Kent State University
`Digital Commons @ Kent State University Libraries
`
`Physics Publications
`
`12-15-1999
`
`Department of Physics
`
`Material-Independent Determination of Anchoring
`Properties on Rubbed Polyimide Surfaces
`
`Bharat R. Acharya
`Kent State University - Kent Campus
`
`Jae-Hoon Kim
`Kent State University - Kent Campus
`
`Satyendra Kumar
`Kent State University - Kent Campus, skumar@kent.edu
`
`Follow this and additional works at: http://digitalcommons.kent.edu/phypubs
`Part of the Physics Commons
`
`Recommended Citation
`Acharya, Bharat R.; Kim, Jae-Hoon; and Kumar, Satyendra (1999). Material-Independent Determination of Anchoring Properties on
`Rubbed Polyimide Surfaces. Physical Review E 60(6), 6841-6846. Retrieved from http://digitalcommons.kent.edu/phypubs/39
`
`This Article is brought to you for free and open access by the Department of Physics at Digital Commons @ Kent State University Libraries. It has been
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`information, please contact earicha1@kent.edu, tk@kent.edu.
`
`Page 1 of 7
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`Tianma Exhibit 1037
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`

`
`PHYSICAL REVIEW E
`
`VOLUME 60, NUMBER 6
`
`DECEMBER 1999
`
`Material-independent determination of anchoring properties on rubbed polyimide surfaces
`
`Bharat R. Acharya, Jae-Hoon Kim, and Satyendra Kumar
`Department of Physics, Kent State University, Kent, Ohio 44242
`~Received 1 July 1999!
`
`A material-independent method for determining liquid-crystal ~LC! anchoring energy on rubbed polyimide
`~PI! surfaces has been devised. This method exploits the changes in the easy axis of rubbed PI film induced by
`exposure to linearly polarized UV ~LPUV! light. The distribution of PI chains in a rubbed film is approximated
`by a Gaussian function and its width determined from the measured rotation of the LC easy axis as a function
`of exposure time. A quasimicroscopic free energy of the LC-substrate interface is used to model LC anchoring
`properties. The experimental and calculated values of the azimuthal anchoring energy are in good agreement
`and found to depend inversely on the width of the distribution function. The measurements of the width of the
`chain distribution function provide a simple LC material-independent method for determining the LC anchor-
`ing properties. With this method, it is also possible to calculate the strength of the interaction between PI
`chains and LC molecules. @S1063-651X~99!04612-7#
`
`PACS number~s!: 78.20.Fm, 42.79.Kr, 42.70.Df
`
`I. INTRODUCTION
`
`The alignment of liquid crystals ~LCs! on solid substrates
`involves a wide variety of interfacial phenomena, such as
`surface ordering, surface transitions, surface wetting, etc.,
`which are not well understood. Technologically, it is crucial
`to have a reliable procedure that permits good control of
`alignment and yields high-quality alignment of LCs used in
`electro-optic devices. Surface treatments, such as obliquely
`evaporated SiOx
`layers, Langmuir-Blodgett films, and
`rubbed polymer films, have been used to obtain homoge-
`neous alignment of LCs @1#. In recent years, photoalignment
`@2–4# has emerged as a promising noncontact technique be-
`cause of its simplicity and easy control of the alignment
`direction and anchoring energy.
`Alignment layers prepared by different techniques, or pro-
`cessed differently using a specific technique, result in differ-
`ent anchoring properties. It is essential to acquire a good
`understanding of anchoring properties of the surfaces in-
`volved to be able to control the LC alignment. Different
`methods based on the Rapini-Papoular phenomenological
`model @5# for the surface free energy, such as surface discli-
`nations @6#, Fre˜edericksz transition @7,8#, high field @9#, Cano
`wedge cell @10#, optical reflectometric method @11#, retarda-
`tion vs voltage ~RV! technique @12#, etc., have been used to
`measure the polar and azimuthal anchoring energies. How-
`ever, the anchoring energies obtained from these methods
`inherently depend on the LC material used, which makes it
`difficult to isolate the contribution of the morphological ef-
`fects from that of chemical interactions.
`In this paper, a fresh and very different approach for de-
`termining the LC anchoring properties on rubbed polyimide
`~PI! surfaces is presented. A simple model is used to describe
`the distribution of PI chains and the LC alignment. Although
`the microscopic origin of alignment of LCs on the PI surface
`is not yet fully understood, the anisotropic distribution of PI
`chains on the surface is believed to be responsible for the
`alignment @13–15#. In an untreated PI film, the PI chains are
`randomly distributed. Surface treatment ~i.e., rubbing! breaks
`the symmetry by reorienting these chains and inducing LC
`
`alignment along the easy axis, i.e., the rubbing direction. The
`width of the azimuthal distribution of these chains can be
`determined from the measurements of the rotation of the
`easy axis of a rubbed PI film as a function of the LPUV
`exposure time. A simple quasimicroscopic model of the free
`energy of the system is proposed and used to calculate the
`azimuthal anchoring energy. The azimuthal anchoring ener-
`gies for different LCs are measured for different rubbing
`strengths. The model’s predictions of the dependence of azi-
`muthal anchoring energy on the width of the distribution
`show good agreement with the experimental results.
`
`II. THE MODEL
`
`Let us assume that the orientation of PI chains can be
`described by a distribution function N o(u,f), where uand f
`describe polar and azimuthal angles of a unit vector along
`the direction of chains as shown in Fig. 1. We further con-
`sider the dependence of the distribution function on the or-
`thogonal polar and azimuthal angles to be separable, i.e.,
`N o(u,f)5N o(u)N o(f). Let
`us
`further
`assume
`that
`
`FIG. 1. Schematic representation of the orientation of the PI
`chain and the rubbing direction in the laboratory frame. m and R
`are unit vectors along the direction of the PI chain and the rubbing
`direction, respectively.
`
`1063-651X/99/60~6!/6841~6!/$15.00
`
`PRE 60
`
`6841
`
`© 1999 The American Physical Society
`
`Page 2 of 7
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`

`
`6842
`
`BHARAT R. ACHARYA, JAE-HOON KIM, AND SATYENDRA KUMAR
`
`PRE 60
`
`f ~u,f!5
`
`E
`
`e 2(f2fr)2/2v2
`p
`e 2(f2fr)2/2v2
`
`0
`
`df
`
`and C represents the average strength of intramolecular in-
`teractions between PI and LC molecules. Any microscopic
`modifications of the films’ surface is reflected in the free
`energy through changes in its width v.
`If p is the pitch of the LC, the natural twist of the director
`~i.e., with no treatment of the top surface!near the top sur-
`face, i.e., at z5d, is f052pd/p. In the framework of the
`continuum elastic theory, the bulk free energy per unit sur-
`face area of the twisted nematic ~TN! cell is given by @17#
`
`F e5
`
`K 2
`2d
`
`~f02ft!2,
`
`FIG. 2. Geometry of the LC cell used in the model. R1 and R2
`are respective rubbing directions on substrates at z50 and z5d.
`The substrate at z50 is assumed to have strong anchoring. Angles
`ft , f, and fr are the usual azimuthal coordinates of the LC direc-
`tor, PI chain, and R2, respectively. The cell is filled with nematic
`LC doped with a chiral material inducing a pitch p.
`
`N o(u,f) for an untreated surface is azimuthally isotropic
`and that the anisotropy induced by rubbing can be approxi-
`mated by a Gaussian distribution centered around the rub-
`bing direction. The distribution of PI chains on rubbed poly-
`imide film can then be described as @16#
`
`N o~u,f!5N o~u!e 2(f2fr)2/2v2,
`
`~2.1!
`
`where fr specifies the rubbing direction, v is the width of
`the distribution, and N o(u) is the normalization factor such
`that
`
`E
`
`pE
`
`0
`
`o
`
`p
`N o~u,f!sin ududf51.
`
`with respect to ft .
`In the weak anchoring limit, the width of the PI chain
`distribution v!‘ and the distribution function N(u,f) be-
`comes independent of f and the surface energy, F s , be-
`comes independent of ft . Consequently, the director orien-
`tation on the surface is determined solely by the natural twist
`f0. On the other hand, in the case of strong anchoring, the
`equilibrium orientation of the director is dictated by a deli-
`cate interplay between the surface and bulk contributions.
`Minimization of Eq. ~2.2! with respect to ft gives
`
`~2.3!
`
`,
`!df
`
`2f0!
`
`t0
`
`2K 2~f
`
`t0
`
`f ~u,f!sin 2~f2f
`
`C5
`
`dE
`
`p
`
`0
`
`t0
`
`where f
`is the actual twist angle that minimizes the total
`free energy.
`It should be noted that when the PI surface has strong
`anchoring, i.e., all PI chains are aligned along the rubbing
`direction, v!0 and the probability distribution function
`f (u,f) vanishes everywhere except at f5fr , where it is
`unity. In this limit, Eq. ~2.3! reduces to
`
`.
`
`~v50 !2f0%
`2K 2$f
`~v50 !%
`d sin 2$fr2f
`
`t0
`
`t0
`
`C5
`
`Let us now consider a cell made with two rubbed substrates
`located at z50 and z5d, as shown in Fig. 2, and filled with
`a chiral doped nematic LC. The substrate at z50 is assumed
`to have strong enough anchoring to perfectly align the direc-
`tor along the rubbing direction, x. The distribution of PI
`chains at the upper substrate at z5d is given by Eq. ~2.1!.
`The interaction between the LC director and PI chains ori-
`ented along the respective directions ft and fcan be written
`function, C sin2(f2ft),
`using
`a Rapini-Papoular-type
`weighted by the distribution function. The azimuthal surface
`free energy per unit area of the interface is given by the
`ensemble average,
`
`This result is similar to the expression previously used to
`determine the azimuthal anchoring energy W f @10,18,19#
`with f
`(v50) replaced by f
`. Unlike the azimuthal an-
`choring energy function W f, C in our model is constant for
`a given LC-PI system. The value of C can be calculated from
`the measured width of the distribution and the equilibrium
`
`t0
`
`t0
`
`E
`
`0
`
`p
`C f ~u,f!sin2~f2ft!df,
`
`1 2
`
`F s5
`
`where f (u,f) is the probability distribution function given
`as
`
`where K 2 is the twist elastic constant of the nematic LC. The
`equilibrium twist angle f
`at the top surface is determined
`by minimization of the total free energy F5F s1F e given as
`
`E
`
`p
`
`0
`
`t0
`
`Cd
`K 2
`
`H ~f02ft!21
`
`F5
`
`K 2
`2d
`
`f ~u,f!sin2~f2ft!dfJ
`
`~2.2!
`
`Page 3 of 7
`
`

`
`PRE 60
`
`MATERIAL-INDEPENDENT DETERMINATION OF . . .
`
`6843
`
`t0
`
`FIG. 4. Theoretical dependence of equilibrium director twist, f
`@the orientation of the LC director on the surface at z5d that mini-
`mizes free energy given by Eq. ~2.2!, see text#, on the width of the
`distribution. The s, h, and n correspond to Cd/ K 251, Cd/ K 2
`510, and Cd/ K 2550, respectively. The values of f0 and fr are
`the same as given in Fig. 3.
`
`Two 26 mm326 mm pieces cut
`from one 52 mm
`352 mm substrate were used for the azimuthal anchoring
`energy measurement for two different nematic LCs, viz., E7
`~BDH Ltd.! and ZLI-4792 ~Merck Chemicals!. The azi-
`muthal anchoring energies on the surfaces were measured
`using the method proposed by Akahane et al. @18#. The other
`set of two 26 mm326 mm pieces was used for LPUV ex-
`posure and for optical retardation measurements. A 450 W
`xenon lamp ~Oriel, model 66021! was used as the UV
`source. The intensity of the collimated beam of LPUV light
`after the UV sheet polarizer ~Oriel, model 27320! on the
`films’ surface was approximately 4.5 mW/cm2 at 350 nm
`wavelength.
`A photoelastic modulator ~PEM90, Hinds Instruments!
`with a fused silica head was used for optical retardation mea-
`surements. The optic axis of the PEM, placed between
`crossed polarizers, was kept at an angle of 45° to the axes of
`polarizer and analyzer. The substrates were mounted on a
`motorized rotation stage in between the PEM and the ana-
`lyzer. A collimated beam of light from a He-Ne laser inci-
`dent normally to the substrate was parallel to the axis of
`rotation of the substrate. The signal from the photo-detector
`placed after the analyzer was fed to a lock-in amplifier ~EG
`& G Princeton Applied Research, model 5210! tuned to 50
`kHz signal from PEM. By monitoring transmitted light from
`the substrate, it was possible to measure the optical retarda-
`tion with a precision of 60.01°.
`
`IV. RESULTS AND DISCUSSION
`
`An untreated PI film possesses azimuthal symmetry and
`hence is optically isotropic. Upon rubbing, the symmetry is
`broken and the distribution of PI chains becomes anisotropic.
`Figure 5 shows the variation of the optical retardation G of
`films as a function of the number ~or extent! of rubbings.
`Initially, the optical retardation induced by rubbing increases
`
`FIG. 3. Variation of total free energy based on Eq. ~2.2! with
`director twist angle for f0557.3°, fr590°, and Cd/ K 2510 for
`different surface properties; ~a! v50.1 radian, ~b! v51.0 radian,
`~c! v52.0 radian, and ~d! v510.0 radian.
`
`director orientation which can be determined using an optical
`technique @18#. A method to measure the width of the distri-
`bution will be described later.
`The validity of the model is tested by studying the equi-
`librium twist as a function of the width of the distribution.
`The total free energy is calculated as a function of the direc-
`tor twist ft for different values of v. Figure 3 shows the
`dependence of the free energy on ft for f0557.3°, fr
`590°, and Cd/ K 2510. It is clear from the figure that for
`large values of v,
`the free energy is minimum at ft
`557.3°. Large values of v correspond to an almost random
`distribution of PI chains, each influencing the orientation of
`the local director. The resultant torque exerted on the direc-
`tor by these chains is zero and the orientation of the director
`is dictated by the natural twist as determined from the mini-
`mum free energy at ft557.3°. On the other hand, when
`more PI chains are oriented along the rubbing direction, v is
`small and the free energy is minimum for a director nearly
`parallel to the rubbing direction, fr590°. However, as seen
`in Fig. 4, the direction of alignment depends not only on the
`width of distribution but also on the strength of the LC-PI
`interaction and the twist elastic constant, K 2. When LC-PI
`interaction is weaker than K 2 ~i.e., the ratio Cd/ K 2 is small!,
`a better alignment of PI chains, i.e., smaller v, is needed to
`generate the same twist angle.
`
`III. EXPERIMENT
`A polyamic acid solution of SE610 ~Nissan Chemical
`Company! was spin-coated on 52 mm352 mm ITO coated
`glass at 3000 rpm for 30 sec. The films were soft-baked at
`100 °C for 10 min for solvent evaporation followed by 1 h of
`hard bake at 220 °C for imidization. Typically this process
`resulted in 460 Å thick films. Those films were then rubbed
`using a metal cylinder wrapped in velvet cloth. The cylinder
`was spun at a constant angular velocity 550 rev/min. In order
`to get substrates with different anchoring properties,
`the
`number of rubbings with the same pressure was varied while
`keeping the velocity of substrates constant at 0.9 m/min.
`
`Page 4 of 7
`
`

`
`6844
`
`BHARAT R. ACHARYA, JAE-HOON KIM, AND SATYENDRA KUMAR
`
`PRE 60
`
`FIG. 5. Variation of optical retardation, G, with the number of
`rubbings ~solid curve is a guide to the eye!.
`
`rapidly, but then, as the chain alignment saturates, the rate of
`increase is diminished.
`When a film having an initial distribution of PI chains
`given by Eq. ~2.1! is exposed for a time t to normally inci-
`dent LPUV light, the resultant distribution function is given
`by @20#
`
`~4.1!
`
`e 2at cos2(fo2f)sin2u,
`
`N o~u,f!5N o~u!e 2(f2fr)2/2v2
`where ais a constant which depends on the PI, uand fare
`the spherical polar coordinates, respectively, of a unit vector
`along the direction of the photosensitive bonds, and f0 is the
`azimuthal orientation of the electric field vector which is
`parallel to the substrate.
`The easy axis of the rubbed PI film is profoundly affected
`by LPUV exposure because of the dissociation of the photo-
`sensitive bonds. The equilibrium orientation, fs , of the easy
`axis is determined from the extremum of the distribution
`function @19#. If fr50, the fs satisfies the equation
`t sin 2~f02fs!1Bfs50,
`where B51/(av2 sin2u).
`By measuring the optical retardation of a rubbed film sub-
`sequently exposed to LPUV with its polarization at an angle
`f0540° with respect to the rubbing direction, the angle
`through which the easy axis of the film rotates can be deter-
`mined as a function of the exposure time. Figure 6 shows the
`time dependence of the rotation angle Df5fs150°. The
`angle Dfis measured with respect to the direction of align-
`ment preferred by the UV which is perpendicular to the di-
`rection of its polarization for SE610 @21#. The solid lines are
`the fits of Eq. ~4.1! to the experimental data. It is clear from
`the figure that as the UV exposure time increases, the easy
`axis rotates and Df decreases and, after a long enough ex-
`posure, becomes zero.
`When a PI film is exposed to LPUV, PI chains are broken
`due to irreversible photodissociation of C-N bonds which are
`along the long axis of the chains. The chains which are par-
`allel to the polarization direction are most affected, whereas
`those that are perpendicular to polarization are unperturbed.
`
`FIG. 6. The angle of rotation, Df, of the easy axis with respect
`to the polarization direction of LPUV as a function of exposure
`time for one (s), two (h ), four (n), five (L), and six („)
`rubbings. The electric field of LPUV was at an angle of 40° with
`respect to the rubbing direction. The solid curves are the best fits to
`Eq. ~4.1!.
`
`After a sufficiently long exposure, the easy axis rotates and
`becomes parallel to the UV’s preferred direction. On the
`other hand, for stronger rubbing, PI chains are better aligned
`and consequently longer exposure time and/or higher UV
`intensity is needed to fully rotate the easy axis.
`From the fits of Eq. ~4.1! to the experimental data, the
`width of the Gaussian distribution is determined using a pre-
`vious value of a50.026 min21 @14#. The value of uis set to
`90° because the chains on a PI film imidized at this tempera-
`ture lie in a two-dimensional plane parallel to the substrate.
`Figure 7 shows the dependence of the width of the distribu-
`tion on the number of rubbings. For weak ~or less! rubbing,
`the width is large due to the nearly random distribution of PI
`chains. However, with increased rubbing strength more PI
`chains are aligned and the width decreases until a saturation
`
`FIG. 7. Dependence of the width, v, of the PI chain distribution
`function on the number of rubbings. The inset shows optical retar-
`dation, G, plotted as a function of the width of the distribution ~the
`solid curves are a guide to the eye!.
`
`Page 5 of 7
`
`

`
`PRE 60
`
`MATERIAL-INDEPENDENT DETERMINATION OF . . .
`
`6845
`
`FIG. 9. Calculated azimuthal anchoring energy, W f, as a func-
`tion of the strength of interaction, C, for the nematic LC E7 for ~a!
`v52.0 radian, ~b! v51.5 radian, ~c! v51.0 radian, and ~d! v
`50.5 radian.
`
`V. CONCLUSION
`
`It has been shown that a simple microscopic model of the
`PI chain distribution and surface free energy can be used to
`describe the LC anchoring properties on rubbed PI films. A
`close agreement between the experimental values and predic-
`tions of the model for the dependence of the azimuthal an-
`choring energy on the width of the distribution validates the
`model. The width of the Gaussian distribution can be mea-
`sured and used to determine the degree of LC alignment
`induced by rubbing. Additionally, the model permits a direct
`experimental determination of the strength of LC-PI interac-
`tion. In conclusion, with the help of the model presented
`here, one can isolate the contribution of the morphological
`changes induced by rubbing from the effect of chemical in-
`teractions. We believe that this simple model can be ex-
`tended to determine the LC anchoring properties of the in-
`terfaces prepared by other techniques.
`
`ACKNOWLEDGMENTS
`
`This work was supported by the NSF Science and Tech-
`nology Center ALCOM Grant No. DMR-89-20147.
`
`FIG. 8. Dependence of the azimuthal anchoring energy, W f, on
`the width of the distribution for nematic LCs ZLI-4792 (s) and E7
`(h). Solid curves are calculated using f
`from the model with
`f0557.3°, fr590°, p540 mm, and Cd/ K 2518 for E7 and
`Cd/ K 2540 for ZLI-4792.
`
`t0
`
`in the alignment of PI chains is reached.
`The azimuthal anchoring energy on these surfaces has
`been measured for nematic LCs E7 and ZLI-4972. Figure 8
`shows the dependence of the anchoring energy on the distri-
`bution width. The solid lines represent calculated values
`from the equilibrium director orientations based on the
`model for fr590°, f0557.3°, and p540 mm for corre-
`sponding LCs. The increase in azimuthal anchoring energy
`with a decrease in the width implies that the number of PI
`chains contributing to the LC anchoring along the rubbing
`direction becomes higher with increasing rubbing strength.
`From the corresponding theoretical fit to the experimental
`data, the value of C is determined to be 1.4131025 J m22
`and 3.9231025 J m22 for E7 and ZLI-4792, respectively.
`The difference between the C values for two LCs indicates
`that the strengths of the LC-PI interaction for these two LCs
`are different owing to their different chemical structures.
`Figure 9 shows the theoretical dependence of azimuthal
`anchoring energy on the strength of LC-PI interaction for E7
`for interfaces with different v. The linear dependence of the
`azimuthal anchoring energy on C suggests that LC anchoring
`is stronger for stronger LC-PI interaction, as anticipated. On
`the other hand, a better microscopic alignment of PI chains
`along the rubbing direction ~i.e., smaller v) leads to a rapid
`increase in azimuthal anchoring energy with an increase in
`the LC-PI interaction.
`
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`BHARAT R. ACHARYA, JAE-HOON KIM, AND SATYENDRA KUMAR
`
`PRE 60
`
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