The mössbauer effect: A potentially ideal probe into Brownian motion

We calculate the Mössbauer spectrum of nuclei embedded in spheres of radius on the order of 1 μm which are suspended in a liquid. We demonstrate that the Mössbauer effect is an ideal means for testing the deductions based upon a generalized Langevin equation which takes into account the effects of acceleration memory on the force and torque of the liquid on a sphere and for studying, generally, the detailed statistical dynamical behavior of Brownian particles. The spectrum is expressed in terms of an integral over an integrand consisting of standard functions. Experimental desiderata are discussed and a list of sample experimental parameters given.     

Structure of glassy polymers. VII. Small-angle X-ray scattering from epoxy resins

The small-angle x-ray scattering (SAXS) from an Epon 812 and two Epon 828 (one amine-cured and one anhydride-cured) epoxy resins has been measured using a Bonse-Hart system. The data cover the angular range (2θ) between 20 sec and 60 min. After correction for absorption, background and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a previously studied polycarbonate sample. The corrected absolute intensity decreases strongly with increasing angle between 20 sec and 2 min, decreases more gradually between 2 and 20–30 min, and reaches a nearly constant asymptotic value at larger angles. The magnitude of the intensity in the constant-intensity region is close to the value predicted by thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at angles smaller than 20–30 min is associated with heterogeneities in the cured resins. These heterogeneities cover a range of sizes in all samples, from less than 100 Å to more than 1000 Å, with the most frequently occurring size in the range 100–200 Å.     

A problem relating to positive linear maps on matrix algebras

In this paper we investigate conditions under which two finite-dimensional density matrices can be transformed simultaneously into two other ones by means of a positive linear map which maps density matrices into density matrices. The result of this paper provides a complete answer in case of the matrix algebra of two-by-two matrices.     

A Landau theory of the Peierls-BCS transition

We introduce a Landau type theory of the Peierls instability-superconductor transition involving two complex order parameters. Under a particular inequality condition among expansion parameters, the theory predicts that the superfluid conductivity should vary as $\text{(T?T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ above the critical region and as $\text{(T}{}^1{}_{\mathrm{<mtext>c</mtext>}}\text{?T)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ below the critical region.     

Octopolar chromophores based on donor- and acceptor-substituted 1,3,5-tris(phenylethynyl)benzenes: impact of meta-conjugation on the molecular and electronic structure by means of spectroscopy and theory

The molecular and electronic structures of a series of all-meta-substituted phenylacetylene mesitylenes peripherally substituted with donor or acceptor (D-A) groups are studied. The impact of meta- and para-substitution patterns is also analyzed by employing Raman and optical spectroscopies in conjunction with theoretical calculations. Outer phenyl rings display a partial quinoid character induced by two different motifs: (i) outer phenyls --> triple bond charge transfer for the cases where these phenyls are substituted with electron-donors; (ii) double electron withdrawing effect in the molecules with the peripheral phenyls substituted with electron acceptors. A moderate tuning of the optical gap is observed in agreement with the partial blockade of pi-electron conjugation exerted by the meta disposition. The orbital structure of the compounds partially preserves that of the mesitylene group showing extra-conjugation due to the addition of the arms, so that conjugation is not entirely obstructed but partially impeded in the ground electronic state (i.e., electron occupied orbitals). As for the excited states, the low-lying energy empty orbitals offer better conditions for full conjugation over the whole molecular scaffold. Interesting optical properties such as overlapping centers along the lowest energy optical excitations and enhanced optical transparency with importance for the application of these materials in optoelectronics have been justified on the basis of the electronic structure. A greater degree of quinoidization, and more allowed pi-electron delocalization, over the entire molecule is recognized in the case of linear phenylacetylenes substituting in para positions the central core.     

Localized electropolymerization on oxidized boron-doped diamond electrodes modified with pyrrolyl units

This paper describes the functionalization of oxidized boron-doped diamond (BDD) electrodes with N-(3-trimethoxysilylpropyl)pyrrole (TMPP) and the influence of this layer on the electrochemical transfer kinetics as well as on the possibility of forming strongly adhesive polypyrrole films on the BDD interface through electropolymerization. Furthermore, localized polymer formation was achieved on the TMPP-modified BDD interface using the direct mode of a scanning electrochemical microscope (SECM) as well as an electrochemical scanning near-field optical microscope (E-SNOM). Depending on the method used polypyrrole dots with diameters in the range of 1-250 microm are electrogenerated.