Deuteron magnetic resonance in liquid crystals : the interplay of molecular ordering and conformational changes

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Deuteron magnetic resonance in liquid crystals : the

interplay of molecular ordering and conformational

changes

B. Deloche, J. Charvolin

To cite this version:

B. Deloche, J. Charvolin. Deuteron magnetic resonance in liquid crystals : the interplay of molecular

ordering and conformational changes. Journal de Physique Lettres, Edp sciences, 1980, 41 (2),

pp.39-42. �10.1051/jphyslet:0198000410203900�. �jpa-00231716�

Deuteron

_magnetic

resonance

in

liquid

_{crystals :}

the

_interplay

of

molecular

_ordering

and

conformational

_changes

_(*)

B. Deloche and J. Charvolin

Laboratoire de _Physique des Solides (**), Université de Paris-Sud, 91405 _Orsay, France (Re~u le 15 novembre _{1979, accepte} le 29 novembre ₁₉₇₉₎

Résumé. 2014 Un

examen des résultats de résonance _magnétique des deutérons dans différents _{systèmes thermotropes}

remet en _question

_{l’interprétation}

récemment _proposée par Bos et Doane suivant

_laquelle

_(i) la conformation molé-culaire

_moyenne

ne _{change pas} avec la

_{température,}

même aux transitions de _phase, et _(ii) les _mésophases uniaxiales et biaxiales

_(Smc)

sont _{respectivement} caractérisées par deux et trois _paramètres d’ordre.

_{Quelques contre-exemples}

indiquent

que ces

_points

ne sont _pas

_généraux

et, dans certains cas, ambigus. Le rôle des _changements

conforma-tionnels ne _peut être

_négligé.

Abstract. 2014 Examination of deuteron

magnetic

resonance data in different

_thermotropic

_systems calls into ques-tion the _{explanation recently}

_proposed

_by Bos and Doane wherein _{(i) the average molecular} conformation does

not _change with _temperature, even at _phase transitions, and _(ii) uniaxial and biaxial _{(Smc) mesophases} are charac-terized _by two and three molecular order _{parameters, respectively.} Some _{counter-examples} indicate that these

points

are not

_general,

and in some cases

_ambiguities

are _present in their _analysis. The role of conformational

changes cannot be

_neglected.

Classification

Physics Abstracts 61.30; 76.60

The use of deuteron

_magnetic

resonance

(DMR)

to

study

the molecular

_dynamics

of

_{liquid crystals}

has increased

_during

recent _years

_[1-7].

The method is

very

specific :

DMR

spectra

of deuterated

liquid

crystals

exhibit well-resolved

_quadrupolar

doublets which characterize the motional

_averaged

orientation of each C-D bond in the molecule. With the flexible mesogens studied until now, two contributions to the motional

_averaging

are

_{anticipated :}

molecular confor-mational

_changes

and motion of the molecule as a

whole. In

_general

the number of orientational order

parameters

required

is

_considerably

_greater

than the number of

_{independent quadrupolar splittings}

which

can be measured. In order to

_simplify

the

_quantitative

interpretation,

a

_currently

used

_{approximation}

is to

describe the molecular orientational order relative to

the director

_by

a

_single

order tensor S common to the

entire mesogen. Then any

splitting bvi

of a deuteron

_D,

may be

simply expressed

in terms of the different

components

A,

B, ...

of this tensor

_{[8] :}

bvj(T) = a~(T)

A(T)

+

_&,(r)

_B(T)

+ °

(1)

(*) Part of this work has been presented at the Seventh Interna-tional _{Liquid Crystals} Conference (Bordeaux 1978).

(**) Laboratoire associe au C.N.R.S.

where

_{ai(T), bi(T),}

..., are averages over the

confor-mational

_changes.

If there are N

_independent

molecu-lar order

_parameters,

then

_they

_may be extracted from the

_splittings

of N + 1 different sites so that one

splitting

may be connected to N others

_by

a linear

relationship.

When

_only

two order

_parameters

are

required,

this linear

_equation

_may be written :

where the

_conformation

constants _c~ and Ck

depend

on the conformational _averages, the a’s and b’s.

Following

such an

_approach,

Bos and Doane

_[9]

recently

concluded that the

_conformation

constants of

complex

mesogens are

independent

of

_temperature.

They

found that ratio

_plots,

such as

_~/5~

vs.

_~/5~,

are

_{always straight}

lines in a

_system

_having

_nematic,

smectic A and smectic B

_phases

_(so

that’the

tempera-ture

_dependence

of one

_splitting

can be determined

from two

_others).

Furthermore a

discontinuity

in the

corresponding

linear

_{ratio plot}

at a nematic-smectic

C transition was

interpreted only

as the manifestation

of the need to introduce a third molecular order

parameter.

This

_procedure

allowed the authors to

draw conclusions about the invariance of the average

conformation of the molecule

_throughout

the entire

mesomorphic

range and the

necessity

of

using

two

L-40 JOURNAL DE _{PHYSIQUE -} LETTRES

or three order

_parameters

for uniaxial or biaxial

(smectic C) mesophases.

One may ask if this

simple

description

is reliable and

_{general, irrespective}

of the

nature of the _{mesogen. In} this _paper we _present a

detailed

_analysis

of the behaviour of different ratio

plots

which conflicts with the Bos and Doane

inter-pretation.

We

_emphasize

the

_complexity

of

_dynamical

process

underlying

the DMR data of

_currently

studied

mesogens.

The

_proposed

_{correspondence}

_[9]

between the symmetry of the

_mesophase

and the number of order

parameters required to

_specify

the

_{splittings bvi(T)}

is not

_general.

This is

_clearly

illustrated in

_figure

1 where we have made a ratio

_plot

(~V2~~1’4

vs.

~3/~4),

similar to the one of Ref.

_{[9], using}

the data on

tereph-thalidene-di-p-d9-butyl-2,6-d2-aniline

or

TBBA-d22

[2].

The

_plot

can be

_approximated

as a

_straight

line in the nematic

phase.

However,

a

discontinuity,

well outside of the error limits of the

_data,

_appears

at the nematic-smectic A transition

_(similar

in

magni-tude to the one observed in Ref.

[9]

at the nematic-smectic C transition of

_{octyloxybenzoic}

acid

_[10]).

On the other

hand,

the

_plot

is continuous at the smectic A-smectic C transition.

Then,

the

_implied

interpretation

is that the number of order _parameters

Fig. 1. - Plot of ratios of deuteron

splittings obtained at different temperatures for _TBBA-d22. The indices of the splittings are

asso-ciated with the position of the _{chain-segment.} The inset shows a

sketch of the data _{(Ref. [2])} from which the splittings were obtained. The magnitude of the indicated error limits results from a statistical

analysis of _{multiple spectra} within the same mesophase.

Fig. 2a) and b). - Two different ratio

plots using splittings obtain-ed from the _compound BOBOA-d19 at various temperatures of the uniaxial smectic A and B _phases. The indices of the splittings are

associated with the _position of the chain-segment.

must be modified at the transition

_involving

no

_phase

symmetry

change,

whereas it remains constant at the transition

_involving

a

_symmetry

_change.

The number of order

parameters

deduced is not

_independent

of the set of

_{splittings bv~}

used in the ratio

_plots.

This is illustrated in

figure

2 where we have studied the uniaxial

smectic A and B

_phases

of

p-butyloxybenzylidene-p-d 1 7-octyl-2,6-p-butyloxybenzylidene-p-d2 -aniline (BOBOA-p-butyloxybenzylidene-p-dI9) [11] using

dif-ferent

_bvi

in the ratios.

_{Contrasting figures}

2a and 2b indicate that the Bos and Doane

_approach

does not

yield

consistent results. Consider the smectic B

_phase,

for

_example.

Two order

_parameters

are sufficient

according

to

_figure

2a

_(the

conclusion in Ref.

_[9]),

whereas a third one is necessary

according

to

_figure

2b. This

discrepancy

reflects the

_{disparate sensitivity}

of the ratio

plots

to the existence of

multiple

order

parameters.

The

_concept

that the _average molecular conforma-tion remains

_unchanged

at

_phase

transitions is not corroborated in some direct observations. Consider the DMR data of

_TBBA-d22,

for

_example.

As indi-cated in Ref.

_[2]

_(see

also the inset of

_figure

_1),

the deuteron

_splittings

of the second and third

_segment

of

the chain remain identical

_throughout

the smectic A range

(bv2(T)

=

8v3(T));

_on

heating

the

_system

into

the nematic

_phase,

two

_quadrupolar

doublets are

observed

_{(~(T~) 7~ 8v3(T)).}

Thus,

unless one modifies the number of order

_parameters,

the _appearance of a

second doublet

_{requires significant changes}

in the molecular conformational _averages at this smectic A-nematic transition. For this

_particular

case,

confor-mational

_changes

_{may be correlated with the} transi-tion between

_{translationally}

ordered and disordered

structures. The same

_type

of

_argument

_may also be used for other

_mesophase

transitions where similar DMR observations have been

_reported

_[7]

_[11].

These difficulties lead us to a critical

_analysis

of the

linearity

of ratio

_plots

such as the one for BOBOA

presented

in

_figure

1 of Ref.

_[9],

i.e.

bv~/bvg

=

C2

bv2/bv$

+ C13

A

Following

the

Bos

and Doane

_analysis,

we look for

the best

_straight

line

_fitting

the ratio of the observed

splittings by

means of a linear

_{least-square regression}

over the entire

_mesomorphic

_range. Such a

_straight

line is found to be characterized

_by

the constants

Fig. 3. -

Comparison of the _experimental and calculated varia-tions of the _{methyl splitting 8v8(T)} of the _{compound BOBOA-d19.} The calculated data were obtained by means of the typical relation

connecting 5vg(7~ to 8v2(?~ and _bv,7(T) when the _splittings varia-tions are assumed to be _{governed by} two order parameters. The calculation procedure is detailed in the text. The characteristic

spectral linewidth is indicated in the Sm A _{phase by} the vertical bar.

~2

= 0.582 and

ë8

= - .1.693. Then the obvious _test

of the

_reliability

of this linear fit

_is,

_going

the other

way

round,

to calculate the _temperature

_dependence

of one of the

_{splittings using}

the

_experimental

values of the two others. We

_attempt

this _process in

_figure

3

for the

_{methyl splitting ~g(~)}

which

_presents

a _very

unusual

_temperature

_{dependence [11]. Although}

the features of the

_experimental

curve are

_reproduced,

it

appears that the calculation does not fit in detail all

the

_experimental

data : the observed

_{discrepancies,}

much

_larger

than the

_spectral

_linewidth,

indicate the determined constants

₇₂

and

_c8

differ from the actual

conformational coefficients

c2(T )

and

_{c8(T )}

which

connect the considered ratios in a

_given

_temperature

range. Moreover, if the two constants are

adjusted

to

_get

a best fit

locally

(in

the

_temperature

_range of

any one

mesophase)

the

disparity

between calculated

and observed

_{8v8(T) persist}

in other

_mesophases.

The

_{irreversibility}

of such a

_procedure

shows that

this

_type

of

_analysis

can

_only

be considered as a

_rough

approximation

of the real

_phenomena.

In fact the lack of

_sensitivity

of the

_{plot presented by}

Bos and

Doane to the variations of the c’s arises

_mainly

from the use of the _very small

splittings ~g [11]

in the

denominator of the

ratios,

yielding extremely

expand-ed scales.

_Figure

3 demonstrates that the ratio

plots

cannot be used to exclude

_changes

in the _average molecular conformation with

temperature

in a

quanti-tative

_analysis

of

_~vi(T).

A

_{precise interpretation}

of the _present DMR data on

thermotropic systems

is not trivial. Since the order

tensor S is

_symmetric

and

traceless,

the

_splittings

for a

mesogen molecule of low symmetry should depend

in

_principle

on five

_independent,

non zero orientational

order

_parameters,

_irrespective

of the _symmetry, uni-axial or

_biaxial,

of the

_mesophase

_(provided

that the

magnetic

field is

_kept

_along

the direction of the mean

molecular

_alignment

_[12]).

Molecular motions more

rapid

than the time scale of DMR

_experiments

_may

effectively

increase the

_symmetry

of the molecule so

that the number of

_required

order

_parameters

is reduced. Under these conditions _any

_change

in this number

_through

the

_mesomorphic

_range is

_necessarily

related to a

_change

in the _average molecular

_symmetry.

So it seems reasonable to

_anticipate

that the number and value of additional order

parameters

in a

_given

mesophase

might

be different for _mesogens from

_quite

different chemical structural classes. The

correspond-ing

effects on the

_{splitting 6vi(T) always}

_appear

inextricably convoluted

with conformational terms

(ai(T),

bi(T)...

in

_Eq.

_(1)).

In view of these

complicat-ing

factors,

one

_simple

_way to

_{interpret qualitatively}

the

_changes

in

_6vi(T)

is to use

_only

the

_principal

order

parameter,

Szz,

and to consider that the conformatio-nal _averages at different molecular sites are

tempera-ture

_dependent

_[11].

Such a

_description

_may be

jus-tified in first

_{approximation by}

the small

_magnitudes

anticipated

for additional order

_parameters.

In the nematic

phase,

for

_example,

the _asymmetry coefficient

L-42 JOURNAL DE _{PHYSIQUE -} LETTRES

AS =

Sxx -

Syy

which has been measured

_[13]

and estimated

_[14]

is very small

compared

to

SZZ

[15].

In a

single

order

_parameter

_approach,

the

_{particularities}

observed in the

_bvi(T)

at

_phase

transitions can be

attributed in

_part

to

_abrupt

_changes

in the value of

Szz

(related

to the

_{thermodynamic}

nature of the

_phase

transition

_[1])

and to

_changes

in the average molecular

conformation

_(related

to

_changes

in the average

orientation of the

_long

axis relative to a

_given

_C-Di

bond

_[11]).

These conformational

_changes,

which

may take

place

in the aromatic

part

as well as in the

aliphatic

part

of the mesogen are corroborated

_by

other

_techniques.

For

_example,

Raman _spectroscopy

shows that the statistical

_weight

of the trans and

gauche

states in the end-chains varies within the nematic

_{phase [16].}

In addition volumetric

measure-ments indicate that the mean lateral area _{per molecule}

increases

_throughout

the smectic _range

_[17].

Corres-ponding

changes

in the _{mesogen average} conforma-tion would be

expected.

The existence of several order _parameters cannot be

ignored

even in uniaxial

mesophases.

From the

examples quoted

above it is clear that the use of

ratio

_plots

does not allow one to determine

_reliably

the exact number and the

_magnitude

of the order

parameters.

A

_{thorough analysis necessarily implies}

the

_{investigation}

of

_multiple

interactions on the same

chemical group or

_rigid

_segment

of the mesogen

_by

means of more

_{sophisticated}

_techniques

such as the

ones

recently

developed

in Ref.

[13]

and

[18].

The authors are _very

_grateful

to Dr. E. T. Samulski

(Storrs,

Connecticut)

and to Professor M. Bloom

(U.B.C., Vancouver)

for

_stimulating

discussions and

a critical

reading

of the

manuscript.

References

[1] Luz, Z., HEWITT, R. C. and MEIBOOM, S., J. Chem. Phys. 61

(1974) 1758.

[2] DELOCHE, B., CHARVOLIN, J., LIEBERT, L. and STRZELECKI, S., J. Physique Colloq. 36 (1975) C1-21.

[3] EMSLEY, J. W., LINDON, J. C. and LUCKHURST, G. R., Mol.

Phys. 30 (1975) 1913.

[4] DIEHL, P. and TRACEY, A. S., Mol. Phys. 30 (1975) 1917.

[5] BOS, P. J., PIRS, J., UKLEJA, P., DOANE, J. W. and MEUBERT, M. E., Mol. _Cryst. and _{Liq. Cryst.} 40 ₍₁₉₇₇₎ 59.

[6] DONG, R. Y., TOMBUCK, E., WADE, C. E., VISINTAINER, J. J. and _BocK, E., J. Chem. Phys. 66 ₍₁₉₇₇₎ 4121.

[7] HSI, S., ZIMMERMAN, H. and Luz, Z., J. Chem. Phys. 69 (1978)

4126.

[8] If a molecular axes _{system (x,} y, z) can be defined, these terms A, B, C... have to be identified with the _{components S03BC03BD}

(03BC, 03BD =

x, y, z) of the order tensor S defined _by A. _Saupe SAUPE, A., Naturforsh 19 a ₍₁₉₆₄₎ 161 .

[9] Bos, P. J. and DOANE, J. W., Phys. Rev. Lett. 40 ₍₁₉₇₈₎ 1030.

[10] The use of dimerized carboxylic acids to study such subtle

aspects of the smectic-nematic transition should be

questioned ; indeed it is known that the lifetime of these

hydrogen bonded _{configurations} in the nematic _phase is controlled by orientational motions of the molecules

(DELOCHE, B. and CABANE, B., Mol. _{Cryst. Liq. Cryst.} 19 ₍₁₉₇₂₎ 25). This association-dissociation _{process may} be profoundly affected at phase transitions and may in turn, modify the _average molecular conformation. [11] DELOCHE, B. and _{CHARVOLIN, J.,} J. Physique 37 (1976) 1497.

DELOCHE, B., Thesis, University of Paris-XI, Orsay (1978). [12] Luz, Z. and MEIBOOM, S., J. Chem. Phys. 59 ₍₁₉₇₃₎ 275.

(See appendix).

[13] EMSLEY, J. W., LUCKHURST, G. R., GRAY, G. W. and MOSLEY, A., Mol. Phys. 35 ₍₁₉₇₈₎ 1499.

[14] VOLINO, F. and DIANOUX, A. J., Mol. Cryst. Liq. Cryst. Lett.

49 ₍₁₉₇₉₎ 153.

[15] In fact there is one order of _{magnitude discrepancy} between the values of 0394S deduced from ratio plots (P. J. Bos and J. W. Doane : communication _presented at the Seventh

Liquid Crystals Conference, Bordeaux 1978 ; to be publish-ed) and that measured _[13].

[16] DESTRADE, C., GUILLON, F. and _{GASPAROUX, H.,} Mol. Cryst. Liq. Cryst. 36 (1976) 115.

[17] GUILLON, D. and _{SKOULIOS, A.,} J. Physique 38 (1977) 79.

[18] HIGGS, T. P. and MACKAY, A. L., Chem. _{Phys. Lipids} 20