Effect of layer charge on chemical and physical properties of synthetic K-fluorine micas

The original publication is available at www.springerlink.com.ArticleJOURNAL OF MATERIALS SCIENCE. 40(21): 5597-5602 (2005)journal articl

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure

Tightness of slip-linked polymer chains

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops which can exchange length between each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip-links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.Comment: 10 pages, 6 figures, REVTeX

Two-stage directed self-assembly of a cyclic [3]catenane.

Interlocked molecules possess properties and functions that depend upon their intricate connectivity. In addition to the topologically trivial rotaxanes, whose structures may be captured by a planar graph, the topologically non-trivial knots and catenanes represent some of chemistry's most challenging synthetic targets because of the three-dimensional assembly necessary for their construction. Here we report the synthesis of a cyclic [3]catenane, which consists of three mutually interpenetrating rings, via an unusual synthetic route. Five distinct building blocks self-assemble into a heteroleptic triangular framework composed of two joined Fe(II)3L3 circular helicates. Subcomponent exchange then enables specific points in the framework to be linked together to generate the cyclic [3]catenane product. Our method represents an advance both in the intricacy of the metal-templated self-assembly procedure and in the use of selective imine exchange to generate a topologically complex product.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) and a Marie Curie fellowship for J.J.H. (ITN-2010–264645). The authors thank the Diamond Light Source (UK) for synchrotron beamtime on I19 (MT7984 and MT8464).This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/nchem.220