Universal properties of relaxation and diffusion in complex materials: Originating from fundamental physics with rich applications

Complex materials are composed of basic units which invariably interact with anharmonic potentials. It is well known that the dynamics of systems with anharmonic interaction are governed by nonlinear Hamiltonian mechanics or chaos. Not known is whether irreversible processes including relaxation and diffusion in complex materials are also governed by chaos. In 1979 I explored this possibility by publishing a theoretical discourse entitled “Universality of low-frequency fluctuation, dissipation and relaxation properties of condensed matter. I” in Comments Solid State Phys. 9, 127 (1979). Based on the physics of chaos, the results from the paper and subsequent developments are general and ready to be used to predict various universal properties of relaxation and diffusion in complex materials with different chemical bonds/compositions and physical structures, and changes when dimension is reduced from bulk to nanometer dimensions. The theory and its predictions are now known as the Coupling Model (CM). The core prediction of the CM was verified subsequently by neutron scattering, light scattering, and molecular dynamics simulations. I recognized that the general predictions of the CM if applied to different processes in various materials have the potential of discovering universal properties and solving many problems in relaxation and diffusion encountered. Lured by the potential of the CM, I and collaborators started in 1979 the study of different processes in various complex materials with the purpose of discovering universal relaxation and diffusion properties. By virtue of its generally applicable predictions, the CM is instrumental in the search and discovery of the universal properties. The outcome of the 44 years of research effort is the collection of a voluminous amount of experimental data supporting the existence of the universal properties reported in this review in widely different relaxation and diffusion processes in diverse complex materials. The materials include: (1) hydrogen bonded and van der Waals molecular glass-forming liquids, mixtures, and glasses; (2) inorganic liquids and glasses; (3) amorphous polymers, polymer blends, polymer rheology and viscoelasticity; (4) semidilute polymer solutions; (5) colloids; (6) water and aqueous mixtures; (7) hydrated and solvated proteins, biomolecules and biopolymers; (8) pharmaceuticals; (9) carbohydrates; (10) solid state ionic conductors; (11) ionic liquids; (12) metallic alloys; (13) nanometer size materials; (14) surface and interface. Many of the universal properties are anomalous and left unexplained by mainstream theories, but all turn out to have explanations from the CM. The discovery of the universal properties expounded in the review is a significant advance in material science that has impact in many disciplines. It is amply and convincingly demonstrated by experimental and simulation data in diverse materials presented in hundreds of figures. Thus it alone should be considered a major advance in interdisciplinary scientific research, irrespective of the explanations given concurrently by the CM or by other theories in the future. Twelve years have gone by since the publication of the monograph entitled “Relaxation and Diffusion in Complex Systems, Springer, NY (2011)” by the author. Many new experimental and simulations data emerging in this period have repeatedly confirmed the universal properties, which constitute the bulk of evidences given in this review. The universal properties have impact on research and development of complex materials including pharmaceuticals, food science, proteins, biomolecules, biopolymers, nano science and technology, ionic liquids, fuel cells, portable energy source, polymers, glass science, and the applications and engineering of all these materials. The review is timely since the 2021 Nobel Prize in Physics was awarded "for groundbreaking contributions to our understanding of complex systems", and shared by Giorgio Parisi "for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales.“The universal properties made known in this review can be considered as complements of the theoretical accomplishment of Parisi. The huge collection of the universal properties in diverse materials assembled, correlated and rationalized altogether in this article serves to enhance the recognition of the existence of fundamental physical laws governing relaxation and diffusion in complex materials and systems, and to promote interest of others in the search for the origin.