A Universal Scaling Analysis of Nonisothermal Kinetics in Block Copolymer Phase Transitions

2013 ◽  
Vol 2 (8) ◽  
pp. 745-748 ◽  
Author(s):  
Julian D. Spring ◽  
Rama Bansil
Keyword(s):  
Phase Transitions ◽  
Block Copolymer ◽  
Scaling Analysis ◽  
Nonisothermal Kinetics ◽  
Universal Scaling

Phase Transitions in Thin Block Copolymer Films

MRS Bulletin ◽  
2010 ◽  
Vol 35 (6) ◽  
pp. 457-465 ◽  
Author(s):  
Edward J. Kramer
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Block Copolymer ◽  
Diblock Copolymer ◽  
Smectic Liquid Crystals ◽  
Material System ◽  
Thermal Generation ◽  
Copolymer Films ◽  
Bcc Structure ◽  
Line Defects

AbstractDavid Turnbull's experiments and theoretical insights paved the way for much of our modern understanding of phase transitions in materials. In recognition of his contributions, this lecture will concentrate on phase transitions in a material system not considered by Turnbull, thin diblock copolymer films. Well-ordered block copolymer films are attracting increasing interest as we attempt to extend photolithography to smaller dimensions. In the case of diblock copolymer spheres, an ordered monolayer is hexagonal, but the ordered bulk is body-centered cubic (bcc). There is no hexagonal plane in the bcc structure, so a phase transition must occur as n, the number of layers of spheres in the film, increases. How this phase transition occurs with nand how it can be manipulated is the subject of the first part of my presentation. In the second part of the talk, I show that monolayers of diblock copolymer spheres and cylinders undergo order-to-disorder transitions that differ greatly from those of the bulk. These ordered 2D monolayers are susceptible to phonon-generated disorder as well as to thermal generation of defects, such as dislocations, which, while they are line defects in 3D, are point defects in 2D. The results are compared to the theories of melting of 2D crystals (spheres) and of 2D smectic liquid crystals (cylinders), a comparison that will allow us to understand most, but not all, of the features of these order-disorder transitions that occur as the temperature is increased.

scholarly journals Decoherent quench dynamics across quantum phase transitions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Wei-Ting Kuo ◽  
Daniel Arovas ◽  
Smitha Vishveshwara ◽  
Yi-Zhuang You
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Excitation Density ◽  
Quench Rate ◽  
Translational Invariance ◽  
Dynamical Exponent ◽  
Universal Scaling ◽  
Quench Dynamics ◽  
Freeze Out

We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})}t-∼τ2νz/(1+2νz) for when the system falls out of equilibrium and the associated freeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})}ξ‾∼τν/(1+2νz) show power-law scaling with respect to the quench rate 1/\tau1/τ, where the exponents depend on the correlation length exponent \nuν and the dynamical exponent zz associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.

scholarly journals Finite- m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

2020 ◽  
Vol 101 (6) ◽  
Author(s):  
Hiroshi Ueda ◽  
Kouichi Okunishi ◽  
Kenji Harada ◽  
Roman Krčmár ◽  
Andrej Gendiar ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Scaling Analysis ◽  
Clock Model ◽  
Entanglement Spectrum

Universal Scaling of Alpha Relaxation in Complex Liquids

2001 ◽  
Vol 56 (12) ◽  
pp. 893-894 ◽  
Author(s):  
A. Kurbatov ◽  
A. Drozd-Rzoska ◽  
S. J. Rzoska ◽  
M. Paluch ◽  
P. Malik ◽  
...  
Keyword(s):  
Dielectric Loss ◽  
Dielectric Relaxation ◽  
Liquid Crystalline ◽  
Isotropic Phase ◽  
Scaling Analysis ◽  
Crystalline Materials ◽  
Universal Scaling ◽  
Molecular Glass ◽  
Complex Liquids ◽  
Liquid Crystalline Materials

Abstract A plot is given, showing the result of a scaling analysis of dielectric loss curves containing, apart from low molecular glass former data (glycerol, dibutyl phtalate), also loss curves of the following liquid crystalline materials, mostly in the iso­ tropic phase: 4-(2-methylbutyl)-4'cyanobiphenyl (5*CB, supercooled isotropic phase), 4-cyano-4-n-alkyl biphenyls (nematogens 5CB and 8CB, isotropic phase), 4-(4-cyano-4-butylcyclohexyl)-4'-octylbiphenyl (laterally substituted nema-togen, isotropic phase), and 4-n-alkyl-4'-isothiocyanatobiphe-nyl (5 and 10 BT, isotropic and SmE phases). The plot applies the scaling formula originally proposed for glassforming, super­ cooled liquids [Dendzik et al.7]. The result supports the recent suggestion that dielectric relaxation in the isotropic phase of nematogens may show some features typical for "glassy" mate­ rials.

scholarly journals UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS

2004 ◽  
Vol 18 (31n32) ◽  
pp. 3977-4118 ◽  
Author(s):  
SVEN LÜBECK
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Equilibrium Phase ◽  
Finite Size ◽  
Universality Class ◽  
Scaling Functions ◽  
Universal Scaling ◽  
Universality Classes ◽  
Non Equilibrium

Non-equilibrium critical phenomena have attracted a lot of research interest in the recent decades. Similar to equilibrium critical phenomena, the concept of universality remains the major tool to order the great variety of non-equilibrium phase transitions systematically. All systems belonging to a given universality class share the same set of critical exponents, and certain scaling functions become identical near the critical point. It is known that the scaling functions vary more widely between different universality classes than the exponents. Thus, universal scaling functions offer a sensitive and accurate test for a system's universality class. On the other hand, universal scaling functions demonstrate the robustness of a given universality class impressively. Unfortunately, most studies focus on the determination of the critical exponents, neglecting the universal scaling functions. In this work a particular class of non-equilibrium critical phenomena is considered, the so-called absorbing phase transitions. Absorbing phase transitions are expected to occur in physical, chemical as well as biological systems, and a detailed introduction is presented. The universal scaling behavior of two different universality classes is analyzed in detail, namely the directed percolation and the Manna universality class. Especially, directed percolation is the most common universality class of absorbing phase transitions. The presented picture gallery of universal scaling functions includes steady state, dynamical as well as finite size scaling functions. In particular, the effect of an external field conjugated to the order parameter is investigated. Incorporating the conjugated field, it is possible to determine the equation of state, the susceptibility, and to perform a modified finite-size scaling analysis appropriate for absorbing phase transitions. Focusing on these equations, the obtained results can be applied to other non-equilibrium continuous phase transitions observed in numerical simulations or experiments. Thus, we think that the presented picture gallery of universal scaling functions is valuable for future work. Additionally to the manifestation of universality classes, universal scaling functions are useful in order to check renormalization group results quantitatively. Since the renormalization group theory is the basis of our understanding of critical phenomena, it is of fundamental interest to examine the accuracy of the obtained results. Due to the continuing improvement of computer hardware, accurate numerical data have become available, resulting in a fruitful interplay between numerical investigations and renormalization group analyzes.

Sign in / Sign up

Export Citation Format

Share Document