Comparative study of electrostatic binding vs. complexation of Cu2+ ions with water‐soluble polymers containing styrene sulphonic acid and/or maleic acid units or their sodium salt forms

The interaction of Cu²⁺ ions with the homopolymer poly(styrene sulfonic acid) (PSSH), as well as with the copolymers of maleic acid (MAc) with styrene sulfonic acid (SSH) or vinyl acetate (VAc), was investigated in dilute aqueous solution through turbidimetry, potentiometry, viscometry, and spectrophotometry in the visible region. Cu²⁺ ions were introduced either through neutralization with Cu(OH)₂ of the acid form of the (co)polymers (PSSH, P(SSH‐co‐MAc) and P(VAc‐co‐MAc)) or through mixing of the sodium salt form of the (co)polymers (PSSNa, P(SSNa‐co‐MANa) and P(VAc‐co‐MANa)) with CuSO₄. Turbidimetry, potentiometry, and spectrophotometry revealed that the first carboxylic group of MAc or both carboxylate groups of MANa are involved in the complexation with Cu²⁺ ions when neutralization with Cu(OH)₂ or mixing with CuSO₄ are applied, respectively. The increased values of the reduced viscosity observed mainly at the first stages of neutralization of P(VAc‐co‐MAc) with Cu(OH)₂ indicate that interchain polymer‐Cu²⁺ complexation takes possibly place. Finally, the spectrophotometric behavior observed upon neutralization of P(SSH‐co‐MAc) with Cu(OH)₂ or mixing of P(SSNa‐co‐MANa) with CuSO₄ revealed that the strength of counterion binding by the sulfonate groups is, in fact, comparable with the complexation of Cu²⁺ ions with the carboxylate groups of MAc. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1149–1158, 2008     

Linearly implicit methods for nonlinear evolution equations

Summary.  We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear evolution equations and extend thus recent results concerning the discretization of nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particular cases implicit–explicit multistep schemes as well as the combination of implicit Runge–Kutta schemes and extrapolation. We establish optimal order error estimates. The abstract results are applied to a third–order evolution equation arising in the modelling of flow in a fluidized bed. We discretize this equation in space by a Petrov–Galerkin method. The resulting fully discrete schemes require solving some linear systems to advance in time with coefficient matrices the same for all time levels. Received October 22, 2001 / Revised version received April 22, 2002 / Published online December 13, 2002 Mathematics Subject Classification (1991): Primary 65M60, 65M12; Secondary 65L06 Correspondence to: G. Akrivis     

Study of the sodium dodecyl sulphate–protein complexes: evidence of their wormlike conformation by treating them as random coil polymers

The Kuhn statistical segment length, A, was determined for the sodium dodecyl sulphate (SDS)–protein complexes in two binding levels of SDS adsorbed onto the protein. These complexes are treated as random coil polymers. For the SDS–protein complex of binding level 1.4 g SDS per gram of protein, the value of A was found equal to 76 and 37 Å in 0.01 and 0.1 M ionic strength, correspondingly. For the complex of binding level 0.4 g SDS per gram of protein, the value of A was found equal to 30 Å. The calculation was based mainly on two equations (Eqs. 4 and 5; Dondos and Benoît, Polymer 18:1161, 1977; Dondos and Staikos, Colloid Polym Sci 273:623, 1995, correspondingly). Our findings are supported by gel permeation chromatography results, drawn according to the “modified universal calibration” and suggest that these complexes should be considered as wormlike polymers presenting a considerable draining effect.     

Numerical simulation of the extrusion of strongly compressible Newtonian liquids

The axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls. Compressibility effects are investigated using both a linear and an exponential equation of state. The numerical results confirm previous reports that the swelling of the extrudate decreases initially as the compressibility of the fluid is increased and then increases considerably. The latter increase is sharper in the case of the exponential equation of state. In the case of non-zero inertia, high compressibility was found to lead to a contraction of the extrudate after the initial expansion, similar to that observed experimentally with liquid foams and to decaying oscillations of the extrudate surface. The time-dependent calculations show that the oscillatory steady-state solutions are stable. These steady-state oscillatory solutions are not affected by the length of the extrudate region nor by the boundary condition along the wall.     

Adaptive weak approximation of stochastic differential equations

Adaptive time‐stepping methods based on the Monte Carlo Euler method for weak approximation of Itô stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading‐order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or deterministic time steps are described. Numerical examples illustrate when stochastic and deterministic adaptive time steps are superior to constant time steps and when adaptive stochastic steps are superior to adaptive deterministic steps. Stochastic time steps use Brownian bridges and require more work for a given number of time steps. Deterministic time steps may yield more time steps but require less work; for example, in the limit of vanishing error tolerance, the ratio of the computational error and its computable estimate tends to 1 with negligible additional work to determine the adaptive deterministic time steps. © 2001 John Wiley & Sons, Inc.     

A quantitative western blot technique using TMB: Comparison with the conventional technique

Numerous molecular biological experiments performed throughout the world require the detection or quantification of a protein of interest. Western blotting is one of the most popular techniques used for this purpose and offers quantitative information with the aid of specialized software. However, its dependence on the picture that is captured, and the background and the absence of a common protocol prevent the technique from being completely quantitative. To overcome these obstacles, we present a simple and reliable assay that is similar to the regular technique, with the exception of the last stage of band visualization and quantification. We propose that small pieces of the blot that include the protein of interest can be cut and dipped in a small volume of 3,3',5,5'-tetramethylbenzidine solution, giving a colorimetric signal with linear dependence on the quantity of the protein. The reaction is stopped with H₂SO₄, and the signal is measured in a plate reader. This modification shows high linearity without additional costs and can be applied for both purified proteins and proteins found in a lysate. The results obtained with our proposed technique were compared with those obtained by the conventional method and proved to be more reliable.