Effect of imperfections on the yielding of two-dimensional foams

The influence of each of the six different types of morphological imperfection - waviness, non-uniform cell wall thickness, cell-size variations, fractured cell walls, cell-wall misalignments, and missing cells - on the yielding of 2D cellular solids has been studied systematically for biaxial loading. Emphasis is placed on quantifying the knock-down effect of these defects on the hydrostatic yield strength and upon understanding the associated deformation mechanisms. The simulations in the present study indicate that the high hydrostatic strength, characteristic of ideal honeycombs, is reduced to a level comparable with the deviatoric strength by several types of defect. The common source of this large knock-down is a switch in deformation mode from cell wall stretching to cell wall bending under hydrostatic loading. Fractured cell edges produce the largest knock-down effect on the yield strength of 2D foams, followed in order by missing cells, wavy cell edges, cell edge misalignments, Γ Voronoi cells, δ Voronoi cells, and non-uniform wall thickness. A simple elliptical yield function with two adjustable material parameters successfully fits the numerically predicted yield surfaces for the imperfect 2D foams, and shows potential as a phenomenological constitutive law to guide the design of structural components made from metallic foams.

Mechanically tunable conjugated polymer distributed feedback lasers

Herein we report a low-threshold organic laser device based on semiconducting poly(9, 9′ -dioctylfluoren-2,7-diyl-alt-benzothiadiazole) (F8BT) encapsulated in a mechanically stretchable polydimethylsiloxane (PDMS) matrix. We take advantage of the natural flexibility of PDMS to alter the periodicity of the distributed feedback grating which in turn tunes the gain wavelength at which the resonant feedback is obtained. This way, we demonstrate that low-threshold lasing [6.1 μJ cm-2 (5.3 nJ)] is maintained over a large stretching range of 0%-7% which translates into a tuning range of about 20 nm. © 2010 American Institute of Physics.

Mode I and Mode II Crack Tip Asymptotic Fields with Strain Gradient Effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

The interaction between poly(vinylpyrrolidone) and reversed micelles of water/AOT/n-heptane

The interactions between poly(vinylpyrrolidone) (PVP) and the reversed micelles composed of water, AOT, and n-heptane are investigated with the aid of phase diagram, measurements of conductivity and viscosity, Fourier transform infrared (FTIR) spectrum, and dynamic light scattering (DLS). The phase diagrams of water/AOT/heptane in the presence of and absence of PVP are given. The conductivity of the water/AOT/heptane reversed micelle without PVP initially increases and then decreases with the increase of water content, ω0 (the molar ratio of water to AOT), while the plots of conductivity (K) versus ω0 of the reversed micelle in the presence of PVP depend on the PVP concentrations. The plot of K versus ω0 with 2.0%wt PVP is similar to that without PVP. Only the ω0,max (the water content that the maximum conductivity corresponds to) is larger than that without PVP. Nevertheless, the conductivity of the reversed micelle containing more than 4%wt PVP always rises with the increase of the water content in the measured range. The DLS results indicate that the hydrodynamic radius (Rh) in the presence and absence of PVP rises with the increase of ω0. The plots with PVP and without PVP have almost the same value when ω0<17; and after that, it quickly increases with the increase of ω0. It is interesting to find that there is almost no effect of the PVP concentration on the viscosity and Rh of the reversed micelle at ω0 = 15. The FTIR results suggest that the contents of SO3--bound water and Na+-bound water both decrease with PVP added, while the content of the bulky-like water increases. However, the trapped water in the hydrophobic chain of the surfactant is nearly unaffected by PVP. It is also found from the FTIR that the carbonyl group stretching vibration of AOT is fitted into two sub-peaks, which center at 1740 and 1729 cm-1, corresponding to the trans and cis conformations of AOT, respectively.

Forced extension of P-selectin construct using steered molecular dynamics

P-selectin, a 70-nm-long cellular adhesive molecule, possesses elastic and extensible properties when neutrophils roll over the activated endotheliam of blood vessel in inflammatory reaction. Transient formation and dissociation of P-selectin/ligand bond on applied force of blood flow induces the extension of P-selectin and relevant ligands. Steered molecular dynamics simulations were performed to stretch a single P-selectin construct consisting of a lectin (Lec) domain and an epithelial growth factor (EGF)-like domain, where P-selectin construct was forced to extend in water with pulling velocities of 0.005-0.05 nm/ps and with constant forces of 1000-2500 pN respectively. Resulting force-extension profiles exhibited a dual-peak pattern on various velocities, while both plateaus and shoulders appeared in the extension-time profiles on various forces. The force or extension profiles along stretching pathways were correlated to the conformational changes, suggesting that the structural collapses of P-selectin Lec/EGF domains were mainly attributed to the burst of hydrogen bonds within the major beta sheet of EGF domain and the disruptions of two hydrophobic cores of Lee domain. This work furthers the understanding of forced dissociation of P-selectin/ligand bond.

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wave-current field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does sx, by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.

The Effect of the Thickness of Fe2 Al5 Phase Layer at Fe/Al Interface on the Mechanics Behavior of Hot Dip Aluminizing Coating

Hot Dip Aluminized Coatings with different thickness were prepared on Q235 steel in aluminum solutions with different temperature for certain time. Through tensile tests and in-situ SEM observations, the effect of the coating's microstructure on the tensile strength of the samples was studied. It was disclosed at certain aluminum solution temperature,transaction layers mainly composed of Fe2 Al5 phase got thicker with time prolonging, and this changed initial crack's extending direction from parallel with to vertical with stretching direction. The change in crack direction decreased tensile strength of samples, thus made the coating easy to break. It was concluded that the existence of thick Fe2 Al5 phase layer was the basic reason for the lowering of tensile strength of the coating.

Atomistic Simulation On Size-Dependent Yield Strength And Defects Evolution Of Metal Nanowires

A simple derivation based on continuum mechanics is given, which shows the surface stress is critical for yield strength at ultra-small scales. Molecular dynamics (MD) simulations with modified embedded atom method (MEAM) are employed to investigate the mechanical behaviors of single-crystalline metal nanowires under tensile loading. The calculated yield strengths increasing with the decrease of the cross-sectional area of the nanowires are in accordance with the theoretical prediction. Reorientation induced by stacking faults is observed at the nanowire edge. In addition. the mechanism of yielding is discussed in details based on the snapshots of defects evolution. The nanowires in different crystallographic orientations behave differently in stretching deformation. This study on the plastic properties of metal nanowires will be helpful to further understanding of the mechanical properties of nanomaterials. (C) 2009 Elsevier B.V. All rights reserved.

Stabilizing to disruptive transition of focal adhesion response to mechanical forces

Strong mechanical forces can, obviously, disrupt cell-cell and cell-matrix adhesions, e.g., cyclic uniaxial stretch induces instability of cell adhesion, which then causes the reorientation of cells away from the stretching direction. However, recent experiments also demonstrated the existence of force dependent adhesion growth (rather than dissociation). To provide a quantitative explanation for the two seemingly contradictory phenomena, a microscopic model that includes both integrin-integrin interaction and integrin-ligand interaction is developed at molecular level by treating the focal adhesion as an adhesion cluster. The integrin clustering dynamics and integrin-ligand binding dynamics are then simulated within one unified theoretical frame with Monte Carlo simulation. We find that the focal adhesion will grow when the traction force is higher than a relative small threshold value, and the growth is dominated by the reduction of local chemical potential energy by the traction force. In contrast, the focal adhesion will rupture when the traction force exceeds a second threshold value, and the rupture is dominated by the breaking of integrin-ligand bonds. Consistent with the experiments, these results suggest a force map for various responses of cell adhesion to different scales of mechanical force. PMID: 20542514

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Parylene-C as a new piezoelectric material

The goal of this thesis is to develop a proper microelectromechanical systems (MEMS) process to manufacture piezoelectric Parylene-C (PA-C), which is famous for its chemical inertness, mechanical and thermal properties and electrical insulation. Furthermore, piezoelectric PA-C is used to build miniature, inexpensive, non-biased piezoelectric microphones.

These piezoelectric PA-C MEMS microphones are to be used in any application where a conventional piezoelectric and electret microphone can be used, such as in cell phones and hearing aids. However, they have the advantage of a simplified fabrication process compared with existing technology. In addition, as a piezoelectric polymer, PA-C has varieties of applications due to its low dielectric constant, low elastic stiffness, low density, high voltage sensitivity, high temperature stability and low acoustic and mechanical impedance. Furthermore, PA-C is an FDA approved biocompatible material and is able to maintain operate at a high temperature.

To accomplish piezoelectric PA-C, a MEMS-compatible poling technology has been developed. The PA-C film is poled by applying electrical field during heating. The piezoelectric coefficient, -3.75pC/N, is obtained without film stretching.

The millimeter-scale piezoelectric PA-C microphone is fabricated with an in-plane spiral arrangement of two electrodes. The dynamic range is from less than 30 dB to above 110 dB SPL (referenced 20 µPa) and the open-circuit sensitivities are from 0.001 – 0.11 mV/Pa over a frequency range of 1 - 10 kHz. The total harmonic distortion of the device is less than 20% at 110 dB SPL and 1 kHz.

变形镜对千赫兹掺钛蓝宝石飞秒激光频谱相位补偿

尝试用光谱展宽的方法从频谱相位(而非时域相位)的角度利用变形反射镜来补偿1kHz飞秒激光系统输出光路的频谱相位畸变，从而提高飞秒激光脉冲的时域强度衬比度，改善其光束质量。频谱相位补偿实验是在一台1kHz掺钛蓝宝石飞秒激光系统输出光路中，针对超短脉冲光束通过传输介质后的频谱相位畸变，引入变形反射镜进行补偿。应用频谱相位干涉直接电场重构(SPIDER)方法和仪器作为测量手段，建立了一套相位测量补偿系统。实验结果表明用变形反射镜可使激光脉冲的相位畸变得到较好的补偿，脉冲的光束质量得到改善。这种方法的主要思想就是

超短脉冲照射下氟化锂的烧蚀机理及其超快动力学研究

研究了超短脉冲激光照射下LiF晶体的破坏机理及其超快动力学过程，利用扫描电镜和原子力显微镜等测试手段，观测了飞秒激光照射下LiF晶体的烧蚀形貌。利用烧蚀面积与激光脉冲能量的对数关系确定了LiF晶体的破坏阈值，并利用非线性玻璃棒展宽脉宽，得到了800nm激光作用下LiF破坏阈值对激光脉宽（50～1000fs）的依赖关系；利用抽运一探针超快探测平台，探测了LiF烧蚀过程中反射率的变化。采用雪崩击穿模型，并根据晶体材料反射率与材料的介电常量的依赖关系，通过数值计算，模拟了材料烧蚀阈值与脉宽的依赖关系及材料激发过

Zirconocenes as models for homogeneous Ziegler-Natta olefin polymerization catalysts

Using density functional theory, we studied the fundamental steps of olefin polymerization for zwitterionic and cationic Group IV ansa-zirconocenes and a neutral ansa- yttrocene. Complexes [H₂E(C₅H₄)₂ZrMe]ⁿ (n = 0: E = BH₂ (1), BF₂ (2), AlH₂(3); n = +: E = CH₂(4), SiH₂(5)) and H₂Si(C₅H₄)₂YMe were used as computational models. The largest differences among these three classes of compounds were the strength of olefin binding and the stability of the β-agostic alkyl intermediate towards β-hydrogen elimination. We investigated the effect of solvent on the reaction energetics for land 5. We found that in benzene the energetics became very similar except that a higher olefin insertion barrier was calculated for 1. The calculated anion affinity of [CH₃BF₃]^- was weaker towards 1 than 5. The calculated olefin binding depended primarily on the charge of the ansa linker, and the olefin insertion barrier was found to decrease steadily in the following order: [H₂C(C₅H₄)₂ZrMe]⁺ > [F₂B(C₅H₄)₂ZrMe] ≈ [H₂B(C₅H₄)₂ZrMe] > [H₂Si(C₅H₄)₂ZrMe]⁺ > [H₂Al(C₅H₄)₂ZrMe].

We prepared ansa-zirconocene dicarbonyl complexes Me₂ECp₂Zr(CO)₂ (E = Si, C), and t-butyl substituted complexes (t-BuCp)₂Zr(CO)₂, Me₂E(t-BuCp)₂Zr(CO)₂ (E = Si, C), (Me₂Si)₂(t-BuCp)₂Zr(CO)₂ as well as analogous zirconocene complexes. Both the reduction potentials and carbonyl stretching frequencies follow the same order: Me₂SiCp₂ZrCl₂> Me₂CCp₂ZrCl₂> Cp₂ZrCl₂> (Me₂Si)₂Cp₂ZrCl₂. This ordering is a result of both the donating abilities of the cyclopentadienyl substituents and the orientation of the cyclopentadiene rings. Additionally, we prepared a series of analogous cationic zirconocene complexes [LZrOCMe₃][MeB(C₆F₅)₃] (L = CP₂, Me₂SiCp₂, Me₂CCP₂, (Me₂Si)₂Cp₂) and studied the kinetics of anion dissociation. We found that the enthalpy of anion dissociation increased from 10.3 kcal•mol^-1 to 17.6 kcal•mol^-1 as exposure of the zirconium center increased.

We also prepared series of zirconocene complexes bearing 2,2-dimethyl-2-sila-4-pentenyl substituents (and methyl-substituted olefin variants). Methide abstraction with B(C₆F₅) results in reversible coordination of the tethered olefin to the cationic zirconium center. The kinetics of olefin dissociation have been examined using NMR methods, and the effects of ligand variation for unlinked, singly [SiMe₂]-linked and doubly [SiMe₂]-linked bis(cyclopentadienyl) arrangements has been compared (ΔG‡ for olefin dissociation varies from 12.8 to 15.6 kcal•mol^-1). Methide abstraction from 1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(CH₃)-(CH₂CMe₂CH₂CH = CH₂) results in rapid β-allyl elimination with loss of isobutene yielding the allyl cation [{1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(η³-CH₂CH=CH₂)]⁺.