Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-23T12:37:09.278Z Has data issue: false hasContentIssue false
  • English
  • Français

Hierarchical Structures that Arise from Self-Assembling Systems

Published online by Cambridge University Press:  21 February 2011

Edmund A. Di Marzio
Edmund A. Di Marzio*
Affiliation:
National Institute of Standards and Technology Gaithersburg, MD 20899
Get access

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.

Keywords

hierarchyself-assemblyphase transitionscoupled transitionscollective variables.
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 255: Symposium Z – Hierarchically Structured Materials , 1991 , 333
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Footnotes

[1] See discussion of Eigen, M. and Winkler, R., in Laws of the Game, (Alfred A. Knopf Publishers, New York, 1981), pp 190–196. Also M. Gardner in Mathematical Games, Scientific American (Oct. 1970 and Feb. 1971).Google Scholar
[2] Baer, Eric (private communication).Google Scholar
[3] If the nth derivative of the fundamental relation (free energy) is discontinuous but the previous n-i derivatives are continuous then the transition is nth order.Google Scholar
[4] Briehl, R. W. and Herzfeld, J., Pro. Nat. Acad. Sci. USA, 26 2740 (1979): J. Herzfeld, J. Chem. Phys. 26, 4185 (1982).Google Scholar
[5] Mandelbrot, B. B., The Fractal Geometry of Nature, (W. H. Freeman, San Francisco, 1982).Google Scholar
[6] Levi-Civita, T., The Absolute Differential Calculus, (Blackie and Son, London, 1950). p9.Google Scholar
[7] Callen, H., Thermodynamics, (J. Wiley and Sons, New York, 1960).Google Scholar
[8] Zwanzig, R., in Lectures in Theoretical Physics, edited by Brittin, W. E., Downs, W. B. and Downs, J., (Interscience, New York, 1961).Google Scholar
[9] Mori, H., Progress Theor. Phys. (Kyoto), 33, 423 (1965).Google Scholar
[10] Haken, H., Synergetics, (Springer-Verlag, Berlin, 1977).Google Scholar
[11] Quoted on p 402 of Reference 5.Google Scholar