Structural relations between lyotropic phases in the vicinity of the nematic phases

J. 42 1427-1440 OCTOBRE 1427Physique (1981) 1981,
Classification
AbstractsPhysics
61.30E - 82.70
Structural relations between lyotropic phases
in the of the nematic (*)vicinity phases
Y. Hendrikx and J. Charvolin
Laboratoire de des Solides Bâtiment Université 91405 France510, Paris-Sud, Orsay, Physique (**),
le le 19 (Reçu février 1981, accepté 5 juin 1981 )
2014 Résumé. Les « des fluides solutions sont phases nématiques lyotropes anisotropes, aqueuses d’agrégats»
finis de molécules orientation en anisotropes Leur amphiphiles. comportement nématique (écoulement, champ
Ces résulte des corrélations orientationnelles entre ces dans le domainemagnétique) agrégats. phases représentent
des cristaux des états d’ordre intermédiaire entre les ordonnées, lamellaire, liquides lyotropes phases hexagonale
ou et les micellaires totalement désordonnées.cubique phases
Dans ce manuscrit on tente de les conditions sont à de des dégager qui l’origine l’apparition phases nématiques
dans le sulfate de A cette fin on le de au système décyl sodium/1-décanol/eau. explore diagramme phase voisinage
de celles-ci. Les différentes sont identifiées leurs textures et leurs structures sont déterminées dif-phases par par
X A fraction de aux de ces études on les effets induits la variation enrayons petits angles. partir peut dégager par
concentration de deux à savoir le décanol et l’eau. la concentration en décanolparamètres importants, Quand
on observe la courbure interfaciale des décroît augmente agrégats amphiphiles que (une phase hexagonale
dont les des infinis sont est substituée une les cylindres progressivement par phase lamellaire; agrégats phases
intermédiaires sont soit des dont les sont des rubans soit dans certains cas des infinis, phases agrégats
Par ailleurs la teneur en eau la courbure interfaciale des augmente, nématiques). lorsque agrégats amphiphiles
croît et les se désordonnent lamellaire est dans un substituéeagrégats progressivement (une phase premier temps
une dont les sont des rubans ensuite une » dont les sont desinfinis, par phase agrégats phase « nématique agrégats
« » une dont les sont des oblats sphéroïdes prolats apparaît, puis phase nématique agrégats sphéroïdes pour
atteindre enfin une micellaire totalement Le et l’eau décanol déterminent donc la phase désordonnée). forme,
les dimensions et des de manières on considérer les « néma-l’organisation agrégats antagonistes : peut que phases
de localisées dans un domaine très étroit du résultent d’un tiques lyotropes », diagramme phase, compromis
entre les actions de ces deux conjuguées paramètres.
2014 Abstract. « Nematic » are fluids made of of moleculeslyotropic phases anisotropic aggregates amphiphilic
in water. Their nematic behaviour orientation in a is related to the orientationaldispersed (flow, magnetic field)
correlations between the which are of finite dimensions. Therefore areaggregates particles they
in the field of of intermediate states of between the well knownexamples lyotropic liquid crystals organization
ordered or cubic and the disordered micellar lamellar, hexagonal phases totally phases.
This an to determine the conditions the occurrence of nematic in theattempt governing paper presents phases
For is sodium this the in thesulfate/1-decanol/water. purpose ternary phase diagram investigated system decyl
first the various are to their of the nematic textures, vicinity phases, lyotropic phases recognized according then
small effects their structures are determined From these observations the inducedthrough angle X-ray scattering.
the two most obvious the concentrations of decanol and are as follows. When thewater, by changing parameters,
is crossed towards decanol concentration curvature of the inter-the phase diagram increasing amphiphile-water
face decreases made of infinite is a lamellar intermediate (an hexagonal phase cylinders replaced by phase, phases
made ribbons and in some cases « nematic » in On the other whenof infinite hand, phases may appear between).
and the the water the curvature of the interface increases content is increased, amphiphile-water stacking
a made of infinite of the becomes more disordered lamellar is first (a phase replaced by phase ribbons,aggregates
thereafter a « nematic » made of then a « nematic » of oblate by phase prolate spheroids, by spheroids
control the or and a micellar Therefore decanol and water sizesdiscs, phase). shapes, finally by fully
and of the and the « nematic » which a limitedpacking aggregates along antagonistic ways phases, occupy very
area in the be considered as from the delicate of these two phase diagram may resulting interplay parameters.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01981004201001427001428
- 1. Introduction. The of lyotropicpolymorphism
illustrates the wide of states ofmesophases range
for molecules in water.organization amphiphilic
The ordered oftypical liquid crystalline phases
made of infinite are amphiphile-water systems aggre-
of molecules which are themselvesgates amphiphilic
with some translational orderarranged long range
dimen-of the in two or three one, (periodicity density
On the other the disorderedsions). hand, totally
micellar are made of finite or phases spherical ellip-
soidal In Lawson and Flautt 1967, aggregates. [1]
made some new small amounts of aphases by adding
chain alcohol and sul-salt - long (1-decanol) (sodium 1. SdS-decanol-water in theFig. Hypothetical phase diagrams
to a classical fate) of the nematic domain from water-amphiphile system (sodium data onvicinity extrapolated existing
related in sulfate or SdS These as closely systems (9). (Concentrations decyl weight per cent.)[2]). phases appeared
fluids whose andanisotropic properties (texture
orientation in a arespontaneous magnetic field)
the rather similar to those of nematics. For this viscous andthermotropic macroscopically phases appear
« In the micellar domain thereason were called nematics ». Since optically anisotropic. they lyotropic
are finite or without other nematic1967, aggregates spheres ellipsoids anymany systems, forming lyotropic
have been the is fluid and to now phases, investigated [3-7]. long range ordering ; phase isotropic.Up they
It is here that the offall into two classes to the orient to remark according way they interesting properties
and are associated in a field are said to be of I fluidity anisotropy together onlymagnetic [7]. They type
when in the nematic domain. The orderedhave a of they orientationally positive anisotropy magnetic
as inter-their nematic therefore be considered director thesusceptibility AX, phases may aligns along
mediate states of order between the field. are said to be of II when 0, translationallyThey type AX
their orients ordered lamellar and and the director to the field. hexagonal phases totallyperpendicular
disordered micellar one. In this we toThe structure of these has been studied paper, try phases
determine the conditions the occurrencegoverning small in therecently through angle X-ray scattering
of the nematic states their structuralby studying SdS-decanol-water It has been shown thatsystem [8].
relations with the ordered or disorderedin these the molecules neighbouring are assembled in phases aggre-
We have therefore the SdS-as in other phases. investigated but whichgates, any lyotropic liquid crystal,
decanol-water mean of are phase diagram by opticalwith orientational order without trans-arranged
observation in order to the lational order. The 1 classify phases according> was shown totype phase (AX 0)
to their within each the structurestexture, then, contain phase, andelongated aggregates (prolate spheroids)
of a few have been determined samples X-raywe to call it « calamitic » by following [9] propose (from
diffraction.The II wasXaÂotpou : reed). type phase (Ax 0)
shown to be made of flat particles (oblate spheroids)
- « and we call it discotic » 2. Sodium sulfate was either[9] (from 03B4i03C3xo03BE: quoit). Samples. decyl
Therefore we a structural classification for these in the or was of commercialadopt prepared laboratory [18]
nematic as or 99 phases was N, (calamitic) Nd (discotic) origin (Merck %),1-decanol p.p.a.
whereas the first as 1 or II was based on > 99 with one, type type identical (Fluka p.p.a. %) ; (samples compo-
either with SdS in themagnetic properties [10]. sition, prepared synthesized
or with the commercial SdS had the sameAt this in order to define the aim of our laboratory stage, work,
it is useful to these nematic properties).compare lyotropic phases
The were in sealed tubes and the classical For this we shall samples prepared bylyotropic phases.
of the of the com-consider the SdS-decanol-water dia- weighting appropriate quantities ternary phase
and ultra-sonicationfrom as it can be data pounds homogeneized through gram extrapolated existing
and To stable all about sodium sulfate-decanol-water and centrifugation. get samples glassdodecyl
material must be without sodium sulfate-decanol-water perfectly clean, any fattyoctyl phase diagrams
furthermore the theThe location of the nematic impurities, temperature during [11]. approximate phases
has to be maintained below 50°Cis shown in 1.relative to other known homogeneization figure phases
in order to the of SdS into decanolThe small nematic is surrounded three prevent domain hydrolysis by
which the from the nematiclamellar and which have [19] displaces sample domains, micellar, hexagonal
domain towards the lamellar one.been the of structural insubject many investigations
In and various the lamellar systems [11-17J. hexagonal
- - domains the are infinite lamel- 3. methods. 3.1 TEXTURES. Theamphiphilic aggregates Experimental
lae or with nature of the ordered lamellar or cylinders, periodically packed long range samples, cylindrical,
order translational one or two disordered were first identified dimensions; nematic, micellar, along by1429
their textures in The their dimensions the of theirobserving polarized light. samples through knowledge
volume concentration. The Guinierwere smeared in between and observed of the geometry glass plates
under a camera is not suitable for such We usedwith heating experiments. polarizing microscope equipped
Laue and camera a monochromatic camera with collimationstage (Leitz). point
= a movable 12 kG(Cu, Kat,À 1,54 Á) equipped with
- of the 3.2 STRUCTURES. The structures samples The resolution of this camerapermanent magnet.
were obtained small diffraction. by angle X-ray (We with the of varies because the film isangle photograph
however we have used it in a limited smallplanar ; only shall use the snotations following s= 2 sin 0where
where it was focused. The wereangle region sample
is the the wave and 2 0vector, scattering length in sealed of diameter held1.5 glass capillaries mm,
the between scattered and incident angle beams.) to the beam. were orientedperpendicular X-ray They
Three different were used to the field in the set-ups according the Themagnetic equatorial by plane.
nature of the sample. director the field > 0 when andaligns along Ax
- orients to the field 0. For3 . 2 .1 Phases with translational order. perpendicular A x long range
both the diffraction were obtainedIn this case the are samples patterns samples naturally polycrystalline
for with the two beam eitherand were studied with a Guinier’s camera for small configurations X-ray they
or to the director. theof studies parallel perpendicular (To get powdered [20] ; (monochro-angle samples
= beam to the director the werematic wave radiation, A, X-ray parallel samples Co, Kal length À. 1,788 9
= oriented the field outside the Lauelinear diameter of the camera 125 by magnetic collimation, mm).
In this two sections of the The were in between mica sheets camera.) way reciprocalseparated bysamples
and to the directorof thickness 0.7 the whole a teflon space, parallel perpendicular mm ; cell,spacer
were access to the whose was ensured a set of and a obtained, respectively, giving averagetighness by joints
and two dimensions of the mechanical was in a thermostated symmetry diffractingclamping, placed
element. The detailed of the diffractionenclosure analysis [21].
were elsewhere From them it This has been used tocamera patterns given [8]. appearsvery successfully
that the are either calamitic > characterize structures of the (here 0)aggregates 0394X lyotropic systems [13].
or discotic beIts is that a wide of (here A x 0).may advantage range angles
with resolution because the - X-rayinvestigated high 3.2.3 Disordered micellar In this casephases.
beam is focused on the curved always photographic from the absence of order us gainingany prevents
film. In the small the(40 angle region [s - A) - 1] the form factor of the direct access to either aggregates
the diffraction to long rangepattern corresponds or their distribution. But if the small isangle scattering
of the A set ofamphiphilic aggregates. organization measured on an absolute scale some mayparameters
reflections is whose access to theobserved, angles give structural canbe found out and a analysis systematic
cell.and to the of the unit symmetry parameters made The absolute measurements werebe [21-23].
From the volume fraction these, occupied byknowing obtained with a with a spectrometer equipped photon
each of the a first compound sample, approximation detector radiation Cu, Kot,counting (monochromatic
of the and dimensions of the can be = shape aggregates Thiswave 1,54 Á, point collimation). length À
the form factorobtained to determine (One [16]. way was described elsewhere set-up [24],experimental
is to theof the quantitatively aggregate compare we shall recall its The intensityjust briefly principle.
intensities of the various reflections. This would solution is collectedof the radiation scattered the by
a better about their Thisprovide description shape. slit a Si-Li detector a circular on protected bythrough
in one has not been done here. However particular a window. The variation of the beryllium measuring
as be mentioned in 5.1.2 andcase will paragraph radius of the is for a ensured, slit,angle given average
discussed in the relative intensities of theII, Appendix distance while the keepingby varying sample-detector
The diffractionreflections were analysed succinctly.) as axis.the incident beam symmetry
= in the region (4.5 provideslarge angle [s A) - 1] enclosed in The mm were thick, perfectlysamples, 1
information about the short of therange organization similar the ones described above cells to .1].[§ 3. 2. tight
in molecules within the allamphiphilic aggregates; for anThe measured scattered a sample energy E(s) by
was the cases studied here a diffuse band observed vector within a solid AQ,s, angle average scattering
of these molecules the local disorder [13].showing whichaccess to the total scattering intensity, I(s), gives
- from the the SdS3.2.2 Oriented nematic These contains terms micelles, coming phases. phases
thein the small the solvent and the windows of show a diffuse band angle region, monomers, only
it was that the are no container. As described in I, possibleindicating aggregates longer arranged Appendix
it waswith translational order. This makes it to estimate the concentration of monomers ; long range
from the scat- 1.8 x 10- 2 therefore it remains smallerdifficult to extract the structure factor found M;
for ourof a these than 10 of the total SdS concentration even tering polycrystalline sample. Fortunately %
its contributionnematic can be oriented a most dilute for this reason field ;phases by magnetic sample;
of the is thus the of the different to the total along scattering intensity sample negli-packing aggregates
directions can access to an estimate of The contribution of the solvent was obtainedbe studied, giving gible. 1430
- from in the measured same 4. Phase We have studied the separate spectra experi- diagram. region
mental conditions as for the the ot the shown in 1 which surroundssamples. Finally phase diagram figure
contribution of the and that of the containersolvent, the nematic In this the concentrationsphases. region
was eliminated the scattered the in cent of by subtracting intensity samples, weight per varyexpressed
the the insolvent from that scattered in the 41.6 to 6.3 SdS 33.5by by samples following ranges : H20 % ;
similar as written in to 57.4 decanol 0 to 13.4 The wascontainers, (1) : % ; %. temperature
22 oC.
Observations between two crossed polarizer plates
of the in their tubes theirsamples preparation permit
coarse classification as bi or mono, triphasic, isotropic
or anisotropic.
- SAMPLES. The 4. 1 ISOTROPIC isotropic samples
which have a low water content to the nematic(close
exhibit a behaviour : domain) very interesting they
black the crossed when atappear between polarizers where Tsample and T’solvent are the transmissions of the
rest but are illuminated flashes of when theyby light and the solvent in their The abso-containers. sample
a shock. This induced are submitted to birefringencym
lute unit volume of a that these contain some unorientedscattering intensity I(s) per suggests samples
of thickness e is : which orient under sample shear ;anisotropic aggregates
couldbut less the alternatively, likely, birefringency
shear of be a deformation under isotropicproduced by
Moreover these also becomeaggregates. samples
field.when are in a anisotropic they put magnetic
the This behaviour will be by forthcomingexplained
structural study.
where S is the section of the incident thebeam, 1e
cross of one electron and scattering [20] Eo
the of the direct incident beam. Later on theenergy
normalized intensities
i.e. the intensities electron of the scattering per sample
will be is the mean used ; of the(p density
was determined with a reference sample). Eo sample
of water. the of water isIndeed, scattering intensity
known to be of s within the of ourindependent range
measurements and to 6.4 equal e-/molec. [25]. Thus,
ti2V
where E(s) is the scattered from which theintensity y~03A9
contribution of the window of the container has been
TH2O the transmission of water measuredsubtracted,
- 2. of textures observed from the centre towardsSequence Fig. the in its container and N number of molecules the when a nematic smearedthe of edge preparation Nd sample
volume. In this the unit absolute in between two i-, allowed to its Bper way, glass plates dry by edgès (line scattering
m in nematic nematic orderedFig. 3). a) Nd phase ; b) Ne phase ; c)
of relation was calculated for eachintensity 1(s) (2) ordered lamellar SdS-cylindrical phase ; d) phase ; e) anhydrous
1.96 x 10- 2 Â -1 x for s 6.77 10- 2 Á -1. decanol mixture.sample 1431
- For sam- with this and4. 2 ANISOTROPIC SAMPLES. is confirmed anisotropic hexagonal symmetry ; point
the of their textures under the the structural inples study polarizing enlightened by study presented
a to the as 5 .1. 2. In the texture intomicroscope provides way identify phases (d) changes again paragraph
thus the firstlamellar or a black area with white crosses four-leaved nematic, cylindrical, refining (or clovers)
coarse classification. The textures of these are of a lamellar whose run in phases typical phase layers average
now well known and a the 4, 6, 11, to the crosses [3, 26] permit rapid plates; correspondparallel glass
identification. This is illustrated the of associated with to defects by sequence Dupin’s cyclides. Finally
textures shown on the of 2. Here at the extreme of the a thin photograph figure right preparation (e) edge
a nematic smeared in between two of SdS-decanol mixture is seen.Nd sample glass anhydrous
was as allowed to its so to establish of the more accurate thanplates A dry by edges phase diagram, picture
a of water concentration from the centre that in now be sketched in 3.gradient 1, figure may figure
towards the of the As Several zones are the limits of which areedge preparation. decanol, delimited,
is insoluble in solubilized SdS it water, sketched because the transfor-entirely by may only approximatively
be assumed that the of decanol is from one to have not beenmations another evaporation negli- phase
2 Thus the of the The next section willgible. photograph figure represents systematically. approached
evolution of the at constant a determination of the structure of sample SdS/decanol ratio, present typical
from the nematic on the left towards more concen- within each zone of this Nd samples phase diagram.
trated on the B drawn on the phases right (line phase
sketched in 3 at the end of this figure para-diagram
- On the extreme left the is 5. Structures. 5.1 PHASES WITH LONG RANGEgraph). (a) stage totally
- in this is the texture of the a homeo- TRANSLATIONAL ORDER. We shall discuss here theblack, Nd sample
a threaded like with Under of three decanol(b) X-ray patterns tropic configuration. drying samples increasing
texture which to the transition of content but almost the same water ratio.grows corresponds amphiphile
the towards a nematic both textures are line 3, sample Nc [27] ; They successively (see Fig. A) : sample
of and nematic are a 52.5 47.5 decanol : 0 (SdS : Nd Nc phases simultaneously %, H20 : %, %), sample
demixion occurs. 47.2 47.6 5.2 at this stage probably (SdS %, %, apparent,
Then a fan-like texture which is charac- 41.9 47.3 decanol : 10.8 In(c) develops y (SdS : %, H20 : %, %).
teristic of two-dimensional of infinite each case the small of the diffractionpacking cylin- angle region
this shows a set of reflections characte-drical narrow 28, 29]. However, aggregates [26, particular pattern
texture observed here is remarkable the ristic of an ordered We have indexedby highly system (Fig. 4).
contrasted areas within the fans. This had not been these determined the of thereflections, symmetry
hitherto observed with classical of lattice and characterized the structure of the cylindrical phases phases
At this this can reference The that define[26]. stage phase following [30]. equations hexagonal symmetry
be described as a but not the of the reflections for the different cylindrical phase necessarily spacing symmetry
- 3. of the SdS-decanol-water where the nematic and their Fig. Region phase diagram (ordered lamellar,lyotropic phases adjacent phases
ordered and are located. disordered (Concentrations in The limits are indicative as we have notcylindrical micellar) weight per cent.) only
studied the transitions. viscous 0 fluid and clear fluid and turbid phase (. anisotropic phases : 0 anisotropic phases : anisotropic phases ;
Q9 indicate isotropic phases : juxtaposed points polyphasic samples).1432
d : of the lamellar distance phase,repeat
u area of the two-dimensional cell.primitive
The of the lattice is determined symmetry by finding
out which fits the observed Whenequation spacings.
the unit cellis the dimensions of the symmetry found,
can be calculated.
- 5.1.1 The texture of thatSample oc 4a). (Fig.
is that of a with infinite sample phase cylindrical
ordered with This isaggregates hexagonal symmetry.
confirmed the of 4a where theby X-ray pattern figure
of the two diffraction orders are in the ratiospacings
can be indexed in accordance with 1,/3-; they equa-
tion therefore the lattice is (8), hexagonal primitive
and the can be denoted V. Luzzati’sphase Ha (following
It is reasonable to assume that the notation). symmetry
of the structure element is than that of thehigher
lattice so that we consider that the sections ofmay
the are circular as shown in 5a. Thecylinders figure
lattice is here which also the distanceparameter, a,
between can therefore be cylinders, calculated,
= a 36.5 À. Then the concentrations ofknowing
and we can deduce the area S of thewater, amphiphile
= normal section of one S 531 hencecylinder, A2,
the diameter D of the D = 26 A and thecylinders,
mean area A the molecule
- occupied by amphiphile with trans-4. Diffraction of Fig. patterns phases long range
= at the 56 Â2 lational order : amphiphile-water interface, A [16].a, hexagonal lattice, Ha phase ;a) sample primitive
centred lattice b) {3, rectangular (space group cmm), R’ phase.sample
the reflections :Indexation of
lamellar lattice, phase.c) sample y, La
one or two dimensionswith along systems periodicities
are :
- Periodic in one dimension : lamellar
with :
ofof the reflection Shkl : reciprocal spacing (Â-’)
- 5. Schematic of cross sections of the latticesFig. representation indices and h, k 1, whose in 4 and of thediffraction are patterns reproduced figure
dimensions and of the unita*, b*, y : angle reciprocal cross section of their structure elements. 2D a) hexagonal lattice, Ha ;
2D 1 D centred lamellar cell, b) rectangular lattice, Râ ; c) lattice, La.1433
- - e. For this II 5 .1. 2 This also shows 5.2.2 type 0)Sample fl (Fig. 4b). sample Sample sample (AX
to a of the are flattened discs with a thickness ofa. texture periodic assembly aggregates corresponding
infinite i.e. to with two-dimensional 20 À an diameter of about 60 theseA ; cylinders, system and average
to each oforder. However the reflections shown in 4b discs are other at distances figure nearly parallel
cannot indexed to the about 37 Á their axis and 72 Á according hexagonal be pri- along perpendicular
mitive as for the best fit is obtainedlattice, a, to it. This is a sample Nd phase.
a centred or of the same has alsolattice, assuming rectangular equation (7). type II, phase system (The Nd,
will be In That noted this situation the been studied L. Amaral et al. These authorsphase R’. by Q. [32].
sections of the can no be circular. also conclude to the existence of lamellar cylinders longer aggregates,
The lattice a ribbonlike ten times the but with diameter linesrectangular suggests shape larger. Also,
this is for an of the which we have observed in our aggregates ; supported by analysis scattering experiments
relative intensities of the reflections are absent from their (see Appendix II). spectra.)
A section of the lattice is shown in 5b. The values here 5.2.1 referfigure Knowing (§ and § quoted 5.2.2)
the lattice the concentrations of rather limited number of studies. to a parameters, amphi- Systematic
molecules and we can deduce the area S of the variations of the dimensions ofwater, phile investigations
= of the normal section of a S 934 A2. If we these with concentrationribbon, aggregates temperature,
assume that the thickness of the ribbon D is that of are and the nature of the on the system way [33].
the in the lamellar bilayer phase (see sample y below)
- = i.e. D 19 then the width ribbon is W - 49 A The of the 5.3 DISORDERED PHASES. structure of theA,
and the area molecule A - 53 A2. in the domain per amphiphile aggregates isotropic (micellar solution)
in similar has been obtained one was for 6 with the same (A X-ray pattern investigated samples SdS/
was dried in decanol ratio instance where a nematic and water contents.up (3.35) Nc sample increasing
the vacuum chamber of the camera : this observation The normalized intensities are shown in 6In(s) figures
with the in and 7. are smooth curves whose maxima atagrees perfectly photograph figure’ 3c.) They
s - do not with the water(36 Â)-1 vary appreciably
- 5. 1. 3 The texture of thisSample y 4c). (Fig. content. Most this holds to the fact that in thoselikely is that of a lamellar The of thesample phase. spacings the mean distances between the systems, aggregatesreflections in 4c are in the ratio can1, 2 ; figure they are to their dimensions the concen-comparable (for be indexed in with accordance (4). Therefore,equation trated micellar solutions withcontaining aggregates the lattice is a lattice onelamellar periodic along diameter - 35 the mean distance would be - 50 Á, Â).dimension as shown in 5c and the willfigure phase Thus both inter and intra interferencesaggregate
be denoted The lattice which is alsoLa. parameter, contribute to the scattered intensities in the vicinity
= the distance two lamellae is A.d between d 37.3
of the shown in 6 and 7. This makes itpeaks figures the concentrations of moleculesKnowing amphiphile the difficult to use the of curvesscattering region and water we can deduce the thickness D of one soap to s corresponding (36 A)-1.
= D 19 and the mean area A lamella, A, per amphi-
= molecule at the 37 A2.phile interface, A
5.2 ORDERED NEMATIC PHASES. - The ofanalysis
our first of oriented with theX-ray diagrams samples
Laue Camera have been elsewhere given [8, 31].
We recall here the essential conclusions forshall just
two 40.32 samples (see Fig. 3) ô (SdS : %, H20 :
52.48 7.2 e 37.50 and %, decanol : %) %, H20 :
55.06 7.44 %).
- 1 > 5 . 2 .1 b. For this sample (A x 0),Sample type
the are which areaggregates elongated cylinders
to each order at a lateral distance ofnearly parallel
about 38 their diameter is about 30 butA ; A, average
we their This is ahave no information about lengths.
On this last it is to Nc phase. point, possible imagine
either infinite in the ordered cylinders (as phases)
or if are mono-finite in the latter ones ; case, they
must be than 150 A which is thedisperse they longer
distance accessible with our alterna-largest apparatus ;
the well be tively, cylinders might very polydisperse
in of the their then the broadening X-raylengths; - 6. Diluted disordered curves Expérimental I.(s)Fig. phases.
be such that the distribution = pattern might length concentrations. C for different (normalized intensities) amphi-
cannot be measured. concentration in of solute of solution.gram phile expressed grams per 1434
- a 8. Schematic of micelle and ofFig. representation spherical
its radial electron in water. I : Paraffinic assumed todensity region,
be without its volume is and its electron water ; densitycompact v,.,
= II : the 0.272 Interfacial e- lA 3; region containing polarpp.,
- 7. Concentrated disordered curves all their and its volume is and itsheads, water; Fig. phases. Experimental gegenions vpo,
= III : Water its electron isfor different concentrations. C electron I.(s) (normalized intensities) amphi- density region, density Ppol;
= concentration in of solute of 0.327 surface of between discontinuity phile expressed grams per gram Pw e-/A3 ; Spar : Ppar
solution. and surface of between discontinuity and p,,; ppol, Spol : ppo, Rpar :
radius of the radius of the micelle.core ; paraiïin Rpo, :
The same was met F. Reiss Husson andproblem by
In order to use Porod’s law we consider that thisV. Luzzati who a method the[22, 23] developed using
can have three values as shown in 8 :at the interference density figure scattering larger angles (beyond
the of the in in the chains to determine water, aggregates; pw paraffinic (volume peaks) shape Ppar vpar),
we shall follow this method here. and in the interfacial Theregion (volume ppo, vpol).
areas of the surfaces of theseThe at > is discontinuity separating intensity larger angles (s (36 A)-1 )
electronic three are denoted of the dominated short fluctuations of the regions (surface paraffinicby range Spar
within the In the and surface of the (outer density aggregates. particular asymp- region) polar region).Sp.,
With these conventions Porod’s formula totic of the the surfaces can beshape intensity depends upon
written as follows :of this as shown Porod [34].of discontinuity density, by
or
number of in the where N is the particles sample.
that Porod’s law does verified when is as a function of the Having apply, log I.(s) plotted logs, points align
a line with 4 as shown in can access to we the along straight slope n - - figure 9, gain geometrical parameters
and we know and In is not known a however it befact, Pw only priori ; may Sparl vpar SpotiSpar if Ppar, Ppol’ Ppol
determined from the of the scattered which access to the mean value of the fluc-integral intensity, gives square
tuations of the electronic over the whole density sample :
or1435
- Table I. the Expression of geometrical parameters
and as the thea function of shape of Spoll’spar Sparlvpar
aggregate.
is the thickness of one paraffin layer.(*) Rpar
nematic this is a reasonable phase, quite assumption
that the are rather well definedconsidering aggregates
- = 9. Check of Porod’s law for two C Fig. samples. amphiphile
in the discotic nematic It is also a reasonablephase [8]. concentration in of solute of solution.grams per gram expressed
for the diluted micellar solutions of assumption long
chain as shown in amphiphiles [35].
The factor in and is The in now consists equations (10) (12) easilyNv,a,IV fitting procedure calculating
is its value calculated for each and from table 1calculated ; replaced by sample choosing vpar ’Sparlvpar
from the increment of the electron of the the whose will be closest to the density aggregates expectedRpar
~ with to i.e. which is 14.3 A whenrelevant of a chain paraffinic region respect water, Ampar, length C 1 o
stretched [36].
it on known .; only depends para- The results of the scatteredexperimental (the integral
~meters the The characteristic of factor[22]. sample
4 n S2 des and the Porod’s intensity limit,In(s) is in an equation (12) expressed equivalentNVpollV in Jo 0
is its value calculated frommanner ; replaced by Vpol
the increment of the electron of the lim as well as the calculated density polar parametersS4) 03C0/2 In(s)
s ~ ~
with to l.e. i.e. and the dimensions and related to thewater, = ~mpol ;region respect region with respect to water, Ampol, ~mpol, vp., Vpol Rp., (pp., Rpar Ppol - Pw of the the three consideredshape aggregates according it on which is not known a depends priori.Ppol are in table II for the different valuestypes) presented One in the is thatdifficulty calculating integral (12) in of the concentration C, gramsamphiphile expressed
our of is limited toknowledge 1n(s) of solute of solution.per gram
- is 5.3.1C0.191. The model thespherical
one which a reasonable 12.3 only gives A).Rpar (Rp., - The error in the small is asangle region negligible, The contains 26 moleculescorresponding aggregate
is small at small s. In the s2In(s) very large angle at the and the area parafhn-average per polar group
S2 was estimated to Porod’s law.region I.(s) according medium interface is 73 Â2.polar
in The equation (10) changegeometrical parameters The of the diluted disordered areaggregates phases
with the of the as.shown in table 1shape aggregates isotropic.
where three of are considered fortypes
- 5. 3. 2 C > 0.191. We can assert the which aggregatesthe general expression
are not Indeed if were thespherical. they spherical
20 A which is too should be - largeaverage Rpar
when to the chain Therefore thecompared length.
of the concentrated disordered aggregates phases
are We is valid. in its to be cannot chooseSubstituting equation (10) by supposed anisotropic. Spo,/Spar
between discotic or calamitic Howeverrelevant the useful aggregates yet. expression, corresponding para-
meter is deduced. to the fact that these micellar are locatedowing phases Spar/vpar
Of course we consider that for each the in the of the it is sample vicinity lyotropic Nd phase, tempting
that are in and size. For to assume the remainby continuity aggregates monodisperse shape aggregates
the micellar the discotic.concentrated close to solutions, 1436
- related to the the Table II. data which access to and parameters shape of aggre-Experimental give different p,.,
concentration C.as the gates amphiphile a function of
As outlined in the and P are related to the volume and to the surfaces of the (*) text, I electronic ofrespectively of discontinuity density
the The increase of the ratio in the concentration near the nematic indicates that the of the amphiphile. 7/P range Nd phase shape aggregates
in the concentrated micellar is not the same as in the diluted micellar phases phases.
’
- Thus the orientation of these A : Structural evolution at constantTable III. Line isotropic samples
under the of a shear or of a field water content and increasing decanol content.application magnetic
above the discussed to (§ 4.1) correspond alignment
of anisotropic objects.
- 6. Discussion. A convenient to summarizeway
the our results of is to describe the structuralstudy
evolution of the the two lines A and Balong samples
drawn on the 3. These two linesphase diagram figure
have been defined on the A is a line atfollowing ways.
constant water content which the(- 48 %) along
ratio increases from 0 to 10.8 thisdecanol/SdS % ;
line has been chosen in order to show the effect of the
alcohol. B is a line at ratioconstant SdS/decanol
which the water content increases from(- 3.35) along are estimated from the These values (*) approximative experi-
40 to - 95 it has been chosen in order to deter- mental data and the sketched in 3. So far the% % ; figure phase diagram
was not beenmine the effect exact limits cannot be as the of the in water at given phase diagram diluting aggregates
a on continuous explored way.constant the of composition amphiphile.
- 6. 1 LINE A. The contain two and the curvatures of the water interfaces:aggregates amphi- amphiphile
SdS and and the first is It must be in mind that within the decanol, philes, progressively kept investigated
substituted the water is theother at constant water content. domain of the by (Fig. 3), phase diagram
The of the is summarized in III. i.e. the curvature of the table continuous sequence phases phase, amphiphile
The evolution of the structure can be summarized water interface is convex. theRigorously speaking
the normal sections of the of the normal section withby considering decreases, aggregates symmetry