ATE245285T1 - Bistabile nematische flüssigkristallvorrichtung - Google Patents

Bistabile nematische flüssigkristallvorrichtung

Info

Publication number
ATE245285T1
ATE245285T1 AT98960042T AT98960042T ATE245285T1 AT E245285 T1 ATE245285 T1 AT E245285T1 AT 98960042 T AT98960042 T AT 98960042T AT 98960042 T AT98960042 T AT 98960042T AT E245285 T1 ATE245285 T1 AT E245285T1
Authority
AT
Austria
Prior art keywords
cell
director
grating
liquid crystal
plane
Prior art date
Application number
AT98960042T
Other languages
English (en)
Inventor
John Clifford Jones
Emma Louise Wood
Guy Peter Bryan-Brown
Original Assignee
Zbd Displays Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zbd Displays Ltd filed Critical Zbd Displays Ltd
Application granted granted Critical
Publication of ATE245285T1 publication Critical patent/ATE245285T1/de

Links

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333—Constructional arrangements; Manufacturing methods
    • G02F1/1337—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers
    • G02F1/13378—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers by treatment of the surface, e.g. embossing, rubbing or light irradiation
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/137—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering
    • G02F1/139—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering based on orientation effects in which the liquid crystal remains transparent
    • G02F1/1391—Bistable or multi-stable liquid crystal cells
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333—Constructional arrangements; Manufacturing methods
    • G02F1/1337—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers
    • G02F1/133707—Structures for producing distorted electric fields, e.g. bumps, protrusions, recesses, slits in pixel electrodes
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333—Constructional arrangements; Manufacturing methods
    • G02F1/1337—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers
    • G02F1/133753—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers with different alignment orientations or pretilt angles on a same surface, e.g. for grey scale or improved viewing angle
    • G02F1/133761—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers with different alignment orientations or pretilt angles on a same surface, e.g. for grey scale or improved viewing angle with different pretilt angles
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/137—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering
    • G02F1/13712—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering the liquid crystal having negative dielectric anisotropy
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/137—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering
    • G02F1/13725—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering based on guest-host interaction
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/137—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering
    • G02F1/139—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering based on orientation effects in which the liquid crystal remains transparent
    • G02F1/1392—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering based on orientation effects in which the liquid crystal remains transparent using a field-induced sign-reversal of the dielectric anisotropy
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/137—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering
    • G02F1/139—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering based on orientation effects in which the liquid crystal remains transparent
    • G02F1/1396—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells characterised by the electro-optical or magneto-optical effect, e.g. field-induced phase transition, orientation effect, guest-host interaction or dynamic scattering based on orientation effects in which the liquid crystal remains transparent the liquid crystal being selectively controlled between a twisted state and a non-twisted state, e.g. TN-LC cell

Landscapes

  • Physics & Mathematics (AREA)
  • Nonlinear Science (AREA)
  • Chemical & Material Sciences (AREA)
  • Crystallography & Structural Chemistry (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • Mathematical Physics (AREA)
  • Liquid Crystal (AREA)
  • Liquid Crystal Substances (AREA)
AT98960042T 1997-12-24 1998-12-16 Bistabile nematische flüssigkristallvorrichtung ATE245285T1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
GBGB9727142.3A GB9727142D0 (en) 1997-12-24 1997-12-24 Bistable nematic liquid crystal device
PCT/GB1998/003787 WO1999034251A1 (en) 1997-12-24 1998-12-16 Bistable nematic liquid crystal device

Publications (1)

Publication Number Publication Date
ATE245285T1 true ATE245285T1 (de) 2003-08-15

Family

ID=10824093

Family Applications (1)

Application Number Title Priority Date Filing Date
AT98960042T ATE245285T1 (de) 1997-12-24 1998-12-16 Bistabile nematische flüssigkristallvorrichtung

Country Status (9)

Country Link
EP (1) EP1042702B1 (de)
JP (1) JP2002500383A (de)
KR (1) KR20010033545A (de)
CN (1) CN1285050A (de)
AT (1) ATE245285T1 (de)
AU (1) AU1572599A (de)
DE (1) DE69816481T2 (de)
GB (2) GB9727142D0 (de)
WO (1) WO1999034251A1 (de)

Families Citing this family (30)

* Cited by examiner, † Cited by third party
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US6924781B1 (en) 1998-09-11 2005-08-02 Visible Tech-Knowledgy, Inc. Smart electronic label employing electronic ink
US6753830B2 (en) * 1998-09-11 2004-06-22 Visible Tech-Knowledgy, Inc. Smart electronic label employing electronic ink
US7460200B2 (en) 2000-03-27 2008-12-02 Helwett-Packard Development Company, L.P. Liquid crystal alignment
EP1139151B1 (de) * 2000-03-27 2007-05-16 Hewlett-Packard Company, A Delaware Corporation Bistabile nematische Flüssigkristallvorrichtung
EP1139150A1 (de) 2000-03-27 2001-10-04 Hewlett-Packard Company, A Delaware Corporation Orientierungsstruktur für Flüssigkristall
FR2808891B1 (fr) * 2000-05-12 2003-07-25 Nemoptic Dispositif bistable d'affichage en reflexion
GB0017312D0 (en) 2000-07-15 2000-08-30 Secr Defence Bistable liquid crystal devices
GB0017953D0 (en) * 2000-07-21 2000-09-13 Secr Defence Liquid crystal device
JP2002082358A (ja) 2000-09-06 2002-03-22 Sony Corp 調光装置及び撮像装置
DE10111452B4 (de) * 2001-03-09 2006-07-20 Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. Bistabile elektrooptische Flüssigkristallanzeigen und Verfahren zu ihrer Herstellung
JP2002363564A (ja) * 2001-06-01 2002-12-18 Minolta Co Ltd 液晶組成物及び反射型液晶表示素子
GB0114998D0 (en) * 2001-06-20 2001-08-08 Secr Defence Liquid crystal device
EP1271225A1 (de) 2001-06-22 2003-01-02 Hewlett-Packard Company, A Delaware Corporation Bistabile nematische Flüssigkristallvorrichtung
GB2382151A (en) * 2001-11-20 2003-05-21 Hewlett Packard Co Liquid crystal device and compositions
EP2209027A1 (de) 2002-02-13 2010-07-21 MERCK PATENT GmbH Sicherheitsmarkierung umfassend einen anisotropen Polymerfilm auf ein Substrat mit einer strukturierten Oberfläche
ATE470166T1 (de) 2002-02-13 2010-06-15 Merck Patent Gmbh Verfahren zur herstellung von einem anisotropen polymerfilm auf einem substrat mit einer strukturierten oberfläche
GB0209917D0 (en) 2002-04-30 2002-06-05 Hewlett Packard Co Bistable nematic liquid crystal device
GB2388201A (en) 2002-04-30 2003-11-05 Hewlett Packard Co Liquid crystal device
ATE359343T1 (de) * 2002-12-11 2007-05-15 Merck Patent Gmbh Flüssigkristallzusammensetzung zur verwendung in bistabilen flüssigkristallanzeigen
ATE368716T1 (de) 2002-12-11 2007-08-15 Merck Patent Gmbh Schnell schaltende flüssigkristallzusammensetzungen zur verwendung in bistabilen flüssigkristallanzeigen
EP1445645A1 (de) * 2003-02-07 2004-08-11 ZBD Displays Ltd, Flüssigkristallvorrichtung
CN102074200B (zh) * 2003-03-31 2012-11-28 伊英克公司 驱动双稳态电光显示器的方法
CN100540631C (zh) * 2003-05-08 2009-09-16 默克专利股份有限公司 用于双稳态液晶器件的液晶组合物
WO2005040899A1 (en) * 2003-10-23 2005-05-06 The Hong Kong University Of Science And Technology Bistable liquid crystal device
US7929094B2 (en) 2004-04-22 2011-04-19 Sharp Kabushiki Kaisha Vertically-aligned liquid crystal display device having a rugged structure which is in contact with the liquid crystal layer
CN100510858C (zh) * 2005-04-18 2009-07-08 胜华科技股份有限公司 一种双稳态液晶显示装置及其驱动方法
JP4797451B2 (ja) * 2005-06-01 2011-10-19 ソニー株式会社 液晶表示装置
US7796038B2 (en) 2006-06-12 2010-09-14 Intelleflex Corporation RFID sensor tag with manual modes and functions
US8830072B2 (en) 2006-06-12 2014-09-09 Intelleflex Corporation RF systems and methods for providing visual, tactile, and electronic indicators of an alarm condition
US10698284B2 (en) 2018-09-24 2020-06-30 Sharp Kabushiki Kaisha ZBD liquid crystal device and methods of operating such device

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB9502635D0 (en) * 1995-02-10 1995-03-29 Secr Defence Liquid crystal device alignment
GB9521106D0 (en) * 1995-10-16 1995-12-20 Secr Defence Bistable nematic liquid crystal device
GB9607854D0 (en) * 1996-04-16 1996-06-19 Secr Defence Liquid crystal device

Also Published As

Publication number Publication date
GB2346978B (en) 2001-12-05
EP1042702B1 (de) 2003-07-16
EP1042702A1 (de) 2000-10-11
GB9727142D0 (en) 1998-02-25
KR20010033545A (ko) 2001-04-25
AU1572599A (en) 1999-07-19
WO1999034251A1 (en) 1999-07-08
CN1285050A (zh) 2001-02-21
DE69816481T2 (de) 2004-04-15
GB0013952D0 (en) 2000-08-02
GB2346978A (en) 2000-08-23
JP2002500383A (ja) 2002-01-08
DE69816481D1 (de) 2003-08-21

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