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2022 | Book

Introduction to Soft Matter Read chapter Read first chapter

Generalized Dynamics of Soft-Matter Quasicrystals

Mathematical Models, Solutions and Applications

Authors: Prof. Tian-You Fan, Dr. Wenge Yang, Dr. Hui Cheng, Prof. Xiao-Hong Sun

Publisher: Springer Nature Singapore

Book Series : Springer Series in Materials Science

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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About this book

This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

Table of Contents

Frontmatter
Chapter 1. Introduction to Soft Matter
Abstract
Soft-matter quasicrystals are observed in liquid crystals, colloids, polymers, and surfactants, etc., which brings new family members to soft matter with crystallographic forbidden symmetry. Soft matter is a type of common material, introduced by Gennes (Angw Chem 31:842–845, 1992) in 1991, including liquid crystals, colloids, polymers, foams, emulsions, surfactants, biomacromolecules, etc. They are neither ideal solid nor simple fluid, but presents characteristics of both solid and fluid, and belongs to an intermediate phase between isotropic fluid and ideal solid macroscopically.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 2. Discovery of Soft-Matter Quasicrystals and Their Properties
Abstract
Quasicrystals have long-range orientational order but no translational symmetry. As a consequence, sharp diffraction spots can occur but are unable to be described by 230 crystallographic space groups in both real and reciprocal spaces. There are three types of quasicrystals: one-, two- and three-dimensional quasicrystals. In one-dimensional quasicrystals, the quasiperiodic arrangement of atoms is along one direction, while the plane perpendicular to which has a regular two-dimensional periodic arrangement.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 3. Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals
Abstract
Elasticity and hydrodynamics of solid quasicrystals are the basis of the dynamics of soft-matter quasicrystals. A brief review of these topics is given in this chapter, which may be beneficial for understanding the dynamics of soft-matter quasicrystals.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 4. Case Study of Equation of State in Several Structured Fluids
Abstract
Equation of state, i.e., the equation connecting pressure and mass density referred here, is one of the fundamental properties for all condensed matter.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 5. Poisson Brackets and Derivation of Equations of Motion in Soft-Matter Quasicrystals
Abstract
Previous chapters provided basic concepts of soft-matter quasicrystals. For practice, we need to establish the equations of motion of the matter, then one can give a quantitative description of their structures and dynamic properties.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 6. Oseen Theory and Oseen Solution
Abstract
In previous chapters, we introduced the physics and mathematics background for studying soft-matter quasicrystals. Like general soft matter, the soft-matter quasicrystals are complex liquids or structured liquids, so the knowledge on conventional liquid dynamics provides the base for further study on soft-matter quasicrystals. In this chapter, we will focus on basic knowledge about liquid dynamics especially the Oseen theory.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 7. Dynamics of Soft-Matter Quasicrystals with 12-Fold Symmetry
Abstract
The discussion in the first 6 chapters provides preparation for the subsequent study. We aim to explore the structures and dynamic properties of soft-matter quasicrystals.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 8. Dynamics of 10-Fold Symmetrical Soft-Matter Quasicrystals
Abstract
In Chap. 7 we discussed the dynamics of soft-matter quasicrystals with 12-fold symmetry observed in liquid crystals, polymers, colloids, and so on. There are some other quasicrystals, e.g., 10-fold symmetry quasicrystals that have been observed but not yet reported, the symmetry of which is similar to that of the 12-fold symmetry quasicrystals, and they also belong to the first type of two-dimensional quasicrystals. This chapter discusses the soft-matter quasicrystals with 10-fold symmetry. The quasicrystal system exhibits some characteristics, for example, a strong coupling between phonons and phasons for these quasicrystals, which is very interesting.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 9. Dynamics of 8-Fold Symmetric Soft-Matter Quasicrystal Models
Abstract
Apart from the observed 12-, 18-, and 10-fold symmetric soft-matter quasicrystals, the 8-fold symmetric soft-matter quasicrystals are plausible to be observed soon. With the consideration of the angles and symmetry, the 8-fold symmetric quasicrystals exhibit similarities with their 5-, 10-, and 12-fold symmetric equivalents.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 10. Dynamics of 18-Fold Symmetric Soft-Matter Quasicrystals
Abstract
The discovery of 18-fold symmetric quasicrystals in colloids by Fischer et al. [1] raised broad fundamental importance. They are topologically different from the previous reports on pentagonal, decagonal, octagonal, and dodecagonal solid quasicrystals and the dodecagonal and decagonal soft-matter quasicrystals.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 11. The Possible 7-, 9-, and 14-fold Symmetry Quasicrystals in Soft Matter
Abstract
The possible 7-, 9-, and 14-fold symmetry quasicrystals are similar to those of 18-fold symmetry, and belong to the second kind of two-dimensional quasicrystals, in which the possible 7- and 14-fold symmetry quasicrystals are more interesting because the phonons and second phasons are coupled apart from the coupling between the first and second phasons.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 12. Re-Discussion on Symmetry Breaking and Elementary Excitations
Abstract
In the first 11 chapters, to establish the generalized dynamics theory of soft-matter quasicrystals, we used the general concepts from the conservation laws and symmetry breaking principle. Based on that some applications have been successfully demonstrated in Chaps. 7–11 via solving the initial- or boundary- or initial and boundary-condition problems of the governing equations of the dynamics.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 13. An Application to the Thermodynamic Stability of Soft-Matter Quasicrystals
Abstract
In Chaps. 7–11 we discussed several quasicrystal systems in soft matter, in which these quasicrystals must be stable thermodynamically, but the validity of this stability is held under certain conditions.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 14. Applications to Device Physics—Photon Band Gap of Holographic Photonic Quasicrystals
Abstract
The most attractive aspect of the application of soft-matter quasicrystals may be in photon band gap. The soft-matter quasicrystals observed so far are two-dimensional structures with quasiperiodic symmetry, and higher fold of orientational symmetry being greater than that of solid one appeared, there is superiority than solid quasicrystals in this respect.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 15. Possible Applications to General Soft Matter
Abstract
In Chaps. 7–11, we have introduced the dynamics of soft-matter quasicrystals from a unified point of view, where the quasiperiodic symmetry has been specially considered for quasicrystal applications in soft matter, such as liquid crystals, polymers, colloids, nanoparticles, surfactants, and macromolecules, etc.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 16. An Application to Smectic A Liquid Crystals, Dislocation, and Crack
Abstract
In the previous chapter, we discuss general soft matter using the theory and method developed for solving soft-matter quasicrystals, where we emphasized one must consider the structure of concrete soft matter. In this chapter, we study a concrete soft matter, i.e., the smectic A liquid crystal and its dislocation and crack problem. These are interesting topics in soft matter. Apart from this, we hope to explore a longstanding puzzle, perhaps a paradox. The solution to the paradox may yield some beneficial results and lessons.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Chapter 17. Conclusion Remarks
Abstract
The modification and supplementary contents in the new edition have been introduced in the text.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
18. Correction to: Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals
Abstract
.
Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
Metadata
Title
Generalized Dynamics of Soft-Matter Quasicrystals
Authors
Prof. Tian-You Fan
Dr. Wenge Yang
Dr. Hui Cheng
Prof. Xiao-Hong Sun
Copyright Year
2022
Publisher
Springer Nature Singapore
Electronic ISBN
978-981-16-6628-5
Print ISBN
978-981-16-6627-8
DOI
https://doi.org/10.1007/978-981-16-6628-5

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