Conformational and orientational characteristics of chain molecules placed in a nematic field : n-decane and 1,6-dimethoxyhexane dissolved in 4'-methoxybenzylidene-4-n-butylaniline (MBBA)

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Conformational and orientational characteristics of chain molecules placed in a nematic field : n-decane and

1,6-dimethoxyhexane dissolved in

4’-methoxybenzylidene-4-n-butylaniline (MBBA)

Yuji Sasanuma

To cite this version:

Yuji Sasanuma. Conformational and orientational characteristics of chain molecules placed in a ne- matic field : n-decane and 1,6-dimethoxyhexane dissolved in 4’-methoxybenzylidene-4-n-butylaniline (MBBA). Journal de Physique II, EDP Sciences, 1993, 3 (12), pp.1759-1778. �10.1051/jp2:1993102�.

�jpa-00247936�

Classification Physic-s Ab.itracts

33.25F 36.20C 61.30G

Conformational and orientational characteristics of chain molecules placed in

_a

nematic field

_:

n-decane and 1,6- dimethoxyhexane ^dissolved in 4'-methoxybenzylidene-4-n- butylaniline (MBBA)

Yuji

Sasanuma

(*)

Department ^of

Polymer Chemistry,

Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro- ku, Tokyo 152,

Japan

(Received J8 Maich J993, revised 3 August J993, accepted J September J993)

Abstract.- Conformational and orientational characteristics of n-decane (n-Cjo) and 1,6-

dimethoxyhexane

(1,6-DMH) chains dissolved in _a

liquid crystal 4'-methoxybenzylidene-4-n- butylaniline

(MBBA) have been

investigated.

The two chain molecules,

although having

the _same

number of skeletal bonds, are known _to take

quite

different

configurations

in the isotropic state.

The phase behavior of the MBBA+1,6-DMH system was observed; the initial slopes

pi

and

pf

of the phase boundaries,

representing

the ability of the solute _to disturb the nematic order, _were determined, and compared with those of the MBBA + n-C

jo system. The thermodyna- mic data show that, in the nematic environment, the n-Cjo molecule is _more

rigid

and extended than 1,6-DMH. Deuterium NMR spectra ^of

partially

deuterated MBBA incorporated in the

solutions _were measured, and the orientational order parameters ^{of the solvent} were evaluated.

Using

the Photinos-Samulski-Toriumi (P-S-T) ^{model and the}

single-ordering-matrix

(SOM) model, 2H-NMR quadrupolar splittings and D-D dipolar couplings observed for the perdeuterated

solutes _were analyzed. ^{The results obtained}

by

the P-S-T model indicate that, _even in the nematic phase, the n-Cjo molecule is very flexible _as in the isotropic phase. On the other hand, the SOM analysis _{gave a} consequence that the n-Cjo chain possesses considerable

rigidity.

Thus, it _can be

concluded that the SOM model rather than the P-S-T model afforded results consistent with the

thermodynamic

data. For 1,6-DMH, the P-S-T simulation did not satisfactorily reproduce the D-D dipolar

couplings

observed, while the SOM scheme achieved the good agreement ^{between the} calculations and observations in all the

examples. According

to the SOM

analysis,

the 1,6-DMH molecule, keeping ^{its inherent} conforrnational

preference,

conforms itself _to the nematic field by

taking anisotropic configurations

such _as Link

(g~ tg~

), c.iankshaft

(g~ tg~

and jog

(g~ tttg~

arrangements.

(*) Present address _: Department ^of Polymer

Physics,

National Institute of Materials and Chemical Research (NIMC), I-I

Higashi,

Tsukuba, Ibaraki 305,

Japan.

1. Introduction.

Addition of non-rodlike solute _{to a}

liquid-crystalline

solvent is known to lead not

only

to _a considerable

depression

of the

nematic-to-isotropic (NI)

transition temperature

T~j

^{of the} pure solvent, but also _to formation of _a

two-phase region [I].

A

typical phase diagram

for such _a

binary

system ^exhibits two linear boundaries in the

region

of low solute concentration (see

Fig. 3).

The

ability

of _a solute _to destabilize the nematic

phase

is often

represented by

^the

slopes p~

and

pi

of the

boundary

lines in the reduced temperature ^T*

(= T/Tm)

_i,s, solute

molar fraction >~

diagram.

The former is related _to the

(T(,

>.~)

boundary

where the

isotropic phase

first appears

(completely disappears)

_on

heating (on cooling),

and the latter to the

(Tj*, x~) boundary

where the nematic

phase completely disappears (first appears)

on

heating

(on

cooling)

viz.,

p~

₌

(dT(/~Lr~)

and

pi

₌

(dTj*/~Lr~).

One _can thus consider that, _as the

boundary

^{lines become} steep, ^{the solute} more

strongly

disturbs the nematic order of the solvent. For _a

large

number of solutes of various

shapes

and sizes, values of the

slopes

have been determined, and their effects _on the nematic order have been studied

[1-13].

Figure

shows

la) pi (the p~

value at infinite

dilution)

_i,s.

VI (the

_core volume of solutes

[14])

and

16) p/~

vs.

V( plots

for

binary

_systems

containing

a

liquid-crystalline

Solvent

4'-methoxybenzylidene-4-n-butylaniline (MBBA)

_:

CH~OC~H~CH

=

NC~H~C~H~.

Experimental pi

values of the

globular

solutes _are found _to range from 0.56 to 1.7, while those of the n-alkanes fall within _{a narrow} range between 0.53 and 0.63 therefore, it iS Shown that the

spherical

Solutes _more

strongly

disturb the nematic order than the chain solutes. The

pi

and

p

_/~ values of the

spherical

molecules increase with the core volume, whereas those of the n-alkanes appear to be almost invariant with the chain

length.

In order to elucidate the

phase

^{behavior of such}

binary

systems ⁱⁿ terms of the

shape,

size, and

flexibility

of solutes and

Solvents,

_a

variety

of theoretical _treatments have been

proposed

I -13,

15-20].

In

particular,

the cubic lattice model

developed by

Martire _et al.

[2, 5-8, 12]

has

successfully provided comprehensive

solutions of the

problem.

The solid lines shown in

figure

I,

being

calculated _on the basis of the

anisotropic repulsive

forces II

3],

_represent the theoretical

p~/

_vs.

V(

_curves for cubic

IA

and

B),

Semiflexible

(Cl,

and

completely rigid ID)

solutes. The

experimental

data for the n-alkanes _are found _to be located _{on or} around the _curve

C,

which _was calculated with mj =

6, fj

= 2,

E~j/k

=

400 K, _JJ1~

= t.~ +

f~,

_i~

= 2, and

E~~/k

=

400

K,

where m,, r,, and

f,

_are,

respectively,

the numbers of

total, rigid

_core, and semiflexible segments ^{of the} component ^I

ii

=

I solvent, and I

=

2 _:

solute),

and k is the Boltzmann _constant. One segment ^{is assumed} to

correspond

to three

methylene

units. The parameter

E~,

represents ^the energy ^to make one of the semiflexible bonds bend in a noncore

direction, thus

being regarded

as a coarse measure of the energy difference between the tiafi.I

and

gauche

state.

By

the cubic lattice treatment

including

attractive forces _as well _as steric

repulsions,

Dowell

[8]

also indicated that the theoretical Semiflexible chain with

E~~/kT

^of 1.4 to 1.8 well

corresponds

to n-alkanes in

liquid crystals. According

to Martire and his co-workers

[1,

?, 5-8,

11-13],

in _a nematic field, n-alkane molecules behave as a chain

composed

of two

completely rigid

and _some additional semiflexible Segments.

In the present

study

the

following binary

systems ^have been treated MBBA ₊ n-decane (n-

Cjo)

and

MBBA+1,6-dimethoxyhexane (1,6-DMH).

As described above, the systems

containing

MBBA have been

extensively

Studied. This is the chief _reason

why

MBBA has been

employed

as the solvent in this

study.

Under the rotational isomeric state (RIS)

approximation,

the conformation of n-alkanes in the free state can be

represented by

their

(a)

_2.0

a .5

.

~f -O .

a

a

m° _o

0.5 °

D

o-o

16) 2.0

.6

u

1.2

.

8 .

cdl

~ m D

O-B

~ D

D2

D

~~k...*.

O O

0.4 ^°

o-o

0 50 loo 150 200 250 300 350 400

V~* (Cm3

mot.1)

Fig. I. Correlations of (a) the

slope pi

Of the

(T(,.i~)

line _at infinite dilution and (b) the slope p_{j~ of the} (Tj*, _,r~ line _at infinite dilution with solute molar volume

VI

114] for binary systems containing

liquid-crystalline wlvent 4'-methoxybenzylidene-4-n-butylaniline (MBBA). The wlutes _{are as} follows _: (O)n-alkanes (n-hexane, n-octane, n-dodecane, n-hexadecane, n-eicosane, and n-tetracosane) [3];

(11) branched molecules (from the left _to the right,

cyclopentane,

2,2-dimethylbutane, tetramethyltin,

cyclooctane, 2,2,4-trimethylpentane,

cis-decalin,

hexamethyldisiloxane, 2,2,4.6,6-pentamethylhep-

tane,

2,2,4,4,6,8,8-heptamethyInonane, tetrabutyllead,

tetrabutyltin,

decamethyltetrasiloxane,

and

tetraoctyltin) [3] _; (.) n-alkanes (n-Octane, _n-nonane, n-decane, n-undecane, n-dodecane, n-tridecane.

and n-tetradecane) [I _; (.) branched molecules (from the left _to the right, tetramethyltin, tetraethyltin.

tetrapropyltin,

^and

tetrabutyltin)

[I Ii (x) 1,6-dimethoxyhexane (this

study).

The solid lines represent the theoretical

p(

_i,.I. vt _curves A, cubic solute in solvent trip 5,

fj

I,

E~j/k

=

400 K B, cubic

wlute in solvent mj 6,

fj

2, E~j/k 400 K C, semiflexible solute tti~ = r~ +

f~,

_r~

= 2,

E~z/k=

400K in wlvent trip = 6,

fj

=2,

E~j/k=

400K; D,

completely rigid

solute in solvent trip 6,

fj

2,

E~j/k

=

400 K [13] (see text). See also the

legend

of

figure

3.

geometrical

_parameters and

only

_two

energies E~ (=0.skcalmol-I)

and E,~

(= ?.0kcal

mol-I) [21, 2?].

A 1,6-DMH molecule,

although having

the _same number of

~keletal bonds _{as an}

n-Cii>,

_may exhibit _a

quite

different

configuration

in _a nematic field.

Spectroscopic

and

dipole

moment studies _on

a,~v-dimethoxyalkanes CH~O(CH~),,OCHI

W Q (Q~)

2 4 6 8 lo

~~~~~~~~

2

~ 4

~ 6

~ 8

~

(~cio)

3 5 7 9

a

(aJ

o

(a~)

a

(a~)

w~

a~ °3

~ 6 8 lo

l,6-Dimethoxyhexane

⁹

(1

,6-DMH)

~ ~ 8

3 ~ 9

P °2 °l2

Fig. 2.-Schematic representation of n-decane (n-Cio) and

1,6-dimethoxyhexane

(1,6-DMH) mol-

ecules and the definition of the statistical

weights.

The symbols in the parentheses denote the statistical

weight

factors used in the

single-ordering-matrix

scheme. The skeletal atoms and bonds _are numbered

successively

from one end _to the other.

~,

=

l to

4)

have

proved

that the bonds

adjacent

to the oxygen ^atoms

preferably

take _a

gauche

form

[23].

On the basis of the temperature

dependence

of NMR vicinal

coupling

constants, Inomata _et a/.

[23]

have carried out the conformational

analysis

of

1,4-dimethoxybutane

(1,4-

DMB)

included in solutions. As _a consequence, the first-order interaction

energies

_were

determined _as follows _:

E~

=

1.0, E~j

= 0.2, and

E~~

₌ ^0.3 kcal mol~ ^'

(cyclohexane) E~

=

1.0, E~j

=

0. I, and

E~~

₌ ^{0.3 kcal mol~}

(dimethylsulfoxide DMSO),

the solvents

used in the NMR measurements

being

cited in the

parentheses. According

to Matsuura et a/.

[24],

the OC-CC bonds of

1,4-DMB

and

1,5-dimethoxypentane prefer

to take the

gauche

arrangement ⁱⁿ

liquid,

while these molecules exist in the all-tians conformation in the

crystalline

state.

Experimental

values of the conformational

energies

of

1,6-DMH ijself

have not been

reported

_yet.

Nevertheless,

it should be

possible

to estimate the reasonable values

from those of

1,4-DMB; I-e-, E~=1.0, E~j=-0.2

to -0.I,

E~~=0.3,

and

E~~

₌

0.skcalmol~~ ((or

the notation of the Statistical

weights,

_See

Fig. 2). Here,

the

E,,

value of n-alkanes is

employed

aS

E~~. Similarly,

the Second-order interaction

energies E~i

and

E~~

_can be assumed _to be 0.47 and 2.0 kcal mol-I

[21-23], respectively.

Recent

developments

in deuterium NMR

techniques

enable _us to

quantify

the orientational order of various flexible chains

placed

in

anisotropic

fields

[25]. Photinos, Samulski,

and

Toriumi have offered _an

elegant

^formula for

representing

^the nematic _mean field, and

applied

it to

analyses

of 2H-NMR _{data observed} for n-alkanes in nematic solvents

[26-29],

and monomer

[28, 30],

and dimer

[31] liquid crystals.

In _our

previous study [32],

a simulation scheme based

on the

Single-ordering-matrix representation

_was

developed,

and

applied

to

analyses

^{of 2H-}

NMR

quadrupolar splittings

and H-H

dipolar couplings

of n-alkanes dissolved in

liquid crystals.

The

primary object

of the present

study

is to reveal the effects of the nematic field _on the conformation and orientation of the _two chain molecules,

n-Cio

and

1,6-DMH.

In this work the

following experiments

and

analyses

were carried out. A

phase diagram

for the MBBA

+1,6-DMH

_{system was} made, and

compared

with that for the

MBBA+n-Cjo

system. ^{Deuterium NMR} spectra ^of

partially

deuterated MBBA

incorporated

in the solutions of various solute concentrations _were measured _at different

temperatures,

^{and the} orientational

order parameters ^{of the solvent} were evaluated.

Using

the Photinos-Samulski-Toriumi

(P-S-T)

model and the

single-ordering-matrix (SOM) model,

the 2H-NMR data observed for the _two

solutes _were

analyzed.

In this

article,

the above results _are

reported,

the

validity

and

applicability

of the two

analytical

models _are

examined,

and the conformational and orientational features of the Solute chains _are discussed in relation to their

shape

and

flexibility

estimated from the

thermodynamic

data.

2. Models for conformational

analysis

of solute molecules.

2,I THE PHOTINOS-SAMULSKI-TORIUMI

(P-S-T)

MODEL. In this treatment, the

potential

V

(f1, n)

of the _mean torque ^for a conformer _n is assumed _to be

expressed

as

[26, 28]

N A~-I

V

(f1, n)

=

io jj

P (s~, s~)

ii jj

P (s~, _s~

~

) (I)

j=i j=i

where

f1represents

the orientation of the molecular frame relative _to the nematic

director,

N is the number of skeletal

bonds,

and P (s~,_s~~,,~) =

(3

_cos

0~

cos

0~

~,,~ s~ s~ ~

~,)/2, 0~ being

the

angle

between the

j-th

bond vector

s~ and the nematic director. The coefficients

io

and

ii

are termed the intermolecular

(solvent-solute) coupling

constants. The orientational distribution function

f(f1, n)

for _a

given

orientation and conformation of the molecule is written _as

E(n) ~ i, (n. >,)

f(fl,

_n

=

G(fi)

e ^~~

(2)

f

where ( is the normalization factor, G

(n

is the conformer rotational kinetic energy

factor,

and

E(n)

is the internal

(conformational)

_energy. Then the thermal average

(F)

of _a

quantity F(fl, n)

is obtained

by averaging

_over all orientations and conformations of the solute

molecules that

is,

(F )

₌

£

dfl F

(fl, n) f(fl,

_n

). (3)

,,

Accordingly,

the 2H-NMR

quadrupolar splitting Av,

^{of the C-D bond of the I-th carbon} atom

(hereafter

referred _{to as} the

C,-D bond)

is

given by

API

₌

~~)~ ^{(P2(CDS °~cD~,)) (4)}

where e~

qQ/h

is the

quadrupolar coupling

constant (= ^{163 kHz}

[33]),

and

P~(cos

o

j~~j, ⁼

(3

cos~

₀

~~~~, l

)/2,

0

~~~~,

being

the

angle

between the

C,-D

bond and the nematic director.

The D-D

dipolar coupling D~~,

^{for the} I-th carbon site is

given by

D~~

₌

~~

h

' ~

~2~,3 ~~2(COS

⁰ _~~~~

))

~~

'

(5)

where

y(h/4 ar~=

2.830 _x

l0~Hzl~,

_r~~ is the D-D distance, and

o~~~~,

^is the

angle

between the nematic director and the interdeutron _{vector at} the I-th carbon site. The

probability

p~"I

of the n-th conformer is obtained from

j E(»)

, ^,>

p~"~ = e ~~

(6)

( where

"(Q.n)

(~~~

= e ~~ dfl (7)

The tians fraction

fq

^{of the}

j-th

bond iS evaluated from

f,j

₌

iP~~°~ ⁽⁸⁾

,>,~

where

nq

^{stands for the conformer whose}

j-th

^{bond takes the} n.ans State. As _{a measure} of the orientational order of the whole chain, the

quantity

_{S~~~,~ was}

proposed [27]

s

(~'("' ~))

cha>n ~/~

j9)

where V* is the V

In,

n) value of the most extended conformer oriented in the nematic

direction.

2.2 THE SINGLE-ORDERING-MATRIX

(SOM)

MODEL.

Following

Boden et al.'s formulation

[34],

the

quadrupolar splitting Av,

is related to the

ordering

matrix _as follows

where

S~ p

is the up component of

the

_ordering

matrix, o~, is theangle between

the

C,-D

_{bond, and} the bar

denotes

the veraging over all allowed

olecule. 10) was obtained by ssuming that the rientational

order parameter

S~ p s _are

identical for all the (the

single-ordering-matrix When the

Z axis so

set

aS

to lie in the _direction of

greatest length,

the _agnitude

biaxiality _Sxx - _Syy iS Small.

In this

treatment [32], the

«

longest

ertia

is

_efined as the

Z

3

qQ cos- I

(the cylindrical-symmetry approximation).

The

quadrupolar splitting

ratio

Av~/Av~

is then free from the

Szz

value.

Therefore,

we have

An,

3

cos2

oz~

= (12)

~"i

₃

cos~

_0z~

Similarly,

_we obtain

D~~,

P

~(cos _9~DD~i)

(j3)

DDDI _P

~(cos

o

jDDii)

To facilitate the

analysis,

k is

assigned

to the central

methylene unit(s).

The relative

importance

of _a

given

conformer can be

expressed

_{as a}

product

of statistical

weights [22].

The Statistical

weight

factor iS

assigned

to the

gauche

State of the bond

(See Fig. 2),

the

weight

of

unity being given

to the

corresponding

tians state. For the terminal

bonds, a threefold

symmetric

rotational

potential

is assumed. On the

expectation

that the second-order interaction such _as

g~ g~

should

rarely

occur in _a nematic

field,

the

weights

w's _{are set}

equal

to zero. The average

cos~

_o

~~

required

in

equation (12)

_can be obtained from

>V->

iC°~~ bat il

_~j

cos~ 0~,

₌ ^{" ~ " ~}

⁽¹⁴⁾

A'->

I fl

I

,i

j=? ,i

~esents

the

weight

for bond _j, I-e-, I, _p, or as- In _a similar _manner,

P,(cos

~

~~~~~

)

_can be calculated.

2.3 PROCEDURE FOR SIMULATION. The simulation based _on the P-S-T model _was carried

out

by varying

values of the intermolecular

coupling constant(s)

until the best agreement between the calculated and observed

quadrupolar splittings

_was attained. The iterative

computation

_was

performed according

to the

simplex

method

[35].

The convergence of the

iteration _was monitored

by

^the

reliability factor,

I

h ",, _obs(1 ^~~ 1/2

i, calcd )~

R(%

,

= 100 _x

(15)

I '~~,,obsd'

i

For the SOM model, the statistical

weight

factors _were treated _as

adjustable

parameters.

Then, the R factor _was calculated

by using (Av,/Av~l's,

instead of

Av,

_s.

3.

Experimental procedures.

3.I SAMPLE PREPARATION

[36].

Undeuterated MBBA available from

Tokyo

Kasei Ltd.

was used without further

purification.

The NI transition temperature was determined to be 45.8 °C

by

the visual method

(i,ide iiifi.a). Partially

deuterated MBBA (MBBA-2,6-d,, see

Fig. 4)

_was

synthesized

from

methoxybenzaldehyde

and

n-butylaniline-?,6-d~,

which _was obtained

by refluxing

undeuterated

n-butylaniline

in

DCI/D~O.

n-Decane-d~~

was used _as

purchased

from MSD

Isotopes. 1,6-dimethoxyhexane

_was

prepared by

the Williamson

synthesis

between 1,6-hexanediol and

methyl

iodide. Perdeuter- ated 1,6-DMH _was

prepared

from

commercially

available

adipic acid-djo

reduction of the

deuterated dibasic acid with

LiAID~ yielded 1,6-hexanediol-dj~. Partially

deuterated 1,6-

DMH's,

I.e.,

1,6-DMH-I,1,6,6-d~

and

1,6-DMH-2,2,5,5-d~

_were

synthesized

from

1,6- hexanediol-1,1,6,6-d4

and

1,6-hexanediol-2,2,5,5-dj, respectively.

The former diol _was obtained

by reducing adipic

acid with

LiAID~,

and the latter

by exchanging

the

a protons ^of

adipic

acid with

NaOD/D~O,

and

reducing

with

LiAlH4.

Solutions _were

prepared

_on scales of several grams. The Solvent and Solute _were mixed in the

isotropic phase.

After

injected

with the

solution,

_an NMR tube of 5 _mm o-d- _was

degassed,

filled with

dry nitrogen

_gas, and sealed, with its lower part ^{immersed in}

liquid nitrogen.

3.2 OBSERVATION OF PHASE BEHAVIOR. The

Sample

temperature was held _constant

by

using

a Haake D3-G thermostat. The appearance

(disappearance)

of the

isotropic phase

^{and the}

disappearance (appearancel

^{of the} nematic

phase

on

heating (cooling)

were ascertained

visually,

and the

corresponding

temperatures were recorded. As the

phase boundary

_was

being approached, heating (cooling)

was

performed

in _a

gradual

_step of 0.I

°C,

and the temperature

was

kept

constant for _at least three hours. Before the next temperature

change,

the

sample

_was

picked

out of the thermostat, heated to be

isotropic,

and shaken

thoroughly.

3.3 2H-NMR MEASUREMENTS. Deuterium NMR spectra were recorded _at 76.65 MHz _{on a}

Jeol JNM-GSX-500 spectrometer

equipped

with _a

variable-temperature

controller. Measure-

ments were carried out under _a

nonspinning

mode. The

partially

deuterated MBBA _was diluted

ten times with undeuterated

MBBA,

and used in the measurements. The diluted MBBA

exhibited the NI transition _at 45.5 °C. In the measurements for the solvent, _ca. 2000 FID

signals

were accumulated. The

spectral

width _{was ca.} 30

kHz,

and the block size _was 16 K. A

zero

filling

and _an FFT

yielded

32 K data

points

_; the

digital

resolution _was 0.94 Hz. In the

measurements for the solutes, 3000-5000 FID

signals

were

averaged.

^The

spectral

width _was

ca. 50

kHz,

and the resolution of the obtained

spectra

was 0.78 Hz.

4. Results and discussion.

4.I PHASE DIAGRAM FOR THE MBBA

+1,6-DMH

SYSTEM.-

Figure

3 shows the

phase

diagram

for the MBBA ₊ 1,6-DMH system obtained

by

the visual method. The open circles

and squares represent the observed data. Linear

least-Squares fittings

_gave values of

p~

= 0.916 and

pi

=

0.804. The

slopes

at infinite

dilution, p~/

and

pj°°,

are

given by [4, 9]

p~/

=

~~ (16)

+

~~~

^~~

P&

+

Pi

and

~

Pi

~'

_~ ~~

«-«°~

Pi~+Pi~

where

« =

pj'-pj~ (18)

60

j ⁵⁰ ~T. isouop>c

~

(

^~~ _isotropic

+ Nemalic

~° (Td' x~

fl ₂₀ ^~~~~'~

lo

2 4 6 8 lo 12

1,6-DMH concentration (mot %)

Fig. 3. Phase diagram for the MBBA ₊ 1,6-DMH system. ^The slope p~ of the (T/. _-ii line where

the isotropic phase appears on heating and the slope pi of the

(Tj*,,;~)

line where the nematic phahe appears on cooling _were evaluated to be O.916 and 0.804 respectively.

and «°~

=

0.107

[37].

From these relations the

p~/

and

p/°

values for

1,6-DMH

were

determined to be 0.899 and 0,8?0

respectively, being larger

than those for

n-Cio

(p(

=

0.597 and

pf

=

0.561

[38]).

^In

figure I,

saltire _crosses, which denote the data

for1,6-

DMH, are found _to be located in the domain of

globular

molecules.

4.2 ORIENTATIONAL ORDER PARAMETERS OF MBBA. Shown in

figure

4 is _a 2H-NMR

Spectrum ^of neat MBBA measured at 27 °C. A

pair

of well-defined doublets _are observed. As illustrated in the

figure,

the

dipolar coupling D~~

and the

quadrupolar splitting

An ^~ _can be evaluated from the _narrow and wide

splitting widths, respectively.

^{If the}

^principal

axes of the

ordering

matrix _are defined _as shown in

figure 4,

the

quantities D~~

and Av ^~ _are related _to the order parameters,

Szz

and

Sxx Syy,

as follows

[39]

~HD ) ^~/)

_{~ZZ ~~}

and

An ^~

=

~

qzz

Szz

+

(Sxx Syy)(qxx qyy) (20)

2 2

where r~~ is the H-D distance (=

2.481),

_{y~ y~} h/4

ar~

=

1.844 _x 10~

Hzl~,

_{and q~~ s are}

the

diagonal

elements of the

quadrupolar

interaction tensor in the

principal-axis

_system of the

ordering

matrix _: q~~ = 116, _qyy

=

90.2,

_qzz

=

25.4 kHz. The

Szz

and

S~~ Syy

^values

can be obtained

by solving

the _two simultaneous

equations (19)

and

(20).

x

D H

2

D H

Ffl

_2DHD

Av~

Fig. 4. Deuterium NMR spectrum ^of neat MBBA, measured _at 27 °C.

In

figure

5 the order parameters

Szz

_s thus evaluated _are

plotted against

the temperature ^ratio

T/T~j,

where

T~j

is the temperature at which the

isotropic phase

_{appears on}

heating

and

disappears

on

cooling.

The data

points

_are found to form _a master curve, which indicates that the

phase

transition _{occurs at}

Szz~

0.29

irrespective

of solute concentration. As _seen from

figures

I and 5, the two solutes affect the transition

temperature T~j differently,

but have an

identical effect on

Sz~.

^{From H-H}

dipolar coupling

data,

Kronberg

et al.

[3

estimated the order

o.70

0.60

< 0.50

#

.

.

0.40

~

" 0.30

0.20

o-i o

0.90 0.92 0.94 0.96 0.98 1.00 1.02

T/T~

Fig.

5.-Onentational order parameter Sz~ ^{of MBBA} as a function of the temperature ^ratio

T/T~,

^where

T,

^{is the} temperature at which _on heating the

isotropic

phase appears for each solution _:

(x) neat MBBA (O) 0.504 mot§b (n-Ciu) _I (a) 2.00 mol§l

(n-Cjjil

(A) 4.05 mot% (n-Ciul

(O) 5.91 mol% (n-Ciul (.) 0.473 molf& (1, 6-DMH) _; (.) 2.06 mol5E (1,6-DMH) (A) ^{4.00 mot%}

(1,6-DMH) _; (+ 6.00 mol% (1, 6-DMH).

parameter ^{of MBBA mixed with} a

variety

^of solutes, and offered _{a master curve}

exhibiting

the

phase

transition at S

0.36,

where S represents ^{the order} parameter ^{of the molecular director}

tilting by

ca. 9° from the pal-a axis of the benzene

ring.

On the basis of '3C-NMR chemical

shielding anisotropies,

Pines _et a/.

[40]

have studied the temperature

dependence

of the order parameter ^of neat MBBA, and concluded that the NI transition _{occurs at} S 0.29. Lee et al.'s S data

[41],

which _were obtained from wide line iH-NMR measurements, _were shown _to be

well fitted _to the temperature

dependence reported by

Pines _et al. Since the difference in

magnitude

between

Szz

and S is

slight,

the results obtained here support Pines et al.'s and Lee et al's observations rather than

Kronberg

et al.'s.

4.3 2H-NMR _{SPECTRA OF soLuTEs.}

Figure

6a shows _a ?H-NMR spectrum ^of

n-Cjo-dm

(0.498

mol%, 27

°C)

dissolved in MBBA.

Following

Janik et a/.

[42],

I-e-, _on the

assumption

that

Av,

^decreases

gradually

from the central

methylene

units towards the

methyl

terminal~, the observed

splittings

_were

assigned

to the individual C-D bonds. As _seen from

figure

6, well-

defined spectra were obtained. On the basis of the

methyl

and

methylene

spectra ^calculated

by

Hsi _et a/.

[43], therefore,

the

quadrupolar splitting [Av,[

and the D-D

dipolar coupling D~~~

^values were determined

directly

from the

peak positions.

Listed in tables II and III _are the

[Av,[

and

D~~~

data of

n-Cio

observed at different temperatures ^and concentrations.

Figures

6b, 6c, and 6d show 2H-NMR spectra ^of

1,6-DMH-dis (0.505

mol%, 27

°C),

1,6-

DMH-1,1,6,6-dj (0.507mol%,

27°C), and

1,6-DMH-2,2,5,5-d4 (0.498mol§fi, 27°C), respectively.

On the basis of these

spectra,

^the

assignment

for

1,6-DMH

_was carried _out. For

1,6-DMH,

the

dipolar splitting

_can observed

only

from the central and its

adjoining methylene

units. In tables V and VI, the

[Av,

and

D~~~

^{values of}

1,6-DMH

_are

given.

(a)

~b)

(C)

(d)

~ 10 kHz

Fig. 6. -Deuterium NMR spectra ^of (a) n-Cio-d~2 (0.498 mot%), (b) 1,6-DMH-djs (o.505 mol%),

(c) 1.6-DMH-I,1,6,6-d4 (0.s07molfb), and (d) 1,6-DMH-2,2,5,5-d4 (0.498molf&) mixed with MBBA, measured at 27 °C.

Table I. Geomett.ica/ pat.aJJ1ete>.s

(~).

Bond Leng(h Bond Angle Dihedr~ Angle

angle angle

(I)

(deg.) (deg.)

c-D I. lo £DOD 107. 9 n-decane

c~c 1.53 c-c-c-c _± I12.5

c~O 1.43 n-decane

£ccc 12. 0 1,6~dimethoxyhexane

co-cc ±100. 0

1,6-dimethoxyhexane DC-CC ±1 17. 0

£cOC Ill.5

c3c4-c5c6~

_±108.0

£OCc I I 1.5 c4c5-c6c7 ^b ±I 12. 5

£c3c4c5 ^~ l I1.5

£c4csc6 ^~ l 12.0

("1 References [21, 23, 45].

(~l For the carbon number~, _see figure 2.

JOUR~AL DE PHYSiQLE >I 1 ' 12 DFCE'IBER 1~9~

Table II. -Rest,/t.I

of

siJJ1iilations

fbr

^2H-NMR

quadiupolar splittings of n-decafie-d~~

dissoli,ed in _{a nematic} soft>eat

4'-metho,tyben=vlidene-4-n-butylaniline (MBBA)

_: temperature

depeiiclent.e.

Photinos-Samuls~.Tonumi model S>ngle-ordering-matrix model

Temp.

Atom Obsda C~cd Bond ftj Atom Obsd C~od ~ Bond It

(°C) _{no no no no.} j

27 7.95 <-> 775 <-) 2 0.614 0.234<-) 0.234(-) 2 0.834

2 25 93 59 24 91 53 3 0 671 2 0.763 <0.76) 0.763 (0.78> 3 0.885

3 30.46 70 30 41 64 4 0 671 3 0.896 <0.90) 0.896 (0.91> 4 0.924

4 32.97 76 33 27 70 5 0 669 4 0.970 <0.97> 0.970 (0.97> 5 0.932

5 33 98 78 34 53 72 5 000 <1.00> 1.000 <1.00>

R (%> 0 93

lTo (kca< moi-j o 170 Szz _{o_294}

Scbmn ⁰ 246

37 6 40 6 21 2 0.600 0.232 ) 0.232 <- 2 0.833

2 20 97 49 20.14 43 3 0 659 2 0.762 <0.77) 0.762 <0.78) 3 0.884

3 24 65 (57 24 6 I (56 4 0 656 3 0.895 (0.89) 0.895 (0 91) 4 0.923

4 26 7 I 62 26 95 56 5 0 655 4 0 970 <0 97> ^0.970 <0.97> 5 0.936

5 27 53 64 27 95 58 5 000 _<100> I.000 _<100>

R _<%> 0 93

~i(kcai mot.1) 0 144 Szz _{o 238}

Schmn 0 199

43 4.84 ( 4 73 ( ) 2 0 590 0 230 ) 0.230 ( ) 2 0.831

2 16.00 35 IS 39 33) 3 0 651 2 0.760 (0.78> 0.760 (0.78) 3 0.883

3 18.83 (40> 1880 (39> 4 0645 3 0.895(0.89> 0.895(0.91) 4 0.925

4 20.43 44 20 59 43 5 0.645 4 0.971 (0.98> 0.971 (0.97) 5 0.948

5 21 04 45 21 37 44) 5 1.000 (100> ^1.000 (1.00)

R (%) 0 89

Go(kcalmoi-i) o 115 Szz _o,181

Schm 0 152

(.~) The n-decane concen(iation _wa~ 0.498 mol%.

(hi In every case, the R value of virtual _{zero was} obtained.

4.4 CONFORMATIONAL _ANALYSIS OF SOLUTE MOLECULES.

4.4.I n-den.une. Between the intermolecular

coupling

constants of the P-S-T model, the

following

relation _was found _to hold for

alkyl

^chain~

placed

in nematic environments

[29, 44]

I,j (C-C,

C-C

= 0.85

I,~(C-C) (21)

where

i'o(a)

and I>, la, ^b are the

coupling

constants related with the

single

_a bond and the correlation between the

adjoining

_a and b bonds,

respectively.

In this

study

^the

approximation

of

equation (21)

_was

employed

^for

n-Cjo.

^Then

I>o(C-C)

is the

only adjustable

parameter.

Using

the internal

energies

of

E~=0.5

and

E~ =2.0kcalmol~~

and the

geometrical

parameters ^{listed in table}

I,

the 2H-NMR

quadrupolar splitting

data _were simulated. Then the

integration

in

equation (3)

_was carried _out

according

_to

12H

^H

F

(f1,

ii)

f(f1,

fi) dfl

=

d#

F (&, #, fi)

f(&, #,

_n j ^sin 0 d&

(22)

0 0

Table III. Results

of

siJJ1ulations

for

^?H-NMR

qitadrupolai slJlittings of n-decafie-d~~

disso/i,ed in MBBA _: concentiatio>i

dependence.

PhoUnos-Samuls~,Tonum> model Single-ordering-matrixmodel

conc.

Atom Obsd~ Calcd Bond It j ^{A(om Obsd Calcd ~ Bond} It_j

no no. no. no.

,~~;, rDD< i&v;< ODD"

<&v;' (ODD;) 'Av<' (LDDi~

$(j~

$ ^s~

~ ~~ ~~~~ ~~z)

~

l.99 749 (-> 7.30 (-> 2 0.611 0.233(-) 0.233 (-> 2 0.834

2 24.50 56 23.52 50 3 0 668 2 0.763 (0.76) 0.763 <0.78> 3 0.884

3 28 76 66 28 72 60 4 0.668 3 0 896 <0.89) 0.896 <0.91> 4 0.925

4 31 16 71 31 43 66 5 0 666 4 0 971 <0.96) 0.971 <0.97) 5 0.939

5 32 lo 74) 32 63 (68 5 1.000 (1.00) 1.000 (1.00)

R (%) 0 94

1i0(kcal mot-') 0.158 SZz 0.277

Sch~n 0.232

3.99 6.72 6.53 2 0 607 0.233 0.233 2 0.834

2 21.99 51 21.09 45 3 0 665 2 0.764 (0 77) 0.764 (0.78) 3 0.884

3 25 82 59 25.77 54 4 0 663 3 0.897 <0.89> ^0.897 <0.91> 4 0.927

4 27.98 64 28. 22 59 5 0.662 4 0 972 (0.97> 0 972 (0.97) 5 0.943

5 28.80 (66 29 30 61 5 1.000 <1.00) 1.000 <1.00)

R <%) 0 97

1i0 (kcalmot.'> 0 143 SZZ 0.248

Schm 0 208

6.07 5.89 ) 5 73 2 0 603 0 232 0 233 2 0 833

2 19.32 (46 18.54 (39 3 0 662 2 0 762 (0.78) 0.762 (078) 3 0.885

3 22 71 52 22.65 48 4 0.658 3 0 896 <0.88) 0.896 <0.91) 4 0.924

4 24.60 57 24 82 52 5 0 658 4 0.970 (0.97> 0.970 (0.97> 5 0.937

5 25 35 59 2578 (54 5 1.000 (1.00> 1.000 (100>

R (go> 0 95

Go (kcal mot-1) 0 127 SZZ _0.219

Sch~n 0 183

(.>) Observed _a( 27 °C.

(b) In every case, the R value of virtual _{zero was} obtained.

where o and # _are the

polar

and azimuthal

angles

that define the nematic director in _a

molecular fixed frame _on the solute. In the numerical

integration,

the step widths in band #

were set

equal

to «II 8. The rotational kinetic energy factor

G(n

in

equation (2)

_was fixed _as

unity

for all the conformations. The

reliability

of the computer program used _was verified

by

its

reproducibility

of Photinos _et al.'s calculations

[26].

In all the

examples,

the R factor _was found _to be minimized down _to 0.9-1.0 %. The results of the simulations _are listed in tables II

(the

temperature

dependence)

and III

(the

concentration

dependence).

It _can also be found that the D-D

dipolar couplings

observed _were well

reproduced by

the calculations. Bond conformations

(specifically

the trams fraction

f,~)

and the order parameter _S~~~,~ ^{of the whole chain} are

given

^{in the tables.}

The results of the simulations based _on the SOM model _are also listed in tables II and III. In every case, the observed

quadrupolar splitting

and

dipolar coupling

ratios _were

reproduced

well

[46].

Although

the _two models

successfully reproduced

the

experimental

observations, the

definite difference between both results _can be found in the bond conformations. From

E

= 0.5 and E

=

2.0 kcal mol~ _~, the

f,~

values of bonds 2 to 5 of

n-Cjo

in the free state at

27 °C _can be evaluated _to be

0.590,

0.650,

0.641,

and

0.643, respectively, being

close to those

in MBBA at 27 °C obtained

by

the P-S-T simulation

(0.614, 0.671, 0.671,

and

0.669,

respectively). Therefore,

these results suggest that, _even in the nematic

phase,

the

n-Cjo

chain is _so flexible _as in the

isotropic phase. According

to the SOM

analysis,

_on the other

hand,

the

n-Cio

molecule possesses some

rigidity.

This

discrepancy

_can be

clearly

_seen from the temperature

dependence

of the reduced average end-to-end distance

71i~~

(see

Fig. 7a). Here,

7 is the average distance between the terminal

methyl

carbons, and r~~~ is the end-to-end distance of the all-tians conformer.

According

to the P-S-T model

(the

data _are

plotted by

_open

circles),

_no

particular change

in 71i~~~ occurs

during

the NI transition. On the contrary, ^{the data}

obtained

by

the SOM model

(open squares)

indicate that the

phase

transition may be

accompanied by

a sizable

change

in the chain extension. As stated in

Introduction,

from

thermodynamic experiments,

Martire et al.

[8, 12, 13]

drew _a conclusion that in _a nematic

field n-alkane solutes behave _{as a} chain

composed

of two

completely rigid

and _some

semiflexible segments.

Therefore,

it _seems reasonable _to conclude that the SOM model rather than the P-S-T model

provided

results consistent with the

thermodynamic

observations.

i~~ i .o

o-g j 3 _0.8 Q

~~

Nematic Isotropic

0.6 (b)

~

og

g 3 0.8 I

o~ Nematic <sotropic

0.6

20 30 40 50 60 70

Temperature (°C)

Fig. 7. Average ^{chain extension} 7fi.~~~ ^of (a) n-Cio and (bl 1,6-DMH _{as a} function of temperature :

(O) the P-S-T model (11) ^{the SOM model. The dotted line} represents ^the temperature

dependence

of the 7fi.~~, ^{value for the}

isotropic

phase. 7 _is the average distance between the terminal

methyl

carbon~, and r~,,~ is the end-to-end distance of the all-tians conformer.

4.4.2

1,6-diJJ1etho,ryhexane. According

to the

bond-length scaling

relations of the P-S-T model

[30,

31,

44],

the intermolecular

coupling

constants defined for

1,6-DMH

_are related to each other as follows _:

joie-o

=

)

^~

io(c-c (23)

and

ii ~°-C

C-C

-

k ii ~C-C,

C-C

~25)

where

i~_~

^and

i~_~

^{denote the C-O and C-C bond}

lengths respectively.

^{Under these}

conditions,

the number of

adjustable

parameters ^{used in} the P-S-T simulation _can be reduced _to two

I,o(C-C)

and

I>j(C-C,

C-C

) (the

two-parameter

approximation).

If

equation (21)

iS assumed _to be valid for 1,6-DMH _aS well,

only I,o(C-C)

iS the

independent

variable

(the single-parameter approximation).

Two sets of internal

energies,

based _on those of 1,4-DMB

(see

footnote b of Tab.

IV),

_were

employed.

The

geometrical

parameters ^used are listed in

table I. The other

computational procedures

were the _{same as} in the _case of

n-Cjo.

Deuterium NMR

quadrupolar splitting

data obtained _at 0.505 mol% and 27 °C were first

attempted

to be

analyzed by using

the P-S-T model. The result~ _are summarized in table IV. It _can be found that the

single-parameter approximation

ill

reproduced

the

experiment (R

5-6 %

). Although adoption

of the _two parameters reduced the R factor to ca. 2 %, the

dipolar couplings

were

calculated to be much smaller than those observed, and

D~o~

was estimated _to be smaller than

D~~~.

These tendencies contradict the observation.

Furthermore, by adjusting

the five parameters

I.o(C-O), io(C-C), I,j(C-O, O-C), I>j(O-C,

^C-C ), and

I,j(C-C,

C-C )

independently

of each

other,

the P-S-T simulation _was

Table IV, -Resit/ts

of

sittiulations

for

1,6-dimetfio,ri,he>.are

hi,

tfie Photifios-Samu/ski- Toriumi model.

<Av, JHz) D~D, ob) )

Parameters Atom

~° Calcd Obsd a

Intemal~nergysolb

A B A B A B

S>ngle parameter Two parameters F>ve parameters

I II 57 11 05 7 86 7 63 8 59 8 59 S60

3 24 24 24 32 22 59 22 87 21.47 2i 49 21.48

4 2724 (57) 2737 (58) 2776 (39) 2776 (40) 2831 (51) 2832 (51) ²⁸³¹ (61)

5 2702 (53) 2709 (53) 2951 (36) 2934 (38) 2971 (46) 2967 (48) 2967 (65)

R (%) 5 6 5 3 7 2 0 05 0 02

10(C-O)~ -I 403 -I 336

$0(C-C)^~ 0178 0 174 -0 145 -0 125 0 222 0 239

ii

_{(C-O, O-C)}~ 2 855 2 747

~l _(O.C,C-C)~ 0 I15 0 066

~

_{(C-C, C-C)}~ 0 435 0 408 0 157 0 135

S ~ham 0 213 0 214 0 279 0 277 0 372 0 369

(") Observed _at 27 °C. The

1.6-dimethoxyhexane

concentration _was 0.505 mol%.

(~) As the fir~t-order interaction

energies,

^the following values _were adopted set A. E~ ^I-Q, E,,, 0.2, E,,~ ₌ 0.3, and E,~~ 0.5 kcal mol~ ^' _{; set} B, E~ ^1.0, E,~j ^0. I, _E,~~

= 0.3, and

E~i ₌ ^0.5 kcal mol~ ^' The second-order interaction

energies

of E~j ^{0.47 and} E~~ ₌ ^{2.O kcal mol~} are

in common to sets A and B.

(C) In the unit of kcal mot-'