12
Orientation of liquid crystal monolayers on polyimide alignment layers: A molecular dynamics simulation study N. F.A. van der Vegt Faculty of Chemical Technology, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands F. Mu ¨ ller-Plathe, A. Geleßus, and D. Johannsmann Max-Planck-Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany ~Received 5 July 2001; accepted 13 September 2001! Detailed atomistic molecular dynamics simulations were performed on monolayers of 48-n-octyl-4-cyanobiphenyl ~8CB! adsorbed onto a surface of poly-m-alkanpyromellitimide ~poly-m-APM!, where m is the number of CH 2 units between the imide moieties. Poly-3-APM and poly-4-APM surfaces served as model surfaces to investigate the influence of microscopic grooves, polar carbonyl groups exposed to the surface, and an anisotropic van der Waals interaction between the liquid crystal ~LC! molecules and the polymer chains. A Lennard-Jones fluid was chosen as the bulk phase in order to mimic the bulk LC phase. The fluid lubricates the motion of the LC molecules and increases the molecular tilt angle. While microgrooves dominate the alignment of isolated molecules, an anisotropic van der Waals interaction with the main chain is stronger in the case of entire monolayers. © 2001 American Institute of Physics. @DOI: 10.1063/1.1415498# I. INTRODUCTION The orientation of nematic liquid crystals ~LCs! close to solid surfaces is of high interest for both fundamental phys- ics and application in liquid crystal displays ~LCDs!. All LCDs contain polymeric alignment layers on their inside sur- faces inducing a well-defined ground state of the cell. 1 Switching is achieved by a competition between an electric field and the orientating action of the cell surface. The aniso- tropic surface–LC interaction by which the surface governs the orientation of the bulk is often termed ‘‘surface orienta- tional anchoring’’ or ‘‘surface anchoring,’’ for short. 2–4 Alignment layers are key components in LC displays. Pre- paring alignment layers capable of generating any kind of bulk orientation ~specified by device engineers! is a formi- dable challenge for molecular engineering. For practical rea- sons it is important that the induced orientation be tilted away from the surface by a ‘‘pretilt’’ angle between 2° and 15°. 5,6 The alignment layer must therefore not only provide an axis parallel to the surface but a direction away from the surface, as well. The current technology mostly relies on mechanical rubbing of polyimide surfaces, 7 where the rub- bing direction defines the in-plane anisotropy. Large efforts are also spent on establishing ‘‘optical buffing’’ 8 in the mar- ket place. Here, anisotropy is created with polarized UV light. At least as important as efficient tools for surface engi- neering is a profound knowledge of the surface–LC interac- tion itself. Despite the enormous practical relevance of sur- face anchoring, the underlying mechanisms are poorly understood. A variety of effects have been proposed which could potentially influence the surface anchoring mechanism. These include anisotropic LC orientational elasticity in con- nection with macroscopic grooves, 9 short-range interactions on the molecular scale, 10–13 surface electric fields, 14 a near- surface order parameter different from the bulk, 12,15 and a coupling of a bending of the nematic director to surface elec- tric fields ~flexoelectricity!. 16 The problem of LC alignment can be conceptually bro- ken up into three separate questions involving: ~a! determi- nation of the structure and the orientation in the polymer substrate, ~b! evaluation of the orientation of an LC mono- layer adsorbed onto a polymer surface, and ~c! determination of the orientation induced in a bulk LC in contact with this LC monolayer. The first problem can be experimentally ad- dressed with different techniques such as IR spectroscopy, 10,17 or near edge x-ray absorption fine structure ~NEXAFS! spectroscopy. 18–22 In these studies it was always found that rubbed polyimide films are molecularly ordered along the rubbing direction. Shear induced plastic flow and crystallization presumably play some role. The orientation in thin LC films can be investigated with similar techniques. Surface optical second harmonic generation ~SHG! has also been applied to thin LC films in a number of experiments. 23–26 In some cases, the same measurements have been subsequently performed on the polymer substrates and the LC films, providing correlations between the orien- tation in the substrate and the film. 27–30 The orientation of the bulk liquid crystal can be easily measured with the crys- tal rotation setup. 30 Underlying this hierarchical concept of LC alignment is the notion that the first few layers of liquid crystal adjacent to the cell wall play a special role. This assumption is, for instance, supported by the ‘‘surface-memory effect.’’ 31,32 If one heats a randomly aligned LC cell to above the nematic– isotropic transition temperature for some limited time and then cools back to the nematic state one finds the same do- main pattern as before the heat treatment. This is usually interpreted in terms of a rather immobile layer of LC mol- ecules close to the wall which retains its orientation even if the bulk is isotropic. When the bulk becomes nematic again, JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 21 1 DECEMBER 2001 9935 0021-9606/2001/115(21)/9935/12/$18.00 © 2001 American Institute of Physics

Orientation of liquid crystal monolayers on polyimide ......Orientation of liquid crystal monolayers on polyimide alignment layers: A molecular dynamics simulation study N. F. A. van

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Page 1: Orientation of liquid crystal monolayers on polyimide ......Orientation of liquid crystal monolayers on polyimide alignment layers: A molecular dynamics simulation study N. F. A. van

JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 21 1 DECEMBER 2001

Orientation of liquid crystal monolayers on polyimide alignment layers:A molecular dynamics simulation study

N. F. A. van der VegtFaculty of Chemical Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

F. Muller-Plathe, A. Geleßus, and D. JohannsmannMax-Planck-Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany

~Received 5 July 2001; accepted 13 September 2001!

Detailed atomistic molecular dynamics simulations were performed on monolayers of48-n-octyl-4-cyanobiphenyl ~8CB! adsorbed onto a surface of poly-m-alkanpyromellitimide~poly-m-APM!, wherem is the number of CH2 units between the imide moieties. Poly-3-APM andpoly-4-APM surfaces served as model surfaces to investigate the influence of microscopic grooves,polar carbonyl groups exposed to the surface, and an anisotropic van der Waals interaction betweenthe liquid crystal~LC! molecules and the polymer chains. A Lennard-Jones fluid was chosen as thebulk phase in order to mimic the bulk LC phase. The fluid lubricates the motion of the LC moleculesand increases the molecular tilt angle. While microgrooves dominate the alignment of isolatedmolecules, an anisotropic van der Waals interaction with the main chain is stronger in the case ofentire monolayers. ©2001 American Institute of Physics.@DOI: 10.1063/1.1415498#

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I. INTRODUCTION

The orientation of nematic liquid crystals~LCs! close tosolid surfaces is of high interest for both fundamental phics and application in liquid crystal displays~LCDs!. AllLCDs contain polymeric alignment layers on their inside sfaces inducing a well-defined ground state of the ce1

Switching is achieved by a competition between an elecfield and the orientating action of the cell surface. The anitropic surface–LC interaction by which the surface govethe orientation of the bulk is often termed ‘‘surface orienta-tional anchoring’’ or ‘‘ surface anchoring,’’ for short.2–4

Alignment layers are key components in LC displays. Pparing alignment layers capable of generating any kindbulk orientation~specified by device engineers! is a formi-dable challenge for molecular engineering. For practical rsons it is important that the induced orientation betiltedaway from the surface by a ‘‘pretilt’’ angle between 2° a15°.5,6 The alignment layer must therefore not only provian axis parallel to the surface but a direction away fromsurface, as well. The current technology mostly reliesmechanical rubbing of polyimide surfaces,7 where the rub-bing direction defines the in-plane anisotropy. Large effoare also spent on establishing ‘‘optical buffing’’8 in the mar-ket place. Here, anisotropy is created with polarized Ulight.

At least as important as efficient tools for surface enneering is a profound knowledge of the surface–LC intertion itself. Despite the enormous practical relevance of sface anchoring, the underlying mechanisms are poounderstood. A variety of effects have been proposed whcould potentially influence the surface anchoring mechaniThese include anisotropic LC orientational elasticity in conection with macroscopic grooves,9 short-range interactionon the molecular scale,10–13 surface electric fields,14 a near-surface order parameter different from the bulk,12,15 and a

9930021-9606/2001/115(21)/9935/12/$18.00

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coupling of a bending of the nematic director to surface eltric fields ~flexoelectricity!.16

The problem of LC alignment can be conceptually brken up into three separate questions involving:~a! determi-nation of the structure and the orientation in the polymsubstrate,~b! evaluation of the orientation of an LC monolayer adsorbed onto a polymer surface, and~c! determinationof the orientation induced in a bulk LC in contact with thLC monolayer. The first problem can be experimentally adressed with different techniques such asspectroscopy,10,17or near edge x-ray absorption fine structu~NEXAFS! spectroscopy.18–22 In these studies it was alwayfound that rubbed polyimide films are molecularly orderalong the rubbing direction. Shear induced plastic flow acrystallization presumably play some role. The orientationthin LC films can be investigated with similar techniqueSurface optical second harmonic generation~SHG! has alsobeen applied to thin LC films in a number oexperiments.23–26 In some cases, the same measuremehave been subsequently performed on the polymer substand the LC films, providing correlations between the orietation in the substrate and the film.27–30 The orientation ofthe bulk liquid crystal can be easily measured with the crtal rotation setup.30

Underlying this hierarchical concept of LC alignmentthe notion that the first few layers of liquid crystal adjaceto the cell wall play a special role. This assumption is,instance, supported by the ‘‘surface-memory effect.’’31,32 Ifone heats a randomly aligned LC cell to above the nemaisotropic transition temperature for some limited time athen cools back to the nematic state one finds the samemain pattern as before the heat treatment. This is usuinterpreted in terms of a rather immobile layer of LC moecules close to the wall which retains its orientation eventhe bulk is isotropic. When the bulk becomes nematic ag

5 © 2001 American Institute of Physics

Page 2: Orientation of liquid crystal monolayers on polyimide ......Orientation of liquid crystal monolayers on polyimide alignment layers: A molecular dynamics simulation study N. F. A. van

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9936 J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 van der Vegt et al.

this surface layer induces the same alignment pattern asfore.

It is also generally agreed that the alignment is inflenced by local interactions at the surface of the alignmlayer. Measuring the surface optical second harmonic gention ~SHG! from LC monolayers, Shen and co-workers haproven that molecular detail matters at least in some caThe anisotropy of the monolayers depended on the chemnature of the substrate and the rubbing conditions.10,12Long-range interactions, for instance based on macroscgrooves in conjunction with LC orientational elasticity9

would not be able to align an LC monolayer.Studies on the orientation of LC monolayers are m

useful under conditions of ‘‘strong anchoring,’’ that is, undconditions where the surface–LC interaction is stronger tthe interaction between the first LC layer and the LC buUnder conditions of strong anchoring an adsorbed LC molayer has an orientation similar to the first layer of molecuof a bulk LC medium. Experimental support for strong achoring was found for the cyanobiphenyl family on polsurfaces with surface optical second harmonic genera~SHG!.33 The fact that these samples generate an SHG siproves the existence of polar orientational order, whichnever observed in the bulk. Apparently, the surface is ablbreak up the quadrupole pairs usually formed by cyanophenyls, which points to a strong surface–LC interaction.the other hand, it should not naively be assumed that theLC films and the first LC layers in an LC cell are equivaleThe presence of the second interface,~LC–vacuum or LC–solvent interface! does affect the orientation.

On the theoretical side, the understanding of LC aligment is currently limited to rather qualitative argumenidentifying possible mechanisms and assessing their relastrengths.2,4 For practical purposes, quantitative predictiofor certain combinations of materials and processing pareters would be desirable. Given that chemical detail dmatter, modeling with continuum theories is problematic.these calculations the material properties have to entesome form of ‘‘effective parameters’’ and it is not clear hoto map the microscopic properties onto the continuum mels. Molecular detail can be accounted for in molecularnamics ~MD! calculations.34 However, the full problem ofsurface anchoring covering molecular details is beyondpower of the current computers. The simulation volumwould have to be of the size of at least the nematic coherelength, which is a few nanometers.35 Also, due to the collec-tive nature of the orientation fluctuations, the orientatiodynamics of liquid crystals is slow.

Importantly, LC films with a thickness in the monolayrange are amenable to molecular dynamics~MD!calculations.36–41 Chemical detail can be included if thsimulations are limited to LC thin films with a few tens omolecules and a relaxation time of less than a nanosecThese calculations can be mapped onto the experimeWhen interfacing the MD calculations with continuum theries covering the entire surface anchoring problem42–44—butnot molecular detail—the central variable will be the nemaorder parameter. Presumably, the near-surface tensor oparameter as determined with MD will enter as some kind

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boundary condition. Understanding the orientation in Lthin films therefore is an important intermediate step towathe full understanding of surface alignment. This problecan be rigorously approached with both experiment atheory.

Several computer simulation studies have been untaken to understand surface-induced LC alignmentsmooth crystalline substrates. Cleaveret al.36,37 and Yoneyaand Iwakabe38 investigated the unit-cell structure o48-n-octyl-4-cyanobiphenyl ~8CB! monolayers adsorbedonto graphite. Alignment of 8CB molecules by smooth poimide oligomer monolayers on graphite have been studiewell.39 Stable LC alignment was found along the polyimidchain direction with zero molecular tilt. Binger anHanna40,41studied the interaction of 5CB and 8CB with crytalline polyethylene, polyvinylalcohol, polypropylene anNylon 6 surfaces. All crystalline surfaces, except polypropene, were found to induce orientation parallel to the polymchain axis.

The purpose of the molecular simulation performedthis study was to obtain a microscopic picture of the monlayer arrangement above two crystalline polyimide surfacThe simulation can elucidate how the polarity of LC moecules, the chemical structure, and the morphology ofsurface can affect the alignment and the tilt of the monolayThe system chosen was a surface monolayer of 8CB osurface of poly-m-alkanpyromellitimide ~poly-m-APM!,where m is the number of CH2 units between the imidemoieties.45 The chemical structures are shown in Fig. 1. Inprevious SHG study a pronounced odd–even effect inalignment with respect to the odd or even number of C2

units was found.26 The odd–even effect was present in bothe LC monolayer orientation and the bulk LC alignmePresumably, the odd–even effect results from the differein packing behavior. We investigated the interaction ofmonolayer of 8CB molecules with surfaces modeling thoof two poly-m-alkanpyromellitimides~poly-m-APM! havingeither three or four methylene groups in the repeating u(m53 or 4!. The molecular structure suggests that the po

FIG. 1. Chemical structure of poly-m-alkane-pyromellitimide~poly-m-APM, m53,4! ~a! and the liquid crystal 8CB~b!.

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9937J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 Orientation of liquid crystal monolayers

3-APM surface is much more corrugated than the polyAPM surface. Also the poly-4-APM surface should displpolar asymmetry along both thex and they direction ~C1vsymmetry! whereas the poly-3-APM has a mirror plane pependicular to the chain direction~C2v symmetry!. These sur-faces can therefore serve as model systems to study thfluence of microscopic surface corrugation and surfsymmetry on the alignment behavior.

II. TECHNICAL DETAILS

A. Force field parameters for 8CB andalkanpyromellitimide

The 8CB model was taken from Cleaveret al.,36,37 whoused it to study 8CB on graphite. Here we summarizemain features. The 8CB model involves a total of 22 intaction sites. All hydrogen atoms in this model have becombined with their neighboring carbon atoms to give sinsite united atoms~CH, CH2, and CH3!. The intramolecularpotential is made up of Lennard-Jones with Coulombic intactions for atoms separated three bonds or more. The spartial charges gives a molecular dipole moment of 5.42bye, close to the experimental value of 5CB in benzene.bond lengths are constrained to their optimized values, whwere obtained usingab initio calculations~HF/6-31G!.46 Va-lence angles are modeled using a harmonic potential.tailed torsion potentials are used for the dihedral angNonbonded Lennard-Jones potentials describing interlecular interactions were taken from the GROMOS forfield47 and were identical to the treatment of 5CB by Picket al.48 Lorentz–Berthelot mixing rules are used to determunlike interactions.

The molecular geometry of the alkanpyromellitimidmonomer was optimized usingab initio calculations~B3LYP6-31G!.46 The equilibrium bond lengths and valence angare shown in Table I. To obtain a molecular model compible to that of the 8CB molecule, all hydrogen atoms wecombined with their neighboring carbon atoms. The foconstants for the valence angle potential were taken fromGROMOS force field.47 A barrier height of 18.4 kJ/mol wasadopted for rotation of the Cimide–N–CH2–CH2 dihedralangle followingab initio ~HF/6-311G** ! calculations on analkanpyromellitimide fragment~not shown!. The potentialenergy function for this dihedral angle has a twofold perioicity. The barrier height for alkyl chain rotations was otained from the Ryckaert and Bellemans parametrizationdescribed by Cleaveret al.36 Ab initio calculations~HF/6-31G! were performed on a pyromellitimide segment containg (CH2!3CH3 segments connected to both its nitrogens, apartial charges were determined by fitting atomic pocharges to the electrostatic potential on the molecular suraccording to the CHELP scheme.49 The charges on the hydrogen atoms were merged with those of their neighborcarbons. The nonbonded Lennard-Jones~united atom! pa-rameters were taken from the GROMOS force field. Paraeters for unlike interactions~polymer–polymer, polymer–8CB! were determined using Lorentz–Berthelot mixinrules. In Table I, all parameters and functional forms ofpotential energy functions used are shown.

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B. Construction and equilibration of polymer crystalsurfaces

In this work we study the molecular interactions betwe8CB andm53 andm54 poly-m-APM crystal surfaces. Theconstructed surfaces were large enough to~i! accommodate astatistically meaningful number of 8CB molecules inmonolayer~approximately 30–40 molecules! and ~ii ! avoidhead-to-tail interactions between periodic images ofsorbed mesogens. The polymer slab in our studies is a th

TABLE I. Potential energy function parameters for alkanpyromellitimidea

Nonbondedinteractionsb

V(r i j )54e@(s/r i j )122(s/r i j )

6#1qiqj /4pe0r i j

e/kJ mol21 s/nm q/e

Caro 0.406 0.3361 0CHaro 0.503 0.3741 0Cimide 0.406 0.3361 10.4O 1.725 0.2626 20.3N 0.877 0.2976 20.4CH2 ~connected to N! 0.586 0.3964 10.2CH2 0.586 0.3964 0

Bond Distance/nm

Caro–Caro 0.1407CHaro–Caro 0.1394Caro–Cimide 0.1493Cimide–N 0.1408Cimide–O 0.1238N–CH2 0.1466CH2–CH2 0.1539

Bond angles

V(f)5(kf/2)(f2f0)2

f0 /deg kf /kJ mol21 rad22

Caro–Caro–Caro 115.3 418.6CHaro–Caro–Caro 122.4 418.6Caro–Caro–Cimide 108.1 418.6Caro–Cimide–O 128.7 418.6Caro–Cimide–N 105.9 418.6Cimide–N–Cimide 112.0 418.6O–Caro–N 125.4 418.6Cimide–N–CH2 124.0 418.6N–CH2–CH2 112.9 460.0CH2–CH2–CH2 111.5 460.0

Dihedral angles

V(t)5(kt/2)@12cosn(t2t0)#, cis at 0°

t0 /deg n kt /kJ mol21

Cimide–N–CH2–CH2 90.0 2 18.40N–CH2–CH2–CH2 180.0 3 11.72CH2–CH2–CH2–CH2 180.0 3 11.72

Harmonic dihedralangles

V(d)5(kd/2)(d2d0)2, cis at 0°

d0 /deg kd /kJ mol21 rad22

CHaro–Caro–Caro–CHaro 0.0 170.0Caro–CHaro–Caro–Cimide 180.0 170.0CHaro–Caro–Caro–Cimide 180.0 170.0CHaro–Caro–Cimide–N 180.0 170.0Caro–Cimide–N–Cimide 0.0 170.0CHaro–Caro–Cimide–O 0.0 170.0O–Cimide–N–CH2 0.0 170.0Cimide–Caro–Caro–Cimide 0.0 170.0

aThe subscripts aro and imide denote aromatic atoms and atoms in the imoiety, respectively.

bNonbonded interactions are excluded between first and second neigh

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9938 J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 van der Vegt et al.

layered crystal, each layer containing 10 parallel alignhexamers. The alkyl chain parts are in the all-trans, fullyextended conformation, yielding a ‘‘planar zig–zag’’ confomation form53 and a ‘‘planar extended’’ conformation fom54. In this arrangement the unit cell is orthorhombic. Tinterchain spacing within each layer was taken from x-crystal data reported by Kazaryanet al.,50 and equals 4.7 Å.The surfacexy dimensions are 64.2346.9 Å2 (m53) and75.9347.5 Å2 (m54). The distance between the layers wchosen 5 Å to obtain the appropriate crystal density of 1g/cm3. The slab thickness of three layers was chosen tosure that an adsorbed mesogen sees a bulk crystal withinteraction cutoff~see below!. In this initial arrangement ofcrystal atoms, the surface normal coincides with the norof the pyromellitimide ring.

To equilibrate the crystal it was necessary to apply potion restraints. We decided to restrain the nitrogen atomthe imide moieties of the chains~a harmonic restraining potential with a force constantk5104 kJ mol21 nm22 wasused!. When restraining the nitrogen positions, the interchspacing~4.7 Å! and the crystal density is preserved, but tchains are still free to relieve unfavorable contacts by roing their planar pyromellitimide parts. Connecting the heand tail parts of the hexamer, i.e., the aliphatic methyleand the imide nitrogen, eliminated undesired effects induby chain ends. By imposing periodic boundary conditionsthe x andy directions, we thus model an infinitely extendesurface layer. The first equilibration runs of approximate10 ps were performed with soft-core interaction potentialsall atoms.51 Small integration time steps~0.01–0.1 fs! wereused together with a strong coupling to the thermostat~videinfra! at 300 K. During these runs initial atom overlaps werelieved. The equilibrations were performed with the fiand third layer of the crystal facing vacuum~no periodicboundary conditions were used in the direction normal tosurface!. Successive equilibration runs of 50 ps were pformed at 300 K with the true potential. During this partthe equilibration phenyl rings optimizedp–p stacking byrotating their plane normals by approximately 48 degr(m53) and 43 degrees (m54) from the surface normal. Weequilibrated several initial unit cells by translating adjacehexamers in the chain direction~x direction! over fixed rela-tive distances, and found that their average energiescreased proportional to the deviation from maximum ristacking in the ideal crystal structure. Therefore only tstructure was further considered in our studies.

On the m53 and m54 surfaces, 8CB molecules firsencounter the carbonyl oxygens when approaching fromvapor or bulk nematic 8CB phase. The 8CB monolaysimulated in this study are stable on these surfaces. Weconstructed crystal surfaces with the phenyl ring normperpendicular to the surface normal~these slabs were noequilibrated; instead, position restraints were applied tocrystal atoms!. The 8CB monolayers simulated on thecrystals faced strong polar carbonyl oxygens and cluste~dewetted! during the simulations.

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C. Simulation details

Molecular dynamics was run using the YASP simulatipackage.51 Constant temperature dynamics was performby weak coupling52 to a temperature bath of 300 K withcoupling time of 0.2 ps. All bond lengths were constrainusing the SHAKE algorithm53 with a relative tolerance of1027. The time step employed was 2 fs. For nonbondedteractions~Lennard-Jones and electrostatic!, a cutoff distanceof 0.9 nm was used. An atomic Verlet neighbor list54 wasused, which was updated every 15 time steps; neighbwere included if they were closer than 1.0 nm. Configutions were saved every 1 ps.

We studied the interaction of isolated 8CB molecuand 8CB monolayers with them53 and m54 surfaces.Placing the 8CB molecules at random positions in randomchosen orientations above the surface set up the sys~molecular centers of mass were placed 5–10 Å abovesurface.! The systems were periodic inx andy direction only.In this way we study polyalkanmellitimide/8CB/vacuum sytems. Before collecting the system trajectories, 100 ps eqbration runs were performed, which was sufficient to ensthat all memory of the initial orientation was lost.

D. Solvent

To understand the orientation of the first adsorbed molayer we would ideally like to study poly-m-APM/monolayer/vacuum and poly-m-APM/monolayer/bulk sys-tems. To simulate a full bulk LC phase at the present levechemical detail demands huge computational resourcestherefore cannot be performed straightforwardly. Howevenematic bulk, if present, will certainly have an effect on whgoes on near the surface. For instance, it will to some exsolubilize the adsorbed molecules, thereby affecting thmolecular tilts ~solvent effect!. Even though the bulk LCcannot be explicitly included into the simulation, one cmimic the bulk~solvent! effect using only few extra degreeof freedom, which capture the bulk 8CB solvent effect inaverage way, albeit at a reduced level of detail. Weproached this question by substituting the bulk 8CB byapolar solvent. Despite its strong electric dipole, the 8molecules in the nematic phase are generally believed toup in neutral ‘‘cybotactic clusters.’’55 Dipolar interactions be-tween molecules in the first adsorbed surface layer and mecules in the bulk are assumed to be screened out.means that the apolar ring and tail parts of the 8CB mecules essentially govern the solvent properties of the bHence, in the simplest~crude! approach we can model thsolvent using structureless particles interacting throughder Waals forces only. This we did by adopting LennaJones~LJ! ‘‘atoms’’ with a large size, chosen such that thbulk solvent above the 8CB monolayer could be simulausing a few hundreds of these atoms. Note that a fully amistic 8CB bulk would increase the system size by sevethousand atoms. The size of the solvent atom was choseresemble the kinetic diameter of carbon tetrachloride~s50.5581 nm!. Its Lennard-Jones well depth was chosen suthat a chemically realistic 8CB molecule favors the interfain the polyalkanmellitimide/8CB/LJ–solvent system. Wi

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9939J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 Orientation of liquid crystal monolayers

this artificial solvent we effectively capture the thermodnamic effect of the bulk on the molecular 8CB tilts: the aplar tail parts of adsorbed 8CBs will be partially solubilizeby the attractive van der Waals background of the bulk.addition to these structural effects, the solvent lubricatesmotion of the 8CB in some cases. These dynamic effectsof minor interest here.

We performed several 50 ps MD runs starting wsingle 8CB molecules dissolved in the bulk part of LJ svents containing 288 solvent particles~poly-4-APM/dissolved 8CB interface systems! with prescribed LJ welldepthse varying betweene52.718 kJ/mol~the value re-

FIG. 2. ~Color! Surface crystal structures form53 ~a! andm54 ~b!. Typi-cal examples~dominant alignment orientations! of adsorbed 8CB moleculesfrom simulations with single molecules are included~nitrogen is shown inblue!.

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ported for CCl4! and e510 kJ/mol. Parameters for unlikinteractions~solvent–8CB, solvent–polymer surface! weredetermined using Lorentz–Berthelot mixing rules. To avocompetitive 8CB/solvent adsorption phenomena, we chthe solvent–surface interaction to be purely repulsive~i.e.,solvent particles interact with surface atoms according tor 212 part of the LJ potential only!. At all values ofe the 8CBmolecule was found to prefer the surface. To avoid evapotion of the solvent, a constant force of 100 kJ mol21 nm21 in2z direction was applied to the solvent particles abovethreshold value of theirz coordinate. This force was chose

FIG. 3. ~Color! Optimized structure for phenylcyanide/N-methylphthalimideinteraction as obtained fromab initio calculations~a!. Contour map of thepoly-4-APM surface free energy2kbT ln P(x,y) ~at 300 K! obtained fromrelative probabilitiesP(x,y) of the cyano-nitrogen atom visiting position(x,y) on the surface~b!. P(x,y) was obtained by normalizing the accumulated histogram of six independent runs with isolated 8CB molecules~totalsimulation time of 4.3 ns! to the lowest nonzero element. The differenbetween the lowest- and highest-energy contour is 4.5 kJ/mol.

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9940 J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 van der Vegt et al.

such that for bothm53 andm54 the solvent number density was approximately 0.5 Lennard-Jones reduced unThreshold values of 3.4 nm (m53) and 3.0 nm (m54)were used.

III. RESULTS

A. Isolated molecules

1. Surface anisotropy

Figure 2 shows the equilibratedm53 andm54 crystalslabs simulated in this work. The carbonyl oxygensshown in red. Them53 crystal shows ‘‘shingles’’ in thedirection of they axis @Fig. 2~a!#; the planar imide parts arrotated away from the surface normal by approximatelydegrees.m54 shows a shingling structure along thex andyaxis @Fig. 2~b!#. The imide parts are rotated away from thsurface normal by approximately 43 degrees.m53 forms aplanar zig–zag structure in6x and contains microscopi‘‘grooves’’ in 6y direction. These parabolically shapegrooves are bounded by two planar imide parts and a lo~‘‘buried’’ in the bulk crystal! alkane–(CH2)3–part. The pe-riodic cell in our study contains three of these grooves. Tm54 periodic cell shows six grooves in6y, however theseare less pronounced rendering this surface to be more flthe molecular scale. The main direction~the chain direction!in the poly-m-alkanpyromellitimide crystal structures is thuaccompanied by a second~perpendicular! direction of microcorrugation.

2. Anchoring of single 8CB molecules

Figures 2~a! and 2~b! also show snapshots from thsimulations of isolated molecules on both surfaces. Onm53, the 8CB molecule quickly finds a6y directed grooveand adopts its orientation to it during a major course~this canbe as long as several nanoseconds! of all simulations per-formed. Inside the groove, the 8CB maximizes nonboncontacts~the polar head of the 8CB directs itself towards tpolar carbonyl moieties on the chain on either side ofgroove, whereas the apolar aliphatic tail prefers the alkparts at the bottom of the groove!. Anchoring is hence pro-vided by polar cyano-carbonyl and multiple van der Wainteractions. Onm54, the picture is quite similar, but th8CB does not fit inside the grooves quite as neatly as om53. Hence, the 8CB is more mobile and larger parts ofsurface are explored, as is illustrated by the two orientatishown in Fig. 2~b!.

In order to get a more detailed insight into the dipoledipole interaction, which presumably influences theangle, quantum-chemical calculations with theGAUSSIAN 98

program package56 were performed. The interaction oN-methylphthalimide with cyanobenzene was used amodel system. Calculations were performed with the 6-31*basis set and, in order to allow stronger mutual polarizatwith the 6-311G(2d,p) basis set57 on the Hartree–Focklevel of theory. The structures forN-methylphthalimide andcyanobenzene were optimized for each basis set. For thteraction, the preoptimized structures were kept and onlycoordinates describing the relative distance and orientawere optimized~the distance between the cyano nitrogen a

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one of the aromatic 2-hydrogens~H2! of the phthalimide, theangle formed by these two and the parent phthalimide cbon, the angle formed by the C and N of the cyano groupH2, and a dihedral angle describing the rotation of the phering around the bond between the cyano C atom and theof the phenyl ring!. Thus, the cyano benzene molecule cmove freely except that the cyano group is constrained toin the plane of the phthalimide molecule. This choice miicks the fact that the positions above and below the melmide planes in the crystal surface would be blockedneighboring chains. The optimized structure for tcyanobenzene/N-methylphthalimide interaction is shown iFig. 3~a!. The cyano group is located above the central hdrogen atom of the aromatic ring system of tN-methylphthalimide molecule. This is in qualitative agrement with the contour plot for the 8CB/poly-4-APM interation obtained from MD simulation@Fig. 3~b!#. The contoursexpress relative anchoring~free! energies and were obtaineby counting the number of visits of the cyano-nitrogen atoon a mesh~0.79 Å30.47 Å! spanning the simulated surfac~the surface is divided into 60 identical windows!. Visits ofdifferent windows have been accumulated in the one shoin Fig. 3~b!. The interaction energies from quantum-chemiccalculation are 4.2 kcal mol21 and 3.8 kcal mol21 for the6-31G* and 6-311G(2d,p) basis set, respectively. For botbasis sets, a second minimum could be identified wherecyano group is directed towards the methyl group. The inaction energies associated with this minimum are weakeramount to 3.1 kcal mol21 ~6-31G* basis set! and 2.7kcal mol21 @6-311G(2d,p) basis set#.

The translational dynamics of the 8CB center of massshown in Fig. 4. This figure shows four 500 ps trajectoriessingle 8CB molecules onm54 and two 500 ps trajectorieon m53. On both surfaces, the translational diffusion is aisotropic and occurs predominantly in the direction of tgroove. Onm54, far larger parts of the groove are samplcompared tom53, and short excursions to neighboringrooves occur. The 8CB spends most of its time exploringspatial anchoring position at the surface and infrequenjumps over distances~in y direction! of approximately 5 Å,which is close to the interchain spacing~4.7 Å! in y. On m53, the 8CB molecule remains strongly fixed and onrarely jumps~we observed typically one jump in6y during1 ns runs! to a neighboring position.

Figures 5~a! and 5~b! show the molecular tilt angle distributions form53 andm54, respectively. The distributionwere averaged over five independent single molecule run500 ps each. The tilt angle was defined as the one betwthe surface normal and the 8CB vector, which points frothe first aliphatic CH2 group ~the one connected to the phenyl ring! to the cyano-nitrogen atom. In addition, the effeof the solvent on the molecular tilts is shown. Onm54,visual inspection showed that the solvent significantly raithe 8CB tilt angle by solvating the aliphatic 8CB tail. Whethe well depth of the solvent–solvent potential is increasfrom 0 ~vacuum! to 4.4 kJ/mol, solvation of the tail parcauses the peak in the tilt angle distribution to shift to 1degrees. Above 4.4 kJ/mol the 8CB tail was found toexpelled from the solvent causing the maximum of the d

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9941J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 Orientation of liquid crystal monolayers

tribution to shift back to the one found in vacuum~notshown!. In the vacuum environment, the maximum occursapproximately 92 degrees. Onm53, the distribution is nar-rower and no significant solvent effect is observed. The pmaximum occurs at 92 degrees, similar to them54/vacuumsystem. On the basis of the snapshots presented in Figs.~a!and 2~b!, it is plausible to assume that the solvent~which isrepelled by the surface! can hardly access the 8CB adsorbonto m53. The 8CB onm54, to a large extent, lies abovthe surface and is better accessible by the solvent.

The slow surface dynamics does not allow to exploreazimuthal angle distribution exhaustively. Nevertheless,azimuthal distributions from independent sets of simulatioare qualitatively similar, despite peak heights showing statical variations. In Fig. 6 we present the azimuthal angsampled in two independent runs~an azimuthal angle of 0degrees corresponds to the1x direction!. On m53, a mol-ecule chooses either1y or 2y alignment and stays in thaorientation. If the solvent is applied rather than a vacuumsignificant changes occur. Onm54, the molecules samplelarger part of this orientational degree of freedom. Somolecules happen to align in1y or 2y, but main chainalignment occurs as well and transitions are observedtween6y and6x. With a solvent present, more orientatioare sampled because the molecule may take advantage osolvent to reorient~the 8CB is temporarily free from thesurface in that case!.

B. Cyanobiphenyl monolayers on poly-3-APM andpoly-4-APM

Simulations of monolayers were performed with 30 8Cmolecules corresponding to surface densities of 1Å2/molecule (m53) and 120 Å2/molecule (m54). On boththe poly-3-APM and poly-4-APM surfaces five independemonolayers were simulated. Trajectories were sampled in~atleast! 500 ps production runs. During the equilibration ruof the initial configurations~the 8CB molecules were homo

FIG. 4. Two-dimensional (x,y) 8CB center of mass surface dynamics om53 andm54. Trajectories of single molecules on the surfaces duringps runs at 300 K are shown. Thex axis corresponds to the poly-m-APMmain chain direction.

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geneously distributed with random orientations just abothe surface! the 8CBs quickly relaxed into a homogeneosurface layer, which did not show significant dynamics ding the production runs. We characterized the 8CB trantion and orientational relaxation dynamics~center of massmean-square displacements, reorientation correlation tiof the 8CB main axis!, however, no significant movemencould be observed at the time scales of our simulations.use of the effective solvent did not change the dynamics

In Figs. 7~a! and 7~b! we present the monolayer packingon m53 andm54, respectively. These packings were simlated with the 8CB facing a vacuum. Onm53 patches canbe identified, which align in predominantly in6x and 6ydirection. Clear defects occur between neighboring diffently oriented patches. The monolayers onm54 are more

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FIG. 5. Distribution of molecular tilt angles of single molecules onm53 ~a!andm54 ~b! at 300 K. Tilt angles,90° correspond to CN groups pointinup, angles.90° to CN groups pointing down. Open symbols denote disbutions obtained from surface/8CB/vacuum runs, filled symbols denotetributions obtained from surface/8CB/solvent runs:s ~vacuum! m ~e52.72kJ/mol! j ~e54.40 kJ/mol!. Distributions were obtained by statistical aveaging over five 500 ps runs.

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9942 J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 van der Vegt et al.

homogeneously packed~fewer defects! on the surface, andpatches can be identified as well, but, in this case, alignmin the chain direction (6x) dominates.

Figures 8~a! and 8~b! show polar representations of thaverage orientations of the 8CB molecules in the monolayon m53 andm54, respectively~one dot represents the timaveraged orientation of a single 8CB in the monolayer!. Theplots contain the orientations of all molecules shown in F7 and confirm the bimodal alignment~6x and 6y! on m53 and the alignment in the main chain direction (6x) onm54. In contrast to a strong surface induced6y alignmentof isolated molecules~Figs. 2 and 6! the monolayer align-ment is determined by a balance of surface induced ancing and packing effects. The surface tries to align the 8molecules in6y ~the direction of the microcorrugation!,whereas efficient monolayer packing occurs in6x ~in 6x

FIG. 6. Distribution of azimuthal angles of single molecules onm53 ~a!and m54 ~b! sampled in two statistically independent runs~denoted asmolecule 1 and 2! at 300 K. Open symbols denote distributions obtainfrom surface/8CB/vacuum runs, filled symbols denote distributions obtafrom surface/8CB/solvent runs with a solvent–solvent LJ well depthe54.4kJ/mol.

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direction the monolayer has optimized 8CB/main-chain ctacts and mutual 8CB contacts!. Due to the stronger6yanchoring in the microscopic grooves onm53, this surfacetends to favor6y alignment of 8CB.

Figure 9 shows the distribution of the molecular tangles of 8CB in the monolayers on both surfaces. No snificant difference in the location of the peak maxima onm53 andm54 can be detected when the monolayers facvacuum. In the presence of a solvent, the peak maximumm54 shifts a few degrees in the direction of larger angindicating that solubilization of the aliphatic 8CB tails favothe anchoring of the cyano group. The effect of the solvenless pronounced than in the single molecule simulations.

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FIG. 7. Snapshots of 8CB monolayer alignment onm53 ~a! andm54 ~b!from surface/8CB monolayer/vacuum simulations at 300 K.

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9943J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 Orientation of liquid crystal monolayers

IV. DISCUSSION

A. Model surfaces and rubbed polyimide surfaces

It is generally agreed that rubbing polyimide surfacesa ‘‘black art’’ and, as a consequence, there is little quanttive information on what, exactly, rubbed polymer surfaclook like. Nevertheless, some qualitative statements canmade. First, IR dichroism shows that the polymer chainsaligned along the rubbing direction.10 Second, it has beenproven with evanescent x-ray diffraction that there is solocal crystalline order~different from the bulk crystallinity!which should have some influence.58 Third, near edge x-rayabsorption fine structure~NEXAFS! measurements hav

FIG. 8. LC orientations in monolayers onm53 ~a! and m54 ~b! fromsurface/8CB/vacuum runs. One point denotes a time-averaged~500 ps! ori-entation of one molecule. The points from five simulated monolayersincluded. The circles denote equal polar angles. A data point in the centthe figure corresponds to a configuration with the molecular main axispendicular to the interface. Data points on the horizontal line corresponmolecules which have their main axis in the plane given by the surnormal and the poly-m-APM main chains.

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shown that the phenyl ring planes often show some inclition with respect to the surface plane,20,22 indicating ashinglelike architecture of the aromatic blocks.

Given that a truly realistic representation of a rubbpolyimide surface is unavailable, we have looked formodel system which exhibits the above-mentioned featuon a qualitative basis and also allows for comparison wexperiment. Obviously, some assumptions implicitly enthe choice of the model surface. Working with single cryssurfaces, we have eliminated both grain boundariesamorphous regions. We reason that grain boundariesamorphous regions would only deteriorate the alignmerather than adding qualitatively new features. We have utwo surfaces which are chemically similar but differ in thesurface topography and therefore allow comparisons.

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FIG. 9. Distribution of molecular tilt angles in monolayers onm53 ~a! andm54 ~b!. Open symbols denote distributions obtained from surfamonolayer/vacuum runs, filled symbols denote distributions obtained fsurface/monolayer/solvent runs with a solvent–solvent LJ well depthe54.4kJ/mol.

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9944 J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 van der Vegt et al.

poly-3-APM surface has deep grooves and a mirror plperpendicular to the main chain direction. The grooves ofpoly-4-APM surface are shallower and there is a shinglearrangement of aromatic blocks along the main chains, tbreaking the mirror symmetry.

Note that a shinglelike arrangement develops not oalongbut alsoperpendicularto the main chain direction. Weterm the direction with the shingles pointing up ‘‘1y. ’’While one might argue that this6y asymmetry is irrelevanin practice because there are equally many grains withshingles pointing to the right and to the left of the rubbidirection, this is not true. The alignment of the main chaalong the rubbing direction is far from perfect. It is quipossible that grains form, in which they axis is not perpen-dicular to the rubbing direction. The shear-induced crystazation may be biased in favor of crystallites with a positiprojection of the1y-direction onto the rubbing directionShingling along they axis may in this way be part of thexplanation of pretilt. While the shinglelike arrangemealong the main chain is a feature specific to poly-4-APsurfaces, shinglingperpendicularto the main chain shouldbe present in most other polyimides—including the commcial ones—as well.

B. Translational and rotational dynamics

In agreement with experiment,31,32 the reorientationaldynamics is frozen in for the first monolayer. There is hoever, a small lateral mobility of the LC molecules on tpoly-4-APM surface. This motion is only found in the preence of the~lubricating! solvent. At this point, we are nointerested in the details of the near-surface dynamics. Atechnical drawback, the loss of ergodicity implies that ecient sampling can only be achieved by multiple simulatioruns with varying initial conditions.

C. Molecular tilt

There are two different prerequisite for the generationpretilt. First, there must be a tilt on the molecular scaSecond, this tilt must be correlated with the azimuthal anthat is, it must be higher parallel to the rubbing direction thantiparallel. The latter effect requires symmetry breakitermed ‘‘shingling’’ here. On the basis of optical second hmonic generation~SHG! experiments,23,33 it has been postulated that the dipolar interaction between the cyano groupthe 8CB and carbonyl group plays a special role in the geration of pretilt because it increases the molecular tilt. Hoever, it is not quite clear, how, exactly, the CwN and theCvO group should be situated with respect to each otheorder provide a net attraction. Since both the oxygen andnitrogen atom carry a partial negative charge, these uhave to avoid each other. The detailedab initio calculationshows that such a geometry is possible@Fig. 3~a!#. Both thenitrogen atom and the oxygen atom are in close proximitythe carbon atom on the other molecule which carries a ptive charge. The cyano groups therefore help to maintavertical polarity of the 8CB layer with the heads pointindownwards, as experimentally found with optical SHG.

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In addition to the dipole–dipole interaction of the Cgroup, there is a second source of molecular tilt whichgiven by a partial solubilization of the alkyl chains in thbulk medium. As Figs. 5 and 9 show, the solvent signcantly increases the molecular tilt, where the effect is lpronounced on packed monolayers than on isolated mecules. We therefore believe that the presence of the bLC, modelled here by including a solvent, contributes topretilt of the first absorbed layer.

D. Alignment along the rubbing direction

As the comparison between isolated molecules a~Figs. 4–6! and entire monolayers~Figs. 7–9! shows, thelateral interaction between adsorbed LC molecules stroninfluences the orientation. In particular, packing effectspear to release the constraining effects of the microgrooWhile isolated molecules can search around for the mfavorable position inside a groove, there will always be mecules left outside the grooves in the case of entire monoers. These molecules would have to sit on the ridges betwthe grooves, which is energetically much less favorable. Tgrooves still are fairly important on the poly-3-APM-surfac~having deeper grooves!. For the poly-4-APM-surface~hav-ing shallow grooves!, the anisotropic van der Waals interation ~favoring alignment with the main chain! wins and theLC molecules line up with the polymer main chain. Anotheffect of packing is that some molecules assume an edgorientation. The overall distribution of 8CB ring normalsrather isotropic~not shown!. NEXAFS measurement of 8CBon PMDA–ODA polyimide have given a similar result.22

This finding contrasts with the behavior on graphite surfacwhere the ring planes are parallel to the substrate even uconditions of high coverage.59

E. Pretilt

Clearly, the issue of pretilt is of highest interest in thcontext of application. Figure 8 addresses this questionshows the directions of the molecular axes in a polar dgram. The shingles of the substrate point upwards into1y direction form53 and into the2y direction and the1xdirection form54. A dot in the center of the diagram indcates a vertical molecule, a dot on the edge, a moleculeits main axis parallel to the surface. Full dots correspondmolecules with the CN bond pointing up, open dots to mecules with the CN group pointing down. As expected,molecules mostly lie flat on the surface with a molecularangle below 20°. The tilt has a small in-plane asymmetrythe sense that the tilt is more positive in certain inplanerections. For instance form54 the left-hand side of the figure contains more black dots than white dots and vice veThis says that, on average, the tilt is negative into the1xdirection and positive into the2x direction. To make thisstatement more quantitative we calculate the order paramtensor of the monolayer, which is

Qi j 512^3ninj2d i j &,

whereni is scalar product of the molecule’s main axis unvector with theith axis of the laboratory frame,d i j is the

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9945J. Chem. Phys., Vol. 115, No. 21, 1 December 2001 Orientation of liquid crystal monolayers

Kronecker symbol, and angular brackets denote thesemble average. While the order parameter is uniaxial inbulk ~Qzz5S the nematic order parameter!, it is biaxial at thesurface. Being a symmetric tensor,Q can be diagonalized toa matrix QD by rotating the coordinate system. In our cathe rotation matrix is close to diagonal, that is, the rotatangles are small.Qzz

D is negative for bothm53 andm54.For m53, Qxx

D and QyyD are of about equal magnitude~Qxx

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D 520.40!. ~These values pertain tthe monolayer/solvent system. The values with monolayin vacuum are nearly identical.! The equivalent ellipsoid resembles a pancake and there is no well-defined nematicrector. In practical terms, this means that the poly-3-APMnot a good alignment layer. The equivalent pancake is tiinto the1x direction by~1464!° and into the1y directionby ~1262!°. The tilting direction corresponds to that of tharomatic blocks, the tilt itself being smaller by about a facof 10.

On the m54 surface,QxxD is larger thanQyy

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D 520.44!, indicating that align-ment along thex direction ~the rubbing direction! is indeedachieved. There also is a significant tilt along thex directionof ~2362!°. Note, however, that the tilt isnegative, that is,against the direction of shingling. This result certainlyunexpected. Interestingly, poly-m-APM has been investi-gated by the Nagoya group with NEXAFS measurement.20,21

While a correlation between shingling in the substrate anpretilt could be very well established for a related compoushingling wasnot found for poly-m-APM. These authorsprovided a picture which was not based on shingling. Wha definite conclusion regarding the relation between the nsurface pretilt, as calculated here, and the bulk LC prefrom experiment cannot be drawn, this example certaiillustrates that molecular details do matter and that the geration of a pretilt can be a rather complicated issue.

V. CONCLUSIONS

Detailed MD simulations of 8CB molecules and monlayers situated on crystalline polyimide surfaces have bperformed with an emphasis on understanding the originmolecular tilt and macroscopic pretilt. A macroscopic incnation of the LC director requires both tilt on the molecuscale and the absence of a mirror plane along the rubdirection. The generation of microscopic tilt is aided bydipole–dipole interaction between the cyano group andcarbonyl groups of the polymer, on the one hand, andpartial solubilization of the aliphatic tails in the bulk, on thother. Breaking of the mirror symmetry along the rubbidirection is provided by a shinglelike arrangement of taromatic blocks. While microgrooves dominate the aligment of isolated molecules they are less effective on enmonolayers due to lateral interactions between the LC mecules.

ACKNOWLEDGMENTS

The authors thank Vladimir Zhubkov and Curt Frank fhelpful discussions.

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