ChemInform Abstract: The Crystal Structures of m,o‐Ce3Pt4Sn6 and Ce1‐xPt6Al13+2x.

Single crystals of Ce₃Pt₄Sn₆ (I) and Ce_1‐xPt₆Al_13+2x (x = 0.207, (II)) are isolated by mechanical fragmentation of specimens grown from self‐fluxes (Sn or Al, resp.) by slow cooling from the melt.     

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a “satellite position” at a distance q from each Bragg peak; that (2) has an intensity that scales with the intensity of the corresponding Bragg peak; (3) falls off as 1/q²; and (4) has a time decay constant that is proportional to 1/Dq². It is thus superfluous to call for a picture of “phason waves” in order to explain such data, especially as such “waves” violate many physical principles.     

Towards finite-dimensional gelation

We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the replicated and crosslink-averaged model as an effective molecular fluid. A Mayer-cluster expansion for moments of the local static density fluctuations is set up. The simplest non-trivial contribution to this series leads back to mean-field theory. The central quantity of mean-field theory is the distribution of localization lengths, which we compute for all connectivities. The highly crosslinked gel is characterized by a one-to-one correspondence of connectivity and localization length. Taking into account higher contributions in the Mayer-cluster expansion, systematic corrections to mean-field can be included. The sol-gel transition shifts to a higher number of crosslinks per particle, as more compact structures are favored. The critical behavior of the model remains unchanged as long as finite truncations of the cluster expansion are considered. To complete the picture, we also discuss various geometrical properties of the crosslink network, e.g. connectivity correlations, and relate the studied crosslink ensemble to a wider class of ensembles, including the Deam-Edwards distribution. Received on 24 April 2002 Published online 14 October 2002 RID="a" ID="a"deceased RID="b" ID="b"e-mail: weigt@theorie.physik.uni-goettingen.de     

Polymer adsorption on heterogeneous surfaces

The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55, 226 (1997)). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain. Received: 29 October 1997 / Revised: 19 December 1997 / Accepted: 6 March 1998