Frank elastic constants and rotational viscosity for nematic solutions of main-chain polymers

HAL Id: jpa-00210903

https://hal.archives-ouvertes.fr/jpa-00210903

Submitted on 1 Jan 1989

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Frank elastic constants and rotational viscosity for nematic solutions of main-chain polymers

Hedi Mattoussi, Madeleine Veyssie

To cite this version:

Hedi Mattoussi, Madeleine Veyssie. Frank elastic constants and rotational viscosity for ne- matic solutions of main-chain polymers. Journal de Physique, 1989, 50 (1), pp.99-106.

�10.1051/jphys:0198900500109900�. �jpa-00210903�

Frank elastic constants and rotational viscosity for nematic solutions of main-chain polymers

Hedi Mattoussi (*) and Madeleine Veyssie

Laboratoire de Physique de la Matière Condensée, Collège de France U.A. 792, ¹¹ place

Marcelin-Berthelot 75231 Paris Cedex 05, ^France

(Reçu ^{le 25} février 1988, accepté ^sous forme définitive ^{le 7} septembre 1988)

Résumé.

Nous avons mesuré les constantes élastiques ^de divergence ^et de flexion pour des solutions de polymères mésormorphes ^de type ^« main-chain ^» dans un cristal liquide nématique

conventionnel. On constate que, à la fois les propriétés statiques ^{et les} propriétés dynamiques

sont considérablement affectées même en régime dilué. L’accroissement notable du coefficient de viscosité de rotation est interprété à partir d’un modèle d’haltère anisotrope, dû à F. Brochard. La conclusion principale qui ^se dégage ^{de cette étude est} que le polymère ^considéré présente ^une anisotropie marquée ^{de sa} conformation ; toutefois, ^cette conformation est très différente d’un schéma de chaîne étirée, ^et correspond à ^une pelote gonflée dans les trois dimensions.

Abstract.

Studying dilute solutions of a main-chain mesomorphic polymer ^{in a} conventional nematic liquid crystal, ^we have measured the splay ^and bend elastic constants, ^as well as the rotational viscosity coefficient in those systems. ^We observed that both static and dynamic properties ^are significantly ^affected by the addition of even a small quantity ^of polymer. ^The large

increment of the rotational viscosity coefficient may be explained in the framework of a model of

anisotropic dumbell, ^{due to} F. Brochard. These viscoelastic effects are compared ^to analogous

measurements obtained in the case of solutions of side-chain polymers. ^The general conclusion we

deduce is that the main-chain polymer ^we study, although exhibiting ^a significant anisotropy ^{as for}

its conformation, ^{does not look like a stretched} chain, ^{but is} largely swollen in three dimensions.

Classification

Physics ^Abstracts

61.25H

6130E

66.20

Introduction.

Main-chain mesomorphic polymers ^are presently ^the subject ^{of numerous chemical and} physical ^{studies. Chemists} synthesize ^{more and more} variety ^of mesomorphic ^{chains with}

variable flexibility, by modifying ^the length ^of the spacers ^as well as the nature of

mesomorphic elements in the backbone. Some physical ^{results are} available, ^{either from} experimental measurements or from theoretical considerations [1-3].

It appears ^now that the physical behaviour for this category ^of mesomorphic polymers ^{is not}

uniform. For instance, ^it has been shown that the nematic order parameter may either be

(*) Present address : Polymer Science and Engineering Department ⁷⁰¹ GRC, University ^of

Massachusetts at Amherst, Amherst, ^MA 01003, ^U.S.A.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500109900

100

much more important than for low molecular weight (l.m.w.) liquid crystals, ^{or of the same}

order of magnitude, depending ^{on the} degree ^of flexibility introduced in the chain. We present ^here experimental ^results concerning ^the co-polyester ^{with the chemical formula}

Its synthesis ^and physicochemical characterization are largely ^{described in reference} [4]. ^In particular ^the high resolution 13C n.m.r. analysis ^confirms the random distribution of x and y

sequences in the copolyester chain. The molar mass MW ^{deduced from} small-angle light scattering technique ^{is about 220.000} corresponding ^{to an} average index of polymerization NW - ^400. Notice also that the clearing temperature (TN _ 1 ) being accompanied by ^a large biphasic ^{domain, has to} be correlated to an important degree ^of polydispersity ^{of this} system.

As for the diamagnetic anisotropy [5], it is of the same order of magnitude ^{as for low}

molecular weight liquid crystals : ,Y a =-- - 1. 4 ^{x 1.-7} (c.g.s.).

Except ^these measurements and a structural investigation [4], by X-ray diffraction in the melt phase, ^{there is no other} information concerning ^this copolyester.

We have chosen to study ^the properties ^{of this} polymer ^{when diluted in a 1.m.w.} liquid crystal ^{solvent. This} approach presents ^several interesting features. First of all, it allows to draw an interesting comparison ^{with classical solutions of} polymers. ^{This method was}

revealed to be fruitful in the case of side-chain mesomorphic ^solutions [6, 7]. ^{It is then} tempting ^{to extend it to the} other class of nematic polymers. Moreover, ^the study ^{of nematic}

solutions permits ^to get information about such systems ^{which are} generally ^{difficult to} study

in the melt phase.

As l.m.w. liquid crystal solvent, ^we have chosen parazoxyanizol (PAA), which has been

extensively ^{studied as} for its nematic properties. Moreover, ^{PAA exhibits a nematic} phase ^at relatively high temperatures ^{and is a favorable} condition, ^when considering ^the high ^{value of}

the clearing point ^{of the} copolyester [5]. ^{Solutions are} prepared by mixing ^the polymer ^and

the PAA in a common solvent i.e. toluene, ^and carefully evaporating ^{under vacuum while} heating during several hours. We studied solutions in the dilute regime, ^with polymer

concentrations less than 6 % in weight.

Using ^these solutions, ^{we have} determined typical ^nematic properties, namely ^the

rotational viscosity y 1 and two Franck elastic constants Kl ^and K3 ^which respectively correspond ^to splay and bend deformations.

The results will be discussed by comparison ^with previous experimental ^{results on} mesomorphic components, ^{and with available} theoretical considerations.

1. Expérimental ^section.

1.1 EXPERIMENTAL PROCEDURE. - The rotational viscosity yi and the elastic ^constants

Kl ^and K3 ^are determined by using ^the classical method of studying ^the dynamics ^{of a}

Fredericks transition under magnetic ^{field, as described in detail} by Pieranski et al. [8] ^{and in}

reference [7]. ^The planar geometry ^{allows us to measure} Kllx., ^and Yilx. ; ^the homeotropic

one gives K3/Xa ^and y *IX. ^where y ^is slightly ^different from yl due ^to the backflow effects

[8]. ^{In the} present ^{case the} samples, ^{with a} thickness of the order of 100 _fJ.m, were orientated either in planar ^{or in} homeotropic geometries. The former case is obtained by uniaxially rubbing ^the limiting ^surfaces while the latter is obtained by ^an esterification technique ^of glass surfaces, ^{as described in reference} [7]. We have then measured Y,/Xa ^and Kl, 3/Xa ^{as a}

function of polymer concentration c and temperature ^T.

We ^note that the addition of a small quantity ^of copolyester ^{chains to the PAA introduces}

some difficulties in orientating ^the samples. ^For example, ^{it was not} possible ^{to have} homogeneous planar samples ^{for solutions with} concentrations higher ^{than 4} %, and it shows

a tendency ^{for a} spontaneous homeotropic orientation when the concentration increases. This may be correlated with similar observations on pure copolyesters [5]. ^{We have thus restricted}

the K, measurements to c 4 %.

1.2 EXPERIMENTAL RESULTS. In principle, ^{for a} quantitative comparison between the

polymeric solutions and the pure nematic solvent, it would be necessary ^to compare their

physical properties ^{for the same} values of the order parameter, ^{or the same reduced} temperature TR

TIT,,. This raises the non-trivial problem ^of the definition of the clearing temperature ^{for a} binary mixture ; it has been theoretically ^shown by ^{F. Brochard} [9] ^that Tc (c :0 0 ) is in fact a « pseudo-transition » temperature located in the biphasic domain ; ^this

has been experimentally ^checked by Dubault et al. [10], for solutions of conventional flexible chains.

In the present ^case, reasonable thermodynamical arguments [7] ^indicate that, ^whatever would be the value of c in the dilute regime, Tc(c) is very close ^to the lower limit of biphasic

domain. Moreover, this lower limit is quasi-independent ^{of the} concentration, ^{so that} 7c(c) ^{is closed to} Tc(O). We may then ^use directly the absolute temperature T, ^when discussing ^our data. It appears, in fact, ^{that this} hypothesis is consistent with the present experimental ^{results as} the behaviour of K, and y 1 ^as functions of the absolute temperature

are very similar for the pure PAA and for the solutions (Figs. ^{1 and} 2).

1.2.1 Elastic constants. In figure 1, ^{we have} plotted the values of K, ^and K3 ^{versus the}

temperature ^T for different values of the concentration. The values obtained for pure PAA

are lower than the ones available in the literature [11]. One may ascribe this difference to the chemical quality ^{of the} product ^{we use,} although ^{it has been} recrystallized ^{in an} organic

Fig. 1. - Variation of the splay (Kl ) ^{and bend} (K3) ^{elastic constants as a} function of the temperature T,

for different values of the polymer concentration c.

102

Fig. ^2.

Variation of (YI/Xa) ^{as a} function of the temperature ^T for different values of the polymer concentration ; y, is the rotational viscosity coefficient and Xa ^the diamangetic anisotropy.

solvent. However, ^{this is not} relevant in the present study, ^{as we look at the} differential effects due to the adjunction ^of chains in the solutions. As for K3, ^{we have to notice that the}

esterification technique ^{did not enable us to} get ^uniform homeotropic samples for pure PAA ;

K ₃

we then deduce K3(0) ^from K1(0) by using ^{the ratio} K3 K i ^{( ) 0 - !(TR) as} determined by KI

previous data for PAA [11].

Tuming ^{now to the} solutions, ^we observe that the presence of ^{even a} small quantity ^of

dissolved chains significantly ^{affects both} K, ^and K3.

For instance, ^we get

for

These effects systematically ^{increase with the} concentration ; notice also that the increments

are of the same order of magnitude ^for K, ^and K3.

1.2.2 Rotational viscosity y,.

In figure 2, ^we _present, ^{on the same} plot, ^the experimental

values of Y1/ X a ^{as a} function of temperature ^T for different concentrations c. It appears that these curves obey ^{an Arrhenian} law, ^as introduced by ^Prost [12] for l.m.w. liquid crystals

where W has the same value for all the concentrations we explored. ^{In order to eliminate the}

temperature effects, ^we plotted ^{the relative} increment of the viscosity coefficient

as a function of the concentration (Fig. 3).

The striking ^{fact is that the} rotational viscosity ^is strongly ^affected by the presence of ^a small percentage ^of polymer ^{chains in solution. For} example àyi/yi ^{reaches 200 % for}

c=4%.

The second remark is that in the dilute regime 0 yl/ yl ^linearly varies with the concentration c-(or, equivalently, with the number of chains per unit volume, 0).

At last, ^we may notice that, ^{in the} homeotropic geometry, the relaxation time of the Fredericks transition gives ^a value of the viscosity coefficient yi smaller than that deduced from planar ^{case, in} agreement ^{with the} backflow effects observed in 1.m.w. nematics [8].

2. Discussion.

2.1 FRANK ELASTIC CONSTANTS Ki ^AND K3. ^{- As described in the} experimental ^{section, the}

effect of solubilizing main-chain macromolecules in a conventional nematic is important, ^even

at low concentrations, ^{and of similar} magnitude ^{for both} splay ^{and bend} distortions. This is

totally ^{different from what we observed} for another class of mesomorphic polymers, i.e. side- chain polymers, where the Frank coefficients are constant even in a wide range of concentrations [6]. In the side-chain _case, this may be easily understood if we consider that,

even in the pure melt system, the elastic constants are of the same order of magnitude ^{as for}

the 1.m.w. nematics [13].

In the case of main-chain polymers, the situation is not so clear. Only a ^{limited number of} experimental ^{data are} available, ^and correspond ^{to different chemical} sequences ^{and chain}

lengths.

-

Zheng-Min and Kléman [14] ^{have measured} K, ^and K3 ^{for a different} copolyester, ^with

index of polymerization ^around 25 ; they ^{observed a} large increase, compared ^{to 1. m.w.}

material, ^more pronounced ^{for the} splay ^constant

- For another product, with index of polymerization ^about 10, Martin et al. [15] ^have

determined the ratio Kl/K3 ^to be of the order of 102.

Theoretical models [16] ^{have been} developed ^{for melt} polymer ; these models generally

consider a highly stretched chain and consequently predict ^a considerable increase in

Kl, ^{but no} important effect for K3. ^In particular, ^{in the de Gennes} description [16], ^which

appears suitable ^for high ^{values of the} polymer length L, ^the Kl ^{increment scales as} L2.

Taking ^{into account the} present results, ^we may consider ^two hypotheses : either the steric hindrance is much less important for dilute solutions than in the melt, leading ^{to an attenuated}

effect on the splay constant ; ^{or the} image ^{of a} stretched chain is inappropriate ^{for the} presently ^studied copolyester. ^{It would mean} that many hairpins [16] may occur, the relevant distance being ^{then defined} by ^two consecutive hairpins, ^{and not} by ^the length ^{of the} polymer.

This last interpretation looks consistant with a structural study ^{of these} polyesters [4], ^which

puts into evidence a conformation of the following type :

104

These elements play the role of an elbow, introducing ^a change of direction along ^{the chain.}

Such accidents are sufficient to induce a conformation of the chain swollen in three

dimensions, rather than an elongated rod. In this framework, ^one may understand that the elastic constant increments do not obey ^the theoretical predictions established for stretched

polymers ; ⁱⁿ particular, ^{we do not} expect ^{a drastic} difference between K, ^and K3. ^{In the} following ^{section we shall see that this} image of swollen coil is supported by ^our experimental

results on the rotational viscosity coefficient.

2.2 ROTATIONAL VISCOSITY y,. - The YI coefficient is related to the dissipative property ^of the system, ^and it is well known, from the conventional polymer solutions, ^{that the} viscosity ^is considerably ^{enhanced even at low} concentrations. Moreover, ^some previous ^{studies have} put into evidence a significant ^increment of the rotational viscosity in nematic solutions. For

instance, ^{Dubault et al.} [7] have determined the effect of ordinary ^{flexible chains} solubilized in a liquid crystal ; ^more recently, ^{we have studied solutions} of side-chain mesomorphic polymers [6, 7] ^{in a wide} range of concentrations. It is then quite interesting ^to compare these results to the present ^ones.

In both _cases, the increment in y, may be explained ^{in the framework of a} hydrodynamical

model proposed by ^Brochard [18]. ^{In this model, the basic} hypothesis is that the polymer

backbone exhibits an anisotropic conformation, ^{when diluted in a} uniaxially ordered solvent.

Consequently, the rotation of the director implies ^a cooperative ^motion of the whole chain, leading ^to large dissipative effects. The existence of such a geometrical anisotropy ^{was not} obvious, a priori, for side-chain systems, but it has been directly ^checked by ^S.A.X.S.

measurements [19]. ^However, for main-chain polymers, ^{the idea of a somewhat} elongated

conformation looks reasonable. The Brochard model allows then the increment of y 1 in the dilute regime ^to be calculated

where 0 ^is the number of chains per unit volume, TR the relaxation time for the polymer, ^and RI, Rl ^the characteristic sizes of the chain parallel ^and perpendicular ^to the nematic director, respectively. ^In this low concentration approximation, Ay, linearly depends ^{on the}

concentration _c, as it is indeed observed in the experimental study. ^{As for the} temperature dependence, ^{it is} mainly ^contained in the relaxation time TR. Thus, ^{it is} reasonable to

postulate that TR presents ^{an arrhenian} behaviour, ^{with the same} activation _energy as the

viscosity coefficients of the pure nematic solvent. This justifies ^{the fact that we have} plotted

the ratio D y l/ yl (Fig. 3) ^{in order to} eliminate the temperature effects. Another relevant parameter ^{is the chain} length, ^{or index of} polymerization. ^{In the Rouse} approximation, ^which

looks appropriate ^for semi-flexible polymer systems, TR scales as N 2, ^{, so that} à Y, may be

expressed ^as

It is then interesting ^to compare the observed effects in the side-chain case [6] (S.C.) ^{with the}

present main-chain (M.C.) one ; ^at first sight, the increments seem to be much larger ^{in M.C.}

than in S.C. For instance, ^{at the same} concentration c of the order of 4 %

Fig. ^3.

Relative variation of the rotational viscosity ï’ ^{as a} function of the concentration c, for different temperatures (dilute regime).

However, from formula (2) the increase of _{yl is} supposed ^to depend ^{on the chain} length ; renormalizing ^for equal ^{index of} polymerization, ^{one obtains} only ^a doubling ^{of the effect.}

This result is not consistent with the naive image ^of main-chain polymers behaving ^as highly elongated rods, ^with RI ^much larger ^than R_L. ^More quantitatively, ^we try ^to estimate the

anisotropic ratio, ^defined by x

RI /R1.. ^{This may be deduced from the} experimental ^values

of à y,, via formula (1), ^{if the} characteristic time TR is known : TR is related to the

hydrodynamic ^radius RH by ^the expression

where n is the viscosity of the medium. In a crude estimate, ^{we use for} RH the value of the radius of gyration [5] ^{measured in a} conventional solvent, ^{and an} average viscosity ^for PAA ;

TR is then found to be 2 x 10-5 s, which has a reasonable order of magnitude. ^We thus obtain

The interesting point ^{is that such a} value of the anisotropy ^{does not at all} correspond ^{to a}

stretched chain but to a swollen coil, largely extending ^{in three} dimensions, although ^not spherical. Notice that this result is consistent with the preceding discussion related to elastic constants in solutions, and also with the X-ray data obtained on those materials [5].

Conclusion.

As expected, ^{we have obtained some relevant} information from the study ^{of the} visco-elastic

properties of dilute nematic solutions of a main-chain mesomorphic polymer. The results relative to the elastic constants and the rotational viscosity ^{in these} systems ^{are of some} interest, ^{as it is not} easy ^to deal with those mesomorphic polymers ^{in their} pure melt state, due to high viscosity ^and difficulties in obtaining ^{suitable oriented} samples. Moreover, ^we have shown that, ^{for the} co-polyester ^we used, the chain-conformation is far from a rod-like one, ^as frequently presumed ^{in the} description of main-chain materials. It would be

interesting ^to check this conclusion of a swollen anisotropic ^coil by ^direct measurements of the

106

characteristic sizes of the polymer, using ^{a small} angle ^diffusion method ; ^{but this} requires ^a supplementary ^{effort in} labelling ^the chains, ^{and would} require ^{a close} cooperation ^between

chemists and physicists.

Acknowledgments.

We are grateful ^{to C.} Noël, who gave ^us the polymeric ^{material we} used, ^{as well as} large

information on the physico-chemical properties ^{of this} product. ^We benefited from fruitful discussions with P. Esnault, M. Kléman and J. Prost, ^{and from} the efficient help ^{of C.}

Casagrande.

References

[1] Polymeric liquid crystals, ^Plenum Publishing Corporation, A. Blumstein ed. (1985).

[2] Polymer liquid crystals, ^Academic Press, New York, ^A. Ciferi, ^{W. R.} Krigbaum ^{and R. B.} Meyer

eds. (1982).

[3] ^WARNER, W., GUNN, J. F. and BAUMGARTNER, ^A. B., ^J. Phys. A ¹⁸ (1985) ^3007.

[4] NOËL, C., FRIEDRICH, C., LAUPRÊTRE, F. , BILLARD, ^{J. and} STRAZIELLE, C., Polymer ²⁵ (1984)

263.

[5] NOËL, C. , MONNERIE, L., ACHARD, ^M. F., HARDOUIN, F., SIGAUD, ^{G. and} GASPAROUX, H. , Polymer ²² (1981) ^578.

[6] MATTOUSSI, H. , VEYSSIÉ, M., CASAGRANDE, C., GUEDEAU, ^{M. A. and} FINKELMANN, H., ^Mol.

Cryst. Liq. Cryst. A ⁴⁴ (1987) ^211.

[7] MATTOUSSI, H., Thesis, ^{P. et M. Curie} University, ^Paris (1987).

[8] BROCHARD, F., PIERANSKI, ^{P. and} GUYON, E., ^J. Phys. ^{France 33} (1972) 681 and 34 (1973) ^35.

[9] BROCHARD, F., C.R. Hebd. Acad. Sci. Paris 289B (1979) ^229.

[10] DUBAULT, A., CASAGRANDE, VEYSSIÉ, ^{M. and} DELOCHE, B., Phys. Rev. Lett. 45 (1980) ^1645.

[11] ^{DE JEU, W. H. ,} CLASSEN, ^W. A., SPRINGT, ^{A. M.} J., ^Mol. Cryst. Liq. Cryst. ³⁷ (1976) ^269.

[12] PROST, J., Thesis, Bordeaux (1973).

[13] ^FABRE, P. , CASAGRANDE, C., VEYSSIÉ, ^{M. and} FINKELMANN, H., Phys. Rev. Lett. 53 (1984) ^993.

[14] ZHENG-MIN, S. and KLÉMAN, M., ^Mol. Cryst. Liq. Cryst. ¹¹¹ (1984) ^321.

[15] MARTINS, ^A. F., ESNAULT, ^{P. and} VOLINO, F., Phys. ^{Rev. Lett. 57} (1986) ^1745.

[16] Cf. P. G. de Gennes and R. B. Meyer in reference [2].

[17] DUBAULT, A., CASAGRANDE, ^{C. and} VEYSSIÉ, M., Mol. Cryst. Liq. Cryst. ⁴¹ (Lett.) (1978) ^239.

[18] ^BROCHARD, F., ^J. Poly. ^{Sci. 17} (1979) ^1367.

[19] MATTOUSSI, H., OBER, R., VEYSSIÉ, M., ^and FINKELMANN, H., Europhys. ^{Lett. 2} (1986) ^233.