Hierarchical Structures that Arise from Self-Assembling Systems
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HIERARCHICAL STRUCTURES THAT ARISE FROM SELF-ASSEMBLING SYSTEMS
Edmund A. Di Marzio National Institute of Standards and Technology Gaithersburg, MD 20899 ABSTRACT A working definition of the term hierarchy that is consistent with past usage is that a hierarchy is an assemblage of assemblages. Self-assembling systems are essential to those hierarchical structures that contain structure on micro and nano distance scales since these tiny structures being so large in number can not be manipulated individually as is possible for larger structures. It is shown how self-assembling structures are nothing more than materials that have undergone a structure inducing phase transition. The induced structures can be either equilibrium structures (example lamellar block copolymers) or kinetic patterns (example snowflakes). Polymer systems provide a rich source of phase transitions. There are at least ten classes of polymer phase transitions. [1] helixrandom coil [2) polymerization or one-dimensional crystallization [3] adsorption [4] collapse transition [5] coilfstretch transition [6] liquidliquid transitions [7] crystallization [8] liquid crystals-plastic crystals [9] glass-amorphous and sol-gel transitions [10] soaps-membranes-micellesvesicles-block copolymers. These phase transitions can interact with each other creating an even richer overlay of self-assembled systems. We discuss three aspects of the building of Hierarchical structures from selfassembling systems. key words: hierarchy, self-assembly, transitions, collective variables. I:
phase transitions,
coupled
SOME DEFINITIONS
In this work we shall discuss the relationship of self-assembled systems to hierarchical structures. Because of the newness of the field and because of the lack of precision in the meaning of the terms we will begin with definitions of these terms and of related concepts. Hierarchical structures are part of a general area of study known as complexity physics which we now describe. For many years the thrust in science was to derive the basic laws. The unstated assumption was that once the basic laws were known the job of the physicist was essentially completed. However, now that the basic laws are known we see that nothing could be further from the truth. The path from the simple laws to those complex entities which we wish to understand is a tortuous one and is the subject of complexity physics. The science of complexity (or complexity physics) is defined as the study of how simple laws lead to complex entities. An incomplete list of problems in complexity physics contains the items self-assembly and hierarchical structures. [1] Cellular Automata [2] Symmetry Breaking [3] Self-organization [4] Self-Assembly [5] Synergetics [6] Hierarchical Structures [7] Emergent Reality [8] Pattern Formation [9] Non-Linear Equations, Limit Cycles, Strange Attractors, Solitons [10] Deterministic Chaos, AntiChaos [11] Neural Nets [12] Kauffman Nets [13] Localization [15] Frustration [16] Fractals [17] Autocatalysis [18] Symbiosis, Chemotaxis [19] Evolution: The
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