Interactions of an anionic surfactant with poly(oxyalkylene) copolymers in aqueous solution

The interactions of sodium dodecyl sulfate (SDS) with poly(ethylene oxide)/poly(alkylene oxide) (E/A) block copolymers are explored in this study: With respect to the specific compositional characteristics of the copolymer, introduction of SDS can induce fundamentally different effects to the self-assembly behavior of E/A copolymer solutions. In the case of the E18B10-SDS system (E = poly(ethylene oxide) and B = poly(butylene oxide)) development of large surfactant-polymer aggregates was observed. In the case of B20E610-SDS, B12E227B12-SDS, E40B10E40-SDS, E19P43E19-SDS (P = poly(propylene oxide)), the formation of smaller particles compared to pure polymeric micelles points to micellar suppression induced by the ionic surfactant. This effect can be ascribed to a physical binding between the hydrophobic block of unassociated macromolecules and the non-polar tail of the surfactant. Analysis of critical micelle concentrations (cmc*) of polymer-surfactant aqueous solutions within the framework of regular solution theory for binary surfactants revealed negative deviations from ideal behavior for E40B10E40-SDS and E19P43E19-SDS, but positive deviations for E18B10-SDS. Ultrasonic studies performed for the E19P43E19-SDS system enabled the identification of three distinct regions, corresponding to three main steps of the complexation; SDS absorption to the hydrophobic backbone of polymer, development of polymer-surfactant complexes and gradual breakdown of the mixed aggregates. (C) 2008 Elsevier Inc. All rights reserved.

Electronic structure of point defects in controlled self-doping of the TiO2 (110) surface: Combined photoemission spectroscopy and density functional theory study

Point defects in metal oxides such as TiO2 are key to their applications in numerous technologies. The investigation of thermally induced nonstoichiometry in TiO2 is complicated by the difficulties in preparing and determining a desired degree of nonstoichiometry. We study controlled self-doping of TiO2 by adsorption of 1/8 and 1/16 monolayer Ti at the (110) surface using a combination of experimental and computational approaches to unravel the details of the adsorption process and the oxidation state of Ti. Upon adsorption of Ti, x-ray and ultraviolet photoemission spectroscopy (XPS and UPS) show formation of reduced Ti. Comparison of pure density functional theory (DFT) with experiment shows that pure DFT provides an inconsistent description of the electronic structure. To surmount this difficulty, we apply DFT corrected for on-site Coulomb interaction (DFT+U) to describe reduced Ti ions. The optimal value of U is 3 eV, determined from comparison of the computed Ti 3d electronic density of states with the UPS data. DFT+U and UPS show the appearance of a Ti 3d adsorbate-induced state at 1.3 eV above the valence band and 1.0 eV below the conduction band. The computations show that the adsorbed Ti atom is oxidized to Ti2+ and a fivefold coordinated surface Ti atom is reduced to Ti3+, while the remaining electron is distributed among other surface Ti atoms. The UPS data are best fitted with reduced Ti2+ and Ti3+ ions. These results demonstrate that the complexity of doped metal oxides is best understood with a combination of experiment and appropriate computations.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

The adsorbed conformation of globular proteins at the air/water interface

External reflection FTIR spectroscopy and surface pressure measurements were used to compare conformational changes in the adsorbed structures of three globular proteins at the air/water interface. Of the three proteins studied, lysozyme, bovine serum albumin and P-lactoglobulin, lysozyme was unique in its behaviour. Lysozyme adsorption was slow, taking approximately 2.5 h to reach a surface pressure plateau (from a 0.07 mM solution), and led to significant structural change. The FTIR spectra revealed that lysozyme formed a highly networked adsorbed layer of unfolded protein with high antiparallel beta-sheet content and that these changes occurred rapidly (within 10 min). This non-native secondary structure is analogous to that of a 3D heat-set protein gel, suggesting that the adsorbed protein formed a highly networked interfacial layer. Albumin and P-lactoglobulin adsorbed rapidly (reaching a plateau within 10 min) and with little chance to their native secondary structure.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

On the difficulties of present theoretical models to predict the oxidation state of atomic Au adsorbed on regular sites of CeO2(111)

The electronic structure and oxidation state of atomic Au adsorbed on a perfect CeO2(111) surface have been investigated in detail by means of periodic density functional theory-based calculations, using the LDA+U and GGA+U potentials for a broad range of U values, complemented with calculations employing the HSE06 hybrid functional. In addition, the effects of the lattice parameter a0 and of the starting point for the geometry optimization have also been analyzed. From the present results we suggest that the oxidation state of single Au atoms on CeO2(111) predicted by LDA+U, GGA+U, and HSE06 density functional calculations is not conclusive and that the final picture strongly depends on the method chosen and on the construction of the surface model. In some cases we have been able to locate two well-defined states which are close in energy but with very different electronic structure and local geometries, one with Au fully oxidized and one with neutral Au. The energy difference between the two states is typically within the limits of the accuracy of the present exchange-correlation potentials, and therefore, a clear lowest-energy state cannot be identified. These results suggest the possibility of a dynamic distribution of Au0 and Au+ atomic species at the regular sites of the CeO2(111) surface.

Density functional theory study of rutile VO2 surfaces

We present the results of a density functional theory (DFT) investigation of the surfaces of rutile-like vanadium dioxide, VO2(R). We calculate the surface energies of low Miller index planes, and find that the most stable surface orientation is the (110). The equilibrium morphology of a VO2(R) particle has an acicular shape, laterally confined by (110) planes and topped by (011) planes. The redox properties of the (110) surface are investigated by calculating the relative surface free energies of the non-stoichiometric compositions as a function of oxygen chemical potential. It is found that the VO2(110) surface is oxidized with respect to the stoichiometric composition, not only at ambient conditions but also at the more reducing conditions under which bulk VO2 is stable in comparison with bulk V2O5. The adsorbed oxygen forms surface vanadyl species much more favorably than surface peroxo species.

Cobalt incorporation in calcite: Thermochemistry of (Ca,Co)CO3 solid solutions from density functional theory simulations

The incorporation of cobalt in mixed metal carbonates is a possible route to the immobilization of this toxic element in the environment. However, the thermodynamics of (Ca,Co)CO3 solid solutions are still unclear due to conflicting data from experiment and from the observation of natural ocurrences. We report here the results of a computer simulation study of the mixing of calcite (CaCO3) and spherocobaltite (CoCO3), using density functional theory calculations. Our simulations suggest that previously proposed thermodynamic models, based only on the range of observed compositions, significantly overestimate the solubility between the two solids and therefore underestimate the extension of the miscibility gap under ambient conditions. The enthalpy of mixing of the disordered solid solution is strongly positive and moderately asymmetric: calcium incorporation in spherocobaltite is more endothermic than cobalt incorporation in calcite. Ordering of the impurities in (0001) layers is energetically favourable with respect to the disordered solid solution at low temperatures and intermediate compositions, but the ordered phase is still unstable to demixing. We calculate the solvus and spinodal lines in the phase diagram using a sub-regular solution model, and conclude that many Ca1-xCoxCO3 mineral solid solutions (with observed compositions of up to x=0.027, and above x=0.93) are metastable with respect to phase separation. We also calculate solid/aqueous distribution coefficients to evaluate the effect of the strong non-ideality of mixing on the equilibrium with aqueous solution, showing that the thermodynamically-driven incorporation of cobalt in calcite (and of calcium in spherocobaltite) is always very low, regardless of the Co/Ca ratio of the aqueous environment.