Session P21: Soft Tribute to John Cahn

The Legacy of John W. Cahn

The soft materials community has a number of consequential intersections with John Cahn's long effort in materials theory and modeling. I have been assigned the challenging task of representing the remainder of John's influence on materials research, that is, on "hard materials." John's impact is so large and diverse in this space that the task is gloriously doomed to failure. Instead I will try and provide a brief taste of John's career, particularly his time at NIST, and hopefully shed light on John's motivations to develop some of his ideas, and how those ideas often anticipated or underpinned entire sub-disciplines of theoretical and computational materials science, especially as they motivated my own research in mesoscale materials modeling.   

Reconciliation of Cahn-Hilliard predictions for spinodal decomposition lengthscales in polymer blends

Spinodal decomposition (SD) of partially miscible polymer blends can yield well-defined nanostructures with prescribed lengthscales and connectivity, and applications ranging from membranes and scaffolds to photovoltaics. Cahn-Hilliard-Cook (CHC) theory estimates the initial, dominant SD wavenumber to be $q_m=\sqrt{\frac{G''}{4k}}$, where $G''$ is the second derivative of the free energy of mixing with respect to concentration and $k$ is a structural parameter which can be computed from the segment lengths and volumes of monomer units. Tuning $G''$, with quench depth into the two phase region, for instance, should thus provide a facile and precise means for designing polymeric bicontinuous structures. The fulfillment of this potential rests on the thermodynamics of available polymer systems, coarsening kinetics, as well as engineering constraints. We extensively review experimental measurements of $G''$ in both one- and two-phase blend systems, and critically examine the accuracy of this fundamental prediction against achievements over the past 4 decades of polymer blend demixing. Despite widespread misconceptions in detecting and describing SD, we find the CHC relation to be remarkably accurate and conclude with design considerations and limitations for polymer nanostructures via SD, reflecting on John Cahn's contributions to the field.   

Liquid Quasicrystals

Following the discovery of quasicrystals by Shechtman and Cahn in 1984$^{\mathrm{1}}$, for the following 20 years the new field of QCs was confined to metal alloys and atomic-scale structures. Then, with the discovery of a liquid crystal phase possessing dodecagonal QC symmetry$^{\mathrm{2}}$], research interest has extended from metal alloys to those where the motifs were no longer single atoms but assemblies of many molecules. In dendron-based liquid quasicrystals (LQC) between 10-50 molecules form a supramolecular sphere with 10$^{\mathrm{3}}$ -- 10$^{\mathrm{4}}$ atoms. In 2007 a 2-d quasiperiodic phase was found in three-arm star ABC polymers$^{\mathrm{3}}$. In 2012 the first linear diblock copolymer was reported to form a sphere-based bulk QC phase, similar to that in dendrimer LQC but on a still larger scale$^{\mathrm{4}}$. In the same year bulk QC domains were reported in ``hard'' nanoporous silica, produced however, again from a ``soft'' lyotropic template$^{\mathrm{5}}$. The symmetry of all confirmed soft QCs so far is 12-fold. Another important development in soft QCs is the observation of complex QC approximants in a number of side-branched polyphilic LC honeycombs, described by multicolour tilings$^{\mathrm{6,7}}$. In fact, recently we found a genuine dodecagonal QC in such systems, the first example of a 2D LQC. Furthermore, we succeeded in direct AFM imaging of the \textit{xy} plane of a dendrimer LQC. The images confirm the ``half-step'' inflation rule, proposed earlier$^{\mathrm{7}}$ but not confirmed until now. (1) D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, \textit{PRL} 1984, \textbf{53}, 1951. (2) X.B. Zeng et al, \textit{Nature} 2004, \textbf{428}, 157. (3) K. Hayashida, et al. \textit{PRL }2007, \textbf{98}, 195502. (4) J. Zhang, F. Bates, \textit{J. Am. Chem. Soc.} 2012, \textbf{134}, 7636. (5) C. Xiao et al \textit{Nature} 2012, \textbf{487}, 349. (6) B. Chen et al \textit{Science} 2005, \textbf{307}, 96. (7) X.B. Zeng et al \textit{Science} 2011, \textbf{331}, 1302. X.B. Zeng and G. Ungar, \textit{Phil. Mag. }2006 \underline {86} 1093.   

Softening and Hardening Mechanisms in Dislocation-Enabled Plasticity

For over half a century, dislocation theories of plasticity have been largely phenomenological; they have not been able to provide predictive first-principles explanations of basic phenomena such as strain hardening or dynamic failure. In this talk, I will summarize the main features of a statistical thermodynamic theory of dislocation-enabled plasticity. This theory now seems to be addressing many of the the central issues successfully. If time permits, I will show how it predicts runaway shear banding instabilities that are observed experimentally.   

Small Angle Neutron Scattering Study in Multi-Component Polymer Systems: Spinodal Decomposition and Beyond

Institute for Advanced Study, Shenzhen University, Shenzhen, China In memory of Professor John Kohn at this symposium, a time resolved SANS study for the early stage of spinodal decomposition kinetics of deuterated polycarbonate/poly(methylmethacrylate) blend will be reviewed which gives a clear proof of the Cahn-Hillard-Cook theory. This early stage of spinodal decomposition kinetics has been observed starting from the dimension (q$^{\mathrm{-l}})$ comparable to the single chain radius of gyration, R$_{\mathrm{g\thinspace }}$, for a binary polymer mixture. The results provide an unequivocal quantitative measure of the virtual structure factor, S (q, $\infty $ ); the relationship of q$_{\mathrm{m}}$ and q$_{\mathrm{c}}$ through rate of growth, Cahn-plot analysis, and singularity in S (q, $\infty $ ); the growth of fluctuation of qR$_{\mathrm{g}}$ \textless 1 and intra-chain relaxation of qRg \textgreater 1. More recent study of using mixed suspensions of polystyrene microspheres and poly(N-isopropylacrylamide) microgels as a molecular model system which has a long range repulsive interaction potential and a short range attractive potential, will also be discussed. In this model system, dynamic gelation, transition to soft glass state and cross-over to hard glass state will be demonstrated and compared with available theories for glass transition in structural materials. Acknowledgements go to: Polymers Division, and NCNR of NIST, and to ICCAS, Beijing, China. Also to my colleagues: M. Motowoka, H. Jinnai, T. Hashimoto, G.C. Yuan and H. Cheng