Understanding Complex Electrochemical Impedance Spectroscopy in Corrosion Systems Using in‐situ Synchrotron Radiation Grazing Incidence X‐ray Diffraction

The difficulty in interpreting electrochemical impedance spectroscopy (EIS) data has limited the potential of the method despite its utility as an electrochemical method for studies of electrode reactions and interfacial structures. Taking the test case of the carbon dioxide corrosion of carbon steel, in‐situ synchrotron radiation grazing incidence X‐ray diffraction (SR‐GIXRD) has been demonstrated to be a powerful technique for validating and understanding the interfacial structures associated with complex EIS data. Carbon dioxide corrosion was found to occur in several steps, which may only be surmised by EIS, but the use of SR‐GIXRD in conjunction with EIS has enabled the establishment of a link between EIS time constants and structural changes associated with the evolution of corrosion products with time. By comparison to previous studies by the authors and others in this field, this communication provides the first direct experimental evidence linking SR‐GIXRD surface compositional data to otherwise indistinctive EIS time constants.     

On some abstract variable domain hyperbolic differential equations

The Cauchy problem is studied for a class of linear abstract differential equations of hyperbolic type with variable domain. Existence and uniqueness results are proved for (suitably defined) weak solutions. Some applications to P.D.E. are also given: they concern linear hyperbolic equations either in non-cylindrical regions or with mixed variable lateral conditions.This work was supported in part by the M.U.R.S.T. (Italy), through 60% and 40% research funds, and by the «G.N.AF.A. of the C.N.R.» (Italy).     

A new enzyme model for enantioselective esterases based on molecularly imprinted polymers

An efficient enzyme model exhibiting enantioselective esterase activity was prepared by using molecular imprinting techniques. The enantiomerically pure phosphonic monoesters 4 L and 5 L were synthesized as stable transition-state analogues. They were used as templates connected by stoichiometric noncovalent interactions to two equivalents of the amidinium binding site monomer 1. After polymerization and removal of the template, the polymers were efficient catalysts for the hydrolysis of certain nonactivated amino acid phenylesters (2 L, 2 D, 3 L, 3 D) depending on the template used. Imprinted catalyst IP4 (imprinted with 4 L) enhanced the hydrolysis of the corresponding substrate 2 L by a factor of 325 relative to that of a buffered solution. Relative to a control polymer containing the same functionalities, prepared without template 4 L, the enhancement was still about 80-fold, showing the highest imprinting effect up to now. In cross-selectivity experiments a strong substrate selectivity of higher than three was found despite small differences in the structure of the substrate and template. Plots of initial velocities of the hydrolysis versus substrate concentration showed typical Michaelis-Menten kinetics with saturation behavior. From these curves, the Michaelis constant K(M) and the catalytic constant k(cat) can be calculated. The enantioselectivity shown in these values is most interesting. The ratio of the catalytic efficiency k(cat)/K(M), between the hydrolysis of 2 L- and 2 D-substrate with IP4, is 1.65. This enantioselectivity derives from both selective binding of the substrate (K(M)L/K(M)D=0.82), and from selective formation of the transition state (k(cat)L/k(cat)D=1.36). Thus, these catalysts give good catalysis as well as high imprinting and substrate selectivity. Strong competitive inhibition is caused by the template used in imprinting. This behavior is also quite similar to the behavior of natural enzymes, for which these catalysts are good models.     

The evolution of polarization in an inhomogeneous birefringert,optically active medium

This note presents a method giving the change of polarization of an e.m. wave propagating in an inhomogeneous medium which is birefringent and optically active. The method has proved useful in a problem where the medium is a plasma with a magnetic field: it can be applied to other cases of interest, e.g. liquid crystals, as is here briefly discussed.     

Hydrodynamic forces and critical stresses in low-density aggregates under shear flow

The distribution of stresses in rigid colloidal aggregates under a shear flow was investigated numerically for particle-cluster and cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. stokesian dynamics was used to calculate the hydrodynamic force on each monomer, while the internal intermonomer interactions were calculated by applying force and torque balances on each primary particle. Although the hydrodynamic forces act mainly on the periphery of the clusters, their filamentous structure propagates and accumulates internal stresses toward the inner region of the aggregates, where consequently the most loaded intermonomer bonds are located. The spatial stress distribution, when scaled by the proper power of the radius of gyration, is independent of aggregate size and fractal dimension. This feature has made it possible to identify the most probable locations of bond failure in the structure and to estimate the relationship between shear rate and particle size for the occurrence of restructuring and of breakage.     

Catalytic conversion of methane to methanol over Cu-mordenite

Methane can be converted to methanol over copper-exchanged mordenite at 200 °C. Methanol could be recovered at the end of the reactor. This multi-step reaction opens the possibility for methane to methanol conversion in a closed catalytic cyclic reaction system.     

One, no one, and one hundred thousand crack propagation laws: A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth

Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m=2-5 in metals and m=10-50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review.     

A method for calculating rheological and morphological properties of constant-volume polymer blend models in inhomogeneous shear fields

We show how to formulate two-point boundary-value problems in order to compute fully-developed laminar channel and tube flow profiles for viscoelastic fluid models. The formulation is applied to Couette and pressure-driven flows separately, or a combination of both. The application of this methodology is illustrated analytically for the Upper-Convected Maxwell Model, and it is applied computationally for the Phan-Thien/Tanner and Giesekus Models. Numerical solutions exist for the last two models [J.Y. Yoo, H.C. Choi, On the steady simple shear flows of the one-mode Giesekus fluid, Rheol. Acta 28 (1989) 13–24; P.J. Oliveira, F.T. Pinho, Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids, J. Fluid Mech. 387 (1999) 271–280; M.A. Alves, F.T. Pinho, P.J. Oliveira, Study of steady pipe and channel flows of a single-mode Phan-Thien–Tanner fluid, J. Non-Newtonian Fluid Mech. 101 (2001) 55–76], allowing verification of the computational technique. Subsequently, the computational algorithm is applied to the constant-volume polymer blend models of Maffettone and Minale [P.L. Maffettone, M. Minale, Equation of change for ellipsoidal drops in viscous flow, J. Non-Newtonian Fluid Mech. 84 (1999) 105–106 (Erratum), J. Non-Newtonian Fluid Mech. 78 (1998) 227–241] and Dressler and Edwards [M. Dressler, B.J. Edwards, The influence of matrix viscoelasticity on the rheology of polymer blends, Rheol. Acta 43 (2004) 257–282; M. Dressler, B.J. Edwards, Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution, J. Non-Newtonian Fluid Mech. 120 (2004) 189–205]. Rheological and morphological properties of the model blends are thus obtained as functions of the spatial position within the channel, applied pressure drop, and shear rate at the wall.     

Regularization of Discontinuous Vector Fields on $${\mathbb{R}^3}$$ via Singular Perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.