A mathematical model of crevice and pitting corrosion—I. The physical model

A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterizing the propagation stage of crevice and pitting corrosion in metals is described. The model predicts the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within an active corrosion cavity as a function of the many parameters on which these depend, such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. The cavity propagation rates are found to be faster in the case of a crevice with passive walls than one with active walls. The distribution of current over the internal surface of a crevice with corroding walls can be assessed using this model, giving an indication of the future shape of the cavity. The model is extended to include a solid hydroxide precipitation reaction and considers the effect of consequent changes in the chemical and physical environment within the crevice on the predicted corrosion rates. In this paper, the model is applied to crevice and pitting corrosion in carbon steel.

Model analysis of dissolved inorganic phosphorus exports from the Yangtze river to the estuary

In this paper, we estimate the inputs of phosphorus (P) to the Yangtze River Basin and exports of dissolved inorganic phosphorus (DIP) from the river to the estuary for the period 1970-2003, by using the global NEWS-DIP model. Modeled DIP yields range from 2.5 kg P km(-2) yr(-1) in 1970 to 4.6 kg P km(-2) yr(-1) in 1985, and then dramatically increase to 14.1 kg P km(-2) yr(-1) in 2003. No significant difference between the modeled and measured values at the level of P = 0.05 is observed. The study also demonstrates variable source contributions of P to the modeled DIP during the period 1970-2003. Point sewage P input accounted for approximately 100% in the period 1970-1985 and substantially decreased to 24.8% in 2003. Chemical fertilizer contributed 25.4% of DIP yields in 1986 and increased continuously to 50.3% in 2003, while a stable trend in manure P contribution averaging 22.9% of DIP yields was shown in the same period. The study concludes that P inputs to the Yangtze River Basin and the river DIP export to the estuary have substantially increased during the study period consequence to human pressure.

Simulated morphological landscape of polymer single crystals by phase-field model

The novel phase field model with the "polymer characteristic" was established based on a nonconserved spatiotemporal Ginzburg-Landau equation (TDGL model A). Especially, we relate the diffusion equation with the crystal growth faces of polymer single crystals. Namely, the diffusion equations are discretized according to the diffusion coefficient of every lattice site in various crystal growth faces and the shape of lattice is selected based on the real proportion of the unit cell dimensions.

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

Banded spherulite patterns are simulated in three dimensions by means of a Coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the hand spacing is decreased with the increase of parameter mu in the Logistic map and increased with the increase of the coupling parameter e for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.

Design of silicone rubber according to requirements based on the multi-objective optimization of chemical reactions

The explicit expression between composition and mechanical properties of silicone rubber was derived from the physics of polymer elasticity, the implicit expression among material composition, reaction conditions and reaction efficiency was obtained from chemical thermodynamics and kinetics, and then an implicit multi-objective optimization model was constructed. Genetic algorithm was applied to optimize material composition and reaction conditions, and the finite element method of cross-linking reaction processes was used to solve multi-objective functions, on the basis of which a new optimization methodology of crosslinking reaction processes was established. Using this methodology, rubber materials can be designed according to pre-specified requirements.

A novel self-consistent-field lattice model for block copolymers

We develop a self-consistent-field lattice model for block copolymers and propose a novel and general method to solve the self-consistent-field equations. The approach involves describing the polymer chains in a lattice and employing a two-stage relaxation procedure to evolve a system as rapidly as possible to a free-energy minimum. In order to test the validity of this approach, we use the method to study the microphases of rod-coil diblock copolymers. In addition to the lamellar and cylindrical morphologies, micellar, perforated lamellar, gyroid, and zigzag structures have been identified without any prior assumption of the microphase symmetry. Furthermore, this approach can also give the possible orientation of the rods in different structures.

Mossbauer spectroscopy and chemical bonds in BaFe12O19 hexaferrite

Barium hexaferrite was synthesized by chemical co-precipitation. Its Mossbauer spectra were obtained. A semi-empirical model, based on the Phillips theory of bonding, has been developed for quantitative explanation of the Mossbauer isomer shifts of Fe ions in BaFe12O19 crystals. The results show that, using the relationship between isomer shifts and covalency, the site assignments in hexaferrites will be resolved easily. This paper provides a powerful tool for studying other members of the hexagonal ferrimagnetic oxides family.

Temperature dependence of the distribution of the first passage time: Results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Go-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T-opt*. The optimal folding temperature T-opt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T-opt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T-opt* and start to diverge when the temperature is lower than T-opt*. The distribution of FPT is close to a log-normal-like distribution at T* greater than or equal to T-opt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Chemical bond properties and Mossbauer spectroscopy in (La1-xMx)(2)CuO4(M=Ba, Sr)

By using the average band-gap model, the chemical bond properties of (La1-x, M-x)(2)CuO4(M=Ba, Sr) were calculated. The calculated covalencies for Cu-O and La-O bond in the compounds are 0.3 and 0.03 respectively. Mossbauer isomer shifts of Fe-57 doped in La2CuO4 and Sn-119 doped in La2CuO4 were calculated by using the chemical surrounding factor defined by covalency and electronic polarizability. Four valence state tin and three valence iron sites were identified in Fe-57 and Sn-119 doped La2CuO4.

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory (SLLFT). For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights of the polydisperse polymer, but the z-average molecular weight ((M) over bar (z)) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of (M) over bar (n) on the spinodal. Moreover, it has been found that the effect of changing (M) over bar (w) on the spinodal is much bigger than that of changing (M) over bar (n) and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature (UCST). However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of upsilon(*)=upsilon(1)(*)=upsilon(2)(*) and (1/r(1)(0))-(1/r(2i)(0))-->(1/r(1)(0)).

Chemical bond properties of REBa2Cu3O7 and its Mossbauer spectroscopy

By using the average bond-gap model, the chemical bond properties of REBa2Cu3O7 were calculated. The calculated covalencies for Cu(1)-O and Cu(2)-O bonds in REBa2Cu3O7 compounds are 0.41 and 0.28 respectively. Mossbauer isomer shifts of Fe-57 doped in EuBa2Cu3O7-x and Sn-119 doped in YBa2Cu3O7-x were calculated by using the chemical surrounding factor, h, defined by covalency and electronic polarizability. The valence states and sites of Fe-57 in EuBa2Cu3O7 and Sn-119 in YBa2Cu3O7-x were identified.

Prediction of C-13-nuclear magnetic resonance chemical shifts for aliphatic amines

Prediction of C-13-nuclear magnetic resonance chemical shifts for aliphatic amines is performed. The topological, geological and electronic descriptors are generated. To reduce the variables, the best subsets of the descriptors are obtained by using leaps-and-bounds regression analysis. The model is achieved using multiple regression with satisfactory results.

Four-level decay model of P-6(7/2) excited state of Eu2+ ion in KMgF3

A four-level model of P-6(7/2) excited state of Eu2+ ion in KMgF3: Eu2+ has been proposed. The decay profiles of the P-6(7/2) excited sstate of Eu2+ are two exponential and the physical implication of each term in the fit equation responsible for the model is interpreted. The data obtained spectroscopically are in good agreement with the fit results.

Study of energy transfer in KMgF3 : Eu-X (X = Gd, Cr, Ce) by the decay model of P-6(7/2) exited state of Eu2+

Energy transfer processes between Eu2+ and Gd3+, Cr3+, Ce3+ ions in KMgF3, which are difficult to study spectroscopically, have been investigated by using the proposed four-level decay model of the P-6(7/2) excited state of the Eu2+ ion. Gd3+ and Ce3+ transfer its energy to the vibronic transition of the P-6(7/2) --> S-8(7/2) transition of Eu2+, whereas Cr3+ receive energy from Eu2+ via the d-d interaction. The energy transfer from the Eu2+ 4f(6)5d level to the Ce3+ 4f5d state is observed spectroscopically, and the energy transfer mechanism is discussed. (C) 2001 Elsevier Science B.V. All rights reserved.