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On the problem of obtaining accurate circular dichroism. Calibration of circular dichroism spectrometers
Bpectrochimica Acts, vol. 92A, PP.717 to 724. Pergamon Press,1976. Printedin Northern Irelar~d
On the problem of obtaining accurate cirqdar dichroism. Calibration of circular dichroism spectrometers b
DA~IDSSON and BENQT NORDEN
Inorganic Chemistry I, Chemical Center, University of Lund, P.O.B. 740, S-220 07 Lund 7, Sweden (Received 22 March 1975) AbstractIt is questioned whether common circular dichroim (CD) spectrometers can be relied upon if they are calibrated at a single wavelength only. A procedure for obtaining the influence of certain instrumental parameters is described, and relations are given to correct the CD. This discussion was found relevant on examination of a particular commercial CD spectrometer for which fairly large corrections were necessary. It is suggested that the different values reported for two common CD standards may bo explained by errorsof the type considered, in different instruments.
INTRODUCTION Circular dichroism
(CD) is easily measured by the
GROSJEAN-LECRAND [l] method, polarized some
light
audio frequency, a
circularly
sinusoidally
modulated
o/237, from
circularly polarizations. leaving
in which linearly
is electro-optically
at
left to right
The intensity of the beam dichroic
at frequency
sample
w/2x.
will
From
vary
the ratio
Lqht scuce
Momxh-
romator
Modulatw
-3mple
between the amplitude of the intensity modulation and the unmodulated obtained
intensity
electronically.
the CD
The fact
is then
DC on!!?
mccfdcr
t.hat the light X
beam during a large fraction of the period (2r/w) will not be circularly polarized makes the instrument
sensitive
to
linear
dichroism,
as will
discussed in papers concerning the adaption
be
t
of a
-1
CD spectrometer for linear dichroism studies [2-41. non-ideal
optical modulation
on the accuracy
of
CD measurements. FUNCTION OF INSTRUMENT The principles of a representative eter are sketched instrument
(Jasco
in Pig.
la.
J-40)
the
linear
with the monochromator,
polarized
with
(Fig. lb).
The modulator
electric
CD spectrom-
vector
polarizer
is
giving
light
parallel
to y
(Pockels’ cell) is excited
by an AC voltage, Vo sin wt, with a frequency, w/2a = 370 Hz. By the phase difference between this voltage
and the modulated
photomultiplier
signal from
the
the sign of the CD is determined
in a synchronous rectifier.
S.
6%8i M
The light intensity after
P
Qk 2
In this particular
combined
the
R
Y
In the present report we scrutinize the influence of
Fig. 1. (a) Principles of a modern CD instrument. (b) Instrumental coordinate system. The light is propagated along the positive z-axis. S symbolizes the light input, R, M, P are different optical elements (retardation plate, sample solution, linear polarizer) which may be inserted in the light path. imposed
by an AC component.
The DC level is
kept at a constant value, Vnd~, independent
passage of a sample exhibiting CD gives rise in the
multiplier high tension.
photomultiplier
(at point D) will therefore be proportional
to an electrical
DC signal super-
of the
total luminous flux, by a servo control of the photo-
717
The alternating signal VAc to the
A. DAVIDSSON
718 ratio
between
the
light intensities. is the Pockels’
modulated
and
unmodulated
The crucial part of the instrument cell.
A certain applied voltage V,,
andB. NORDEN (1).
S describes the positive definite instantaneous
S = (En2 + Eu2, 2E&
00s 6, 2Esv
Ez2 -
corresponds to an induced phase lag 6, for light of a certain wavelength
and polarization.
To keep
sin 8,
components
Ev2}t
(1)
of the electric vector, E,, E, along the
6, constant, V,,( 2) must follow a certain wavelength
x and y axes (Fig. lb), and 6 is the relative phase
program [I].
difference between E, and E,. The action of an optical element (R, M or P) on the light introduced
THEORY The following treatment Jasco CD Spectrometer, any other instrument
is obtained by multiplying
with an operator (fi, 2
is worked out for the
but should also apply to
using the Legrand-Grosjean
principle. We adopt the nomenclature
f%rst introduced by
or $),
and the appearing
light is described by a new S matrix, $S.
For example,
S
&,
%S
or
with all elements as in Fig. lb,
the light appearing from P would be l%?l%J.
The
optical elements of interest are the following:
R is
STOKES [5] i.e. that a general light beam can be
the so called Pockels’
represented by a 4 x 1 column matrix where the
with variable induced phase lag, 6, oriented with
f&t
element
is the
intensity,
describe the polarization conveniently
written
state.
and
the
others
This matrix
horizontahy
X is
as in Equation
cell, i.e. a retardation
plate
its optic axes in the xy plane, the principal (slow) The an angle ,9 with the x-axis.
axis forming
corresponding operator, I?, is given by Equation (2). P is a perfect polarizer, oriented
0
/l
(
R(B, 6) =
0
0
sin2 sg + CO822g co9 6
0
co9 2/? sin 6
0
co9 2g sin 2/9(1 -
r-b: from
the
z-axis,
28 sin 6
co9 6 00s 6)
at normal incidence with its axis of extinction an angle
-00s
0
i.e.
the
-sin
sin 28 sin s
is given by Equation
(3).
co9 6)
(2)
28 sin 6
co9 2j3 + sin2 2/I cos 6) 1
at
electric
(4).
LD (decadic (
vector will appear with the angle a to the x axis. 9
\
sin 2/? co8 28(1 -
Similar descriptions
yc = total average absorbance yZ+ = ln 10/2(&,
-
\
Fy) lc
are used
Q(u)= / 1
(
(
sin 2cr
Q
0
COB2a
sins 2a
0
sin 2u co8 2a
0
0
0
sin 2a
0
cos2a
sin2ucos2a
0
\
--In 10/2(&r -
ya, =
-(2n/l)(nr
-
yb, = ln 10/2(&+&o 1
(3)
\ yar = (2”/U~+*so
-
)
~$0
c0s22a
is the pathlength
(4)
n,)Z E_& Q6”)Z
absorbance unit.s) is defined as (E, -
/ .zv) . Z . C (1
in cm, and C the concentration
in M with respect to linearly dichroic species).
by WALEER [6].
A sample M may be represented
according
[7], for the general case that it
exhibits
yb, =
to Gs circular
birefringence
dichroism
(CD)
and
(CB) and linear dichroism
circular (LD) and
E,
and E, axe the absorption coefficients for the electric vector parallel to two mutually orthogonal CD (decadic axes, n and v, in the x, y-plane. absorbanoe units) is consequently
(sr -
sr)
. I . C,
linear birefringence (LB). We adopt the parameters of GG (further developed by TROXELL and
where Edand .+ denote absorption coefficients for left and right ciraularly polarized light. CB (in
SCHERAOA) [8] for the latter phenomena
radians)
(Equation
is 2p(nr -
n,)Z/t
where
ng and
n,. are
719
On the problem of obtaining accurate circular dichroism refractive
indices
polarized light. Equation
(4),
for
left
and
right
y = 271, where
density of molecules.
q is the
(7), where the phase lag
ny. In
/IO
number
0
(
fzxO10
The operator & of the sample
may now be written as in Equation $
&, Equation
circularly
LB is by consequence nn -
(6).
= e--VCe-YD where
0
0
toss
\o
0
sill8
o\
O
-sin8
6 /
COB
1
6 = 6, sin wt is induced by the alternating
b,
0
a3
-a2
b,
-a3
0
aI
\h
a2
H=
In
the
instrument
(5)
1)
If the Pockels’
along
normalized
intensity,
the positive
z-axis.
Assuming
S is given by Equation
(6).
K (radians),
light
= {l,O,
enters the Pockels’
with p = a/4 [Equation &&,
0, -1>t
(8)).
cell exhibits a static birefringence,
with
(6, sin
its principal
ot)}t
(8)
axis forming
an
angle &, with one of the electrically induced optic axes, this effect must be considered by the separate action
This s
excita-
One readily obtains
V,,sincot).
RS = (1, 0, sin (6, sin wt), -cos
monochromatic
linearly polarized light (electric vector parallel to y) propagates
(V =
the S matrix for the appearing light (Equation
0 /
-al
(Fig.
tion voltage
(7)
of a retardation
operator &,,
(6)
yields Equation
cell, which is oriented
reaching
(2)], yielding the operator
plate
and its associated
K), which by means of Equation
the
(2)
(Q), which thus describes the light
photomultiplier
when
no
element
(M or P) is present.
K)fiS = (1, sin 28, sin K sin (6, sin wt) + CO8 2gs sin 2&(1
-
00s K) cos (6, sin wt),
sin (6, sin wt) ~0s K + co8 28, sin K cos (6, sin cat), cos 2/3s sin K sin (6s Sin cut) -
(sin2 28,
+ CO8228, co9 K) cos (6, sin
DETERKNATION OF TEE INSTRUMESTAL PARAXETEES 6,. p,, AND K A polarizer, P, is introduced at an angle, a. resulting light intensity I(a,
ot) = *{I
I(a,
wt)}t
the first element (>
The
D
instruments
(Fig.
on an oscilloscope
lacking a servo regulation
(or, for
of the DC
(3)):
$(a)&&,
Equation
(10).
K)&’ The AC
signal to be observed
ot) is obtained from
+ sin 2a[sin 2& sin K sin (6, sin ot)
la)
in the matrix
from Equation
+ co9 28, sin 2&,(1 - co9 K) cos (6s sin wt)]
+ co9 Ba[cos 2/l, sin K sin(d, sin cut) - (Sin2Z/3, + at point
(9)
2&
C0S2
component:
CO9
K)
the ratio
CO9
(6,
between
Sin
wt)])
the AC
voltages) is then given by Equation
(10)
and DC
(11).
VcW*
Cos K)
2r -
co8 2a(sin2 28, + cosz 2& cos K)] 00s (S, sin ot)}
I
28s sin K) sin (6, sin cot) + [sin 2a co8 2j3, sin 2&( 1 -
:r
s
o ((1 + sin 2a sin 2/J, sin K + cos 2a cos
cos K) -
cos 2a(sin22&
+ oos2 28, cos K)] cos (6, sin ot))dwt
Deter&nation
of 6,.
The polarizer is set in a = 0 and From
the corresponding
oscilloscope
2Vno0 (AC”/2*‘/2 COB8, = 2Vno’J (ACn/2.‘/2 + ACs.-+ACU/2. -
T/Z positions. signals,
the
absolute
differences
Equation
(12), between opposite extrema yield the
value
of 6,.
Equation
AC”*Ut, AC’12BWt, defined
Equation
(12)
_ AC~S’/~) _ ACs.‘jzACni2.n/2 -WI2 (ACU/z*U/z + ACs.U/s)/(AC’/s,-‘12 + ACs.+)/(ACU/s,
412
+ A,-$. -W/s) +
A@.
in
can be derived from
(11).
_ ACOS’/~) + AC0.r/2AC+.‘/2
AC% -X12ACU/‘. -U/“(ACD/%+
(11)
-42)
A. DAVIDSSON
720
andB.
NORDEN
where AC”.“t
= VDc”JV;;/V;;
-
Detewnination of & and K. The polarizer is rotated to the distinct position (CQ, 0 < cc0 < p/2)
at
which
the
oscilloscope
picture gives a pure sinusoidal wave form.
=
sin K cos 28,
IV~~~12/V$j’12
-
(12)
Equation
(13).
By inserting a, cut = 0, ~12 etc. in
Equation
(ll),
one obtains Equation
(14), where
aC was defmed in Equation (12). From the observed Q, AC’12*ri2, ACn/2-“/2~, AC”.n/2, AC”*-fl/”
From
Equation (11) it is redized that co9 (6, sin ot) = 0 in this casa and the amplitude will be given by AC%/Vnos
V;;“/V;c”“I
and the 8, estimated above, Equation give ~~ and K.
V~~-“12/V$~-“~2
= I/sin 6, Vno0[1/(AC”/2’r/2
-
(13) and (14)
1 = 2 sin 6, sin K cos 2(cr, - PO)
ACn12*-Rla) + l/(AC”*R/2 -
(13)
AC’*-“/‘)]
(14)
CIRCULAR DICRROISM If the circular dichroism tropic)
of an ordinary
solution is measured,
Equation
(iso-
negligible birefringence in the sample cell windows, the
output
multiplier
light
intensity
is given
matrix
&(?a,,
defined
in Equation
by
reaching
the
yb,)&l,,
where
(This
easily calculated if the operator 2
is first power
via Equation
AC = IV$/V$
-
(16) from
I = + log,,{[AC
the difference AC
cos 2/l, sin K &(1 + cos So) -
has a filter effect
the
first
retaining
(cot) components
second term in Equation contribution,
while
term
(cf.
only
. V,,.
(r2a.
The
1A&I ZC = ]2yb,/ln 101,
(16)
to be observed on the oscilloscope:
2 cos K sin a01 2 COBK sin 6, -
CD
ground
Results).
The
the
factor
is transformed
Wi(6,)
sin
tgh[(ln 10/2)CD] 1 + @[(hi
amplification.
relation
between
Equation
(18)
The signal gives
the
the real CD and the recorded,
CD,., presuming the gain constant I< to be governed by a correct (“calibrated”)
rosponse at very low
(co9 ~/co8 Ko) . (JI(6,)2/J,(6,,) (COS
,+OS
KO).
10/2)CD][cos
cos K .
lim K CD-O
EXPERIIURNTAL The measurements were carried out on a “Jasco J-40 CD Spectropolarimeter” (1973). The parameters a,, B,, and K were determined using both a Polaroid, (Zeiss) and a Clan polarizer (Bernherd H&e) with identical results. Both 6, and K appeared to decrease
=
4J,(S,)K/r
1 25,(6,,)
formula,
Equation
instrumental
10)
-
is calibrated. (19),
We which
at which the
then
obtain
shows
CD, must be corrected.
00s 2/?, sin ~(1 + cos 8,)&Q
+ CD,
cos
-
W.
sin
4
+
cos
(19)
In 10 00s ~/77
6,, and ~~ refer to the wavelength instrument
In 10) -
(J,(s~)~/J,(s~,)I~
(17)
28, sin ~(1 + cos 6,)/2]
ot,
is finally rectified and appears on the recorder after further
2 cos K sin 8, + AC]}
CDr =
sin (to sin wt) of as
AC]/
+ cos 6,) -
i
(16) will then give a zero
J,(60) being the first Bessel coefficient.
CD = logI
(16)
V$2/Vjj;laI
The signal at D proceeds to the main amplifier frequency
from ICD] =
ot) + cm 219,sin K cm (6, sin 41 tgh(yb,)[cos 28, sin K]i(l + cos 6,)
[AC cos 28, sin K &l which
dwt
dichroism,
K sin (6, sin
AC = Itgh(yb,)I[AC cos 2Bo sin K +( 1 + cos 6,) ICD
D, Equation
absolute,
integration
is now
obtained
(15)
by
The intensity thus obtained is given by
1 -
cot)
averaged
matrices.)
-tgh(yb,)[cos
sinh (yb,)[oos K sin(60sin
where the numerator is the denominator circular
VAC -=
we derive, in
the
signal to be observed at point
W&3
is more
expanded by its factor e_rR into a sum of operator
VD
(ll),
-t cos 28, sin K cos (6, sin ot)]
in the
&
matrix
From this Equation
I = e-Yc[cosh (75,) -
photo-
first element
K)&‘, (5).
the
(15).
analogy with Equation
and we can assume
HOW%
CD,
how
the the
1w
during about 2hr after starting the instrument, so all experiments had to be done after a heating time of at least 2hr. Epiandrosterone was obtained in 1968 from Jouan Q&tin Ltd, Yeris, with the specification AE = 3.30 M-1 cm-‘.
On the problem of obtaining The oscilloscope, Techtronix 602A Dual beam, was triggered by using the sinusoidal voltage from the oscillator for the Pock&’ cell. It was calibrated internally, but also by using a Weston element.
WXUIXM
721
dichroism
oirculm
-16
100 -
RESULTS Equation
(19) is valid
D is linearly
point
deflection, are picked
up (otherwise was found
V dc
relevant
accurate
pass of the main
frequencies
(18) and
are depicted,
(19)
of the instrument within
1 ‘A for the
for CD studies. amplifier
Fig. 2, where the transmitted
at
recorder
or even harmonics
Equation
The linearity
scrutinized band
to the
and if no overtones
must be modified). range
if the AC component
transformed
The narrow
is illustrated
intensities
2
in
Wavelength.
at different
as observed
A
at point
nm
Fig. 3. Static birefringence, K, and phase lag amplitude, S,, estimatedat different wavelengths ona J-40 spectrometer, by means of Equations. (12-14).
is inserted at D.
when a signal from a tone generator
voltage
cell, which was also con-
of the Pockels’
firmed by direct measurement As
expected,
obtained
.il_/
The shorter
birefringence
wavelengths,
Equation
Hz
Ae(M-r
length
for the instrument
at different wavelengths.
dependence
should
be
(17)
has been
dichroism
to
an
inaccurate programming function for the excitation
AF (31-i cm-l)
2( f )DICo(enhlC1~*
Ae instr 1.91 * 0.07
3.23 f
at
0.04
cm-l)
= 3.21 f
(491 nm),
instead
on
to
O-03
the
(calibration
the
as CD
standard
the
:
0.03 (304 nm) and 1.79 &-
respectively.
The
instrument
necessity
been
of
of both
304 nm is explained
knowing
6, and
corresponding recorder
yield
the
K. The
wavelength agreement
calibrated
As from V,, eq. (17)
l-84
1.79 f 0.04
3.21 f
at
by the fact that the instrument
A& from A&i,,,, by eq. (19)
3.23
yield
suitable
3.23 + 0.03 and 1.91 & 0.07, thus illustrat-
dependence had
applied
and 2[Co ens]Cl,*NaC1~6H,O
NaCl.GH,O
Epiandrosterone
was 300-
3) increases
with
epiandrosterone.
Table 1. sample
&
for transparent
of two samples,
epiandrosterone
deflections ing
The wave-
attributed
K (Fig.
as expected
from Roussel-Jouan)
Fig. 2. Filter effect in the electronics. Appearing intensity at point a for V,o of varying frequency at point D (12 mV). Figure 3 shows the 8, obtained
same (between
matter.
soo standards:
in question
the
wavelengths
&, = (4.6 & 0.6)‘. static
_ circular
,
on the programmer.
approximately
at different
860nm):
4k, Frequency
600
600
400
As Literature (references)
1.89 1.91 1.95 1.82
(a) (b) (c) (d)
3.29 3.34 2.96 3.04
(e) (f) (g) (h)
0.03
(a) = [9], (b) University of Copenhagen, Jouan, 1968, [(c) 19641, (d), (g), (h) Teohnical University of Denmark, Lyngby, Jouan, [lo] [(d) (h) 1974, (g) 19731, (e) Jouan--&u&in substance lot specification, (f) = [4].
If
A. DAVIDSSON and B. NORDEN
722
the AE from the recorded CD at 491 nm is corrected
with wavelength
by means
constant,
of Equation
with that above from
(19) a As more agreeing Equation
(17), Table
1 is
in such a way that ac/(a -
c) is
one also knows that the induced phase
lag amplitude,
a,,, is constant.
obtained. DISCUSSION We
have
Pockels’
above
taken
for
granted
that
the
cell is correatly oriented with respect to
the z-axes (with its induced optic axes &x/4 the z-axis).
from
Small deviations are difhcult to detect,
but as has been shown in Ref. [l] their influence on the CD output can in general be neglected. ever, the possibility
of such a deviation,
How-
say with
an angle w from ~14, should be kept in mind when the photomultiplier
output
CD determina tions.
(The alternating
will in principle COB2w.)
then
is used for absolute
be reduced
component
by the factor
The fact that the BE obtained by means
of Equation
(17) is somewhat lower than the value
from Equation
(19) may be explained by such an
effect, but also by a stray light effeot. The
fact
that
birefringence
we have neglected
may
be worth
sample
discussing.
If
cell
entrance window exhibits a small birefringence the CD is approximately
obtained
from
a certain cell is to be used permanently,
p. one
can of course include p in the static parameters
K
and &, ifit is possible to perform the determination with the polarizer between the entrance and exit cell windows. made (e.g.
A more
by comparing camphor
convenient
acid in isotropic
PVA)
inside (CDi) and without (CD,) the cell, respectively:
p = arccos (CDJCD,)
present
study
[4].
The cell used in the
was found free from birefringence
by this method. In
Fig.
pictures
4
we
summarize
of the signal from
some
oscilloscope
the photomultiplier.
Before any detailed calculations are done one can get
qualitative
information
about
the
optical
function. If the cosinoidd curves obtained with a polarizer at 0 or 7112do not limp (i.e. if a = b and c = din Fig. 4), there is no static birefringence (i.e. K = 0). Furthermore, if these curves are invariant
I ?r
I 27
wt Fig. 4. Oscilloscope pictures (point D) for different cases: Polarizer with vertical position (cc = 0), a = ACO.~“, b = AC%-“2 (a, b w 600 mV), horizontal position (a = a/2), G = ACDIB*“‘, d = AC’l’*-“l* (c, d w 300 mV).
Polarizer at position
a,, (in the present
study 47”), e = AC% (e w 4 mV). Solution with representative circular dichroism (f = 40 mV).
check of p is
the CD of a film standard
sulphonic
0
p,
the re-
corded circular dichroism, CD,., by CD = CD&OS When
1
the
REFEREBCES M. LE~IUND and M. GROSJEAN, PI L. VELLUZ, Optical Circular Dkhroiam Academic Press. ew York, 1966. d. DAVIDSSON and B. NORD~N Chem. Ser. 8, (1975). r.31 d. DAVLDSSON and B. NORDI~N, Chm. Phya. Lett.
PI
28,39, 221, (1974). Acta Chem. Stand. 27, 4021, (1973). r41 B. NORD~N, Cambridge Phil. SW. 9, 399, r.51 G. STOICES, Traw. (1962).
PI M. J. WALKER, Amer. J. Phys. 22, 170, (1954). [71 N. GTj, J. Phys. Sot. Japan, 25, 88, (1967). PI T. C. TROXELL and H. A. SCHERAQA, AIacromolecule.3 4, 619, (1971).
PI A. J. MCCAFFERY and S. F. MASON, Molec. 6, 369, (1963). [lo]
H. P. JENSEN, Personal communication.
Phys.
On the problem of obtaining accurate cirqdar dichroism. Calibration of circular dichroism spectrometers b
DA~IDSSON and BENQT NORDEN
Inorganic Chemistry I, Chemical Center, University of Lund, P.O.B. 740, S-220 07 Lund 7, Sweden (Received 22 March 1975) AbstractIt is questioned whether common circular dichroim (CD) spectrometers can be relied upon if they are calibrated at a single wavelength only. A procedure for obtaining the influence of certain instrumental parameters is described, and relations are given to correct the CD. This discussion was found relevant on examination of a particular commercial CD spectrometer for which fairly large corrections were necessary. It is suggested that the different values reported for two common CD standards may bo explained by errorsof the type considered, in different instruments.
INTRODUCTION Circular dichroism
(CD) is easily measured by the
GROSJEAN-LECRAND [l] method, polarized some
light
audio frequency, a
circularly
sinusoidally
modulated
o/237, from
circularly polarizations. leaving
in which linearly
is electro-optically
at
left to right
The intensity of the beam dichroic
at frequency
sample
w/2x.
will
From
vary
the ratio
Lqht scuce
Momxh-
romator
Modulatw
-3mple
between the amplitude of the intensity modulation and the unmodulated obtained
intensity
electronically.
the CD
The fact
is then
DC on!!?
mccfdcr
t.hat the light X
beam during a large fraction of the period (2r/w) will not be circularly polarized makes the instrument
sensitive
to
linear
dichroism,
as will
discussed in papers concerning the adaption
be
t
of a
-1
CD spectrometer for linear dichroism studies [2-41. non-ideal
optical modulation
on the accuracy
of
CD measurements. FUNCTION OF INSTRUMENT The principles of a representative eter are sketched instrument
(Jasco
in Pig.
la.
J-40)
the
linear
with the monochromator,
polarized
with
(Fig. lb).
The modulator
electric
CD spectrom-
vector
polarizer
is
giving
light
parallel
to y
(Pockels’ cell) is excited
by an AC voltage, Vo sin wt, with a frequency, w/2a = 370 Hz. By the phase difference between this voltage
and the modulated
photomultiplier
signal from
the
the sign of the CD is determined
in a synchronous rectifier.
S.
6%8i M
The light intensity after
P
Qk 2
In this particular
combined
the
R
Y
In the present report we scrutinize the influence of
Fig. 1. (a) Principles of a modern CD instrument. (b) Instrumental coordinate system. The light is propagated along the positive z-axis. S symbolizes the light input, R, M, P are different optical elements (retardation plate, sample solution, linear polarizer) which may be inserted in the light path. imposed
by an AC component.
The DC level is
kept at a constant value, Vnd~, independent
passage of a sample exhibiting CD gives rise in the
multiplier high tension.
photomultiplier
(at point D) will therefore be proportional
to an electrical
DC signal super-
of the
total luminous flux, by a servo control of the photo-
717
The alternating signal VAc to the
A. DAVIDSSON
718 ratio
between
the
light intensities. is the Pockels’
modulated
and
unmodulated
The crucial part of the instrument cell.
A certain applied voltage V,,
andB. NORDEN (1).
S describes the positive definite instantaneous
S = (En2 + Eu2, 2E&
00s 6, 2Esv
Ez2 -
corresponds to an induced phase lag 6, for light of a certain wavelength
and polarization.
To keep
sin 8,
components
Ev2}t
(1)
of the electric vector, E,, E, along the
6, constant, V,,( 2) must follow a certain wavelength
x and y axes (Fig. lb), and 6 is the relative phase
program [I].
difference between E, and E,. The action of an optical element (R, M or P) on the light introduced
THEORY The following treatment Jasco CD Spectrometer, any other instrument
is obtained by multiplying
with an operator (fi, 2
is worked out for the
but should also apply to
using the Legrand-Grosjean
principle. We adopt the nomenclature
f%rst introduced by
or $),
and the appearing
light is described by a new S matrix, $S.
For example,
S
&,
%S
or
with all elements as in Fig. lb,
the light appearing from P would be l%?l%J.
The
optical elements of interest are the following:
R is
STOKES [5] i.e. that a general light beam can be
the so called Pockels’
represented by a 4 x 1 column matrix where the
with variable induced phase lag, 6, oriented with
f&t
element
is the
intensity,
describe the polarization conveniently
written
state.
and
the
others
This matrix
horizontahy
X is
as in Equation
cell, i.e. a retardation
plate
its optic axes in the xy plane, the principal (slow) The an angle ,9 with the x-axis.
axis forming
corresponding operator, I?, is given by Equation (2). P is a perfect polarizer, oriented
0
/l
(
R(B, 6) =
0
0
sin2 sg + CO822g co9 6
0
co9 2/? sin 6
0
co9 2g sin 2/9(1 -
r-b: from
the
z-axis,
28 sin 6
co9 6 00s 6)
at normal incidence with its axis of extinction an angle
-00s
0
i.e.
the
-sin
sin 28 sin s
is given by Equation
(3).
co9 6)
(2)
28 sin 6
co9 2j3 + sin2 2/I cos 6) 1
at
electric
(4).
LD (decadic (
vector will appear with the angle a to the x axis. 9
\
sin 2/? co8 28(1 -
Similar descriptions
yc = total average absorbance yZ+ = ln 10/2(&,
-
\
Fy) lc
are used
Q(u)= / 1
(
(
sin 2cr
Q
0
COB2a
sins 2a
0
sin 2u co8 2a
0
0
0
sin 2a
0
cos2a
sin2ucos2a
0
\
--In 10/2(&r -
ya, =
-(2n/l)(nr
-
yb, = ln 10/2(&+&o 1
(3)
\ yar = (2”/U~+*so
-
)
~$0
c0s22a
is the pathlength
(4)
n,)Z E_& Q6”)Z
absorbance unit.s) is defined as (E, -
/ .zv) . Z . C (1
in cm, and C the concentration
in M with respect to linearly dichroic species).
by WALEER [6].
A sample M may be represented
according
[7], for the general case that it
exhibits
yb, =
to Gs circular
birefringence
dichroism
(CD)
and
(CB) and linear dichroism
circular (LD) and
E,
and E, axe the absorption coefficients for the electric vector parallel to two mutually orthogonal CD (decadic axes, n and v, in the x, y-plane. absorbanoe units) is consequently
(sr -
sr)
. I . C,
linear birefringence (LB). We adopt the parameters of GG (further developed by TROXELL and
where Edand .+ denote absorption coefficients for left and right ciraularly polarized light. CB (in
SCHERAOA) [8] for the latter phenomena
radians)
(Equation
is 2p(nr -
n,)Z/t
where
ng and
n,. are
719
On the problem of obtaining accurate circular dichroism refractive
indices
polarized light. Equation
(4),
for
left
and
right
y = 271, where
density of molecules.
q is the
(7), where the phase lag
ny. In
/IO
number
0
(
fzxO10
The operator & of the sample
may now be written as in Equation $
&, Equation
circularly
LB is by consequence nn -
(6).
= e--VCe-YD where
0
0
toss
\o
0
sill8
o\
O
-sin8
6 /
COB
1
6 = 6, sin wt is induced by the alternating
b,
0
a3
-a2
b,
-a3
0
aI
\h
a2
H=
In
the
instrument
(5)
1)
If the Pockels’
along
normalized
intensity,
the positive
z-axis.
Assuming
S is given by Equation
(6).
K (radians),
light
= {l,O,
enters the Pockels’
with p = a/4 [Equation &&,
0, -1>t
(8)).
cell exhibits a static birefringence,
with
(6, sin
its principal
ot)}t
(8)
axis forming
an
angle &, with one of the electrically induced optic axes, this effect must be considered by the separate action
This s
excita-
One readily obtains
V,,sincot).
RS = (1, 0, sin (6, sin wt), -cos
monochromatic
linearly polarized light (electric vector parallel to y) propagates
(V =
the S matrix for the appearing light (Equation
0 /
-al
(Fig.
tion voltage
(7)
of a retardation
operator &,,
(6)
yields Equation
cell, which is oriented
reaching
(2)], yielding the operator
plate
and its associated
K), which by means of Equation
the
(2)
(Q), which thus describes the light
photomultiplier
when
no
element
(M or P) is present.
K)fiS = (1, sin 28, sin K sin (6, sin wt) + CO8 2gs sin 2&(1
-
00s K) cos (6, sin wt),
sin (6, sin wt) ~0s K + co8 28, sin K cos (6, sin cat), cos 2/3s sin K sin (6s Sin cut) -
(sin2 28,
+ CO8228, co9 K) cos (6, sin
DETERKNATION OF TEE INSTRUMESTAL PARAXETEES 6,. p,, AND K A polarizer, P, is introduced at an angle, a. resulting light intensity I(a,
ot) = *{I
I(a,
wt)}t
the first element (>
The
D
instruments
(Fig.
on an oscilloscope
lacking a servo regulation
(or, for
of the DC
(3)):
$(a)&&,
Equation
(10).
K)&’ The AC
signal to be observed
ot) is obtained from
+ sin 2a[sin 2& sin K sin (6, sin ot)
la)
in the matrix
from Equation
+ co9 28, sin 2&,(1 - co9 K) cos (6s sin wt)]
+ co9 Ba[cos 2/l, sin K sin(d, sin cut) - (Sin2Z/3, + at point
(9)
2&
C0S2
component:
CO9
K)
the ratio
CO9
(6,
between
Sin
wt)])
the AC
voltages) is then given by Equation
(10)
and DC
(11).
VcW*
Cos K)
2r -
co8 2a(sin2 28, + cosz 2& cos K)] 00s (S, sin ot)}
I
28s sin K) sin (6, sin cot) + [sin 2a co8 2j3, sin 2&( 1 -
:r
s
o ((1 + sin 2a sin 2/J, sin K + cos 2a cos
cos K) -
cos 2a(sin22&
+ oos2 28, cos K)] cos (6, sin ot))dwt
Deter&nation
of 6,.
The polarizer is set in a = 0 and From
the corresponding
oscilloscope
2Vno0 (AC”/2*‘/2 COB8, = 2Vno’J (ACn/2.‘/2 + ACs.-+ACU/2. -
T/Z positions. signals,
the
absolute
differences
Equation
(12), between opposite extrema yield the
value
of 6,.
Equation
AC”*Ut, AC’12BWt, defined
Equation
(12)
_ AC~S’/~) _ ACs.‘jzACni2.n/2 -WI2 (ACU/z*U/z + ACs.U/s)/(AC’/s,-‘12 + ACs.+)/(ACU/s,
412
+ A,-$. -W/s) +
A@.
in
can be derived from
(11).
_ ACOS’/~) + AC0.r/2AC+.‘/2
AC% -X12ACU/‘. -U/“(ACD/%+
(11)
-42)
A. DAVIDSSON
720
andB.
NORDEN
where AC”.“t
= VDc”JV;;/V;;
-
Detewnination of & and K. The polarizer is rotated to the distinct position (CQ, 0 < cc0 < p/2)
at
which
the
oscilloscope
picture gives a pure sinusoidal wave form.
=
sin K cos 28,
IV~~~12/V$j’12
-
(12)
Equation
(13).
By inserting a, cut = 0, ~12 etc. in
Equation
(ll),
one obtains Equation
(14), where
aC was defmed in Equation (12). From the observed Q, AC’12*ri2, ACn/2-“/2~, AC”.n/2, AC”*-fl/”
From
Equation (11) it is redized that co9 (6, sin ot) = 0 in this casa and the amplitude will be given by AC%/Vnos
V;;“/V;c”“I
and the 8, estimated above, Equation give ~~ and K.
V~~-“12/V$~-“~2
= I/sin 6, Vno0[1/(AC”/2’r/2
-
(13) and (14)
1 = 2 sin 6, sin K cos 2(cr, - PO)
ACn12*-Rla) + l/(AC”*R/2 -
(13)
AC’*-“/‘)]
(14)
CIRCULAR DICRROISM If the circular dichroism tropic)
of an ordinary
solution is measured,
Equation
(iso-
negligible birefringence in the sample cell windows, the
output
multiplier
light
intensity
is given
matrix
&(?a,,
defined
in Equation
by
reaching
the
yb,)&l,,
where
(This
easily calculated if the operator 2
is first power
via Equation
AC = IV$/V$
-
(16) from
I = + log,,{[AC
the difference AC
cos 2/l, sin K &(1 + cos So) -
has a filter effect
the
first
retaining
(cot) components
second term in Equation contribution,
while
term
(cf.
only
. V,,.
(r2a.
The
1A&I ZC = ]2yb,/ln 101,
(16)
to be observed on the oscilloscope:
2 cos K sin a01 2 COBK sin 6, -
CD
ground
Results).
The
the
factor
is transformed
Wi(6,)
sin
tgh[(ln 10/2)CD] 1 + @[(hi
amplification.
relation
between
Equation
(18)
The signal gives
the
the real CD and the recorded,
CD,., presuming the gain constant I< to be governed by a correct (“calibrated”)
rosponse at very low
(co9 ~/co8 Ko) . (JI(6,)2/J,(6,,) (COS
,+OS
KO).
10/2)CD][cos
cos K .
lim K CD-O
EXPERIIURNTAL The measurements were carried out on a “Jasco J-40 CD Spectropolarimeter” (1973). The parameters a,, B,, and K were determined using both a Polaroid, (Zeiss) and a Clan polarizer (Bernherd H&e) with identical results. Both 6, and K appeared to decrease
=
4J,(S,)K/r
1 25,(6,,)
formula,
Equation
instrumental
10)
-
is calibrated. (19),
We which
at which the
then
obtain
shows
CD, must be corrected.
00s 2/?, sin ~(1 + cos 8,)&Q
+ CD,
cos
-
W.
sin
4
+
cos
(19)
In 10 00s ~/77
6,, and ~~ refer to the wavelength instrument
In 10) -
(J,(s~)~/J,(s~,)I~
(17)
28, sin ~(1 + cos 6,)/2]
ot,
is finally rectified and appears on the recorder after further
2 cos K sin 8, + AC]}
CDr =
sin (to sin wt) of as
AC]/
+ cos 6,) -
i
(16) will then give a zero
J,(60) being the first Bessel coefficient.
CD = logI
(16)
V$2/Vjj;laI
The signal at D proceeds to the main amplifier frequency
from ICD] =
ot) + cm 219,sin K cm (6, sin 41 tgh(yb,)[cos 28, sin K]i(l + cos 6,)
[AC cos 28, sin K &l which
dwt
dichroism,
K sin (6, sin
AC = Itgh(yb,)I[AC cos 2Bo sin K +( 1 + cos 6,) ICD
D, Equation
absolute,
integration
is now
obtained
(15)
by
The intensity thus obtained is given by
1 -
cot)
averaged
matrices.)
-tgh(yb,)[cos
sinh (yb,)[oos K sin(60sin
where the numerator is the denominator circular
VAC -=
we derive, in
the
signal to be observed at point
W&3
is more
expanded by its factor e_rR into a sum of operator
VD
(ll),
-t cos 28, sin K cos (6, sin ot)]
in the
&
matrix
From this Equation
I = e-Yc[cosh (75,) -
photo-
first element
K)&‘, (5).
the
(15).
analogy with Equation
and we can assume
HOW%
CD,
how
the the
1w
during about 2hr after starting the instrument, so all experiments had to be done after a heating time of at least 2hr. Epiandrosterone was obtained in 1968 from Jouan Q&tin Ltd, Yeris, with the specification AE = 3.30 M-1 cm-‘.
On the problem of obtaining The oscilloscope, Techtronix 602A Dual beam, was triggered by using the sinusoidal voltage from the oscillator for the Pock&’ cell. It was calibrated internally, but also by using a Weston element.
WXUIXM
721
dichroism
oirculm
-16
100 -
RESULTS Equation
(19) is valid
D is linearly
point
deflection, are picked
up (otherwise was found
V dc
relevant
accurate
pass of the main
frequencies
(18) and
are depicted,
(19)
of the instrument within
1 ‘A for the
for CD studies. amplifier
Fig. 2, where the transmitted
at
recorder
or even harmonics
Equation
The linearity
scrutinized band
to the
and if no overtones
must be modified). range
if the AC component
transformed
The narrow
is illustrated
intensities
2
in
Wavelength.
at different
as observed
A
at point
nm
Fig. 3. Static birefringence, K, and phase lag amplitude, S,, estimatedat different wavelengths ona J-40 spectrometer, by means of Equations. (12-14).
is inserted at D.
when a signal from a tone generator
voltage
cell, which was also con-
of the Pockels’
firmed by direct measurement As
expected,
obtained
.il_/
The shorter
birefringence
wavelengths,
Equation
Hz
Ae(M-r
length
for the instrument
at different wavelengths.
dependence
should
be
(17)
has been
dichroism
to
an
inaccurate programming function for the excitation
AF (31-i cm-l)
2( f )DICo(enhlC1~*
Ae instr 1.91 * 0.07
3.23 f
at
0.04
cm-l)
= 3.21 f
(491 nm),
instead
on
to
O-03
the
(calibration
the
as CD
standard
the
:
0.03 (304 nm) and 1.79 &-
respectively.
The
instrument
necessity
been
of
of both
304 nm is explained
knowing
6, and
corresponding recorder
yield
the
K. The
wavelength agreement
calibrated
As from V,, eq. (17)
l-84
1.79 f 0.04
3.21 f
at
by the fact that the instrument
A& from A&i,,,, by eq. (19)
3.23
yield
suitable
3.23 + 0.03 and 1.91 & 0.07, thus illustrat-
dependence had
applied
and 2[Co ens]Cl,*NaC1~6H,O
NaCl.GH,O
Epiandrosterone
was 300-
3) increases
with
epiandrosterone.
Table 1. sample
&
for transparent
of two samples,
epiandrosterone
deflections ing
The wave-
attributed
K (Fig.
as expected
from Roussel-Jouan)
Fig. 2. Filter effect in the electronics. Appearing intensity at point a for V,o of varying frequency at point D (12 mV). Figure 3 shows the 8, obtained
same (between
matter.
soo standards:
in question
the
wavelengths
&, = (4.6 & 0.6)‘. static
_ circular
,
on the programmer.
approximately
at different
860nm):
4k, Frequency
600
600
400
As Literature (references)
1.89 1.91 1.95 1.82
(a) (b) (c) (d)
3.29 3.34 2.96 3.04
(e) (f) (g) (h)
0.03
(a) = [9], (b) University of Copenhagen, Jouan, 1968, [(c) 19641, (d), (g), (h) Teohnical University of Denmark, Lyngby, Jouan, [lo] [(d) (h) 1974, (g) 19731, (e) Jouan--&u&in substance lot specification, (f) = [4].
If
A. DAVIDSSON and B. NORDEN
722
the AE from the recorded CD at 491 nm is corrected
with wavelength
by means
constant,
of Equation
with that above from
(19) a As more agreeing Equation
(17), Table
1 is
in such a way that ac/(a -
c) is
one also knows that the induced phase
lag amplitude,
a,,, is constant.
obtained. DISCUSSION We
have
Pockels’
above
taken
for
granted
that
the
cell is correatly oriented with respect to
the z-axes (with its induced optic axes &x/4 the z-axis).
from
Small deviations are difhcult to detect,
but as has been shown in Ref. [l] their influence on the CD output can in general be neglected. ever, the possibility
of such a deviation,
How-
say with
an angle w from ~14, should be kept in mind when the photomultiplier
output
CD determina tions.
(The alternating
will in principle COB2w.)
then
is used for absolute
be reduced
component
by the factor
The fact that the BE obtained by means
of Equation
(17) is somewhat lower than the value
from Equation
(19) may be explained by such an
effect, but also by a stray light effeot. The
fact
that
birefringence
we have neglected
may
be worth
sample
discussing.
If
cell
entrance window exhibits a small birefringence the CD is approximately
obtained
from
a certain cell is to be used permanently,
p. one
can of course include p in the static parameters
K
and &, ifit is possible to perform the determination with the polarizer between the entrance and exit cell windows. made (e.g.
A more
by comparing camphor
convenient
acid in isotropic
PVA)
inside (CDi) and without (CD,) the cell, respectively:
p = arccos (CDJCD,)
present
study
[4].
The cell used in the
was found free from birefringence
by this method. In
Fig.
pictures
4
we
summarize
of the signal from
some
oscilloscope
the photomultiplier.
Before any detailed calculations are done one can get
qualitative
information
about
the
optical
function. If the cosinoidd curves obtained with a polarizer at 0 or 7112do not limp (i.e. if a = b and c = din Fig. 4), there is no static birefringence (i.e. K = 0). Furthermore, if these curves are invariant
I ?r
I 27
wt Fig. 4. Oscilloscope pictures (point D) for different cases: Polarizer with vertical position (cc = 0), a = ACO.~“, b = AC%-“2 (a, b w 600 mV), horizontal position (a = a/2), G = ACDIB*“‘, d = AC’l’*-“l* (c, d w 300 mV).
Polarizer at position
a,, (in the present
study 47”), e = AC% (e w 4 mV). Solution with representative circular dichroism (f = 40 mV).
check of p is
the CD of a film standard
sulphonic
0
p,
the re-
corded circular dichroism, CD,., by CD = CD&OS When
1
the
REFEREBCES M. LE~IUND and M. GROSJEAN, PI L. VELLUZ, Optical Circular Dkhroiam Academic Press. ew York, 1966. d. DAVIDSSON and B. NORD~N Chem. Ser. 8, (1975). r.31 d. DAVLDSSON and B. NORDI~N, Chm. Phya. Lett.
PI
28,39, 221, (1974). Acta Chem. Stand. 27, 4021, (1973). r41 B. NORD~N, Cambridge Phil. SW. 9, 399, r.51 G. STOICES, Traw. (1962).
PI M. J. WALKER, Amer. J. Phys. 22, 170, (1954). [71 N. GTj, J. Phys. Sot. Japan, 25, 88, (1967). PI T. C. TROXELL and H. A. SCHERAQA, AIacromolecule.3 4, 619, (1971).
PI A. J. MCCAFFERY and S. F. MASON, Molec. 6, 369, (1963). [lo]
H. P. JENSEN, Personal communication.
Phys.