Observation of quasi two-dimensional nematic order in a system of rigid rods

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Observation of quasi two-dimensional nematic order in a system of rigid rods

Michael Fisch, Charles Rosenblatt

To cite this version:

Michael Fisch, Charles Rosenblatt. Observation of quasi two-dimensional nematic order in a system of rigid rods. Journal de Physique II, EDP Sciences, 1994, 4 (1), pp.103-110. �10.1051/jp2:1994117�.

�jpa-00247942�

Classification Physic-s Abstracts

61.30 E 64.70M 82.70D

Observation of quasi two-dimensional nematic order in

_a

system ^of rigid rods

Michael R. Fisch

(I. *)

and Charles Rosenblatt (2.

**)

IIj Department of Physics, John Carroll University,

University

Heights, ^{Ohio 44118, U.S.A.}

(~)

Department

of Physics, Case We~tem Reserve

University,

Cleveland, Ohio 44106-7079, U-S-A-

(Received 29 Jul; 1993, >.ei,ised in final form 14 Septemher J993, accepted 5 Octobe>. 1993)

Abstract. Phospholipid tubules _were

suspended

_on the surface of _an aqueous solution. At low

density,

_a rarefied nematic phase with weak onentational order _was observed. At high

density

the tubules phase separated into _a well ordered high density phase and _an isotropic phase with

virtually

no tubules present. ^Results are

compared

to theories for two-dimensional

ordering

of hard rods.

Introduction.

Almost _a decade ago aqueous solutions of

diacetylene

lecithin

1,2-bis(10,

12,

tricosadiynoyl)- sn-glycero-3-phosphocholine

(«

DC~,~PC

»)

(Fig.

II were found _to form rod-like microstruc- tures,

consisting

of

bilayers wrapped

^around a hollow _core

[1-4].

These structures, also known

as _« tubules _{», are}

relatively straight,

tens or even hundreds of microns in

length,

and 0.3- 0.75 _~m in diameter. The wall thickness ranges from _{one to} fifteen

bilayers [5], depending

in part on how the tubules _are

prepared,

and is

typically

uniform _{over an} entire tubule or over a

very

large region

of the tubule. These

objects

_are

structurally

robust, since the

diacetylene

in the

lipid

_may be

easily polymerized.

For this _reason research _on these materials and their

phase

behavior has

proceeded

in two distinct directions. On the _one hand, research groups have

focused on fundamental scientific

questions [6-10],

such _as

trying

to understand the intemal

structure of the tubules and their interactions. On the other hand, these tubules may be useful in

a

variety

^of

applications,

^for

example,

in

composites,

in order to

exploit

these structure8 one must be able to

reproducibly

and

controllably manipulate dispersed

tubules and understand

their interactions, both with each other and with

confining

surfaces. To this end _{we are}

involved in _an

ongoing

_program in which the tubules _are treated _as structured colloidal

(*) E-mail addre>s

fisch@jcvaxa,jcu.edu.

(**) E-mail add>.ess

[email protected].

104 JOURNAL DE PHYSIQUE II N°

+

OCH2CH2N(CH3)3

O=P-O~

O

O

CH2

(

CH3(CH2~9CmC-CWC(CH2)HOOCH

O

I

CH3(CH2)9CWC-CmC(CH2)BCOCH2

Fig. I. Schematic representation of

DC~ ~PC

molecule.

particles.

To date

experiments studying

the

orientability

of tubules in both electric and

magnetic

fields

[5,

11,

12],

the effects of

suspending

tubules in _a

ferrofluid[13],

the interactions of tubules with

acrylic

and

glass

surfaces

[14],

the effects of

pH

and temperature

on tubule-tubule interactions

[15],

and the observation of _a three-dimensional

(3d),

_or bulk, nematic

phase [16]

^{have been}

performed.

in this paper we report observations of _a

quasi-two-dimensional (2d)

nematic

phase

composed

of these structures

floating

_on the surface of _{a more} dense

isotropic

fluid. In order to

accomplish

this task _a

judicious

choice of

pH (to

stabilize the tubules

against aggregation)

and

underlying

fluid

density

and

viscosity

was

required. By carefully choosing

these parameters

we were able to achieve _a situation in which the tubules

largely

remain _on the surface of the fluid _{as a} 2d

phase,

the rotational kinetics of the tubules _{were not too} slow, and the tubules

were stabilized

against

flocculation. Here the screened Coulombic interactions _were suffi-

ciently

strong so as to prevent very close

approach

where the attractive

dispersion

forces

dominate

[15].

However, the

Debye length

was still very small

compared

to the size of _a

tubule.

Theoretical

background.

Three-dimensional nematic

phases

mediated

by

steric interactions of anisometric

particles

are

well-known and well studied

[17-31].

It is well-known both

experimentally

and

theoretically

that the transition from the

orientationally

disordered

isotropic phase (I)

to the

orientationally

ordered nematic

phase (N)

is first order. The situation in _two dimensions is less well defined.

Theoretically

it appears that the transition may be either first order _or continuous and of the Kosterlitz-Thouless type ^with a tricritical

point separating

the two types ^of

phase

transitions.

Further, these results indicate that

long

range orientational order may ^not exist in such two-

dimensional nematics.

One of the first theoretical calculations _was

performed by Zwanzig [321

_{on a system}

consisting

^of dilute solutions of very

large

aspect ratio

particles.

He concluded that in 2d the

N - I transition is continuous. Vieillard-Baron

[33] performed

Monte Carlo calculations of

hard

ellipses

^confined to a

plane.

These results indicate that the N _- I

phase

transition is very

possibly

^first order. A similar result _was obtained

by

Tobochnik and Chester

[34] using

Monte Carlo

techniques

to

study

2d nematic

phases. They

concluded that if the

pair potential

between

objects

is

non-separable (in

their words _« realistic

interpanicle potentials

»),

long

range order exists in the nematic

phase.

Furthermore, if

long

_range order exists, then the Kosterlitz-

Thouless

theory

^of 2d

phase

transitions _{can not} be used to

explain

the N

- I

phase transition,

and this transition would, in fact, be first order. These last _two results should be contrasted with the Monte Carlo simulations of _a two-dimensional fluid of

infinitely

thin hard rods of finite

length

discussed

by

Frenkel and

Eppenga [35].

This model system ^has an

isotropic phase

at low densities and _a

« nematic _»

phase (not

the usual nematic because it lacks

long

range orientational order) at

higher

densities. Their simulations indicate that there is _no

long

_range order in this system, ^{but rather}

only algebraic

order, thus the N

- I transition is

predicted

to be of the Kosterlitz-Thouless type, ^{and is therefore} not first order. A similar, less

complete,

calculation for hard

ellipses

showed similar behavior. The N

- I

phase

^transition in the hard

ellipse

system ^{has been} of

continuing

and

increasing

theoretical interest. For instance, Boublik

[36]

used scaled

particle thery

to

study

^this

problem.

More

recently Cuesta, Tejero,

and Baus

[37]

studied this system

using density

functional

theory

to

predict

that the

N

- I transition is continuous for this system. Ward and Lado

[38]

used the Percus-Yevick

equation

to obtain the _same result. Cuesta and Frenkel

[39]

studied this system ^for

ellipses

of several different aspect ratios. For _an aspect ^{ratio of four}

they

find the transition to be first order, while for _an aspect ^{ratio of six it is} continuous. Thus

they predicted

that there is _a

tricritical

point separating

these two types ^{of behavior. Ferreira} et al.

[40]

used both the Percus- Yevick and

hypernetted

chain

integral equation

theories and

density

functional

theory

to

verify

these last results, in

particular

the continuous _nature of the N

- I transition for

larger

aspect ratio

particles.

Therefore, to summarize, unlike the three-dimensional _case where both

theory

and

experiment unequivocally

find the N

- I

phase

transition to be first order, ⁱⁿ two- dimensions the

predictions

indicate that the N

- I

phase

^transition _may be either first order _or of the Kosterlitz-Thouless type,

possibly depending

on the aspect ^{ratio of the}

particles.

Two-dimensional behavior has been

experimentally

observed in

thermotropic liquid crystal

films

[42] by

_means ^of various

scattering probes. However,

for systems ^dominated

by

steric interactions, such _as tobacco mosaic virus

(TMV)

_or

poly benzyl glutamate,

these theoretical

predictions

have been difficult _to

verify.

These small

particles

_cannot be

directly

observed

using

standard

optical microscopy,

and _are difficult _to

manipulate

in

relatively

small numbers.

From this

perspective

the tubules are a better system because

they

can be

easily imaged

and studied

using

standard

optical microscopy techniques,

and in

principle,

if not in fact, can be

easily manipulated.

Experimental procedure.

The

phospholipid DCS, ~PC

was obtained from Avanti Polar

Liquids

and used without further

purification.

The tubules _were

prepared using

a modification of the

technique

of Lu,

Rosenblatt,

and

Yager [41],

168 mg of

DCS_~PC

was dissolved in _a mixture of 28.3 g of

prefiltered

reagent

grade

^{methanol and 6.3} g of

prefiltered ultra-pure

water. The

resulting

solution _was heated to

approximately

60 °C, where it is clear, and then

slowly

^cooled.

Upon cooling

to _room temperature, the solution _was

cloudy, indicating

that tubules had formed in the solution. The final concentration of the solution

corresponds

to 4

mg/ml

of

lipid

in _a 85/15

(by volume)

methanol/water mixture. Examination of _a

sample

of this solution

using optical microscopy

^revealed needle-like tubules. The

density

of the tubules _was assumed _to be the

same as that determined

by

Lu _et al.

[16],

1.093

g/cm3.

The _mean

length

of the tubules _was found to be

approximately

50 _~m. To calculate the _mean number of tubules per unit volume _a

typical

tubule diameter _was assumed to be d

w 0.5 _~m

II-13]

and,

building

on earlier work,

the average wall thickness _was taken _as

601[43].

_{From these two numbers, and} the _mean

length

^of the tubules and their _mass

density,

the mean number

density

_n ^{is calculated}

n w 1.6 _x

10'° tubules/cm~.

106 JOURNAL DE PHYSIQUE II N°

The

underlying

fluid

supporting

the 2d tubule

layer

consisted of _a 50-50

(by volume)

mixture of

D~O

and

glycerol.

The

resulting

fluid mixture has a

density

^of

approximately

1.17

g/cm3

and _a shear

viscosity approximately

4-5 times that of pure water. The tubules could thus float

on the surface of the fluid and still have a

not-too-long

rotational relaxation time. This time _was estimated

by observing

the flow

birefringence

of _a

rotationally relaxing sample

^and was found to be

substantially

less than _one minute. We _note that HCI _was added _to the mixture to

bring

the

pH

to 2.75. In this

pH

_range the head group of the lecithin is

protonated, giving

rise _to the desired Coulombic stabilization with _a

screening length

of order

501;

_this

_length

_{is much}

smaller than the characteristic external

lengths

of _a tubule.

The

sample

chamber _was machined from _a

single piece

^of

acrylic.

It had _a width of

approximately

2.5 _cm. The

length

of the part ^{of the chamber that contained the}

sample

^could

be varied from 7 _cm to less than I _mm

using

two movable tenon barriers that _were constrained to translate

parallel

to the

long

axis of the chamber. The bottom of the cell consisted of _a

microscope

slide, which had _no observable

birefringence

when observed

through

_a

polarizing microscope.

The top of the chamber _was open,

allowing

a close

approach

of the

microscope objective.

In

practice,

the _open space ^at the top ^of the chamber _was covered with

parafilm

to

reduce

evaporation

^of the fluid and the

settling

of dust _onto the

samples.

The

length

of the _«

through

_» could be

continuously

varied

by moving

one or both of the teflon barriers. In the present

experiment

one of the barriers _was fixed and the other _was

connected to a stepper motor and

speed

reducer _so that the surface _area of the

sample

could be

reduced _{a constant rate.} For the data

reported

herein the barrier _was moved in _{at a}

speed

u _I 1.5 _x

10~~

_{cm/s. Thus}

L/v,

where L is the mean

length

^of a tubule, is greater ^{than the} reorientation time observed in the

birefringence experiments, facilitating experiments

_per-

formed in

quasi-equilibrium.

Note that

piles

of tubules _{were not} observed _near the barriers.

Funher time _was allowed for the establishment of

equilibrium by stopping

the

compression

for

10-30 min before the

photomicrographs

were taken _; in _{no case was a}

sigificant change

in

tubule orientation observed

during

this

equilibration

time.

In _a

typical experiment

the stock solution of tubules _was diluted with methanol _{to a} number

concentration of

approximately

1.6x107cm-3.

Approximately

0.2cm3 of diluted

methanol/water-lipid

solution _was

carefully placed

at several random locations _on the surface of the

glycerin-D~O

solution. The tubules have a

density

less than that of the

glycerin-D~O

solution and hence remain _on the surface. The methanol is soluble in both water and

glycerin,

and hence _some will mix into the bulk.

Moreover, independent experiments

indicate that

0.2 cm3 _{of methanol could} evaporate ^from the surface in about 15 min. This is well below the initial

equilibrium

time of1-2 h. Hence, _we believe that

vinually

no methanol and

only

tubules

were left _on the surface. This _was further reinforced

by

our

microscopic

observations which indicate that the

depth

of focus _over which the tubules _were in focus _{was no more} than a few microns. This

length

is less than the _mean

length

of _a tubule, hence the system ^is

nearly

two-

dimensional.

Furthermore,

_we did _not observe

pile-ups

of tubules.

The initial _area of the

sample

was

10cm~,

_{and thus the initial 2d} concentration _was

n13x10~ tubules/cm~. Assuming

_{an average} tubule

length, L150~m

_we find

P'= nL~

m

7.6,

_{very near} the _mean

density, p'm

7.8 at which Frenkel and

Eppenga [35]

predict

_a nematic should form in

infinitely

thin rods. Note, however, that the

preceding

calculation is rather crude and the estimate of the

experimental p'

could be in _error

by

_a factor of two. This surface

density

_was increased

by reducing

the _area of the

sample by moving

one of the movable barriers. In

practice,

because _a

microscope objective

has to be close _to the

sample,

the _area could

only

be increased

by

_a factor of four. Thus p' could be varied from

approximately

8 _to 30.

Finally,

note that the entire

experiment

was

performed

at room

temperature,

approximately

22 °C.

Results.

The

goal

of present

study

was to form and observe 2d nematic-like

phases

of tubules _on the surface of _a fluid. We limited ourselves _to visual observation of the

resulting

surface

phases.

Therefore, _our results consist of

representative pictures

at different surface densities of tubules

on the fluid surface. All

photographs

_were taken under _a

microscope

with the

sample

between crossed

polarizers.

Figure

2 shows _a

photograph

of _a

typical sample

at the initial

density p'm

8. This is very

near the minimum

density

which Frenkel and

Eppenga [35] predict

_a nematic

phase

should

form. The

depth

of focus of the

microscope

is such that

only

the tubules _on top ^{of the fluid} are

in focus. Because of the inherent

graininess

of the

photograph,

it is much easier _to discern the streaks

corresponding

to the local tubule orientation than the actual tubules. In

spite

of this rather low

density

of tubules the

imaged region

^of the

sample

appears rather well

aligned.

Concomitant rotation of both the

polarizer

and

analyzer by

^45° causes the

large light region

in the

figure

to become dark,

offering

further evidence for

fairly

_strong local

alignment.

(Note

that the

polarizers,

rather than the

trough,

were rotated _to avoid

disturbing

the tubules.

)

Other locations _on the surface had

similarly

well

aligned regions

however, the overall

alignment

was not uniform.

l

"

3

~~_

~ .

~ -'

Fig. 2. Photograph of _a typical sample at the minimum density studied.

Figure

3 is _a

picture

of the _same

sample

at a lower

magnification (by

_a factor of

2.5)

and _a

higher sample density, p'

m Ii. At this

density

the director orientation is less uniform than at the lower

density

shown in

figure

2. There _are distinct dark and

bright regions

of

comparable

area. These _areas

change

in relative

brightness

as the

polarizers

are rotated. This is indicative

of domain formation. This is further shown in

figure

4 which

corresponds

to

p'w18.

This

picture

shows several domains. Note that each domain is

uniformly

oriented,

although

in _a different direction than its

neighbor.

Moreover, within each domain _the order parameter is

larger

than that shown in

figure

2.

Finally figure

5 shows the _same part ^{of the}

sample

with the

108 JOURNAL DE PHYSIQUE II N°

~~,

^~'~'R

~~

"

q.

~

~ ~

~

i~

~

[ t

~4 4

~

t~

Fig.

3.

Photograph

of the sample, at lower magnification, and _a density 1.4x larger than in figure 2.

l~ f II ~

~lL

Fig. 4. Photograph of the sample at a density of 2. lx the initial density. Note the formation of domains and the large orientational order parameter within each domiin. The out of focus bright _{spots are} due to dust panicles.

,h

~~l

~'

fj

~ 4.

f ~',

p ~ V

y

~~

/

'~

4

~..

>.

>

,

~

K

Fig. 5.

Photograph

of the _same part ^{of the} sample _as in figure 4 with the polarizer and analyzer rotated by 45°.

polarizers

rotated

by

^45°.

By comparing

this

figure

to

figure

4. It is established that there _are

fairly large regions

with _a low concentration of tubules I,e,

regions

which remain dark

independent

of

sample-polarizer

orientation. Thus these last two

picture

shows _a

sample

that has in part

phase separated

into

coexisting

nematic and

isotropic phases

with different

concentrations. If this is indeed the _case then the

phase

transition must be first order. An altemate

explanation

is that the tubules have become _so

compressed

that

they

have started to aggregate.

Although

we think this is

highly unlikely,

the present

study

can not rule _out this latter

possibility. Finally

the

phenomena

shown in the last three

figures

is reversible upon

expanding

the surface the

sample

retraces back

through

the earlier steps ^shown to the form shown in

figure

3.

Conclusions.

In conclusion, _we have observed what appears to be _a two-dimensional nematic

phase consisting

of tubules on the surface of _an

isotropic

fluid. Phase

separation

between

isotropic

and nematic

phase

has been observed. Such

phase separation

is indicative of _a first order

phase transition,

and _as such is _at variance with _some theories

describing phase

transitions of

ellipses

on surfaces. The _ease with which this system can be made, _as well _as the

large

size of the tubules, make it _an

interesting

system ^{for further}

study.

Acknowledgments.

We wish _to thank Rolfe Petschek for useful conversations _on this work. This work _was

supported by

the National Science Foundation under grants DMR-9007442 and

by

the NSF's

Advanced

Liquid Crystalline Optical

Materials

(ALCOM)

Science and

Technology

Center

under grant DMR-8920147.

l10 JOURNAL DE PHYSIQUE II N°

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