Anomalous Dynamics of Forced Translocation

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N^2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (sub-diffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N^2 and N^{1+\nu}, respectively, where \nu is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).Comment: 13 pages, RevTeX4, 16 eps figure

A Palladium-oxo complex. Stabilization of this proposed catalytic intermediate by an encapsulating polytungstate ligand

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Terminal gold-oxo complexes

In contradiction to current bonding paradigms, two terminal Au-oxo molecular complexes have been synthesized by reaction of AuCl3 with metal oxide-cluster ligands that model redox-active metal oxide surfaces. Use of K10[alpha2-P2W17O61].20H2O and K2WO4 (forming the [A-PW9O34]9- ligand in situ) produces K15H2[Au(O)(OH2)P2W18O68].25H2O (1); use of K10[P2W20O70(OH2)2].22H2O (3) produces K7H2[Au(O)(OH2)P2W20O70(OH2)2].27H2O (2). Complex 1 crystallizes in orthorhombic Fddd, with a=28.594(4) A, b=31.866(4) A, c=38.241(5) A, V=34844(7) A3, Z=16 (final R=0.0540), and complex 2 crystallizes in hexagonal P6(3)/mmc, with a=16.1730(9) A, b=16.1730(9) A, c=19.7659(15) A, V=4477.4(5) A3, Z=2 (final R=0.0634). The polyanion unit in 1 is disorder-free. Very short (approximately 1.76 A) Au-oxo distances are established by both X-ray and 30 K neutron diffraction studies, and the latter confirms oxo and trans aqua (H2O) ligands on Au. Seven findings clarify that Au and not W is present in the Au-oxo position in 1 and 2. Five lines of evidence are consistent with the presence of d8 Au(III) centers that are stabilized by the flanking polytungstate ligands in both 1 and 2: redox titrations, electrochemical measurements, 17 K optical spectra, Au L2 edge X-ray absorption spectroscopy, and Au-oxo bond distances. Variable-temperature magnetic susceptibility data for crystalline 1 and 2 establish that both solids are diamagnetic, and 31P and 17O NMR spectroscopy confirm that both remain diamagnetic in solution. Both complexes have been further characterized by FT-IR, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and other techniques