Langmuir 1994,10, 3201-3206
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Anchoring Phase of Liquid Crystal Mixtures Studied by Scanning Tunneling Microscopy Yasushi Iwakabe,* Katsumi Kondo, Syuichi Oh-hara, and Akio Mukoh Hitachi Research Laboratory, Hitachi Ltd., Hitachi, Ibaraki 319-12, Japan
Masa-hiko Hara and Hiroyuki Sasabe Frontier Research Program, The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-01, Japan Received December 15, 1993. I n Final Form: May 16, 199@ The anchoring structures of binary mixtures of 4'-n-octyl-4-cyanobiphenyl(8CB) and 4'-n-dodecyl-4cyanobiphenyl (12CB) on molybdenum disulfide (MoSz) are directly observed by scanning tunneling microscopy (STM)in order to investigate the boundary condition ofliquid crystal mixtures at the moleculesubstrate interface. On the basis of the highly reproducible STM images, the anchoring structures of binary mixtures are clearly divided into three categories. a homogeneous single-row type consisting of only 8CB (in the case of 8CB:12CB = 90:10,80:20, and 70:30 (mol %I), an inhomogeneous (mixed) doublerow type consisting of 8CB and 12CB (60:40,50:50,40:60,and 30:70),and a homogeneous double-row type consisting of only 12CB (20230 and 10:90). The ratio of 8CB and 12CB adsorbed on MoS2 substrate in all mixtures is different from that in the bulk. Furthermore, a new phase transition only available at the boundary is confirmed for the first time. The correlation between those anchoring structures of liquid crystal mixtures and the bulk phase diagram is discussed from the viewpoint of anchoring phase formation and selective adsorption of mixtures at a molecular level.
Introduction The substrate alignment of liquid crystal molecules is a widely-used technique to produce director configurations in liquid crystal monodomain cells, such as flat-panel displays, optical shutters, and related optoelectronic devices. It has been well known that the orderings of adsorbed molecules in the anchoring region near the substrate, which we call here "anchoring phases", are strongly affected by the substrate surface structure and the balance ofmolecule-molecule and molecule-substrate interactions. However, the actual mechanism of their orientation at the interface is still unclear because there have been technical difficulties in the structural analysis of the anchoring phases at a molecular level. Recently, scanning tunneling microscopy (STM) has been successfully applied to direct observations of organic monolayers on solid substrates, especially liquid crystal mono1ayers.l The STM images of such monolayers have been reported for s m e c t i ~ , ~ n -e ~m a t i ~ ,and ~ , ~antiferroelectic liquid c r y s t a h 8 Actually, high-resolution STM images now allow the real-space analysis ofthe molecular alignment a t the interface on the individual molecular scale. However, those observations have so far been carried out only with pure liquid crystal systems, since with a mixture of liquid crystals, it has been difficult to distinguish clearly between the different molecules, mainly due to inhomogeneous sample formation on solid substrates. Abstract published in Advance A C S Abstracts, June 15, 1994. (1) Frommer, J. E. Angew. Chem., Int. Ed. Engl. 1992, 31, 1265. (2) Foster, J. S.; Frommer, J. E. Nature 1988, 333, 542. (3) Smith,D. P. E.; Horber, H.; Gerber, Ch.; Binnig, G. Science 1989, 245, 43. (4) Hara, M.; Iwakabe, Y.; Tochigi, K.; Sasabe, H.; Garito, A. F.; Yamada, A. Nature 1990, 344, 228. ( 5 ) Smith, D. P. E.; Horber, J. K. H.; Binnie, G.; Neioh, H. Nature 1990, 344, 641. (6)Iwakabe, Y.; Hara, M.; Kondo, K.; Tochigi, K.; Mukoh, A,; Garito, A. F.: Sasabe, H.: Yamada. A. JDn. J . ADDZPhvs. 1990.29. L2243. (7) Iwakabe, Y.'; Hara, M.'; Konho, K.; Tobigi, K.;Mukoh, A:;Yamada, A.; Garito, A. F.; Sasabe, H. Jpn. J . Appl. Phys. 1991, 30, 2542. ( 8 ) Hara, M.; Umemoto, T.; Takezoe, H.; Garito, A. F.; Sasabe, H. Jpn. J . Appl. Phys. 1991, 30, L2052. @
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As in practice mixed liquid crystals have been widely but empirically used for flat-panel displays without precise information on the substrate alignment, it is very important to investigate the anchoring phases of mixed systems in order to reveal the actual alignment mechanism. It is also of interest to compare the ratio of mixed molecules a t the interface with that in the bulk, since such STM images can provide real features of the miscibility in the anchoring region at a molecular level. Previously, we reported the anchoring structure of the 60:40 (mol %) binary mixture of 4'-n-octyl-4-cyanobiphenyl (8CB) and 4'-n-dodecyl-4-cyanobiphenyl(12CB) on MoSz by STM.9 The STM images indicated that the technique was not only resolving the individual molecules, but it was also making a clear distinction between the 8CB and 12CB molecules by their different alkyl chain lengths. Furthermore, we also proposed that MoSz is a more suitable substrate than graphite to observe the intrinsic anchoring structures, because of the higher degree of freedom allowed for the alignment of rodlike molecules on M o S ~ . ~ In this paper, we present STM images of various bulk compositions of 8CB-12CB mixtures on MoS2. We then consider the selective adsorption of liquid crystal mixtures and discuss the anchoring mechanism at the interface from the viewpoint of anchoring phase formation.
Experimental Section The liquid crystals 8CB and 12CB, shown in Figure 1,were obtained from BDH Ltd. (Poole, U.K.) and were used directly from their sealed containers. Each mixture was prepared by mixing 8CB and 12CB into a sample tube, heating until the mixture was completelyisotropic,maintaining the isotropicphase until complete mixingwas assured,and then coolingthe mixture to room temperature. Mixtures thus obtained have not shown a significant phase separationin optical microscopeinvestigation. The sample for STM imaging was prepared by placing a drop of the mixture on the surface of a freshly cleaved MoSz substrate which had been heated to 100 "C. After slowing cooling the (9) Iwakabe,Y.;Hara, M.; Kondo, K.; Oh-hara, S.;Mukoh, A,; Sasabe, H. Jpn. J . Appl. Phys. 1992,31, L1771.
0 1994 American Chemical Society
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Figure 1. Molecular structures of the liquid crystals: (a) 4‘n-octyl-4cyanobiphenyl(8CB),(b)4’-n-dodecyl-4-cyanobiphenyl
(12CB). sample to room temperature, a sharp platinudiridium tip was positionedat the liquid crystal-MoSe interfaceand scannedover it. All images were obtained in air and in the constant-current mode. Typical operating conditions were 0.2-0.3 IA and 1.02.0 V (tip negative). The STM system used in this study was a commericallyavailableNanoScope I1 (DigitalInstruments, Inc., Santa Barbara, CA). The STM images were digitally filtered to remove only high-frequency noise.
Results and Discussion Homogeneous Single-Row Phase. STM images of the 90:10, 80:20, and 70:30 (mol %) binary mixtures of 8CB and 12CB on MoSz exhibit the same structure as a homogeneous single-rowtype consisting of only 8CB, Parts a and b of Figure 2 show the typical STM images of the homogeneous single-row structure of the 80:20 and 70:30 (mol %) binary mixtures. Individually distinguishable rodlike patterns and regular alignment are observed. As we have claimed previously,6each rodlike pattern shows the individual liquid crystal molecules. The bright oval areas represent the aromatic cyanobiphenyl groups, and the less bright rodlike areas represent the aliphatic alkyl chains. The length of all the less bright rodlike areas is almost the same as that of the bright oval areas. As both the alkyl chain and cyanobiphenyl in 8CB are about 11 A long, those liquid crystals can be recognized as 8CB molecules, following the same manner as we discussed in our previous paper.6 The STM images of pure 8CB samples, on the other hand, exhibited a homogeneous single-row structure in which cyanobiphenyl head groups and long alkyl tails alternate in each row.* Figure 3a shows a model of the anchoring struct
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Figure 2. STM images of the mixtures of 8CB and 12CB, from (a) 8CB:12CB = 80:20 (mol %) t o (f) 10:90(mol %) on MoS2. A higher-magnificationSTM image of the mixture (c)60:40(mol%) showingclear mixed double-rowrepeating units has been reported in our previouspaper.g The numbers in parentheses are the tunnel current,bias voltage (tipnegative), and image area. C-S-N-I and C-S-I are phase sequences in the bulk.
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Figure 3. Moclels showing the anchoring structures on the MoS2: (a, top) homogeneous 8CB single-row plhase, (b, middle) inhomogen !OUS (mixed) double-row phase, (c, bottom) homogeneous 12CB double-row phase.
3204 Langmuir, Vol. 10, No. 9, 1994 phase on MoSz. The STM images ofthe 90:10,80:20, and 70:30 (mol %) binary mixtures of 8CB and 12CB on MoSz exhibit the same homogeneous single-row structure as those of pure 8CB samples, consisting of only 8CB molecules. In spite of the presence of 12CB in the bulk, STM iamges revealed that only 8CB molecules exist on MoS2, forming the homogeneous 8CB single-row phase a t the boundary. Inhomogeneous (Mixed)Double-RowPhase. The STM images of the 60:40,50:50,40:60, and 30:70 (mol %) binary mixturs of 8CB and 12CBon MoSz exhibit the same structure as a n inhomogeneous (mixed) double-row type consisting of 8CB and 12CB. Parts c and d of Figure 2 show the typical STM images of the mixed double-row structure of the 60:40 and 30:70 (mol %)binarymixtures. Again, the bright oval areas represent the aromatic cyanobiphenyl groups and the less bright rodlike areas the aliphatic alkyl chains. In the rodlike areas, however, there are two kinds of patterns, differing in length.g The length of the shorter one is almost the same as that of the bright oval area. As the lengths of the alkyl chain and cyanobiphenyl in 8CB are the same, this shorter rod corresponds to the alkyl chain of 8CB. The longer one, on the other hand, is longer than the bright oval area, and it can be assigned to the alkyl moiety of 12CB, for which the alkyl chain is longer than the cyanobiphenyl moiety. Therefore, it is possible to distinguish clearly between 8CB and 12CB molecules by comparing the rodlike areas individually. Furthermore, the STM images revealed that both 8CB and 12CB are mixed on the MoSz a t the molecular level and arranged regularly, not randomly, forming double-row repeating units, as we pointed out with a higher-magnification STM image of the mixture in our previous paper.g Figure 3b shows a model of the lattice of the inhomogeneous (mixed)double-rowphase deduced from the STM images. Both 8CB and 12CB exhibit the double-row structure in which cyano groups are facing one another. The repeating unit along the molecular row is an 8CB12CB unit cell composed of a n 8CB subunit and a 12CB subunit. Each subunit alternates in the row, and the end of the 8CB subunit aligns with that of the 12CB subunit along the direction of the alkyl chains. In the 8CB-12CB unit cell, the 8CB subunit usually consists of three pairs of 8CB molecules and, occasionally, of two or four parts. In contrast, the 12CBsubuint usually consists of five pairs of 12CB molecules but sometimes of four or six pairs. The average number of 8CB and 12CB molecules in their own subunits is about 6 and 10,respectively. The STM images of the 5050 and 40:60 (mol %) binary mixtures of 8CB and 12CB have also been obtained in the same manner as those of 60:40 and 30:70 (mol %). That is, the ratio of 8CB and 12CB on MoSz is about 35, while that in the bulk is in the range from 60:40 = 3:2 to 30:70 = 3:7. Therefore, the ratio of 8CB and 12CB a t the boundary is independently determined from that in the bulk. Homogeneous Double-Row Phase. The STM images of the 20230 and 10:90 (mol %) binary mixtures of 8CB and 12CB on MoSz exhibit the same structure as a homogeneous double-row type consisting of only 12CB. Parts e and f of Figure 2 show the typical STM images of the homogenous double-row structure of the 20:80 and 10:90 (mol %) binary mixtures. Since all of the lengths of the less bright rodlike areas are longer than the bright oval areas, the former can be assigned to the alkyl moiety of 12CB, as its alkyl chain is longer than the cyanobiphenyl moiety. Figure 3c shows a model of the homogeneous 12CB double-row phase of 8CB- 12CB mixtures on MoS2. In our previous paper,7 the STM images indicated that pure 12CB samples formed successive double-row units
Iwakabe et al. composed of 10 12CB molecules, or alternating doublerow units composed of 8 and 10 molecules in each row on MoS2. The STM images of the 20:80 and 10:90 (mol %) binary mixtures are the same as those of pure 12CB samples. Again, in spite of the presence of 8CB in the bulk, only 12CB molecules form the anchoring phase a t the boundary. Interpretation of Single-Row and Double-Row Structures. Previously, we reported the anchoring structures ofa homologous series ofpure mCBs ( m= 7-12, number of carbon atoms in the alkyl chains) on MoSz determined by STM in which the structures were clearly divided into two categories, a single-row (monolayer)type (7CB, 8CB, 9CB, and 11CB) and a double-row (bilayer) type (lOCB and 12CB)7. We then proposed the origin of the two types of anchoring structures from the veiwpont of their phase sequences in the bulk. Firstly, while lOCB and 12CB only have a smectic (S)liquid crystal phase between isotropic (I) and solid crystal (C) phases, STM images ofboth moleculeson MoS2 exhibit the same doublerow structure equivalent to the bulk smectic phase ordering. Then it is reasonable to assume that the doublerow structure on MoSz is formed at the interface when the phase transition takes place from the isotropic to the ordered smectic liquid crystal phase in the bulk. This double-row structure then can be attributed to the anchoring structure of the smectic phase. Secondly,while 7CB has only a nematic (N)liquid crystal phase, the STM image of 7CB on MoSz exhibits a single-row structure. Comparing the results for 7CB (phase sequence I-N-C) with those for 10CB and 12CB (I-S-C), the single-row structure can be attributed to the anchoring structure of the nematic phase. In the same manner, if the liquid cyrstals have a phase sequence of I-N-S-C, the molecules should be ordered on the surface of MoSz in the nematic phase which actually appears first when the temperature is decreased during the sample preparation. In fact, the STM images of pure 8CB samples, for example, which possess a nematic phase in a higher temperature region than a smectic phase in the bulk (I-N-S-C), exhibit a single-row structure on MoS2. From this point of view, we proposed that the single-row and double-row structures are attributed to the formation of the anchoring structures from the nematic and smectic phases, respectively. Following the report of our STM results of homologous mCBs on M O S ~on , ~the other hand, there arise some questions and counterexamples against our interpretation. The argument has two aspects for the main. One is an exception in l l C B being remeasured and revised as a smectic liquid crystal without a nematic phase, and another is counterexamples showing some different anchoring structures from homogeneous single-row or double-row types. In the former,'OJ1 it has turned out that the N-S transition on l l C B samples was caused by a n impurity of the material and the pure l l C B shows no nematic phase, resulting in the new phase sequence of I-S-C for the pure sample. If there is no nematic phase for l l C B , the origin of the single-row structure of l l C B cannot be explained by our proposal. While the l l C B sample measured formerly had shown the I-N-S-C phase sequence, the temperature region of the nematic phase was only 0.5 "C and N-S transition showed nearly the first-order phase transition similar to the I-S phase transition. In this sense, one should reconsider the anomalies of l l C B behavior among the mCBs which generally have the second-order N-S phase transition (10)Smith, D. P. E.; Shirota, K. Personal communication (11) Data Sheet distributed by BDH Ltd. (Poole, U.K.).
Anchoring Phase of Liquid Crystal Mixtures S : Smectic
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Figure 4. Phase diagram of the 8CB-12CB binary mixture in the bulk obtained by DSC analysis and optical microscope investigation. The dotted line indicates a series of new transition points showing a certain phase separation, while the phase type itself has not been identified yet. (a)-(fj correspond to the ratio of the mixtures which are imaged by STM shown in Figure 2.
and remeasure the induced phase transitions with impurities andlor a t a substrate boundary. In the case of the latter there are a small number of counterexamples which do not allow such a generalization for the anchoring mechanism. Actually, there has been reported a certain multiplicity of the packing structures observed by STM with some metastable states of liquid crystals, while reproducibility strongly depends on preparing homogeneous monodomain samples. Those exceptions imply that one should reconsider the substrate dependence of the anchoring structures again, for example, including a thermal history during the sample preparation. We also intend to further study the dependence of anchoring structures on the balance of molecule-molecule and molecule-substrate interactions by introducing other types of substrates than MoSz or graphite. While there might exist various possible models for the origin of the anchoring structures, the miscibility test using mixtures has long been accepted as one ofthe most useful and simple methods to study the aspects of phase sequences in the liquid crystal field. Actually in the case of mixtures, bulk phase sequences can be changed continuously in various compositions. Figure 4 shows a phase diagram of 8CB-12CB binary mixtures in the bulk obtaind by differential scanning calorimetry (DSC) analysis and optical microscope investigation. Below 40 mol % 12CB,there are nematic and smectic liquid crystal phases (I-N-S-C), but above it, there exists only a smectic phase between the isotropic and crystal phases (I-S-C). Simply but clearly, a complete set of STM images in various compodtions in numerous such studies revealed that the anchoring structures are drastically changed from the single-row type to the double-row type a t 40 mol % 12CB, while there are two types of double-row structures as shown in Figures 2 and 3. This fact strongly supports our interpretation for the origin ofthe anchoring structures based on the phase sequences in the bulk. Namely, the single-row and double-row structures are determined by the I-N and I-S phase transitions, respectively. While the compositions in all STM images are completely different from those in the bulk, one important finding is the fact that 8CB formed not a single-row but a doublerow ordering with 40-70 mol % 12CB. Again, this is (12) Foster, J. S.; Frommer, J. E.; Spong,J. K. Proc. SPIE, Liq. Cryst. Chem., Phys. Appl. 1989,1080, 200. (13)Heckl, W. M. Thin Solid Films 1992,210/211, 640.
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Figure 5. Summary of the anchoring structures with concentration of 12CB observed by STM on MoSz as a function of the mole percent 12CB in the bulk. Again, (a)-(fj correspond to the ratio ofthe mixtures shown in Figure 2. The ratio of 8CB and 12CB observed by STM in mixed double-row repeating units is kept constant at about 3:5 for the mixtures, 8CB:12CB = 60:40 = 3:2 (c), 5050 = 313, 40:60 = 3A.5, and 30:70 = 3:7 (d).
because there is no nematic phase above 40 mol % 12 CB, and this fact also supports our interpretation.
Correlation between the Bulk Phase Diagram and Anchoring Phase Formation of Mixtures. In Figure 5, we summarized the anchoring structures with the ratio of 8CB and 12CB observed by STM on MoS2 as a function of the mole percent 12CB in the bulk mixture. As noted above, it is evident that the anchoringphases ofthe binary mixtures of 8CB and 12CB on MoSz can be clearly divided into three categories. First, we will discuss the anchoring structures of the 90:10,80:20, and 70:30 (mol %)binarymixtures showing the homogeneous 8CB single-row phase. As below 40 mol % 12CB in the phase diagram binary mixtures of 8CB and 12CB have a nematic phase between the isotropic and smectic phases, the molecules should be ordered on the MoSz surface when the nematic phase appears from the isotropic phase. Actually, the phase transition from isotropic to nematic in these binary mixtures must be induced by 8CB, because there is no capability to form the nematic phase in 12CB. Following our interpretation, it is natural to predict that a single-row structure can be observedby STM, because the phase transition takes place from isotropic to nematic phases. Since these mixtures have shown a continuous miscibility without a significant phase separation, it has been considered that 12CB should be mixed with the 8CB nematic ordering. It is surprising, however, that 12CB molecules are absent on MoSz, in spite of the presence of 12CB in the bulk. We assume that this is because such a homogeneous single-row structure consisting of only 8CB is energetically favorable on MoSz substrate in this mole percent region showing the phase sequence of I-N-S-C. If 12CB molecules migrate into the 8CB single-row structure, the substrate area covered with the molecules would decrease and the structure would lead to energetically unfavorable vacancies. Therefore, only 8CB molecules have selectively adsorbed on MoS2 and formed the homogeneous 8CB single rows. In addition, such homogeneous single rows imply that 8CB must be dominant molecule when the I-N phase transiton takes place, a t least a t the boundary. On the other hand, the anchoring structures of binary mixtures above 40 mol % 12CB exhibit the double-row phase. As we mentioned above, the origin of the doublerow structure itself can be explained from the viewpoint
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3206 Langmuir, Vol. 10, No. 9,1994 of phase sequences without the nematic phase (I-S-C). In these 12CB-rich binary mixtures, however, there are two types of double-row structures, inhomogeneous (mixed) and homogeneous. It is surprising again that the ratio of 8CB and 12CB is kept constant a t about 3:5 in the case of the mixed double-row phase, and for the homogeneous double-row phase, there are no 8CB molecules adsorbed on MoS2, in spite of the presence of 8CB in the bulk. For the mixed double-row structure, we attribute this behavior to an anchoring structure consisting of one 8CB subunit (three pairs of 8CB molecules) and one 12CB subunit (five pairs of 12CB molecules) in the 8CB-12CB unit cell being energetically favorable a t the b ~ u n d a r y . ~ If 8CB subunits or 12CB subunits continue in each row, the substrate area covered with the molecules would decrease and the structure would lead to energetically unfavorable vacancies in the same manner we discussed for the homogeneous 8CB single rows. Although there might be other possible orderings in which 8CB and 12CB align randomly in a unit cell, such a structure would also lead to energetically unfavorable vacancies. Therefore, the energetically favorable mixed double-row repeating units shown in Figure 3b determine the ratio of 8CB and 12CB a t the boundary, resulting in the inconsistencywith that of 8CB and 12CB in the bulk. Anchoring Phase Transition at the Boundary. By increasing the mole percent 12CB, gradually the 12CB molecule becomes dominant for the I-S phase transition ,resulting in the homogeneous double-row structure consisting of only 12CB being energetically favorable a t the boundary. Namely, there exists additional phase transition a t the boundary from inhomogeneous to homogeneous double-row phases, while the bulk phase sequences remain the same. For this important finding, here we propose one ofthe possible interpretations briefly as follows. As we described above, the ratio of 8CB and 12CB in the inhomogeneous double-row phase is kept constant at about 3 5 , which is determined by the energetically favorable mixed double-row repeating units a t the boundary. While its average is 3 5 , there was observed by STM a certain possible fluctuation of the ratio, 8CB:12CB = 3 f 15 f 1. This ratio can be extended to the extreme range such as 4:4 < 8CB:12CB < 2:6, which is equivalent to the mole percent range from 50:50 to 257.5 8CB to 12CB. On the other hand, the anchoringphase transition at the boundary from inhomogeneous to homogeneous double-rowphases occurred between 30:70 and 20:80 (mol
%). Ifwe assume here 50:50 zz 2575 (mol %) 8CB to 12CB is the maximum tolerable range against keeping the mixed double-rowrepeating units, it can be interpreted that such repeating units are not allowed for the ratio of 20:80 (mol %), resulting in the anchoring phase transition to the homogeneous double-row structure consisting of only 12CB. In addition, a certain phase separation can be observed from 30:70 (mol %) in the bulk as shown in Figure 4. These new transition points (following a dotted line in Figure 4) suggest that there might be a critical ratio of the mixtures for the mixed liquid crystal ordering even in the bulk. Further measurements for the guest-host liquid crystal mixtures are in progress, and extended discussions of anchoring phase transitions will be reported separately.
Conclusions We now have a complete set of the anchoring structures for various compositions from 0 to 100 mol % 8CB-12CB binary mixtures. If we consider those anchoring structures from the viewpoint of anchoring phase transition, we can summarize the correlation between the bulk phase diagram and anchoring phase formation of mixtures as follows. Below 40 mol % 12 CB, the anchoring phase sequence is isotropic-“homogeneous 8CB single-row phase”, while the bulk phase sequence is I-N-S-C. From 40 to 70 mol %, the anchoring phase sequence is isotropic“inhomogeneous (mixed) double-row phase”, and above 80 mol %, it is isotropic-“homogeneous 12CB double-row phase”, while the bulk one is I-S-C. The important finding in this I-S-C region is the existence of the anchoring phase transition only available a t the boundary, which is confirmed for the first time. Although there is no necessity to have the anchoring phase transitions a t the same temperature where the bulk I-N or I-S phase transition occurs, it is evident that such anchoring phase transitions are dominantly induced by the I-N or I-S phase transition and there is a strong correlation between the anchoring phase formation and the bulk phase diagram. In addition, the energetically favorable repeating units a t the boundary and phase separations also play an important role in the anchoring phase formation ofliquid crystal mixtures. Finally, there arises another question on the distribution ofthe molecules which are excluded from the anchoring phases. We can assume, however, the anchoring region near the substrate surface has enough space to adjust the inconsistent ratio a t the boundary to the bulk one and to provide a transition area from the anchoring phase to the bulk ordering.
