8pactrochimicaActa,Vol.25A,pp.401to 405. PergamonPrean1969. PrintedhNorthemIreland

Complete circular dichroism tensor parameter in uniaxial crystds-I Theory. Application to benzil and a-NiS0,4H80

F. CASTAGO* Institute de Quimioa Fiske “Rocasolano.” C.S.I.C., Serrano 119, Madrid, Spain

(Received 16 June 1968)

Abstract-A method for the measurement of circular diohroism through different directions in unisxial crystals is proposed. It depends on the knowledge of two straightforward experimental magnitudes: the oircular diahroism of the slab through the optioal axis and its powder.

The method has been applied to hexagonal benzil in the 470-300 nm region and the band at 3900 L% of rhombic a-NiSOI+3Hs0.

I%lWHODS of measuring the optical activity in uniaxial crystals in directions different from the optical axis have been devised by BRUHAT and GRIVET [l] and by SZIYESSY and MUNSTER [2]. Both studies were concerned with a-quartz (class 32 or Dd, which seems to be the only optically active and birefringent crystal fully investi- gated. The tensor components of the optical activity obtained by SZWESSY et al. were :

Sll = 922 = k5.82 . 1O-s; g,, = &12*96. 10-s; gIl = 0 at A, = 5100 B

with the upper sign to right-handed quartz with a right-handed choice of axis. The ratio gn/gss is -0.45, whilst BRUEUT et al. give -0.51 for 5461 A and -0.57 for 2537 A.

The angle of rotation of the plane polarized light through a sample with different right and left refraction indices is given by

g = F (n, - n,) 0

An analogous phenomenological relstion exists in the absorption bands for the ellipticity of the emergent light (or the circular dichroism) and the left and right absorption indices ei [3] :

CD. = ; (xl - x7) = 2.3 y (eI - E,) 0

irrespective of the aggregation state of the sample. These expressions are identical from a fornml point of view and therefore the type of symmetry found in the optical

* Ramsay Memorial Fellow (1966).

PI i?l

II31

G. BRUIZAT and R. GRIVET, J. Phys. Radium, 6,12 (1935). C. MC?NSTER and G. SZIVESSY, Phys. 2. 36, 101 (1936); G. SZJYESSY end C. MONSTER, Ann.Ph~s.a0,703 (1934). S. F. MASON, Quart. Rev., 17, 20 (1963); P. CRABBE, Optioal Rotatory me&on a& Ck~lar Diohroism in Organic Chemdy. Holden-Day (1966) M. LOWRY, Optical Rotatory Power. Dover Reprint (1936).

401

402 F. cAf.ST_&O

rotation will be applicable to the circular dichroism (C.D.). So, the tensor of the C.D. is an axial second-rank order one (pseudo-scalar).

The relations between the tensor components, gi,, are given in a standard text [4] and they are not repeated here. In the case of uniaxial crystals belonging to classes 3, 32, 6, 622, 4 and 422, the coefficients gri (applicable to optical rotation as well as to the circular dichroism, C.D.) perpendicular to the optioal axis are equal: gii = gas; gi, = 0 and gss # 0, in general. The uniaxial class 22 m is not enantio- morphous and grr = 0 except if i = 1, j = 2. The same applies to z, in which

911 = --ssz, g12 # 0 and 9, = 0. Other uniaxial crystals cannot possess optical activity. In the rest of the paper a distinction between the classes with C.D. in which CD,, = 0 and the others will be arbitrarily introduced. So, the next para- graphs refer to the symmetries with CD,, = 0.

In those uniaxial crystals in which CD,, # 0 this quantity can be measured straightforwardly, (provided that crystals of the appropriate thickness perpen- dicular to the optical axis can be obtained), since no birefringtmce exists along this privileged direction. The second relation we propose towards a complete knowledge of the C.D. coefficients comes from a study of random orientated crystals in a suitable media, such as, KBr or KC1 discs, nujol, C&F,,, (C,F,),N, some liquid crystals of the nematic and smetic type, and the like. A required condition is that the substance does not interact with the supporting medium.

Randomly orientated crystals composed of moleoules smaller than the wave- length of the light exhibit an optical rotation and a C.D. which, as a function of the directional coefficients [a], is

CD = CD,,X, . X,

to 3, 32, 6, 622, 4, 422 = CD,,Xi . Xi

in the ease of random orientation. = CD,, . Xl8 + CD,zX22 + CDmXs2

= WC-41 + CD,) Since this sum and CD,, me known, the coefficients CD,, = CD,, are obtained

by simple subtraction of i(3CD - CD,,). So the cumbersome procedure for the study of birefringent monocrystals is avoided in the present method.

In the non-enantiomorphic class 42 m, gl, = 0 except CD,, # 0. The averaging over the product Xi . X2 is zero. Therefore the powder has not circular diohroism. Analogously it happens for the class 2 with CDlg # 0, CD,, = CD,, # 0. So, the method fails in both classes.

EXPERIMENTAL

Crystals of benzil were recrystallized twice and grown from benzene. KCl, saturated nujol with benzil, and (&F&N were used giving a similar pattern of bands. Crystals of a-NiSO, * 6H,O were grown [5] at 44 f 2’C from water, and nujol was used to obtain mull-spectra by means of the Roussel-Jouan Dichrograph.

[4] J. F. NYE, Phyakd Pvopertk of Cry&&. Oxford University Press (1957); L. D. LANDAU and E. M. Lmmz, E,?e&rod~m~ of Cmtimmw Media. Pergamon Press (1969).

[5] M. LEVY, Arm. Phy8. Pa&, 5,163 (1960) and references therein.

Complete oirouhw dichroif3m tensor paramettx in uniaxial oryatals-I 403

Figuree 1 rend 2 report

Fig. 1

RESULTS B;ND DISCUSSION

the values of CD,i = CD,* for the hexagonal benzil and tetragonal a-NiSO,*GH,O crystals. The values of CD, are taken from EL-SAYED [6] and from MATEIEU and VTJLDY [7], respectively. To match the results of EL- SAYED, use is made of the relative circulsr dichroism tensor parameters ((q - E,)/ E)$i = Pir. Besides, it is assumed that the extinction coefficients along z, LC and y are the ss,me. The extinction coefficients through the axis for a-NiSO,*6H,O were borrowed from TREEIN [8] and checked by experiment.

The 356-450 nm band of benzil is composed of, at least, two sub-bands with the maxima at 359 and 400 nm and a probable one at 434 nm. With a right-handed choice of axis the absorption bands of the right-handed crystals have a positive circular dichroism perpendicular to the optical axis. Moreover the 310 nm band has an opposite sign.

In a-NiSO,-GH,O, the two bands near 3870 b with polarizations parallel and perpendiculsr to the optical axis looking at the crystal perpendicular to it, exhibit a circular dichroism of opposite signs, being positive if right-handed axis and crystal

[Sl N. K. CELGJDEURI and EC. A. EL-SAYED, J. Chm. Phys. 47,1133 (1967). [7] J. P. &.bTHIEU and G. VULDY, COP@. Rend. 222,223 (1946).

404 F. cAsT&O

1 (er -c,)do*

(9)

Fig. 2

are into play. The high of maxima-or the areas-of the bands are proportional to their relative absorption coefficients [SJ. As Fig, 2 shows the shift of the two absorption bands reach 130 A, a magnitude rather higher than that reported by TREEEN ES] from absorption m~s~ements.

Unfortunately no data exist to confirm the accuracy of our measurements, which depends on the values of CD,,. M~THIEU and V~DY [7] considered possible errors which at the peak of CD. are at least 4%. The data of ZSWESSY and M@XSTER, and BRUHAT and GRIVET differ at least ES] by 10%. In the ideal case where C& is accurately known, the author estimates by comparison of measure- ments of CD. in KC1 and KBr, nujol and (C&F&N and solution [lo], an error of less than 10%. This is not so bad if compared with the results for quartz upon which rest the complete phenomenological theory.

[S] R. -KIN, 00-t. &&. 220,85 (1945). [Q] C. D. RWU=~W and S. RAMASESHAN, C7y&l OptiCS. Ha&b. Phys. (Edited by S.

FLfiQclE),Vol.XXVI/l. f&ringer (1961). [lOI A.J.MaC!-Rx,S.F. MASON and B.S. NoRIvIAN,C~~.COWWW~.~BI( 1966); F. CAST&O,

unpublished results.

Complete circular dichroism tensor parameter in uniaxial crystals-I 406

A source of error is the reflected light. If circularly right polarized light is reflected to a different degree from left, unpredictable errors arise. However, this is not characteristic of powders in isotropic media [9] and workers in the field consider it negligible or inside experimental error. These have been our assumptions as well.

Acknow&dge7nents-This paper was prepared while the author held a post-doctoral fellowship at Ea& Anglia University (Norwich). I am indebted to Prof. S. F. MASON for continuous and encouraging help, to Dr. J. &WON for kindly preparing of benzil crystal and, finally, to Drs. K. JACKSON and R. B. HOMER for scanning the spectra of cr-NiS0,*6ELs0 and for useful discus- sions.