Non-homogeneous Substrate Research Articles

Modelling of metallic inclusions on non-homogeneous dielectric substrates

ABSTRACT In this article, modelling is done for Square Split Ring Resonators (SSRR) as a quasi-static equivalent circuit in a non-homogeneous environment. The authors propose a new relationship for the relative permittivity for a metallic inclusion etched on top of a dual substrate in a non-homogeneous medium. The stacking sequence of the substrates plays a vital role in the response of the SSRR. This paper highlights the change brought about by the dielectric materials’ stacking order on resonant frequency and quality factor. The analytical and numerical study of SSRR etched on the dual substrates shows a good correlation of values. A comparative study indicates a better fit of the proposed formula for the effective permittivity over the conventional averaging method. This article highlights the advantages of using a dual substrate material for fabricating metamaterial structures for different applications. The advantage of the proposed permittivity equation is its applicability to all kinds of geometries. Three different substrate materials were used for the performance study of the SSRR (FR4, Rogers RT/Duroid 5880 and Alumina).

A multiband patch antenna with embedded square split ring resonators in non-Homogeneous substrate

The authors have attempted to influence an embedded square split ring resonator (SSRR) response in a stacked non-homogeneous substrate to demonstrate a quad-band antenna. The purpose is to produce multiband operations of a microstrip patch antenna. The highlighted factor is the effect of embedding an SSRR and the differing relative permittivity of the substrate on the side length of the SSRR. The analysis shows that a non-homogeneous dual substrate patch produces multiple bands compared to a single substrate patch antenna without any parameter change. A dual substrate antenna fabricated using FR4 and Rogers RT/Duroid 5880 copper clad sheets with a dimension of 85.6x54x0.908 mm3 (0.314λ0x0.198λ0x0.003λ0). The antenna resonates at 1.1, 2.45, 3.65 and 5.25 GHz in the L-, S- and C-bands. It is possible to employ the patch antenna in WLAN (dual-band) and WiMAX applications and suitable for mobile broadcast service at 1.1 GHz. The authors compare the simulated and measured results of a prototype in the article. The maximum measured gain is 5.48 dBi at 1.1 GHz and 4.025 dBi at 3.65 GHz. The measured bandwidth is 60 MHz (1.2%) at 5.25 GHz.

Transient response of several cracks in a nonhomogeneous half-layer bonded to a magneto-electro-elastic coating

In this study, we examine the fracture analysis of a non-homogeneous half-layer reinforced by a magneto-electro-elastic (MEE) coating with multiple interface and embedded cracks in a non-homogeneous substrate under impact loadings. Material properties of the functionally graded (FG) orthotropic substrate are assumed to vary exponentially in the thickness direction of the half-layer. First, the analytical solution is developed by considering a dynamic mechanical dislocation with time-dependent Burgers vector be situated at the substrate and interface by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the medium containing embedded and interface cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the dynamic stress intensity factors (DSIFs). The effects of crack spacing, the length and position of the cracks and FGM exponent as well as crack interaction are studied.

Transient response of cracked nonhomogeneous substrate with piezoelectric coating by dislocation method

The transient response of a functionally graded material (FGM) orthotropic strip with a piezoelectric coating weakened by multiple cracks is investigated. The system is subjected to out-of-plane mechanical and in-plane electrical loading. The properties of the nonhomogeneous substrate are assumed to vary exponentially along the thickness and the energy dissipation is modeled by viscous damping. In this study, the rate of the gradual change of the shear moduli, mass density, and damping constant are assumed to be same. At first, the transient response of a Volterra-type dislocation in an FGM orthotropic strip is obtained analytically. Imposing a distributed dislocation density on the crack surface and using the Fourier and Laplace integral transforms, the problem is reduced to a system of singular integral equations for a substrate weakened by multiple cracks in the form of Cauchy singularity; which are solved numerically to obtain the dynamic stress intensity factors at the crack tips. Finally, the effects of the geometrical parameters, material properties, viscous damping and cracks arrangement on the dynamic fracture behavior of the interacting cracks are studied.

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

Laterally periodic nanostructures have been investigated with grazing-incidence small-angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerical solution of Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, owing to the discrepancy between the incident wavelength and the finite-element size. This drawback vanishes for GISAXS because of the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art electron-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows the detailed reconstruction of the grating line shape for thick non-homogeneous substrates as well. The reconstructed geometric line-shape models are statistically validated by applying a Markov chain Monte Carlo sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nanometre uncertainty.

Determination of kinetics and heat of hydrolysis for non-homogenous substrate by isothermal calorimetry.

The competitiveness of the second-generation bioethanol by biotechnological process requires an effective and quantitative control of biochemical reactions. In this study, the potential of isothermal calorimetry technique to measure heat and kinetics of a non-homogeneous substrate enzymatic hydrolysis is intended. Using this technique, optimum temperature of the enzymes used for lignocellulosic molecules hydrolysis was determined. Thus, the amount of substrate-to-enzyme ratio was highlighted as an important parameter of the hydrolysis yield. Furthermore, a new enzymes' cocktail efficiency consisting of a mix of cellulases and cellobiose dehydrogenase (CDH) was qualified by this technique. The results showed that this cocktail allowed the production of a high amount of gluconic acid that could improve the attractiveness of these second-generation biofuels. From the set of experiments, the hydrolysis heat of wheat straw was derived and a meaningful value of -32.2±3.2Jg-1 (gram reducing sugars product) is calculated. Then, isothermal measurements were used to determine kinetic constants of the cellulases and CDH mix on wheat straw. Results showed that this enzyme cocktail has an optimal rate at 45°C in the range of temperatures tested (40-55°C).

Automatic cell detection in bright-field microscopy for microbeam irradiation studies

Automatic cell detection in bright-field illumination microscopy is challenging due to cells’ inherent optical properties. Applications including individual cell microbeam irradiation demand minimisation of additional cell stressing factors, so contrast-enhancing fluorescence microscopy should be avoided. Additionally, the use of optically non-homogeneous substrates amplifies the problem. This research focuses on the design of a method for automatic cell detection on polypropylene substrate, suitable for microbeam irradiation. In order to fulfil the relative requirements, the Harris corner detector was employed to detect apparent cellular features. These features-corners were clustered based on a dual-clustering technique according to the density of their distribution across the image. Weighted centroids were extracted from the clusters of corners and constituted the targets for irradiation. The proposed method identified more than 88% of the 1,738 V79 Chinese hamster cells examined. Moreover, a processing time of 2.6 s per image fulfilled the requirements for a near real-time cell detection-irradiation system.

Analytical Modeling of Composite-to-Masonry Prisms Bond

The composite-to-substrate interfacial stresses transfer mechanism is one of the critical issues in externally-bonded structural strengthening by means of composite fabrics. In this work, an analytical approach for modeling the debonding process of a composite on a non-homogeneous substrate is developed and applied to simulate the loss of bond of FRP on brick masonry. The analytical formulation is based on the experimental outcomes of bond shear tests, which are part of a Round Robin activity involving several laboratories. The experimental work is the follow up of a previous one [1], and comprises 12 single-lap shear tests of four kinds of unidirectional reinforcement, i.e., glass, carbon, basalt and steel, applied with epoxy resin to masonry prisms composed by five clay bricks and four mortar joints. The analytical simulations of the experimental tests rely upon a bi-linear non-homogeneous bond-slip law that was calibrated using the experimental population. Eventually, the analytical results are compared to experimental ones both, in terms of global (load to displacement curve) and local behavior (strain profile on the reinforcement for increasing load values).

Avalanche dynamics of elastic interfaces

Slowly driven elastic interfaces, such as domain walls in dirty magnets, contact lines wetting a nonhomogeneous substrate, or cracks in brittle disordered material proceed via intermittent motion, called avalanches. Here we develop a field-theoretic treatment to calculate, from first principles, the space-time statistics of instantaneous velocities within an avalanche. For elastic interfaces at (or above) their (internal) upper critical dimension d≥d(uc) (d(uc)=2,4 respectively for long-ranged and short-ranged elasticity) we show that the field theory for the center of mass reduces to the motion of a point particle in a random-force landscape, which is itself a random walk [Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model]. Furthermore, the full spatial dependence of the velocity correlations is described by the Brownian-force model (BFM) where each point of the interface sees an independent Brownian-force landscape. Both ABBM and BFM can be solved exactly in any dimension d (for monotonous driving) by summing tree graphs, equivalent to solving a (nonlinear) instanton equation. We focus on the limit of slow uniform driving. This tree approximation is the mean-field theory (MFT) for realistic interfaces in short-ranged disorder, up to the renormalization of two parameters at d=d(uc). We calculate a number of observables of direct experimental interest: Both for the center of mass, and for a given Fourier mode q, we obtain various correlations and probability distribution functions (PDF's) of the velocity inside an avalanche, as well as the avalanche shape and its fluctuations (second shape). Within MFT we find that velocity correlations at nonzero q are asymmetric under time reversal. Next we calculate, beyond MFT, i.e., including loop corrections, the one-time PDF of the center-of-mass velocity u[over ·] for dimension d<d(uc). The singularity at small velocity P(u[over ·])~1/u[over ·](a) is substantially reduced from a=1 (MFT) to a=1-2/9(4-d)+... (short-ranged elasticity) and a=1-4/9(2-d)+... (long-ranged elasticity). We show how the dynamical theory recovers the avalanche-size distribution, and how the instanton relates to the response to an infinitesimal step in the force.

Inkjet printing of individual polymer micro parts self-shaped with hemispherical caps

Droplet deposition has been so ubiquitous over a decade for the production of micro parts using versatile liquid-based methods such as inkjet-printing technology. One of key elements for success in the design involves the use of non-homogeneous substrates to effectively control the complex morphologies of solute deposit during evaporation. However, there are still few studies investigating contours of the solid contents self-formed and even released as the solvents evaporate. This paper reports a droplet vaporization deposition (DVD) method that can significantly improve the controllability over the curvatures of micro parts utilizing the heterogeneous PDMS (Polydimethysiloxane) substrates based on soft-lithography technique. Experimental and analytical results indicate that the profile curvatures and contact angles (up to ∼90°) for the hemispherical parts formed after droplet evaporation were simply varied by different droplet volumes (single droplet ∼10pl) placed on the cavity-structured surfaces, thus providing the capability of control over solid contours. In this way, the individual micro parts released from the mold substrates could be applied in many applications, in particular the current self-assembly processes.

Collective diffusion in the presence of substrate inhomogeneities and particle–particle interactions

A novel variational analytic approach to collective diffusion allowing the density dependent collective diffusion coefficient to be calculated in systems of interacting particles adsorbed on a crystalline substrate is presented. The approach, based on a kinetic lattice gas model extracts the diffusion coefficient directly from the master equations which account for the microscopic kinetics of the system in which microscopic processes underlying the diffusion are particle jumps between neighboring adsorption sites. Variational parameters minimizing the evaluated diffusional eigenvalue of the microscopic rate matrix are ‘geometrical’ and ‘correlational’ phases accounting, for the local potential energy landscape experienced by the adsorbed particle and the local correlations, respectively, i.e. an instantaneous occupation pattern of adsorption sites around the particle. Selected results, collective diffusion as a function of particle coverage, for the system of interacting particles adsorbed on a one dimensional non-homogeneous substrate with steps and for a system of non-interacting particles adsorbed on a two dimensional striped–stepped surface are presented and discussed. It is demonstrated in the latter case that the mean field approach which is known in the literature overestimates the diffusion coefficient and corresponds to the variational result in the limit of infinitely fast hopping kinetics in the direction parallel to steps.

Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems

Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. In our model particles reside and jump randomly between adsorption sites modeled as potential wells with different depths. Site blocking is the only allowed particle-particle interaction mechanism. It is shown that the value of the diffusion coefficient in one lattice direction depends nontrivially on the rate and the character of the particle jumps in other directions. The collective diffusion coefficient increases, eventually approaching values predicted within the mean-field approximation when the jump rate increases in the direction perpendicular to that in which the diffusion coefficient is measured. Analytical predictions of our model are supported by the Monte Carlo simulation performed for selected systems.

Ritz variational principle for collective diffusion in an adsorbate on a non-homogeneous substrate

A systematic approach on collective diffusion in an interacting lattice gas adsorbed on a non-homogeneous substrate is formulated. It is based on a variational Ritz procedure of determining a diffusive eigenvalue of a transition rate matrix describing microscopic kinetics of particle migration processes in the system. Form of a trial eigenvector and a choice of variational parameters are discussed and justified on physical grounds. Reed-Ehrlich factorization of the collective diffusion coefficient into the thermodynamic and kinetic factors is explicitly shown to emerge naturally from the variational approach, and closed expressions for both factors are derived. Validity of the approach is tested by applying it to the simplest case of diffusion of noninteracting adparticles across steps on a stepped substrate (modeled by a Schwoebel barrier). The coverage dependence of collective diffusion coefficient, obtained in an algebraic form, agrees very well with the results of Monte Carlo simulations. It is demonstrated that the results obtained provide a substantial improvement over the mean-field theory results for the same system. Generalizations necessary to include interparticle interactions are listed and discussed.

Photoresist-free printing of amorphous silicon thin-film transistors

Conventional fabrication of amorphous silicon thin-film transistors (a-Si TFTs) requires patterning numerous photoresist layers, a subtractive process that is time consuming and expensive. This letter describes transistor fabrication by a photoresist-free approach in which polymer etch masks are letterpress printed from flexible polyimide stamps. Pattern registration is achieved through optical alignment since the printed masks are thin and optically transparent. This modified fabrication scheme produces transistor performance equivalent to conventionally fabricated a-Si TFTs. The ability to directly print etch masks onto nonhomogeneous substrates brings one step closer the realization of flexible, large-area, macroelectronic fabrication.