EPR relaxation study of a liquid crystal

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EPR relaxation study of a liquid crystal

F. Pušnik, M. Schara, M. Šentjurc

To cite this version:

F. Pušnik, M. Schara, M. Šentjurc. EPR relaxation study of a liquid crystal. Journal de Physique,

1975, 36 (7-8), pp.665-669. �10.1051/jphys:01975003607-8066500�. �jpa-00208300�

EPR RELAXATION STUDY OF A LIQUID ^CRYSTAL

F.

PU0160NIK,

^M.

SCHARA,

^M.

0160ENTJURC

Institute ^« Jo017Eef Stefan _»,

University

^of

Ljubljana, Ljubljana, Yugoslavia

(Reçu

^{le 9}

décembre 1974, accepté

^le

24 février 1975)

Résumé. ²⁰¹⁴ La dynamique moléculaire des phases nématique ^et smectique ^{A de} 4-n-butoxy-

benzilidene-4’-n-octylaniline

^{est évaluée à} partir ^des spectres ^RPE de molécules marquées ^dissoutes.

Les calculs de la moyenne P4 > pour la phase nématique ^ont été étendus à la phase smectique ^A

en utilisant le potentiel de McMillan.

Abstract. ²⁰¹⁴ Molecular dynamics in the nematic and smectic A phases ^of 4-n-butoxy-benzylidene- 4’-n-octylaniline have been evaluated from the EPR data of the dissolved spin ^label probes. ^Calcula-

tions of the average P4 > concerning the nematic phase have been extended using ^McMillan’s potential for the smectic A

phase.

Classification Physics ^Abstracts

7.130 ^- 8.632

1. Introduction. ^-

Liquid crystals

^{have been inten-}

sively

^studied

by

^{NMR in order to collect} information

on molecular

dynamics [1, 2].

^On the other

hand,

dissolved

paramagnetic

^centers have shown them- selves to be useful

[3, 4]

ⁱⁿ

characterizing

^molecular

motion in

liquid crystals [5].

In order to calculate the correlation time charac-

terizing

the rotational molecular motion from the linewidth of the

paramagnetic

^centers dissolved in a

liquid crystal,

^it is necessary ^to know at least the

thermodynamic

averages such

as P2(COS 0) )

^and

P4(COS 0) >,

^{where 0 is the}

angle

between the

long

axis of the molecule and the direction of the

magnetic

field

which,

^{in this}

study,

coincides with the

preferred

direction. The first average is

actually

the orienta- tional order

parameter n >

^{and can} be derived from

hyperfine splitting

measurements. The second average ^must be

computed by

^{the use of a model}

Hamiltonian

describing

the interactions between the molecules. In the nematic

phase,

this calculation has been done

by

Glarum and Marshall

[6]

^{for a VAA}

paramagnetic probe

^{with the}

Maier-Saupe

interaction Hamiltonian.

We extend the calculation from reference

[6]

^to

liquid crystals

with both nematic and smectic A

phases.

The

Hamiltonian, according

^to McMillan’s

theory

^for

the smectic A

phase [7]

and Luckhurst’s Hamiltonian for the nematic

phase [8], completed

^for the smectic A

phase,

^were considered. Our calculations were per- formed for the

paramagnetic probe

^{of VAA} type, with the

hyperfine

^tensor symmetry ^axis

(magnetic

symmetry

axis) being perpendicular

^to the molecular

long ^axis,

and for the

probe

with that axis

parallel

^{to it.}

2.

Expérimental.

^-

4-n-butoxybenzylidene-4’-n- octylaniline (4-8) (1)

^{was examined}

by

^two

spin

^labels.

The first was a cholesterol type one,

spiro (5

^a-choles-

tane-3,2’-oxazolidin)-3’ yloxyl 4,4’ dimethyl (S.L. 1),

and the second was a

spin

^labelled

fatty acid, 2-(3-car- boxypropyl) - 4,4 - dimethyl -

^{2 -}

tridecyl -

^{3 - oxazoli-}

dinyloxyl (S.L. 2). They

^are

schematically presented

in

figure

^{1. The} axes x, y, ^{z are} the main axes of the

hyperfine

tensor, and ^{z is} the

magnetic

symmetry ^axis.

The

(4-8) liquid crystal [9]

exhibits three

liquid crystalline phases : nematic,

^{smectic A} and smectic B

phase.

The transition temperatures ^{for the} pure

sample

^{are :}

isotropic-nematic TIN

⁼

79 OC,

^nematic- smectic A

TNA

⁼

63 °C,

smectic A-smectic B

ÏAB

^{= 48 °C.}

FIG. 1. ^- Formula and principal ^{axes of the} hyperfine ^{tensor of} spiro (5 a-cholestane-3,2’-oxazolidin)-3’ yloxyl ^4,4’ dimethyl (above) ^and

2-(3-carboxypropyl)-4,4-dimethyl-2-tridecyl-3-oxazoli-

dinyloxyl (below) spin probes, ^{where z} stands for the magnetic

symmetry axis for both molecules.

(1) Kindly provided by ^the Liquid Crystal Institute, ^{Kent State} University, ^Ohio.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01975003607-8066500

666

The

samples

^were evacuated and sealed in 2 mm

diameter

glass

^tubes up ^{to a}

height

^{of 5 mm in order to}

keep

^the

temperature gradient

^below

1 °C/cm.

^The temperature ^was controlled to ± ^{0.2 OC. The concen-} tration of the

spin

label molecules in the

liquid crystal

solvent was 0.1

%.

Therefore the

original

^transition temperatures ^{were shifted}

by

^less than 2 °C. The shifted values

TIN

^were used for the reduced tempe-

rature

T/T1N.

The spectra ^{were taken on a} Varian E-9 X-band

spectrometer.

^It should be mentioned that

during cooling

^from the nematic down to the smectic A

phase,

the

magnetic

^{field was raised to 16 kG to avoid line}

broadening

^caused

by

^a

macroscopic

disorientation.

3. The order

parameter.

^-

According

^{to the nota-}

tion in

[10],

^the Hamiltonian for the molecular

interaction, proposed by McMillan,

^can be written in the molecular field

approximation

^as

where

Vo, a

^{and b are constants}

depending

^{on the}

structure of the

liquid crystal molecules, and n ),

z

>, and a >

^are

orientational,

translational and mixed order parameters of these molecules.

The Hamiltonian for the dissolved

spin

^label

molecules,

where the interaction between them is

neglected

because of their _very low concentration

(

^0.1

%),

^{takes the}

following

^form

[ 11 ]

Here the

subscript

^{L denotes}

quantities referring

^to

the

spin

^label

molecules ; and

q

>, ( Q >, and r >

are the order parameters ^{of the}

liquid crystal

^mole-

cules, being

the solution of the selfconsistent

equations

where _p is the

corresponding density

^{matrix :}

and fl

⁼

1/kT. Using

this solution in _eq.

(2),

^the

equivalent

averages for the

spin

label molecules can

be calculated from

with the

density

^matrix PL ⁼

e - O"-/Tr

^e-fJJeL.

During

^our

calculations,

the constant à was fixed to ô ⁼ 0.65

[7]

ⁱⁿ both Hamiltonians

(1)

^and

(2).

^{For the}

constants

Vo

^{and a,} such values should be

chosen,

^so that the

computed

^{and the}

experimental

^transition

temperatures ^{coincide. The model}

gives

^the

experi-

mental transition temperatures ^{for the examined}

(4-8) liquid crystal

^{when a = 0.42. The constants}

VL

^and aL are

adjusted

^to

produce

^the best accordance of the results _{from eq.}

(4a) (solid

^{lines in}

Fig. 2)

^{with the}

measured orientational order

parametér ( nL > (circles

in

Fig. 2).

FIG. 2. ^- The orientational order parameter nL > ^{for S.L. 1} (above) and S.L. 2 (below) ^as functions of reduced temperature.

Circles are measured values and solid lines are calculated results from the model described in the text with the constants VL ^{= 1.4} Vo and OEL ^{= 2.7 a for S.L.} 1, and VL ^{= 0.29} Vo and (XL ^{= 2.7 a for}

S.L. 2. The dashed lines are fits using ^an extended Hamiltonian with

VL ^{= 2.1} Vo, (XL ⁼ 1.23 0e in the smectic A phase, ^and VL = (20.2 - ^19.0 T) Vo in the nematic phase for S.L. 1. The

corresponding values for S.L. 2 are : VL ^{= 0.37} Vo, (XL ⁼ 0.15 a

in the smectic A phase, and VL ⁼ (2.85 - ^2.6 T) Vo in the nematic

phase.

The

agreement

of the calculated solid lines with the measured

points

is excellent in the smectic A

phase,

^but

it is not as

good

in the nematic

phase. Therefore,

a modified molecular field Hamiltonian was assumed :

The new

term k n’ > n’

^{is a} modification of the rotational

potential :

as

suggested by Humphries

and Luckhurst

[8].

The values of Ô ⁼ 0.65

[12]

^{and x = - 0.25}

[8]

were

unchanged.

^{The constants in}

(5)

^were

supposed

to be temperature

independent,

and the values of

Vo

and a were determined

by

^{the same}

procedure.

One can get the Hamiltonian for the

spin

^label

molecule

by adding

^{the term -}

VL K 11’ > 11L

^to

expression (2).

^The parameter

VL

^is

proposed

^{to be}

continuous at

TNA,

^{constant in the smectic A}

phase

and

changing linearly

^with

temperature

ⁱⁿ the nematic

phase (instead

^{of an}

implicitly

introduced temperature

dependence

^{in ref.}

[4, 5]).

4. The linewidth. ^- The width of the line corres-

ponding

^to the transition with the

projection

^{of the}

nitrogen

^nuclear

spin

^{M can be}

expressed [6]

^as

From the measured width of the three

lines,

^the

coefficient B could be obtained. If the motion is slow

compared

^to the microwave

frequency, and,

^{if either}

g ^or A possesses

cylindrical

symmetry, the coefficient B takes the form

[6] :

where a

single spectral density

^{was assumed.} Here coo is the microwave

frequency,

gxx,

Axx...

^{are the main}

values of _g and A tensors in the directions _{x, y,} z

signed

ⁱⁿ

figure 1, g = 1/3

^{Tr g, and}

J(0)

^{is the}

spectral density

^{at zero}

frequency.

Assuming

^the strong collision model of motion and its slowness

(wo

te

1),

^the

spectral density

^can

be written as

where _{’te is} a correlation

time,

and 0 is the

angle

between the

magnetic symmetry

^{axis and the}

magnetic

field direction. The

isotropic

value of the first term in eq.

(8) equals 4/45,

^{so that} eq.

(7)

^can take the form

where _(p represents ^{the ratio}

The constant y for the nitroxide

probe (precisely

^for

the S.L. 1 with _gxx ⁼ 2.008

9,

_gyy ^{= 2.005}

8,

gzz = 2.002

1, Axx

⁼

Ayy

⁼

^{5.8, Azz}

^{= 30.8 G}

[13])

is

equal

^to y ^{= -} 0.68 x

109 G/s.

The

expression

ç is determined

by

the distribution of the

magnetic

symmetry ^axes. The distribution of the molecular

long

^axes

being

^the same, ç takes different

values,

^{if the}

magnetic

symmetry ^{axis is}

perpendicular

^to the molecular

long

^axis

(qJ 1.),

^{or if}

that axis is

parallel

^to the molecular axis

(qJ Il).

A

single

correlation time was used to describe the molecular

motion,

while Luckhurst’s more proper

description [4]

^{involves two} correlation times

(To

and

T2).

^{In the case} of the S.L.

1,

the term in Luck- hurst’s

expression

^{for the} coefficient B

containing

^the

second correlation time _i2, vanishes because of the axial symmetry ^{of A tensor. Thus our}

single

^correla-

tion time _Te is

equal

^to io. But there is a difference in the case of the S.L. 1 : both terms in Luckhurst’s

expression,

^{that with} io ^as well as that with _i2, contri- bute to the relaxation rate ; ^{and one can obtain} eq.

(9) by assuming

io = i2 = te and

summing

^{these two}

terms. A

study

^{where the} temperature

dependence

^of

two correlation times will be derived from the

angular dependence,

^is in progress.

The static contribution to the

linewidth,

qJ.l ^or qJ Il ’

was calculated

separately

^{for both}

spin.

^labels

using

the Hamiltonian

(2)

^{and the}

equivalent improved

^one

with the _proper constants

VL

^and aL. The correlation time Te ^can be evaluated from _eq.

(9).

In

figure

^{3 . I both} averages, qJ.l and _{(p 11,} are pre- sented as functions of the order

parameter n >

^{in the}

nematic

phase,

^where çi is

equivalent

^to the result in reference

[6].

FIG. 3. ^- I. The average, defined in

expression

^{(9), for a molecule}

with symmetry axis of the hyperfine coupling ^tensor being parallel

to the long molecular axis

«p 11),

and that for the case when both axes are perpendicular «(,01.). ^{The two averages are related} by

(,0 1. ⁼

?[3

)j + 5(1 - q

> )2].

^{II. The} temperature dependence of the averages (,01. and (p

for

^S.L. 1 and S.L. 2 respectively. ^{Line a}

is the result of McMillan’s Hamiltonian, ^and line b ^{is the} result with Luckhurst’s correction included:

5. Results and discussion. ^- In order to evaluate the

dynamics

^{of the}

liquid crystal molecules,

^the temperature

dependence

^{of the} coefficient B from eq.

(6)

^is

given

ⁱⁿ

figure

^{4 and}

figure

^{5. The corres-}

ponding

correlation

times te

^are calculated

by

^{the aid}

of the derived function _ç,

given

ⁱⁿ

figure

^{3 . II.}

It should be stressed that there is

qualitative

^diSe"

668

rence in the linewidth parameter

B(T)

variation for the

spin

labels chosen in this

experiment.

The functions _ç from _eq.

(9), characterizing

^{the static}

properties

^{of the}

dissolved

spin

^label molecules in the

liquid crystal

environment do in fact diminish the differences in the calculated correlation times for both S.L.

samples.

The influence of the chosen interaction Hamiltonian

on the final

7:c(T)

results is

negligible,

except ^{in the} nematic

phase

^of the S.L. 1. Here the

change

^is

pri- marily produced by

^the temperature variation of

VL.

The

insensitivity

^{of S.L. 2 to}

changes

of the interaction Hamiltonian follows from the fact that in this molecule the

magnetic

symmetry ^{axis is}

parallel

^{to the}

long

molecular

axis,

^and that the value of the orientational order

parameter

^{and its}

changes

^{are small}

(Fig.

²

below).

FIG. 4. ^- The temperature dependence ^of coefficient B from eq. (5) and correlation time _te (closed circles and solid line) ^for S.L. 1, dissolved in liquid crystal (4-8). Open circles and dashed line represent the correlation time computed using the dashed fit of the orientational order parameter ^from figure ^1. The différence between

both calculations is remarkable only in the nematic phase.

If we try ^to compare the evaluated correlation times of both

labels,

^we find that the average Te values are

twice as

large

for the flexible

fatty

^acid

spin

^label

molecule. In the nematic

phase

the S.L. 2 shows a

thermally

^activated

slowing

down of motion which is continued in the smectic A

phase,

except ^{for small} deviations at the transition temperatures.

The temperature ^variation

of tc

ⁱⁿ the nematic

phase

for the S.L.

1, presented by

^a dashed line in

figure 4,

is calculated

by

^{use of the}

corresponding

^function (p,

given

ⁱⁿ

figure

^{2.2b. In our}

opinion,

^{it is more reliable}

than the solid line

(a)

variation of _’tc,

keeping

^{in mind}

that the same interaction Hamiltonian

provides

^a

good

fit to the

experimental

^order parameter ^data

(b)

ⁱⁿ

figure

^{2. In this case,} the activation

energies

of rotatio- nal motion for the S.L. 1 and the S.L. 2 molecules are

comparable.

FIG. 5. ^- The temperature dependence ^of coefficient B from eq. (5) and correlation time Te for S.L. 2 dissolved in liquid crystal

(4-8).

However,

^a

qualitative

difference in

te (T)

^shows up in the smectic A

phase

^{for the two} S.L. molecules. It

might

^be

explained by supposing

^{the flexible}

fatty

^acid

chain of S.L. 2 conforms with the tail motion of the

liquid crystal molecules,

while the

sturdy

^{S.L. 1}

molecules

adapt

^to the central

rigid

parts.

It should be mentioned that the motion of a flexible chain is more

complex ;

the correlation function is at least a

weighted

^{sum of}

exponential

functions. The rotational motion of the

nitrogen

^{atom can be then}

determined

by

^a distribution of correlation times. The correlation

thne Tc corresponds

ⁱⁿ this model to a

weighted

average ^over the distribution.

The translational order of the smectic A

phase only

allows the differences in the type of motion of the central and tail parts ^{of the}

liquid crystal

^{molecules to}

show _up.

Thus,

these differences are cancelled in the nematic

phase

^{due to} continuous translational

motion, and, therefore,

^the resemblance of the activation

energies

^{in this}

mesophase

^can be understood.

The

shortening

^of Tc with decreased

temperature

ⁱⁿ the smectic A

phase,

^{as detected}

by

^{the S.L.}

1,

^{can be} caused

by phase

transition

anomalies,

^{which are also}

observable,

^{but less}

pronounced,

^{at the}

isotropic-

nematic transition.

The flexible

fatty-acid

^molecules

perhaps

^{do not}

give quite

^{an authentic}

picture

^{of the}

long

axis motion because of their

flexibility.

^{In order to} get ^an

adequate information,

it would be desirable to use a

rigid spin

label molecule with the

long

^{axis of the}

hyperfine

tensor

parallel

^to the molecular

long

^axis.

References

[1] ^{DE GENNES, P.} G., ^The Physics of Liquid Crystals (Clarendon Press) ^1974.

[2] DOANE, ^J. W., TARR, C. E., NICKERSON, M. A., Phys. ^Rev.

Lett. 33 (1974) ^620.

[3] POLNASZEK, C. F., BRUNO, G. V., FREED, J. H., J. Chem. Phys.

58 (1973) ^3185.

[4] LUCKHURT, ^G. R., SETAKA, M., ZANNONI, C., Mol. Phys., ²⁸ (1974) 49.

[5] ZUPAN010CI010C, I., ^et al., Liquid Crystals and Ordered Fluids 2

(1974) ^525.

[6] GLARUM, ^S. H., MARSHALL, J. H., J. Chem. Phys. ⁴⁶ (1967) ^55.

[7] MCMILLAN, W. L., Phys. ^{Rev. A 4} (1971) ^1238.

[8] HUMPHRIES, ^R. L., LUCKHVIST, ^G. R., ^Chem. Phys. ^{Lett. 17} (1972) 514.

[9] MURPHY, J. A., DOANE, ^J. W., Hsu, ^J. J., FISHEL, D. L., Mol.

Cryst. Liq. Cryst. ²² (1973) ^133.

[10] BLINC, R., LUGOMER, S.,

ZEK0160,

B., Phys. ^{Rev. A 9} (1974) ^2214.

[11] LUCKHURST, G. R., Mol. Cryst. Liq. Cryst. ²¹ (1973) ^125.

[12] MCMILLAN, ^W. L., Phys. Rev. A 6 (1972) ^936.

[13] HEMMINGA, ^M. A., ^Chem. Phys. ⁶ (1974) ^87.