LINEAR CHAIN MODELS AND SOUND VELOCITIES IN MOLECULAR ORGANIC CRYSTALS

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LINEAR CHAIN MODELS AND SOUND VELOCITIES IN MOLECULAR ORGANIC

CRYSTALS

C. Ecolivet

To cite this version:

C. Ecolivet. LINEAR CHAIN MODELS AND SOUND VELOCITIES IN MOLECULAR ORGANIC CRYSTALS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-578-C6-580.

�10.1051/jphyscol:19816168�. �jpa-00221246�

JOURNAL DE PHYSIQUE

CoZZoque C6, suppZe'ment au n012, Tome 4 2 , dgcembre 1981 page C6-578

L I N E A R C H A I N MODELS AND SOUND V E L O C I T I E S I N MOLECULAR ORGANIC CRYSTALS

C. Ecolivet

Groupe de Physique CristaZZine, E.R.A. au C.N.R.S. n0070015, Universite' de Rennes, Campus de BeauZieu, 35042 Rennes Cedex, France

A b s t r a c t Longitudinal sound velocities in crystals of elongated aromatic molecules have been measured by Brillouin scattering and are found to be faithfully described by a simple linear chain model, whereas a similar beha- viour is observed for compressibility and thermal expansion. A particular at- tention has been paid to the p-polyphenyls and polyacenes series.

1. INTRODUCTION Despite the width of the aromatic rings ; p-polyphenyls and

-

polyacenes are good examples of chain-like molecules which crystallizes in parallel stacks, themselves parallel to the molecular long axis. This kind of stacking is far from being unusual in molecular and specially in flat molecules crystals which most of the time belong to the monoclinic P 2 /a symmetry group. This is exactly what hap-

1

pens for naphtalene, biphenyl, dibenzyl and many others.

We will consider here a simple chain model for crystals of molecules composed of a various number of aromatic rings and look at the sound longitudinal velocities along the stacking direction, intra and intermolecular bonds will be represented by springs of force constants resp. K and K2.

1

2 . LONGITUDINAL SOUND VELOCITIES I N p-POLYPHENYLS and POLYACENES Let us

-

consider first the p-polyphenyls which are represented on Fig.1 as a function of the

"'2 molecular ring n u e r ; the

..

being the length of the crystallographic

n =

mm _-

F ~t can be shown very easily that

K,-= K, K,

n:4 the longitudinal sound velocity along the

- .

L 4

molecule with n rings as :

Fig, 1 Pol yphenyls chain model for longi- tudinal wave propagation.

Where Mn is the mass of the molecule.

The k value can be obtained from I.R. experiments on biphenyl which frequen-

l -1

cy mode is about 334 cm this gives K1

-

obtained a t 300 K and 5 K of the 3 f i r s t elements of t h e polyphenyls s e r i e s from sound v e l o c i t i e s obtained bv B r i l l o u i n s c a t t e r i n g ( 1 1 .

3. COMPRESSIBILITY and THERMAL EXPANSION ANISOTROPIES 'Phe l i n e a r compres-

-

s i b i l i t y 6 which can be expressed a s a function of t h e e l a s t i c compliance moduli Sik w r i t e s down f o r monoclinic c r y s t a l s

Table 1 I n t e r m o l e c u l a r f o r c e c o n s t a n t K2 f o r b i p h e n y l p - t e r p h e n y l , p - q u a t e r p h e n y l a t room t e m p e r a t u r e a n d n e a r l i q u i d h e l i u m t e m p e r a t u r e .

We see on t h i s t a b l e an e x c e l l e n t agreement a t low temperature when vibra- t i o n s a r e more harmonic, it i s a l s o noticeable t h a t t h e e f f e c t of K1 i s n e g l i g i b l e and it should only be d e t e c t a b l e f o r n > 10.

where A. = C Sik k

n c,(h NAM,(g)

Vn(m/s) K2(N/m)

For a l l the c r y s t a l s studied h e r e experimental d a t a show the same anisotropy f o r compressibility and thermal expansion. A counter example found i n the l i t t e r a - Table 2 I n t e r m o l e c u l a r f o r c e c o n s t a n t K 2 f o r n a p h t a l e n e a n d a n t h r a c e n e

a t room t e m p e r a t u r e .

Table 2 give the same r e s u l t s taken from u l t r a s o n i c measurements previously reported i n t h e l i t t e r a t u r e f o r the 2 f i r s t elements of t h e polyacenes a t room tem- perature.

From these d a t a one can c l e a r l y s e e t h a t these organic c r y s t a l s which look r a t h e r complicated can be s u r p r i s i n g l y well described by simple chain models ; mo- reover these models a l s o describe t h e e f f e c t of deuteration and t h e absence of sound v e l o c i t y v a r i a t i o n i n d i r e c t i o n s perpendicular t o t h e chains when n v a r i e s .

a) TESLENKO

b) AFANASSIEVA

)

C) HUNTINGTON (3) 2

8.66 130 35403 3620b 3.55 3.71

3 11.16

178 3860C

3.54

C6-580 JOURNAL DE PHYSIQUE

t u r e w a s d i b e n z y l and it m o t i v a t e s a new d e t e r m i n a t i o n o f i t s e l a s t i c p r o p e r t i e s , f o r t h e maximum of c o m p r e s s i b i l i t y found a l o n g t h e molecular long a x i s looked r a - t h e r u n e a l i s t i c . S t r u c t u r e , sound v e l o c i t i e s c o m p r e s s i b i l i t y and thermal expansion

+ -+

i n t h e [ a , c ) p l a n e can b e s e e n on f i g u r e 2.

Fig. 2 S t r u c t u r e , sound v e l o c i t i e s , l i n e a r compressibil i t y and thermal expansion ( l e f t to r i g h t ) o f d i b e n z y l . The dashed c u r v e i n t h e c e n t e r diagram + i s r e - l a t e d t o t h e t r a n s v e r s e mode p o l a r i z e d a l o n g b, whereas t h e d o t t e d l i n e i n t h e r i g h t diagram corresponds t o t h e thermal e x p a n s i o n a ( . 2 5 10-3 K-I p e r d i v i s i o n ) and t h e o t h e r c u r v e t o t h e l i n e a r c o m p r e s s i b i l i t y 6, (15.10-12 m2 N I p e r d i v i s i o n )

This i s a t y p i c a l example o f the r e s u l t s we c a n e x p e c t f o r such k i n d of c r y s - t a l s where t h e f o r c e s have a s h o r t range n a t u r e .

References

1. C. ECOLIVET, T h e s i s 1981 Rennes.

2 . V.F. TESLENKO and G. AFANASSIEVA, quoted i n "Molecular C r y s t a l s and Molecu-

l e s " &.I. KITAIGORODSKY Acad. P r e s s New-York, 1973.

3 . H.B. MINTINGlDN, S.G. GANGOLI, J . L . MILLS, J. Chem. Phys., 50, (19691, 3844.