Temperature dependence of chlorine NQR in 2-chloro 5-nitrobenzoic acid and 4-chloro 3-nitrobenzoic acid

(1)

Temperature dependence of chlorine NQR in 2-chloro 5-nitrobenzoic acid and 4-chloro 3-nitrolwnzoic acid

V S S S A S T R Y and J R A M A K R I S H N A

Department of Physics, Indian Institute of Science, Bangalore 56001-2 MS received 5 March 1976; after revision 18 May 1976

Abstract. Temperature dependence of chlorine nuclear quadrupole resonance in 2-ehloro 5-nitrobenzoic acid and 4-chloro 3-nitrobenzoic acid has been investigated in the region 77°K to room temperature. No phase transition has been observed.

The results are analysed to obtain the torsional frequencies and their temperature dependence. A nonlinear temperature dependence is obtained for the torsional frequencies.

Keywords. NQR; temperature dependence; internal motions, 1. Introduction

In this paper we r e p o r t the results obtained from a study o f the temperature dependence o f asC1 N Q R frequency in two chlorine derivatives o f benzoic acid, namely;

2-chloro 5-nitrobenzoic acid (substance-I) a n d 4-chloro 3-nitrobeazoic acid (substaztce II). Their N Q R frequencies at 7 7 ° K are already k n o w n (Bray 1957).

Even t h o u g h the quadrupole coupling c o n s t a n t for a g o o d n u m b e r o f chlorine derivatives o f be.nzoicacid are k n o w n , n o t m u c h seems to have been d o n e in these compotmds with regard t o the t e m p e r a t u r e d e p e n d e n c e o f N Q R , which is sensitive to internal motions, especially the low lying librations (torsional oscillations) a n d phase trazlsitions i f any.

A D e a n ' s type self-quenched super-regenerative s p e c t r o m e t e r (Das a n d H a h n 1958) was used to observe the resonances, a~d the frequencies were measured with a BC 221 frequency meter. A h o m e - m a d e solid s t a t e lock-in-amplifier was used to record the signals. The signal-to-noise r a t i o could be improved, typically by a factor o f 50, using this lock-in-system with a time c o n s t a n t o f 4 secor_ds. T h e sample was kept in a low t e m p e r a t u r e cell a n d the t e m p e r a t u r e was varied f r o m 77 ° K to a b o u t 300 ° K. The t e m p e r a t u r e was measured with a c o p p e r - c o n s t a n t a n thermocouple and a Pye p o t e n t i o m e t e r . The t e m p e r a t u r e stability a~.d accuracy of measuremel~t were b e t t e r t h a n q - 0 - 5 ° K. B o t h the substances were obtained f r o m Sigma Chemicals C o m p a n y , U S A and powder sTtmples were used in the prese~.t work. While substartce-I gave a visual signal- to-noise r a t i o (S/N) o f a b o u t 5 at 77 ° K and remair.ed almost the same up to 300 ° K, substav.ce-II gave a weak signal at 77 ° K (visual S/N ,-~ 2) and the signal weakened co~_siderably with the ip.crease o f temperature. A t 300 ° K, this signal could only be r e c o r d e d with a S/N ratio o f 6 to 10.

146

(2)

Temperature dependence of NQR in benzoic acids

147 2. M e t h o d o f calculation

The results from the experiments have bee~l analysed by two methods, one with a view to evaluate the temperature coefficient, g, of torsional frequencies, using Brown's approach (Brown 1960) and the other to evaluate numerically fo unit fu av.d hence g, using Bayer's equation (Bayer 1951). The two methods are sum- maxised briefly here. On the basis of Bayer's theory, the temperature dependence of NQR frequency, for axially symmetric field gradients, is given by

Vr 1 3 h 1 3h 1

Vo = 8zraa,f,

exp ( h f , / k T )

-- 1

8~ ~

A,f~

exp

(h fu/KT)

- - 1 " (1) Here it is assumed that the NQR frequev.cy of the statiop.ary molecule is equal to that (vo) at 0 ° K. f , and fu are the torsional frequev.cies of the molecules about the principal X and Y axes of the EFG tensor. A, and A v are the corresponding

moments of intertia. This equation as generalised by Kushida (1955) becomes

3kT~" 1

^{h ~}

~ I

V

rvo = 1 --8rr~ ~ , A,f, z ---32zr 2 k---T AG (2)

4 i

where

h f J k T ~

1 (high temperature approximation).

The effect of volume change with temperature, in the case of molecular solids, has been introduced by Brown (1960) through the temperature dependence of the torsional frequencies. He assumed a linear temperature dependence for the torsional frequepcies on the basis of tke observations of Ichishima (1950).

Thus

f~ =--A°(1 - - g , t) (3)

where t is the temperature measured from any reference point. Fixing the origin at some point in the high temperature region, say To°K and neglecting the

I[T

term in eq. (2), Brown showed that

where

dv !

lTo

d2Vdt z To

1 + 2Tog

= 4 g + 6Tog 2 (4)

and

g = ( g ) = ( ~

g ~ z ) / / ( ~ 1 )

g~ = (g~) = A,f2 ~ "

The average value of the temperature coefficient g of the torsional

~alt be evaluated using eqs (3) and (4).

(5 a)

(5 b)

frequencies The method adopted in the present case

(3)

to evaluate f . and f . is similar to the one described by Vijaya and Ramakrishna

(1970).

3. Results and discussion

The observed variation of NQR frequency with temperature (vr versus T curve) for both the substances is shown in figures 1 a and 1 b. The values o f j . and fv at each temperature are estimated using the method mentioned earlier and the

£

z

Z

36.8 --

Figure 1 a.

acid.

[ 1 f I

75 150 225 300

,,,,, TEMPERATURE (og~

Temperature variation of NQR frequency in 2.¢hloro 5-nitrobenzoic

37.3

37.7

g u. 3%5

37 3

I I I I

75 150 2 2 5 300

TEMPERATURE ( ' K )

Figure 1 b. Temperature variation o f N Q R frequency in 4-chloro 3-nitrobcnzoi¢

acid,

(4)

Temperature dependence of NQR in benzoic acids 149

70

~E z o 50-- u.l

)0--

o

Figure 2 a. Temperature variation

. I . I I

I00 200 3O0

TEMPERATURE (°K)

of ~ and f~ in 2-chloro5-nitrobenzoic acid

60

t

,?, ~c

E.

o 3O

2C 0

e

~ - . ~ fx

I ! ,

~00 20O

IEMPERAIURE (°K)

300

Figure 2 b. Temperature variation of f¢ and f~ in 4-chloro ~nitrob~mzoic

(5)

results are presented in figures 2 a artd 2 b. The values o f As, AN, v,, for b o t h the substances a r e p r e s e n t e d in tabl~ i . The values o f g , and gv are evaluated in the region 250 ° K-300 ° K (high t e m p e r a t u r e region) a n d the ,~alue o f g is obtained using eq. (5 a). The value o f g has also been evaluated using Brown's approach.

F o r this, data in the region 250 ° K - 3 0 0 ° K is fitted to a parabolic e q u a t i o n using the m e t h o d o f least squares. The values o f gs, g , , a n d g obtained f r o m the n u m e r i c a l m e t h o d and also the value o f g obtained f r o m Brown's m e t h o d are shown in table 2. The maximum e r r o r in the estimation o f g using the latter m e t h o d is expected to be :k 0-0001, c o r r e s p o n d i n g to a mean square deviation o f a b o u t 5 ( K H z ) ~ in the parabolic fit o f the e x p e r i m e n t a l data. It is f o u n d that t h e value o f the temperature coefficient o f torsional frequencies obtained using B r o w n ' s m e t h o d compares well with the one obtained by the numerical m e t h o d in the case o f 4-ehloro 3-nitrobenzoic acid, while the agreement is n o t so good in the case o f 2-chloro 5-nitrobenzoic acid.

It may be p o i n t e d out from figures 2 a a n d 2 b t h a t the variations o f the torsional frequencies are n o t quite linear with temperature. The values o f the torsional frequencies t e n d t o level off at lower a n d higher temperatures and this behaviour is m o r e p r o n o t m c e d in the case o f 2-chloro 5-nitrobenzoic acid. We have recently studied (under publication) the t e m p e r a t u r e dependence o f a-~C1 N Q R in o-chloro a n d m-chlorobenzoic acids and f o u n d that the numerical m e t h o d and B r o w n ' s m e t h o d give comparable results hi the case o f m-chlorobenzoic acid, while in the case o f o-chlorobe~.zoic acid the a g r e e m e n t was n o t so good. Also the torsional frequencies showed a t e n d e n c y t o level off at lower and higher temperatures, this b e h a v i o u r being more p r o n o t m c e d in o-chlorobenzoic acid. A R a m a n study o f the low lying liberatio~tal motions may t h r o w m o r e light on this peculiar b e h a v i o u r o f t h e frequencies.

Table 1. Molecular constants used in Bayer's equation.

i

As A'~

Substance

× 10-~0gmcm 2 × 10-aagmcm 2

P O

MHz

2-chloro 5-nitrobenzoic

acid 2100.3

4-chloro 3-nitrobenzoic

acid 2513- 7

Table 2. Temperature coefficients of torsional

1320.5 1728-1

i

frequencies

Substance

37.424 37.946

Numerical method Brown's method

(o C_I) (oc_i)

gs gy g g

2-chloro 5-nitrobonzoic acid 4-chloro 3-nitrobcnzoic acid

0. 0007 0. 0006 0" 0007 0" 0018

0.0009 0.0010 0.0010 0.0008

i

(6)

Temperature dependence o f N Q R in benzoic acids

Acknowledgement

O n e o f t h e a u t h o r s (VS) tha~n.ks C S I R , N e w Delhi, for f i , a n c i a l s u p p o r t . 151

References

Bayer H 1951 Z. Physik. 130 227 Bray P 1957 J. Chem. Phys. 27 551 Brown R J C 1960 J. Chem. Phys. 32 116

Das T P and Hahn E L 1958 Nuclear Quadrupole Resonance Spectroscopy Solid State Phys.

Suppl. 1 p 90, eds F Seitz and D Turnbull (Academic Press) Ichishima I 1950 J. Chem. Soc. Japan 71 607

K.ushida T 1955 J. ScL Hiroshima Univ. Ser A Phys. Chem. 19 327 Vijaya M S and Ramakrishna J I970 Mol. Phys. 19 131