Mesomorphic side chain polysiloxanes : a structural study of the smectic B phase

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Mesomorphic side chain polysiloxanes : a structural study of the smectic B phase

P. Davidson, A.M. Levelut

To cite this version:

P. Davidson, A.M. Levelut. Mesomorphic side chain polysiloxanes : a structural study of the smectic B phase. Journal de Physique, 1989, 50 (17), pp.2415-2430. �10.1051/jphys:0198900500170241500�.

�jpa-00211070�

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Mesomorphic side chain polysiloxanes : ^a structural study ^of

the smectic B phase

P. Davidson and A. M. Levelut

Laboratoire de Physique ^des Solides, ^associé ^au C.N.R.S., Université Paris XI, ^Bât. 510, ⁹¹⁴⁰⁵ Orsay Cedex, ^France

(Reçu ^{le 30} ^mars 1989, accepté sous forme définitive ^{le 25 mai} 1989)

Résumé.

²⁰¹⁴

Cet article décrit une étude structurale par diffraction des rayons X de quelques polysiloxanes mésomorphes ^en peigne, ^en phase smectique ^B (SB ). ^Comme ^{nous ne} disposions

pas de véritables monocristaux, ^cette ^étude â ^{été faite} ^sur des échantillons alignés ^sous champ magnétique êt présentant ^donc ûne géométrie ^de

^«

^fibre

^».

^Nous présentons d’abord la structure de cette phase SB polymère. ^Son organisation êst similaire à celle des phases SB classiques (de mésogènes conventionnels) : ^les ^c0153urs mésogènes ^sont perpendiculaires âux couches et, dans ûne seule couche, ^sont empilés ^{en un} ^réseau hexagonal ^à deux dimensions. Les squelettes polymères

sont confinés entre les couches de c0153urs mésogènes, ^dans ^une épaisseur ^{de 6 ± 1} Å le long ^du

directeur. Nous comparons cette structure avec celles des cristaux formés par certains polymères

de la même série et avec celles des phases SB classiques. ^Du premier point ^de vue, il semble que la

phase SB polymère puisse être considérée comme un « paracrystal » bidimensionnel ; ^du second, le fait que ^{nous ne} disposions pas d’un vrai monodomaine de phase SB polymère ^nous empêche ^de

l’identifier comme une phase hexatique ^{B. Nous} présentons ensuite les fluctuations qui ^affectent

la structure de cette phase SB polymère. Comme dans les phases SB classiques, ^les ^c0153urs mésogènes, ^au sein d’une couche, ^se placent localement aux n0153uds d’un réseau de type ^chevrons

avec une longueur de cohérence de l’ordre de 20 Å. De plus, ^{dans la} phase SB polymère, ^les squelettes ^corrèlent ^cet ^{ordre à} ^courte ^distance ^sur quelques couches voisines. Par ailleurs, ^la.

nature polymérique ^du composé ^induit ^une modulation transverse probablement displacive ^des

couches (ondulations). ^Sa longueur de cohérence vaut aussi environ 20 Å. Cette modulation est fortement couplée âu ^réseau hexagonal bidimensionnel et pourrait ^être âussi couplée âux

fluctuations de type chevrons. Des mouvements longitudinaux ^des ^c0153urs mésogènes ^autour ^de

leurs positions moyennes dans les couches ônt aussi été détectées. Certains de ces mouvements ont fréquemment ^été observées dans les phases SB classiques tandis que d’autres ^sont plus compliqués êt difficiles à visualiser dans l’espace direct. Nous les analysons brièvement ên termes d’ondes de déplacement transverses semblables à des phonons.

Abstract. 2014 This paper presents ân X-ray diffraction study of the smectic B (SB) phase ^that ^some mesomorphic side chain polysiloxanes display. ^Since ^no ^true monocrystals ^were available, ^this study ^was performed ôn magnetically aligned samples which possess â fiber geometry. ^{We have} first investigated ^the ^structure ^{of this} polymeric SB phase. Îts organization is similar to those of the classical SB phases (of ^small mesogens) : ^the mesogenic ^{cores are} perpendicular ^to ^the layers and, within a layer, packed ^{on a} ^2D hexagonal lattice. ^The polymeric ^backbones âre confined between the layers ôf mesogenic ^cores, ⁱⁿ â width of 6 ± 1 Å along ^the director. We discuss this structure in Classification

Physics ^Abstracts

61.30 - 61.40K

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500170241500

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relation to those of the crystals ^that ^some polymers ^{of the} ^same ^series display ^{and then} ^to ^{those of}

the classical SB phases : ^{from the} ^first point ^of view, it appears that the polymeric SB phase may be regarded ^{as a} 2 dimensional « paracrystal

^».

From the second _one, the lack of a true monocrystal ^{of the} polymeric SB phase prevents ^us ^from definitely identifying ^it ^{as a} ^stacked

hexatic phase. ^We have then investigated the fluctuations which affect the structure of this

polymeric SB phase. ^As in classical SB phases, ^the mesogenic ^cores ^within ^a layer, pack ^themselves locally ^{on a} 2-dimensional herring bone array of cohérence length of the order of 20 Å. _Moreover,

in the polymeric SB phase, ^this short range order is also correlated along ^a ^few adjacent layers by

the polymeric backbones. In addition, ^the polymeric ^nature ^{of the} compound înduces â ^transverse probably displacive local modulation of the layers (undulations). Îts ^cohérence length ^{is also} roughly ²⁰ Å. This modulation is strongly coupled ^to the 2-dimensional hexagonal lattice and

might ^{also be} coupled ^to ^the herring bone array. Longitudinal motions of the mesogenic ^cores

about their mean positions ^{in the} layers have been detected too. Some of these motions are

usually ^seen in the classical SB phases whereas the others are more complicated and difficult to

represent in direct space. We briefly analyse ^{them in} ^terms ^of transverse displacive ^waves ^similar

to phonons.

Introduction.

Mesomorphic side chain polymers ^have recently attracted wide interest in view of potential applications in the field of non linear optics [1, 2]. ^These compounds often exhibit nematic

(N), smectic A (SA) ^and smectic C (Sc) phases which have been thoroughly ^studied.

Moreover, the smectic B (SB) phase has sometimes been reported, ^too [3, 4]. This paper presents ^a structural study ^{of this} ^new polymeric SB phase.

First let us recall the structure of the conventional SB phase (Hereafter, by conventional

SB phase, ^we ^mean ^the SB phase displayed by the usual low molecular weight liquid crystals) [5, 6] (Fig. 1) : âs any smectic phase, ît is characterized by the existence of layers. ^The mesogenic ^cores âre perpendicular ^to ^the layers ând âre located within a layer ^{on a} ^2D hexagonal lattice. They ^rotate rapidly about their long axes as was demonstrated by ^nuclear magnetic ^resonance [7] and incoherent quasielastic ^neutron scattering experiments [8]. În â previous paper [9], ôn the basis of X-ray diffraction patterns, ^we have detected an additional short range order : within â layer, ^the mesogenic ^cores pack themselves on a local 2D herring-

bone array. This short range order is related ^to the cooperative ^nature of the rotation of the

mesogenic ^cores about their long axes as was demonstrated by ^coherent ^inelastic ^neutron scattering experiments [10]. ^At long distance, ^the herring ^bone correlations vanish so that the lattice retains its hexagonal symmetry.

The conventional SB phases may be classified into ^two groups according ^to ^the interlayer

correlations [6, 11-13] :

-

if these correlations extend on a long range, then the molecules ^are 3-dimensionally

correlated and the phase is called crystal B ;

-

another phase ^made ^of stacks of 2D hexagonal ^lattices and called a stacked hexatic B

phase has also been predicted [11] ând ^was ôbserved experimentally [13]. ^{In such} â phase, ône

defines the nearest neighbour ^bond orientational order of the hexagonal lattice. The

positional order within a layer ^is only short range whereas the bond orientational order remains long range and is 3-dimensionally correlated.

Let us also recall a few facts about the crystallization ^of polymers [14, 15]. Compared ^to

usual crystals (i.e. crystals ^{of small} molecules), good quality crystals ^of ^most polymers ^are

difficult to obtain and they ^contain â ^variable âmount ôf amorphous ^material depending upon

the crystallization conditions. Their X-ray diffraction patterns display reflections which are

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Fig. ^1.

^-

^Molecular organization ⁱⁿ â layer ôf â conventional SB phase [6]. ^{M :} mesogenic ^core, ^{C :} aliphatic ^chain. â ^{and b} âre ^the ^vectors ^{of the} hexagonal lattice. ^The cylinders represent ^the envelope ôf

the rotating molecules. In a crystal ^B phase, ^such layers ^are long range correlated along their normal and their packing eventually present superstructures. ^A stacked hexatic B phase is made of stacks of such

layers.

often not resolution limited and the widths of the reflections may increase with increasing scattering angle. ^Moreover, ^the intensity ^of these reflections usually ^decreases quickly ^with increasing scattering angle (quicker ^{than the} general decrease of the atomic form factors).

Several ideas based on the notion of disorder, ^account ^{for such} ^a ^{behavior :}

Disorders may be classified into ^two types [14-16] according ^to ^the statistical distributions which describe them. We shall illustrate the difference between the two types of disorder by considering their effects on the lattice vectors. If the fluctuations of two neighbouring ^lattice

vectors (i.e. ^the ^vectors ^between neighbouring ^lattice points) ^are correlated, then the disorder is called of the first type. ^This ^{kind of} disorder, ^a good example of which is thermal agitation,

does not affect the lattice long range order. Its only ^{effect is} ^to decrease the intensity ^{of the}

reflections by â factor of the Debye ^Waller type, ^without altering ^their ^widths ^which simply depend upon the size of the crystallites. Îf ^two neighbouring ^lattice ^vectors âre âllowed ^to

fluctuate independantly, then the lattice long range order is destroyed. Consequently, ^the

widths of the reflections do not depend only ^on ^the size of the crystallites any ^more but also on

the average square value of the fluctuations. Moreover, ^the widths of the reflections increase with the indices of the reflections, that is with increasing scattering angle ; however, ^their

integrated intensities are not affected. Hosemann has called « paracrystal » [14] ^a crystal

modified by ^a disorder of the second type ^{and this} concept is often used in the field of

polymeric crystals.

In this context, ^we ^{found it} interesting ^first ^to determine the crystallographic parameters ^of this new polymeric SB phase ^{and then} ^to study in which way the polymeric ^nature ^{of the} compound modifies the organization ^{of the} phase. ^In particular, ^we have tried to examine two

questions.

-

Do the ideas mentioned above, ^{about the} structures of conventional SB phases ^{and of} polymeric crystals, apply ^to ^this ^new polymeric SB phase ?

-

How is the local order of the mesogenic ^cores ^affected by chemically grafting ^them ^{on a} polymer ?

R. Duran et al. have presented ân X-ray diffraction study [17] ôf â polymeric SE phase. They have shown that the SE phase is lamellar with the mesogenic ^cores packed ôn â

2D rectangular ^lattice ^within ^a layer. ^No 3D correlations were to be seen. These authors

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consider that the polymeric SE phase may be of â hexatic nature comparable ⁱⁿ ^some way ^to the SI phase ôf conventional _mesogens and that the backbones are aligned along ^the (11) directions of the rectangular lattice, ^therefore strongly coupled ^to this lattice. The lack of well enough ôriented samples ^did ^not ^{allow the} study ôf ^the mesogenic ^cores local order.

Among ^the polymers ^which ^were reported ^to present ^a SB phase ^{in the} literature, ^we ^have

chosen a series of mesomorphic ^side ^chain polysiloxanes synthesized by M. Mauzac et al. [18].

This series was already ^well characterized [18] and furthermore we thought ^that the presence of Si atoms in the backbones would increase the form factor of the molecule and give

additional information about the backbones. These polymers correspond ^to the formula :

and we shall call them Pn, m âccording ^to the number of methylene groups in the spacer and in the alcoxy ênd chain. The tacticity ^{of these} polymers has been characterized by 29Si _{NMR ;} they ^can be considered as completely âtactic [19].

We have chosen to study five of these polymers ^which ^were also studied by X-ray

diffraction in the SA phase [20]. ^Their polymorphism is recalled in table 1 :

Table I.

^-

Phase transition temperatures (’C) of polymers P3,4, P4,4, P3,s, P4,s ^and P5,8- (Tg : ^glass transition, Tm : melting point, Tc: clearing point) [18].

It seems that the existence of the SB phase is related to the presence of the long aliphatic

end chains [18]. Polymers P3, 4 ^and P4, 4 ^have ^been ^added ^so ^that ^we ^shall ^{be able} ^to ^compare

the polymeric SB phase ^{with the} polymeric crystals ^of ^similar compounds.

1. Experimental.

Aligned samples ^{could be} ^obtained by slowly cooling ^them (5°C/hour) ^{from the} isotropic phase ^to ^the SA phase ⁱⁿ ^a magnetic ^field (1.7 T). ^These samples ^were ^contained ⁱⁿ

Lindemann capillary tubes of 1.5 mm diameter. Therefore our samples present ^a cylindrical

symmetry around the magnetic ^field direction. In addition, ^a ^small mosaicity ^{of about} ^5° ^exists

in our magnetically aligned samples. ^These magnetically aligned samples ^do ^not ^show ^as ^much

information as real monodomains of SB phase. Such monodomains have sometimes been obtained by melting ^of single crystals ^of ^low ^molecular weight liquid crystals [9]. ^{However in}

the present case, single crystals ^are unlikely ^to be grown due to the polymeric ^nature ^{of the}

compound.

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The samples ^were ^examined ^with ^two ^different X-ray ^set ups :

-

a conventional Guinier camera equipped ^with ^a cylindrical quartz monochromator

(03BB CuKa 1 = 1.5405 A) helped ^us ^to ^measure ^the crystallographic parameters ^{of the} SB phase ^and ^to examine the profiles ^{of the} reflections ;

-

another set up already ^described [21] revealed the presence of ^some diffuse scattering :

a punctually ^focussed monochromatic X-ray ^beam (03BB CuKa

⁼

1.541 À) ^was ^obtained by

reflection on a doubly ^bent graphite monochromator. The sample ^{in its} capillary ^{tube is} ^set ⁱⁿ

an oven heated by ân âir ^stream (temperature regulation ^± ¹ °C). ^The ôven îs placed ^between

the two poles ^of ^an electromagnet. ^The ^camera is evacuated in order to suppress air-

scattering. ^The diffracted X-rays âre ^collected ^{on a} cylindrical ^film ât â ^distance

R

⁼

60 mm from the sample.

2. Structure of the polymeric SB phase.

Figure ^{2a shows} ân oriented diffraction pattern ôf polymer P3,8 ^{in the} SB phase ând figure ^2b îs

a schematic representation ^{of this} pattern. ^{In the} following, ^we ^shall try ^to ^use ^the information

given by ^this pattern ^{in order} ^to describe the structure of the polymeric SB phase.

-

Along ^the magnetic field direction (meridian), ^one ^{can see a} ^series ^of equidistant Bragg

reflections (a) : ^these ^are the reflections on the smectic layers. ^The analysis ^{of the} powder patterns show that these reflections are resolution limited. (The resolution of our apparatus ^is àq -* 10- 2 A - where _{q is the} momentum transfer vector : q

⁼

4 7T sin 0 / A). The smectic

period d îs roughly equal ^to ^the length f ôf the side chains measured ôn Dreiding

stereomodels in an extended configuration [18]. (d

⁼

^{30.1 Â} ^for P3,8, d

⁼

^32.3 ^À ^for P4,8 ^{and d}

⁼

^{33.0 A} ^for P5,8). Therefore, ^no interdigitation ^can be detected.

Fig. ^2. - (a) X-ray diffraction pattern ^of polymer P3,8 ^{in the} SB phase. ACuKo!

⁼

^1.54 Â, sample-film

distance : 60 mm, H is the magnetic ^field ^direction (meridian). (b) ^Schematic representation ^of figure ^2a. (a) Bragg reflections on the smectic layers. (b) ^First (10) equatorial reflection of the 2D

hexagonal ^lattice (the ^{two next} ^ones 11 and 20 can be seen in Fig. 7a).

A first difference between the polymeric and the conventional SB phases consists in the

large ^{number of} meridional reflections that can be seen in the former case. We have shown

[20] that this large number is related to the distribution of the polymer backbones. We measured the intensities of the Bragg reflections on the layers and derived the projection ^of

the electron density profile along the director in the polymeric SB phase. ^We could localize the

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polymer backbones in sublayers ⁶ À wide along the director between two adjacent sublayers

of mesogenic ^cores (Fig. 3) (see also Ref. [3]).

-

In the directions perpendicular ^to the meridian (equator), ^we ^find ^a series of 3 rather

sharp reflections (b), ^{the first} being by ^far ^the strongest (the ^two ôther ônes ^can ^be ^seen ⁱⁿ Fig. 7a). ^These equatorial reflections show that the layers âre ^not liquid-like âs ⁱⁿ â SA ôr Sc phase ^but solid-like. The correspond ^to ^lattice spacings : ^4.45 Â, ^2.55 Á, ^2.23 ^Â

which are in a ratio 1, 1/ J3, 1/ 4. ^They ^are ^{the first} spacings displayed by ^a ^2D hexagonal

lattice of parameter ^{a = 5.15} À. (The ^same ^value ^{of a} îs obtained for P3,8, P4,g ând P5,8. ^{It is} quite comparable ^to ^those found in the case of conventional SB phases [5] ; ⁱⁿ particular ^{it leads} ^to â value of about 23 Â2 for the molecular area of a mesogenic core).

Another difference between the polymeric and conventional SB phases ^consists ^{in the} larger

number of equatorial reflections displayed by the former one. This suggests ^that ^the Debye

Waller factor of the polymeric SB phase should be smaller than that of the conventional

SB phase. ^This point will be considered later. Moreover, ^we ^do ^not detect, ^undemeath ^{the 10} reflection, any diffuse ring which would be due to an amount of material still in the

SA phase. ^This SA phase plays here the role of the amorphous ^material ⁱⁿ â ûsual polymeric crystal. Therefore, ^the âmount of material still in the SA phase (i.e. ^not organized ^{in the} SB phase) îs probably less than 5 %.

Fig. ^3.

^-

Organization of the backbones along the director in the 83 phase [20] : the backbones are

squeezed ⁱⁿ ^regions ^{of width} ^{6 Â along} the director.

An analysis ^{of the} powder patterns shows that the equatorial reflections are not resolution limited. Figure ⁴ presents ^the microdensitometric profile of the 10 reflection compared ^to ^that

of the beam and to that of the SA equatorial ^diffuse ^crescent. The fact that the widths of the

equatorial reflections are not resolution limited _{may be} explained in several ways. First let ûs consider the polymeric SB phase ^{as a} polymeric crystal : ^the ^width ôf â given reflection _{may be} due to the juxtaposition ôf ^two ^close reflections, ôr ^to the small size of the crystallites ôr êven

to a second order type ^of ^disorder. ^We ^can also compare the polymeric SB phase ^to ^the

conventional SB phase ^and ^the ^width of the 10 reflection will make us think that the polymeric

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SB phase ^{is of} ^a ^hexatic ^nature ^rather ^than ^a crystal ^{B. In the} following, ^we shall examine the widths of the equatorial reflections according ^to these various possibilities.

-

We have first tried to account for the width of the 10 reflection by assuming the presence of a 101 3-dimensional reflection. Figure ⁵ shows that the experimental width of the 10 reflection cannot be explained by the presence of ^two 100 and 101 resolution limited reflections. (We ^have âlso ^checked ^that ^the experimental ^width ^cannot ^{either be} explained by varying ^the ^widths ^{of these} ^two reflections if they âre kept equal.) Therefore, ^{the 10} equatorial reflection is not broadened by â hypothetical 3-dimensional 101 reflection.

Fig. 4. Fig. 5.

Fig. ^4.

^-

Intensity profiles (in arbitrary units) ^{of :} 1) the direct beam ; 2) ^{the 10} equatorial reflection of the 2D hexagonal lattice in the polymeric SB phase ; 3) ^the equatorial ^diffuse ring ^{in the} SA phase. qo represents only the central value of each profile.

Fig. ^5.

^-

Tentative deconvolution of the experimental ¹⁰ equatorial reflection (curve 1) înto ^two hypothetical resolution limited 100 and 101 reflections (dashed lines). ^There îs ân ôbvious discrepancy

between curve 1) ^and ^curve 2) ^which represents ^the ^sum ^{of the} ^two hypothetical reflections.

- Then, the widths of the equatorial reflections may be due ^to the small size of the

crystallites. Ât ^this point, ^let ûs ^consider figure 6 which shows the X-ray diffraction pattern ôf the crystalline phase ôf â magnetically aligned sample ôf polymer P3,4 cooled from the

SA phase (the ^same type ^of pattern is observed in the case of polymer P4,4). ^This ^pattern ^shows

many additional reflections compared with that of P3,8 ând ^can ônly be indexed in a 3- dimensional lattice. The equatorial reflections of these crystalline phases âre ^not ^resolution

limited either, ^but nonetheless, they ^are all of the same width. Therefore, ^we ^can ^account ^for

this experimental ^width by ^the effect of the size of the crystallites : ^we estimate this size using

Scherrer’s formula [16] :

This leads to a value L

⁼

150 Á. this size may also be interpreted ^{as a} typical ^distance

between defects.

However, ^{in the} ^case ^{of the} polymeric SB phase, ^a microdensitometric recording ^{of the}

reflections shows that the 11 reflection is nearly ^twice ^as ^wide ^as the 10 reflection. Therefore,

the widths of the equatorial reflections are not only braught ^about by ^the ^small size of the

crystallites.

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b)

Fig. ^6.

^-

(a) X-ray diffraction pattern ^of polymer P3,4 ⁱⁿ ^the crystalline phase. ÀCuKa =

1.54 Á, sample-film distance : 60 mm. H is the magnetic field direction (meridian). (b) ^Schematic representation ^of figure ^6a. (a) ^{00 f} reflections. (b) hk 0 reflections. (c) ^hke reflections with h =1= 0, k =1= ^{0 and} l= 0. The presence of these reflections (c) shows that the organization ^{is 3-}

dimensional here.

- Then, ^we may consider that the widths of the equatorial reflections are due to some

disorder of the second type (i. e. ^the polymeric SB phase ^{is of} â paracrystalline nature). ^Two neighbouring ^lattice ^vectors ^fluctuate independantly around their mean value : a. They âre equal ^to â ⁺ Aa and their statistical distribution is characterized by the average square

(âa2). ^If ^we follow Hosemann’s point ^{of view} [22] that the reflections can still be detected for

(h 0394a2 > 1/2 )/a 0.3 and if we consider that the 30 reflection cannot be detected, ^then ^we

estimate (âa2) 1/2 = ^0.7 ^A. (This last value is only ^an ^{order of} magnitude). Therefore, ^the

widths of the equatorial reflections can be explained by assuming that the distances between

neighbouring molecules fluctuate independantly by ^{about 10} ^%.

The presence of â second type disorder does not exclude the existence of a first type disorder such as thermal agitation. To evaluate the part ôf ^first type disorder, ^{i. e .} ^to êvaluate

the Debye ^Waller factor, it is necessary ^to ^measure the integrated intensities of the equatorial

reflections and to determine their dependance upon scattering angle. However, ^we only ^see

three orders of reflection and the last one does not allow a good determination of its

integrated intensity ^so ^that ^we shall go ^no further than stating ^{that the} Debye Waller factor of this polymeric SB phase ^must be smaller than that (2 B -- ²⁰ [5] ) ^of ^a conventional

SB phase ^as ^mentioned previously.

Now, ^we ^can also compare the polymeric and conventional SB phases ^and first, ^we ^must

stress the following point : ^we ^do ^not ^detect ^{either in} figure ^2a ^{or on} ^the powder patterns any hkl line with h # 0, k =F ^{0 and} l # 0. As mentioned above, ^a hypothetical 3-dimensional 101 line close to the 10 reflection cannot be detected either. Since there is no evidence of any long

range 3D correlations then the polymeric SB phase ^should ^not ^{be called} crystal ^{B and the} packing ^{of the} mesogenic ^cores ⁱⁿ 2-dimensional. For that reason, we also tried to explain ^the experimental width of the 10 reflection by assuming ^that ^within ^a layer, ^{the 2D} hexagonal

lattice is perfect and infinite but that the layers ^are completely uncorrelated. (We already ^used

a similar approach ⁱⁿ â previous study ^{of the} conventional SF phase [23]). Ûnder ^such assumptions, ^{in the} reciprocal space, the nodes of the hexagonal ^lattice ^become ^rods elongated along the meridian. The width of these rods is resolution limited and their length îs

about 2/c ^{A- 1.} ^The diffracted intensity ^is ^obtained by projecting these rods on the Ewald

sphere. However these assumptions ^lead ^to ^a 10 reflection still much smaller than the

experimental ^one. Therefore the 2D hexagonal lattice ^{of the} mesogenic ^cores ^does ^not ^show ^a

true positional long range order. The absence of such ^a positional long range order is precisely

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one of the characteristic features of the hexatic phase. Indeed, the width of the 10 reflection in the polymeric SB phase ^is à (2 0) = ^0.75° ^{which is} comparable ^to that observed by ^Pindak

et al. [13] in the stacked hexatic SB phase ^of conventional _mesogens. Consequently, ^it ^was tempting ^to try ^to ^fit ^the intensity profile ^{of the 10} reflection along ^the equator with different theoretical curves. A fit of the wings ^{of the} reflection with a power law in q-

^a

[9] ^led ^to ^a

value : a - 1. 1 hard to account for except ^that ^it ^means ^{that the} ^structure ^could hardly ^been

considered a 3D crystal. Â ^{fit with} â Lorentzian (awaited ^for â ^hexatic organization) ^was ^not satisfactory êither. However, ^we must stress the fact that we do not have a true single ^domain

and then our intensity profile ^also integrates ^some intensity scattered in other diffuse areas

such as the diffuse spots ^described ^and ^called (b) in reference [9]. Furthermore, ^we may also

integrate â very small contribution due to a part of the material that would have kept â SA organization (the equivalent ^{of the} amorphous part ôf â polymeric crystal). On the other

hand, the revolution symmetry ^{about the} ^director ôf ôur samples prevents ûs ^from probing ân

eventual long range orientational order characteristic of a stacked hexatic B phase.

Finally, ^we ^need ^to reconcile the two points ^of view of 2D paracrystal and stacked hexatic B

phase : âs ^far âs the correlations within a layer âre concerned, ^the ^two approaches âre ^similar except ^{that the} paracrystal theory only specifies ^the average square value of the fluctuations whereas the model of the stacked hexatic phase gives â ^detailed microscopic description ^{of the} organization ând postulates ^{that the} reflection profile ^{should be} â Lorentzian curve. We could not reliably ^measure ^this profile ^{and thus} ^we ^failed ^to verify this Lorentzian dependance. Âs

far as the interlayer correlations are concerned, they âre ^not ^relevant ^to ^{the idea} ôf â ^2D paracrystal ^whereas they ^{should be} long range for the bond orientational order parameter âs

was observed by Pindak et al. [13]. However, ôur ^{lack of} ^true monodomains of the polymeric SB phase ^did ^not âllow ûs ^to probe ^such interlayer correlations and prevented ûs ^from obtaining â complete determination of the phase ^structure.

3. Fluctuations and local order in the polymeric SB phase.

Figure ^{7a shows} ân overexposed X-ray diffraction pattern ôf polymer P3,8 ^{in the} polymeric SB phase ând figure ^7b îs â scheme of this pattern. Ône can see some intensity diffracted in four different types of diffuse areas : (c), (d), (e) ând (f). În â ^first step, ^we ^shall ^describe these diffuse areas which are of two kinds :

-

some are diffuse spots ^much ^broader than those of the 2D hexagonal ^lattice ^located

around points ^{of the} X-ray diffraction pattern. Because of the fiber geometry ôf ôur sample, they correspond ^to ^the intersections with the Ewald sphere ôf â series of tori present ⁱⁿ reciprocal space. The diffuse spots (c) âre located in the equatorial plane âround 1 q 1

⁼

² ^03C0 /3.4 Â - 1. By carefully inspecting them, ^we notice that they âre slightly split ^{off the} equator. The diffuse spots (d) âre aligned along ^rows parallel ^to the meridian and are located in the same planes âs ^the 00 f Bragg spots. ^The ^diffuse spots (c) ând (d) âre ôf â ^different

nature as we shall see below but might ^be related in some way ;

-

some are diffuse lines on the X-ray diffraction pattern ^which correspond ^to ^the

intersection with the Ewald sphere ^of ^a ^{series of} planes ⁱⁿ reciprocal space. The diffuse lines

(e) ^can ^be ^seen in the direction of the meridian to which they ^are perpendicular. They go

through ^the Bragg spots 00 1 towards the rows of diffuse spots (d). ^The ^diffuse ^lines (f) ^are

similar to the diffuse lines (e) ⁱⁿ ^that they ^can ^{also be} ^seen ^{in the} ^direction ^of ^the ^meridian ^to

which they ^are perpendicular, ⁱⁿ ^that they go through ^{the first} Bragg spots ⁰⁰¹ and in that they

extend towards the rows of diffuse spots (d) ^on ^which they superimpose. They ^are ^different

from the diffuse lines (e) in that the closer they get ^to ^the ^diffuse spots (d), ^the ^more they ^tilt

with respect ^to ^the equator.

(11)

Fig. ^7.

^-

(a) Overexposed X-ray diffraction pattern ^of polymer P3,8 ^{in the} SB phase. ACuKa

⁼

1.54 Â, sample-film distance : 60 mm. H is the magnetic field direction (meridian). (b) Schematic representation ^of figure ^{7a :} (a) reflections on the smectic layers ; the fact that their size increases with their order is only ^due ^to ^a slight mosaicity ; (b) 10, 11 ^{and 20} equatorial reflections of the 2D hexagonal lattice ; (c) ^diffuse spot ^located along ^the equator around [ q 1

⁼

² ir/3.4 Â - 1. By carefully inspecting figure 7a, one ^can notice that this spot ^is slightly split ^{off the} equator ; (d) ^diffuse spots

^«

^1/2 0 f

^»

located in the same planes ^as ^the ^{00 f} Bragg spots. ^The

^«

^{1/2 0 5}

^»

^and

^«

1/2 0 6 » diffuse spots ^cannot ^be detected and the

^«

1/2 0 2

^»

diffuse spot ^can hardly ^be seen ; (e) diffuse lines going through the 003 and 004 Bragg spots ^and perpendicular ^to ^the meridian ; (f) diffuse lines starting from the 001 Bragg spots and extending towards the rows of diffuse spots (d).

In the following, ^we try ^to analyse all these elements (c), (d), (e) ^and (f) separately ^as they

arise from distinct and a priori weakly correlated disorders.

Let us start with the diffuse spots (c). They ^{show that} ^an additional short range order exists in the structure. Their wavevector q

⁼

2 03C0 /3.4 ^{Â- 1} ^is simply ^related ^to that of the hexagonal

lattice (3.4/4.45

⁼

2/ J7). ^{We have} already ^observed [9] such diffuse spots ^on ^the X-ray

diffraction patterns of the conventional SB phase. ^Their positions ⁱⁿ reciprocal space break the

hexagonal symmetry ^since they only present ^a rectangular symmetry : ^a ^2D hexagonal lattice

may also be described by â ^centered rectangular ^lattice, ^the positions ât ^the ^corners ând ât ^the

center of the cell being identical. The diffuse spots (c) ^{show that} locally, ^these ^two positions

are not equivalent any ^more (Fig. 8). ^Such ^an organization, ^called Herring bone array, extends only ^{on a} ^small ^distance, roughly l = ²⁰ ^Â. (Actually, ^because of the fiber geometry of our samples, ^we ^have ^no direct evidence that the diffuse spots (c) ^indeed ^{break the}

symmetry of the 2D hexagonal lattice. We suppose that it is ^so because of the complete

analogy between these spots ^{and those} ^seen in reference [9].)

(12)

What is new in the polymeric SB phase ^is that, carefully inspecting figure 7a, ^we ^notice ^that

the diffuse spot (c) ^is slightly split ^{off the} equator. ^This splitting ^is large enough ^to ^be ^sure ^that

it is not due to the mosaicity ^of ^our sample. ^This ^means ^{that the} herring ^bone short range order is slightly correlated along the meridian. This feature was not observed in the case of conventional mesogens and we can see here the influence of the polymer backbone. A relative decrease (or ^{even a} complete cancellation) ^{of the} intensity ^{of the} ^diffuse spot (c) along ^the equator may be obtained by assuming ^the following arrangement ^{of the} mesogenic

cores : let us consider a mesogenic ^core ⁱⁿ â given position ôf ^the herring ^bone ^lattice (say ât

the center of the rectangular ^cell ^for instance), ^{we assume} that, statistically, ^the mesogenic

cores located just ^{below and} ^above ^{the first} ^one ^{in the} adjacent layers occupy the other

position ôf the lattice (here, ^the ^corner ^{of the} rectangular cell). (See Fig. 9) Projected ôn ^the equatorial plane, ^the rectangular ^lattice ^turns ^back ^to ^the înitial hexagonal ône. ^{In that} ^case, îf

these correlations were perfect, ^the intensity ^of ^the ^diffuse spot (c) ^on ^the equator ^{should be} cancelled. However, since this intensity ^{is still} important, then these longitudinal correlations

are weak. From the extension of the diffuse spots (c) along ^the meridian, ^we deduce that these correlations are short range, limited ^to the nearest neighbours ^{in the} adjacent layers. Here, the influence of the polymer tacticity ^{should be} important.

Fig. 8. Fig. 9.

Fig. ^8.

^-

Herring bone array fluctuations [9] ^{in the 2D} hexagonal ^lattice. (x) ^nodes ^{of the 2D} hexagonal

lattice. Three rectangular cells have been represented which show the three possible orientations of the

herring bone array fluctuations with respect ^to ^{the 2D} hexagonal lattice.

Fig. ^9.

^-

Herring bone lattice correlations along adjacent layers. Solid lines : molecular sections of the

mesogenic ^cores ⁱⁿ ^a given layer. ^Dashed lines : molecular sections of the mesogenic ^cores ^{in the} ^two adjacent layers.

Let us now turn to the diffuse spots (d) : they ^are aligned along ^rows parallel ^to ^the

meridian in figure 7a. These rows of diffuse spots correspond ^to ^the intersection with the Ewald sphere ^of ^a ^{series of} tori. These tori have the meridian for axis and are located in the

same planes âs ^the ^{00 f} Bragg spots. ^The component ôf ^their ^wave ^vector along ^the equator îs roughly half of that of the 10 reflection of the 2D hexagonal lattice. (We shall discuss this

point later.) Therefore, ^{in the} following, ^we shall denote these diffuse spots

^«

^1/2 0 f

^»

^to

remind that they ^are located in the same planes ^as ^the ^{00 l} Bragg spots.

(13)

These diffuse spots ^were already ôbserved ôn ^the X-ray patterns ôf P3,8, P4,8 ând P5,8 ^{in the} SA phase ^{but with} â ^lesser ^contrast. They âre ^similar ^to ^those already ôbserved ôn

the X-ray patterns ôf â mesomorphic ^side ^chain polymethacrylate [24]. They ^were interpreted by ^the existence of a purely displacive transverse modulation, î.e. ^to undulations of the layers.

In the case of the polymethacrylate described in reference [24], only ^one ^diffuse spot ^could be detected. Conversely, ^{in the} present ^case ^a whole series of diffuse

«

1/2 0 f

^»

can be seen.

However, ^we ^do ^not ^see ^the

^«

^1/2 ^{0 5}

^»

^and

^«

^1/2 ⁰ ⁶

^»

^diffuse spots. Moreover, ^the intensity

ratios of the diffuse spots

^«

^1/2 0 3 »/« 1/2 0 1

^»

and

^«

1/2 0 4 »/« 1/2 0 1

^»

is much larger ^than

those of the Bragg spots ^003/001 ând ^004/001. (The intensity ^{of the} ^first ^diffuse spot ^{is hard} ^to evaluate because of the presence of the diffusion (f) ^which superimposes îtself ând displaces

the maximum. However, taking this effect into account should decrease even more the

intensity ^{of the}

^«

^1/2 ^{0 1}

^»

^diffuse spot relatively ^to ^the others.) These remarks show that, ⁱⁿ opposition ^to those of the Bragg spots, ^the intensities of the diffuse spots (d) ^do ^not simply

follow the structure factor variation along the meridian.

We can qualitatively ^account ^{for these} ^facts by using ^{the model} developed in reference [24].

Let us assume a sinusoidal transverse displacement ^{of the} layers ^of amplitude uz, then the

integrated intensity ^{of the} ^various ^«1/20l» spots will vary ^as Jf(zrfuz/c) ^where

JI is the Bessel function of order 1. If we now consider that a smectic layer ^undulates ^{as a} whole, ^{then the} integrated intensity ^{of the}

^«

^{1/2 0} ¹

^»

spots ^{will be} ^described by ^the product :

Jf( ’TTeuz/c) ^x fool ^where fool ^{is the} ^structure factor of the 00 f Bragg reflection measured in reference [9]. Figure 10 shows the function Jf( zrfuz/c ) with uz = 3 A ; this function will be maximum for 3, l=4 ^{and close} ^to ^zero forl = 5, l ^{= 6 in} good agreement ^{with the} experimental ^results.

Fig. ^10.

^-

^Function Jf( ’TT f uz/ c). JI ^{is the} ^{1 st} order Bessel function. f is (2 d / À ) ^sin ⁰ ^which ^{on a} ^diffuse

spot

^«

^{1/2 0} f

»

is simply its order of reflection. (+) values of the function J;( ’TTfuz/ c) for each reflection.

(.) integrated intensity of the diffuse spots : J;(’TTfuz/c) ^x fool.

Therefore, ^the ^diffuse spots ^can ^be interpreted ^as undulations of the layers, ^without distortion, ^of amplitude approximately ³ Â. This value is in fair agreement with the width

(6 ^± ¹ Â ) ^{of the} region ^of ^backbones found in the projection of the electron density along ^the

director [20]. The coherence length along ^the equator ^of this short _range order, ^derived ^from

the extension of the diffuse spots (d) ^is roughly ²⁰ Â.

(14)

The presence of the diffuse line (f) prevents ^us ^from measuring ^the

^«

^{1/2 0 0}

^»

^diffuse spot

(on ^the equator) if it exists. Therefore, ^{it is} ^not quite ^sure whether the distortion which gives

rise to the row of diffuse spots (d) ^is ^purely displacive ^or ^not and then whether our model fully

describes it or not.

At this point, it should be noted that other examples of various orders coexisting ^with ^a ^2D hexagonal lattice may be found in the existing literature about the structures of liquid crystals.

Leadbetter et al. [25, 26] have observed some satellites around the 001 Bragg spot ^{in the} SB phase ^of ^some conventional mesogens. They ^were ^shown ^to arise from undulations of the smectic layers. However these undulations are quite different from those observed in the present ^case because the former ones are pretransitional effects related to the existence of a

SH phase ^{below the} SB phase. Furthermore, ^their period ^was approximately 80 Â indepen- dantly ^{of the} compound studied and in no way related to the hexagonal lattice.

A relation between a 2D hexagonal ^{order and} ^an antiferroelectric order has already ^been

shown in the hexatic phase ôf â polar mesogen [27]. ^However, ^{in that} ^case, ^the ^two types ôf order were incommensurate as the antiferroelectric order did not couple îtself strongly ^with

the hexatic lattice. Moreover, the antiferroelectric order correlation length ^was ^about ^ten

times larger than that of the layer undulations described above.

The origin of the undulations of the layers may be explained [24] ^either by ^a ^reaction ^{of the}

backbones to their confinement imposed by ^the ^smectic ^field ^or by ^a difference between the

grafting density ^{and the} packing density ôf ^the mesogenic ^cores ^which imposes â ^local splay configuration ^to the spacers. Anyway, ^the polymeric ^nature ^{of the} compound plays ân important role in the origin ^{of the} undulations, ^the period of which is determined by ^the packing ând êlastic properties ^{of the} system. Thus, ^the period of these undulations measured in reference [24] and also in the SA phase ôf polymers P3,8, P4,8 ând P5,8 îs ^roughly

20 ± 5 Á. The interaction of these undulations with the 2D hexagonal order decreases this value to roughly 9 A (a ~3= 9 À ) which is about twice the distance between the simplest

and densest planes (10) ^{of the 2D} hexagonal lattice. ^We ^can illustrate this effect by adopting

the following image (Fig. 11 ) : the presence of the extremity by ^which ^the mesogenic ^core ^is grafted ^on the backbone allows us to define an

«

up

^»

^or

^«

down

^»

direction for the mesogenic

core, similar to the direction of the dipole ôf â polar mesogen. On the molecular scale, â coupling between this direction and the undulations _may exist : the mesogenic ^cores may

Fig. ^11.

^-

Coupling ^between ^the layer undulations and the 2D hexagonal lattice. (+) mesogenic ^cores

displaced in the direction of c. (e) mesogenic ^cores displaced in the direction opposite ^to ^c.

(15)

alternately point upwards ^when they ^are displaced along the meridian in one direction (say

+ z) and downwards in the other (say - z). ^Since ^our samples present ^a ^fiber geometry, ^we

cannot determine the local symmetry ^{of the} undulations ; ⁱⁿ particular, ^we ^cannot experimentally choose between rectangular ^and hexagonal symmetries. ^However, ^the

undulations which consist in displacing ^a mesogenic ^core along ⁺ ^z ^{and its} neighbour along

-

z cannot keep ^a hexagonal symmetry ^if ^we ^{want to} avoid frustration effects. (Such

frustration effects arise when such a distribution of

^«

up » and

^«

down

^»

directions need to be set on a 2D hexagonal ^lattice. Therefore, ^{it is} likely ^{that the} undulations only ^retain â rectangular symmetry ^similar ^to that of the Herring bone lattice. Furthermore, the similar values of the coherence lengths (--- 20 Â) ^{of these} ^two ôrders prompt ûs ^to propose â possible

relation between the two. We may âssume that in a given layer, ^the mesogenic ^cores ^which point upwards âre displaced ⁱⁿ ône ^direction (say ⁺ z) ând occupy the positions ât ^the ^corners

of the rectangular ^{cell for} ^instance, ^{with the} opposite situation in the next two layers, just

above and below that considered.

The last two elements of the X-ray diffraction pattern âre ^the ^diffuse ^lines (e) ând (f). În ^the following, ^we ^shall try ^to analyse ^the ^disorders responsible ^{for such} â ^diffuse scattering ⁱⁿ

terms of spatially periodic displacement ^waves. ^These ^{waves are} ^similar ^to phonons except that our technique ^does ^not âllow ûs ^to determine if these waves are dynamic ôr ^{static in}

nature. (They could also be dynamic ^at high temperature and frozen in under Tg.) ^Typical

dynamic techniques ^such âs ^NMR ôr ^neutron înelastic scattering âre ^needed ^to clarify ^this point. Moreover, ^the amplitude ^{of these} displacement ^waves may be much larger ^{than the} typical ônes ôf phonons.

The diffuse lines (e) ^were already observed in the SB phase of conventional mesogens [5, 9J

and in the SA phases ^of P3,8, P4,8, P5,8 [20] ^{and of} ^some mesomorphic side chain

polymethacrylates [24]. They ^were interpreted ^as ^the scattering by ^molecules displaced by ^a

few Â along ^the director from their mean position ^within ^the layer. ^In ^our ^case, the coherence

length along the director of this movement is roughly 50 A (2-3 mesogenic cores). ^The ^mean displacement ^{of the} mesogenic ^cores ^is ^estimated ^to ^{àz -*} ³ ^± ¹ Â. (This value also

corresponds ^to the fact that we do not observe the first diffuse lines which would go through

the first Bragg spots ^{001 and} 002.) Âs ^mentioned above, ^such â disorder may also be analysed [16] ⁱⁿ ^terms ôf transverse displacive ^waves ôf ^wave ^vectors parallel ^to ^the layers-i.e. ^these

waves propagate in the directions parallel ^to ^the layers. ^The intensity of the diffuse scattering (e) ^also implies ^{that the} amplitude ^of this modulation should be large (a ^few Ângstrôms).

The diffuse lines (f) ^{are more} ^difficult ^to explain by â model of disorder in direct space because they ^{tilt with} respect ^to ^the equator ând ^because they âre ^curved. Therefore, ^we ^shall only ^make â ^few simple ^remarks âbout ^{them :} ^we interpret the diffuse lines (f) âs being ^the

locus of the wavevectors of transverse displacive ^waves ^similar ^to those which give ^rise ^to ^the

diffuse lines (e). ^{For such} wavevectors, the amplitudes ^{of these} ^waves should be rather large

so that a fairly important X-ray diffracted intensity ^can ^be detected. Inelastic neutron

scattering experiments ^are needed in order to study ^these ^waves ^{and check} ^our interpretation.

The fact that the diffuse lines (f) ^{reach the} ^diffuse spots (d) shows that there is some coupling

between the undulations of the layers ^and ^these transverse displacive ^{waves :} ^their

wavevectors tilt as their moduli become comparable ^to the molecular dimensions. This effect makes a representation ^{of this} ^disorder in direct space ^even ^more complicated ^and ^we ^did ^not analyse it any further.

Conclusion.

The polymeric and conventional SB phases ^are ^similar ⁱⁿ that, ^{in both} cases, the mesogenic

cores are perpendicular ^to ^the layers and, ^within ^a layer, packed ^{on a} ^2D hexagonal lattice.

Mesomorphic side chain polysiloxanes : a structural study of the smectic B phase

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Mesomorphic side chain polysiloxanes : a structural study of the smectic B phase

P. Davidson, A.M. Levelut

To cite this version:

P. Davidson, A.M. Levelut. Mesomorphic side chain polysiloxanes : a structural study of the smectic B phase. Journal de Physique, 1989, 50 (17), pp.2415-2430. �10.1051/jphys:0198900500170241500�.

�jpa-00211070�

Mesomorphic side chain polysiloxanes : a structural study of

the smectic B phase

P. Davidson and A. M. Levelut

Laboratoire de Physique des Solides, associé au C.N.R.S., Université Paris XI, Bât. 510, 91405 Orsay Cedex, France

(Reçu le 30 mars 1989, accepté sous forme définitive le 25 mai 1989)

Résumé.

Cet article décrit une étude structurale par diffraction des rayons X de quelques polysiloxanes mésomorphes en peigne, en phase smectique B (SB ). Comme nous ne disposions

pas de véritables monocristaux, cette étude a été faite sur des échantillons alignés sous champ magnétique et présentant donc une géométrie de

fibre

sont confinés entre les couches de c0153urs mésogènes, dans une épaisseur de 6 ± 1 Å le long du

directeur. Nous comparons cette structure avec celles des cristaux formés par certains polymères

de la même série et avec celles des phases SB classiques. Du premier point de vue, il semble que la

phase SB polymère puisse être considérée comme un « paracrystal » bidimensionnel ; du second, le fait que nous ne disposions pas d’un vrai monodomaine de phase SB polymère nous empêche de

l’identifier comme une phase hexatique B. Nous présentons ensuite les fluctuations qui affectent

la structure de cette phase SB polymère. Comme dans les phases SB classiques, les c0153urs mésogènes, au sein d’une couche, se placent localement aux n0153uds d’un réseau de type chevrons

avec une longueur de cohérence de l’ordre de 20 Å. De plus, dans la phase SB polymère, les squelettes corrèlent cet ordre à courte distance sur quelques couches voisines. Par ailleurs, la.

nature polymérique du composé induit une modulation transverse probablement displacive des

couches (ondulations). Sa longueur de cohérence vaut aussi environ 20 Å. Cette modulation est fortement couplée au réseau hexagonal bidimensionnel et pourrait être aussi couplée aux

fluctuations de type chevrons. Des mouvements longitudinaux des c0153urs mésogènes autour de

Physics Abstracts

61.30 - 61.40K

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500170241500

relation to those of the crystals that some polymers of the same series display and then to those of

the classical SB phases : from the first point of view, it appears that the polymeric SB phase may be regarded as a 2 dimensional « paracrystal

From the second one, the lack of a true monocrystal of the polymeric SB phase prevents us from definitely identifying it as a stacked

hexatic phase. We have then investigated the fluctuations which affect the structure of this

polymeric SB phase. As in classical SB phases, the mesogenic cores within a layer, pack themselves locally on a 2-dimensional herring bone array of cohérence length of the order of 20 Å. Moreover,

in the polymeric SB phase, this short range order is also correlated along a few adjacent layers by

the polymeric backbones. In addition, the polymeric nature of the compound induces a transverse probably displacive local modulation of the layers (undulations). Its cohérence length is also roughly 20 Å. This modulation is strongly coupled to the 2-dimensional hexagonal lattice and

might also be coupled to the herring bone array. Longitudinal motions of the mesogenic cores

about their mean positions in the layers have been detected too. Some of these motions are

usually seen in the classical SB phases whereas the others are more complicated and difficult to

represent in direct space. We briefly analyse them in terms of transverse displacive waves similar

to phonons.

Introduction.

Mesomorphic side chain polymers have recently attracted wide interest in view of potential applications in the field of non linear optics [1, 2]. These compounds often exhibit nematic

(N), smectic A (SA) and smectic C (Sc) phases which have been thoroughly studied.

Moreover, the smectic B (SB) phase has sometimes been reported, too [3, 4]. This paper presents a structural study of this new polymeric SB phase.

First let us recall the structure of the conventional SB phase (Hereafter, by conventional

bone array. This short range order is related to the cooperative nature of the rotation of the

mesogenic cores about their long axes as was demonstrated by coherent inelastic neutron scattering experiments [10]. At long distance, the herring bone correlations vanish so that the lattice retains its hexagonal symmetry.

The conventional SB phases may be classified into two groups according to the interlayer

correlations [6, 11-13] :

if these correlations extend on a long range, then the molecules are 3-dimensionally

correlated and the phase is called crystal B ;

another phase made of stacks of 2D hexagonal lattices and called a stacked hexatic B

phase has also been predicted [11] and was observed experimentally [13]. In such a phase, one

defines the nearest neighbour bond orientational order of the hexagonal lattice. The

positional order within a layer is only short range whereas the bond orientational order remains long range and is 3-dimensionally correlated.

Let us also recall a few facts about the crystallization of polymers [14, 15]. Compared to

usual crystals (i.e. crystals of small molecules), good quality crystals of most polymers are

difficult to obtain and they contain a variable amount of amorphous material depending upon

the crystallization conditions. Their X-ray diffraction patterns display reflections which are

Fig. 1.

Molecular organization in a layer of a conventional SB phase [6]. M : mesogenic core, C : aliphatic chain. a and b are the vectors of the hexagonal lattice. The cylinders represent the envelope of

the rotating molecules. In a crystal B phase, such layers are long range correlated along their normal and their packing eventually present superstructures. A stacked hexatic B phase is made of stacks of such

layers.

often not resolution limited and the widths of the reflections may increase with increasing scattering angle. Moreover, the intensity of these reflections usually decreases quickly with increasing scattering angle (quicker than the general decrease of the atomic form factors).

Several ideas based on the notion of disorder, account for such a behavior :

Disorders may be classified into two types [14-16] according to the statistical distributions which describe them. We shall illustrate the difference between the two types of disorder by considering their effects on the lattice vectors. If the fluctuations of two neighbouring lattice

vectors (i.e. the vectors between neighbouring lattice points) are correlated, then the disorder is called of the first type. This kind of disorder, a good example of which is thermal agitation,

does not affect the lattice long range order. Its only effect is to decrease the intensity of the

reflections by a factor of the Debye Waller type, without altering their widths which simply depend upon the size of the crystallites. If two neighbouring lattice vectors are allowed to

fluctuate independantly, then the lattice long range order is destroyed. Consequently, the

widths of the reflections do not depend only on the size of the crystallites any more but also on

the average square value of the fluctuations. Moreover, the widths of the reflections increase with the indices of the reflections, that is with increasing scattering angle ; however, their

integrated intensities are not affected. Hosemann has called « paracrystal » [14] a crystal

modified by a disorder of the second type and this concept is often used in the field of

polymeric crystals.

Mesomorphic side chain polysiloxanes : ^a structural study ^of

Laboratoire de Physique ^des Solides, ^associé ^au C.N.R.S., Université Paris XI, ^Bât. 510, ⁹¹⁴⁰⁵ Orsay Cedex, ^France

(Reçu ^{le 30} ^mars 1989, accepté sous forme définitive ^{le 25 mai} 1989)

Cet article décrit une étude structurale par diffraction des rayons X de quelques polysiloxanes mésomorphes ^en peigne, ^en phase smectique ^B (SB ). ^Comme ^{nous ne} disposions

pas de véritables monocristaux, ^cette ^étude â ^{été faite} ^sur des échantillons alignés ^sous champ magnétique êt présentant ^donc ûne géométrie ^de

^fibre

sont confinés entre les couches de c0153urs mésogènes, ^dans ^une épaisseur ^{de 6 ± 1} Å le long ^du

de la même série et avec celles des phases SB classiques. ^Du premier point ^de vue, il semble que la

phase SB polymère puisse être considérée comme un « paracrystal » bidimensionnel ; ^du second, le fait que ^{nous ne} disposions pas d’un vrai monodomaine de phase SB polymère ^nous empêche ^de

l’identifier comme une phase hexatique ^{B. Nous} présentons ensuite les fluctuations qui ^affectent

la structure de cette phase SB polymère. Comme dans les phases SB classiques, ^les ^c0153urs mésogènes, ^au sein d’une couche, ^se placent localement aux n0153uds d’un réseau de type ^chevrons

avec une longueur de cohérence de l’ordre de 20 Å. De plus, ^{dans la} phase SB polymère, ^les squelettes ^corrèlent ^cet ^{ordre à} ^courte ^distance ^sur quelques couches voisines. Par ailleurs, ^la.

nature polymérique ^du composé ^induit ^une modulation transverse probablement displacive ^des

couches (ondulations). ^Sa longueur de cohérence vaut aussi environ 20 Å. Cette modulation est fortement couplée âu ^réseau hexagonal bidimensionnel et pourrait ^être âussi couplée âux

fluctuations de type chevrons. Des mouvements longitudinaux ^des ^c0153urs mésogènes ^autour ^de

Physics ^Abstracts

relation to those of the crystals ^that ^some polymers ^{of the} ^same ^series display ^{and then} ^to ^{those of}

the classical SB phases : ^{from the} ^first point ^of view, it appears that the polymeric SB phase may be regarded ^{as a} 2 dimensional « paracrystal

From the second _one, the lack of a true monocrystal ^{of the} polymeric SB phase prevents ^us ^from definitely identifying ^it ^{as a} ^stacked

hexatic phase. ^We have then investigated the fluctuations which affect the structure of this

polymeric SB phase. ^As in classical SB phases, ^the mesogenic ^cores ^within ^a layer, pack ^themselves locally ^{on a} 2-dimensional herring bone array of cohérence length of the order of 20 Å. _Moreover,

in the polymeric SB phase, ^this short range order is also correlated along ^a ^few adjacent layers by

might ^{also be} coupled ^to ^the herring bone array. Longitudinal motions of the mesogenic ^cores

about their mean positions ^{in the} layers have been detected too. Some of these motions are

usually ^seen in the classical SB phases whereas the others are more complicated and difficult to

represent in direct space. We briefly analyse ^{them in} ^terms ^of transverse displacive ^waves ^similar

Mesomorphic side chain polymers ^have recently attracted wide interest in view of potential applications in the field of non linear optics [1, 2]. ^These compounds often exhibit nematic

(N), smectic A (SA) ^and smectic C (Sc) phases which have been thoroughly ^studied.

Moreover, the smectic B (SB) phase has sometimes been reported, ^too [3, 4]. This paper presents ^a structural study ^{of this} ^new polymeric SB phase.

bone array. This short range order is related ^to the cooperative ^nature of the rotation of the

mesogenic ^cores about their long axes as was demonstrated by ^coherent ^inelastic ^neutron scattering experiments [10]. ^At long distance, ^the herring ^bone correlations vanish so that the lattice retains its hexagonal symmetry.

The conventional SB phases may be classified into ^two groups according ^to ^the interlayer

if these correlations extend on a long range, then the molecules ^are 3-dimensionally

another phase ^made ^of stacks of 2D hexagonal ^lattices and called a stacked hexatic B

phase has also been predicted [11] ând ^was ôbserved experimentally [13]. ^{In such} â phase, ône

defines the nearest neighbour ^bond orientational order of the hexagonal lattice. The

positional order within a layer ^is only short range whereas the bond orientational order remains long range and is 3-dimensionally correlated.

Let us also recall a few facts about the crystallization ^of polymers [14, 15]. Compared ^to

usual crystals (i.e. crystals ^{of small} molecules), good quality crystals ^of ^most polymers ^are

difficult to obtain and they ^contain â ^variable âmount ôf amorphous ^material depending upon

Fig. ^1.

^Molecular organization ⁱⁿ â layer ôf â conventional SB phase [6]. ^{M :} mesogenic ^core, ^{C :} aliphatic ^chain. â ^{and b} âre ^the ^vectors ^{of the} hexagonal lattice. ^The cylinders represent ^the envelope ôf

the rotating molecules. In a crystal ^B phase, ^such layers ^are long range correlated along their normal and their packing eventually present superstructures. ^A stacked hexatic B phase is made of stacks of such

often not resolution limited and the widths of the reflections may increase with increasing scattering angle. ^Moreover, ^the intensity ^of these reflections usually ^decreases quickly ^with increasing scattering angle (quicker ^{than the} general decrease of the atomic form factors).

Several ideas based on the notion of disorder, ^account ^{for such} ^a ^{behavior :}

Disorders may be classified into ^two types [14-16] according ^to ^the statistical distributions which describe them. We shall illustrate the difference between the two types of disorder by considering their effects on the lattice vectors. If the fluctuations of two neighbouring ^lattice

vectors (i.e. ^the ^vectors ^between neighbouring ^lattice points) ^are correlated, then the disorder is called of the first type. ^This ^{kind of} disorder, ^a good example of which is thermal agitation,

does not affect the lattice long range order. Its only ^{effect is} ^to decrease the intensity ^{of the}

reflections by â factor of the Debye ^Waller type, ^without altering ^their ^widths ^which simply depend upon the size of the crystallites. Îf ^two neighbouring ^lattice ^vectors âre âllowed ^to

fluctuate independantly, then the lattice long range order is destroyed. Consequently, ^the

widths of the reflections do not depend only ^on ^the size of the crystallites any ^more but also on

the average square value of the fluctuations. Moreover, ^the widths of the reflections increase with the indices of the reflections, that is with increasing scattering angle ; however, ^their

integrated intensities are not affected. Hosemann has called « paracrystal » [14] ^a crystal

modified by ^a disorder of the second type ^{and this} concept is often used in the field of

In this context, ^we ^{found it} interesting ^first ^to determine the crystallographic parameters ^of this new polymeric SB phase ^{and then} ^to study in which way the polymeric ^nature ^{of the} compound modifies the organization ^{of the} phase. ^In particular, ^we have tried to examine two

Do the ideas mentioned above, ^{about the} structures of conventional SB phases ^{and of} polymeric crystals, apply ^to ^this ^new polymeric SB phase ?

How is the local order of the mesogenic ^cores ^affected by chemically grafting ^them ^{on a} polymer ?

R. Duran et al. have presented ân X-ray diffraction study [17] ôf â polymeric SE phase. They have shown that the SE phase is lamellar with the mesogenic ^cores packed ôn â

2D rectangular ^lattice ^within ^a layer. ^No 3D correlations were to be seen. These authors

Among ^the polymers ^which ^were reported ^to present ^a SB phase ^{in the} literature, ^we ^have

chosen a series of mesomorphic ^side ^chain polysiloxanes synthesized by M. Mauzac et al. [18].

This series was already ^well characterized [18] and furthermore we thought ^that the presence of Si atoms in the backbones would increase the form factor of the molecule and give

additional information about the backbones. These polymers correspond ^to the formula :

and we shall call them Pn, m âccording ^to the number of methylene groups in the spacer and in the alcoxy ênd chain. The tacticity ^{of these} polymers has been characterized by 29Si _{NMR ;} they ^can be considered as completely âtactic [19].

We have chosen to study five of these polymers ^which ^were also studied by X-ray

diffraction in the SA phase [20]. ^Their polymorphism is recalled in table 1 :

Phase transition temperatures (’C) of polymers P3,4, P4,4, P3,s, P4,s ^and P5,8- (Tg : ^glass transition, Tm : melting point, Tc: clearing point) [18].

end chains [18]. Polymers P3, 4 ^and P4, 4 ^have ^been ^added ^so ^that ^we ^shall ^{be able} ^to ^compare

the polymeric SB phase ^{with the} polymeric crystals ^of ^similar compounds.

Aligned samples ^{could be} ^obtained by slowly cooling ^them (5°C/hour) ^{from the} isotropic phase ^to ^the SA phase ⁱⁿ ^a magnetic ^field (1.7 T). ^These samples ^were ^contained ⁱⁿ

Lindemann capillary tubes of 1.5 mm diameter. Therefore our samples present ^a cylindrical

symmetry around the magnetic ^field direction. In addition, ^a ^small mosaicity ^{of about} ^5° ^exists

in our magnetically aligned samples. ^These magnetically aligned samples ^do ^not ^show ^as ^much

information as real monodomains of SB phase. Such monodomains have sometimes been obtained by melting ^of single crystals ^of ^low ^molecular weight liquid crystals [9]. ^{However in}

the present case, single crystals ^are unlikely ^to be grown due to the polymeric ^nature ^{of the}

The samples ^were ^examined ^with ^two ^different X-ray ^set ups :

a conventional Guinier camera equipped ^with ^a cylindrical quartz monochromator

(03BB CuKa 1 = 1.5405 A) helped ^us ^to ^measure ^the crystallographic parameters ^{of the} SB phase ^and ^to examine the profiles ^{of the} reflections ;

another set up already ^described [21] revealed the presence of ^some diffuse scattering :

a punctually ^focussed monochromatic X-ray ^beam (03BB CuKa