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Benzene `dimers' in polystyrene films
Chemical Physics Letters 391 (2004) 216–219 www.elsevier.com/locate/cplett
Benzene ‘dimers’ in polystyrene films Sudeshna Chattopadhyay, Alokmay Datta
*
Surface Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India Received 13 February 2004; in final form 22 March 2004 Available online 25 May 2004
Abstract Benzene ‘dimers’ formed by excitation transfer interaction (J ), in weakly disordered aggregates, have been observed in atactic thick) spin-coated on fused quartz, through presence of a doublet in the main vibronic M1 -band in polystyrene films (200–2500 A 1 1 the A1g ! B2u optical singlet band. Only V-shaped ‘dimers’ were found with dihedral angle (a) varying from 90° to 107° with no apparent dependence on film thickness. A model for the ‘dimer’ consistent with observed J ðaÞ yields the value of the transition moment and provides the ‘dimer’ geometry. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Supramolecular aggregates are important means to extend electron delocalization and this extended delocalization maybe used for exciton transport [1]. The simplest supramolecular aggregate is of course the socalled ‘physical dimer’ [2], a pair of molecules strongly correlated by non-bonded, short-range interactions. Molecular benzene is known to form such ‘dimers’ in condensed phases [3,4], and in jet-cooled beams [5]. Quantum mechanical calculations predict ‘slipped parallel’, ‘T-shaped’ [6] and ‘V-shaped’ [7] configurations for these dimers. In benzene crystals both the ‘T-shaped’ and the ‘slipped parallel’ forms exist as neighbouring rings, as observed from crystallography [3,4], whereas in jet-cooled beams the dominant dimeric configuration is the ‘V-shaped’ form [5]. In polystyrene, benzene rings are coupled through the backbone chain but are otherwise free to interact and form aggregates within a broad range of configurations. Presence of ‘physical dimers’ of benzene is thus a distinct possibility in polystyrene, even in absence of correlations such as tacticity, imposed by the polymer
*
Corresponding author. Fax: +91-33-2337-4637. E-mail address: [email protected] (A. Datta).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.04.107
backbone on the rings. In the confined geometry of films molecular configurations may differ from the equilibrium configuration [8] and this may prefer such ‘dimer formation’. Also, due to the ring-segregating interactions of particular film/substrate interfaces [9], ‘dimer formation’ may be enhanced. Again, due to the absence of conjugation paths along the polymer backbone, the p-electrons in the benzene rings are localized and it is known that the optical spectra of polystyrene is determined by excitons localized on these rings [10]. Thus any delocalization effect in the optical spectra of polystyrene is related to correlations among the rings and an analysis of these effects would lead to an understanding of these correlations. In this communication we present results of transmission ultraviolet (UV) spectroscopy around the first singlet optical transition in films of atactic polystyrene spin-coated on fused quartz substrates. We have studied films of thickness varying from 200 to 2500 A and have analyzed the 1 A1g ! 1 B2u transition band using the theory of coupled two-level systems [11] to interpret the main vibronic M1 band. We have detected clear evidence of weakly disordered aggregates of V-shaped benzene dimers formed by the resonant transfer interaction, and have extracted a geometry of the ‘dimer’ that shows no clear dependence on polystyrene film thickness.
S. Chattopadhyay, A. Datta / Chemical Physics Letters 391 (2004) 216–219
217
2. Experiment The tacticity of the polystyrene (PS) (Mw ¼ 560 900) was characterized by FTIR spectroscopy (Perkin–Elmer Spectrum GX FTIR Spectrometer, USA), in the 3600– 350 cm1 range with a resolution of 4.0 cm1 , at 20 °C. Shapes and positions of absorption peaks of the PS sample matched standard characteristic atactic PS peaks [12] while the characteristic peaks of isotactic and syndiotactic polystyrene [12,13] were absent. From these results it was confirmed that the PS sample was almost purely atactic, i.e., completely amorphous in its bulk were state. Polystyrene films of thickness 215–2510 A prepared by spin coating on quartz substrates from 5.5 to 18 mg/ml toluene solutions, at angular velocities varying from 4.03 to 0.68 krpm using a photo-resist spin-coater (Headway Inc, USA). Fused quartz substrates (1 in. 1 in. 1 mm) were cleaned using piranha solution, i.e., they were put in a mixture of 70% conc. H2 SO4 and 30% H2 O2 and boiled for 20 min. Transmission UV spectra of the film of different thickness were recorded (using a GBC Cintra 10e spectrometer, Australia) in the 350–190 nm (28 500–52 600 cm1 ) scan range at the scan speed of 5 nm per minute with 1.5 nm slit width. Film thickness was measured from interference (Kiessig) fringes obtained in the grazing incidence X-ray reflectivity of the films using Cu Ka1 radiation from a rotating-anode source and a 3-circle Diffractometer (Enraf Nonius FR591, The Netherlands) [14,15].
3. Results and discussion All the main peaks in the UV band around 260 nm (38 400 cm1 ) in absorption spectra of polystyrene films are shown in Fig. 1. These peaks were assigned to different vibronic transitions within the 1 A1g ! 1 B2u singlet, from comparison with the experimentally observed peaks of crystalline benzene [16]. The results are presented in Table 1. The transition 1 A1g ! 1 B2u is orbitally forbidden and is allowed only through mixing with the in-plane vibration mode (corresponding to m010 in benzene [16,17]) of E2g symmetry, which is not totally symmetric. This vibration has the value of about 525 cm1 in the excited electronic state and gives rise to the first intense band M1 in the spectrum at 38 250 cm1 . Progression of bands containing the terms M2 ; M3 ; M4 , etc. originate from further mixing with the totally symmetric ‘breathing vibration’ of the benzene ring in polystyrene (this mode is m02 [16] for pure benzene) which has the frequency about 923 cm1 in the excited electronic state. In the long-wave portion of the spectrum, the hot band B00 is arising from excited vibration (m10 ) levels of the ground electronic state. thick In the inset of Fig. 1 the M1 -band of a 2510 A PS film is shown with doublet splitting of the band. Let
thick polystyrene Fig. 1. Transmission ultraviolet spectrum of a 2510 A film on fused quartz in the vibronic band (1 A1g ! 1 B2u ) around 38 400 cm1 (260 nm). The assignments of various peaks are shown. Inset: The M1 doublet. Dotted lines indicate individual peaks in the gaussian fit (solid line) to the data (open circles).
us consider a group of nearest neighbour benzene rings in the polystyrene film. The rings maybe nearest neighbours on the polystyrene chain or may occupy neighbouring positions due to the specific configuration of the chain in the film, or they may even be pendant groups of different entangled chains. This group of benzene rings behaves, according to optical spectroscopy [10], as a cluster of nearly free benzene molecules. The split in the M1 -band can then be explained as arising from the excitation transfer interaction, which causes the mixing of the singly excited (one-exciton) states of individual molecules and leads to formation of correlated clusters [11]. The doublet splitting of the M1 -band indicates that pairs of benzene rings are involved in these clusters. To our knowledge this is the first clear indication of benzene ‘dimers’ in polystyrene. The excitation transfer interaction between two translationally inequivalent benzene rings, taken as two two-level molecules that do not have permanent dipole moments either in ground or in excited states (as in benzene), will mix the states of individual rings. The resulting ‘dimer’ will have the two new energy states with energies E ¼ x0 jJ j (in units of h) where x0 is the transition energy corresponding to unperturbed ring and jJ j is the excitation transfer interaction magnitude. Thus there will be two peaks in the absorption spectrum separated by 2jJ j and having the intensity ratio, Iþ =I ¼ ð1 þ cos aÞ=ð1 cos aÞ ¼ cot2 ða=2Þ;
ð1Þ
with a the angle between both transition dipoles, i.e. the dihedral angle between rings of the ‘dimer’ [11]. In Table 2 we present values of jJ j, a and d1 , d2 (FWHMs of the lower and higher energy components of the doublet, respectively) and the ratio d2 =d1 observed for polystyrene films of thickness varying from 200 to
218
S. Chattopadhyay, A. Datta / Chemical Physics Letters 391 (2004) 216–219
Table 1 Transitions in the A1g ! ðB2u :E2g Þ band in typical PS film (2510 A) Transition (mode)
Peak in PS film (cm1 )
Peak in benzene crystala (cm1 )
B00 ðm10 ; 1
M2 ðm10 ; m2 ; 0 ! 1; 0 ! 1Þ
37 113 37 679 38 062 38 447 39 146
M3 ðm10 ; m2 ; 0 ! 1; 0 ! 2Þ M4 ðm010 ; m2 ; 0 ! 1; 0 ! 3Þ
40 048 40 957
37 200 37 835 38 351 38 360 39 275 39 285 40 205 41 130
! 0Þ K1 (crystal field perturbation, 0 ! 0) M1 ðm010 ; 0 ! 1Þ
a
Ref. [16].
Table 2 Dimer parameters obtained from M1 -doublet Thickness of the film (A)
Dimer dihedral angle (a; °)
(180 a; °)a
Excitation transfer interaction (jJ j; cm1 )
FWHM of lower energy component (d1 ; cm1 )
FWHM of higher energy component (d2 ; cm1 )
Ratio d2 =d1
215 400 600 840 1087 1200 1289 1840 2148 2510
97.9 94.1 101.7 100.0 95.7 106.7 105.1 101.0 99.0 90.9
82.1 85.9 78.3 80.0 84.3 73.3 74.9 79.0 81.0 89.1
206.0 221.0 202.5 215.0 217.5 200.0 203.0 200.0 218.5 227.0
381 423.4 381.0 377.6 429.8 404.9 406.9 426.2 409.0 483.3
520 520.25 520.0 520.1 548.9 588.6 590.3 602.4 550.7 560.5
1.365 1.229 1.365 1.377 1.277 1.454 1.451 1.414 1.347 1.160
a
To be compared with [5].
The value of d2 =d1 is almost constant for all 2500 A. pffiffiffi samples and its average value is 1:343 2, as is expected for exchange narrowing in ‘dimers’ in weak disorder [11,18]. From Table 2 we find no clear dependence of either the interaction magnitude or the dihedral angle on thickness of film. This suggests an ‘average dimer geometry’ effectively independent of film thickness, about which the geometry fluctuates in the samples studied by us. The theoretical expression for excitation transfer interaction between translationally inequivalent molecules is 2
5
J ¼ ððl1 l2 Þjr12 j 3ðl1 r12 Þðl2 r12 ÞÞ=jr12 j in units of h: ð2Þ Here l1 and l2 are the transition dipole moments of the two benzene rings, lying in the planes of the rings, with jl1 j ¼ jl2 j ¼ l, and r12 is the displacement between the centres of the dipoles, where the transition dipole moments l1 and l2 make angles h1 and h2 respectively with r12 (shown in Fig. 2a). Then we have a ¼ h1 h2 :
ð3Þ
Again, at equilibrium tan h1 ¼ 2 tan h2 :
ð4Þ
Fig. 2. (a) The benzene ‘dimer’ model geometry for polystyrene films and (b) best fit of J ðaÞ (line) using this model for experimental values of J against a (open circles with error bars). See text for details.
S. Chattopadhyay, A. Datta / Chemical Physics Letters 391 (2004) 216–219
Using Eqs. (3) and (4) the expression for J ðaÞ reduces to J ¼ Cðl
2
3 =r12 Þ½1=2 cos a
þ 3=2 cosf2h1 ag;
ð5Þ
where h1 has two values given by ðÞ
h1
¼ tan1 ½ð3 ð9 þ 8 tan2 aÞ 1
1=2
Þ=2 tan a:
ð6Þ
In Eq. (5) J is in cm , the conversion constant C is 3 5:69 1033 , and l2 =r12 is in (C)2 /m. We used Eq. (5) to 3=2 fit the observed values of J and a with l=r12 as fitting parameter. The interaction is attractive only if a is acute ðþÞ ðÞ and h1 ¼ h1 , or if a is obtuse and h1 ¼ h1 . However, fit with the data is obtained only for obtuse values of a ðÞ and h1 ¼ h1 . The best fit of J ðaÞ from a Levenberg– Marquardt procedure is shown in Fig. 2b along with the observed values. This fit is well within the experimental error bars obtained from the gaussian fits of individual spectral peaks. As values of J and a are obtained from independent measurements, the good fit of data with the J ðaÞ given by Eq. (5) confirms our claim of ‘physical dimer’ formation by excitation transfer interaction. Also, the goodness of fit is consistent with the proposition of weakly disordered ensembles of the ‘dimers’. Eq. (2) rules out the formation of T-shaped ‘dimer’ as that would make J vanish. In benzene crystals the neighbouring rings form either the (translationally equivalent) ‘slipped parallel’ or the (translationally inequivalent) ‘T-shaped’ physical dimer [19]. Since the latter does not contribute to the splitting only the much smaller resonant exchange interaction (b) between translationally equivalent molecules [2] is active giving rise to the small split in Table 1. ‘Benzene dimers’ in polystyrene, on the other hand, are seen to be always ‘V-shaped’. The value of the fitted parameter comes out to be (1.666 0.007) 1016 (C m)/(m)3=2 or 0.05D (m)3=2 . In [6,19], the range of our observed a-values, r12 ¼ 5 A hence we have l 0:56D, a value which is difficult to compare with previous data as direct methods of evaluating transition dipole moments of benzene are rare. From the data the mean value of a ¼ 99:35° 4:8°. The corresponding values of h1 ¼ 59:28° and h2 ¼ 40:07° [6,19] and from Eqs. (6) and (3). With r12 ¼ a ¼ 5 A in these values of the angles, b ¼ 4:356 A, c ¼ 3:262 A, Fig. 2a. We can assume this set of values to represent the ‘average dimer geometry’. It should be noted that the calculated value of J (210.9 cm1 ) corresponding to the mean value of a ¼ 99:35° and best fit value of l=r3=2 (using Eq. (5)) gives an excellent match with the mean value of J (211:05 9:3 cm1 ), obtained independently from experiment. We have provided, to our knowledge, the first direct and conclusive evidence of formation of benzene ‘di-
219
mers’ in polystyrene films. We have confirmed that, these ‘dimers’ are formed by the excitation transfer interaction, the ‘dimers’ form weakly disordered ensembles and there exists an average dimer geometry that does not exhibit any clear dependence on polymer film thickness. Polymers in general and polystyrene in particular are known to undergo configurational changes under confinement [8,14,20]. Hence this lack of clear dependence of dimer geometry on polystyrene confinement indicates a corresponding lack of dependence on polymer configuration. This suggests an enthalpic, rather than entropic, nature of the interaction involved [8]. Thus the excitation transfer interaction is, at least, as active between benzene rings of different polystyrene chains as between rings of the same chain under different configurations, and benzene ‘dimer formation’ is an important part of the cohesive interactions in polystyrene. References [1] C. Taliani, Proceedings of the International School of Physics, Organic Nanostructures: Science and Applications, IOS Press, Amsterdam, 2002, p. 187. [2] M. Pope, C.E. Swenberg, in: H. Frohlich, P.B. Hirsch, N.F. Mott (Eds.), Electronic Processes in Organic Crystals, Oxford University Press, New York, 1982, p. 40. [3] M.M. Thiery, J.M. Leger, J. Chem. Phys. 89 (1988) 4255. [4] S. Oikawa, M. Tsuda, H. Kato, T. Urabe, Acta Cryst. B 41 (1985) 437. [5] K.O. B€ ornsen, H.L. Selzle, E.W. Schlag, J. Chem. Phys. 85 (1986) 1726. [6] S. Tsuzuki, T. Uchimaru, K. Sugawara, M. Mikami, J. Chem. Phys. 117 (2002) 11216. [7] R.L. Jaffe, G.D. Smith, J. Chem. Phys. 105 (1996) 2780. [8] R.A.L. Jones, W. Richards, Polymers at Surfaces, Interfaces, Cambridge University Press, Cambridge, 1999. [9] O.N. Tretinnikov, Langmuir 16 (2000) 2751. [10] C.B. Duke, T.J. Fabish, Phys. Rev. Lett. 37 (1976) 1075. [11] J. Knoester, Proceedings of the International School of Physics, Organic Nanostructures: Science and Applications, IOS Press, Amsterdam, 2002, p. 149. [12] A. Lee Smith, Applied Infrared Spectroscopy, Wiley, New York, 1979, p. 19. [13] X.M. Xie, A. Tanioka, K. Miyasaka, Polymer 34 (1993) 1388. [14] M.K Sanyal, J.K. Basu, A. Datta, S. Banerjee, Europhys. Lett. 36 (1996) 265. [15] J.K. Basu, M.K. Sanyal, Phys. Rep. 363 (2002) 1. [16] V.L. Broude, Sov. Phys. Uspekhi 4 (1962) 584. [17] D.C. Harris, M.D. Bertolucci, Symmetry and Spectroscopy, Dover, New York, 1989. [18] E.W. Knapp, Chem. Phys. 85 (1984) 73. [19] E.R. Bernstein, S.D. Colson, R. Kopelman, G.W. Robinson, J. Chem. Phys. 48 (1968) 5596. [20] W. Zhao, X. Zhao, M.H. Rafailovich, J. Sokolov, L.J. Fetters, R. Plano, M.K. Sanyal, S.K. Sinha, B.B. Sauer, Phys. Rev. Lett. 70 (1999) 1453.
Benzene ‘dimers’ in polystyrene films Sudeshna Chattopadhyay, Alokmay Datta
*
Surface Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India Received 13 February 2004; in final form 22 March 2004 Available online 25 May 2004
Abstract Benzene ‘dimers’ formed by excitation transfer interaction (J ), in weakly disordered aggregates, have been observed in atactic thick) spin-coated on fused quartz, through presence of a doublet in the main vibronic M1 -band in polystyrene films (200–2500 A 1 1 the A1g ! B2u optical singlet band. Only V-shaped ‘dimers’ were found with dihedral angle (a) varying from 90° to 107° with no apparent dependence on film thickness. A model for the ‘dimer’ consistent with observed J ðaÞ yields the value of the transition moment and provides the ‘dimer’ geometry. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Supramolecular aggregates are important means to extend electron delocalization and this extended delocalization maybe used for exciton transport [1]. The simplest supramolecular aggregate is of course the socalled ‘physical dimer’ [2], a pair of molecules strongly correlated by non-bonded, short-range interactions. Molecular benzene is known to form such ‘dimers’ in condensed phases [3,4], and in jet-cooled beams [5]. Quantum mechanical calculations predict ‘slipped parallel’, ‘T-shaped’ [6] and ‘V-shaped’ [7] configurations for these dimers. In benzene crystals both the ‘T-shaped’ and the ‘slipped parallel’ forms exist as neighbouring rings, as observed from crystallography [3,4], whereas in jet-cooled beams the dominant dimeric configuration is the ‘V-shaped’ form [5]. In polystyrene, benzene rings are coupled through the backbone chain but are otherwise free to interact and form aggregates within a broad range of configurations. Presence of ‘physical dimers’ of benzene is thus a distinct possibility in polystyrene, even in absence of correlations such as tacticity, imposed by the polymer
*
Corresponding author. Fax: +91-33-2337-4637. E-mail address: [email protected] (A. Datta).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.04.107
backbone on the rings. In the confined geometry of films molecular configurations may differ from the equilibrium configuration [8] and this may prefer such ‘dimer formation’. Also, due to the ring-segregating interactions of particular film/substrate interfaces [9], ‘dimer formation’ may be enhanced. Again, due to the absence of conjugation paths along the polymer backbone, the p-electrons in the benzene rings are localized and it is known that the optical spectra of polystyrene is determined by excitons localized on these rings [10]. Thus any delocalization effect in the optical spectra of polystyrene is related to correlations among the rings and an analysis of these effects would lead to an understanding of these correlations. In this communication we present results of transmission ultraviolet (UV) spectroscopy around the first singlet optical transition in films of atactic polystyrene spin-coated on fused quartz substrates. We have studied films of thickness varying from 200 to 2500 A and have analyzed the 1 A1g ! 1 B2u transition band using the theory of coupled two-level systems [11] to interpret the main vibronic M1 band. We have detected clear evidence of weakly disordered aggregates of V-shaped benzene dimers formed by the resonant transfer interaction, and have extracted a geometry of the ‘dimer’ that shows no clear dependence on polystyrene film thickness.
S. Chattopadhyay, A. Datta / Chemical Physics Letters 391 (2004) 216–219
217
2. Experiment The tacticity of the polystyrene (PS) (Mw ¼ 560 900) was characterized by FTIR spectroscopy (Perkin–Elmer Spectrum GX FTIR Spectrometer, USA), in the 3600– 350 cm1 range with a resolution of 4.0 cm1 , at 20 °C. Shapes and positions of absorption peaks of the PS sample matched standard characteristic atactic PS peaks [12] while the characteristic peaks of isotactic and syndiotactic polystyrene [12,13] were absent. From these results it was confirmed that the PS sample was almost purely atactic, i.e., completely amorphous in its bulk were state. Polystyrene films of thickness 215–2510 A prepared by spin coating on quartz substrates from 5.5 to 18 mg/ml toluene solutions, at angular velocities varying from 4.03 to 0.68 krpm using a photo-resist spin-coater (Headway Inc, USA). Fused quartz substrates (1 in. 1 in. 1 mm) were cleaned using piranha solution, i.e., they were put in a mixture of 70% conc. H2 SO4 and 30% H2 O2 and boiled for 20 min. Transmission UV spectra of the film of different thickness were recorded (using a GBC Cintra 10e spectrometer, Australia) in the 350–190 nm (28 500–52 600 cm1 ) scan range at the scan speed of 5 nm per minute with 1.5 nm slit width. Film thickness was measured from interference (Kiessig) fringes obtained in the grazing incidence X-ray reflectivity of the films using Cu Ka1 radiation from a rotating-anode source and a 3-circle Diffractometer (Enraf Nonius FR591, The Netherlands) [14,15].
3. Results and discussion All the main peaks in the UV band around 260 nm (38 400 cm1 ) in absorption spectra of polystyrene films are shown in Fig. 1. These peaks were assigned to different vibronic transitions within the 1 A1g ! 1 B2u singlet, from comparison with the experimentally observed peaks of crystalline benzene [16]. The results are presented in Table 1. The transition 1 A1g ! 1 B2u is orbitally forbidden and is allowed only through mixing with the in-plane vibration mode (corresponding to m010 in benzene [16,17]) of E2g symmetry, which is not totally symmetric. This vibration has the value of about 525 cm1 in the excited electronic state and gives rise to the first intense band M1 in the spectrum at 38 250 cm1 . Progression of bands containing the terms M2 ; M3 ; M4 , etc. originate from further mixing with the totally symmetric ‘breathing vibration’ of the benzene ring in polystyrene (this mode is m02 [16] for pure benzene) which has the frequency about 923 cm1 in the excited electronic state. In the long-wave portion of the spectrum, the hot band B00 is arising from excited vibration (m10 ) levels of the ground electronic state. thick In the inset of Fig. 1 the M1 -band of a 2510 A PS film is shown with doublet splitting of the band. Let
thick polystyrene Fig. 1. Transmission ultraviolet spectrum of a 2510 A film on fused quartz in the vibronic band (1 A1g ! 1 B2u ) around 38 400 cm1 (260 nm). The assignments of various peaks are shown. Inset: The M1 doublet. Dotted lines indicate individual peaks in the gaussian fit (solid line) to the data (open circles).
us consider a group of nearest neighbour benzene rings in the polystyrene film. The rings maybe nearest neighbours on the polystyrene chain or may occupy neighbouring positions due to the specific configuration of the chain in the film, or they may even be pendant groups of different entangled chains. This group of benzene rings behaves, according to optical spectroscopy [10], as a cluster of nearly free benzene molecules. The split in the M1 -band can then be explained as arising from the excitation transfer interaction, which causes the mixing of the singly excited (one-exciton) states of individual molecules and leads to formation of correlated clusters [11]. The doublet splitting of the M1 -band indicates that pairs of benzene rings are involved in these clusters. To our knowledge this is the first clear indication of benzene ‘dimers’ in polystyrene. The excitation transfer interaction between two translationally inequivalent benzene rings, taken as two two-level molecules that do not have permanent dipole moments either in ground or in excited states (as in benzene), will mix the states of individual rings. The resulting ‘dimer’ will have the two new energy states with energies E ¼ x0 jJ j (in units of h) where x0 is the transition energy corresponding to unperturbed ring and jJ j is the excitation transfer interaction magnitude. Thus there will be two peaks in the absorption spectrum separated by 2jJ j and having the intensity ratio, Iþ =I ¼ ð1 þ cos aÞ=ð1 cos aÞ ¼ cot2 ða=2Þ;
ð1Þ
with a the angle between both transition dipoles, i.e. the dihedral angle between rings of the ‘dimer’ [11]. In Table 2 we present values of jJ j, a and d1 , d2 (FWHMs of the lower and higher energy components of the doublet, respectively) and the ratio d2 =d1 observed for polystyrene films of thickness varying from 200 to
218
S. Chattopadhyay, A. Datta / Chemical Physics Letters 391 (2004) 216–219
Table 1 Transitions in the A1g ! ðB2u :E2g Þ band in typical PS film (2510 A) Transition (mode)
Peak in PS film (cm1 )
Peak in benzene crystala (cm1 )
B00 ðm10 ; 1
M2 ðm10 ; m2 ; 0 ! 1; 0 ! 1Þ
37 113 37 679 38 062 38 447 39 146
M3 ðm10 ; m2 ; 0 ! 1; 0 ! 2Þ M4 ðm010 ; m2 ; 0 ! 1; 0 ! 3Þ
40 048 40 957
37 200 37 835 38 351 38 360 39 275 39 285 40 205 41 130
! 0Þ K1 (crystal field perturbation, 0 ! 0) M1 ðm010 ; 0 ! 1Þ
a
Ref. [16].
Table 2 Dimer parameters obtained from M1 -doublet Thickness of the film (A)
Dimer dihedral angle (a; °)
(180 a; °)a
Excitation transfer interaction (jJ j; cm1 )
FWHM of lower energy component (d1 ; cm1 )
FWHM of higher energy component (d2 ; cm1 )
Ratio d2 =d1
215 400 600 840 1087 1200 1289 1840 2148 2510
97.9 94.1 101.7 100.0 95.7 106.7 105.1 101.0 99.0 90.9
82.1 85.9 78.3 80.0 84.3 73.3 74.9 79.0 81.0 89.1
206.0 221.0 202.5 215.0 217.5 200.0 203.0 200.0 218.5 227.0
381 423.4 381.0 377.6 429.8 404.9 406.9 426.2 409.0 483.3
520 520.25 520.0 520.1 548.9 588.6 590.3 602.4 550.7 560.5
1.365 1.229 1.365 1.377 1.277 1.454 1.451 1.414 1.347 1.160
a
To be compared with [5].
The value of d2 =d1 is almost constant for all 2500 A. pffiffiffi samples and its average value is 1:343 2, as is expected for exchange narrowing in ‘dimers’ in weak disorder [11,18]. From Table 2 we find no clear dependence of either the interaction magnitude or the dihedral angle on thickness of film. This suggests an ‘average dimer geometry’ effectively independent of film thickness, about which the geometry fluctuates in the samples studied by us. The theoretical expression for excitation transfer interaction between translationally inequivalent molecules is 2
5
J ¼ ððl1 l2 Þjr12 j 3ðl1 r12 Þðl2 r12 ÞÞ=jr12 j in units of h: ð2Þ Here l1 and l2 are the transition dipole moments of the two benzene rings, lying in the planes of the rings, with jl1 j ¼ jl2 j ¼ l, and r12 is the displacement between the centres of the dipoles, where the transition dipole moments l1 and l2 make angles h1 and h2 respectively with r12 (shown in Fig. 2a). Then we have a ¼ h1 h2 :
ð3Þ
Again, at equilibrium tan h1 ¼ 2 tan h2 :
ð4Þ
Fig. 2. (a) The benzene ‘dimer’ model geometry for polystyrene films and (b) best fit of J ðaÞ (line) using this model for experimental values of J against a (open circles with error bars). See text for details.
S. Chattopadhyay, A. Datta / Chemical Physics Letters 391 (2004) 216–219
Using Eqs. (3) and (4) the expression for J ðaÞ reduces to J ¼ Cðl
2
3 =r12 Þ½1=2 cos a
þ 3=2 cosf2h1 ag;
ð5Þ
where h1 has two values given by ðÞ
h1
¼ tan1 ½ð3 ð9 þ 8 tan2 aÞ 1
1=2
Þ=2 tan a:
ð6Þ
In Eq. (5) J is in cm , the conversion constant C is 3 5:69 1033 , and l2 =r12 is in (C)2 /m. We used Eq. (5) to 3=2 fit the observed values of J and a with l=r12 as fitting parameter. The interaction is attractive only if a is acute ðþÞ ðÞ and h1 ¼ h1 , or if a is obtuse and h1 ¼ h1 . However, fit with the data is obtained only for obtuse values of a ðÞ and h1 ¼ h1 . The best fit of J ðaÞ from a Levenberg– Marquardt procedure is shown in Fig. 2b along with the observed values. This fit is well within the experimental error bars obtained from the gaussian fits of individual spectral peaks. As values of J and a are obtained from independent measurements, the good fit of data with the J ðaÞ given by Eq. (5) confirms our claim of ‘physical dimer’ formation by excitation transfer interaction. Also, the goodness of fit is consistent with the proposition of weakly disordered ensembles of the ‘dimers’. Eq. (2) rules out the formation of T-shaped ‘dimer’ as that would make J vanish. In benzene crystals the neighbouring rings form either the (translationally equivalent) ‘slipped parallel’ or the (translationally inequivalent) ‘T-shaped’ physical dimer [19]. Since the latter does not contribute to the splitting only the much smaller resonant exchange interaction (b) between translationally equivalent molecules [2] is active giving rise to the small split in Table 1. ‘Benzene dimers’ in polystyrene, on the other hand, are seen to be always ‘V-shaped’. The value of the fitted parameter comes out to be (1.666 0.007) 1016 (C m)/(m)3=2 or 0.05D (m)3=2 . In [6,19], the range of our observed a-values, r12 ¼ 5 A hence we have l 0:56D, a value which is difficult to compare with previous data as direct methods of evaluating transition dipole moments of benzene are rare. From the data the mean value of a ¼ 99:35° 4:8°. The corresponding values of h1 ¼ 59:28° and h2 ¼ 40:07° [6,19] and from Eqs. (6) and (3). With r12 ¼ a ¼ 5 A in these values of the angles, b ¼ 4:356 A, c ¼ 3:262 A, Fig. 2a. We can assume this set of values to represent the ‘average dimer geometry’. It should be noted that the calculated value of J (210.9 cm1 ) corresponding to the mean value of a ¼ 99:35° and best fit value of l=r3=2 (using Eq. (5)) gives an excellent match with the mean value of J (211:05 9:3 cm1 ), obtained independently from experiment. We have provided, to our knowledge, the first direct and conclusive evidence of formation of benzene ‘di-
219
mers’ in polystyrene films. We have confirmed that, these ‘dimers’ are formed by the excitation transfer interaction, the ‘dimers’ form weakly disordered ensembles and there exists an average dimer geometry that does not exhibit any clear dependence on polymer film thickness. Polymers in general and polystyrene in particular are known to undergo configurational changes under confinement [8,14,20]. Hence this lack of clear dependence of dimer geometry on polystyrene confinement indicates a corresponding lack of dependence on polymer configuration. This suggests an enthalpic, rather than entropic, nature of the interaction involved [8]. Thus the excitation transfer interaction is, at least, as active between benzene rings of different polystyrene chains as between rings of the same chain under different configurations, and benzene ‘dimer formation’ is an important part of the cohesive interactions in polystyrene. References [1] C. Taliani, Proceedings of the International School of Physics, Organic Nanostructures: Science and Applications, IOS Press, Amsterdam, 2002, p. 187. [2] M. Pope, C.E. Swenberg, in: H. Frohlich, P.B. Hirsch, N.F. Mott (Eds.), Electronic Processes in Organic Crystals, Oxford University Press, New York, 1982, p. 40. [3] M.M. Thiery, J.M. Leger, J. Chem. Phys. 89 (1988) 4255. [4] S. Oikawa, M. Tsuda, H. Kato, T. Urabe, Acta Cryst. B 41 (1985) 437. [5] K.O. B€ ornsen, H.L. Selzle, E.W. Schlag, J. Chem. Phys. 85 (1986) 1726. [6] S. Tsuzuki, T. Uchimaru, K. Sugawara, M. Mikami, J. Chem. Phys. 117 (2002) 11216. [7] R.L. Jaffe, G.D. Smith, J. Chem. Phys. 105 (1996) 2780. [8] R.A.L. Jones, W. Richards, Polymers at Surfaces, Interfaces, Cambridge University Press, Cambridge, 1999. [9] O.N. Tretinnikov, Langmuir 16 (2000) 2751. [10] C.B. Duke, T.J. Fabish, Phys. Rev. Lett. 37 (1976) 1075. [11] J. Knoester, Proceedings of the International School of Physics, Organic Nanostructures: Science and Applications, IOS Press, Amsterdam, 2002, p. 149. [12] A. Lee Smith, Applied Infrared Spectroscopy, Wiley, New York, 1979, p. 19. [13] X.M. Xie, A. Tanioka, K. Miyasaka, Polymer 34 (1993) 1388. [14] M.K Sanyal, J.K. Basu, A. Datta, S. Banerjee, Europhys. Lett. 36 (1996) 265. [15] J.K. Basu, M.K. Sanyal, Phys. Rep. 363 (2002) 1. [16] V.L. Broude, Sov. Phys. Uspekhi 4 (1962) 584. [17] D.C. Harris, M.D. Bertolucci, Symmetry and Spectroscopy, Dover, New York, 1989. [18] E.W. Knapp, Chem. Phys. 85 (1984) 73. [19] E.R. Bernstein, S.D. Colson, R. Kopelman, G.W. Robinson, J. Chem. Phys. 48 (1968) 5596. [20] W. Zhao, X. Zhao, M.H. Rafailovich, J. Sokolov, L.J. Fetters, R. Plano, M.K. Sanyal, S.K. Sinha, B.B. Sauer, Phys. Rev. Lett. 70 (1999) 1453.