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Complete circular dichroism tensor parameter in uniaxial crystals—I theory
8pactrochimicaActa,Vol.25A,pp.401to 405.PergamonPrean1969. PrintedhNorthemIreland
Completecircular dichroism tensor parameter in uniaxial crystds-I Theory. Application to benzil and a-NiS0,4H80 F. CASTAGO* Institutede 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 investigated. The tensor components of the optical activity obtained by SZWESSYet al. were : Sll = 922 =
k5.82
. 1O-s;
g,,
=
10-s;
&12*96.
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 G. BRUIZAT and R. GRIVET,J. Phys. Radium, 6,12 (1935). i?l C. MC?NSTER and G. SZIVESSY, Phys. 2. 36, 101 (1936); G. SZJYESSY end C. MONSTER, Ann.Ph~s.a0,703
(1934).
II31S. F. MASON, Quart. Rev., 17, 20 (1963); Ck~lar Power.
Diohroism in Organic Chemdy. Dover Reprint (1936).
P. CRABBE, Optioal Rotatory me&on a& Holden-Day (1966) M. LOWRY, Optical Rotatory 401
F.
402
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 enantiomorphous and grr = 0 except if i = 1, j = 2. The same applies to z, in which Other uniaxial crystals cannot possess optical g12 # 0 and 9, = 0. 911 = --ssz, 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 paragraphs 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 perpendicular 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 wavelength 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
Oxford University Press (1957); L. D. LANDAU Pvopertk of Cry&&. Media. Pergamon Press (1969). and E. M. Lmmz, E,?e&rod~m~ of Cmtimmw [5] M. LEVY, Arm. Phy8. Pa&, 5,163 (1960) and referencestherein.
Complete oirouhwdichroif3mtensor paramettx in uniaxial oryatals-I
403
Fig. 1
RESULTSB;NDDISCUSSION Figuree1 rend 2 report 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 MATEIEUand VTJLDY[7], respectively. To match the results of ELSAYED,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, LCand 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).
F.
404
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 TREEENES]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 BRUHATand GRIVETdiffer at least ES]by 10%. In the ideal case where C& is accurately known, the author estimates by comparison of measurements 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, FLfiQclE),Vol.XXVI/l.
[lOI
A.J.MaC!-Rx,S.F. unpublishedresults.
C7y&l
OptiCS. Ha&b.
Phys. (Edited by S.
f&ringer (1961). MASON
and B.S. NoRIvIAN,C~~.COWWW~.~BI(
1966);
F. CAST&O,
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. JACKSONand R. B. HOMER for scanning the spectra of cr-NiS0,*6ELs0 and for useful discussions.
Completecircular dichroism tensor parameter in uniaxial crystds-I Theory. Application to benzil and a-NiS0,4H80 F. CASTAGO* Institutede 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 investigated. The tensor components of the optical activity obtained by SZWESSYet al. were : Sll = 922 =
k5.82
. 1O-s;
g,,
=
10-s;
&12*96.
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 G. BRUIZAT and R. GRIVET,J. Phys. Radium, 6,12 (1935). i?l C. MC?NSTER and G. SZIVESSY, Phys. 2. 36, 101 (1936); G. SZJYESSY end C. MONSTER, Ann.Ph~s.a0,703
(1934).
II31S. F. MASON, Quart. Rev., 17, 20 (1963); Ck~lar Power.
Diohroism in Organic Chemdy. Dover Reprint (1936).
P. CRABBE, Optioal Rotatory me&on a& Holden-Day (1966) M. LOWRY, Optical Rotatory 401
F.
402
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 enantiomorphous and grr = 0 except if i = 1, j = 2. The same applies to z, in which Other uniaxial crystals cannot possess optical g12 # 0 and 9, = 0. 911 = --ssz, 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 paragraphs 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 perpendicular 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 wavelength 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
Oxford University Press (1957); L. D. LANDAU Pvopertk of Cry&&. Media. Pergamon Press (1969). and E. M. Lmmz, E,?e&rod~m~ of Cmtimmw [5] M. LEVY, Arm. Phy8. Pa&, 5,163 (1960) and referencestherein.
Complete oirouhwdichroif3mtensor paramettx in uniaxial oryatals-I
403
Fig. 1
RESULTSB;NDDISCUSSION Figuree1 rend 2 report 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 MATEIEUand VTJLDY[7], respectively. To match the results of ELSAYED,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, LCand 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).
F.
404
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 TREEENES]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 BRUHATand GRIVETdiffer at least ES]by 10%. In the ideal case where C& is accurately known, the author estimates by comparison of measurements 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, FLfiQclE),Vol.XXVI/l.
[lOI
A.J.MaC!-Rx,S.F. unpublishedresults.
C7y&l
OptiCS. Ha&b.
Phys. (Edited by S.
f&ringer (1961). MASON
and B.S. NoRIvIAN,C~~.COWWW~.~BI(
1966);
F. CAST&O,
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. JACKSONand R. B. HOMER for scanning the spectra of cr-NiS0,*6ELs0 and for useful discussions.