Adhesion Characterization and Enhancement between Polyimide-Silica Composite and Nodulated Copper for Applications in Next-Generation Microelectronics.

As the need for high-speed electronics continues to rise rapidly, printed wiring board (PWB) requirements become ever-more demanding. A typical PWB is fabricated by bonding dielectric films such as polyimide to electrically conductive copper foil such as rolled annealed (RA) copper and is expected to become thinner, flexible, durable, and compatible with high-frequency 5G performance. Polyimide films inherently feature a higher coefficient of thermal expansion (CTE) than copper foils; this mismatch causes residual thermal stresses. To attenuate the mismatch, silica nanoparticles may be used to reduce the CTE of PI. A nodulated copper surface can be used to enhance the Cu/PI adhesion by additional bonding mechanisms that could include a type of mechanical bonding, which is a focus of this study. In this investigation, a 90° peel test was used to measure the peel strength in copper/polyimide/copper laminates containing nodulated copper and polyimide reinforced with 0, 20, and 40 wt % silica nanoparticles. The influence of silica nanoparticles on the peel strength was quantitatively evaluated. Laminates incorporating polyimide films lacking silica nanoparticles had a ∼3.75× higher peel strength compared with laminates reinforced with 40% silica. Their failure surfaces were analyzed by using scanning electron microscopy (SEM), energy-dispersive X-ray analysis (EDX), and X-ray photoelectron spectroscopy to identify the mode of failure and to understand bonding mechanisms. The key bonding mechanism, mechanical interlocking, was achieved when the polyimide surrounded or engulfed the copper nodules when the laminate was created. Post-testing failure surface analysis revealed the presence of copper on the polyimide side and polyimide on the copper side, indicating mixed mode failure. An analytical model was developed to determine the impact of applied pressure, temperature, and time on the polyimide penetration and mechanical interlocking around the copper nodules. The model was validated by measuring the peel strength on another set of specimens fabricated using increased temperature and pressure that showed a 3× increase in peel strength compared to lower temperature/pressure processing conditions. This enhanced adhesion resulted from the lower polymer material viscosity at higher temperatures, which fosters deeper and more complete penetration around the copper nodules during processing at higher pressures for longer durations. The methodology of combining peel testing, viscosity and CTE measurement, SEM/EDX, surface chemical analysis, and penetration depth calculation developed herein enables the calculation of the desired processing parameters to enhance functionality and improve adhesion.

A fully nonlinear viscohyperelastic model for the brain tissue applicable to dynamic rates.

Understanding the mechanical response of the brain to external loadings is of critical importance in investigating the pathological conditions of this tissue during injurious conditions. Such injurious loadings may occur at high rates, for example among others, during road traffic or sport accidents, falls, or due to explosions. Hence, investigating the injury mechanism and design of protective devices for the brain requires constitutive modeling of this tissue at such rates. Accordingly, this paper is aimed at critically investigating the physical background for viscohyperelastic modeling of the brain tissue with scrutinizing the elastic fields pertinent to large, time dependent deformations, and developing a fully nonlinear multimode Maxwell model that can mathematically explain such deformations. The proposed model can be calibrated using the simple monotonic uniaxial deformation of the sample extracted from the tissue, and does not require additional information from relaxation or creep experiments. The performance of the proposed model is examined using the experimental results of two different studies, which reveals a desirable agreement. The usefulness, limitations, and future developments of the proposed model are discussed in this paper.

Hyperelastic modeling of the human brain tissue: Effects of no-slip boundary condition and compressibility on the uniaxial deformation.

Being extremely soft, brain tissue is among the most challenging materials to be mechanically quantified. Despite recent advances in mechanical testing of ultra-soft matters, there still exists a need for robust procedures to analyze their behavior at large deformation. In this paper, it is shown how failing to taking into account the precise boundary conditions can result in substantial variation from the "assumed" ideal behavior, even for the case of simple loading conditions such as the uniaxial mode. For an accurate analysis, the mathematical modeling is combined with the finite element simulation to interpret the mechanical behavior of the brain tissue based on the comprehensive experiments conducted by Budday et al. (2017). It is demonstrated herein that only an Ogden hyperelastic model with both negative and positive nonlinearity constants can predict the mechanical behavior of the brain tissue in tension and compression, and the tension-compression asymmetry might arise from the difference in compressibility behavior in tension and compression. This hypothesis is utilized for modeling the mechanical behavior of the brain tissue in uniaxial loading condition and exhibits excellent agreement with the experiments. This study also provides a comprehensive explanation for nonlinear analysis of soft matters, in general, and the brain tissue, in particular, with thoroughly describing the concept of hyperelasticity and modeling incompressible or compressible behaviors utilizing the Ogden strain energy function.

A combined experimental, modeling, and computational approach to interpret the viscoelastic response of the white matter brain tissue during indentation.

Viscoelastic properties of the white matter brain tissue are systematically studied in this paper utilizing indentation experiments, mathematical modeling, and finite element simulation. It is first demonstrated that the internal stiffness of the instrument needs to be thoroughly obtained and incorporated in the analysis as its contribution to the recorded mechanical response is significant for experiments on very compliant materials. The flat-punch monotonic indentation is then performed indirectly on sagittal plane slices with pushing a large rigid coverslip into the sample surface. The recorded load and displacement data are used for calibrating different viscoelastic models and presenting numerical values for the model elements. Consequently, the accuracy of the findings based on the theoretical models is investigated by performing finite element simulations which suggest a considerable substrate effect that causes violation of the semi-infinite half-space assumption in modeling of the material behavior. Accordingly, correction factors for adjusting the viscoelastic constants are obtained and presented. Since the Maxwell model shows a superior capability in rendering the mechanical response of the brain, an extension of this model to Multimode Maxwell viscoelastic solid is proposed for modeling the tissue behavior under a more complex load-hold-unload indentation cycle that shows acceptable agreement with experimental observations.

An Indirect Indentation Method for Evaluating the Linear Viscoelastic Properties of the Brain Tissue.

Indentation experiments offer a robust, fast, and repeatable testing method for evaluating the mechanical properties of the solid-state materials in a wide stiffness range. With the advantage of requiring a minimal sample preparation and multiple tests on a small piece of specimen, this method has recently become a popular technique for measuring the elastic properties of the biological materials, especially the brain tissue whose ultrasoft nature makes its mechanical characterization very challenging. Nevertheless, some limitations are associated with the indentation of the brain tissue, such as improper surface detection, negative initial contact force due to tip-tissue moisture interaction, and partial contact between the tip and the sample. In this study, an indirect indentation scheme is proposed to overcome the aforementioned difficulties. In this way, the indentation force is transferred from a sharp tip to the surface of the tissue slices via a rigid coverslip. To demonstrate the accuracy of this method, the linear viscoelastic properties of the white and gray matters of the bovine brain samples are measured by imposing small cyclic loads at different frequencies. The rate, regional, directional, and postmortem time dependence of the viscoelastic moduli are investigated and compared with the previous results from cyclic shear and monotonic experiments on the brain tissue. While findings of this research present a comprehensive set of information for the viscoelastic properties of the brain at a wide frequency range, the central goal of this paper is to introduce a novel experimentation technique with noticeable advantages for biomechanical characterization of the soft tissue.

The effect of the physical properties of the substrate on the kinetics of cell adhesion and crawling studied by an axisymmetric diffusion-energy balance coupled model.

In this paper an analytical approach to study the effect of the substrate physical properties on the kinetics of adhesion and motility behavior of cells is presented. Cell adhesion is mediated by the binding of cell wall receptors and substrate's complementary ligands, and tight adhesion is accomplished by the recruitment of the cell wall binders to the adhesion zone. The binders' movement is modeled as their axisymmetric diffusion in the fluid-like cell membrane. In order to preserve the thermodynamic consistency, the energy balance for the cell-substrate interaction is imposed on the diffusion equation. Solving the axisymmetric diffusion-energy balance coupled equations, it turns out that the physical properties of the substrate (substrate's ligand spacing and stiffness) have considerable effects on the cell adhesion and motility kinetics. For a rigid substrate with uniform distribution of immobile ligands, the maximum ligand spacing which does not interrupt adhesion growth is found to be about 57 nm. It is also found that as a consequence of the reduction in the energy dissipation in the isolated adhesion system, cell adhesion is facilitated by increasing substrate's stiffness. Moreover, the directional movement of cells on a substrate with gradients in mechanical compliance is explored with an extension of the adhesion formulation. It is shown that cells tend to move from soft to stiff regions of the substrate, but their movement is decelerated as the stiffness of the substrate increases. These findings based on the proposed theoretical model are in excellent agreement with the previous experimental observations.

An analytical approach to study the intraoperative fractures of femoral shaft during total hip arthroplasty.

An analytical approach which is popular in micromechanical studies has been extended to the solution for the interference fit problem of the femoral stem in cementless total hip arthroplasty (THA). The multiple inhomogeneity problem of THA in transverse plane, including an elliptical stem, a cortical wall, and a cancellous layer interface, was formulated using the equivalent inclusion method (EIM) to obtain the induced interference elastic fields. Results indicated a maximum interference fit of about 210 µm before bone fracture, predicted based on the Drucker-Prager criterion for a partially reamed section. The cancellous layer had a significant effect on reducing the hoop stresses in the cortical wall; the maximum press fit increased to as high as 480 µm for a 2 mm thick cancellous. The increase of the thickness and the mechanical quality, i.e., stiffness and strength, of the cortical wall also increased the maximum interference fit before fracture significantly. No considerable effect was found for the implant material on the maximum allowable interference fit. It was concluded that while larger interference fits could be adapted for younger patients, care must be taken when dealing with the elderly and those suffering from osteoporosis. A conservative reaming procedure is beneficial for such patients; however, in order to ensure sufficient primary stability without risking bone fracture, a preoperative analysis might be necessary.