scholarly journals Blue-phase liquid crystal droplets

2015 ◽  
Vol 112 (43) ◽  
pp. 13195-13200 ◽  
Author(s):  
José A. Martínez-González ◽  
Ye Zhou ◽  
Mohammad Rahimi ◽  
Emre Bukusoglu ◽  
Nicholas L. Abbott ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Systematic Study ◽  
Liquid State ◽  
Bulk Properties ◽  
Surface Anchoring ◽  
Phase Liquid ◽  
Blue Phase ◽  
Blue Phases ◽  
Spherical Droplets

Blue phases of liquid crystals represent unique ordered states of matter in which arrays of defects are organized into striking patterns. Most studies of blue phases to date have focused on bulk properties. In this work, we present a systematic study of blue phases confined into spherical droplets. It is found that, in addition to the so-called blue phases I and II, several new morphologies arise under confinement, with a complexity that increases with the chirality of the medium and with a nature that can be altered by surface anchoring. Through a combination of simulations and experiments, it is also found that one can control the wavelength at which blue-phase droplets absorb light by manipulating either their size or the strength of the anchoring, thereby providing a liquid–state analog of nanoparticles, where dimensions are used to control absorbance or emission. The results presented in this work also suggest that there are conditions where confinement increases the range of stability of blue phases, thereby providing intriguing prospects for applications.

scholarly journals The influence of orienting layers on blue phase liquid crystals in rectangular geometries

2018 ◽  
Vol 10 (4) ◽  
pp. 100 ◽  
Author(s):  
Marzena Maria Sala-Tefelska ◽  
Kamil Orzechowski ◽  
Filip A. Sala ◽  
Tomasz R. Woliński ◽  
Olga Strzeżysz ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electric Field ◽  
Low Voltage ◽  
Bragg Reflection ◽  
Phase Liquid ◽  
Blue Phase ◽  
Blue Phases ◽  
Alignment Layers ◽  
Polymer Stabilized

In this paper, the influence of homeotropic and homogeneous orienting layers is presented in a cell filled with chiral nematic liquid crystals stabilized in a blue phase. The change of selective Bragg reflection from red to blue light was observed for homogeneous layers in rectangular geometries. The growth of blue phase crystals domains in a glass cell as well an influence of temperature and the electric field on such a structure, are also presented. Full Text: PDF ReferencesF. Reinitzer, Beitrage zur Kenntniss des Cholestherins, Monatsh Chem. 9, 421-441, (1888). CrossRef J. Yan, M. Jiao, L. Rao, and S.-T. Wu, "Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite", Opt. Express 18, 11450-11455 (2010) CrossRef Y. Chen, D. Xu, S.-T. Wu, S.-i. Yamamoto, Y. Haseba, "A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal", Appl. Phys. Lett. 102, 141116 (2013) CrossRef Y. Huang, H. Chen, G. Tan, H. Tobata, S. Yamamoto, E. Okabe, Y.-F. Lan, C.-Y. Tsai, and S.-T. Wu, "Optimized blue-phase liquid crystal for field-sequential-color displays", Opt. Mater. Express 7, 641-650 (2017) CrossRef V. Sridurai, M. Mathews, C. V. Yelamaggad, G. G. Nair, "Electrically Tunable Soft Photonic Gel Formed by Blue Phase Liquid Crystal for Switchable Color-Reflecting Mirror", ACS Appl. Mater. Interfaces, 9 (45), 39569-39575 (2017) CrossRef E. Oton, E. Netter, T. Nakano, Y. D.-Katayama, F. Inoue, "Monodomain Blue Phase Liquid Crystal Layers for Phase Modulation", Sci. Rep. vol.7, 44575 (2017) CrossRef Q. Liu, D. Luo, X. Zhang, S. Li, Z. Tian, "Refractive index and absorption coefficient of blue phase liquid crystal in terahertz band", Liq. Cryst., Vol. 44, No. 2, pp. 348-354 (2017) CrossRef Y. Li, Y. Liu, Q. Li, S.-T. Wu, "Polarization independent blue-phase liquid crystal cylindrical lens with a resistive film", Appl. Opt., Vol. 51, No. 14, pp. 2568-2572 (2012) CrossRef M. M. Sala-Tefelska, K. Orzechowski M. Sierakowski, A. Siarkowska, T.R. Woliński, O. Strzeżysz, P. Kula, "Influence of cylindrical geometry and alignment layers on the growth process and selective reflection of blue phase domains", Opt. Mater. 75, 211-215, (2018) CrossRef H. Claus, O. Willekens, O. Chojnowska, R. Dąbrowski, J. Beeckman, K. Neyts, "Inducing monodomain blue phase liquid crystals by long-lasting voltage application during temperature variation", Liq. Cryst. 43 (5), 688-693, (2016) CrossRef M. Takahashi, T. Ohkawa, H. Yoshida, J. Fukuda, H. Kikuchi, M. Ozaki, "Orientation of liquid crystalline blue phases on unidirectionally orienting surfaces", J. Phys. D: Appl. Phys. 51 (10), 104003 (2018) CrossRef P. Joshi, X. Shang, J. De Smet, E. Islamai, D. Cuypers, G. Van Steenberge, S. Van Vlierberghe, P. Dubruel, H. De Smet, "On the effect of alignment layers on blue phase liquid crystals", Appl. Phys. Lett. 106, 101105 (2015) CrossRef K. Orzechowski, M.W. Sierakowski, M. Sala-Tefelska, P. Joshi, T.R. Woliński, H.D. Smet, "Polarization properties of cubic blue phases of a cholesteric liquid crystal", Opt. Mater. 69, 259-264 (2017) CrossRef P.-J. Chen, M. Chen, S.-Y. Ni, H.-S. Chen, Y.-H. Lin, "Influence of alignment layers on crystal growth of polymer-stabilized blue phase liquid crystals", pt. Mater. Express 6, 1003-1010 (2016) CrossRef CrossRef

scholarly journals Tunable light beam steering device using polymer stabilized blue phase liquid crystals

2017 ◽  
Vol 9 (1) ◽  
pp. 11 ◽  
Author(s):  
Pankaj Joshi ◽  
Oliver Willekens ◽  
Xiaobing Shang ◽  
Jelle De Smet ◽  
Dieter Cuypers ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Liquid Crystalline ◽  
Beam Steering ◽  
Polymer Dispersed ◽  
Phase Liquid ◽  
Blue Phase ◽  
Blue Phases ◽  
Polymer Stabilized ◽  
Polarization Independent

A polarization independent and fast electrically switchable beam steering device is presented, based on a surface relief grating combined with polymer stabilized blue phase liquid crystals. Switching on and off times are both less than 2 milliseconds. The prospects of further improvements are discussed. Full Text: PDF ReferencesD.C. Wright, et al., "Crystalline liquids: the blue phases", Rev. Mod. Phys. 61, 385 (1989). CrossRef H. Kikuchi, et al., "Polymer-stabilized liquid crystal blue phases", Nat. Mater. 1, 64 (2002). CrossRef Samsung, Korea, SID exhibition, (2008).J. Yan, et al., "Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite", Opt. Express 18, 11450 (2010). CrossRef L. Rao, et al., "A large Kerr constant polymer-stabilized blue phase liquid crystal", Appl. Phys. Lett. 98, 081109 (2011). CrossRef Y. Hisakado, et al., "Large Electro-optic Kerr Effect in Polymer-Stabilized Liquid-Crystalline Blue Phases", Adv. Mater. 17, 96 (2005). CrossRef K. M. et al., "Submillisecond Gray-Level Response Time of a Polymer-Stabilized Blue-Phase Liquid Crystal", J. Disp. Technol. 6, 49 (2010). CrossRef Y. Chen, et al., "Level set based topology optimization for optical cloaks", Appl. Phys. Lett. 102, 251106 (2013). CrossRef H. Choi, et al., "Fast electro-optic switching in liquid crystal blue phase II", Appl. Phys. Lett. 98, 131905 (2011). CrossRef Y.H. Chen, et al., "Polarization independent Fabry-Pérot filter based on polymer-stabilized blue phase liquid crystals with fast response time", Opt. Express 19, 25441 (2011). CrossRef Y. Li, et al., "Polarization independent adaptive microlens with a blue-phase liquid crystal", Opt. Express 19, 8045 (2011). CrossRef C.T. Lee, et al., "Design of polarization-insensitive multi-electrode GRIN lens with a blue-phase liquid crystal", Opt. Express 19, 17402 (2011). CrossRef Y.T. Lin, et al., "Mid-infrared absorptance of silicon hyperdoped with chalcogen via fs-laser irradiation", J. Appl. Phys. 113, (2013). CrossRef J.D. Lin, et al., "Spatially tunable photonic bandgap of wide spectral range and lasing emission based on a blue phase wedge cell", Optics Express 22, 29479 (2014). CrossRef W. Cao, et al., "Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II", Nat. Mat. 1, 111 (2002). CrossRef S.T. Hur, et al., "Liquid-Crystalline Blue Phase Laser with Widely Tunable Wavelength", Adv. Mater. 25, 3002 (2013). CrossRef A. Mazzulla, et al., "Thermal and electrical laser tuning in liquid crystal blue phase I", Soft. Mater. 8, 4882 (2012). CrossRef C.W. Chen, et al., "Random lasing in blue phase liquid crystals", Opt. Express 20, 23978 (2012). CrossRef O. Willekens, et al., "Ferroelectric thin films with liquid crystal for gradient index applications", Opt. Exp. 24, 8088 (2016). CrossRef O. Willekens, et al., "Reflective liquid crystal hybrid beam-steerer", Opt. Exp. 24, 1541 (2016). CrossRef M. Jazbinšek, et al., "Characterization of holographic polymer dispersed liquid crystal transmission gratings", J. Appl. Phys. 90, 3831 (2001). CrossRef C.C. Bowley, et al., "Variable-wavelength switchable Bragg gratings formed in polymer-dispersed liquid crystals", Appl. Phys. Lett. 79, 9 (2001). CrossRef Y.Q. Lu, et al., "Polarization switch using thick holographic polymer-dispersed liquid crystal grating", Appl. Phys. 95, 810 (2004). CrossRef J.J. Butler et al., "Diffraction properties of highly birefringent liquid-crystal composite gratings", Opt. Lett. 25, 420 (2000). CrossRef R.L. Sutherland et al., "Electrically switchable volume gratings in polymer-dispersed liquid crystals", Appl. Phys. Lett. 64, 1074 (1994). CrossRef X. Shang, et al., "Electrically Controllable Liquid Crystal Component for Efficient Light Steering", IEEE Photo. J. 7, 1 (2015). CrossRef J. Yan, et al., "Extended Kerr effect of polymer-stabilized blue-phase liquid crystals", Appl. Phys. Lett. 96, 071105 (2010). CrossRef H.S. Chen, et al., "Hysteresis-free polymer-stabilized blue phase liquid crystals using thermal recycles", Opt. Mat. Exp. 2, 1149 (2012). CrossRef J. Yan. et al., "Dual-period tunable phase grating using polymer stabilized blue phase liquid crystal", Opt. Lett. 40, 4520 (2015). CrossRef H.S. Chen, et al., "Hysteresis-free polymer-stabilized blue phase liquid crystals using thermal recycles", Opt. Mat. Exp. 2, 1149 (2012). CrossRef H.C. Cheng, et al., "Blue-Phase Liquid Crystal Displays With Vertical Field Switching", J. Disp. Technol. 8, 98 (2012). CrossRef

scholarly journals Investigation of Kerr effect in a blue phase liquid crystal using wedge-cell technique

2017 ◽  
Vol 9 (2) ◽  
pp. 54 ◽  
Author(s):  
Kamil Orzechowski ◽  
Marek Wojciech Sierakowski ◽  
Marzena Sala-Tefelska ◽  
Tomasz Ryszard Woliński ◽  
Olga Strzeżysz ◽  
...  
Keyword(s):  
Refractive Index ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electric Field ◽  
Kerr Effect ◽  
Beam Steering ◽  
Phase Liquid ◽  
Blue Phase ◽  
Blue Phases ◽  
Polymer Stabilized

In this work an alternative method for refractive index measurement of blue phase liquid crystal in the Kerr effect has been described. The proposed wedge method uses simple goniometric setup, allowing for direct index measurements for any wavelengths and index values. This is significant advantage comparing to other methods, usually having limitations of the measurement range as well as necessity complicated calculation to obtain refractive indices values. The results are reliable and agree well with the subject literature. Full Text: PDF ReferencesW. Cao et al., "Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II", Nat. Mater. 1, 111-113 (2002). CrossRef S. Meiboom, M. Sammon, W.F. Brinkman, "Lattice of disclinations: The structure of the blue phases of cholesteric liquid crystals", Phys. Rev. A. 27, 438 (1983). CrossRef S. Tanaka et al., "Double-twist cylinders in liquid crystalline cholesteric blue phases observed by transmission electron microscopy", Sci. Rep. 5, 16180 (2015). CrossRef Y. Li and S.-T. Wu, "Polarization independent adaptive microlens with a blue-phase liquid crystal", Opt. Express 19(9), 8045-8050 (2011). CrossRef N. Rong et al., "Polymer-Stabilized Blue-Phase Liquid Crystal Fresnel Lens Cured With Patterned Light Using a Spatial Light Modulator", J. of Disp. Technol. 12(10), 1008-1012 (2016). CrossRef J.-D. Lin et al., "Spatially tunable photonic bandgap of wide spectral range and lasing emission based on a blue phase wedge cell", Opt. Express 22(24), 29479-29492 (2014). CrossRef P. Joshi et al., "Tunable light beam steering device using polymer stabilized blue phase liquid crystals", Photon. Lett. Poland 9(1), 11-13 (2017). CrossRef Ch.-W. Chen et al., "Temperature dependence of refractive index in blue phase liquid crystals", Opt. Mater. Express 3(5), 527-532 (2013). CrossRef Y.-H. Lin et al., "Measuring electric-field-induced birefringence in polymer stabilized blue-phase liquid crystals based on phase shift measurements", J. Appl. Phys. 109, 104503 (2011). CrossRef J. Yan et al., "Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite", Opt. Express 18(11), 11450-11455 (2010). CrossRef K.A. Rutkowska, K. Orzechowski, M. Sierakowski, "Wedge-cell technique as a simple and effective method for chromatic dispersion determination of liquid crystals", Photon. Lett. Poland 8(2), 51-53 (2016). CrossRef O. Chojnowska et al., "Electro-optical properties of photochemically stable polymer-stabilized blue-phase material", J. Appl. Phys. 116, 213505 (2014). CrossRef J. Yan et al., "Extended Kerr effect of polymer-stabilized blue-phase liquid crystals", Appl. Phys. Lett. 96, 071105 (2010). CrossRef M. Chen et al., "Electrically assisting crystal growth of blue phase liquid crystals", Opt. Mater. Express 4(5), 953-959 (2014). CrossRef J. Kerr, Philos. Mag. 50, 337 (1875).

scholarly journals Diffusionless transformation of soft cubic superstructure from amorphous to simple cubic and body-centered cubic phases

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jie Liu ◽  
Wenzhe Liu ◽  
Bo Guan ◽  
Bo Wang ◽  
Lei Shi ◽  
...  
Keyword(s):  
Liquid Crystals ◽  
X Ray Diffraction ◽  
Photonic Materials ◽  
Simple Cubic ◽  
Cubic Phases ◽  
Transmission Electron ◽  
Phase Liquid ◽  
Blue Phase ◽  
Blue Phases ◽  
Temperature Window

AbstractIn a narrow temperature window in going from the isotropic to highly chiral orders, cholesteric liquid crystals exhibit so-called blue phases, consisting of different morphologies of long, space-filling double twisted cylinders. Those of cubic spatial symmetry have attracted considerable attention in recent years as templates for soft photonic materials. The latter often requires the creation of monodomains of predefined orientation and size, but their engineering is complicated by a lack of comprehensive understanding of how blue phases nucleate and transform into each other at a submicrometer length scale. In this work, we accomplish this by intercepting nucleation processes at intermediate stages with fast cross-linking of a stabilizing polymer matrix. We reveal using transmission electron microscopy, synchrotron small-angle X-ray diffraction, and angle-resolved microspectroscopy that the grid of double-twisted cylinders undergoes highly coordinated, diffusionless transformations. In light of our findings, the implementation of several applications is discussed, such as temperature-switchable QR codes, micro-area lasing, and fabrication of blue phase liquid crystals with large domain sizes.

scholarly journals Theoretical approach of a polymer stabilized blue phase beam steering

2017 ◽  
Vol 9 (1) ◽  
pp. 14
Author(s):  
Jose Francisco Algorri ◽  
Virginia Urruchi ◽  
Noureddine Bennis ◽  
Jose Manuel Sanchez-Pena
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Response Time ◽  
Deflection Angle ◽  
Beam Steering ◽  
Phase Plate ◽  
First Case ◽  
Phase Liquid ◽  
Blue Phase ◽  
Polymer Stabilized

Nematic liquid crystal (LC)-based beam steering has been reported for wide applications. However, for conventional nematic LC beam steering the thickness is of several microns in order to have a wider deflection angle. The response time is relatively slow and the diffraction efficiency is low. In this work, novel beam steering based on polymer stabilized blue phase liquid crystal (PS-BPLC) has been designed and theoretically analyzed. This special mesophase of the chiral doped nematic LC has several advantageous characteristics, for example no need for alignment layers, microsecond response time and an isotropic voltage-off state. The results reveal control over phase retardation. The direction of the steered beam can be tuned by voltage. Depending on voltage configuration, either diffractive beam steering (0.5deg deviation for 1st order) or a tunable continuous phase (tunable deviation of 0.002deg) can be obtained. In the first case, the deflection angle could be tuned by stacks of samples. The second option has the same phase shift for the TE and TM modes so unpolarized light could be used. Full Text: PDF ReferencesF. Feng, I. White, T. Wilkinson, "Free Space Communications With Beam Steering a Two-Electrode Tapered Laser Diode Using Liquid-Crystal SLM", J. Lightwave Technol. 31, 2001 (2013). CrossRef E. Oton, J. Perez-Fernandez, D. Lopez-Molina, X. Quintana, J.M. Oton, M.A. Geday, "Reliability of Liquid Crystals in Space Photonics", IEEE Photonics Journal 7, 1 (2015). CrossRef J. Stockley, S. Serati, "Multi-access laser terminal using liquid crystal beam steering", IEEE in Aerospace Conference, 1972 (2005). CrossRef D. Zografopoulos and E. Kriezis, "Switchable beam steering with zenithal bistable liquid-crystal blazed gratings", Opt. Lett. 39, 5842 (2014). CrossRef Benedikt Scherger, et al., "Discrete Terahertz Beam Steering with an Electrically Controlled Liquid Crystal Device", J. Infrared. Millim. Terahertz Waves 33, 1117 (2012). CrossRef M.A. Geday, X. Quintana, E. Otón, B. Cerrolaza, D. Lopez, F. Garcia de Quiro, I. Manolis, A. Short, Proc. ICSO, Rhodes, Greece, pp. 1-4 (2010). CrossRef Y. Chen, S.-T. Wu, "The outlook for blue-phase LCDs", Proc. SPIE 9005, Advances in Display Technologies IV, 900508 (2014). CrossRef G.D. Love, A.F. Naumov, "Modal liquid crystal lenses", Liq. Cryst. Today 10, 1 (2000). CrossRef V. Urruchi, J.F. Algorri, J.M. Sánchez-Pena, M.A. Geday, X. Quintana, N. Bennis, "Lenticular Arrays Based on Liquid Crystals", Opto-Electron. Rev. 20, 38 (2012). CrossRef J.F. Algorri, G. Love, and V. Urruchi, "Modal liquid crystal array of optical elements", Opt. Express 21, 24809 (2013). CrossRef J.F. Algorri, V. Urruchi, N. Bennis, J. Sánchez-Pena, "Modal liquid crystal microaxicon array", Opt. Lett. 39, 3476 (2014). CrossRef J.F. Algorri, V. Urruchi, B. Garcia-Camara, J.M. Sánchez-Pena, "Generation of Optical Vortices by an Ideal Liquid Crystal Spiral Phase Plate", IEEE Elect. Dev. Lett. 35, 856 (2014). CrossRef D. Xu, Y. Chen, Y. Liu, S. Wu, "Refraction effect in an in-plane-switching blue phase liquid crystal cell", Opt. Express 21, 24721 (2013). CrossRef Z. Ge, S. Gauza, M. Jiao, H. Xianyu, S.T. Wu, "Electro-optics of polymer-stabilized blue phase liquid crystal displays", Appl. Phys. Lett. 94 101104 (2009). CrossRef J. Yan et al., "Extended Kerr effect of polymer-stabilized blue-phase liquid crystals", Appl. Phys. Lett. 96, 071105 (2010). CrossRef X. Wang, D. Wilson, R. Muller, P. Maker, D. Psaltis, "Liquid-crystal blazed-grating beam deflector, Appl. Opt. 39, 6545 (2000). CrossRef

scholarly journals Temperature-insensitive electro-optic response of polymer-stabilized blue phases

2017 ◽  
Vol 5 (3) ◽  
pp. 518-521 ◽  
Author(s):  
Gaby Nordendorf ◽  
Jürgen Schmidtke ◽  
David Wilkes ◽  
Heinz Kitzerow
Keyword(s):  
Liquid Crystal ◽  
Electro Optic ◽  
Phase Liquid ◽  
Blue Phase ◽  
Blue Phases ◽  
Polymer Stabilized

Polymer-stabilized blue phase liquid crystal in-plane switching cell.

scholarly journals InP/ZnS quantum dots doped blue phase liquid crystal with wide temperature range and low driving voltage

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jiayue Tang ◽  
Fashun Liu ◽  
Mengli Lu ◽  
Dongyu Zhao
Keyword(s):  
Quantum Dots ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Quantum Dot ◽  
Electric Field ◽  
Driving Voltage ◽  
Practical Application ◽  
Temperature Range ◽  
Phase Liquid ◽  
Blue Phase

Abstract Blue-phase liquid crystals (BPLCs) are regarded as potential materials for the exploitation of next-generation optical devices due to the rapid response, wide viewing angle, and simple industrial production procedures. However, practical application of traditional BPLCs is limited by their narrow temperature range and high driving voltage. Herein, we demonstrated that doping of chiral molecular isosorbide hexyloxybenzoate (R811) into BPLCs is able to increase the temperature range. More importantly, addition of InP/ZnS quantum dots (QDs) with oleylamine surface groups could also effectively broaden the temperature range of the BPLCs further while decreasing the driving voltage, which is attributed to the quantum dot trapped by BPLCs lattice defect that reduces its free energy. Since the trapped quantum dot subsequently forms a local electric field under electric field, the effective electric field of the surrounding liquid crystal molecules is enhanced and the rotation of the liquid crystal molecules is accelerated. Specially, the temperature range is widened by 1.4 °C, and the driving voltage is reduced by 57%, under the optimal concentration of R811 and lnP/ZnS QDs. The accomplishment we proposed in this work is a prospective optimization which makes the practical application of blue phase liquid crystals one step closer.

Nucleation and Growth of Blue Phase Liquid Crystals on Chemically-Patterned Surfaces: A Surface Anchoring Assisted Blue Phase Correlation Length

2021 ◽  
Author(s):  
Xiao Li ◽  
Kangho Park ◽  
Orlando Guzmán ◽  
Jose Adrian Martinez-Gonzalez ◽  
James Dolan ◽  
...  
Keyword(s):  
Liquid Crystals ◽  
Correlation Length ◽  
Condensed Matter ◽  
Orientational Order ◽  
Phase Correlation ◽  
Patterned Surfaces ◽  
Surface Anchoring ◽  
Essential Parameter ◽  
Phase Liquid ◽  
Blue Phase

In condensed matter, the correlation length is an essential parameter which describes the distance over which a material maintains its structural properties. In liquid crystals, for orientational order parameter this...

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