DOI: 10.1021/la9016245 A Langmuir XXXX, XXX(XX), XXX–XXX pubs.acs.org/Langmuir © XXXX American Chemical Society Theoretical Issues Relating to Thermally Reversible Gelation by Supermolecular Fiber Formation † Jack F. Douglas* Polymers Division, NIST, Gaithersburg, Maryland 20899 Received May 6, 2009 Existing models of the thermodynamics and dynamics of self-assembly are summarized to provide a context for discussing the difficulties that arise in modeling supermolecular fiber assembly and the formation of thermally reversible gels through fiber growth and branching. Challenging problems in this field, such as the physical origin of fibers of uniform diameter and fiber twisting, the kinetics of fiber growth, the hierarchical bundling of fibers into “superfibers”, fiber branching, gelation through fiber impingement and the associated phenomenon of fractal fiber network and spherulite formation, and the origin and control of structural polymorphism in the fiber and superfiber geometry, are discussed from a personal perspective. Suggestions are made for integrating current research efforts into a more coherent multiscale description of fiber formation and gelation on molecular, mesoscopic, and macroscopic scales. Introduction The theoretical description of supermolecular self-assembly is limited to rather simple models such as linear and branched polymers or model compact structures such as spherical micelles and equilibrium vesicles. There has also been recent interest in modeling viral capsid and other protein shells such as clathrin in which proteins organize at equilibrium through the association and dissociation of monomers into “polymeric” cages. Wormlike micelles have been successfully modeled as a kind of equilibrium polymerization, 20 but some evidence indicates that a sequential or nucleated assembly can be involved (see below). Specifically, Douglas et al. 1 have shown theoretically that this type of activated assembly can alter the “cooperativity” of the self-assembly transi- tion (quantifying the extent to which the self-assembly thermo- dynamic transition approaches a true phase transition) from simple equilibrium polymerization models that simply assume the unconstrained reversible association of molecules or particles into polymer chains. This type of a sequential or “activated” assembly is common in the formation of complex biological structures such as clathrin protein cages involved in endocytosis and the capsid shells of viruses. This phenenomenon has also been noted in small molecules that exhibit supermolecular chain assembly, 2 and much effort has recently been made to develop the theory of activated or chemically initiated self-assembly; a Supporting Information file provides an extended list of references related to this and other topics indirectly related to fiber assembly. Many supermolecular polymers and fibers form chiral structures, and an equilibrium polymerization model has been developed that allows for a thermodynamic transition of the assembled chains from an angularly uncorrelated to a helical state. Whereas these self-assembly models provide insight into the formation of fibers by self-assembly and their thermally reversible gelation, fiber assembly involves the confrontation of many additional effects, and the next section describes a personal perspective on the recent modeling of particular aspects of fiber self-assembly. Special Features of Fiber Self-Assembly Fiber formation 3,4 is evidently a kind molecular self-assembly, but the assembly of fibers exhibits distinct features from the equilibrium polymerization of linear and branched polymer chains. The molecules within the fiber cross-section are normally highly ordered locally, as in a crystal, but along the fiber axis there can be considerable fluctuations and branching as in synthetic and equilibrium polymers. Fiber growth thus seems to be a hybrid process that is somehow intermediate between equilibrium polymerization and the formation of ordinary crystallized struc- tures where 3D long-range molecular order exists over large distances. Gelation in assembled fiber systems is certainly a different physical process than the formation of macroscopic branched polymers through reversibly associating monomer units. This type of gel is often brittle and will break like a rigid solid rather than deform like a flexible rubbery material, or if they do not break, these stiff fiber networks strain stiffen rather than strain soften as in flexible polymer networks. Treatment of this type of self-assembly and the consequent gels formed from them requires the consideration of a whole series of basic theoretical questions. Why and How Fibers Form. First, how and why do fibers form in the first place? Then there is the question of what factors limit the diameter of the fibers, one of the more conspicuous features of this type of growth process. There have been several recent efforts to address these problems. The tendency of mole- cules and particles to form 1D polymeric structures is a natural consequence of having directional intermolecular potentials, as in fluids of magnetic nanoparticles and in nanoparticles such as CdSe quantum dots, which commonly have large electrical dipole moments. Dipolar interactions (or other highly directional inter- actions such a directional hydrogen bonding and π-π stacking interactions 5,6 ) are often involved, often in concert and in combi- nation with van der Waals and many-body “hydrophobic” † Part of the Molecular and Polymer Gels; Materials with Self-Assembled Fibrillar Networks special issue. (1) Douglas, J. F.; Dudowicz, J.; Freed, K. F. J. Chem. Phys. 2008, 128, 224901. (2) Jonkheijm, P.; van der Schoot, P; Schenning, A. P. H. J.; Meijer, E. W. Science 2006, 313, 80. (3) Terech, P.; Weiss, R. G. Chem. Rev. 1997, 97, 3133. (4) Molecular Gels: Materials with Self-Assembled Fibrillar Networks; Weiss, G., Terech, P., Eds.; Springer:The Netherlands, 2006. (5) Brunsveld, L.; Folmer, B. J. B.; Meijer, E. W.; Sijbesma, R. P. Chem. Rev. 2001, 101, 4071. (6) Sijbesma, R. P.; Beijer, F. H.; Brunsveld, L.; Folmer, B. J. B.; Ky Hirschberg, J. H. K.; Lange, R. F. M.; Lowe, J. K. L.; Meijer, E. W. Science 1997, 278, 1601.