Acoustic analysis of a rectangular cavity with general impedance boundary conditions

A Fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls. The sound pressure is expressed as the combination of a three-dimensional Fourier cosine series and six supplementary two-dimensional expansions introduced to ensure (accelerate) the uniform and absolute convergence (rate) of the series representation in the cavity including the boundary surfaces. The expansion coefficients are determined using the Rayleigh-Ritz method. Since the pressure field is constructed adequately smooth throughout the entire solution domain, the Rayleigh-Ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions. To unify the treatments of arbitrary nonuniform impedance boundary conditions, the impedance distribution function on each specified surface is invariantly expressed as a double Fourier series expansion so that all the relevant integrals can be calculated analytically. The modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions, including nonuniform impedance distributions.     

Comparison of Surface Tension Components and Hansen Solubility Parameters Theories. Part I: Explanation of Protein Adsorption on Polymers

Surface tension components and Hansen solubility parameters are two different theories used to explain and predict the compatibility and miscibility for polymer blends, composite polymer materials, and additives in polymer matrix. In this paper, the adsorption mechanism of bovine serum albumin (BSA) on eight polymers (PC, POM, PBT, PPO, PSF, PVDF, PEI, and PES) was researched through surface tension components and Hansen solubility parameters theories. The adsorption amounts of BSA on the polymers were measured through static adsorption experiments. It was found that the BSA adsorption amount cannot be directly correlated with the Hansen solubility parameters. However, there is high correlation between the Lifshitz-van der Waals component of surface tension of the polymers and BSA adsorption amount. With the increase in van der Waals value, the BSA adsorption amount on the polymers increases, but there still exists a complicated behavior. The protein adsorption mechanism is complex.     

p-Chlorophenol adsorption on activated carbons with basic surface properties

The adsorption of p-chlorophenol (PCP) from aqueous solution on activated carbons (ACs) with basic surface properties has been studied. The ACs were prepared by two methods. The first method was based on the modification of a commercial CWZ AC by high temperature treatment in an atmosphere of ammonia, nitrogen and hydrogen. The second approach comprised the carbonization followed by activation of N-enriched polymers and coal tar pitch using CO₂ and steam as activation agent. The resultant ACs were characterized in terms of porous structure, elemental composition and surface chemistry (pH_PZC, acid/base titration, XPS). The adsorption of PCP was carried out from an aqueous solution in static conditions. Equilibrium adsorption isotherm was of L2 type for polymer-based ACs, whereas L3-type isotherm was observed for CWZ ACs series. The Langmuir monolayer adsorption capacity was related to the porous structure and the amount of basic sites. A good correlation was found between the adsorption capacity and the volume of micropores with a width < 1.4 nm for polymer-based ACs. Higher nitrogen content, including that in basic form, did not correspond to the enhanced adsorption of PCP from aqueous solution. The competitive effect of water molecule adsorption on the PCP uptake is discussed.     

Adsorption of model charged proteins on charged surfaces with grafted polymers

The adsorption of model charged proteins on charged surfaces with and without grafted polymers is studied using a molecular approach. The ability of the polymer layer to reduce the amount of proteins adsorbed on top of the surface (primary adsorption) and at the same time to increase the adsorption of the proteins on top of the polymer layer (secondary adsorption) is presented. It is found that charging the free ends of the chains can result in an efficient way to enhance adsorption at the tip of the brush. Increasing the surface coverage of the polymers with charged free ends enhances the amount of proteins adsorbed at the tip of the polymer layer, while at the same time strongly reduces the number of proteins adsorbed directly onto the surface. The interplay between the attractive van der Waals protein-surface interactions, the steric polymer-protein interactions and the effect of the electrostatic interactions in determining the final adsorption is discussed. The manipulation of solution conditions to tune the amount of secondary adsorption is presented.     

Regulation of chicken egg lysozyme functional properties by interaction with 5-methylresorcinol

The surface activity and dynamics of adsorption surface layer formation of individual solutions of 5-methylresorcinol (MR) and its mixed solutions with lysozyme on air/solution (0.05 M phosphate buffer, pH 6.0) interface under conditions of MR maximally exceeding hydrolytic activity of lysozyme are studied using method of dynamic drop tensiometry. The thermodynamic parameters of adsorption are determined based on the isotherms. It is established that MR possesses lower surface activity in comparison to traditional surfactants. Methylresorcinol increases the surface activity and lysozyme adsorption rate at the air/solution interface in the entire concentration range covered.     

Two-dimensional self-assembly in diblock copolymers

Diblock copolymers confined to a two-dimensional surface may produce uniform features of macromolecular dimensions (approximately 10-100 nm). We present a mathematical model for nanoscale pattern formation in such polymers that captures the dynamic evolution of a solution of poly(styrene)-b-poly(ethylene oxide), PS-b-PEO, in solvent at an air-water interface. The model has no fitting parameters and incorporates the effects of surface tension gradients, entanglement or vitrification, and diffusion. The resultant morphologies are quantitatively compared with experimental data.     

Thermodynamic characterization of a dichloromethane-xenon film adsorbed on (0001) graphite

Xenon adsorption between 95 and 115 K on graphite pre-plated with a dichloromethane monolayer results in a partial displacement of the pre-adsorbed layer and in the formation of a two-dimensional (dichloromethane-xenon) solution. When the dichloromethane pre-plating is in the sub-monolayer range, a xenon monolayer is condensed on the bare part of the surface before the composite layer organization. For dichloromethane coverages greater than a monolayer, kinetic problems arise for the formation of xenon bilayer patches, which implies in this case its separation from the two-dimensional solution.     

The impact of carbon surface chemical composition on the adsorption of phenol determined at the real oxic and anoxic conditions

The results of phenol adsorption-desorption isotherms (at 310 K) measured on the series of activated carbons (D43/1, NORIT RO 0.8, D55/2) are presented. The effect of carbon surface chemical composition on phenol adsorption determined at real oxic and anoxic conditions is discussed. To obtain the real anoxic conditions the two station controlled atmosphere chamber with two catalyst heater units (Plas Labs, Lansing, MI, USA) was applied. It is shown that the adsorption under oxic conditions is always larger than that determined for anoxic ones for all studied carbons. The analysis of those differences shows that in the range of micropore filling they decrease with the equilibrium phenol mole fraction in solution. Contrary they increase after micropores being filled. The average differences between the adsorption properties are the linear function of the concentration of surface acidic groups (assigned from the Boehm's method as “carboxylic”) calculated per the apparent BET surface area of studied carbons.     

The transient response of a transversely isotropic cylinder under a laser point source impact

The transient response of a transversely isotropic cylinder under a laser point source impact is solved theoretically. The radial displacement generated by the laser under the ablation regime is numerically calculated by introducing Fourier series expansion and two-dimensional Fourier transform. The validity of this theoretical solution is demonstrated on a fiber reinforced composite cylinder with a strong anisotropy. Experimental displacements are detected at the cylinder surface by the laser ultrasonic technique, and are analyzed by the ray trajectories. Corresponding theoretical displacements are calculated numerically and compared to the experimental signals. Good agreement is found. The diffraction effect caused by the cusp is observed in both theory and experiment.     

Application of non-Fourier heat flux theory in thermally stratified flow of second grade liquid with variable properties

The characteristics of thermal stratification and temperature dependent thermal conductivity in two-dimensional (2D) stretched flow of second grade liquid are analyzed. Thickness of nonlinear stretching surface is variable. New model for heat flux by Cattaneo [2] and Christov [3] is utilized to capture the salient features of thermal relaxation time. Mathematical formulation is modeled employing boundary layer concept. Convergent series solution are obtained for the nonlinear systems. Outcoming results are presented graphically to discuss the characteristics of sundry parameters. Skin friction coefficient is tabulated and examined for various embedded parameters. Our analysis reveals that temperature distribution enhances via larger variable thermal conductivity parameter while it reduces for larger thermal relaxation time and thermal stratified parameters.     

New approximate solution for time-fractional coupled KdV equations by generalised differential transform method

In this paper,the generalised two-dimensional differential transform method (DTM) of solving the time-fractional coupled KdV equations is proposed.The fractional derivative is described in the Caputo sense.The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial.An illustrative example shows that the generalised two-dimensional DTM is effective for the coupled equations.     

Conformal invariance and perturbations in the two-dimensional Ising model: Surface defects

The influence of homogeneous surface perturbations on the surface critical behavior of the two-dimensional Ising model is studied through finite-size scaling and conformal invariance. Quantum chains of up to 2000 spins are studied in the fermionic version of the model. The results are deduced from the numerical solution of an eigenvalue equation for the excitation spectrum and show that conformal invariance still works for irrelevant surface perturbations.     

Phase Transition in Two-Dimensional Josephson-Junction Arrays

The self-charging model of two-dimensional Josephson-junction arrays at T = 0 is studied by the coupled cluster expansion method. The calculated results for the mass gap converge nicely. Besides the critical point, we also determine the critical parameters at T = 0. The system displays a second-order phase transition and the results are consistent with those obtained by other methods.     

Analytical evaluation of cylindrical exponential integrals arising in radiative transfer

New analytical results are presented performing to cylindrical exponential integral (CEI) functions for integer and noninteger values of parameter n. These integrals are often employed of two-dimensional radiative transfer in an absorbing-emitting medium and determination of the radiative flux in cylindrical media. The simple and efficient algorithm for the calculation of these functions is developed. The series expansion relations established in this work are accurate enough in the whole range of parameters.     

Interaction mechanism between copolymer inhibitor and β-dicalcium silicate surface based on molecular dynamics simulation

Copolymer inhibitor with multifunctional groups has a good effect on inhibiting the secondary reaction in the clinker leaching process for alumina production, but the inhibition mechanism of the copolymer is not clear yet. In this paper, molecular dynamics simulation was used to study the adsorption process of the copolymer inhibitor with multifunctional groups, such as acrylic acid-vinyl alcohol copolymer (PAV) and acrylic acid-hydroxypropyl acrylate copolymer (PAH), on the β-dicalcium silicate (C₂S) crystal surface, and reveal its inhibiting mechanism. Meanwhile, the polyacrylic acid (PAA) with only the carboxyl group also is simulated for comparing the inhibition effect with copolymer inhibitors. The results show that the binding energy between copolymer (PAV, PAH) and β-C₂S is greater than that of PAA with a single functional group. The order of binding energy is as follows: PAH?>?PAV?>?PAA. In aqueous solution, the water molecule can restrict the degree of deformation of polymers, increase the distance between polymers and β-C₂S and then lead to weakening of the adsorption of polymers on the crystal surface. The comprehensive and coordination effect of carboxyl and hydroxyl functional groups in PAV and PAH can strengthen the adsorption of copolymers on the β-C₂S surface. The different spatial distribution of multifunctional groups in the molecular structure has a different influence on the adsorption of the copolymer. The results can provide a theoretical basis for researching new and highly effective copolymer inhibitors with multifunctional groups.

Compared the adsorption state: The comprehensive and coordinate action of carboxyl and hydroxyl groups of the inhibitor with multifunctional groups make the inhibitor have a stronger adsorption ability on the surface of β-C₂S than that with a single functional group. The results obtained in this paper can provide a theoretical basis for the research and development of new and highly effective polymeric inhibitors with multifunctional groups.

Highlights

The interaction between copolymer and β-C₂S was investigated by MD simulation.

The binding energy order between polymers and β-C₂S is PAH?>?PAV?>?PAA.

The presence of water molecules can weaken the adsorption of the copolymer on the surface of β-C₂S.

The comprehensive and coordinate action of carboxyl and hydroxyl groups of the inhibitor with multifunctional groups make the inhibitor have a stronger adsorption ability on the surface of β-C₂S than that with a single functional group.     

Nanoparticle Distribution in Three‐Layer Polymer–Nanoparticle Composite Films: Comparison of Experiment and Theory

The distribution of hydrophobic nanoparticles deposited on a hydrophilic polymer film is investigated by scanning electron microscopy, transmission electron microscopy, and atomic force microscopy before and after spin‐coating a polymer solution on the particle film and drying it at room temperature. Various polymers and solvents are used. To reach equilibrium, all investigated systems are annealed additionally above the glass transition temperature (T_g) of the polymers. The compatibility of the interacting components is estimated by calculating their surface energy, solubility, and mutual interaction parameters. The experimental results show a redistribution of the particles on both interfaces of the polymer film. This corresponds to the calculated immiscibility of particles and polymers. The distribution of the nanoparticles at the interfaces is related mainly to the vapor pressure of the solvent, that is, kinetic effects during spin‐coating. Only minor contributions result from surface energy, solubility, and interaction parameters.     

Photonic band gaps in two-dimensional photonic crystals of core-shell-type dielectric nanorod heterostructures

A new type of two-dimensional photonic crystal (PC) called core-shell-type PC composed of a nanorod heterostructure array in a square or triangular lattice such that a dielectric nanorod is covered by a thin interfacial layer is studied. Using the plane-wave numerical expansion method, we study the modification of the band gap spectrum when the nanorods are covered by other material, and reveal that the photonic band gap is considerably enhanced in size for both square and triangular lattice. The effects of structural parameters on the band gaps are also studied. The results show that there exist optimal parameters to open large gaps, and TE (Transverse-electric) band gaps are favored in a triangular lattice.     

Self-assembled and fluorescence enhancement of semiconductor nanoparticles induced by surfactant adsorption

When semiconductor colloidal CdS nanoparticles and nonylphenol are mixed together in dimethyl sulfoxide at room temperature, a self-assembling process is induced. In the course, the size tunable properties of CdS nanoparticles are amplified. A blue shift in the emission spectrum and a strong photoluminescence enhancement are observed without significant change in the absorption features of the colloidal nanoparticles. These results are attributed to the adsorption of nonylphenol onto the nanoparticles surface and to the association process of the surfactant molecules. The surfactant adsorption process provides a nanoparticle surface passivation and induces an associative phase that enlarges the photoluminescence stability. This strategy opens the possibility to improve simultaneously physicochemical and photoluminescence properties of nanocrystals in solution as well as to control their deposition on two-dimensional surfaces.     

Reversible random sequential adsorption of dimers on a triangular lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca2+ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.     

A solvable model for localized adsorption in a coulomb system

A model for an interface with localized adsorption is presented, in which the surface has a distribution of sticky adhesive sites in contact with a Coulomb fluid. Contrary to the current literature on the electrical double layer the surface charge is in dynamic equilibrium with the bulk fluid. The sum rules obeyed by the one- and two-body correlation functions are investigated. Explicit results are obtained for a solvable model, the two-dimensional one-component plasma at reduced temperature 2. The effect of the granularity of the adsorbed charge on the adsorption isotherm is discussed.