Observation of the parabolic focal conic structure and a disclination/dislocation relationship in a dilute lyotropic phase

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Observation of the parabolic focal conic structure and a disclination/dislocation relationship in a dilute lyotropic

phase

W.J. Benton, E.W. Toor, C.A. Miller, T. Fort

To cite this version:

W.J. Benton, E.W. Toor, C.A. Miller, T. Fort. Observation of the parabolic focal conic structure and a disclination/dislocation relationship in a dilute lyotropic phase. Journal de Physique, 1979, 40 (1), pp.107-110. �10.1051/jphys:01979004001010700�. �jpa-00208879�

Observation of the parabolic ^{focal conic}

^structure

and

a

disclination/dislocation relationship

in

a

dilute lyotropic phase

W. J. Benton, ^{E. W.} Toor, C. A. Miller and T. Fort, ^Jr.

Department of Chemical Engineering, Carnegie-Mellon University Pittsburgh, Pennsylvania 15213, ^U.S.A.

(Reçu ^{le 2 mai} 1978, ^{révisé le} 15 septembre 1978, accepté ^{le 18} septembre 1978)

Résumé. ²⁰¹⁴ On observe une structure de domaines focaux paraboliques ^{(PFC) dans un cristal} liquide lyotrope ^en phase lamellaire. La théorie de cette structure et son observation dans un cristal liquide thermotrope ^en phase smectique ^{A ont été} présentées récemment par Rosenblatt et al. [1]. ^{Cette structure se forme} spontanément ^dans

une phase lyotrope ^{et certains details peuvent être vus au} microscope polarisant ^{avec une} resolution inhabituelle.

En particulier ^deux disinclinaisons de signes opposés peuvent être observées au n0153ud d’une dislocation coin et on fait appel ^{au groupe} spatial d’un réseau tetragonal pour les interpreter.

Abstract. ²⁰¹⁴ Observations of the parabolic focal conic (PFC) ^{structure are} reported ^{in a} dilute lamellar lyotropic liquid crystalline phase. Only recently ^did Rosenblatt et al. [1] present ^the theory ^{of this structure} and its observa- tion in a thermotropic ^{smectic A} phase. ^{The PFC structure forms} spontaneously ^{in the} lyotropic phase, and various structural details exhibit unusual resolution from polarizing microscopy. ^In particular ^two disclinations of oppo- site sign ^are clearly ^{observed at} the node of an edge dislocation and are conveniently explained ^{in terms of the} tetragonal lattice space group.

Classification Physics Abstracts 61.70

1. Introduction. ^- Recently, Rosenblatt et al. [1 ]

presented

^the theory ^{of a new defect} structure, ^the

parabolic

focal conic (PFC) structure, and

reported

its observation in the thermotropic ^{smectic A} phase

of

cyanobenzilidene

octyloxyaniline (CBOOA) ^after shearing.

Subsequently,

^Kléman

[2]

calculated the energy of

bending

^{in the PFC} structure. This note describes our observation of the PFC structure in

a dilute lamellar

lyotropic

phase containing ^{a surfac-}

tant/co-surfactant

mixture in NaCI brine. Because the PFC structure forms

spontaneously

^{in our sys-}

tem, ^{we have} been able to obtain

photomicrographs

which show various features of the structure very

clearly. ^{We have} also obtained clear images ^{of a}

particular

type ^{of defect in the PFC structure itself.}

The surface active agent ^{we used is a}

synthetic

alkyl aryl

petroleum

sulfonate. This surfactant and similar materials are of considerable interest because, under

appropriate

conditions, their solutions exhibit

extremely ^low interfacial tensions with hydrocarbons

in the _range of 10-3 or 10-4 dyne/cm

[3].

^{As a result} they ^are

prime

candidates for use in processes ^now

being

developed

for enhanced _recovery of petroleum

from

underground

reservoirs

[4].

Solutions of these surfactants exhibit various liquid

crystalline phases

in concentration ranges of interest for the micellar

flooding

recovery process [5]. One of these phases

exhibits the PFC structure discussed below.

2.

Expérimental ;

materials. ^- The surfactant, ^a synthetic

alkyl

aryl

petroleum

sulfonate, ^is

predomi-

nantly ^the monoethanolamine salt of dodecylorthoxy-

lene sulfonic acid (PDM-337, kindly

supplied

by

Exxon

Corp.).

^{It contained 84}

%

^{active sulfonates}

and was used as received without further

purification

or analysis.

Tertiary-amyl

^alcohol (reagent

grade)

was mixed with the surfactant to form a surfactant/

co-surfactant mixture (63/37

by

volume). This mixture

was then added to NaCI in distilled

H20 forming

^a

brine composition ^{of 9}

%

PDM-337/t-amyl alcohol, 2.5

%

^{NaCI and} 88.5 %

H20.

The solutions were

mixed initially ^{for 30} seconds with a vortex mixer and again ^{after 24} hours, ^{then left in sealed test tubes} for one week.

3.

Technique.

^- Samples ^{of the solution were}

introduced into

rectangular optical

capillaries ^with

an optical pathlength ^{of 200} jum (Vitro Dynamics, Inc., ^New Jersey) by

capillary

action. The

capillaries

were then sealed with a fast setting two-part epoxy

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004001010700

108

resin and fastened to standard

microscope

^slides.

Observation was conducted by polarizing

microscopy

(Nikon PoH) ^{at room} temperature ( ~ ²⁴ oc.

4. Observations. ^- In

capillaries

^{treated as des-} cribed,

samples

^can be observed over a period ^of

weeks.

Initially

^the

sample

^{shows a} disordered, ^uni-

axial weak birefringence between crossed polarizers.

Within an hour the solution commences a spontaneous reorientation, relaxing ^toward lower energy ^states.

The process of textural

change

^{exhibits a} complex

unfolding

mechanism.

Regions

^{in the}

capillary

^become

pseudo-isotropic,

^{where a}

majority

of the lamellae

are in a

perpendicular

orientation with respect ^{to the}

capillary

^wall.

Adjacent regions

^{transform into linear}

arrays of conic structures (i.e.

myelinic

sheaths),

which can extend for the

length

^{of the}

capillary.

Subsequently the interstitial

pseudo-isotropic regions

transform into cellular _arrays.

Figure

la, ^{b and c shows the}

striking regularity

of these cellular _arrays where the arrays ^are in per-

pendicular

orientation with the

capillary

wall. This series of

photomicrographs

^{is focused in} registration

at

depths

^of 0,

approximately

100, ^{and 200} J.1m in ^a 200 J.1m

capillary

^{with the}

polarizer

^and analyser ^at

zero

degrees

^with respect ^{to the} orientation of the cellular _{array in} the capillary.

Figure

la, ^{focused on the} upper surface of the

capillary,

^{shows a}

regular

array of

points

^{with four-}

fold rotation symmetry, where the black lines or

brushes connect each of the points

forming

^a square array. At the _upper centre of the

image

^the quadrant

array of

points

^{is broken} by ^a

single triangle,

^the

upper ^vertex of which has five-fold symmetry ^seen

as five brushes. Below the triangle ^{an additional}

column of _squares is added to the array. The

triangle

thus constitutes the distortion of _{the upper} surface pattern ^{due to an}

edge

dislocation.

In

figure

^{1 c the} quadrant array of points ^{on the}

lower surface is in

overlapping

planar tessellation with the _array of

points

^{on the} upper surface (Fig. ^la

and see

Fig.

3) whereby ^the

points

^{on the lower}

surface are at the centres of the _squares formed by

the

points

^{at the} upper surface. The pentagon ^occurs due to a distortion of the square array ^at the node of the dislocation. Four of the

points defining

^the penta-

gon,have

^four-fold symmetry, ^{but the fifth}

point

^{at the}

lower centre of the pentagon ^has three-fold symmetry.

Note the termination of the brush at the point ^with

three-fold symmetry. ^This

point

^{and the} point ^with

five-fold symmetry ^{on the} upper surface indicate rotational defects of opposite

sign

^at the node of the dislocation.

By

focusing

^{from the} upper surface towards the

mid-plane

^{there is a} simultaneous motion of brushes downward that

eventually

^{meet in}

pairs

^{at the mid-} plane and become a new set of brushes. The new

brush

positions

^{are shown in} figure ^{lb which is focused}

slightly

^{above the} exact centre.

Fig. ^{1. -} Photomicrographs of the PFC texture in a dilute lamellar

lyotropic phase focused in registration ^at depths of a) ⁰ pm, b) ¹⁰⁰ gm and c) ²⁰⁰ um through ^a rectangular optical capillary ^{with an} optical pathlength of 200 kim. Crossed polars +. See ^{text. Bar} equals

35 pm.

Figure ^{2 is focused in} registration ^with

figure

^lb

near the

mid-plane

^of the cellular _array. The

polarizer

and

analyser

^are crossed but now rotated

through

⁴⁵⁰

with respect ^to

figure

^lb. Clearly observed is a white line matrix, which is the parabola ^{network itself.}

The sharper square pattern ^{is formed} by parabolae

opening upward

^and

terminating

^on the upper surface.

The more diffuse _square pattern ^{is in}

overlapping

planar

tessellation with respect ^{to the}

sharper

square pattern and is formed

by

parabolae ^{oriented anti-}

Fig. ^{2. -} Photomicrograph ^{of PFC structure in} registration ^with figure ^{1 b at the core} of the cellular _array. Crossed polars ^{x .}

See text. Bar equals ³⁵ pm.

parallel, opening

downward and terminating ^{on the}

lower surface. Both these _square patterns ^are mapped

as dotted lines in figure ^3. The black dots in

figure

³ represent ^the

anchoring points

of half the

parabolae

on the _upper surface and the circles represent ^the anchoring

points

^{of half the}

parabolae

^{on the lower}

surface. The brush

positions

ⁱⁿ figure ²

designates

^the region of intersection of two

parabolae

^{which are}

in

perpendicular

^{vertical planes and which open in}

opposite

directions. Note that the brushes are centred where the

parabolae

intersect ; ⁱⁿ contrast, the brushes

are centred at the

points

^{of the} square array in

figure

^la

and c where the

parabolae

^{anchor at the surfaces.}

Another feature to note is the distortion of the cellular _array

radiating diagonally

downward and outward from the node of the dislocation which is visible in both figures ^{1 and 2.} This is the stress field distortion associated with the node of the dislocation.

Fig. ^{3. -} Schematic lattice mapping ^from figure ^{la and c, and} figure ^{2 as follows :} a) e Anchoring points ^of parabolae ^{on the}

upper surface ^- figure la). b) ⁰ Anchoring points ^of parabolae ^on

the lower surface - figure ^{1 c.} c) ...:... White line matrix of figure ^2.

The intersecting parabolae. d) 2013201320132013 (i) Diagonal weaker network of lines from figure ² connecting 1 and 0 ; (ii) Tetrahedral cells of PFC structure. See text. Bar equals ³⁵ J1m.

Also visible in

figure

^{2 is a weaker}

diagonal

^array

of lines which _appear to

join

^the

points

^on the upper surface with those on the lower,surface. ^This diagonal

array is represented ⁱⁿ figure ^{3 as} solid lines.

A factor

contributing

^{to the} excellent resolution of the PFC structure in this lyotropic phase is that the

spacing

between surfactant bilayers ^is several times that of the individual lamellae of the smectic A

phase.

This increased bilamellar spacing increases the dimen- sions of the defect cores which facilitates observa- tion of various structural details.

The cellular _arrays of the PFC structure appear

gradually ^{out of the}

pseudo-isotropic

regions ^with

an

accompanying

^{increase in}

birefringence.

^The

reasons for this spontaneous ^{formation are not} clear,

although

^the

relatively

^low

viscosity

of this dilute

lyotropic

phase presumably ^{assists in the} annealing

process. The ^structure transforms to lower _energy states without

application

of external mechanical forces, ^{as is}

required

^{for the formation of the PFC}

structure in the

thermotropic

^{smectic A} phase [1].

Moreover, ^the strong interaction between surfactant molecules and

capillary

^{wall favors} structures with

a

perpendicular

orientation.

5. Discussion. ^- Rosenblatt et al. [1]

] describe

^the

PFC structure as consisting of intersecting parabolae

oriented

antiparallel

and rotated 90° about the z

axis to each other (Point-Group

D2D).

^{While this view}

of the structure in terms of the

points

^{on the} upper and lower surfaces is useful, ^further

insight

^{can be}

gained

by

viewing

^{it in terms} of the lattice formed by ^the

solid lines of figure 3. The space group of this two- dimensional lattice is

P4/n

^{where there is a four-fold}

inversion axis and a four-fold rotation axis perpen- dicular to the plane. ^{In terms} of this lattice the PFC structure may be considered as an array of tetrahedra and

pyramids

which close pack ^{as a} two-dimensional array between the _upper and lower surfaces of the

optical capillary.

^{For the PFC structure} the essential

packing element is the tetrahedron defined by ^and

containing

^two

intersecting parabolae.

^{The vertices}

of the tetrahedron are the

points

^{where the}

parabolae

intersect _{the upper} and lower surfaces. The interstitial spaces between the tetrahedra are

pyramids

^whose

bases are squares ^on the _upper and lower surfaces.

Both in our system ^{and in that studied} by ^Rosen-

blatt et al. [1] the tetrahedra are

highly

elongated.

In figures ^{1 and 2 the}

edges

^{of the} tetrahedra along ^the

upper and lower surfaces are about 30-40 pm ⁱⁿ

length,

while the

edges connecting

^{the upper and}

lower surfaces are about 200 _{pm in} length. ^{The corres-}

ponding

dimensions in the smectic A

phase

[1] ] ^are

10-20 pm and about _{500 pm in}

length.

It is

precisely

^this

elongation

of the tetrahedra which allows defects of the type ^{shown in} figures ^{1 and 2}

to occur. In the immediate vicinity ^{of the defect site}

some distortion of the tetrahedra takes

place.

^{So that}

the

intersecting parabolae

^{can retain}

perpendicularity,

110

the spacing ^between

parabolae

^{at the} anchoring ^sites

on the surfaces changes ^to accommodate the packing arrangement. This distortion is

propagated

along

two axes from the nodal

point

^{where two of the tetra-}

hedra are common to both the

point

with five-fold symmetry ^{and the}

point

with three-fold symmetry.

If the tetrahedra were

regular,

this distortion would be considerable and thus

energetically

unfavorable because

intersecting parabolae

would lie in non-

perpendicular planes.

But in the present system, distortion of the

elongated

tetrahedra is

slight,

^and

the

parabolae

^{are in}

planes

^{which are}

perpendicular.

To within the _accuracy of measurement, intersecting

parabolae

^near the defect site in figure ^{2 were found to}

be

perpendicular.

The solid lines in

figure

^{3 connect the}

points

^{on the}

upper surface to the

points

^on the lower surface and

are the

long edges

^{of the} tetrahedra. At the defect

site, ^{which as} indicated above is viewed as the node of an

edge

dislocation, ^{there is a} rearrangement ^{of the} tetrahedra. Here the basic four-fold symmetry ^of

points

^is

rearranged

^{into a five-fold} symmetry ^{at a}

single point

^{on the} upper surface which is a common vertex of five tetrahedra. Each solid line radiating

from this

point

^{is a common} edge ^{of two} of the five tetrahedra. Inversely ^a

point

^of three-fold symmetry is found on the lower surface, where three tetrahedra meet at a common vertex. Two tetrahedra are common to both these points. ^This rearrangement ^{of the tetra-} hedra is

accompanied

by

changing

^the shape ^{of two}

interstitial

pyramids.

^One

pyramid

^{whose base is on}

the lôwer surface becomes

pentagonal,

^{and one whose}

base is on the _upper surface becomes

triangular.

The

point

^{with five-fold} symmetry ^on the upper surface and the

point

^with three-fold symmetry ^{on the}

lower surface constitute two rotational defects or

disclinations of

opposite sign.

^{In a}

simple

^two-

dimensional _square or

hexagonal

lattice it is useful to consider an

edge

dislocation as the resultant of two

wedge

disclinations of opposite sign

[6].

Clearly

the situation here is similar, yet nevertheless more

complex

because of the tetragonal ^lattice. Thus, ^a systematic study ^{of defects in the} tetragonal ^lattice

and indeed in other arrangements ^{which are more}

complex

^{than the}

simple

square and hexagonal lattices

but which are

periodic

ⁱⁿ two-dimensions would be useful.

The secondary ^{and more diffuse}

diagonal

array of lines seen in

figure

²

apparently

^{indicates a further}

microscopic bending

^{of the}

bilayers

^{in addition to that}

along

^the

parabolae.

This additional network of lines

joins

^the

points

^{of the} upper surface with the points

of the lower surface, traversing entirely

through

^the

thickness of the

capillary.

^This

diagonal

^{network of}

lines is shown schematically ⁱⁿ

figure

^{3 as} solid lines.

These lines are located in interstitial regions ^{of the}

PFC network and are

evidently

the resulf of a further

bilayer distortion

required

ⁱⁿ

fitting

together

adjacent

cells.

Moreover, ^{the novel} ability demonstrated here to resolve clearly both rotational defects at the disloca- tion node and the stress field of the dislocation suggests that this

lyotropic

system may be useful for dynamic

experimental

studies where defect behaviour

during glide

of dislocations can be observed

directly.

Acknowledgment.

^- This research is

supported by

the U.S. Department ^of Energy, Contract N° EY-76- S-02-0018.

References

[1] ROSENBLATT, ^Ch. S., PINDAK, R., CLARK, N. A. and MEYER, ^R. B., J. Physique ³⁸ (1977) ^1105.

[2] KLÉMAN, M., J. Physique ³⁸ (1977) ^1511.

[3] HEALY, ^{R. N. and} REED, ^R. L., Trans. AIME 257 (1974) ^491.

[4] FOSTER, W. R., J. Pet. Technol. 25 (1973) ^205.

[5] BENTON, ^W. J., HWAN, R., MILLER, C. A. and FORT, T., Jr., Proceedings of ^ERDA Symposium ^on Enhanced Oil and

Gas Recovery, Tulsa, Oklahoma, August ^30-31 septem- ber 1, 1977.

[6] HARRIS, ^W. F., in Fundamental Aspects of Dislocation Theory,

Ed. Simmons, J. A., de Wit R. and Bullough, ^R. (Nat.

Bur. St., Washington, D.C.) Sp. ^{Publ. # 317} (1), 1970,

p. 579-592.