Planar nematic anchoring on rough anisotropic substrates: an elastic model

Barberi, R.; Giocondo, M.; Sayko, G.V.; Zvezdin, A. K.

doi:10.1016/0375-9601(96)00119-3

Cited by 8 publications

(10 citation statements)

References 10 publications

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“…Measurements of contour lengths have been used in the past to obtain the fractal dimensions of metal oxide films. 25,37,39 We used the following procedure to determine contour lengths from AFM images of thin films of gold. First, AFM images were exported as 512 × 512 matrices.…”

Section: Visual Inspection Of Real Space and Fouriermentioning

confidence: 99%

“…Although some past studies have evaluated the elastic energy density from such a representation of a surface as we do not believe this method to be generally correct. 37 Although many different sets of {A k , q k } can be used to represent a given surface profile, the elastic energy density is not the same for each set. This conclusion is supported by the observation that the profile a single mode surface can be described by either a single sine function of amplitude A or by a set of m sine functions with scaled amplitudes A/m; the free energy density given by eq 8 is not the same for both representations of the surface.…”

Section: Analysis Of the Root Meanmentioning

confidence: 99%

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Quantitative Characterization of Obliquely Deposited Substrates of Gold by Atomic Force Microscopy: Influence of Substrate Topography on Anchoring of Liquid Crystals

1999

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We report the use of atomic force microscopy (AFM) to characterize quantitatively the structural anisotropy within ultrathin (thickness of ∼10 nm) obliquely deposited films of gold and thereby calculate the influence of this anisotropy on the orientations of liquid crystals (LCs) supported on these surfaces. Whereas visual inspection of AFM images (real space or reciprocal space) reveals no obvious structural anisotropy within these gold films, a quantitative analysis of the AFM profiles does show a subtle level of anisotropy on wavelengths comparable to the lateral dimensions of the gold grains (∼30 nm). Our analysis reveals the root-mean-square (rms) slope of the surface topography to be ∼1°greater in a direction parallel to the direction of deposition of the gold as compared to the perpendicular direction. We also demonstrate the rms curvature of the grains of gold to be greatest in a direction parallel to deposition. Because the amplitude of the surface roughness (∼2 nm) is small compared to its wavelength (∼30 nm), the influence of the surface roughness on the orientations of supported LCs can be described through an elastic mechanism of anchoring. By combining the multimode Berreman-de Gennes model for the elastic free energy density of a nematic LC with AFM profiles of the topography of obliquely deposited gold films, we calculate the azimuthal anchoring energy of the supported LC to be ∼0.015 mJ/m 2 , a value that is consistent with estimates of anchoring energies obtained by fabrication of twisted nematic LC cells. The results reported in this paper provide a route to the characterization of surfaces with designed levels of anisotropy suitable for control of the anchoring of LCs. This capability will, we believe, find application in studies aimed at exploring the use of LCs for amplification and transduction of events of molecular recognition (e.g., antigenantibody) at surfaces.

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Section: Visual Inspection Of Real Space and Fouriermentioning

confidence: 99%

Section: Analysis Of the Root Meanmentioning

confidence: 99%

Quantitative Characterization of Obliquely Deposited Substrates of Gold by Atomic Force Microscopy: Influence of Substrate Topography on Anchoring of Liquid Crystals

1999

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“…Adjacent regions of planar and homeotropic anchoring within a single substrate have been created, for example, by microcontact printed polar and apolar thiols, respectively, on an obliquely evaporated ultra-thin gold layer. Whereas many experimental and theoretical studies have focussed on the understanding of the interactions and phase behavior of NLCs in contact with either geometrically structured substrates (see e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13]) or chemically patterned substrates (see e.g., [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]), NLCs near geometrically structured and chemically patterned substrates have not been investigated yet. In view of the rich behavior of NLCs even on geometrically structured or chemically patterned substrates, a combination of both surface treatments may open new possibilities for an improved performance of NLC cells.…”

Section: Introductionmentioning

confidence: 99%

Phase behavior of a nematic liquid crystal in contact with a chemically and geometrically structured substrate

2005

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A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank-Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal between the patterned grating surface and a flat substrate with strong homeotropic anchoring.

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“…An expression for the effective free energy function of the system [Eq. (6)] was derived by determining an effective surface free energy characterizing the anchoring energy at the patterned surface [Eq. (8)].…”

Section: Discussionmentioning

confidence: 99%

“…Whereas the influence of homogeneous confining substrates on nematic liquid crystals is now well understood, the phase behavior of nematic liquid crystals in contact with chemically or geometrically patterned substrates is still debated. One might suppose that theoretical calculations based on continuum theories should resolve the properties of nematic liquid crystals in contact with patterned substrates [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. However, such calculations are numerically demanding because two-or three-dimensional grids have to be used because of the broken symmetry due to the surface pattern.…”

Section: Introductionmentioning

confidence: 99%

Effective free-energy method for nematic liquid crystals in contact with structured substrates

2007

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We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free-energy function characterizing the patterned substrate, we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimizations of the free-energy functional were performed in order to test the predictions of the effective free-energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition, the effective free-energy method allows one to determine the energy barriers between two states in a bistable nematic device.

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Planar nematic anchoring on rough anisotropic substrates: an elastic model

Cited by 8 publications

References 10 publications

Quantitative Characterization of Obliquely Deposited Substrates of Gold by Atomic Force Microscopy: Influence of Substrate Topography on Anchoring of Liquid Crystals

Quantitative Characterization of Obliquely Deposited Substrates of Gold by Atomic Force Microscopy: Influence of Substrate Topography on Anchoring of Liquid Crystals

Phase behavior of a nematic liquid crystal in contact with a chemically and geometrically structured substrate

Effective free-energy method for nematic liquid crystals in contact with structured substrates

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