- Email: [email protected]
Dynamics of discotic methoxy triphenylene molecules from quasielastic neutron scattering and molecular dynamics simulations
Chemical Physics 292 (2003) 185–190 www.elsevier.com/locate/chemphys
Dynamics of discotic methoxy triphenylene molecules from quasielastic neutron scattering and molecular dynamics simulations G.J. Kearley a,*, F.M. Mulder a, S.J. Picken b, P.H.J. Kouwer b, J. Stride c a b
Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands Polymer Materials and Engineering, PME, Department of Materials Science and Technology, Julianalaan 136, 2628 BL Delft, The Netherlands c Institute Laue Langevin, BP156 Grenoble, 38042 Cedex 09, France Received 10 October 2002; in final form 18 February 2003
Abstract Quasielastic neutron scattering measurements on hexakismethoxytriphenylene (HMT) shows molecular motion at timescales of 0.1 and 7.3 ps at 370 K. Deuteration of the methoxy tails, suppresses the signal for the slower motion, whilst the signal from the more rapid motion of the triphenylene cores persists. A molecular dynamics simulation on an isolated model of 4 HMT molecules reveals the slower methoxy motion to be a torsion of the whole methyl group around the core to oxygen bond. The faster motion is due to lateral sliding of the cores with respect to each other. A harmonic core-motion arising from tilting of the disks in the simulation may correspond to a strongly damped motion seen in the experimental data. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Discotic liquid crystalline materials are formed from disklike poly-aromatic molecules that are stacked in such a way that there is p electron overlap of adjacent molecules that forms a one-dimensional path along which charge can migrate. This has aroused interest in these materials for nanoscale devices such as light-emitting diodes, field-effect transistors [1–4] and photo voltaics [5]. Conduction
*
Corresponding author. E-mail address: [email protected] (G.J. Kearley).
between the aromatic cores can be calculated from first principles methods, but the calculated values exceed the measured values by a considerable margin [6]. This is thought to be due to intracolumnar disorder, and whilst there is a wealth of evidence from the effects of side-chains etc., no direct measure of core and tail dynamics has been made. Quasielastic neutron scattering is an ideal technique for this type of measurement, but suffers from the difficulty that the signal from such complex systems is difficult to understand unambiguously [7]. In an initial study, which is to be broadened to much larger systems, we focus on the simplest possible system hexakis(n-methoxy)triphenylene (HMT,
0301-0104/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00083-1
186
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
2.2. 2,3,6,7,10,11-Hexakismethoxytriphenylene-d18 (D-HMT)
Fig. 1. Schematic illustration of the HMT molecule. The selective deuteration of the methoxy groups is indicated.
Fig. 1), and use selective deuteration to highlight the motions of the aliphatic side-chains and aromatic cores separately. Further, since such systems have motions over a wide range of timescales, we use a molecular dynamics simulation in order to understand which motions arise in the picosecond timescale.
A mixture of catechol (3.4 g, 31 mmol), CD3 I (10.0 g, 69 mmol), K2 CO3 (13.8 g, 0.10 mmol), KI (1.4 g, 9.5 mmol) and acetone (70 ml) was refluxed over the weekend. The reaction mixture was cooled and the solids were filtered off. The solvent and the excess of CD3 I were evaporated. The product was diluted with hexane, filtered and the hexane was evaporated to yield a colourless liquid (4.3 g, 30 mmol, 95%). 1 H NMR (CDCl3 , 200 MHz): d 6.2–6.8 (m, 4H, aromatic CH). 13 C NMR (CDCl3 , 200 MHz): d 149.02, 120.82, 111.30 (aromatic CH); 54.99 (h, OCD3 ). To a solution of veratrole-d6 (4.3 g, 30 mmol) in dry CH2 Cl2 (50 ml) was added MoCl5 (8.8 g, 32 mmol). The black mixture was stirred for 1 h at room temperature under inert atmosphere and poured into cold methanol. The solids were filtered, dissolved in warm CHCl3 and reprecipitated in methanol (2), yielding pure D-HMT (2.29 g, 5.3 mmol, 54%) as a white crystalline powder. 1 H NMR (DMSO-d6 , 200 MHz): d 8.00 (s, 6H, aromatic CH). 13 C NMR (DMSO-d6 , 200 MHz): d 148.63, 122.58, 105.01 (aromatic CH); 54.48 (h, OCD3 ).
2. Experimental
2.3. QENS
HMT and the selectively deuterated D-HMT were prepared by oxidative trimerisation of the corresponding veratroles using molybdenum(V) chloride [8].
Quasielastic neutron spectra were obtained using the IN6 spectrometer at the Institute Laue Langevin in France. An incident wavelength of was selected to give the correct compromise 5.9 A between energy range and energy resolution. Samples were sealed in thin-walled aluminium containers and temperature control was achieved using a standard oven. The sample thickness was controlled to give a scattering probability of 10%. Corrections for detector efficiency were made by normalisation using spectra from a 1 mm plate of vanadium in place of the sample. The background scattering was estimated from the spectra obtained from the empty sample container. This background was subtracted from both the sample and vanadium spectra before normalisation. Corrections for sample shape, and self shielding, were made and the corrected data converted to SðQ; xÞ using the program INX [9].
2.1. 2,3,6,7,10,11-Hexakismethoxytriphenylene (HMT) To a solution of veratrole (4.5 g, 33 mmol) in dry CH2 Cl2 (50 ml) was added MoCl5 (9.6 g, 35 mmol). The black mixture was stirred for 1 h at room temperature under inert atmosphere and poured into cold methanol. The solids were filtered, dissolved in warm CHCl3 and reprecipitated in methanol (2), yielding pure HMT (2.48 g, 6.1 mmol, 61%) as a white crystalline powder. 1 H NMR (DMSO-d6 , 200 MHz): d 7.99 (s, 6H, aromatic CH); 2.50 (s, 18H, OCH3 ). 13 C NMR (DMSO-d6 , 200 MHz): d 148.63, 122.60, 105.04 (aromatic CH); 55.77 (h, OCH3 ).
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
3. Results and discussion In the first instance the quasielastic spectra were fitted using a global fitting routine over spectra at 15 different momentum-transfer values (Q-values) with the constraint that all spectra were composed of either one or two Lorentzian components whose widths are constant in Q plus an elastic component defined by the measured resolution function. The total intensity (quasielastic + elastic) was constrained to be constant after correction by a single Debye–Waller factor and a single time-of-flight constant flat-background. It proved extremely difficult to completely avoid contamination of the incoherent elastic scattering by coherent Braggscattering, but nevertheless, the data for the isotopically normal compound clearly required two Lorentzian components to fit the measured quasielastic signal. Fitted widths and intensities are collected in Table 1. On deuteration of the methyl tails, the narrower Lorentzian quasielastic component is suppressed and the spectra were satisfactorily fitted using a single quasielastic contribution. From these results we conclude that the narrower component corresponding to a timescale of 0.1 ps (at 370 K) arises from motion of the methoxy tails, whilst the broader component corresponding to a timescale of 7.3 ps (at 370 K) is due to motion of the triphenylene cores. At first this result seems surprising because the cores are considerably heavier than the tails, so in order to understand this further we undertook a molecular dynamics simulation. Our model is of 4 HMT disks and was built by constructing a single disk whose energy was minimised. For this purpose we
187
used a commercial implementation of the Compass force field [10] with a proprietary minimisation algorithm. The minimum energy corresponds to alternate up/down conformations of the methoxy groups with respect to the triphenylene core (see Fig. 1). The model was built by successive addition of energy-minimised HMT molecules with further minimisation after each addition. The resulting structure is shown in Fig. 2 in which the in good agreement disk–disk separation is 3.58 A with crystallographic data [11]. Each disk is oriented at 60° with respect to its neighbours, which is in conflict with the value normally associated with triphenylenes: 45°. The 60° conformation proved to be remarkably stable, the system minimising back to this from almost any other starting orientation. We noticed, however, that with longer tails and tails with side substituents, orientations around 45° were indeed formed. The model was thermalised at 400 K and then molecular dynamics simulations of 1.1 ns were performed. Our model is rather small and ignores all intercolumn interactions. Further, the correlation length of motions along the column is also somewhat limited, and simulations at 300 K gave rise to sharp inelastic peaks due to harmonic modes. In the simulation at 370 K these modes are strongly damped and lead to calculated spectra resembling those measured at the same temperature. In the following analysis we emphasise that the aim is to
Table 1 Widths of the quasielastic components of the experimental spectra as a function of temperature Temperature (K)
Width 1 (meV)
Width 2 (meV)
Width 2 (meV) methoxy D
300 370 470
0.041 0.075 0.140
4.93 4.37 4.96
4.13 3.37 4.06
A global fitting routine was used to help overcome the problems of incomplete Bragg-peak subtraction, and correlation of the broader peak with the background signal.
Fig. 2. Minimum energy configuration of the 4-molecule HMT column used for the molecular dynamics simulation.
188
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
understand the nature of the picosecond motions of the methoxy tails, and why these should be slower than the motion of the triphenylene core. The results of the simulation must therefore be in reasonable agreement with the measured data, and any discrepancy should be consistent with the known limitations of the model. The trajectories from the MD simulation were analysed using the NMOLDYN [12] routines to produce the measured elastic incoherent structure factors (EISF) and scattering functions (SðQ; xÞ) of the isotopically normal and methoxy deuterated samples. The resulting EISFs are compared with experiment in Fig. 3. Both experiment and simulation show a considerable decrease in EISF on methoxy-deuteration, and the EISFs from the simulation are comparable to those from the experiment. Some of this disagreement is due to incomplete removal of coherent Bragg scattering. Care was taken to account for the finite experimental resolution (the experimental resolution is around 50 ps, while the simulation accesses times up to almost 1 ns, i.e., many time windows of the 50 ps neutron coherence time). This is clear from
Fig. 3. Observed EISF at 370 K for isotopically normal HMT (crosses) and methoxy deuterated HMT (squares) compared with the corresponding EISFs (broken line and solid line, respectively) from the MD simulation. The lower values from the simulation point to slower motions that are not resolved in the experiment.
Fig. 4. Comparison of observed spectra (dashed line) and spectra calculated from the MD simulation (full line) over a 1 ). Observed and range of momentum transfers (0.3–1.8 A calculated spectra are normalised to the same maximum value. The maximum intensity in the figure corresponds to 10% of the maximum peak-height.
Fig. 4 in which the observed and simulated SðQ; xÞ are illustrated. In this figure the simulated data have been convoluted with a Gaussian function that represents the experimental resolution, and the agreement between observation and calculation is quite reasonable. The main difference is at high Q, where it was particularly difficult to separate the experimental background properly, and this appears to be the principle difference between the two sets of spectra at high Q. The most important result of the simulation is that the simulated SðQ; xÞ for the core hydrogens gives rise to the broader quasielastic component, whilst the simulated SðQ; xÞ for the methyl groups gives the narrower peak, in good agreement with the experimental data on the two isotopomers (see Fig. 5). Inspection of the simulation reveals that the methyl rotations are rapid and arise outside the time-window of the quasielastic scattering. The slow methyl motion that gives rise to the narrow quasielastic component is due to motion of the whole CH3 group around the core to oxygen bond. Although the exact core motion will clearly depend on the completeness of the model, the current simulation does reproduce the salient features of the measured dynamics on the picosecond timescale, and we can draw some conclusion about the most important degrees of freedom. The core
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
Fig. 5. Spectra of methoxy deuterated (front) and isotopically normal (back) HMT. The dashed line represents measured spectra and the continuous line represents the molecular dynamics simulation.
motion has two main components. First, the cores show no significant signs of rotations over the 1 ns of the simulation. Second, the predominant motion is a sliding of the disks one over another, normally so as to preserve overlap of aromatic rings. Finally, no pure translational motion along the column axis was observed, but the disks tilt relative to each other. In this respect it is interesting to note that the inelastic peak in the experiment and in the simulation is present in the isotopically normal and the methoxy-deuterated samples. These peaks are weak and only visible by looking at the 1% level of the elastic-peak intensity. Whilst the simulation at 300 K gave sharp inelastic peaks, at 370 K these became broad. The observed spectrum at 300 K is compared with the calculated spectrum at 370 K in Fig. 6 and it is conceivable that the two broad experimental features at 3 and 6 meV correspond to the groups of peaks at around 2 and 3 meV in the simulation. In the simulation it is clear that these arises from disk tilting, and thus gives intensity in the methyl deuterated and isotopically normal compounds. The model that we use is rather simple and we have to be careful not to over interpret the data with such a simple model. There are three approximations that we have to consider. First, the limited length of the column means that modes along the
189
Fig. 6. Observed spectrum at 300 K (solid line) compared with MD simulation at 370 K (broken line) showing weak inelastic features. The maximum of the figure corresponds to 2% of the peak intensity. The MD simulation at 300 K gave very sharp inelastic features due to the small size of the model.
column will be seriously curtailed, and also softened. Second, neighbouring columns would be expected to damp modes along the chains and to stiffen the lateral degrees of freedom. Finally, fixing two core atoms on the ends of the columns will restrict rotational motion, and harden motions along the chain. It can be seen that these limitations often work in opposite directions and we cannot exclude that some of the agreement between the simulation and experiment is due to fortuitous cancellations. The present work is a compromise between the more traditional analysis of quasielastic spectra and the mesoscopic modelling methods normally used for large complex systems.
4. Conclusions Quasielastic scattering can be used to study the motion of discotic cores, but an MD simulation is required in order to understand which motions are observed. In moving to larger, technologically important discotic systems the deuteration of the tails, or tail substituents, becomes more difficult and it is important to establish which molecular dynamics methods (in particular force-fields) work on smaller model system. Whilst torsional motions of the methoxy group about their bond to the core can be separated from
190
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
the motions of the core itself, in other respects the tails follow the motions of the cores. This is clear from the observation of the inelastic signal in both isotopic samples and in the simulation. The most important core motion on the picosecond timescale is lateral sliding of one disk with respect to its neighbours in the column. It would be interesting to perform a more complete simulation for a group of longer columns to see how to learn more about the long-range effects of longitudinal core modes, and the effect of intercolumnar interactions on the sliding motions of the disks.
References [1] A.J. Berresheim, M. M€ uller, K. M€ ullen, Chem. Rev. 99 (1999) 1747.
[2] S. Chandrasehkar, S. Krishna Prasad, Contemp. Phys. 40 (1999) 237. [3] H. Eichorn, J. Porphorins Phtalocyanines 4 (2000) 88. [4] I. Seguy, P. Destruel, H. Bock, Synth. Met. 15 (2000) 111. [5] L. Schmidt-Mende, A. Fechtenk€ otter, K. M€ ullen, E. Moons, R.H. Frien, J.D. MacKenzie, Science 293 (2001) 1119. [6] B.R. Wegewijs, L.D.A. Siebbeles, Phys. Rev. B 65 (2002) 245112. [7] A.V. Belushkin, M.J. Cook, D. Frezzato, D. Haslam, A. Ferrarini, D. Martin, J. McMurdo, P.L. Nordio, R.M. Richardson, A. Stafford, Mol. Phys. 93 (1998) 593. [8] S. Kumar, M. Manickam, Chem. Commun. 1615 (1997). [9] F. Rieutord, INX – Program for time-of-flight data reduction userÕs guide, Internal report 90RI17T Institute Laue Langevin, Grenoble, France (1990). [10] H.J. Sun, Phys. Chem. 102 (1998) 7338. [11] T. Wang, D. Yan, J. Luo, E. Zhou, O. Karthaus, H. Ringsdorf, Liq. Cryst. 23 (1997) 869. [12] G.R. Kneller, V. Keiner, M. Kneller, M. Schiller, Comput. Phys. Commun. 91 (1995) 191.
Dynamics of discotic methoxy triphenylene molecules from quasielastic neutron scattering and molecular dynamics simulations G.J. Kearley a,*, F.M. Mulder a, S.J. Picken b, P.H.J. Kouwer b, J. Stride c a b
Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands Polymer Materials and Engineering, PME, Department of Materials Science and Technology, Julianalaan 136, 2628 BL Delft, The Netherlands c Institute Laue Langevin, BP156 Grenoble, 38042 Cedex 09, France Received 10 October 2002; in final form 18 February 2003
Abstract Quasielastic neutron scattering measurements on hexakismethoxytriphenylene (HMT) shows molecular motion at timescales of 0.1 and 7.3 ps at 370 K. Deuteration of the methoxy tails, suppresses the signal for the slower motion, whilst the signal from the more rapid motion of the triphenylene cores persists. A molecular dynamics simulation on an isolated model of 4 HMT molecules reveals the slower methoxy motion to be a torsion of the whole methyl group around the core to oxygen bond. The faster motion is due to lateral sliding of the cores with respect to each other. A harmonic core-motion arising from tilting of the disks in the simulation may correspond to a strongly damped motion seen in the experimental data. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Discotic liquid crystalline materials are formed from disklike poly-aromatic molecules that are stacked in such a way that there is p electron overlap of adjacent molecules that forms a one-dimensional path along which charge can migrate. This has aroused interest in these materials for nanoscale devices such as light-emitting diodes, field-effect transistors [1–4] and photo voltaics [5]. Conduction
*
Corresponding author. E-mail address: [email protected] (G.J. Kearley).
between the aromatic cores can be calculated from first principles methods, but the calculated values exceed the measured values by a considerable margin [6]. This is thought to be due to intracolumnar disorder, and whilst there is a wealth of evidence from the effects of side-chains etc., no direct measure of core and tail dynamics has been made. Quasielastic neutron scattering is an ideal technique for this type of measurement, but suffers from the difficulty that the signal from such complex systems is difficult to understand unambiguously [7]. In an initial study, which is to be broadened to much larger systems, we focus on the simplest possible system hexakis(n-methoxy)triphenylene (HMT,
0301-0104/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00083-1
186
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
2.2. 2,3,6,7,10,11-Hexakismethoxytriphenylene-d18 (D-HMT)
Fig. 1. Schematic illustration of the HMT molecule. The selective deuteration of the methoxy groups is indicated.
Fig. 1), and use selective deuteration to highlight the motions of the aliphatic side-chains and aromatic cores separately. Further, since such systems have motions over a wide range of timescales, we use a molecular dynamics simulation in order to understand which motions arise in the picosecond timescale.
A mixture of catechol (3.4 g, 31 mmol), CD3 I (10.0 g, 69 mmol), K2 CO3 (13.8 g, 0.10 mmol), KI (1.4 g, 9.5 mmol) and acetone (70 ml) was refluxed over the weekend. The reaction mixture was cooled and the solids were filtered off. The solvent and the excess of CD3 I were evaporated. The product was diluted with hexane, filtered and the hexane was evaporated to yield a colourless liquid (4.3 g, 30 mmol, 95%). 1 H NMR (CDCl3 , 200 MHz): d 6.2–6.8 (m, 4H, aromatic CH). 13 C NMR (CDCl3 , 200 MHz): d 149.02, 120.82, 111.30 (aromatic CH); 54.99 (h, OCD3 ). To a solution of veratrole-d6 (4.3 g, 30 mmol) in dry CH2 Cl2 (50 ml) was added MoCl5 (8.8 g, 32 mmol). The black mixture was stirred for 1 h at room temperature under inert atmosphere and poured into cold methanol. The solids were filtered, dissolved in warm CHCl3 and reprecipitated in methanol (2), yielding pure D-HMT (2.29 g, 5.3 mmol, 54%) as a white crystalline powder. 1 H NMR (DMSO-d6 , 200 MHz): d 8.00 (s, 6H, aromatic CH). 13 C NMR (DMSO-d6 , 200 MHz): d 148.63, 122.58, 105.01 (aromatic CH); 54.48 (h, OCD3 ).
2. Experimental
2.3. QENS
HMT and the selectively deuterated D-HMT were prepared by oxidative trimerisation of the corresponding veratroles using molybdenum(V) chloride [8].
Quasielastic neutron spectra were obtained using the IN6 spectrometer at the Institute Laue Langevin in France. An incident wavelength of was selected to give the correct compromise 5.9 A between energy range and energy resolution. Samples were sealed in thin-walled aluminium containers and temperature control was achieved using a standard oven. The sample thickness was controlled to give a scattering probability of 10%. Corrections for detector efficiency were made by normalisation using spectra from a 1 mm plate of vanadium in place of the sample. The background scattering was estimated from the spectra obtained from the empty sample container. This background was subtracted from both the sample and vanadium spectra before normalisation. Corrections for sample shape, and self shielding, were made and the corrected data converted to SðQ; xÞ using the program INX [9].
2.1. 2,3,6,7,10,11-Hexakismethoxytriphenylene (HMT) To a solution of veratrole (4.5 g, 33 mmol) in dry CH2 Cl2 (50 ml) was added MoCl5 (9.6 g, 35 mmol). The black mixture was stirred for 1 h at room temperature under inert atmosphere and poured into cold methanol. The solids were filtered, dissolved in warm CHCl3 and reprecipitated in methanol (2), yielding pure HMT (2.48 g, 6.1 mmol, 61%) as a white crystalline powder. 1 H NMR (DMSO-d6 , 200 MHz): d 7.99 (s, 6H, aromatic CH); 2.50 (s, 18H, OCH3 ). 13 C NMR (DMSO-d6 , 200 MHz): d 148.63, 122.60, 105.04 (aromatic CH); 55.77 (h, OCH3 ).
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
3. Results and discussion In the first instance the quasielastic spectra were fitted using a global fitting routine over spectra at 15 different momentum-transfer values (Q-values) with the constraint that all spectra were composed of either one or two Lorentzian components whose widths are constant in Q plus an elastic component defined by the measured resolution function. The total intensity (quasielastic + elastic) was constrained to be constant after correction by a single Debye–Waller factor and a single time-of-flight constant flat-background. It proved extremely difficult to completely avoid contamination of the incoherent elastic scattering by coherent Braggscattering, but nevertheless, the data for the isotopically normal compound clearly required two Lorentzian components to fit the measured quasielastic signal. Fitted widths and intensities are collected in Table 1. On deuteration of the methyl tails, the narrower Lorentzian quasielastic component is suppressed and the spectra were satisfactorily fitted using a single quasielastic contribution. From these results we conclude that the narrower component corresponding to a timescale of 0.1 ps (at 370 K) arises from motion of the methoxy tails, whilst the broader component corresponding to a timescale of 7.3 ps (at 370 K) is due to motion of the triphenylene cores. At first this result seems surprising because the cores are considerably heavier than the tails, so in order to understand this further we undertook a molecular dynamics simulation. Our model is of 4 HMT disks and was built by constructing a single disk whose energy was minimised. For this purpose we
187
used a commercial implementation of the Compass force field [10] with a proprietary minimisation algorithm. The minimum energy corresponds to alternate up/down conformations of the methoxy groups with respect to the triphenylene core (see Fig. 1). The model was built by successive addition of energy-minimised HMT molecules with further minimisation after each addition. The resulting structure is shown in Fig. 2 in which the in good agreement disk–disk separation is 3.58 A with crystallographic data [11]. Each disk is oriented at 60° with respect to its neighbours, which is in conflict with the value normally associated with triphenylenes: 45°. The 60° conformation proved to be remarkably stable, the system minimising back to this from almost any other starting orientation. We noticed, however, that with longer tails and tails with side substituents, orientations around 45° were indeed formed. The model was thermalised at 400 K and then molecular dynamics simulations of 1.1 ns were performed. Our model is rather small and ignores all intercolumn interactions. Further, the correlation length of motions along the column is also somewhat limited, and simulations at 300 K gave rise to sharp inelastic peaks due to harmonic modes. In the simulation at 370 K these modes are strongly damped and lead to calculated spectra resembling those measured at the same temperature. In the following analysis we emphasise that the aim is to
Table 1 Widths of the quasielastic components of the experimental spectra as a function of temperature Temperature (K)
Width 1 (meV)
Width 2 (meV)
Width 2 (meV) methoxy D
300 370 470
0.041 0.075 0.140
4.93 4.37 4.96
4.13 3.37 4.06
A global fitting routine was used to help overcome the problems of incomplete Bragg-peak subtraction, and correlation of the broader peak with the background signal.
Fig. 2. Minimum energy configuration of the 4-molecule HMT column used for the molecular dynamics simulation.
188
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
understand the nature of the picosecond motions of the methoxy tails, and why these should be slower than the motion of the triphenylene core. The results of the simulation must therefore be in reasonable agreement with the measured data, and any discrepancy should be consistent with the known limitations of the model. The trajectories from the MD simulation were analysed using the NMOLDYN [12] routines to produce the measured elastic incoherent structure factors (EISF) and scattering functions (SðQ; xÞ) of the isotopically normal and methoxy deuterated samples. The resulting EISFs are compared with experiment in Fig. 3. Both experiment and simulation show a considerable decrease in EISF on methoxy-deuteration, and the EISFs from the simulation are comparable to those from the experiment. Some of this disagreement is due to incomplete removal of coherent Bragg scattering. Care was taken to account for the finite experimental resolution (the experimental resolution is around 50 ps, while the simulation accesses times up to almost 1 ns, i.e., many time windows of the 50 ps neutron coherence time). This is clear from
Fig. 3. Observed EISF at 370 K for isotopically normal HMT (crosses) and methoxy deuterated HMT (squares) compared with the corresponding EISFs (broken line and solid line, respectively) from the MD simulation. The lower values from the simulation point to slower motions that are not resolved in the experiment.
Fig. 4. Comparison of observed spectra (dashed line) and spectra calculated from the MD simulation (full line) over a 1 ). Observed and range of momentum transfers (0.3–1.8 A calculated spectra are normalised to the same maximum value. The maximum intensity in the figure corresponds to 10% of the maximum peak-height.
Fig. 4 in which the observed and simulated SðQ; xÞ are illustrated. In this figure the simulated data have been convoluted with a Gaussian function that represents the experimental resolution, and the agreement between observation and calculation is quite reasonable. The main difference is at high Q, where it was particularly difficult to separate the experimental background properly, and this appears to be the principle difference between the two sets of spectra at high Q. The most important result of the simulation is that the simulated SðQ; xÞ for the core hydrogens gives rise to the broader quasielastic component, whilst the simulated SðQ; xÞ for the methyl groups gives the narrower peak, in good agreement with the experimental data on the two isotopomers (see Fig. 5). Inspection of the simulation reveals that the methyl rotations are rapid and arise outside the time-window of the quasielastic scattering. The slow methyl motion that gives rise to the narrow quasielastic component is due to motion of the whole CH3 group around the core to oxygen bond. Although the exact core motion will clearly depend on the completeness of the model, the current simulation does reproduce the salient features of the measured dynamics on the picosecond timescale, and we can draw some conclusion about the most important degrees of freedom. The core
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
Fig. 5. Spectra of methoxy deuterated (front) and isotopically normal (back) HMT. The dashed line represents measured spectra and the continuous line represents the molecular dynamics simulation.
motion has two main components. First, the cores show no significant signs of rotations over the 1 ns of the simulation. Second, the predominant motion is a sliding of the disks one over another, normally so as to preserve overlap of aromatic rings. Finally, no pure translational motion along the column axis was observed, but the disks tilt relative to each other. In this respect it is interesting to note that the inelastic peak in the experiment and in the simulation is present in the isotopically normal and the methoxy-deuterated samples. These peaks are weak and only visible by looking at the 1% level of the elastic-peak intensity. Whilst the simulation at 300 K gave sharp inelastic peaks, at 370 K these became broad. The observed spectrum at 300 K is compared with the calculated spectrum at 370 K in Fig. 6 and it is conceivable that the two broad experimental features at 3 and 6 meV correspond to the groups of peaks at around 2 and 3 meV in the simulation. In the simulation it is clear that these arises from disk tilting, and thus gives intensity in the methyl deuterated and isotopically normal compounds. The model that we use is rather simple and we have to be careful not to over interpret the data with such a simple model. There are three approximations that we have to consider. First, the limited length of the column means that modes along the
189
Fig. 6. Observed spectrum at 300 K (solid line) compared with MD simulation at 370 K (broken line) showing weak inelastic features. The maximum of the figure corresponds to 2% of the peak intensity. The MD simulation at 300 K gave very sharp inelastic features due to the small size of the model.
column will be seriously curtailed, and also softened. Second, neighbouring columns would be expected to damp modes along the chains and to stiffen the lateral degrees of freedom. Finally, fixing two core atoms on the ends of the columns will restrict rotational motion, and harden motions along the chain. It can be seen that these limitations often work in opposite directions and we cannot exclude that some of the agreement between the simulation and experiment is due to fortuitous cancellations. The present work is a compromise between the more traditional analysis of quasielastic spectra and the mesoscopic modelling methods normally used for large complex systems.
4. Conclusions Quasielastic scattering can be used to study the motion of discotic cores, but an MD simulation is required in order to understand which motions are observed. In moving to larger, technologically important discotic systems the deuteration of the tails, or tail substituents, becomes more difficult and it is important to establish which molecular dynamics methods (in particular force-fields) work on smaller model system. Whilst torsional motions of the methoxy group about their bond to the core can be separated from
190
G.J. Kearley et al. / Chemical Physics 292 (2003) 185–190
the motions of the core itself, in other respects the tails follow the motions of the cores. This is clear from the observation of the inelastic signal in both isotopic samples and in the simulation. The most important core motion on the picosecond timescale is lateral sliding of one disk with respect to its neighbours in the column. It would be interesting to perform a more complete simulation for a group of longer columns to see how to learn more about the long-range effects of longitudinal core modes, and the effect of intercolumnar interactions on the sliding motions of the disks.
References [1] A.J. Berresheim, M. M€ uller, K. M€ ullen, Chem. Rev. 99 (1999) 1747.
[2] S. Chandrasehkar, S. Krishna Prasad, Contemp. Phys. 40 (1999) 237. [3] H. Eichorn, J. Porphorins Phtalocyanines 4 (2000) 88. [4] I. Seguy, P. Destruel, H. Bock, Synth. Met. 15 (2000) 111. [5] L. Schmidt-Mende, A. Fechtenk€ otter, K. M€ ullen, E. Moons, R.H. Frien, J.D. MacKenzie, Science 293 (2001) 1119. [6] B.R. Wegewijs, L.D.A. Siebbeles, Phys. Rev. B 65 (2002) 245112. [7] A.V. Belushkin, M.J. Cook, D. Frezzato, D. Haslam, A. Ferrarini, D. Martin, J. McMurdo, P.L. Nordio, R.M. Richardson, A. Stafford, Mol. Phys. 93 (1998) 593. [8] S. Kumar, M. Manickam, Chem. Commun. 1615 (1997). [9] F. Rieutord, INX – Program for time-of-flight data reduction userÕs guide, Internal report 90RI17T Institute Laue Langevin, Grenoble, France (1990). [10] H.J. Sun, Phys. Chem. 102 (1998) 7338. [11] T. Wang, D. Yan, J. Luo, E. Zhou, O. Karthaus, H. Ringsdorf, Liq. Cryst. 23 (1997) 869. [12] G.R. Kneller, V. Keiner, M. Kneller, M. Schiller, Comput. Phys. Commun. 91 (1995) 191.