7
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Field Dependence of the Magnetic Susceptibility of the L i q u i d Crystal Phase of p-Azoxyanisole C. H. MASSEN and J. A. POULIS Technological University of Eindhoven, Eindhoven, The Netherlands R. D. SPENCE Michigan State University, East Lansing, Mich.
We have studied the field- and temperature-dependence of the susceptibility of the liquid crystal phase of p-azoxyanisole for fields from 201 to 2550 gauss. The results at the highest fields agree with those of Föex at 8000 gauss, but at lower fields the susceptibility becomes field-dependent. The experimental results may be adequately represented by a simple theoretical expression obtained from statistical considerations. The only adjustable parameter in the theoretical formula is an effective mass which arises from interactions between the molecules and amounts to ~2 X 10 gram. -11
'he r e l a t i o n of t h e m a g n e t i c s u s c e p t i b i l i t y of t h e l i q u i d c r y s t a l phase t o t h a t of t h e s o l i d phase is a c o m p l i c a t e d , m a n y - b o d y p r o b l e m . T h e e n ergy of t h e s y s t e m depends n o t o n l y o n t h e o r i e n t a t i o n of t h e molecules w i t h respect to t h e m a g n e t i c field b u t also o n t h e i r o r i e n t a t i o n w i t h respect to each other. T o o b v i a t e t h i s d i f f i c u l t y , one i n t r o d u c e s a set of n o n i n t e r a c t i n g q u a s i p a r t i c l e s (swarms) of mass M (S). T h e energy is t h e n
Ε
lVl
=
-~2
Σ,
, (Xx
. 2 S
l
n
ι
Λ
0»
+
\ TT2
Λ
XII
cos θί)Η
(D
where t h e s u m extends o v e r q u a s i - p a r t i c l e s . H e r e χ a n d χ „ are t h e d i a m a g n e t i c s u s c e p t i b i l i t i e s p e r p e n d i c u l a r a n d p a r a l l e l to t h e axis of t h e m o l e cules, a n d 0; is t h e angle between t h e m a g n e t i c field, H, a n d t h e axis of t h e molecules i n t h e z t h q u a s i - p a r t i c l e . U s i n g t h e s t a n d a r d procedures of ±
72 Porter and Johnson; Ordered Fluids and Liquid Crystals Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
7.
MASS E N A N D POULis
Magnetic
Susceptibility
73
s t a t i s t i c a l mechanics (4), one finds for t h e s u s c e p t i b i l i t y of t h e l i q u i d c r y s t a l phase, X = XX +
(x„ -
Xx) ~ (log
β^άμ)
(2)
where HM , 2^γΓ CXii 2
£ =
. Xx)
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a n d μ = cos 0, E q u a t i o n s 1 a n d 2 c o n t a i n a single a d j u s t a b l e p a r a m e t e r , M, w h i c h i n p r i n c i p l e c a n be o b t a i n e d b y m e a s u r i n g χ at one t e m p e r a t u r e , T , a n d one field, H. H o w e v e r , i t is i m p o r t a n t t o a t t e m p t t o check t h e v a l i d i t y of E q u a t i o n 1. S i n c e t h e absolute t e m p e r a t u r e v a r i e s l i t t l e t h r o u g h o u t t h e l i q u i d c r y s t a l phase, t h e o n l y p r a c t i c a l m e t h o d for e x a m i n i n g t h e general correctness of t h e p r e v i o u s expressions is t o v a r y field H. T h e small value of χ i m p l i e s t h a t a balance of considerable s e n s i t i v i t y is needed for s m a l l fields. C o m p l i c a t i o n s of t w o different k i n d s arise. T h e s w a r m s m a y be embedded i n n o r m a l l i q u i d , w h i c h does n o t c o n t r i b u t e t o t h e v a r i a t i o n of t h e observed s u s c e p t i b i l i t y w i t h t h e a p p l i e d field, i m p l y i n g a r e d u c t i o n of t h e effective v o l u m e of t h e s w a r m s . O n e f u r t h e r c o m p l i c a t i o n arises f r o m t h e fact t h a t t h e w a l l s of t h e c o n t a i n e r exert a n o r i e n t i n g force o n t h e molecules w h i c h cannot be o v e r c o m e e v e n b y t h e a p p l i c a t i o n of large (10 oersteds) m a g n e t i c fields. T h i s a g a i n reduces t h e effective v o l u m e of m a t e r i a l w h i c h m a y be oriented b y t h e field. I f one assumes t h a t t h e m o l e cules i n t h e l a y e r of m a t e r i a l o n t h e w a l l s h a v e a n o r i e n t a t i o n t h a t v a r i e s r a n d o m l y f r o m place to place over t h e surface of t h e vessel, t h e s u s c e p t i b i l i t y of t h e surface l a y e r is t h e n j u s t t h a t of t h e l i q u i d phase. T h e effective v o l u m e of t h e s a m p l e m a y t h e n be d e t e r m i n e d b y m e a s u r i n g t h e χ i n a large m a g n e t i c field a n d c o m p a r i n g t h e v a l u e so o b t a i n e d w i t h t h e v a l u e of X„ w h i c h w o u l d be the s u s c e p t i b i l i t y if t h e m a t e r i a l were c o m p l e t e l y a n d u n i f o r m l y aligned. 4
Experimental
Method
and
Results
A l t h o u g h for p-azoxyanisole ( P A A ) a n u m b e r of measurements i n elec t r i c fields h a v e been reported (1, 5), o n l y F ô e x (2) r e p o r t e d measurements i n a h i g h m a g n e t i c field. I n t h i s p a p e r we report t h e results of m a g n e t i c s u s c e p t i b i l i t y measurements o n P A A , w h i c h h a v e been o b t a i n e d b y u s i n g t h e F a r a d a y m e t h o d w i t h a sensitive balance described b y P o u l i s et al. (6). T h e sample consisted of 0.2841 g r a m of P A A h e l d i n a n e v a c u a t e d s p h e r i c a l q u a r t z container. M e a s u r e m e n t s were m a d e at fields of 2550, 1050, 275, a n d 200 oersteds at a n u m b e r of temperatures i n t h e l i q u i d c r y s t a l a n d l i q u i d phase. T h e absolute a c c u r a c y of t h e s u s c e p t i b i l i t y measurements was a b o u t 3 % , d e t e r m i n e d b y the i r r e p r o d u c i b i l i t y i n the a d j u s t m e n t of
Porter and Johnson; Ordered Fluids and Liquid Crystals Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
74
ORDERED FLUIDS A N D LIQUID CRYSTALS
the sample to the place where t h e c a l i b r a t i o n is t a k e n a n d b y t h e correction for t h e q u a r t z container i n w h i c h t h e P A A was stored.
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T h e t e m p e r a t u r e dependence of t h e s u s c e p t i b i l i t y for t h e field strengths used is s h o w n i n F i g u r e 1, where t h e curves are d r a w n to fit best to t h e measured p o i n t s . T h e s u s c e p t i b i l i t y at 2550 oersteds is i n good agreement
90
100
110
120
130
140
T C E
Figure 1.
Field dependence of χ — xu id of p-azoxyanisole qu
+ Ο • Ο
200 oersteds 275 oersteds 1050 oersteds 2550 oersteds
w i t h t h a t observed b y F o e x (2) at 8000 oersteds a n d m a y therefore be c o n sidered characteristic of the c o m p l e t e l y oriented l i q u i d c r y s t a l phase. Ac c o r d i n g to F o e x (2) t h e p r i n c i p a l susceptibilities of c r y s t a l l i n e P A A are X* =
- 0 . 6 5 5 Χ 10" , 6
X y
=
- 0 . 6 3 4 X 10~ , 6
X x
= - 0 . 4 0 8 X 10~ c.g.s. 6
T h e ζ d i r e c t i o n lies a l o n g t h e l o n g axis of the molecule, a n d therefore X i Χιι
= =
h (χ* +
χ) υ
X*
I n F i g u r e 2 we h a v e p l o t t e d t h e q u a n t i t y (χ — x )/(xw — x±) c a l c u l a t e d f r o m E q u a t i o n 2, as a f u n c t i o n of ξ*. T h e three e x p e r i m e n t a l p o i n t s h a v e been f i t t e d to t h e t h e o r e t i c a l c u r v e b y a s s u m i n g t h a t a field of 2550 oer steds produces essentially complete a l i g n m e n t of t h e molecules (represent ed b y t h e p o i n t p l o t t e d at the u p p e r r i g h t of F i g u r e 2) a n d u s i n g a v a l u e of 2 Χ 10 grams for t h e q u a s i - p a r t i c l e mass, M. T h e agreement between the t h e o r y a n d observations is q u a l i t a t i v e l y satisfactory b u t not sufficiently good t h a t one m a y regard t h e t h e o r y as liquid
- 1 1
Porter and Johnson; Ordered Fluids and Liquid Crystals Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
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7.
MASSEN AND
pouLis
Figure 2.
Magnetic
75
Susceptibility
Predicted and observed values of
χ — xuquid
m o r e t h a n a r o u g h p i c t u r e of a r a t h e r c o m p l i c a t e d s i t u a t i o n .
T h e value
of M d e r i v e d f r o m these measurements is larger t h a n t h a t d e r i v e d f r o m o t h e r m e t h o d s (8), b u t at present there appears to be no r e a d y e x p l a n a t i o n of t h i s fact. Acknowledgmen
t
W e express o u r g r a t i t u d e to t h e E i n d h o v e n H o g e s c h o o l F o n d s for f i nancial aid in this work.
Literature
Cited
(1) Carr, E. F., Spence, R . D., J. Chem. Phys. 22, 1481 (1954). (2) Föex, G., Trans. Faraday Soc. 29, 958 (1933). (3) Gray, G. W., "Molecular Structure and Properties of Liquid Crystals," Academic Press, London, 1962. (4) Landau, L. D., Lifshitz, Ε. M . , "Course of Theoretical Physics," Vol. 5, "Statistical Physics," Pergamon Press, London-Paris, 1958. (5) Maier, W., Barth, G., Wiehl, Η. Ε., Z. Elektrochem. 58, 674 (1954). (6) Poulis, J. Α., Massen, C. H., van der Leeden, P., Appl. Sci. Res. B9, 133 (1961). RECEIVED February 11,
1966.
Porter and Johnson; Ordered Fluids and Liquid Crystals Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
