side-chain polymeric crystal effets sont caract6ris6s par une valeur classique pulsed electrical field was used to study the characterised by a

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1 J. Phys. II Fnce 2 (1992) FEBRUARY 1992, PAGE 209 effect in isotopic phse of side-chin polymeic Ke cystl liquid L bit flingence induite p un chmp Iectique impulsionnel t6 utilis6e pou R4sum4. Ies effets p tnsitionnels ssoc16s h l phse isotope d'un polysiloxne h chines studie Les 6sultts obtenus montent que ces effets sont cct6is6s p une vleu clssique lt6ies. l'exposnt sttique et une vleu nomle de l'exposnt dynlnique. Ce demie 6sultt de moments induced by electicl field nd pemnent moments of mesogenic dipol molecules. between tendency to ode, imposed by mesogenic elements, nd competition to disode, imposed by polyme skeleton [Ii. tendency hve ecently studied isotopic phse of polycylte, poly[(cyloxy-6-hexyloxy)- We bbevited to PA60CB, with molecul mss Mw of , nd 4-cyno-4'-biphenyl], (*) Unit6 de Recheche Associ e u CNRS n 851. Clssifiction Physics Abstcts K 64.70M V. Reys (I), Y. Donoy (I), D. Collin (I), P. Kelle () nd P. Mtinoty (') Lbotoie d'ultsons et de Dynlnique des Fluides Complexes (*), Univesit6 Louis (1) 4 ile Blise Pscl, Stsboug Cedex, Fnce Psteu, () Lbotoie L on Billouin, C.E.N. Scly, Gif-sun-Yvette Cedex, Fnce (Received 21 Decembe1990, evised lo Octobe 1991, ccepted 7Novembe 1991) monte que l th60ie dynlnique des cistux liquides de bs poids mo16culie n'est ps u cs pesent. Les expeiences mettent 6glement en Evidence une competition ente pplicble moments dipolies induits p le chmp 61ectique et les moments pemnents des molecules les m6sogbnes. Abstct. The bieflingence induced by pulsed electicl field ws used to study effects ssocited with isotopic phse of side-chin polysiloxne. The esults petnsitionl show tht se effects e chcteised by conventionl vlue of sttic exponent obtined nd n bnoml vlue of dynmic exponent, which shows tht dynmic oy of low molecul weight liquid cystls does not pply. The esults lso evel competition between 1. Intoduction. Side-chin liquid cystl polymes e composed of pincipl chin onto sides of which goups hve been gfted, by mens of spce. These new compounds e mesogenic object of intense esech, since y hve specil popeties ssocited with pesently

2 identicl to tht of mesogenic elements of P(o. This compound shll be efeed to s Tj 108 C Tsmc" 46 C Tsc" 3 C TNT" 59 C Fig. 1. Chemicl fomuls nd tnsition tempetues fo P(o nd MPHOB. 210 JOURNAL DE PHYSIQUE II N 2 of 3.38 [2]. This study hs shown tht sttic popeties of locl polydispesity ode e compble to those of pentylcynobiphenyl (PCB), which is low oienttionl weight liquid cystl (LMWLC) with fomul simil to tht of mesogenic molecul of polyme. Howeve, dynmic popeties of locl oienttionl ode elements e vey diffeent fom those of PCB. This diffeence is ppent on elxtion time of oienttionl ode pmete, which is bout 500 times gete thn tht of PCB, nd which with n exponent of ode of 1.5 thn I. diveges ode to check whe se e genel effects, we hve studied no side-chin In The compound in question ws polysiloxne chcteised by degee of polyme. nd mesogenic goups which e diffeent fom those of PA60CB. The esults polymeistion obtined confim bnoml vlue of dynmic exponent nd conventionl vlue of sttic exponent. They lso evel competition between dipol moments induced by electic field nd pemnent moments of mesogenic molecules. Befoe pesenting nd discussing ou esults (Sect. 4), we shll fist of ll descibe polyme studied nd used (Sect. 2), nd n biefly eview Lndu-de Gennes oy of technique phse of low molecul weight liquid cystls (Sect. 3). isotopic 2. Mteils nd methods. The fomul nd phse digm of polysiloxne studied e shown in figue I. Its molecul mss Mw is , nd its polydispesity is I. I. It shll subsequently be efeed to s P(o, whee 6 nd 80 epesent numbe of methylene goups in spce, nd of polymeistion, espectively. In ode to scetin influence of chin on degee oienttionl ode, we hve lso studied 4-methoxyphenyle 4'-((5-hexenyl) oxy) locl benzote, which is liquid cystl of low molecul weight, with fomul (cf. Fig, I) MPHOB. 180 CH (CH)-Si-O-[Si-O[o-Si-(CHb (ch)-o-g-coz-g-o-ch MPHOB CHCH-(CH)-O-9-CO-9-O-CH

3 vicinity of Nemtic-Isotopic tnsition. The biefingence ws mesued t A, with i dution ws djusted in such wy s to ensue sttiony biefingence. tempetue, ise nd decy times of electic field wee less thn 0.2 Ls. This is much less thn The tnsition hve j good signl-to-noise tio. The vition of An with nemtic-isotopic E found to be line fo ll electic fields used. ws nd I wee mesued simultneously on sme smple, which hd been An/E, pio to expeiments, nd mesuements tken unde n inet tmosphee. degssed witten s : S(3 n np 8p) (1) of opticl xis, nd S is scl which fixes molecul oienttionl te in eltion to In isotopic phse, fee enegy pe unit volume cn be expessed s function of development of Qp in following wy : Fo + jaq up Qp jbop Qfly Qy + c (Q«p Qp«) + (2) which, using (I), cn lso be witten s : coefficient B wee zeo, n system would involve second-ode Nemtic-Isotopic If t tempetue Tf. Tht this is not cse indictes tht tnsition is of fist tnsition (T Tf), tht coefficients B nd C e only vey slightly dependent on tempetue. This nd T Tf N 2 KERR EFFECT IN THE ISOTROPIC PHASE OF Po 211 The biefingence induced by pulsed electic field ws used to simultneously detemine intensity nd chcteistic time of locl oienttionl ode, which ppes in 5 mw He-Ne lse s light-souce, nd 10 mm long Ke cell with n inte-electode of 2.2 mm, cell-tempetue being kept constnt to within ± 0.05 C. The electicl length wee ectngul in shpe, with mximum mplitude of 500V, nd fo ech pulses elxtion time of locl oienttionl ode of polyme, which could efoe be detemined. The induced biefingence in P(o is vey wek (ppoximtely 100 times weke thn in PA60CB), nd only mesuements tken in fist 8 degees bove intensity mesuements wee lso cied out on sme set-up. Fo Sctteed-light esons, se mesuements wee only tken fo one obsevtion ngle, chosen so pcticl s to coespond to 90 to incident bem. 3. Review of Lndu-de Gennes model [3]. Fo unixil nemtic, ode pmete is symmeticl tenso of zeo tce which cn be Q«p " whee n, np e components of unit vecto ( diecto) which indictes diection opticl xis. F F Fo+(AS-(BS+ (CS+. (3) ode, nd occus t tempetue T Tf. The Lndu model ssumes tht A of fee enegy enbles us to show tht sctteed-light intensity I development to (Q) ) scles s : (popotionl which shows tht I diveges when T- Tf.

4 Q«p ode pmete by eltion : (Sp ) " (P) minimizing fee enegy. With E long Oz, we find : E (6) I). )$ hs been clculted by Mie nd Meie [4], tking ccount of contibutions of (As ' " hf' (8) N is numbe of molecules pe unit volume, Au molecul polisbility whee v pemnent dipole, nd p men ngle between pemnent dipole nd nisotopy, eqution : I/(I if is fcto which descibes ective field An 8 80(An)mx 7TN F' v(3 cos p I, " so (Ae)$ fi " " " 3 of electicl field to be detemined. Fo ectngul field, one obtins fo ise-nddecy biefingence : AnR(t) Ano(I e/) (l l) whee 212 JOURNAL DE PHYSIQUE II N 2 In pesence of dc electic field E, tem (1/2) so e(j E Ep must be dded to (2) whee so is vcuum pemittivity, nd e(j dc dielectic tenso. e(j is linked to 8«p + (A8x) Q«fl (5) whee Ae ejj e epesents nisotopy of e fo pefectly oiented nemtic, nd (1/3)(2 e + ejj). The ode poduced by electic field E cn be clculted by P S 9 (T Tf) This leds to n electiclly induced biefingence given by mk (AS )f AmK S l) whee An (e)/- (e,)/, nd An is nisotopy of efctive index in oiented nemtic phse (S induced nd pemnent dipoles. Bsed on Onsge model, this clcultion gives (he )$ 4 MN + Au 2 kb T long xis of molecule. F' with 8 MN (P 1)/3(2 P + I) nd & men molecul polisbility. h 3/(2 P + I) is f fcto which descibes cvity field. In se conditions, An/E is witten : 2 kb T E 9 (T Tf In pesence of n electicl field, behvio of ode pmete is govemed by whee v is locl fiction coefficient. Eqution (10) is obtined ssuming tht e is no flow, I-eno coupling to gdients of velocity field. This eqution enbles tnsient biefingence ssocited with switch-on nd cut-off An (t ) Ano e / ( l16) VIA is ode pmete elxtion time nd Ano sttiony biefingence, given by eqution (7).

5 STATIC INVESTIGATIONS. We shll begin by pesenting sttiony electicllyinduced 4,I. biefingence dt tken fom MPHOB, which will be necessy in ode to intepet esults obtined fo polyme. Figue 2 shows tht biefingence is negtive thoughout whole of tempetue-nge studied, nd chnges sign t tempetue vitully biefingence cn be witten ccoding to eqution (9) s : ewitten : (T Tl) 2 k T (13) Tf) (T T E i MPHOB u -100 w g -150 O 10/T ( K) Fig. 2. Vition of (An/E)(T Tf) tio s function of I/T fo MPHOB whee Tf is vitul N 2 KERR EFFECT IN THE ISOTROPIC PHASE OF Po Results nd discussion. of ode of 80 C. Such behvio hs been encounteed in o compounds [5], nd To existence of competition between electicl moment induced by field nd eflects pemnent moment pope to molecules. It should, indeed, be emembeed tht 2 F'v2(3 cos p 1) (12) ( whee F' v(3 cos p 1)/2 k T nd Au e contibutions of pemnent dipoles nd dipoles induced by field espectively fl is given by 8 hf ' eo( An ), MN fl If To is clled tempetue t which biefingence is cncelled out, eqution (12) cn be fl Au (14),T"7g.56 c fl T( second ode tnsition tempetue nd An biefingence induced by n electicl field E. The esults show tht An chnges sign t tempetue To. The solid line epesents fit with eqution (14) (see text).

6 whee tempetue To is given by : F'(3 cos p 1) The fct tht To is positive implies ei tht F'(3 cos p -1) < / (15) ; F'(3 cos p I) must efoe be negtive. [5] expeimentl points wee nlysed with eqution (14) which indictes tht vition of The (An/E)(T Tf ) s function of I IT must be line, nd esults in figue 2 show tht this is indeed cse. The pmetes coesponding to this nlysis e : Tf To (2 758 ± Ii x 10 m V K. epesents clculted cuve, nd coesponds to following pmetes : q 140 I g 80 Tf To /T ( K) Fig. 3. Sme s fo figue 2, but fo P(o. The dt show tht biefingence is positive. The solid line 214 JOURNAL DE PHYSIQUE II N 2 2 k Au 0 nd Au 0, o tht F'(3 cost p -1) < 0 nd Au 0. Fo elongted nemtic molecules, Au is lwys positive ± 0.01 C ± 0.02 C fl Au between dipol moments induced by electicl field nd Competition moments of mesogenic molecules must lso exist in cse of polyme. pemnent We hve efoe nlyzed esults obtined fo P(o, using eqution (14). Figue 3 shows tht expeimentl esults obtined e well ccounted fo by this eqution. The solid line ± 0.04 C ± 0.3 C flu (5 744 ± 196 x 10 m V K 160 p6 c 120 m loo T( best fit with eqution (14). The tempetue To t which biefingence chnges sign is epesents nge of occuence of isotopic phse. outside

7 intensity mesuements. The esults obtined e given in figue 4. They wee nlyzed light following lw : using following pmetes : lo T* Io + esidues (fo exmple ctlyst). This fit shows tht intensity of light synsis by locl oienttionl ode diveges s (T- Tf), which gees with sctteed Q ' ' 80 N 2 KERR EFFECT IN THE ISOTROPIC PHASE OF P(o 215 It must be noted tht tempetue To of P(o is not identicl to tht of MPHOB. This lso pplies to slope of stight line epesenting vition of An/E(T Tf) with T. These diffeences e eflection of influence of polyme skeleton on tio of induced nd pemnent moments of mesogenic molecules. In ode to confim vlue of Tf in eltion to polyme, we hve lso tken sctteed- 1 (16) T-Tc nd fit to expeimentl plot, shown s solid line in this sme figue, coesponds to ± (. u. ) M 10 (. u. ) (5.30 ± 0.63) x ± 0.13 C Constnt lo ccounts fo tempetue-independent psitic effects which could be due to pedictions. Note tht, to within expeimentl eo, vlue of Tf is sme s oeticl deduced fom nlysis of An/E-cuve. tht z.5 d z-o l T( c) Fig DYNAMIC INVESTIGATIONS. These mesuements only concem polyme, s chcteistic time ssocited with MPHOB is too shot to be detemined with set-up use. expeimentl in obtined fo ech tempetue wee nlysed using single-time exponen- ecodings The til, s suggested in equtions (ll) nd (llb). These nlyses show tht, fo ech of

8 216 JOURNAL DE PHYSIQUE II N 2 does indeed coespond to single-time exponentil (single-ode moment close to zeo, o Gennes model is witten L Alp, it is necessy to know vition of v with tempetue. fist of ll supposed ml vition of v to be henin in ntue, s in cse of We conventionl liquid cystls [6]. If this wee cse, would be : w/k T wfi T (1.04 ± 0.63) x llj SK exp f I(18) v v (T ) + 2 T. With this ml vition of v, chcteistic time would be C, lj (Tf pevious cse. fmewok of de Gennes model, we hve ssumed tht vies ccoding to powe consideed, chcteistic time ssocited with switch-on of field is tempetues to tht ssocited with cut-off. Anlysis of se sme ecodings, using Gussin simil distibution of exponentils, o stetched exponentil, confims tht tnsient egime coefficient of ode of one). The vlues of shown below coespond to those stetching when field is cut off. detemined In ode to detemine citicl behvio of, which ccoding to Lndu-de (17) b T- Tc. 5 shows tht it is, indeed, possible to nlyze expeimentl esults using this Figue The fit is obtined with following pmetes eqution. b ± 223 K ± 0.02 C It should, howeve, be pointed out tht vlue of Tf is incomptible with tht detemined fom sttic dt (induced biefingence o sctteed-light intensity). It is efoe necessy to pply to fit vlue of Tf obtined fom sttic mesuements, but when this is done, it is no longe possible to obtin good fit, s cn be seen fom figue 6. (17) is not efoe stisfctoy desciption, of divegence of. Eqution possibility consists in using Willims-Lndel-Fey fee-volume oy Ano [7] which pedicts tht viscosity will vy s function of tempetue, ccoding to (W.L.F.) lw : whee Ci nd C e constnts, T glss tnsition tempetue nd v viscosity t C Ci(T-T) exp (19) T Tc C2 + (T T) The nlyses cied out with this eqution, in which vlues of Tf nd Tg e imposed 3 C), show tht it does not ccount fo citicl behvio of, s in Since none of conventionl behvios of v gives stisfctoy ccount of ou dt within lw. In this eventulity, epesenting s function of T Tf in logithmic coodintes should stight line, nd esults in figue 7 show tht this is, indeed, cse. The give of is well ccounted fo by lw : divegence (20) (T Tf )

9 p6 40 p6 40. * «N 2 KERR EFFECT IN THE ISOTROPIC PHASE OF P(o m 30 'o o zo lo lo e ig. 5. ig. 6.

10 218 JOURNAL DE PHYSIQUE II N 2 Tf p (57.50 ± 15.8) x fo PA60CB, nd would thus ppe to be intinsic to side-chin liquid-cystl peviously polymes. sttic behvio of liquid-cystl polymes is identicl to tht of low molecul-weight liquid but tht i dynmic behvio is completely diffeent, indicting tht clssicl cystls, See, fo exmple, Poceedings of Intemtionl Confeence on Liquid-Cystl Polymes, Mol. [Ii Liq. Cyst. (1987) 153 nd 155. Cyst. REYS V., DORMOY Y., GALLANT J. L. nd MARTINOTY P., Phys., Rev. Lett. 61 (1988) [2] DE GENNES P. G., Mol. Cyst. Liq. Cyst. 12 (1971) 193. [3] with 1.49 ± 0.15 C 10 S K ± 0.18 C The tnsition tempetue Tf is identicl to tht detemined by sttic dt, nd this mkes nlysis cedible. The vlue of exponent p(1.5) confims vlue found 5. Conclusions. In this ticle, we hve demonstted tht nemtic-isotopic tnsition of P(o is chcteised by conventionl vlue of sttic exponent (I), nd n bnoml vlue of exponent (1.5). These esults confim those obtined peviously on no sidechin dynmic polyme, PA60CB, with diffeent physico-chemicl chcteistics. They suggest tht desciption of low molecul-weight liquid cystls does not pply to m. We hve dynmic shown existence of competition between dipol moment induced by electicl lso field nd pemnent moments of molecules. This competition does not exist fo PA60CB. Refeences MATER W. nd METER G., Z. Nttlfiosch. 16 (1961) 262. [4] BISCHOmERGER T., Yu R. nd SHEN Y. R., Mot Cyst. Liq. Cyst. 43 (1977) 287. [5] STINSON T. W. nd LITSTER J. D., Phys. Rev. Lett. 25 (1970) 503. [6] See fo exmple BERRY G. C. nd FOX T. G., Advnces in Polyme Science (Spinge-Velg N-Y- [7] ) p. 261; FERRY J. D., Viscoelstic Popeties of Polymes (Wiley, N-Y-, 1980).