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DYNAMICS OF PHONON INTERACTIONS IN ORGANIC SOLIDS
P. Prasad
To cite this version:
P. Prasad. DYNAMICS OF PHONON INTERACTIONS IN ORGANIC SOLIDS. Journal de
Physique Colloques, 1981, 42 (C6), pp.C6-563-C6-565. �10.1051/jphyscol:19816163�. �jpa-00221241�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZt?ment au n O I Z , Tome 42, ddcembre 2982 page C6-563
D Y N A M I C S OF PHONON INTERACTIONS IN ORGANIC S O L I D S
P . N . P r a s a d
Department o f Chemistry, S t a t e U n i v e r s i t y of New Yo'ork a t Buffalo, BuffaZo, New York 14214, U.S.A.
Abstract.
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I n v e s t i g a t i o n s c a r r i e d o u t on t h r e e aspects o f phonon i n t e r a c t i o n s are presented i n t h i s paper. The phonon dephasing induced by anharnlonic phonon-pnonon s c a t t e r i n g i s i n v e s t i g a t e d by teciperature dependence o f l i n e w i d t h s , lineshapes and frequencies i n t h e Raman spectra. The dephasing of phonons i n o r g a n i c s o l i d s i s found t o be p r i m a r i l y caused by a T1-r e l a x a t i o n i n v o l v i n g a three-phonon i n e l a s t i c s c a t t e r i n g . Second,fa s i m i l a r i n v e s t i g a t i o n on dephasing o f v i b r a t i o n s w i t h i n t h e molecule suggests t h a t For these i n t r a m o l e c u l a r v i b r a t i o n s w i t h frequencies g r e a t e r than t w i c e t h e Debye c u t - o f f frequency, i t i s t h e f o u r t h - o r d e r anharmonic c o u p l i n g w i t h phonons l e a d i n g t o an e l a s t i c s c a t t e r i n g which p r o v i d e t h e dominant mechani sin f o r dephasing i n o r g a n i c s o l i d s . F i n a l l y , t h e r o l e o f phonon i n t e r a c t i o n s i n determining s o l i d s t a t e r e a c t i v i t y i s discussed and a new concept o f phonon a s s i s t e d r e a c t i o n i s introduced. A thermal i n t e r m o l e c u l a r r e a c t i o n i s found t o be a s s i s t e d by a phonon mode s o f t e n i n g . A photochemical dimeriza- t i o n r e a c t i o n i s shown t o be a s s i s t e d by a s t r o n g - e l e c t r o n phonon c o u p l i n g i n t h e e x c i t e d s t a t e whereby a p o l a r o n i s formed.
Phonons i n organic s o l i d s are l a t t i c e v i b r a t i o n s d e r i v e d from hindered e x t e r n a l motions o f b o t h r o t a t i o n a l and t r a n s l a t i o n a l characters. Phonon i n t e r a c - t i o n s p l a y an important r o l e i n determining p h y s i c a l and chemical p r o p e r t i e s o f filolecular s o l i d s . ' This paper presents t h e r e s u l t s o f i n v e s t i g a t i o n s on t h r e e aspects o f phonon i n t e r a c t i o n s : ( i ) phonon r e l a x a t i o n and dephasing induced by anharmonic phonon-phonon s c a t t e r i n g ; ( i i) phonon induced dephasing o f i n t r a m o l ecul a r v i b r a t i o n s ( r e l a t i v e atorzlic motions w i t h i n the molecule) ; and ( i i i ) phonon
a s s i s t e d s o l i d s t a t e r e a c t i o n s .
The dephasing o f an o p t i c a l phonon can occur by two mechanisms: (a) T1-re- l a x a t i o n caused by an i n e l a s t i c phonon-phonon s c a t t e r i n g which a l s o leads t o a p o p u l a t i o n r e l a x a t i o n ; (b) T Z - r e l a x a t i o n caused by an e l a s t i c phonon-phonon s c a t t e r i n g which creates o n l y a phase r e l a x a t i o n . The T 1 - r e l a x a t i o n can occur by booth t h i rci and f o u r t h o r d e r anharnonic i n t e r a c t i o n s , where as t h e l e a d i n g c o n t r i b u t i o n t o t h e T h - r e l a x a t i o n i s d e r i v e d Prom t h e f o u r t h o r d e r anharmonicity term. Ue have i n v e s t i g a t e d t h e n a t u r e o f pnonon dephasing by s t u d y i n g t h e temperature dependence o f t h e phonon frequencies, lineshapes and l i n e w i d t h s o f o p t i c a l t r a n s i t i o n s i n t h e Raaan s p e c t r a i n t h e range Z°K t o room temperature.
The 2'1: l i n e w i d t h and lineshape a r e assumed t o represent t h e O°K l i m i t . To c o r r e c t f o r t h e f i n i t e s l i t width, a computer c o n v o l u t i o n s i m u l a t i o n program was developed. Such a study f o r t h e 33 cm-' Raman a c t i v e phonon o f p-dichlorobenzene
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816163
C6-564 JOURNAL DE PHYSIQUE
snows that the lineshapes are Lorentzian at all temperatures. The linewidths (corrected for slit width) are obtained as a function of temperature.
Atheoretical fit for these data points is provided
bya model which assumes a T1-relaxation of the optical phonon
(33cm-') into two pnonons of half the frequency. This fit of the relaxation into sucn a simple model appears to hold only for very low frequency optical phonons which can decay l'nto acoustic phonons having a nonotonic and smooth-density of states distribution. In the case of naphthalene optical phonons
(w>55cm-') it is found that one has to use a combination of T1-relaxation processes to account for the observed temperature dependence of the l i n e ~ i d t h . ~ In structurally disordered crystals it is found that the phonons still remain delocalized and a temperature dependence study can be used to separate the linewidth contributions due to disorder and that due to anharmonic interactions.
The general conclusion of this study is that the dephasing of optical phonons in organic crystals occurs predominantly by a Tl-relaxation involving cubic anharmonic interaction terms. Also, another general observation is that the higher the phonon frequency, the faster is the relaxation tine. This result can be explained by the increased number of relaxation pathways whicli becone available at higher frequencies.
An important approximation used to describe the lattice dynamics of organic crystals is the rigid-body approxin~ation which decouples the external lattice phonons from the intranolecular vibrations. Coupling between the intramolecular vibrations and the lattice phonons play an important role in dephasing of the intramolecular vibrations in organic solids. Again temperature dependence of the linewidtii, the lineshape and the frequency of an intranolecular vibration observed in the Ranan spectra is used to investigate the vibrational dephasing.
It is found that for a vibration whose frequency is larger than twice the Debye cut of frequency, the depnasing is predominantly caused by an elastic scattering with phonons involving a mixed mode fourth-order anharnonic interactions. This process requires population of piionons and, thus, are highly inefficient at
liquid heliurt~ temperatures giving rise to sharp spectral transitions of intramolecu- lar vibrations at the liquid helium tenperature.
The third aspect of phonon interactions discussed in this paper is the concept of phonon assisted reactions introduced recently by this research group.
This concept also unifies the understanding of both physical and chemical transformations in terms of importance of phonon interactions. 1Je show that, like phase transitions in solids, a thermal reaction can be assisted by node softening which leads to overdamped large anplitude oscillations, Such large amp1 itude motions can provide pathways for the reaction to occur especially if the reaction is inter~~olecular in nature. The case of thermal rearrangement
reaction of methyl -p-dimethylaninobenzene sulfonate which involves an intermolecular
transfer of a methyl group was investigated by the Raman phonon spectra. The
softening of a phonon node of frequency 25 cm-' was observed supporting the concept of a phonon assisted thermal reaction. Similarly, a photochemical reaction (particularly dimerization and polymerization) can be assisted by a strong electron-phonon coupling which can trap the excitation as well as provide a preformation of the product lattice configuration. The photodimerization reaction of 2,6-dimethyl benzoquinone was investigated. The 6OK electronic absorption spectra of tnis crystal showed most of the intensity in the phonon side band as compared to the zero-phonon line. This clearly indicated the
formation of a polaron due to strong electron-phonon coupling. Thus, the reaction is assisted by the formation of a polaron.
Finally, our work shows that piionon spectroscopy can be used in a number of practical applications. The phonon spectra can readily be used to identify various polymorphs of a solid drug. It can also be used to investigate if a reaction proceeds by a homogeneous mechanism where the reactant and the product form a solid solution.
References
1. Prasad, P.
H . ,Hol. Cryst. Liq. Cryst. 2, 63 (1979).
2.
Bellows,
J.C. and Prasad,
P. N . , 3 .Chem. Phys. 70, 1864 (1979)
3 .
