Journal of Electron Spectroscopy and Related Phenomena 98–99 (1999) 189–207
`
`Liquid crystal alignment by rubbed polymer surfaces: a
`microscopic bond orientation model
`J. Sto¨hr*, M.G. Samant
`IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95120 USA
`
`Dedication by J. Sto¨hr — This paper is dedicated to Dick Brundle who for many years was my colleage at the IBM Almaden Research Center.
`Dick was responsible for my hiring by IBM, and over the years we interacted with each other in many roles — as each other’s boss or simply as
`colleagues. One thing never changed, we were friends and running buddies. I sure miss those runs with Dick through the Almaden hills and our
`lively discussions. I am sure that he will be missed as an editor of the Journal of Electron Spectroscopy, too!
`
`Received 24 October 1997; accepted 26 December 1997
`
`Abstract
`
`We discuss the microscopic origin of a previously poorly understood phenomenon, the alignment of a nematic liquid crystal
`(LC), consisting of rod-like molecular units, when placed on a rubbed polymer surface. After giving a brief review of the
`phenomenon and its technological utilization in flat panel displays we discuss the use of surface sensitive, polarization
`dependent near edge X-ray absorption spectroscopy for the study of rubbed polymer surfaces. These measurements are
`shown to provide a microscopic picture for the origin of the alignment process. It is shown that the LC orientation direction
`is set by an asymmetry in the molecular bonds, i.e. of the charge, at the rubbed polymer surface. The experimental results are
`explained by a general theory, based on tensor order parameters, which states that the minimum energy state of the interaction
`between the LC and oriented polymer surface corresponds to maximum directional overlap of the respective anisotropic charge
`distributions. q 1998 Elsevier Science B.V. All rights reserved.
`
`Keywords Liquid crystals; Polymer surfaces; Polyimides; Maximum overlap model; Tensor order parameters
`
`1. Introduction
`
`When a nematic liquid crystal (LC), consisting of
`an assembly of aligned rod-like molecules, is placed
`on a rubbed polymer surface it exhibits both in-plane
`and out-of-plane orientation of the rods. The in-plane
`alignment direction of the rods typically coincides
`with the rubbing direction. The average upward tilt
`angle of the rods from the polymer surface plane,
`which is typically a few degrees, is referred to as
`the pretilt angle. It is an important fact that the LC
`
`* Corresponding author. Tel.: 1 1-408-927-2461; Fax: 1 1-
`408-927-2100; e-mail: stohr@almaden.ibm.com
`
`pretilt is unidirectional. For example, for rubbed poly-
`imide surfaces the rods tilt up from the rubbing direc-
`tion and therefore the tipped-up ends of the rods point
`into, not opposite to, the rubbing direction. The origin
`of the LC alignment mechanism has been debated
`ever since its discovery 90 years ago [1,2] but no
`definitive understanding has emerged. Such an under-
`standing is not only an interesting scientific but an
`important
`technological problem since todays flat
`panel displays are largely based on LCs which modu-
`late light transmission from the back to the front of the
`display through changes
`in LC alignment, as
`discussed in more detail below.
`In general, the LC alignment has to originate from
`
`0368-2048/99/$ - see front matter q 1998 Elsevier Science B.V. All rights reserved.
`PII: S0368-2048(98)00286-2
`
`Page 1 of 19
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`
`symmetry breaking at the surface of the polymer
`substrate. Over the years asymmetries in either the
`macroscopic topographical or microscopic molecular
`structure of the polymer surface have been proposed
`for the preferred rod direction in the LC [3,4]. Inde-
`pendent of any asymmetry of the polymer surface, the
`origin and size of out-of-plane LC tilt angles have
`been explained in terms of the van der Waals interac-
`tion between asymmetric LC molecules and the
`polymer surface, modelled as a semi-infinite dielectric
`medium [5]. Because such a model ignores any aniso-
`tropy of the polymer surface on a molecular level it
`cannot account for the unidirectional LC pretilt direc-
`tion, however. While a variety of methods, in parti-
`cular linear and non-linear optical methods, can be
`used to determine the precise alignment direction of
`the LC molecules, even for monolayer films [6], it is
`more difficult to obtain detailed information regarding
`the molecular structure of
`the polymer surface.
`Conventional linear optics techniques lack surface
`sensitivity and second harmonic generation cannot
`be used because the polymer molecules typically
`have inversion symmetry. Nevertheless, early propo-
`sals of the molecular orientation at
`the polymer
`surface were based on bulk-sensitive optical and
`infra-red measurements carried out on thin films [7–
`12].
`More recently, surface sensitive grazing incidence
`X-ray scattering (GIXS) studies on semicrystalline
`BPDA-PDA polyimide demonstrated the preferential
`near-surface alignment of polyimide chain segments
`along the rubbing direction, linking it to the preferred
`in-plane alignment direction of the LCs [13]. These
`studies are consistent with the conventional view that
`LC alignment on the polymer surface originates from
`a quasi-epitaxial
`interaction. Because of the long
`structural coherence length within the LC, the LC
`alignment has been thought to originate from ordered
`regions at the surface with parallel chain segments [7],
`possibly in the form of microcrystalline nucleation
`sites [14]. In this model the LC rods are envisioned
`to align parallel to the polymer chain segments in the
`crystalline regions. Surface sensitive studies have also
`been carried out using the near edge X-ray absorption
`fine structure (NEXAFS) technique [15–19]. These
`studies also showed the preferential near-surface
`alignment of polyimide chain segments along the
`rubbing direction [17] and the decay of the alignment
`
`from the surface toward the bulk of the film. NEXAFS
`studies also gave clear evidence for a preferential out-
`of-plane tilt of phenyl rings at polyimide surfaces
`[15,16,18,19]. This tilt was linked with the pretilt
`angle of the LC on the surface. Some of the NEXAFS
`studies utilized partially ordered (semi-crystalline)
`polyimides like BPDA-PDA [17] and PMDA-ODA
`[18] and the suggested LC alignment models impli-
`citly assumed the presence of ordered surface regions
`giving rise to epitaxial effects. These studies did not
`address the known fact that LC alignment also occurs
`on surfaces of disordered polymers. In fact, such poly-
`mers are typically used in the manufacturing of flat
`panel displays. Most recently NEXAFS studies on a
`disordered polyimide [19] suggested that LC align-
`ment only requires a statistically significant preferen-
`tial bond orientation at the polymer surface, without
`the necessity of crystalline or quasi-crystalline order.
`A general directional interaction model was proposed
`in which the LC direction is guided by a ‘‘p-like
`interaction’’ between the LC molecules and the aniso-
`tropic polymer surface.
`Here we report surface-sensitive and polarization-
`dependent NEXAFS measurements on a variety of
`polymers. The experimentally observed anisotropy
`of the NEXAFS intensity at the polymer surface is
`analyzed in terms of the preferred orientation of
`phenyl and CyO functional groups at the surface.
`The molecular orientation at the polymer surface is
`quantified by the derivation of orientation factors,
`previously utilized for the description of LCs, and
`the relevant equations are derived. From the measure-
`ments a simple general model for LC alignment
`emerges which is based on the existence of preferred
`bond orientation at
`the rubbed polymer surface,
`without the necessity for crystalline or microcrystal-
`line order. In particular, the observed asymmetric out-
`of-plane bond orientation is argued to be the micro-
`scopic origin of the LC pretilt direction. A model is
`presented that links the asymmetric molecular orien-
`tation at the polyimide surface to the rubbing process.
`Finally, we develop a simple but powerful theory for
`the origin of LC alignment that is based on symmetry.
`It uses tensor order parameters to describe the aniso-
`tropic interaction between the LC and the aligned
`polymer surface and clearly shows that the interaction
`energy between a uniaxial LC and a biaxial polymer
`surface is minimized if the p orbital densities of the
`
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`
`191
`
`Fig. 1. Schematic of a laptop computer flat panel display, as described in the text. On the computer screen we show the structure of a 5 OCB
`liquid crystal molecule.
`
`two systems have maximum directional overlap. This
`theory supports the empirically derived p interaction
`model [19].
`
`2. The role of liquid crystals in flat panel displays
`
`Today’s laptop computers use flat panel displays
`
`Illustration of the rubbing process. A thin polymer film,
`Fig. 2.
`coated on top of an ITO electrode layer which is deposited on a
`glass plate, moves underneath a rotating rubbing wheel whose drum
`is coated with a velour bristle cloth. Also shown is the typical shape
`of a polymer chain, resembling a ball with a radius of gyration of
`about 10 nm and the monomer structure of BPDA-PDA polyimide,
`studied in this paper.
`
`light weight and compact size
`their
`because of
`[20,21]. It is envisioned that such displays will gradu-
`ally replace conventional cathode ray tubes in many
`applications from desk-top computer to television
`screens. In such a display, schematically shown in
`Fig. 1, the picture on the screen is composed of
`many pixels, approximately 300 £ 300 micrometer
`in size, of different colors and intensities [22]. In
`each pixel the desired color is created by ‘‘mixing’’
`blue, green and red primary colors of different inten-
`sities by means of a patterned color filter array as
`shown in Fig. 1. The intensity of each color is adjusted
`by using liquid crystals to change the light intensity
`transmitted from the back to the font of the display.
`The LC is composed of rod like molecules which
`prefer to align themselves so that the long directions
`of the rods are parallel. The structure of a typical LC
`molecule is shown on the computer screen in Fig. 1.
`The LC is filled into the gap, a few microns wide,
`between two polyimide films coated onto indium-
`tin-oxide (ITO) electrodes which in turn are deposited
`onto two glass-plate cross polarizers. In order for the
`display to work the LC molecules have to be anchored
`down nearly parallel to the surfaces of the polyimide
`films but on opposite sides point into the perpendi-
`cular directions of the two crossed polarizers. They
`thus form a twisted helix from one side to the other.
`When the light from a light source in the back of the
`display crosses the first polarizer it is polarized along
`the long axis of the LC molecules anchored to it. As
`
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`
`Fig. 3. Illustration of the liquid crystal pretilt angle 1. For a rubbed polyimide film the pretilt always points into the rubbing direction, indicated
`by a double-stem arrow. In a display, the liquid crystal is filled into the gap between two opposing polyimide coated glass plates which are
`rubbed in orthogonal directions, as shown. The rod-like liquid crystal molecules are anchored down with their long axis parallel to the rubbing
`direction on both ends and form a twisted helix across the gap. Because of the well defined LC pretilt direction at the anchoring points only a
`counterclockwise 908 rotation of the helix is possible when viewed from above, as shown on the right. This avoids the formation of reverse tilt
`domains as discussed in the text.
`
`the light progresses through the LC the helical LC
`structure changes the polarization of the light from
`linear to elliptical so that part of the light is trans-
`mitted by the second, perpendicular, polarizer. Since
`the light transmission depends on the orientation of
`the LC rods it can be changed by rotation of the rods.
`This is accomplished by application of a small
`voltage, pixel by pixel, by means of microscopic
`ITO electrodes independently driven by a transistor
`array. As the voltage is increased the LC long axis
`becomes increasingly parallel
`to the electric field
`direction, which is parallel
`to the light direction.
`The light polarization becomes less affected by the
`LC and the light transmission is reduced because of
`the crossed polarizers. Thus the orientational changes
`in LC alignment are the heart of the LC display
`providing its gray scale or color contrast.
`One of the most important yet scientifically least
`understood steps in the making of a flat panel display
`is the directional anchoring of the LC molecules to the
`polymer films. The current method simply consists of
`unidirectional rubbing of a polyimide film, which is
`about 100 nm thick, with a velour cloth. In practice
`this is done with a rubbing machine, as shown in Fig.
`2, where the polymer coated glass plate moves under-
`neath a rotating drum whose surface consists of velour
`bristles. The rubbing process is specified by the rota-
`tion speed of the drum, the speed of the plate, and the
`‘‘pile impression’’, characterizing the offset
`in
`distance between the drum surface and the polyimide
`surface. Polyimide is chosen because its high glass
`transition temperature assures that the rubbed surface
`
`remains stable even at elevated temperatures. After
`the rubbing process the LC molecules align with
`their long axis parallel to the rubbing direction and
`point up from the surface by a small pretilt angle. The
`size of the pretilt angle depends on the exact monomer
`structure of the polyimide, i.e. it varies with changes
`in main as well as side chain structure, and it depends
`on the structure of the LC molecules, as well.
`The pretilt angle is of particular technological
`importance and, in practice, has to exceed about 38
`for the proper functioning of the display. The reason is
`illustrated in Fig. 3. If the pretilt angle is zero, there
`exists an ambiguity in the twisting of the LC helix
`between the two anchored, orthogonal, ends. Both
`908 clockwise and anticlockwise rotation is possible,
`leading to the formation of clockwise and anticlock-
`wise LC domains, referred to as reverse tilt domains
`[21]. At the boundary between two such domains the
`LC orientation is ill defined leading to artifacts in the
`image on the computer screen, e.g. shadows. In the
`presence of a clearly defined pretilt angle and pretilt
`direction, i.e. into the rubbing direction, only one 908
`twist is possible and therefore the LC will align as a
`single domain. Fig. 3 clearly indicates that a well-
`defined pretilt direction is of fundamental importance.
`For example, if a pretilt angle existed with equal prob-
`ability parallel and antiparallel to the rubbing direc-
`tion, the rotation sense of the helix would remain
`undefined and the reversed domain problem could
`not be eliminated. It is apparent that a detailed under-
`standing of the origin of LC alignment is of great
`technological
`importance. Such an understanding
`
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`193
`
`experimental geometries shown in Figs. 5(a) and
`(b). Here we have chosen our sample coordinate
`system with the x axis along the rubbing direction
`and the z axis along the surface normal. The sample
`could be rotated about a vertical axis resulting in a
`change of the X-ray incidence angle from the surface
`u, and independently about the surface normal z,
`changing the azimuthal angle F of the incident X-
`rays, defined in Fig. 5(c). In the ‘‘parallel’’ geometry
`the major component of the electric field vector, ~E1,
`which lies in the horizontal plane at a 908 angle from
`the incident X-ray wave vector, was oriented in the
`(2x; z; 1x) plane of the sample coordinate system at a
`polar angle u from the sample normal z. For conve-
`nience we define u to be positive for F 08 ~E1 in (1x,
`z) quadrant) and negative for F 1808 ~E1 in (2x, z)
`quadrant). In the ‘‘perpendicular’’ geometry ~E1 was
`oriented in the (2y, z, 1 y) plane at an angle u from
`the sample normal z. Here we define u to be positive
`for F 908 ~E1 in (1y, z) quadrant and negative for
`F 2708 ~E1 in (2y, z) quadrant). X-ray absorption
`was recorded by means of surface sensitive electron
`yield detection [24]. We used a cylindrical mirror
`analyzer (CMA) to monitor the KLL Auger electron
`yield (AEY) which probes only the first nanometer
`from the free surface [17,25]. Simultaneously, we
`measured the sample current with a picoammeter.
`The so obtained total electron yield (TEY) spectra
`probe about 10 nm below the surface [17]. The spectra
`were divided by the total electron yield signal from a
`highly transmissive ( , 80%) gold grid, again
`measured with a picoammeter. A pre-edge back-
`ground was then subtracted from the normalized
`spectra and the edge jump far above the K-edge
`(340–380 eV) was arbitrarily scaled to unity. This
`procedure produces spectra in which all resonance
`intensities correspond to the same number of C or O
`atoms in the sample, as discussed elsewhere [24]. An
`example of the resulting normalized TEY and AEY
`spectra is shown in Fig. 6. Here we compare spectra of
`an unrubbed BPDA-PDA polyimide, recorded at X-
`ray incidence angles u 908 and u 208. Tests were
`performed regarding radiation damage of the investi-
`gated polymers. At the experimental conditions used
`here, characterized by an X-ray spot size of 0.5 £
`1 mm2 and a sample photo-current of about 5 £
`10211 A at 320 eV, no time dependent changes in
`the spectra were observable.
`
`Fig. 4. LC orientation and pretilt angle in rubbed polyimides and in
`polystyrene. We show only the first monolayer of the LC molecules
`on the rubbed surfaces. More precisely, the LC pretilt angle 1 is
`defined as the average out-of-plane tilt angle of the rods in the bulk
`of the LC.
`
`would allow the development of non-contact alterna-
`tives to the mechanical low-tech rubbing process and
`the development of new, possibly non-polymeric,
`materials which are useful as an alignment layer.
`Below we shall present NEXAFS measurements on
`a variety of rubbed polyimide surfaces and on poly-
`styrene which are shown to provide important new
`insight into the magical alignment process. Polyi-
`mides and polystyrene were chosen for a particular
`reason. As shown in Fig. 4 it is empirically known
`that rubbed surfaces of the two different materials
`align LCs quite differently. All rubbed polyimides
`align LCs along the rubbing direction, with the pretilt
`direction pointing into the rubbing direction. Rubbed
`polystyrene, by contrast, aligns LCs perpendicular to
`the rubbing direction with zero pretilt [8,23]. This
`extreme behavior has to be explained by any reason-
`able model.
`
`3. Experimental details
`
`the
`NEXAFS measurements were performed at
`Stanford Synchrotron Radiation Laboratory on the
`wiggler beam line 10-1 using nearly linearly polarized
`soft-rays with an energy resolution of , 100 meV at
`the carbon K-edge. Spectra were recorded in the
`
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`
`Fig. 5. Parallel (a) and perpendicular (b) experimental geometries used for the NEXAFS measurement. The X-rays are incident on the sample at
`an incidence angle u from the surface. The major component of the electric field vector ~E1 of the elliptically polarized X-rays lies in the
`horizontal plane at the angle u from the sample normal, which is taken as the z axis of the sample frame. The smaller component ~E2 is in the
`vertical direction and lies on the surface of the sample. The sample is rotatable about a vertical axis and around its normal z. The rubbing
`direction is taken along the x axis of the sample frame, as shown in (c). The orientation of the electric field vector and a single molecular p
`orbital in the sample frame are specified by spherical angles, are shown. Because the rubbing process is unidirectional it causes a mirror
`symmetry about the (x,z) plane at the polymer surface, as shown in (d). In general, the molecular symmetry at the surface will only have one-fold
`symmetry about the z axis because the directions x and 2x are inequivalent. As shown in the text one may, however find a molecular frame
`) in which the molecular distribution has at least twofold symmetry about all three axes. This frame is rotated by an angle g about the y (cid:136)
`0
`0
`0
`(x
`,y
`,z
`0
`axis, relative to the sample frame.
`y
`
`We investigated several polyimides and a sample
`of polystyrene. The molecular monomer structures
`are given in Fig. 7. The polyimides were dissolved
`in an organic solvent and spin coated onto 10 £
`10 cm2 ITO coated glass plates to a thickness of
`less than 100 nm. After heating to 858C to remove
`the solvent, the samples were baked at 1808C for
`60 min. Samples were rubbed using a rayon-cloth
`rubbing machine
`at
`200 rpm rotation
`speed,
`25 mm/s plate speed and a pile impression of
`0.6 mm. For the NEXAFS measurements we used
`1 £ 1 cm2 pieces, cut from the unrubbed and rubbed
`sample plates. Polystyrene films of 96 K and 514 K
`molecular weight were dissolved in toluene and spin
`coated onto cleaned Si (100) wafers having a native
`
`oxide layer. Film thicknesses were kept below 100 nm
`to avoid excessive charging in the X-ray beam. The
`samples were heated to 808C to remove the solvent
`and then heated at 1508C for 1 h to relax the films. The
`films were rubbed at room temperature with a velour
`cloth under a load of 2 g/cm2 over a distance of
`300 cm at a speed of 1 cm/s as described elsewhere
`[17,26].
`Before we discuss experimental results we shall
`briefly derive the equation describing the angular
`dependence of the NEXAFS intensity for the case of
`a rubbed polymer surface. Because of
`the low
`symmetry of such systems the angular dependence
`is different
`from that encountered in previous
`NEXAFS studies.
`
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`195
`
`4. Angular dependence of NEXAFS intensity and
`molecular orientation
`
`4.1. NEXAFS intensity in sample frame
`
`As shown in Fig. 6, NEXAFS spectra of polymers
`consist of several peaks or resonances. Because of
`their peak-like shape the lowest-energy resonances
`in the 280–290 eV range are particularly suited for
`an intensity analysis. These resonances arise from
`transitions of a 1s core electron into unoccupied mole-
`cular p* orbitals and their angular dependence
`directly yields the orientation of the molecular p
`system [24]. In principle, the higher-energy s reso-
`nances in the 290–310 eV range could also be used to
`study molecular orientation effects but
`in the
`following we shall restrict our discussion to the p
`resonances. The experimental geometries are speci-
`fied in Fig. 5. For elliptically polarized X-rays the
`angle-dependent NEXAFS intensity I(cid:133)u; F; a; f(cid:134) for
`the p system of a single molecule in the sample frame
`(cid:255)
`(cid:1)
`(x,y,z) is given as [24]
`(cid:255)
`
`I u; F; a; f
`
`(cid:8)
`
`(cid:1)
`
`(cid:1)
`(cid:255)
`(cid:134) I2 u; F; a; f
`
`
`
`(cid:133)
`1 1 2 P
`
`(cid:133)1(cid:134)
`
`:
`
`C P I1 u; F; a; f
`
`Here C is a normalization constant and P is a
`polarization factor describing the relative intensity
`contributions of the orthogonal electric field vector
`components ~E1 and ~E2 of the elliptically polarized
`X-rays [24]. The polarization factor depends on the
`storage ring energy and the beam line optics. Our
`0:80 ^ 0:02,
`experiments were carried out with P
`as discussed below. The general angular depen-
`dence of
`the NEXAFS intensity is derived by
`considering the geometry illustrated in Fig. 5 (c).
`In the figure we show both the electric field vector
`~E of the X-rays and the molecular p orbital as
`vectors. Because the electromagnetic wave oscil-
`lates and the experiment averages over many exci-
`tation events the electric field vector ~E, on average,
`is actually a two-directional vector, so that
`its
`(u,F)
`orientation
`is
`equivalent
`to
`(2u 1 1808; F 1 1808). This
`leads
`to
`the
`following general form of the NEXAFS intensities
`I1 and I2 for the p system of a single molecule in
`
`Fig. 6. Normalized NEXAFS spectra of unrubbed BPDA-PDA
`polyimide are shown for normal (908) and grazing (208) X-ray inci-
`dence angles. Spectra recorded by KLL Auger yield detection are
`shown on top and by means of total electron yield detection at the
`bottom. The spectra are normalized to a unit edge jump in the
`energy range 340–380 eV where all curves coincide. The peaks
`below 290 eV correspond to core electron transitions to unfilled
`p* orbitals, those above 290 eV to s* orbitals in the polymer.
`
`(cid:133)2(cid:134)
`
`Zp
`
`0
`
`Z2p
`(cid:255)
`
`0
`
`(cid:255)
`(cid:1)
`
`(cid:133)4(cid:134)
`In our case the x,z plane is a mirror plane so that
`f a; 2f
`f a; f
`: This
`leads
`to two distinct
`(F 08; 1808)
`and
`‘‘perpendicular’’
`‘‘parallel’’
`(F 908; 2708) experimental geometries as shown
`in Figs. 5 (a) and (b), and the respective NEXAFS
`
`the sample frame (x,y,z), [24]
`I1(cid:133)u; F; a; f(cid:134)
`cos2u cos2a
`1 sin2u sin2a(cid:133)cos2F cos2f1 sin2F sin2f(cid:134)
`sin2u sin2a(cid:133)cosF cosf1 sinF sinf(cid:134);
`1 1
`2
`I2(cid:133)u; F; a; f(cid:134) (cid:136) sin2a(cid:133) sin2F cos2f1 cos2F sin2f(cid:134):
`(cid:133)3(cid:134)
`For a distribution of molecules characterized by a
`distribution function f(a,f) of the p orbitals,
`the
`NEXAFS intensity is given by
`
`I u; F(cid:133) (cid:134)
`(cid:255)
`(cid:1)
`
`(cid:1)
`
`(cid:255)
`
`(cid:1)
`
`f a; f
`
`sina da df:
`
`I u; F; a; f
`
`Page 7 of 19
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`196
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`
`Fig. 7. Total electron yield NEXAFS spectra in the region of the p resonances for several unrubbed polyimides and for polystyrene, recorded
`for normal (908) and grazing (208) X-ray incidence angles. The changes in fine structure arise from the different chemical environments of the
`carbon atoms in the samples as illustrated by filled circles and discussed in the text. The monomer structures of the polymers are shown on the
`right.
`
`A
`
`sin2u1 C
`
`sin2u;
`
`intensities can be written as,
`(cid:133)5(cid:134)
`k(cid:133)u(cid:134)
`k
`k
`k 1 B
`I
`(cid:133)6(cid:134)
`I’(cid:133)u(cid:134)
`A’ 1 B’sin2u
`where we have defined u to be positive in the (1x,1z)
`and (1y,1z) quadrants and negative in the (2x,1z)
`k
`k
`k
`, A’,
`and (2y,1z) quadrants. The constants A
`, B
`, C
`and B’ depend on the actual distribution function
`k
`and A’ also depend on the polarization
`f a; f
`and A
`factor P.
`
`(cid:255)
`
`(cid:1)
`
`4.2. NEXAFS intensity in molecular frame
`
`In order to specify the average molecular alignment
`in the sample frame and to correlate this alignment
`with that of the LC molecules it is convenient to find
`0
`0
`0
`in which the molecular
`the molecular frame x
`,y
`,z
`distribution is symmetric, i.e. has two-fold or higher
`0
`0
`0
`and z
`axes. For a
`symmetry, with respect to the x
`,y
`
`rubbed surface, the 1x rubbing direction is distinct
`from the 2x direction and the molecular distribution
`has only a onefold rotational symmetry about the
`sample z and x axes, while it has twofold symmetry
`about the y axis. This leads to the different forms of
`Eqs. (5) and (6). In particular, Eq. (5) is seen to be
`asymmetric with respect to u. In realizing that Eq. (5)
`can be written in the form [8],
`(cid:133)7(cid:134)
`k(cid:133)u(cid:134)
`cos2(cid:133)u2 g(cid:134)
`k
`k 1 b
`k 22b
`k
`k
`k 1 b
`cos2g,
`cos2g; B
`where A
`and
`a
`k
`k
`sin2g we see that
`the molecular system
`b
`C
`0
`0
`0
`is simply obtained by rotation of the sample
`,z
`,y
`x
`0
`x,y,z system by an angle g about the y
`axis as
`y
`illustrated in Fig.5(d). The rotation angle is given by,
`k
`(cid:133)8(cid:134)
`
`I
`
`a
`
`k
`
`tan2g
`
`22C
`k
`B
`The angle g is negative for clockwise rotation and
`
`:
`
`Page 8 of 19
`
`

`
`J. Sto¨hr, M.G. Samant / Journal of Electron Spectroscopy and Related Phenomena 98–99 (1999) 189–207
`0
`
`197
`
`(cid:133)15(cid:134)
`(cid:133)16(cid:134)
`
`0g:
`
`intensity can always be
`the total
`polarized light
`obtained by measurements along three orthogonal
`directions, independent of the relative orientation of
`the sample coordinate system.
`For the more general case of elliptical polarization
`0
`0
`0
`and a relative rotation of the (x
`) frame by an
`,y
`,z
`0
`angle g about the y
`axis we obtain the following
`y
`equations:
`CfP(cid:133)fx
`0sin2g(cid:134) 1 (cid:133)1 2 P(cid:134)fy
`0g;
`0cos2g1 fz
`0 1 (cid:133)1 2 P(cid:134)(cid:133)fx
`0sin2g(cid:134)g;
`CfPfy
`0cos2g1 fz
`CfP(cid:133)fx
`0cos2g(cid:134)
`0sin2g1 fz
`(cid:133)17(cid:134)
`0sin2g(cid:134)g;
`1 (cid:133)1 2 P(cid:134)(cid:133)fx
`0cos2g1 fz
`(cid:133)18(cid:134)
`CfP(cid:133)fx
`0cos2g(cid:134) 1 (cid:133)1 2 P(cid:134)fy
`0sin2g1 fz
`and I’
`Here I
`z correspond to the measured NEXAFS
`intensities in the parallel and perpendicular geome-
`tries, respectively. These intensities differ because
`the smaller elliptical ~E2 component lies along the y
`and x axes, respectively.
`From these equations the orientation factors are
`derived as:
`
`kz
`
`Ix
`
`Iy
`
`I’
`z
`
`kz
`
`I
`
`!
`
`
`1 1 sin2g
`Pcos2g
`
`k
`
`A’ 1 B
`
`;
`
`(cid:133)19(cid:134)
`
`(cid:133)20(cid:134)
`
`:
`
`(cid:16)
`
`k 1 B’
`
`B
`
`(cid:133)21(cid:134)
`
`0
`
`0 1 fz
`the
`
`1
`total
`
`(cid:133)22(cid:134)
`
`(cid:17)
`
`:
`
`Itot
`
`A
`
`k 1 B’
`Itot
`
`k
`
`A’ 1 B
`
`;
`
`
`
`!
`
`1 2 cos2g
`Pcos2g
`
`(cid:17)
`
`(cid:16)
`
`A
`
`3 2
`
`0
`
`fx
`
`0
`
`fy
`
`0
`
`fz
`
`Itot
`
`Itot
`0 1 fy
`The normalization condition fx
`yields
`the
`following expression for
`integrated intensity Itot
`C
`k 1 A’
`1 3P 2 1
`2P
`The polarization factor can also be directly obtained
`as
`
`k
`B’ 2 B
`k 2 A’ 1 B’ 2 B
`
`P
`
`A
`
`k :
`
`(cid:133)23(cid:134)
`
`y
`
`(cid:1)
`
`positive for anticlockwise rotation about the y
`axis.
`
`(cid:255)
`
`4.3. Molecular orientation factors
`
`(cid:255)
`
`(cid:1)
`
`Since the molecular orientation function f a; f
`cannot be determined by NEXAFS (see Eq. (4)) we
`need a different way to characterize the orientational
`anisotropy. This can be done by simply using three
`orientation factors that describe the relative alignment
`along three orthogonal axes, without actual knowl-
`edge of the orientation function itself [27]. Because
`0
`0
`0
`)
`of the twofold molecular symmetry in the (x
`,y
`,z
`frame the orientation factors are simply the projec-
`tions of f a; f
`along the three axes. This metho-
`dology has previously been extensively used for the
`description of the orientational properties of liquid
`crystals themselves [27,28]. The anisotropy of the
`molecular p system can therefore be described by
`0
`0
`0, fy
`, and fz
`, which are defined as
`orientation factors fx
`the lowest order non-vanishing projections, according
`to
`
`Z
`Z
`Z
`
`0
`
`fx
`
`0
`
`fy
`
`0
`
`fz
`
`sin2a cos2f f(cid:133)a; f(cid:134)dV;
`
`sin2a sin2f f(cid:133)a; f(cid:134)dV;
`(cid:255)
`(cid:1)
`
`cos2a f a; f
`
`dV:
`
`(cid:133)9(cid:134)
`
`(cid:133)10(cid:134)
`
`(cid:133)11(cid:134)
`
`R
`
`(cid:255)
`
`(cid:1)
`
`0
`
`One can envision the orientation factors as the frac-
`0
`0
`0
`, and z
`axes,
`tions of molecules aligned along the x
`, y
`0 1 fy
`0 1 fz
`0
`respectively, and we have fx
`1 for a
`f a; f
`dV:
`normalized distribution
`1) and that
`Assuming linearly polarized light (P
`0
`0
`) are iden-
`the coordinate systems (x,y,z) and (x
`,z
`,y
`tical, we see from Eqs. (2) and (4) that the NEXAFS
`intensities along the x, y and z axes directly determine
`the orientation factors, i.e.
`(cid:133)12(cid:134)
`0 ;
`C fx
`Ix
`(cid:133)13(cid:134)
`(cid:133)14(cid:134)
`Iz
`C fz
`0 1 fz
`0 1 fy
`0
`1 determines
`where the normalization fx
`the constant C to reflect the total integrated NEXAFS
`Ix 1 Iy 1 Iz: Note that for linearly
`intensity C
`Itot
`
`Iy
`
`C fy
`
`0 ;
`
`0 ;
`
`Page 9 of 19
`
`

`
`198
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`J. Sto¨hr, M.G. Samant / Journal of Electron Spectroscopy and Related Phenomena 98–99 (1999) 189–207
`
`number the C atoms around the phenyl ring in poly-
`styrene beginning with the one attached to the chain,
`we see that atom 1 is different by symmetry from atom
`4 and from atoms 2, 3, 5, and 6, with atoms 3 and 5
`and 2 and 6 being equivalent.
`The spectra of the various polyimides differ signif-
`icantly, owing to the different monomer structures.
`Particularly interesting is the spectrum of BPDA-
`PDA polyimide which contains two different kinds
`of phenyl rings, associated with the central PDA
`group (unshaded) and the BPDA groups (shown
`shaded) in Fig. 7. The BPDA groups form a planar
`system with the CyO bonds so that their p systems are
`parallel and conjugated. Because of conjugation
`effects the CyO p resonance is shifted to lower
`energy by about 0.5 eV relative to that in the other
`two polyimides labelled JSR-1 and NISS-3. Also, the
`phenyl p resonance around 285 eV is composed of
`several overlapping structures. From the