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Almeida RAL, Takeuchi KA. Phase-ordering kinetics in the Allen-Cahn (Model A) class: Universal aspects elucidated by electrically induced transition in liquid crystals. Phys Rev E 2021; 104:054103. [PMID: 34942720 DOI: 10.1103/physreve.104.054103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Accepted: 09/27/2021] [Indexed: 11/07/2022]
Abstract
The two-dimensional (2D) Ising model is the statistical physics textbook example for phase transitions and their kinetics. Quenched through the Curie point with Glauber rates, the late-time description of the ferromagnetic domain coarsening finds its place at the scalar sector of the Allen-Cahn (or Model A) class, which encompasses phase-ordering kinetics endowed with a nonconserved order parameter. Resisting exact results sought for theoreticians since Lifshitz's first account in 1962, the central quantities of 2D Model A-most scaling exponents and correlation functions-remain known up to approximate theories whose disparate outcomes urge experimental assessment. Here we perform such assessment based on a comprehensive study of the coarsening of 2D twisted nematic liquid crystals whose kinetics is induced by a superfast electrical switching from a spatiotemporally chaotic (disordered) state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we first show the sharp evidence of well-established Model A aspects, such as the dynamic exponent z=2 and the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of the two-point spatial correlators and show that their nontrivial decay beyond the Porod's scale can be captured in a free-from-parameter fashion by Gaussian theories, namely the Ohta-Jasnow-Kawasaki (OJK) and Mazenko theories. Regarding time-related statistics, we corroborate the aging hypothesis in Model A systems, which includes the collapse of two-time correlators into a master curve whose format is, actually, best accounted for by a solution of the local scaling invariance theory: the same solution that fits the 2D nonconserved Ising model correlator along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent in Model A class, in disfavor of the exact outcome for the diffusion and OJK equations. Finally, we observe a fractal morphology for persistence clusters and extract their universal dimension. Given its accuracy and possibilities, this experimental setup may work as a prototype to address further universality issues in the realm of nonequilibrium systems.
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Affiliation(s)
- Renan A L Almeida
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan.,Departmento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, MG, Brazil.,Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Kazumasa A Takeuchi
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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Lal J, Lurio LB, Liang D, Narayanan S, Darling SB, Sutton M. Universal dynamics of coarsening during polymer-polymer thin-film spinodal dewetting kinetics. Phys Rev E 2020; 102:032802. [PMID: 33076025 DOI: 10.1103/physreve.102.032802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 08/23/2020] [Indexed: 06/11/2023]
Abstract
The dewetting dynamics of a supported bilayer polymer thin film on a solid substrate is investigated using grazing incidence x-ray photon correlation spectroscopy. We find that the top layer dewets via the spinodal mechanism. The kinetics of the dewetting is studied by monitoring the time evolution of the surface diffuse x-ray scattering intensity. We study the time evolution of fluctuations about the average surface structure by measuring the two-time x-ray intensity fluctuation correlation functions. Using these two-time correlation functions we quantify the crossover from early-time diffusive dynamics to hydrodynamics. The early diffusive regime satisfies dynamic universality. The two-time correlation functions also quantify the onset of hydrodynamic effects. The hydrodynamic regime is observed during the spinodal dewetting process as these interactions are not screened.
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Affiliation(s)
- J Lal
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - L B Lurio
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - D Liang
- Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S Narayanan
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S B Darling
- Chemical Sciences and Engineering, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M Sutton
- Physics Department, McGill University, Montréal, H3A 2T8, Canada
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4
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Yeung C. Direct test of the Gaussian auxiliary field ansatz in nonconserved order parameter phase ordering dynamics. Phys Rev E 2018; 97:062107. [PMID: 30011535 DOI: 10.1103/physreve.97.062107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2017] [Indexed: 11/07/2022]
Abstract
The assumption that the local order parameter is related to an underlying spatially smooth auxiliary field, u(r[over ⃗],t), is a common feature in theoretical approaches to non-conserved order parameter phase separation dynamics. In particular, the ansatz that u(r[over ⃗],t) is a Gaussian random field leads to predictions for the decay of the autocorrelation function which are consistent with observations, but distinct from predictions using alternative theoretical approaches. In this paper, the auxiliary field is obtained directly from simulations of the time-dependent Ginzburg-Landau equation in two and three dimensions. The results show that u(r[over ⃗],t) is equivalent to the distance to the nearest interface. In two dimensions, the probability distribution, P(u), is well approximated as Gaussian except for small values of u/L(t), where L(t) is the characteristic length-scale of the patterns. The behavior of P(u) in three dimensions is more complicated; the non-Gaussian region for small u/L(t) is much larger than that in two dimensions but the tails of P(u) begin to approach a Gaussian form at intermediate times. However, at later times, the tails of the probability distribution appear to decay faster than a Gaussian distribution.
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Affiliation(s)
- Chuck Yeung
- School of Science, Pennsylvania State University at Erie, The Behrend College, Erie, Pennsylvania 16563, USA
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Krishnamurthy KS, Tadapatri P, Viswanath P. Dislocations and metastable chevrons in the electroconvective inplane normal roll state of a bent core nematic liquid crystal. SOFT MATTER 2014; 10:7316-7327. [PMID: 25088013 DOI: 10.1039/c4sm00906a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We report experimental results on the formation, dynamics, and annihilation of edge dislocations of opposite topological charge in the electroconvective inplane vortex state of a bent core nematic liquid crystal. The approach of paired, oppositely charged defects toward each other is a two-step process. Near constant velocity at large separation and accelerated motion close to annihilation are found, as in the case of nematic rolls belonging to standard electroconvection. Periodic arrays of dislocations of alternating polarity form upon a sudden, strong elevation of the control parameter. Chevron structures that appear between undulatory defect chains are metastable, and their decay with time is accompanied by an exponential reduction in the dislocation density. The initial periodicity of defect chains also drops exponentially with increasing field.
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Saracco GP, Gonnella G. Monte Carlo study of the phase transition in the critical behavior of the Ising model with shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:051126. [PMID: 20364966 DOI: 10.1103/physreve.80.051126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2009] [Indexed: 05/29/2023]
Abstract
The critical behavior of the Ising model with nonconserved dynamics and an external driving field mimicking a shear profile is analyzed by studying its dynamical evolution in the short-time regime. Starting from high-temperature disordered configurations (fully disordered configurations, FDC), the critical temperature Tc is determined when the order parameter, defined as the absolute value of the transversal spin profile, exhibits a power-law behavior with an exponent that is a combination of some of the critical exponents of the transition. For each value of the shear field magnitude, labeled as gamma, Tc has been estimated and two stages have been found: (1) a growing stage at low values of gamma, where Tc approximately gammapsi and psi=0.52(3), and (2) a saturation regime at large gamma. The same values of Tc(gamma) were found studying the dynamical evolution from the ground-state configuration with all spins pointing in the same direction. By combining the exponents of the corresponding power laws obtained from each initial configuration, the set of critical exponents was calculated. These values, at large external field magnitude, define a critical behavior different from that of the Ising model and of other driven lattice gases.
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Affiliation(s)
- G P Saracco
- Instituto de Investigaciones Fisicoquímicas y Aplicadas, CCT La Plata-CONICET, UNLP, Casilla de Correo 16, Sucursal 4 (1900) La Plata, Argentina
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Corberi F, Lippiello E, Zannetti M. Influence of thermal fluctuations on the geometry of interfaces of the quenched Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011109. [PMID: 18763921 DOI: 10.1103/physreve.78.011109] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2008] [Indexed: 05/26/2023]
Abstract
We study the role of the quench temperature Tf in the phase-ordering kinetics of the Ising model with single spin flip in d=2,3 . Equilibrium interfaces are flat at Tf=0 , whereas at Tf>0 they are curved and rough (above the roughening temperature in d=3 ). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent z=2 of the size of domains L(t) approximately t 1/z is unaffected by Tf, other exponents related to the interface geometry take different values at Tf=0 or Tf>0 . For Tf>0 a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at Tf=0 , to the asymptotic regime with curved interfaces characteristic of Tf>0 . Furthermore, it is shown that the roughening length, although subdominant with respect to L(t) , produces appreciable correction to scaling up to very long times in d=2 .
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Affiliation(s)
- Federico Corberi
- Dipartimento di Matematica ed Informatica, Università di Salerno, via Ponte don Melillo, Fisciano SA, Italy
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Minoura K, Kimura Y, Ito K, Hayakawa R. Dynamics of Annihilation Process of Disclination Pairs in Nematic Liquid Crystals. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/10587259708041847] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Kiyoshi Minoura
- a Department of Applied Physics, Faculty of Engineering , University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo , 113 , Japan
| | - Yasuyuki Kimura
- a Department of Applied Physics, Faculty of Engineering , University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo , 113 , Japan
| | - Kohzo Ito
- a Department of Applied Physics, Faculty of Engineering , University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo , 113 , Japan
| | - Reinosuke Hayakawa
- a Department of Applied Physics, Faculty of Engineering , University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo , 113 , Japan
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Sopik J, Sire C, Chavanis PH. Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011112. [PMID: 16907065 DOI: 10.1103/physreve.74.011112] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2005] [Indexed: 05/11/2023]
Abstract
We consider the dynamics of a gas of free bosons within a semiclassical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein "collapse" within this model. We find that at the Bose-Einstein condensation temperature Tc, the chemical potential mu(t) vanishes exponentially with a universal rate that we compute exactly. Below Tc, we show analytically that square root mu(t) vanishes linearly in a finite time t coll. After t coll, the mass of the condensate grows linearly with time and saturates exponentially to its equilibrium value for large time. We also give analytical results for the density scaling functions, for the corrections to scaling, and for the exponential relaxation time. Finally, we find that the equilibration time (above Tc) and the collapse time T coll(below Tc) both behave like -T -3 c ln|T-Tc|, near Tc.
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Affiliation(s)
- Julien Sopik
- Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier 118, Route de Narbonne, 31062 Toulouse Cedex 4, France
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Rapapa NP, Bray AJ. Effect of shear on persistence in coarsening systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:046123. [PMID: 16711894 DOI: 10.1103/physreve.73.046123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2006] [Indexed: 05/09/2023]
Abstract
We analytically study the effect of a uniform shear flow on the persistence properties of coarsening systems. The study is carried out within the anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with nonconserved scalar order parameter. We find that the persistence exponent theta has a nontrivial value: theta = 0.5034 in space dimension d = 3, and theta = 0.2406 for d = 2, the latter being exactly twice the value found for the unsheared system in d = 1. We also find that the autocorrelation exponent lambda is affected by shear in d = 3 but not in d = 2.
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Affiliation(s)
- N P Rapapa
- School of Physics and Astronomy, The University, Oxford Road, Manchester M13 9PL, United Kingdom
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11
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Song W, Tu H, Goldbeck-Wood G, Windle AH. Effect of the Elastic Constant Anisotropy on Disclination Interaction in the Nematic Polymers. J Phys Chem B 2005; 109:19234-41. [PMID: 16853484 DOI: 10.1021/jp052919g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work, disclination interaction behavior in relation to Frank elastic constant anisotropy in nematics has been studied. A large number of (+(1/2), -(1/2)) disclination pairs are revealed by spontaneous band texture in a semiflexible copolyester. The pairs show no preferential relative orientation, with the intervening fields showing intermediate patterns. A two-dimensional tensor lattice model considering unequal elastic constants is applied to simulate the interaction behavior and patterns of disclination pairs in the presence of elastic anisotropy. Scaling laws for disclination density rho(t) as a function of time step t with different elastic anisotropy are obtained as t(-nu). The value of the exponent nu decreases as elastic anisotropy is increased. Obviously, elastic anisotropy slows the texture coarsening. The simulations also show that angular forces arise in the presence of elastic anisotropy and change the patterns of pairs during the texture coarsening. When disclination density is considerably decreased, some +(1/2) disclinations start to rotate to the energetically favored patterns depending on the sign of the elastic anisotropy. As a result of the disclination rotation, the distribution of patterns of pairs continues to change during the annihilation. However, disclination pairs are influenced not only by elastic anisotropy but also by disclination interaction during the whole annihilation. Therefore, in a real system, the dependence of pairs on elastic anisotropy is not as strong as the theoretical prediction for an isolated pair, and the full pattern range of disclination pairs can be observed.
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Affiliation(s)
- Wenhui Song
- Department of Materials Science and Metallurgy, Cambridge University, Pembroke Street, Cambridge CB2 3QZ, UK.
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12
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Cirillo ENM, Gonnella G, Saracco GP. Monte Carlo results for the Ising model with shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:026139. [PMID: 16196676 DOI: 10.1103/physreve.72.026139] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2005] [Indexed: 05/04/2023]
Abstract
We study the kinetics of domain growth in the Ising model with nonconserved dynamics under the action of a stochastic driving field that mimics the action of a shear flow. At late times, we found multistriped configurations with constant transversal size and linear growth in the direction of the flow. In cases with weak shear, a regime characterized by the decreasing of the transversal size is found that could correspond to previous theoretical investigations. This behavior is confirmed by the analysis of the structure factor patterns.
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Affiliation(s)
- E N M Cirillo
- Dipartimento de Metodi e Modelli Matematici, Facoltà di Ingegneria, Universita di Roma La Sapienza, via A. Scarpa 16, 00161 Rome, Italy
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13
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Sire C. Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench. PHYSICAL REVIEW LETTERS 2004; 93:130602. [PMID: 15524696 DOI: 10.1103/physrevlett.93.130602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2004] [Indexed: 05/24/2023]
Abstract
We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')<<L(t)<<L(t')(phi) well inside the scaling regime, the spin autocorrelation function behaves like s(t)s(t') approximately L(t')(-(d-2+eta))[L(t')/L(t)](lambda(')(c)). For the O(n) model in the n-->infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.
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Affiliation(s)
- Clément Sire
- Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France.
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Nagaya T, Gilli JM. Experimental study of spinodal decomposition in a 1D conserved order parameter system. PHYSICAL REVIEW LETTERS 2004; 92:145504. [PMID: 15089551 DOI: 10.1103/physrevlett.92.145504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2002] [Indexed: 05/24/2023]
Abstract
We study the zigzag instability coarsening of splay-bend walls formed in a nematic liquid crystal under external fields. The vertexes of zigzag can be considered as kinks in a one-dimensional order parameter system and the geometrical constraints associated with the necessary equal length sum of zig and zag segments impose a conserved quantity in this Cahn-Hilliard-type problem. In the late stage of coarsening, the characteristic length of the system L(t) shows a logarithmic increase in time and the dynamical scaling law holds. We then try to extract the nontrivial asymptotic scaling exponent lambda of the two-time correlation function, defined by lim(<phi(0,t)phi(0,t('))> approximately [L(t)/L(t('))](-lambda). The scaling exponents with respective time references, t(')=32 and 64 s, after quench are found to be lambda approximately 2 which is larger than the value with respective time reference t(')=0, predicted by numerical simulation.
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Affiliation(s)
- Tomoyuki Nagaya
- Department of Electrical and Electronic Engineering, Faculty of Engineering, Okayama University, 3-1-1 Tsushimanaka Okayama, 700-8530 Japan
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Wang Y, Chung TS, Cheng SX, Xu J. Dynamics of Defect Annihilations in Polymerization of Aromatic Liquid Crystalline Polyesters. J Phys Chem B 2004. [DOI: 10.1021/jp030570w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Yan Wang
- Department of Chemistry, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, and Department of Chemistry, Wuhan University, Wuhan 430072, People's Republic of China
| | - Tai-Shung Chung
- Department of Chemistry, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, and Department of Chemistry, Wuhan University, Wuhan 430072, People's Republic of China
| | - Si-Xue Cheng
- Department of Chemistry, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, and Department of Chemistry, Wuhan University, Wuhan 430072, People's Republic of China
| | - Jingmei Xu
- Department of Chemistry, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, and Department of Chemistry, Wuhan University, Wuhan 430072, People's Republic of China
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16
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Bray AJ. Coarsening dynamics of phase-separating systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2003; 361:781-792. [PMID: 12871625 DOI: 10.1098/rsta.2002.1164] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
When a system such as a binary liquid is cooled rapidly from a homogeneous phase into a two-phase region, domains of the two equilibrium phases form and grow ('coarsen') with time. In the absence of an external drive, such as gravity or an imposed shear flow, a dynamical-scaling regime emerges in which the domain morphology is statistically self-similar at different times, up to an overall length-scale (coarsening scale) that grows with time. In the first part of the paper, the scaling phenomenology will be reviewed and the time-dependence of the coarsening scale will be discussed in the context of a number of different physical systems and scaling regimes. In the second part, the influence of an external drive, in particular a shear flow, will be addressed and recent developments reviewed. Interesting open questions include the late-time behaviour under shear and whether the coarsening continues indefinitely or is ultimately arrested by the shear flow.
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Affiliation(s)
- A J Bray
- Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
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Nagaya T, Gilli JM. Experimental study of coarsening dynamics of the zigzag wall in a nematic liquid crystal with negative dielectric anisotropy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:051708. [PMID: 12059578 DOI: 10.1103/physreve.65.051708] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2001] [Indexed: 05/23/2023]
Abstract
When a homeotropically aligned nematic liquid crystal cell is placed above two permanent magnets forming a magnetic quadrupole, a straight splay-bend wall, or a so-called Ising wall, is formed. With a material of positive dielectric anisotropy, it has been shown that the application of an electric field perpendicular to the plates leads to a zigzag instability of the wall, exclusively related to the elastic anisotropy of the liquid crystal. In this case, the coarsening process of the zigzag is very slow, which in turn leads to experimental difficulties concerning its quantitative investigation. If a material of negative dielectric anisotropy is used under an electric field with low voltage and low frequency, two convective rolls appear along the Ising wall due to the charge focusing effect, which is also responsible, at a higher voltage in the homogenous tilted regions, for the appearance of Williams domains electrohydrodynamic instability. If the voltage is higher than a threshold value, the straight Ising wall spontaneously breaks into a zigzag shape and a fast coarsening of the zigzag proceeds, associated with the annihilation of two neighboring vertices. In the present paper, the coarsening dynamics of this system, which can be considered as a one-dimensional Ising situation, are investigated experimentally. At late times, the average width of the zigzag increases logarithmically with time. This finding is consistent with the theory and also with the numerical simulation of a one-dimensional Cahn-Hilliard situation having a conserved order parameter. The scaling analysis of size distribution of the Ising domain, the shape of the power spectrum, and of the correlation function of the Ising order parameter, as well as the number density correlation functions of kinks also confirms that the dynamical scaling law predicted for one-dimensional conservative systems holds for the coarsening process. As supposed from symmetry arguments, it is confirmed that this experiment constitutes a one-dimensional analog of spinodal decomposition.
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Affiliation(s)
- Tomoyuki Nagaya
- Faculty of Education, Okayama University, 3-1-1 Tsushimanaka Okayama, 700-8530, Japan.
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18
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Boyer D, Viñals J. Grain boundary pinning and glassy dynamics in stripe phases. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:046119. [PMID: 12005938 DOI: 10.1103/physreve.65.046119] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2001] [Indexed: 05/23/2023]
Abstract
We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the nonadiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value R(g) approximately lambda(0)epsilon(-1/2)exp(absolute value of a/square root of epsilon), where epsilon<<1 is the dimensionless distance away from threshold, lambda(0) the stripe wavelength, and a a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.
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Affiliation(s)
- Denis Boyer
- School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306-4120, USA
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19
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Brown G, Rikvold PA. Numerical confirmation of late-time t(1/2) growth in three-dimensional phase ordering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:036137. [PMID: 11909195 DOI: 10.1103/physreve.65.036137] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2001] [Indexed: 05/23/2023]
Abstract
Results for the late-time regime of phase ordering in three dimensions are reported, based on numerical integration of the time-dependent Ginzburg-Landau equation with nonconserved order parameter at zero temperature. For very large systems (700(3)) at late times, t> or =150, the characteristic length grows as a power law, R(t) approximately t(n), with the measured n in agreement with the theoretically expected result n=1/2 to within statistical errors. In this time regime R(t) is found to be in excellent agreement with the analytical result of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. 49, 1223 (1982)]. At early times, good agreement is found between the simulations and the linearized theory with corrections due to the lattice anisotropy.
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Affiliation(s)
- Gregory Brown
- School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306-4120, USA.
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20
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Dierking I. Domain Growth Scaling at the Isotropic-to-Cholesteric Liquid Crystal Transition. J Phys Chem B 2000. [DOI: 10.1021/jp002337t] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- I. Dierking
- Department of Physics, Division of Microelectronics and Nanoscience, Chalmers University of Technology, S-41296 Göteborg, Sweden
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21
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Cavagna A, Bray AJ, Travasso RD. Ohta-jasnow-kawasaki approximation for nonconserved coarsening under shear. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:4702-4719. [PMID: 11089010 DOI: 10.1103/physreve.62.4702] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2000] [Indexed: 05/23/2023]
Abstract
We analytically study coarsening dynamics in a system with nonconserved scalar order parameter, when a uniform time-independent shear flow is present. We use an anisotropic version of the Ohta-Jasnow-Kawasaki approximation to calculate the growth exponents in two and three dimensions: for d=3 the exponents we find are the same as expected on the basis of simple scaling arguments, that is, 3/2 in the flow direction and 1/2 in all the other directions, while for d=2 we find an unusual behavior, in that the domains experience an unlimited narrowing for very large times and a nontrivial dynamical scaling appears. In addition, we consider the case where an oscillatory shear is applied to a two-dimensional system, finding in this case a standard t(1/2) growth, modulated by periodic oscillations. We support our two-dimensional results by means of numerical simulations and we propose to test our predictions by experiments on twisted nematic liquid crystals.
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Affiliation(s)
- A Cavagna
- Department of Physics and Astronomy, The University, Oxford Road, Manchester M13 9PL, United Kingdom
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22
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Rapapa NP, Bray AJ. Corrections to scaling in the phase-ordering dynamics of a vector order parameter. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:1181-8. [PMID: 11969878 DOI: 10.1103/physreve.60.1181] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/1999] [Indexed: 11/07/2022]
Abstract
Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal time pair correlation function has the form C(r,t)=f0(r/L)+L(-omega)f1(r/L)+., where L is the coarsening length scale. The correction-to-scaling exponent omega and the correction-to-scaling function f1(x) are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general omega is a nontrivial exponent which depends on both the dimensionality d of the system and the number of components n of the order parameter. Corrections to scaling are also calculated for the nonconserved one-dimensional XY model, where an exact solution is possible.
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Affiliation(s)
- N P Rapapa
- Department of Physics and Astronomy, The University, Manchester M13 9PL, United Kingdom
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23
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Wang W, Shiwaku T, Hashimoto T. Experimental study of dynamics of topological defects in nematic polymer liquid crystals. J Chem Phys 1998. [DOI: 10.1063/1.475532] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Majumdar SN, Sire C. Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model. PHYSICAL REVIEW LETTERS 1996; 77:1420-1423. [PMID: 10063074 DOI: 10.1103/physrevlett.77.1420] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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26
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Kim B, Lee SJ, Lee JR. Coarsening dynamics of field-induced inversion domain walls in smectic-C films. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:6061-6066. [PMID: 9964965 DOI: 10.1103/physreve.53.6061] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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27
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Rojas F, Bray AJ. Structure factor tail for the ordering kinetics of nonconserved systems without topological defects. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:4686-4695. [PMID: 9964796 DOI: 10.1103/physreve.53.4686] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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28
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Yeung C, Rao M, Desai RC. Bounds on the decay of the autocorrelation in phase ordering dynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:3073-3077. [PMID: 9964613 DOI: 10.1103/physreve.53.3073] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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29
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Majumdar SN, Sengupta AM. Nonequilibrium dynamics following a quench to the critical point in a semi-infinite system. PHYSICAL REVIEW LETTERS 1996; 76:2394-2397. [PMID: 10060686 DOI: 10.1103/physrevlett.76.2394] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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30
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Sire C, Majumdar SN. Coarsening in the q-state Potts model and the Ising model with globally conserved magnetization. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:244-254. [PMID: 9963428 DOI: 10.1103/physreve.52.244] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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31
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Majumdar SN, Huse DA. Growth of long-range correlations after a quench in phase-ordering systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:270-284. [PMID: 9963430 DOI: 10.1103/physreve.52.270] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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32
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Rutenberg AD, Bray AJ. Energy-scaling approach to phase-ordering growth laws. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:5499-5514. [PMID: 9963283 DOI: 10.1103/physreve.51.5499] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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33
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Sire C, Majumdar SN. Correlations and coarsening in the q-state Potts model. PHYSICAL REVIEW LETTERS 1995; 74:4321-4324. [PMID: 10058471 DOI: 10.1103/physrevlett.74.4321] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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34
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Bray AJ, Derrida B. Exact exponent lambda of the autocorrelation function for a soluble model of coarsening. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:R1633-R1636. [PMID: 9962943 DOI: 10.1103/physreve.51.r1633] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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35
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Majumdar SN, Huse DA, Lubachevsky BD. Growth of long-range correlations after a quench in conserved-order-parameter systems. PHYSICAL REVIEW LETTERS 1994; 73:182-185. [PMID: 10056750 DOI: 10.1103/physrevlett.73.182] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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36
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Alexander FJ, Huse DA, Janowsky SA. Dynamical scaling and decay of correlations for spinodal decomposition at Tc. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:663-667. [PMID: 9975727 DOI: 10.1103/physrevb.50.663] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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37
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Pargellis AN, Green S, Yurke B. Planar XY-model dynamics in a nematic liquid crystal system. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:4250-4257. [PMID: 9961717 DOI: 10.1103/physreve.49.4250] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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38
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Chuang I, Yurke B, Pargellis AN, Turok N. Coarsening dynamics in uniaxial nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:3343-3356. [PMID: 9960387 DOI: 10.1103/physreve.47.3343] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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