain [3,9]. From a number of alternative unit cells the one covering the single molecules best was selected and described by the length of the two unit cell vectors and their angle. Fig. 2 shows the results calculated from the different images together with the obtained calibration factors as a function of time. Several conclusions can be drawn from Fig. 2. (1) The c~calibration factor is reproducible within 0.02%, indicating that the variation in both the detection algorithm and the x calibration factor of the instrument was less than 0.02%. (2) The drift (dr) was (320±4)pms1, which at the scanning speed used could give an angle error of 37°. This is a large but very reproducible error and it turned out that it was due to minor damage of the scanning elements which caused non-orthogonal scanning. In this sense we were able to use the image processing as a diagnostic tool. Because the error was so stable, it was also possible to correct for this error. (3) The estimated c 5 calibration factor was 0.839 ± 1%, which is about 50 times less stable than for the x direction owing to the fact that it has the drift (d5) embedded. This may be unimportant for the restoration of the actual HUPG image but reflects some of the
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uncertainty when used for correction of the DDB unit cell. (4) Based on 29 images, we can calculate the statistics of the DDB unit cell. The long vector of the DDB unit cell was calculated as (3.73 ±0.02) nm (about 0.8%), which corresponds to 15.16 ±0.12 graphite unit cell vectors. This confirms previous results [3], which at a lower accuracy indicated that the long DDB unit cell vector was 3.80 nm ±10% (based on five images) and incommensurate with the graphite substrate. (5) The short vector was found to be 0.549 nm ± 0.4%, corresponding to 2.23 ±0.01 times a graphite unit cell vector and therefore clearly incommensurate with the graphite substrate. (6) The DDB unit cell angle is 120.8°±0.6°,which
indicates close but not exact alignment with the graphite lattice. 3.4. Commensurability analysis Although perfect commensurability between the graphite substrate and the DDB molecular layer was not found, the self-assembling process seems to be highly influenced by the graphite substrate. This is confirmed by Fig. 3, where a profile through a Fourier peak associated with the graphite is shown. From the source image in Fig. 3(a) the lamella width is visible simultaneously with the graphite. The Fourier peak corresponding to the DDB lamellae can therefore be observed in the same direction as the graphite peak in Fig. 3(b). This peak is thus seen as the inner peak of Fig. 3(b) and the corre-
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Fig. 2. Results obtained from a series of DDB images. In (a) the x- and y-calibration factors determined from the graphite images are plotted. Note that the x-calibration factor is much more stable. In (b) the measured drift in the x direction is drawn. The length of the long DDB unit cell vector is shown in (c). They have been detected for the individual images and corrected by the calibration data shown in (a) and (b). (d) shows the length of the short unit cell vector and (e) the unit cell angle also after correction.
sponding Fourier profile in Fig. 3(c) at a frequency 15.16 times lower than the graphite peak. The incommensurability between the short vector of the DDB unit cell and the graphite can also be analysed in the Fourier domain. In Fig. 4 a DDB image and its Fourier transform are shown. In the Fourier domain satellite peaks can easily be found. These satellite peaks correspond to a superstructure in the spatial domain with a short unit cell vector that is 4.4 times the short vector of a single DDB unit cell but has the long unit cell vector and angle in common with the single DDB unit cell.
4. DODS—DODSe mixture and dynamics For the DUDS and DODSe self-assembled molecules we will in the following describe a simulation technique of the STM imaging mechanism in the constant-current mode. The results of the simulations give us a feeling for the expected height variations and can be compared with the measured STM images. The dynamic adsorption and dissolution of individual molecules measured in the STM images are analysed using a thermodynamic model, from which quantitative results for the rate of desorption are found. Surface layers formed from one
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solution are reported, but many similar solutions have been studied. This solution was prepared with a ratio of DUDSe : DUDS of 1:2. The experiments were performed at a temperature of 295 K. 4.1. Calculation of tunnel currents Tunnel currents were calculated for a model consisting of a single molecule adsorbed on a graphite layer. The
local density of states (LDOS) was calculated for states with energies up to eV above the Fermi level, where e is the elementary charge value and V is the applied bias voltage. The tunnel current is proportional to the LDUS in the Tersoff—Hamann [10,11] approximation. Tunnelling through the adsorbed molecule was taken into account by multiplying the density from each single orbital by its projection on the p~orbitals of the graphite
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layer. The semiempirical PM3 method [12,13] was used to calculate orbitals for the graphite molecule model, Densities were calculated using the expansion coefficients from the semiempirical calculation and atomic basis functions based on Slater-type orbitals (STOs) [14]. Tn the outer part of the valence region the atomic orbitals were fitted to an expression of the type R
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where R~1(r)is the radial part of the wavefunction and A, B and ~ are parameters to be fitted. .The use of this simplified expression improves the computational speed compared with the use of the original expansion in STUs. Two types of molecules were studied: CH3CH2SS CH2CH3 and CH3CH2SeSeCH2CH3. The graphite was modelled with one layer of graphite containing 48 carbon atoms, terminated by hydrogen atoms if necessary. The carbon—sulphur skeleton was kept planar and parallel to the graphite surface. The molecule— graphite distance was fixed at 3.4 A. The geometry for the disulphide compound was optimized under these restrictions. Exactly the same geometry was used for the diselenide compound, but sulphur was replaced by selenium. Simulated constant-current images showing the distance of the tip from the graphite are presented in Fig. 5. The images are calculated using a bias of 1.5 V. The difference between sulphur and selenium is maximum for this bias. The experimental images are measured at a bias of 1 V. An asymmetry in the simulated image is caused by interactions between the underlying graphite and the molecule. The images are calculated for a fixed LDOS rather than for a fixed current (which is assumed
to be proportional to the LDOS). An LDUS of l0~ A3 is used, corresponding to an average distance of 7 A between the graphite and the tip. This is a reasonable value, since changing the LDUS by a factor of 10 only results in minor changes in the calculated image. The height profiles shown in Fig. 6 are calculated along the lines which connect the maximum values in Fig. 5. These peaks represent CH 3 Se, Se andbetween CH3 respectively in Fig. 6(a), The largest difference selenium and the methyl group is 1.0 A, whereas the difference between sulphur and the methyl group is 0.7 A. The difference between the height over selenium and sulphur is thus 0.3 A. The theoretical model can be improved in several ways. First, the LDUS from neighbouring molecules adds to the total current over a given atom. Uwing to the slower decay of the LDOS of a selenium or a sulphur atom compared with that of a carbon atom, a more extensive calculation including neighbouring molecules will result in a larger current over a selenium or sulphur atom relative to the current over a carbon atom. Secondly, all non-hydrogen atoms in the molecule are placed at a distance of 3.4 A from the graphite. This may not be correct and differences in latitudes over the graphite will also result in differences in the profiles. Finally, various improvements in the basic model, inclusion of d-basis functions and the effect of an electric field in the calculation should be considered. 4.2. Thermodynamic models During the experiment the adsorbed molecules exist in equilibrium with molecules in solution. Various models may be used to describe this equilibrium and the underlying kinetics. In the simplest model the solu-
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The bonding between the graphite surface and a selenium compound is assumed to be weaker than the bonding between the graphite surface and a sulphur compound. The difference in bonding energy, e = Ese..graphite E~graphite, which is positive, is the only parameter entering the model. In this case the equilib—
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Self-assembled organic molecules at the solid/liquid interface
processes are assumed to be of first order. The adsorption process may be assumed to be activationless and the rate constant for adsorption of a selenium compound can be assumed to be equal to the rate constant for adsorption of a sulphur compound. Adsorption is assumed to be much faster than desorption. The rate constants for desorption of the two kind of compounds differ and their ratio is given by k
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image to be shifted according to the detected maximum correlation coordinate, For subsequent images the calculated displacement was always less than half the length of the short unit cell vector. From the aligned images we detected and classified the DODS—DODSe molecules automatically. This was done by detecting all significant peaks associated with the SS and SeSe pairs. These peaks were then classified as belonging to DUDS or DUDSe depending on their height values. The classification threshold was selected dynamically on an image-by-image basis to give the
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Observing a collection of n0 DUDSe molecules in the adsorbed layer, the number of DUDSe molecules at these sites decays towards the equilibrium composition. The average fraction of selenium-containing molecules for such a collection as a function of time is
we can follow the molecules from image to image and detect molecules which are exchanged by a molecule of the other type. It ts therefore possible to get statistics about the molecular mixture rate on the surface and also the molecular dynamics.
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Using the above models, the observed data allow for the determination of the difference in bonding energy as well as the rate constant for desorption of the sulphur and selenium compounds:
4.4. DODS—DODSe results Fig. 7 shows an example of two DODS—DODSe images recorded with a time separation of 7 s. As for the DDB molecules, these molecules also assemble into long lamellae. The DUDSe molecules are seen as those having the highest contrast in their kernels; see also the profiles across the kernels shown in Fig. 8. Qualitatively the observed and simulated profiles agree. In both cases selenium appears as the highest atom and the difference between selenium and sulphur is approximately onethird of the difference between selenium and the aliphatic
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4.3. Image processing and analysis ofDODS—DODSe For the DODS—DUDSe molecule images we focus on the adsorption and dissolution of individual molecules. For this purpose we have recorded 32 images with a separation time of 7 s. To overcome drift problems, we align all images pairwise to give maximum correlation. This is done by calculation of the cross-correlation function, detection of the maximum correlation peak at the subpixel level and subsequent resampling of the
The exchange ratios for the two species are shown in Fig. 9(b). The exchange ratio is defined as the fraction of molecules which in the subsequent image are exchanged by a molecule of the other type. For DUDSe this is equal to 1 n50(7 s)/n0. n0 is the number of DODSe molecules in the first two subsequent images. The positions occupied by these n0 molecules are occupied by either DUDSe or DUDS molecules in the subsequent image recorded 7 s later. n50(7 s) is the number of positions still occupied by DUDSe molecules.
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Se/f-assembled organic molecules at the solid/liquid interface
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Fig. 7. STM images of DODS and DODSe surface layer, 40 nm x 40 nm. The images were recorded with a time difference of 7 s. The image in (b) is translated to give maximum correlation with the image in (a). The kernels of the molecules are seen as the light parts and the lightest parts are associated with the DODSe kernels. The differences in the two images reflect the molecular dynamic.
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The exchange ratio was found to be 0.67 ±0.05 for DUDSe and 0.28 ±0.05 for DUDS (observed exchanges per 7 s). Inserting these results into eqns. (6) and (7), the mean lifetimes on the surface for DUDS and DUDSe were found to be 1.5 and 1.3 s respectively. Within a 95% confidence limit (assuming gaussian distributions) the standard deviations for the exchange rate and the mixture ratio result in an upper bound for these lifetimes of 3.0 and 1.8 s for DUDS and DODSe respectively, The standard deviations are too large to give a lower bound, because the argument to the logarithmic term in Eq. (6) may become negative. However, it is rare to find a molecule exchanged by the other type during the time
it takes to scan an individual molecule. If an exchange does occur, it is observed as a molecule which has DUDS height values for some scan lines and DODSe height values for the scan lines recorded several milliseconds later. Since the scan speed corresponds to 54 ms per scan line, we conclude that the mean lifetime is more than about 100 ms. In a few cases we can observe an exchange event from one scan line to another, but we have never observed vacancies. This indicates that the exchange events have a duration of less than 50 ms. From the images we found a tendency for clustering, as quantified in Fig. 9(c). The graph shows the distribution of DUDSe molecules located in different cluster
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sizes. The result is compared with a random distribution of a compound with the same mixture ratio. Because the curves are significantly different, we conclude that for DODSe, with the given mixture ratio, clusters of two molecules are more favourable than other cluster sizes. This clustering behaviour has not been analysed further, but it could be described within a thermodynamic model including an unfavourable interaction between neighbouring molecules of different kinds,
tion gave us also estimates of the differences in bonding energy and dynamics. The mean lifetimes for the molecules on the substrate were about 1—2 s and highest for the DUDS molecules, This relatively high stability makes it possible to produce stable molecular surface layers which may be used for in situ chemical modifications. Longer molecules and/or lower temperatures would slow down the dynamics. When the exchange events occurred, they appeared within 50 ms. A significant clustering of the molecules was also observed.
5. Summary Acknowledgment We have demonstrated that it is possible to measure unit cells from self-assembled molecules with an uncertainty less than 1%. This is achieved by having up-todate calibration data from the underlying substrate and by use of high precision unit cell detection algorithms. For the molecular compounds we were able to distinguish between the two different species in agreement with the theoretical predictions. By use of specially designed image-processing techniques, statistical calcula-
We thank L. Nielsen for useful discussions.
References [I] [2]
J Rabe and S Buchholz, Phys. Rev. Lett., 66(1991)2096 L. Madsen, J. Jørgensen, K. Carneiro, M. Jorgensen and J. Garnaes, Synth. Met., 55 (1993) 335.
J. F. Jorgensen et a!.
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Se/f-assembled organic molecules at the solid/liquid interface
[3] J. Jorgensen, L. Madsen, J. Garnaes and K. Carneiro, J. Vac. Sd. Technol. B, 12 (1994). [4] J. Rabe and S. Buchholz, Science, 253 (1991) 424. [5] D. Parks, N. Clark, D. Walba and P. Beale, Phys. Rev. Lett., 70 (1993) 607. [6] L. Askadskaya and J. Rabe. Phys. Rev. Lett., 69 (1992) 1395. [7] L. Madsen, Scanning tunnelling microscopy: an implementation and some applications, Ph.D. Thesis, LTF, DTH, Lyngby, Denmark, 1990.
211
[8] 0. Albrektsen, L. L. Madsen, J. Mygind and K. A. Morch, J. Phys. E: Sd. Instrum., 22 (1989) 39. [9] J. Jørgensen, Scanning probe microscopy image restoration and analysis, Ph.D. Thesis, IMSOR, DTH, Lyngby, Denmark, 1993. [10] D. H. J. Tersoff, Phys. Rev. Lett., 50 (1983) 1998. [11] D. Hamann, Phys. Rev. B, 31(1985) 805. [12] J. J. P. Stewart, J. Comput. Chem., 10(1989)10. [13] J. J. P. Stewart, MOPAC QCPE No. 455, 1990. [14] E. Clementi, IBM J. Res. Develop., 2 (1965).
201
Dynamics and structure of self-assembled organic molecules at the solid—liquid interface J. F. Jørgensena, N. Schmeissera, J. Garnaesa, L. L. Madsena,b, K. Schaumburg”, L. Hansen, P. Sommer~Larsenc ~DanishInstitute of Fundamental Metrology, Building 307, Lundtoftevej 100, DK-2800 Lyngby, Denmark bCentrefor Interdisciplinary Studies of Molecular Interactions, Department of Chemistry, University of Copenhagen, Fruebjerguej 3, DK-2100 Copenhagen, Denmark The Engineering Academy of Denmark, Department of Chemistry (DIA-K), Building 375, DK-2800 Lyngby, Denmark
Abstract We have analysed scanning tunnelling microscope (STM) images of self-assembled didodecylbenzene (DDB) molecules physisorbed on graphite from a DDB solution using octylbenzene as solvent. The DDB images were obtained alternating with images of the graphite substrate using two different bias voltages. The well-known lattice constant of the graphite substrate was used for an accurate determination of the calibration factors and drift of the STM. The DDB unit cells were detected and measured in the Fourier domain and corrected by the calibration data. The commensurability between the graphite lattice and the DDB lattice was analysed. Although the graphite lattice and the DDB lattice planes are parallel, incommensurability was observed as superstructures in the Fourier pattern. The molecules dioctadecyldiselenide and dioctadecyldisulphide also form well-ordered monolayers when adsorbed on graphite from solution. Dioctadecyldiselenide and dioctadecyldisulphide form ideal mixtures. It is therefore of interest to determine to what extent the molecules form mixed structures when physisorbed on the graphite substrate. Theoretical and experimental observations show that S and Se atoms yield markedly different contrasts in the STM images. When imaging mixed surface layers, the dynamic adsorption and dissolution of individual molecules can be followed. A time scale ofaround 1 s was found for this process. The ratio between fractions of adsorbed molecules of different species was found to be very similar to the ratio in solution, indicating a small difference in bonding energy.
1. Introduction Regular patterns of self-assembled molecules have been observed in a number of cases at the interface between organic solutions and solids [1—3]. Most studies have been performed on highly oriented pyrolytic graphite (HOPG). Long-chain aliphatic compounds appear to have a strong affinity for graphite. To illustrate this, we analyse the commensurability between selfassembled didodecylbenzene (DDB, H25 C12(C6H4) C12H25) molecules and an HOPG substrate. Such commensurability analysis done qualitatively in the spatial domain has been reported by other groups [4,5]. Here we apply a subpixel Fourier technique for quantitative measurements. In compounds where functional groups have been inserted, the self-assembled layers still exist, but the stability is found to be reduced depending on the functional group inserted. Self-assembled layers have been suggested as starting materials for performing in situ chemical modifications locally on the surface layer. This technique might lead to nanometre patterns on the surface. In order to evaluate the feasibility of this
SSDI 0257-8972(94)002304-9
approach, it is necessary first to determine the mean residence time of molecules in the surface layer, i.e. the mean time from adsorption to desorption. Molecular dynamics at domain boundaries has been studied before [4,5] and also dynamics observed at different temperatures has been reported [6]. Here we report quantitative measurements of the mean residence time for the individual molecules in ordered layers far from the domain boundaries. The problem is that exchange of identical molecules in the surface layer will not be visible, save the infrequent situations where an exchange leads to fractional occupancy of a lattice site. The problem may be overcome by use of a binary mixture. The requirement will be that the two molecular species should form ideal mixtures in solution and should form mixed surface layers including both molecules. The molecules should be sufficiently different that the scanning tunnelling microscopy (STM) technique can distinguish the species in the surface layer. The above considerations have led us to use dioctadecyldisuiphide (DODS, H37C18SSC18H37) and dioctadecyldiselenide (DODSe, H37C18SeSeC18H37) as a pair of analogous molecules for these experiments.
Elsevier Science S.A.
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Self-assembled organic molecules at the solid/liquid interface
Sulphur and selenium belong to the same group in the periodic table and their chemical properties are very similar, The long-chain aliphatic compounds in question show perfect miscibility in solution. Initial studies showed that DUDS forms stable surface layers with a packing consistent with space-filling molecular models. The expectation based on this finding is that DUDS and DODSe will form mixed surface layers of the same packing structure, Compared with sulphur, selenium is more metallic in character and more polarizable. As a result, the electron tunnel current is larger through selenium than through sulphur. Consequently, we expect the apparent height measured by STM for the two molecules to appear distinguishable. We confirm this by theoretical calculations and from STM measurements. 2. Preparation and scanning technique Samples were prepared by dissolving the molecules of interest in octylbenzene as dilute solutions. Binary mixlures were prepared by mixing known quantities of the single-component solutions. A drop of the solution is placed on the HOPG substrate and scanning of the surface is performed during the period where the droplet slowly evaporates, thereby increasing the concentration of the molecular species of interest in the drop. For a certain concentration interval the molecules form a monolayer on the graphite. The instrument used comprised a self-made scanning tunnelling microscope (STM) [7,8] and a Rasterscope 3000 with an STM 9 ~.tmscanning tube and with the scanning tip facing downwards. Cut PtIr tips were used. The scanned regions were 10—40 nm square with a resolution of 256 x 256 or 128 x 128 pixels; the scan rate was typically one image per 7 ~ 3. Didodecylbenzene We have shown [3] that self-assembled DDB molecules can be imaged by STM using a bias voltage of about I V. At lower bias voltages of about 0.1 V the tunnelling mechanism is different and the STM images show the contrast of the HUPG substrate. We will demonstrate that the well-known lattice of HOPG is useful for calibration and subsequent measurements of the adsorbed surface layer unit cell. 3.1. Image processing and analysis For the DDB molecules, where we want an accurate measurement of the unit cell, we apply a novel calibration and drift elimination technique based on Fourier analysis. The calibration factors are calculated from low voltage STM images showing the graphite substrate. The detection and measurement of the DDB unit cell are also done in Fourier space and carried out on the
images recorded with a high bias voltage. The measured DDB unit cells were corrected by using the calibration values calculated from the graphite images, which were recorded within 44 s before or after. 3.2. Calibration For the calculation of the calibration factors a novel technique [3,9] has been utilized. The advantage of this technique is that it is automatic and can estimate the drift in the fast-scanning direction, which makes it more reliable. The technique is based on the detection and measurement of the position of Fourier peaks associated with the graphite lattice. The determination of calibration factors and the subsequent restoration are illustrated in Fig. 1. The fact that we can measure the drift in the fastscanning direction (dr) makes it possible to perform a perfect restoration of the distorted image. As will be demonstrated, the calibration factor for the fast-scanning direction (cr) can be determined with a standard deviation less than 0.02%. However, it is not possible from a single image to tell how much of the scan range in the slow-scanning direction is caused by the calibration factor (cv) and how much is caused by the drift (dr) in this direction. This is not important when correcting the DDB unit cells, but it is crucial to have up-to-date c~values. 3.3. DDB unit cell measurements The DDB oblique unit cell was calculated by measuring the position of the associated peaks in the Fourier domain [3,9]. From a number of alternative unit cells the one covering the single molecules best was selected and described by the length of the two unit cell vectors and their angle. Fig. 2 shows the results calculated from the different images together with the obtained calibration factors as a function of time. Several conclusions can be drawn from Fig. 2. (1) The c~calibration factor is reproducible within 0.02%, indicating that the variation in both the detection algorithm and the x calibration factor of the instrument was less than 0.02%. (2) The drift (dr) was (320±4)pms1, which at the scanning speed used could give an angle error of 37°. This is a large but very reproducible error and it turned out that it was due to minor damage of the scanning elements which caused non-orthogonal scanning. In this sense we were able to use the image processing as a diagnostic tool. Because the error was so stable, it was also possible to correct for this error. (3) The estimated c 5 calibration factor was 0.839 ± 1%, which is about 50 times less stable than for the x direction owing to the fact that it has the drift (d5) embedded. This may be unimportant for the restoration of the actual HUPG image but reflects some of the
J. F. Jorgensen et a!.
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Fig. I. Graphite image and its spectrum highly distorted by drift. The distortion is best seen from the skew ellipse passing through the lattice peaks in the Fourier transform. The lines connecting origin and the two lattice peaks are reciprocal lattice vectors. Their sum is clearly pointing at the third lattice peak, which indicates that the three lattice peaks are due to the hexagonal lattice. From the detected peaks in (b) the lateral calibration factors and the drift are found. In (c) and (d) the restored image and its Fourier spectrum are shown.
uncertainty when used for correction of the DDB unit cell. (4) Based on 29 images, we can calculate the statistics of the DDB unit cell. The long vector of the DDB unit cell was calculated as (3.73 ±0.02) nm (about 0.8%), which corresponds to 15.16 ±0.12 graphite unit cell vectors. This confirms previous results [3], which at a lower accuracy indicated that the long DDB unit cell vector was 3.80 nm ±10% (based on five images) and incommensurate with the graphite substrate. (5) The short vector was found to be 0.549 nm ± 0.4%, corresponding to 2.23 ±0.01 times a graphite unit cell vector and therefore clearly incommensurate with the graphite substrate. (6) The DDB unit cell angle is 120.8°±0.6°,which
indicates close but not exact alignment with the graphite lattice. 3.4. Commensurability analysis Although perfect commensurability between the graphite substrate and the DDB molecular layer was not found, the self-assembling process seems to be highly influenced by the graphite substrate. This is confirmed by Fig. 3, where a profile through a Fourier peak associated with the graphite is shown. From the source image in Fig. 3(a) the lamella width is visible simultaneously with the graphite. The Fourier peak corresponding to the DDB lamellae can therefore be observed in the same direction as the graphite peak in Fig. 3(b). This peak is thus seen as the inner peak of Fig. 3(b) and the corre-
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Fig. 2. Results obtained from a series of DDB images. In (a) the x- and y-calibration factors determined from the graphite images are plotted. Note that the x-calibration factor is much more stable. In (b) the measured drift in the x direction is drawn. The length of the long DDB unit cell vector is shown in (c). They have been detected for the individual images and corrected by the calibration data shown in (a) and (b). (d) shows the length of the short unit cell vector and (e) the unit cell angle also after correction.
sponding Fourier profile in Fig. 3(c) at a frequency 15.16 times lower than the graphite peak. The incommensurability between the short vector of the DDB unit cell and the graphite can also be analysed in the Fourier domain. In Fig. 4 a DDB image and its Fourier transform are shown. In the Fourier domain satellite peaks can easily be found. These satellite peaks correspond to a superstructure in the spatial domain with a short unit cell vector that is 4.4 times the short vector of a single DDB unit cell but has the long unit cell vector and angle in common with the single DDB unit cell.
4. DODS—DODSe mixture and dynamics For the DUDS and DODSe self-assembled molecules we will in the following describe a simulation technique of the STM imaging mechanism in the constant-current mode. The results of the simulations give us a feeling for the expected height variations and can be compared with the measured STM images. The dynamic adsorption and dissolution of individual molecules measured in the STM images are analysed using a thermodynamic model, from which quantitative results for the rate of desorption are found. Surface layers formed from one
J. F. Jorgensen et al.
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solution are reported, but many similar solutions have been studied. This solution was prepared with a ratio of DUDSe : DUDS of 1:2. The experiments were performed at a temperature of 295 K. 4.1. Calculation of tunnel currents Tunnel currents were calculated for a model consisting of a single molecule adsorbed on a graphite layer. The
local density of states (LDOS) was calculated for states with energies up to eV above the Fermi level, where e is the elementary charge value and V is the applied bias voltage. The tunnel current is proportional to the LDUS in the Tersoff—Hamann [10,11] approximation. Tunnelling through the adsorbed molecule was taken into account by multiplying the density from each single orbital by its projection on the p~orbitals of the graphite
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layer. The semiempirical PM3 method [12,13] was used to calculate orbitals for the graphite molecule model, Densities were calculated using the expansion coefficients from the semiempirical calculation and atomic basis functions based on Slater-type orbitals (STOs) [14]. Tn the outer part of the valence region the atomic orbitals were fitted to an expression of the type R
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where R~1(r)is the radial part of the wavefunction and A, B and ~ are parameters to be fitted. .The use of this simplified expression improves the computational speed compared with the use of the original expansion in STUs. Two types of molecules were studied: CH3CH2SS CH2CH3 and CH3CH2SeSeCH2CH3. The graphite was modelled with one layer of graphite containing 48 carbon atoms, terminated by hydrogen atoms if necessary. The carbon—sulphur skeleton was kept planar and parallel to the graphite surface. The molecule— graphite distance was fixed at 3.4 A. The geometry for the disulphide compound was optimized under these restrictions. Exactly the same geometry was used for the diselenide compound, but sulphur was replaced by selenium. Simulated constant-current images showing the distance of the tip from the graphite are presented in Fig. 5. The images are calculated using a bias of 1.5 V. The difference between sulphur and selenium is maximum for this bias. The experimental images are measured at a bias of 1 V. An asymmetry in the simulated image is caused by interactions between the underlying graphite and the molecule. The images are calculated for a fixed LDOS rather than for a fixed current (which is assumed
to be proportional to the LDOS). An LDUS of l0~ A3 is used, corresponding to an average distance of 7 A between the graphite and the tip. This is a reasonable value, since changing the LDUS by a factor of 10 only results in minor changes in the calculated image. The height profiles shown in Fig. 6 are calculated along the lines which connect the maximum values in Fig. 5. These peaks represent CH 3 Se, Se andbetween CH3 respectively in Fig. 6(a), The largest difference selenium and the methyl group is 1.0 A, whereas the difference between sulphur and the methyl group is 0.7 A. The difference between the height over selenium and sulphur is thus 0.3 A. The theoretical model can be improved in several ways. First, the LDUS from neighbouring molecules adds to the total current over a given atom. Uwing to the slower decay of the LDOS of a selenium or a sulphur atom compared with that of a carbon atom, a more extensive calculation including neighbouring molecules will result in a larger current over a selenium or sulphur atom relative to the current over a carbon atom. Secondly, all non-hydrogen atoms in the molecule are placed at a distance of 3.4 A from the graphite. This may not be correct and differences in latitudes over the graphite will also result in differences in the profiles. Finally, various improvements in the basic model, inclusion of d-basis functions and the effect of an electric field in the calculation should be considered. 4.2. Thermodynamic models During the experiment the adsorbed molecules exist in equilibrium with molecules in solution. Various models may be used to describe this equilibrium and the underlying kinetics. In the simplest model the solu-
J. F. Jorgensen et al.
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Se/f-assembled organic molecules at the solid/liquid interface
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tion of sulphur and selenium compounds constitutes an ideal dilute solution and the adsorbed molecules are assumed to form an ideal solid solution.
The bonding between the graphite surface and a selenium compound is assumed to be weaker than the bonding between the graphite surface and a sulphur compound. The difference in bonding energy, e = Ese..graphite E~graphite, which is positive, is the only parameter entering the model. In this case the equilib—
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208
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J. F. Jorgensen et al.
Self-assembled organic molecules at the solid/liquid interface
processes are assumed to be of first order. The adsorption process may be assumed to be activationless and the rate constant for adsorption of a selenium compound can be assumed to be equal to the rate constant for adsorption of a sulphur compound. Adsorption is assumed to be much faster than desorption. The rate constants for desorption of the two kind of compounds differ and their ratio is given by k
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image to be shifted according to the detected maximum correlation coordinate, For subsequent images the calculated displacement was always less than half the length of the short unit cell vector. From the aligned images we detected and classified the DODS—DODSe molecules automatically. This was done by detecting all significant peaks associated with the SS and SeSe pairs. These peaks were then classified as belonging to DUDS or DUDSe depending on their height values. The classification threshold was selected dynamically on an image-by-image basis to give the
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Observing a collection of n0 DUDSe molecules in the adsorbed layer, the number of DUDSe molecules at these sites decays towards the equilibrium composition. The average fraction of selenium-containing molecules for such a collection as a function of time is
we can follow the molecules from image to image and detect molecules which are exchanged by a molecule of the other type. It ts therefore possible to get statistics about the molecular mixture rate on the surface and also the molecular dynamics.
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Using the above models, the observed data allow for the determination of the difference in bonding energy as well as the rate constant for desorption of the sulphur and selenium compounds:
4.4. DODS—DODSe results Fig. 7 shows an example of two DODS—DODSe images recorded with a time separation of 7 s. As for the DDB molecules, these molecules also assemble into long lamellae. The DUDSe molecules are seen as those having the highest contrast in their kernels; see also the profiles across the kernels shown in Fig. 8. Qualitatively the observed and simulated profiles agree. In both cases selenium appears as the highest atom and the difference between selenium and sulphur is approximately onethird of the difference between selenium and the aliphatic
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dual images. The mean value calculated after 32 images is 0.44 ±0.11, which is different from the liquid phase ratio of 0.5. The partition coefficient in Eq. (2) is found
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4.3. Image processing and analysis ofDODS—DODSe For the DODS—DUDSe molecule images we focus on the adsorption and dissolution of individual molecules. For this purpose we have recorded 32 images with a separation time of 7 s. To overcome drift problems, we align all images pairwise to give maximum correlation. This is done by calculation of the cross-correlation function, detection of the maximum correlation peak at the subpixel level and subsequent resampling of the
The exchange ratios for the two species are shown in Fig. 9(b). The exchange ratio is defined as the fraction of molecules which in the subsequent image are exchanged by a molecule of the other type. For DUDSe this is equal to 1 n50(7 s)/n0. n0 is the number of DODSe molecules in the first two subsequent images. The positions occupied by these n0 molecules are occupied by either DUDSe or DUDS molecules in the subsequent image recorded 7 s later. n50(7 s) is the number of positions still occupied by DUDSe molecules.
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the aliphatic chains is five times that found in the simulations. It is also seen that there are fewer DUDSe molecules than DUDS molecules. This is quantified in Fig. 9(a), showing the DUDSe—DUDS mixture ratio for the indivi-
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Fig. 7. STM images of DODS and DODSe surface layer, 40 nm x 40 nm. The images were recorded with a time difference of 7 s. The image in (b) is translated to give maximum correlation with the image in (a). The kernels of the molecules are seen as the light parts and the lightest parts are associated with the DODSe kernels. The differences in the two images reflect the molecular dynamic.
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The exchange ratio was found to be 0.67 ±0.05 for DUDSe and 0.28 ±0.05 for DUDS (observed exchanges per 7 s). Inserting these results into eqns. (6) and (7), the mean lifetimes on the surface for DUDS and DUDSe were found to be 1.5 and 1.3 s respectively. Within a 95% confidence limit (assuming gaussian distributions) the standard deviations for the exchange rate and the mixture ratio result in an upper bound for these lifetimes of 3.0 and 1.8 s for DUDS and DODSe respectively, The standard deviations are too large to give a lower bound, because the argument to the logarithmic term in Eq. (6) may become negative. However, it is rare to find a molecule exchanged by the other type during the time
it takes to scan an individual molecule. If an exchange does occur, it is observed as a molecule which has DUDS height values for some scan lines and DODSe height values for the scan lines recorded several milliseconds later. Since the scan speed corresponds to 54 ms per scan line, we conclude that the mean lifetime is more than about 100 ms. In a few cases we can observe an exchange event from one scan line to another, but we have never observed vacancies. This indicates that the exchange events have a duration of less than 50 ms. From the images we found a tendency for clustering, as quantified in Fig. 9(c). The graph shows the distribution of DUDSe molecules located in different cluster
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sizes. The result is compared with a random distribution of a compound with the same mixture ratio. Because the curves are significantly different, we conclude that for DODSe, with the given mixture ratio, clusters of two molecules are more favourable than other cluster sizes. This clustering behaviour has not been analysed further, but it could be described within a thermodynamic model including an unfavourable interaction between neighbouring molecules of different kinds,
tion gave us also estimates of the differences in bonding energy and dynamics. The mean lifetimes for the molecules on the substrate were about 1—2 s and highest for the DUDS molecules, This relatively high stability makes it possible to produce stable molecular surface layers which may be used for in situ chemical modifications. Longer molecules and/or lower temperatures would slow down the dynamics. When the exchange events occurred, they appeared within 50 ms. A significant clustering of the molecules was also observed.
5. Summary Acknowledgment We have demonstrated that it is possible to measure unit cells from self-assembled molecules with an uncertainty less than 1%. This is achieved by having up-todate calibration data from the underlying substrate and by use of high precision unit cell detection algorithms. For the molecular compounds we were able to distinguish between the two different species in agreement with the theoretical predictions. By use of specially designed image-processing techniques, statistical calcula-
We thank L. Nielsen for useful discussions.
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J Rabe and S Buchholz, Phys. Rev. Lett., 66(1991)2096 L. Madsen, J. Jørgensen, K. Carneiro, M. Jorgensen and J. Garnaes, Synth. Met., 55 (1993) 335.
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Se/f-assembled organic molecules at the solid/liquid interface
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[8] 0. Albrektsen, L. L. Madsen, J. Mygind and K. A. Morch, J. Phys. E: Sd. Instrum., 22 (1989) 39. [9] J. Jørgensen, Scanning probe microscopy image restoration and analysis, Ph.D. Thesis, IMSOR, DTH, Lyngby, Denmark, 1993. [10] D. H. J. Tersoff, Phys. Rev. Lett., 50 (1983) 1998. [11] D. Hamann, Phys. Rev. B, 31(1985) 805. [12] J. J. P. Stewart, J. Comput. Chem., 10(1989)10. [13] J. J. P. Stewart, MOPAC QCPE No. 455, 1990. [14] E. Clementi, IBM J. Res. Develop., 2 (1965).