Combined Tilt and Thickness Measurements on Nematic Liquid Crystal Samples

Transcription

1 This artile was downloaded by: [Mihigan State University] On: 10 February 2015, At: 11:16 Publisher: Taylor & Franis Infora Ltd Registered in England and Wales Registered Nuber: Registered offie: Mortier House, Mortier Street, London W1T 3JH, UK Moleular Crystals and Liquid Crystals Publiation details, inluding instrutions for authors and subsription inforation: Cobined Tilt and Thikness Measureents on Neati Liquid Crystal Saples H. A. Van Sprang a a Philips Researh Laboratories, P.O. Box 80, , JA Eindhoven, The Netherlands Published online: 24 Sep To ite this artile: H. A. Van Sprang (1991) Cobined Tilt and Thikness Measureents on Neati Liquid Crystal Saples, Moleular Crystals and Liquid Crystals, 199:1, 19-26, DOI: / To link to this artile: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Franis akes every effort to ensure the auray of all the inforation (the Content ) ontained in the publiations on our platfor. However, Taylor & Franis, our agents, and our liensors ake no representations or warranties whatsoever as to the auray, opleteness, or suitability for any purpose of the Content. Any opinions and views expressed in this publiation are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Franis. The auray of the Content should not be relied upon and should be independently verified with priary soures of inforation. Taylor and Franis shall not be liable for any losses, ations, lais, proeedings, deands, osts, expenses, daages, and other liabilities whatsoever or howsoever aused arising diretly or indiretly in onnetion with, in relation to or arising out of the use of the Content. This artile ay be used for researh, teahing, and private study purposes. Any substantial or systeati reprodution, redistribution, reselling, loan, sub-liensing, systeati supply, or distribution in any for to anyone is expressly forbidden. Ters & Conditions of aess and use an be found at ters-and-onditions

2 Mol. Cryst. Liq. Cryst., 1991, Vol. 199, pp Reprints available diretly fro the publisher Photoopying peritted by liense only Gordon and Breah Siene Publishers S.A. Printed in the United States of Aeria Cobined Tilt and Thikness Measureents on Neati Liquid Crystal Saples H. A. van SPRANG Philips Researh Laboratories, P.O. Box JA Eindhoven, The Netherlands (Reeived July 25, 1990) A new tehnique is presented whih enables siultaneous easureent of saple thikness and diretor tilt of non-twisted neati liquid rystal ells up to about 20 p thik. It is shown that only n,, and n,, the ordinary and extra ordinary refrative indies of the liquid rystal, are required with no ore than three digit auray. Keywords: Neati liquid rystals, birefringene It is oon knowledge that on any surfaes non-zero diretor tilt angles an be obtained for the diretor of a neati liquid rystal. In the ourse of tie a nuber of experiental tehniques has been developed whih enable easureent of this tilt angle. Unfortunately, no suh tehnique an be generally applied to arbitrary saples, as all of the have their own restritions. A suary of those ethods appliable to noral, flat substrate overed, test ells is presented in Table I. The only ethod appliable over the whole range of tilt angles is the agneti null ethod. For use with lassial (non superonduting) agnets of about 2 T one requires saples of ore than 10 p thikness. For studying the tilt in saples of thikness below 10 p we are left with either a apaitive1 or an interferoetri In both ethods a strong dependeny is observed of the tilt angle obtained on the saple thikness. We wanted to find a ethod whih allows for aurate deterination of tilt angles without a need to easure (in a preparatory easureent) ell thikness or apaitane of an epty ell beause the saple thikness ight easily hange during introdution of liquid rystal. The ethod we propose is based on the rystal rotation ethod4p5 but it is ore powerful due to the fat that we easure the optial phase shift instead of the transission as a funtion of the rotation angle. In Figure 1 a blok diagra is shown of the experiental set up. The liquid rystal saple is anufatured in suh a way that no twist, splay or bend are present. It an be rotated around an axis parallel to the substrates. The diretor is in a plane perpendiular to the rotation axis of the saple. The inident linear polarized light is in general elliptially polarized upon exit [497]/19

3 20/[498] H. A. VAN SPRANG TABLE I Coparison of ethods to easure tilt angles Aessible Required Range Auray Method 0 (7 8 (") Quantities d (k) Referenes Rearks Magneto opti null 0-90 ethod Capaitive 0-90 Interferoetry Crystal rotation Conosopy >10 1 Only for non-twisted saples 0.1 o, Ell, EL - 1 Requires C,, eas. on epty ell; suited for twisted saples 0.5 d, n,, rqi - 2, 3 Requires d to be onstant before and after filling 0.2 n,, 4 1 >10 4, S 8 < 9" in twisted strutures 0.2 n,,n,, >20 6 Coputer d He - Ne Phase eter FIGURE 1 Blok diagra of the experiental set-up. He-Ne indiates a He-Ne laser, B a Bea expander, P a fixed polarizer, Q a quarter waveplate, RA a rotating analyser and PD a photodetetor. The rotation of the saple (Motor Drive M.D.) and the applied voltage V are ontrolled by a Miro oputer. fro the saple. The quarter wave plate transfors it into linear polarized light with a rotation of the plane of polarization equal to 6. This value is then easured using a rotating analyser as desribed before in Referene 7. The expression for the phase differene in ters of the angle of inidene 4 with the substrate noral and the diretor tilt 0 with respet to the substrate is.' \ PD where n2 = nzos% + nssin20

4 TILT AND THICKNESS MEASUREMENTS [4991/21 It is this equation whih is used diretly in our proedure. First, the phase differene 6 is easured for a san of fro -30" to 30". The seond step is a fit of these data to the above equation using d and 8 as unknown variables. This leads to an alost independent deterination of d and 8 due to the fat that both variables our in a different way in the expression for 6. Obviously d is diretly proportional to 6 and deterines the position of the 6-+ urve on an absolute sale while 0 deterines the shape of the urve. As an be learnt fro the expression for 6 only n, and no are left as "known" paraeters. We easured the relevant indies in a slightly odified Pulfrih Refratoeter whih has an auray of better than 1. In Table I1 we present the refrative indies for ROTN 3010 around roo teperature. This liquid rystal has been used in all saples presented here. The fit of the experiental data to the theoretial forula is perfored on an IBM ainfrae oputer using standard IMSL Fortran software. A typial exaple of the results is shown in Figure 2 for a 1.91 p thik ell with a Polyiid orienting layer. Obviously there is a sattering of the experiental data around the fitted results, expressed as a standard deviation of In Figure 3 we show the results for an o TABLE I1 Refrative indies for ROTN 3010 at A = 632 n Y.- 0 I? 0) Angle of inidene (") - FIGURE 2 Phase Retardation versus rotation angle for a 1.91 p thik PI ell with 8 = 0.27". Measured at 22.2"C.

5 221[500] H. A. VAN SPRANG Angle of inidene (")- FIGURE 3 Phase Retardation V.S. rotation angle for a 2.16 prn thik SiO, saple with R = 25.13". Masured at 25.3"C. - 4 t 2 e 0 a,," tij Angle of inidene (")- t L e L w Angle of inidene (") - FIGURE 4 Coparison of the deviation of the fitted data fro the experiental data as a funtion of th rotation angle: a) data for ell in Figure 2, b) data for ell in Figure 3. evaporated SiOz layer whih had been rubbed subsequently. As an be seen the shape of the urve is different as is the observed deviation of the fit fro the experiental data whih aounts to a standard deviation of 0.54" only in Figure 3. In Figure 4 we opare the SiOz and PI ell. Apparently in the PI ell the deviation onsists of abrupt hups as a funtion of + while a gradual hange is observed in Figure 4b for the SiO, ell. To understand this differene the experiental tehnique ust be onsidered in ore detail. During the experient the saple rotates over 60" and the laser bea (diaeter L- 1 ) passes through

6 TILT AND THICKNESS MEASUREMENTS [501]/23 slightly different positions at the liquid rystal-orienting layer interfae. Fro the photographs in Figure 5 it is iediately lear that PI is uh less hoogeneous at a irosopi sale than is SO,. Thus inhoogeneity is supposed to be the reason for the substantial noise in PI saples. Although individual differenes our, it is generally true that SO, ells exhibit a ore gradually hanging noise FIGURE 5 Miro photographs showing the strutural differene between: a) PI oriented and b) rubbed SiO, oriented saples. The photographs were taken under dark-field illuination and using rossed polarizers. (Magnifiation 100 x). See Color Plate I.

7 24/[502) H. A. VAN SPRANG as a funtion of d, than PI saples. Figures 6-8 ontain further illustrations of the ethod. Although the ethod is powerful, it also has its liitations. We an suarize the as follows: 1. For ells with 6 (632 n) > 360", or equivalently d8n > 1.58 p, it is neessary to know the absolute value of 6 and not the value odulo (360") as deterined in the setup of Figure 1. For this reason we use saples supplied with IT0 eletrodes to whih an inreasing voltage up to 1OV is applied. The nuber of ties a 360" phase jup is enountered is registered by the oputer and used to deterine 6 at + = 0. For saples uh thiker than 20 p, the phase jups ight our within a too sall voltage range and hene the 6 value ould be wrong by 360" or ore. 2. As disussed before a ertain inhoogeneity ight lead to a higher noise level. This does not see to greatly influene the auray of the fitted results. 3. The auray of the refrative index data is very iportant to obtain aurate _ % 450 P M - -?? ul w 430 v C.- I 0 R1 % 0 L I I I I I I I I I I I 250 I I I I Angle of inidene (")- FIGURE 7 Phase retardation vs rotation angle for a 61.8 p SiOz ell with 8 = 22.85". Measured at 25.0"C.

8 TILT AND THICKNESS MEASUREMENTS [503]/ C.- 0 E a s? %!. a I I I I I I I I Angle of inidene ( ) - FIGURE 8 Phase Retardation vs rotation angle for a p SiOz ell with 0 = Measured at 2 I.4 C. TABLE 111 Influene of the variation of n, and n,, on the obtained 0 and d values n, ( 1 d (l TABLE IV Variation of n, and no for a thin saple n, n0 f3 ( 1 d (w) and d values fro the fit. In Table I11 we show how n, and no influene the results for the data of Figure 7. In general this allows for the onlusion that for values of n, and no within 1 fro their exat value an auray in e is still obtained of better than 0.1 deg while the thikness is ore aurate than 0.1 p. Fro Tables IV and V siilar results an be extrated for the data displayed previously in Figures 4 and 6 respetively. Thus in general the sae onlusions hold independent of tilt or thikness. Conluding we an say that the ethod is apparently aurate enough for appli-

9 26/[ 5041 H. A. VAN SPRANG TABLE V Variation of 0 and d with n, and n,, ation to experiental saples without twist having a tilt between 0-90" degrees and a thikness up to about 20 p. Inhoogeneity of the orienting layer leads to noise in the experiental data whih does not signifiantly influene the results of the fit. The ethod desribed above yields a reliable way to deterine both tilt angle and thikness in ells whih are ade under noral TN proessing onditions but without a twisted diretor pattern. Referenes 1. T. J. Sheffer and J. Nehring, J. Appl. Phys., 48, 5 (1977) and referenes therein. 2. R. Sion and D. M. Niholas, J. Phys. D., 18, 1423 (1985). 3. T. Opara, J. W. Baran and J. Zija, Crysr. Res. Tehn., 23, 1073 (1988). 4. B. B. Kosowski, M. E. Beker and D. A. Mlynski. Displays April 1984, A. Koitow, G. Hawk and H. D. Koswig, Cryst. Res. Tehn., 19, 253 (1984). 6. W. A. Crossland, J. H. Morrissy and B. Needha, J. Phys. D., 9, 2001 (1976). 7. H. A. van Sprang, J. Physique, (1983).