Lines in liquid crystalline phases of biopolymers

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Lines in liquid crystalline phases of biopolymers

F. Livolant

To cite this version:

F. Livolant. Lines in liquid crystalline phases of biopolymers. Journal de Physique, 1989, 50 (13),

pp.1729-1741. �10.1051/jphys:0198900500130172900�. �jpa-00211027�

Lines in liquid crystalline phases ^of biopolymers

F. Livolant

Centre de Biologie Cellulaire (CNRS), ^{67 rue Maurice} Günsbourg, ⁹⁴²⁰⁰ Ivry-sur-Seine, ^France (Reçu ^{le 12} janvier 1989, accepté ^{le 29 mars} 1989)

Résumé.

L’ADN, ^{le PBLG et} le xanthane sont trois polymères qui donnent des phases

cristallines liquides cholestériques ^en solution concentrée. Nous avons analysé différentes structures rencontrées dans ces phases que ^nous regroupons ^sous le terme de ^« lignes ^{» car elles}

ont en commun de se présenter, ^au microscope polarisant, ^{sous forme de} lignes ^{claires sur un fond}

sombre. Il s’agit soit de discontinuités moléculaires, soit de surfaces correspondant ^à l’interface entre deux phases ^{de nature} différente, ^{soit de} parois de twist que l’on ^rencontre dans les textures

homéotropes ^{où le twist est} empêché. L’analyse ^{de telles} structures renseigne ^{sur la nature de la} phase ^dans laquelle ^{on les rencontre.}

Abstract.

DNA, PBLG and xanthan are three polymers ^which give cholesteric liquid crystalline phases ⁱⁿ concentrated solution. We analyzed ^different structures encountered in these

phases ^{that we call « lines » because} they ^all appear, in the polarizing microscope, ^as illuminated lines in a dark background. They correspond ^{either to molecular} discontinuities, ^{or to surfaces} separating ^two phases of different nature or to twist walls which are observed in homeotropic

textures where the twist is prevented. ^The analysis ^{of such} structures gives information about the nature of the phase ^{in which} they ^{are observed.}

Classification

Physics ^Abstracts

61.30

61.70

1. Introduction.

The bibliography ^of liquid crystalline polymers is extensive but comments about their textures are rare. Those considered are mainly fingerprints, polygons ^{and banded} patterns. ^{Certain of} these studies come from biological polymers. ^Robinson [1, 2] ^studied the cholesteric phases given by ^a polypeptide (PBLG) ^{and a} nucleic acid (DNA). ^More recently, beautiful liquid crystalline phases ^were obtained with polysaccharides [3-6]. Many ^{of these} polymers produce

textures which need to be analysed in detail. Some of them were studied recently (nucleic acids, polypeptides ^and polysaccharides) for their cholesteric and hexagonal phases. ^The

nature of the phase depends ^on the concentration of polymers. ^{When it is} regularly increased,

cholesteric spherulites appear first in the isotropic phase [7, 8]. ^These spherulites ^{coalesce to}

form a cholesteric phase [9]. When the concentration is further increased, ^the cholesteric

phase transforms into a columnar hexagonal ^one [10].

The textures which have been studied so far are those given by ^a distribution of parallel layers showing ^focal domains, polygonal fields and fan-shaped ^textures. However, cholesterics

are fundamentally nematics and threads are present. This work deals with lines observed in

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500130172900

1730

these biological polymers when the helical pitch ^is large ^{or when the} cholestericity ^is prevented by ^certain anc1’"lorage constraints such as homeotropic conditions.

The examination of liT _es ir polymer phases ^is undoubtedly ^more difficult than in liquid crystalline phases of sr.all rriolecules mainly because the birefringence ^is weak and also because polymers ^{are often} polydisperse. This situation leads to easy confusion between different domains corresponding ^{either to the} isotropic phase ^{or to} homeotropic ^and planar

textures of the cholest eric phase. ^The study of these lines is often a way ^to recognize ^the

nature of these domains. Most of them were already observed and interpreted in classical

liquid crystal [11-14]. ^New situations occurs also in these polymers and will be considered.

In this paper the phases ^are always observed between crossed polars ^{with a} background

which is usually dark. What we mainly ^see corresponds ^to brilliant lines as illustrated in the

plates. Actually, the observed lines are not always ^true lines in the usual geometrical meaning. They ^can be due either to molecular discontinuities which lead to the presence of thin threads as in nematics or to the interface between two phases, ^{or to} molecular distortions such as twist walls which extend in a definite volume which will be analysed in detail.

2. Material and methods

MATERIALS. - Calf thymus ^DNA (Merck) ^{was sonicated to} obtain molecules whose lengths

range from 0.15 ^to 1.6 _um. It was then diluted in 10 mM Tris-Cl- buffer (pH8) ^{added with}

1 mM EDTA. Two methods were improved ^to obtain these liquid crystalline phases ^{of DNA}

in a reproducible way. They ^are described in detail in [15] and will be recalled briefly ^here.

-

A 1 mg/ml solution of DNA is added drop by drop ^{to a} solution of 400 mg/ml polyethylene glycol (PEG ^{MM 8} 000) ^{in 2 M KCI. A} phase segregation ^{occurs and each} polymer concentrates in a separate phase. ^{The DNA} precipitates ^are deposited between slide and coverslip and the cholesteric organization appears in ^a few minutes at the periphery ^{of the} aggregate.

-

A drop ^{of a} mixture of DNA (t’om ^{5 to 10} mg/ml) ^{and KCI} (0.2 ^{to 0.4} M) ^is deposited

between slide and coverslip and stored several weeks at 4 °C. The solution concentrates

progressively ^{and a} cholesteric organization appears in small regions ^limited by ^air.

Two kinds of poly-ybenzyl-L-glutamate ^were used : PBLG (MM ²⁸ 000, Sigma) ^and

PBLG (MM 20 000) synthesized by the Centre de Biophysique Moléculaire (Orléans, France). ^{A small amount of} powder ^was deposited ^{onto a slide, a} drop of dioxan added and

immediately covered with a coverslip.

Xanthan (MM 200 000) ^was purified ^and kindly provided by Rinaudo and Milas

(CERMAV, CNRS, Grenoble, France). ^{It was} prepared in aqueous solution (distilled ^water,

60 % NaCI or KCI) ^{and used as} described for PBLG. Interesting patterns ^{were created in} xanthan by addition of a drop of. concentrated saline solution to a preparation ^{made in}

distilled water. This produces strong variations of the helical pitch ^over short distances for two reasons : local dilution of the preparation and addition of salt.

MICROSCOPICAL TECHNIQUES.

Preparations ^were observed in a Leitz (Orthoplan Pol) ^{or a}

Nikon (Optiphot ^X Pol) polarizing microscope, either between crossed polars ^{or between} opposite ^circular polarizer ^and analyser. To determine the molecular orientations, ^a _quartz first order retardation plate ^{was inserted at 45° between} polarizer ^and analyser. ^{The use of} circularly polarized light is very convenient since it is ^not required in these conditions to orientate the layers ^{at 45° from the} polars directions, ^{all the} birefringent patterns ^are directly

visible.

DRAWING CONVENTIONS. - We used the nail convention in which molecules are represented by ^lines, nails and points ^when they ^are respectively parallel, oblique and normal to the

representation plane. ^The tip of the nail indicates the extremity of the molecule which is

pointed towards the observer. In several _cases, nails were omitted to clarify ^the drawing.

3. Results.

When concentrated solutions of polymers ^{are observed between crossed} polars, many regions

appear black. This extinction corresponds ^{to three} major different situations : an isotropic phase, ^a homeotropic ^{or a} planar ^{texture in a} cholesteric phase.

Isotropic phases ^and homeotropic domains appear completely extinguished ^between

crossed polars either because there is no birefringence ^or because the optical axis of the medium is parallel ^{to the} microscope axis. With small molecules, ^{such as} MBBA, ^the homeotropic phases ^are recognized by ^{the « flicker » effect of} light scattering ^{due to thermal}

fluctuations. However, ^this effect is not easily ^{seen in} liquid crystalline polymers ^{such as}

PBLG and this leads to easy confusion between isotropic ^and homeotropic domains. The low

intensity ^of light scattering ^{between crossed} polars ^{is due to} high viscosity ^{due to the} high length ^{of the} polymers ^{and to the weak} birefringence.

Planar cholesteric textures can present iridescent colours which are due mainly ^{to a}

selective reflection of circularly polarized light. ^{Such a} phenomenon ^{has been} interpreted by

de Vries [16]. ^{In the} microscope, ^{the other} circularly polarized component ^{of the} light ^is

transmitted and shows similar colours. However, these colours which characterize the cholesteric organization ^are only observed when the helical pitch ^{of the structure is close to}

the wavelength of the visible light. When the helical pitch ^{is out} of this range, the planar

cholesteric textures appear grey ^{or even} dark and they ^can be confused with homeotropic ^or isotropic phases. ^{As will be seen} below, ^{the nature of the} bright lines observed in these phases

is useful in the recognition ^of phases ^{and textures.}

3.1 BRILLIANT LINES IN THE HOMEOTROPIC PHASE.

Homeotropic phases ^{were obtained}

with low molecular weight PBLG without any special ^{treatment of the} glass surfaces. The

untwisting of the cholesteric phase ^{was observed} only in very thin preparations ^{and was} probably ^{due to a} spontaneous anchoring of the molecules to the slide and coverslip. Isotropic

and homeotropic phases coexist here in the same preparation (Plate 1). They ^{can be} distinguished by shifting slightly ^the coverslip : isotropic domains remain black whereas

homeotropic ^{domains turn} illuminated because molecules are forced to align obliquely ^or

even parallel ^{to the} preparation plane. ^Molecules regain very quickly ^their original

orientation when the shift ceases.

Two main types ^{of lines are} observed : the lines which delimit the homeotropic ^domains

from the isotropic phase and the lines which are observed only within the homeotropic phase

and which are usually very bright. ^{The use of a} quartz first order retardation plate (À ) gives information about the nature of these lines. The slow axis of this plate is oriented at

45° relative to the polarizers, ^the polarization ^colour being ^{red 1} (sensitive tint). ^{In PBLG the} highest refractive index of the molecule is parallel ^to its helical axis. Consider first the case of

a line with molecules mainly parallel ^{to this} line, ^{at least in} projection ^{onto the} preparation plane. Through ^a rotation of the stage, ^{the line can be made} parallel ^to the slow axis of the À retardation plate and the red 1 turns to blue (the highest refractive index of both the material and the plate ^are superimposed). ^{On the} contrary, if molecules are mainly ^{normal to the} line,

the colour turns orange ^or yellow. ^The ellipsoid of indices will be cut according ^{to an} ellipse

which is oriented either parallel ^{or normal to the line.}

A first type of lines is seen at the interface separating ^the homeotropic domains and the

Plate 1.

Homeotropic ^{textures in PBLG.} (a) ^{The dark} regions observed between crossed polars correspond ^{either to a} homeotropically aligned phase (h) ^{or to an} isotropic phase (i). Bright ^{lines are of}

two kinds : those limiting ^the homeotropic domains from the isotropic phase (1) and inversion walls in the homeotropic phase (2). ^Their brightness is different. (x 425 ; + ). (b) ^Double spiralized patterns of inversion walls in the homeotropic phase. (x 410 ; + ). (c) Undulating patterns appearing ^{in a} homeotropic ^domain. (x 370 ; + ). (d) Homeotropic domain in which pairs of inversion walls are

associated to the interface line. They correspond ^{sometimes to} invaginations of the interface line.

(x ^{370 ;} +). (e) Homeotropic domain transformed into a cholesteric structure by ^{one of the two}

processes illustrated in c and d. (x ^{365 ;} +). (f) Large homeotropic region ^{with numerous inversion}

walls. (x ^{190 ;} + ) . (g) Cholesteric texture grown from the homeotropic phase. Note the closed lines

inserted in the structure (x 1 020 ; + ).

isotropic phase (Plate la). ^Their brightness ^{is not} very strong ^{and we} determined that molecules ^were aligned ^{more or less} parallel ^{to the} observation plane ^{after a} rotation of about 90°. The hypothesis ^{of a bend wall can be ruled out} by ^{the use} of the retardation plate.

Molecules present mainly ^a twist effect and the light intensity of the line depends ^{on the} importance of the twist : it is maximum when molecules lie exactly ^{in the} preparation plane.

The use of the retardation plate ^{does not} permit ^{us to} choose between the two possible

distributions of molecules at the interface with the isotropic phase ^{which are drawn in} figure ^{1. However,} cholesteric PBLG spherulites ⁱⁿ equilibrium ^{with the} isotropic phase ^show

concentric layers indicating ^a parallelism between molecules and interface [8]. ^{From these}

remarks we propose the model of figure ^{la with} the natural twist and an amount of splay ^and

bend. The ^use of the retardation plate ^{is not} sufficient to determine the twist handedness but contrary ^to the situation observed at the interface between homeotropic ^and isotropic phases

with ^a nematic product ^{such as MBBA} the presence of ^{a constant} twist orientation is likely

here since there is no interruption of these walls all along the interface. It is probably ^left-

handed as in the cholesteric phase ^{in the same solvent.}

Fig. ^1. - Homeotropic domains limited by ^slide (s) ^and coverslip (c) ^are surrounded by ^the isotropic phase. ^{Molecules twist near} the interface with the isotropic phase and the twist axes are lying radially ⁱⁿ

the preparation plane. ^The long ^axes of the horizontal sections of the ellipsoids of indices are aligned parallel ^to the interface line. The two situations a and b are theoretically possible but the situation a is much more probable (see text). The molecular orientations are given ⁱⁿ transverse and in apical ^view.

The second type of lines is observed in the homeotropic phase. They ^{are very} bright ^and

appear much larger ^{in the} micrographs (Plate ^{la, b, f,} g). They correspond ^to inversion walls

along which molecules present ^{a rotation of 180°} of their orientation. It is a pure twist and there is ^no bend since molecules ^are aligned parallel ^{to the line as} determined by ^the

retardation plate. These lines may be either closed ^or open with ^two free ends or linked to the

line limiting the domain (Fig. 2). The free end of an inversion wall corresponds ^to

1734

Fig. ^2.

Possible evolutions of the bright lines observed in the homeotropic phase. ^Lines limiting ^the homeotropic domains from the isotropic phase (1) correspond ^to loci where molecules are more or less

aligned ^{in the} preparation plane ^{after a} rotation of about 90° (a). Instead of rotating rapidly ^{at the}

interface of the domain, molecular orientations may twist regularly ^{from the centre} of the domain to its

periphery. The domain is then birefringent (b). Lines of the first type ^{can also} invaginate ^{inside the} homeotropic domain and transform into lines of the second type (c). Continuation of this process ^can

produce domains which are entirely cholesteric (d). Inversion walls (type 2) may also form inside of the

homeotropic domain and these lines are either closed, open (with ^{two + 7r} disclinations) ^{or linked to the}

interface birefringent ^line (e).

a + 7T disclination whose defect line is normal to the preparation plane (Fig. 2e). ^In large homeotropic domains these lines can form also spiralized patterns (Plate 1b) ^and spirals ^are

either left-handed or right-handed ^{with a} large majority ^of right-handed orientations. This reveals a dissymmetry in the behaviour of molecules at the interface between the slide and the

coverslip. Homeotropic ^textures obtained with helical molecules are constrained systems : ^the twist occurring spontaneously between molecules is prevented, probably ^{on account of} strong anchorage conditions to the glass surfaces but the twist is finally ^relaxed along these lines.

They ^{become more and} more numerous in certain regions ^and gather ^{to form a} cholesteric

phase ^{in which numerous} closed lines are seen (Plate lf, g).

Connections exist between these two kinds of lines. The lines limiting ^the homeotropic

domains can invaginate (Plate Id) ^{and transform into} pairs of lines of the second type. ^These invaginations ^{can become numerous and fill} entirely ^the homeotropic domain which transforms into a cholesteric one (Plate le, Figs. 2c, d). ^Such patterns ^{can be} formed either by

this process ^or by the undulation process illustrated in plate lc and which will be described elsewhere.

3.2 DEFECT LINES IN PLANAR CHOLESTERIC TEXTURES.

Tear-drops and related patterns. - Cholesteric liquid crystalline phases ^were obtained with

DNA, PBLG and xanthan. The half helical pitch (P/2 ) varies with the polymer ^concen-

tration. It can reach 1.5 _um in DNA, ²⁰ um in xanthan and 100 um in PBLG. Values as small

as 33 nm were measured in xanthan solutions by ^electron microscopy (unpublished results).

The defect lines of this phase ^are followed in planar textures ; they ^are either thin or thick threads. The molecular distributions corresponding ^{to these two} situations are recalled in

figures 3a, ^{b in} transverse and apical ^views. The relative occurrence of these two kinds of defects was studied in transverse view in the three polymers [9]. ^It appeared ^that p /2 dislocations were predominant ^{in DNA} and xanthan whereas the p dislocations were

much more represented in PBLG. In planar ^{textures we} only analysed thick threads and they

are shown in plate ^2.

Fig. ^3. - Edge dislocation lines observed in transverse section (a) and their visualization in an apical

view (b). Thin threads correspond ^to dislocations whose Burgers’ ^{vector value}

p /2. Thick threads are

associated to dislocations whose Burgers ^vector

p.

The classical « tear-drops » figures, described and analysed by Bouligand [11] ^{in MBBA}

twisted by addition of cholesterol benzoate are found also in DNA (Plate 2a, b), ^{and in}

xanthan (not illustrated).

The arrangement ^{of the} layers leading ^{to such} figures ^{is redrawn in} figure 4 and the detailed

explanation given ^{in the} legend ^{of the} figure. The interest was to obtain with long polymers

the same typical patterns than those described with small liquid crystal molecules. Such ^« tear-

drop » patterns ^are characteristic of cholesteric phases ^{and can be used as a} good ^{tool to}

define these phases ^{as well with} long and small molecules.

These « tear-drops ^» lines form different textures with either nested or overlapping cusp-

points. They correspond ^{to different} dispositions of cholesteric layers.

The core structure of the tear drop ^{line is a} double fold which corresponds ^{to the} beginning

of a double spiral. This is drawn in plane ^{2 of the} figure ^4. The passage from ^a simple ^{« tear} drop » ^{to a} system ^{of nested « tear} drops ^{» is} produced by ^the winding of this double fold which creates a true double spiral. ^These patterns ^{are seen in PBLG} (Plate 2c). ^{The number}

of nested « tear-drops » depends ^{on the} amplitude ^{of the} winding. ^This amplitude ^varies continuously whereas the number of nested ^« tear drops ^{» is a discrete} parameter. ^{Each new} line appears when the winding angle ^{exceeds a threshold} angle leading ^{to a new séries of}

vertical directors. The Burgers ^vector associated to the two edge-dislocations ^is always ^a

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Plate 2. - Defect lines observed in planar cholesteric textures of DNA, PBLG and xanthan. (a, b) « Tear-drops » ^{in DNA} (x 1390 ; ^{a :} .1. , ^{A ; b :} + ). ^(c) Concentric « tear-drops » ^{in PBLG} (x 360 ; ’+ ). (d, ^{e) Series of} overlapping lines with cusp points ^{in PBLG} (d) and xanthan (e). (d :

x 560 ; ^{e : x} 630 ; +). (f) ^Another pattern ^of overlapping ^lines (x ^{435 ;} + ). (g) Intricated lines observed in xanthan at the boundary between the planar concentrated region (p ) ^{and the} peripheral

diluted one (r), after infiltration of a drop ^{of a} saline solution (x 370 ; + ).

Fig. ^4. - Interpretative drawing ^{of a} « tear-drop » ^defect (redrawn ^after Bouligand, 1974). ^The

contrasted line corresponds ^to loci where molecules are parallel ^{to the} microscope ^{axis. Several}

transverse section planes ^{are drawn} along this line. In plane 1, the cholesteric order is slightly ^distorted

and a double fold appears in plane 2. This double fold may be considered ^{as a set} of two edge

dislocations separated by ^{a distance} of p/2. ^These edge-dislocations ^{are in} reality ^a single ^{one because}

the edge-dislocation visible in plane 3 follows the cholesteric helicity ^{and forms an helical arc} by ^rotation

from plane ^{3 to} plane ^{4 and to} plane 5. The rotation angle ^is - p since the cholesteric liquid ^is supposed

to be left-handed and the vertical displacement (p/2 ) compensates the vertical shift due to the double fold.

multiple of p. When it equals 2 p ^{there is} formation of two nested « tear-drops ». ^This

situation is given ^{as an} exemple ⁱⁿ figure 5. Numerous series of nested « tear-drops ^{» were}

obtained by Bouligand [11] ^{in other materials and their} importance in the formation of cholesteric spherulites showing ^a radius of disclination has been pointed ^out previously [8].

Overlapping ^lines with cusp points ^were obtained in PBLG (Plate 2d). ^{In xanthan} (Plate 2e, f), they ^were produced by addition of a drop ^{of a} NaCI solution which infiltrates the

preparation made in distilled water. It is generally ^{difficult to follow} completely these lines because there are often important changes ^{in the} orientation of the cholesteric axis (Plate 2e)

or because the lines form an inextricable mess (Plate 2f).

Two different structures can account for these patterns ^{and are} presented ⁱⁿ figure ^{6. The}

first one corresponds ^{to a} simple folding ^{of the} cholesteric structure with formation of two associated edge-dislocations À - ^{À + . The number of} layers added between these dislocations determines the number of lines. When the Burgers ^vector equals 2 p, ^{there are two lines} (Fig.

6a) ; ^{when it} equals 3 p ^{there are three lines} (Fig. 6b) ^{and so on. It is} topologically impossible

for such lines to close and form « tear-drops ^{» such as those described in} figure ^5, because the

path of the line described in the succession of planes 3, 4, ^{5 in} figure ⁴ corresponds ^{in the}

structure to a rotation of 180° (p /2) of the molecular orientations. In the case of figures ^6a

and 6b the two branches of each ^« V-shaped ^» pattern ^are separated respectively by p ^and

3 p /2. ^{On the} contrary, ^{it is} possible ^to continue these lines ^to form « spindle-shaped »

patterns, ^{such as} those described in [11].

The alternative situation corresponds ^to successive foldings ^{of the} layers ^which produce

numerous edge-dislocations k - ^{À + of} value p (Fig. 6c). ^{In contrast} with the first situation,

these lines can form ^« tear-drops ^». This situation is much more unstable than the first one

because the layers ^{can slide} laterally ^{the ones over the others and the different «} tear-drops ^»

separate.

1738

Fig. 5. - Nested tear-drops ^{in a} left-handed cholesteric. The structure described in figure ^{4 has been}

wound and edge-dislocations equal ^now 2 p which induces the formation of two nested ^« tear-drops ^».

It is very difficult to determine which situation corresponds ^{to the} patterns given ⁱⁿ plate 2d,

e, f. However, ^we suppose ^{that the structure} given ⁱⁿ figures 6a, ^{b is that} occurring ⁱⁿ plate ^2d

whereas the other one (Fig. 6c) may be attributed ^to plate 2e, f. The first situation produces quite stable lines which are moreover very close together ^since they ^are separated only by ^half

the helical pitch (p/2 ). ^{On the} contrary, the second situation is much more unstable which could explain why the lines of plate 2e, ^{f were} moving ^{when we} observed them. Besides, ^the distance separating ^{two lines can be} large in the situation shown in figure ^6c especially ^near

the cusp points and this is also observed in plate 2e, ^f.

Other patterns. - Some other particular aspects ^{were obtained} by the method mentioned

previously : ^a drop ^{of a 6 % NaCI solution was} deposited ^{at the} edge ^{of the} coverslip ^and

infiltrated into the preparation by capillarity. ^This produces ^a concentration gradient ⁱⁿ polymer and ions from the periphery ^{to the center of the} preparation. ^Low polymer

concentration and high ^ionic strength ^{are obtained at the} periphery ^{and these two} parameters

are known to increase the pitch of the cholesteric phase in xanthan [17]. ^The patterns ^of plate 2g ^are observed in such preparations, ^{between a central} region p of small helical pitch

and low ionic strength ^{and a} peripheral region r ^of larger pitch ^{- and} high ^ionic strength.

They ^are reminiscent of clearcut variations of contrast or color in Grandjean-Cano

Fig. ^{6. - Two} possible interpretations ^{of the} overlapping ^lines presented ⁱⁿ plate 2d, e, f. (a, b) A simple fold of the cholesteric structure leads to the formation of two associated edge-dislocations

À - k ’ whose value determines the number of lines (2 lines when b

2 p, 3 lines when it equals 3 p).

Such lines cannot close to form ^« tear-drops ^». (c) Successive foldings of the cholesteric structure with formation of numerous k - k ’ dislocations of value _p. Their number determines the number of lines.

These lines can give ^{either «} tear-drops ^{» or «} spindle-shaped ^» patterns.

preparations [18, 19] ^which correspond ^to abrupt changes ^of rotatory power along dislocation lines. However, ^the Grandjean ^lines align parallel ^to each other and delimit domains in which the number of cholesteric layers is different whereas here, ^{one or a} few defect lines draw successive loops ^which overlap ^{as the} oblique projection ^{of an helix onto an} oblique plane.

This line delimits different regions ^whose optical density ^increases by successive steps. ^Four different grey hues (1, ^2, 3, 4) ^{can be seen in} plate 2g. ^The complete path of the line cannot be followed completely except ^{in the} right part ^{of the} micrograph (arrow). ^A schematic and

hypothetical path of this dislocation is drawn in figure ^7.

1740

Fig. ^7. 2014 (a) ^{Path of a} defect line running helically (from ^Plate 2g). (b) The existence of an helical loop changes the level of the line by 2p and suppresses ^a cholesteric layer (p) inside of the loop. (c) ^The

situation b is drawn in a perspective view. It appears clearly that the number of layers varies in the different domains limited by the defect line.

These steps originate ^{from the} obliquely spiralized path ^{of an} edge dislocation 03BB - 03BB+ of value p : the line goes from ^a level 0 to a level 2014 2p ^{after a rotation of 360°. A} supplementary layer is added outside of the loop (Fig. 7b), ^{the addition} of material inside of it

being topologically impossible [11]. ^The shape ^{of this curve is} determined by the orientation of the polymer concentration gradient : ^the loops ^are pointed towards the less concentrated

region.

The pattern ^{shown in} plate 2g corresponds probably ^to figure 7b, given ^{in a} perspective

view in figure 7c. The number of layers is different from one domain to the other : if it equals

x inside of the loop, ^{it will} equal x ⁺ 1 in the less concentrated region ^{and x + 2 in the more}

concentrated one. This would explain the different light intensities observed in these different domains. We can deduce from these observations that the peripheral part ^{of the} preparation (at ^the bottom of the micrograph) ^{is less} concentrated in polymer ^{which was verified} experimentally ^{since the} preparation ^{was diluted} by addition of a saline solution. Moreover,

since the preparation thickness remains constant, ^the helical pitch ^{has to} be smaller in the central part ^{of the} preparation than in the outer part. This is in agreement ^{with data obtained} by Rinaudo and Milas [17] ^who observed that the helical pitch ^is larger ^{in saline solution than}

in distilled water, ^{for a} given xanthan concentration.

Conclusion.

Three different polymers ^were analysed : ^a polypeptide, ^a polysaccharide ^{and a} poly-

nucleotide. We show that most of the defect lines analysed ⁱⁿ classical liquid crystals ^{are also}

observed with these extremely long molecules. Some of the defects can therefore be used to characterize the cholesteric phase. The thin threads which correspond ^to p/2 dislocations

were not observed in the planar cholesteric textures. They exist however since they ^are very

numerous in the fingerprint patterns [9]. ^Their observation requires very thin preparations

and large domains with uniform planar ^{textures. Such} situations are rarely ^{obtained when the}

molecular length ^is high ^and polydisperse. Homogeneous fractions of DNA 500 A in length

allowed us recently ^to follow their path. Preliminary observations do not reveal significant

differences with the classical liquid crystals.

Acknowledgment.

We are grateful ^{to Dr. Y.} Bouligand ^for reading ^the manuscript and discussion.

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