ESR line shapes that are appropriate for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals were calculated by the stochastic Liouville method. Because of the symmetry possessed by vanadyl, the analysis and interpretation of these line shapes was simplified considerably. Spectral line shapes agreed well with experimental spectra of VOAcAc in the nematic liquid crystal Phase V and BEPC. Deviations from Brownian rotational diffusion were noted. A slowly fluctuating torque analysis yielded good agreement with the experimental spectra

Bruno, G. V.

Eastman, M. P.

Lawson, J. O.

English

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Interim Progress Report
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ESR Studies of the Slow Tumbling of
Vanadyl Spin Probes In Nematic Liquid Crystals
m 4
by
Dr. Michael P. Eastman
Dr. Gerald V. Bruno
Dr. Juan O. Lawson
The University of Texas at E1 Paso
El Paso, Texas 79968
MMAY 1577
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Abstract
ESR line shapes that are appropriate for slowly tumbling
vanadyl spin probes in viscous nematic liquid crystals have been
calculated by the stochastic Liouville method. Because of the
symmetry possessed by vanadyl, the analysis and interpretation
of these line shapes is simplified considerably. Spectral line
shapes agreed well with experimental spectra of VOAcAc in the
nematic liquid crystal Phase V and BEPC. Deviations from
Brownian rotational diffusion were noted. A slowly fluctuating
torque analysis yielded good agreement with the experimental
spectra.
1
Introduction
The application of paramagnetic spin labels in a variety of
experiments has resulted in obtaining a wide range of structural
and dynamical information. 1 In particular, the class of complexes
2+
containing the vanadyl ion VO is being used increasingly as a
spin probe. 2 In a recent paper, we have applied the stochastic
Liouville method to calculate ESR line shapes in the slow tumbling
region for vanadyl complexes in an
allows one to extract quantitative
correlation times ( T )in the region
tumbling E9R spectra occur when th,
to a macromolecule (radius 5-50 A)
isotropic media. 3 This analysis
information for the rotational
-10
	
-7
10 -10 sec/rad. These slow
a vanadyl ion is rigidly attached
or when a vanadyl complex is
dissolved in a viscous medium.
Currently, there is much interest in the dynamical properties
of liquid crystals. The purpose of this paper is to study spin
2+
probes in viscous nematic liquid crystals. Because many VO com-
plexes have very nearly axially symmetric magnetic parameters which
is the same degree of symmetry possessed by nematic liquid crystals,
the subsequent theoretical analysis is simplified and the results
are easier to interpret than spin probes with less symmetry. Previous
2+
workers recognized this feature of VO complexes but have encountered
difficulty in the quantitative interpretation of the ESR line
shapes because of the slow tumbling aspects inherent in viscous
nematic liquid crystals. 4 Our approach is to analyse the ESR
line shapes by the stochastic Liouville method as developed by
^	 t
2
PBF for slow tumbling in an anisotropic media 5
Vanadyl acetylacetonate (VOAcAc) was chosen as our vanadyl
spin probe because it has excellent ESR spectroscopic properties
and because it has very nearly axially symmetric magnetic para-
meters. In addition, our previous detailed work with VOAcAc
in a viscous isotropic medium minimized Qxpezimental problems. 	 ..
The nematic mixture Phase V from EM Laboratories was the first
nematogen studied in this work because it is nematic at low
temperatures and has a wide nematic temperature range. A second
nematic liquid crystal, butyl-p-(p-ethoxyphenoxycarbonyl)phenyl
carbonate (BEPC), which is a single component liquid crystal,
was studied, and the results obtained were compared to those
for the Phase V mixture.
3Experimental
Degassed samples of nematic liquid crystals doped with
vanadyl acetylacetonate (VOACAC) were prepared by standard
vacuum line techniques. VOAcAc was purchased from Alfa Products
and recrystallized from acetone. The nematic liquid crystal
butyl-p-(p-ethoxyphenoxycarbonyl)phenyl carbonate (BEPC) was
obtained from Eastman Kodak and recrystallized from methanol.
The nematic mixture Phase V was purchased from EM Laboratories
and used without further purification. VOAcAc concentrations
(_5 x 10 ^M) were low enough so that contributions to the line-
shapes from intermolecular interactions were negligible.
ESR spectra were taken at X band with a Varian (V-4502)
spectrometer system. 100 k Hz field modulation was used with low
enough modulation amplitude that no distortion in lineshapes was
observed. Microwave powers were low enough to preclude saturation
effects. Temperature was controlled by a Varian E-257 variable
temperature unit and measured with a copper-constantine thermo-
couple. The temperature gradiez.t over the active region of the
cavity was 1-2°C. Spectral calibrations were obtained using a
Brucker B-NM-12 gaussmeter or from the hyperfine splitting of
VOAcAc in toluene at 20C.
..•• A
z4
Theory
PBF have developed a method for calculating slow tumbling
ESR line shapes in an anisotropic solvent such as a nematic
liquid crystal. 5 This method is based upon the stochastic
Liouville method6 and is a generalization of the approach of
Nordio and co-workers ? for the motionally narrowed ESR line
	
&b.. ,
widths of a Brownian particle in liquid crystal.. Here, we apply
this general theory to vanadyl spin probes in nematic liquid
crystals. Previous st:dies have given the appropriate spin
Hamiltonian for VOAcAc. 3,8 In particular, the use of axially
symmetric magnetic tensor parameters has been established. The
_11
motionally narrowed line widths (T < 8 x 10	 sec/rad) calculated
with axially symmetric magnetic parameters differ by less than
0.5% from those calculated with completely asymmetric tensor
values. 8 Alsu, our slow tumbling study in an isotropic solvent
showed that the use of axially symmetric: magnetic parameters gave
excellent agreement with experimental line shapes for slow
-11 	 _9
tumbling T _ 8 x 10 -1 x 10 sec/rad. Only with the appearance
of features in the ESR line shapes that are characteristic of a
rigid limit line shape does the use of completely asymmetric
parameters improve the fit to experimental line shapes. 3 Because
VOAcAc aligns itself with the VO bond perpendicular to the
director of the nematic liquid crystal, the rotation about the
VO bond should be relatively fast and thus average the x and y axis
magnetic asymmetry.
-L;e rotational diffusion for a molecule undergoing Brownian
rotation in the presence of a cylindrically symmetric restozirg
15
torque T is described by 
	
at (11,t) ° RV 2 P(i2 ,t) - R ,	 ^ [sinR (T)P(n,t) ]	 (1)
where R is rotational diffusion coefficient, V 2 is the rotational
diffusion operator, and $ is the angle between the molecular Z-axis
(VO bond) and the director. The director is taken to be parallel to
the large do magnetic field. For the axially symmetric VOAcAc, the
simple Maier-Saupe type potential 
U(s) = Y costs
	
(2)
2
is suitable and yields
	
T = - as = 2 Y sinscoss
	
(3)
2
Note that for U(s) =0, Eq.(1) describes the familiar isotropic
Brownian rotational diffusion. VOAcAc, an oblate symmetric top
molecule, has s eq=n/2 so that Y2 is positive.
From Eqs. (1)-(3), the equations for a nematic liquid crystalline
solvent may be obtained as in PBF 5 by adding to the left hand side
of each equation for the isotropic liquid [Eqs. (A.i)-(A.3) in
reference 31.
-i x T 1x2 CL (j) + i z-IX(1 - A)I N(L,L') (-)n L 2 L)(_L  2 L'45 	 O,n	 3	 63 L ,	 CO 0 0n 0 n
x C
	 105 T 1X2 1 N(L,L') ()(-n
L 4 L' CO; n (j)	 (4)O, n (3 ) + L	 CO 0 0 	 0 n
i6
and by changing the right hand side of Eq. (A.1) of reference 3
to be
[(2L+1) II O ]	 0,0(0,s,0)exp[2	
2
A cos s ] sinsds	 (5)
O
where
Ir
I 0= 	 exp[-lf	 2X cos s]sinsds	 (6)
0
and a = -a 2/kT. The absorption line shape Z is now given by
_18	
--Jr
Z" = Im1 0 	(2L+1) [ S ZL ' 0(a)exp[2 
>' 
cos 
z 
s]sinsds]CL (j)
j=1L even	 p
where j refers to the eight allowed transitions.
For anisotropic viscosity,
2 L
i TL 1 CO^ n M = i[TL1L (6+1) + (T11_Tl1)6]C O,n (j)	 (7)
_1	 _1in Eqs. (A. 1)-(A.3) of reference 3 and T = T1, in Eq. (4) above.
TI S is the rotational correlation time about an axis parallel to
the director and T .L refers to an axis perpendicular to the di ;actor.
The equilibrium distribution P O (R) is giver. by
P0 (st) = exp ( a cost s )/472 S exp ( a cos z a) sin sds	 (8)
a
The order parameter S is then
S = <P (0 =SP 2 ( a)P 0 (a) da	 (9)2 
where
P (s) _ V
	
2
2	
3 cos a -1)	 (10)
7Because VOAcAc is a much smaller molecule than the liquid
crystal solvent molecules, the above diffusion equation for a
Brownian particle may be expected to be modified for inertial
effects. 10 One worthwhile modification to these equations involved
the local solvent structure inducing a slowly flucuating torque
on our spin probe. 11-13
The resulting equations explicitly contain inertial effects
to lowest order and correspond to a model in which this torque
flucuates between two values with a lifetime of Tm . These added
equations are of the form 12
i m Tm ]CO,n^p,m + [L(L+1) kI ] z [1Tp+' CO^n, p+l,m +
L
VP— X CO ,n, p-1,m] + [kT 61 ] [V—P m+l CL 	+I im 	O,n,p-1,m+l
jr-p+1	 CLO,n,p+l,m-1] = dp'O dm,0	 (11)
where m=0, 1 and p=0, 1. I is the moment of inertia of the spin
probe. Also
.... R
T m = TL,n ( V & L n	 -1)	 (12)
8Results and Discussion
In order to simulate slow tumbling spectra, one must know
the components of the g and A tensors which occur in the spin
Hamiltonian. These values may vary slightly with solvent. The
Al l and gib components are readily determined from a rigid limit
spectrum. This spectrum was obtained by slowly cooling the liquid
crystal sample through the nematic range with the do magnetic
field turned off and then taking the spectrum at 77 0K. The A 1
and gl values may then be obtained from the isotropic a 0 and go
values gotten from the liquid crystal samples above the nematic-
isotropic clearing point transition temperature. Our values for
the magnetic parameters were essentially the same as those obtained
in toluene. 3,8 For Phase V, A ll _ -184 G, Ai - -68 G, gi, = 1.943,
g1 = 1.982. For BEPC, A 1) = -185 G, A .L = -68G, g I = 1.943, and
g1, = 1.9 8 2.
Experimental ESR spectra were obtained for the nematic range
72 0 to -29 0 C for Phase V and 82 0 to 37 0C for BEPC. All spectra
contained very asymmetric line shapes indicative of the slow
tumbling region. In fact, the isotropic spectra taken just above
the nematic-isotropic clearing point were obviously in the slow
tumbling region. Although there was considerable supercooling
below the nematic-solid freezing point, no d. ;-scontinuities were
observed in the ESR spectra or in their subsequent analysis.
Simulated spectra corresponding to a Brownian particle in a
liquid crystal solvent were calculated from Eq.(7) and Eqs. (A.1)-
(A.3) of reference 3 modified by Eq.(B.3) of reference 3 for non-
secular effects and by Egs.(4) and (5) for an anisotropic solvent.
I
I
9Spectra were simulated by varying essentially only two parameters:
T, the rotational correlation time, and A, which is proportional
to the orienting potential. In general, the effect of increasing
/A/(A is negative for VOAcAc)is to decrease the separation between
hyperfine lines and to decrease the line widths. An increase in
T will generally broaden lines,decrease line separation (in the
slow tumbling region) and increase asymmetry in the lines. Although
the simulated spectra were in reasonable agreement, there were
significant and consistent descrepancies between calculated and
experimental spectra. The calculated high-field "hyperfine lines"
are more narrow than observed experimentally while the low-field
lines were too broad. When Eq.(8) for anisotropic viscosity was
incorporated into the above equations, the simulated spectra were
in very good agreement with the experimental spectra. The spectra
were in this case fit by varying three parameters Tjj , Ty, and A.
It was noted that as the temper--ture was lowered the ratio
of Ty /Tjj increased. Also, the best fits indicated that T11 was
becoming shorter with decreasing temperature. Because these results
seemed implausible, the flucuating torque approach was tried.
This analysis, although approximate, attempts to account for the
small size of spin probe relative to the liquid crystal molecular
size. Here we now incorporate Egs.(12) and (13) into the above
Brownian rotation equations. Very good fits were obtained by
letting &L,0=2 and ^L,n=10(n^i0) and varying two parameters,
T and A. See Table I.
r
f	
I	
+
i
TABLE
Ordering Parameter (S) and
as a Function of Temp
Temp( 0 C)	 Sa'b
69 -0.11
55 -.14
41 -.18
34 -.22
20 -.26
6 -.29
-9 -.33
-26 -.36
a) Obtained from simulated :pec
analysis with &L,0=2 and &L,
b) Calculated numerically from
I
T-i ^
11
Table Ib
Ordering Parameter (S) and Rotational Correlation
Time (T) as a Function of Temperature for BEPC
Temp ( 0 C)	 Sa'b	 Ta(x10 
_9
sec/rad)
81 -.16 0.18
75 -.18 0.25
65 -.20 0.34
56 -.22 0.57
46 -.25 0.91
38 -.28 1.2
a. BEPC liquid crystal. Obtain.:3 from simulated spectra using
flucuating torque analysis with EL,0-2 ar3 &L,n=10 (n^0).
b. Calculated numerically from Eq.(10).
12
Conclusion
The stochastic Liouville method as developed by PBF has been
applied to ;.he calculation of slowly tumbling ESR line shapes for
vanadyl complexes in nematic liquid crystals. Quantitative
information about the ordering and rotational diffusion was
obtained for VOAcAc in Phase V for the nematic temperature range
69 0C (S = -0.11, T = 1.1 x 1.0 10 rad) to -26 0C (S- -.36,
T = 9.2 x 10 9 rad)' For BEPC, the nematic temperature range
81 0C to 38 0 C corresponded to v-lues (S = -0.16, T = 1.8 x 10
_10 sec
rad^
and(S = -0.28, T = 1.2 x 10 
9 
raa)respectively. Deviations from
Brownian rotational diffusion was noticed and unquestionably arose
from the relatively small size of the vanadyl probe. Application
of a flucuating torque model approximated this effect and improved
the fits to experimental spectra.
The success of this approach encourages us to investigate
2+
larger VO probes (which would more nearly minic the liquid crystal
itself) as well as to pursue the study of the highly viscous
smectic liquid crystals.
Also, the quantitative analysis of the spin probe ordering
(and rotational motion) would allow one to monitor the ordering
of liquid crystal subjected to both static and alternating
electri- fields.
13
References
1. "Spin Labelling: Theory and Application", L. Berliner, Ed.,
Academic Press, New York, N.Y., 1976.
2. (a) N.D. Chasteen, R.J. DeKoch, B. Rodgers, and M.W. Hanna,
J.Am.Chem.Soc. 95, 1301(1973); (b) R.J. DeKoch, D.J. West,
J.C. Cannon, and N.D. Chasteen, Biochemistry 13, 4347 (1974);
(c) R.F. Campbell and M.W. Hanna, J.Phys.Chem. 80, 1892 (1976).
3. G.V. Bruno, J.K. Harrington, and M.P. Eastman, J.Phys.Chem.
(in press, June 1977).
4. (a) G.R. Luckhurst, "ESR Relaxation in Liquids", L.T. Muus and
P.W. Atkins, Ed., Plenum Press, New York, N.Y. 1972 Chapter XV.
(b) G.C. Fryburg and E. Gelerinter, J.Chem.Phys. 52, 3378 (1970).
(c) M. Schara and M. Sentjurc, Solid State Commun. 8, 593
(1970).
5. C.F. Polnaszek, G.V. Bruno, and J.H. Freed, J.Phys.Chem.
58, 3185 (1973).
6. J.L. Freed, G.V. Bruno, and C.F. Polnaszek, J.Phys.Chem.
75, 3385 (1971).
7. P.L. Nordio and P. Busolin, J.Chem.Phys. 55, 5485 (1971).
8. R. Wilson and D. Kivelson, J.Chem.Phys. 44, 154 (1966).
9. W. Maier and A. Saupe, Z. Naturforsch A, 13, 564 (1958).
10. G.V. Bruno and J.H. Freed, J.Phys.Chem. 78, 935 (1974).
11. L.P. Hwang and J.H. Freed, J.Chem.Phys. 63, 118 (1975).
12. C.F. Polnaszek, Ph.D. Thesis, Cornell University, Ithaca,
N.Y. 1975.
13. C.F. Polnaszek and J.H. Freed, J.Phys.Chem. 79, 2283 (1975).


ESR studies of the slow tumbling of vanadyl spin probes in nematic liquid crystals

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