The scattering theory of C. Wilcox in elasticity

We extend the abstract time‐dependent scattering theory of C.H. Wilcox to the case of elastic waves. Most of the results are proved with the minimal assumption that the obstacle satisfies the energy local compactness condition (ELC). This holds especially for the existence and unitarity of the wave operators. Copyright © 2002 John Wiley & Sons, Ltd.     

Buckling in a solid Langmuir monolayer: light scattering measurements and elastic model

Above a surface pressure threshold , we detect a buckled state in the low temperature solid phase of a phospholipid monolayer spread at the air-formamide interface. Stable ripples are observed with a Brewster angle microscope, and light scattering provides measurements mNm^-1, wavelength m and amplitude of a few nm for the deformation. A model, coupling the monolayer thickness and elongation, and consistent with the monolayer texture, is also presented. Received: 18 August 1997 / Revised: 9 December 1997 / Accepted: 29 January 1998     

Tilt model of inverted amphiphilic mesophases

We present an alternative model of structure and energetics of the inverted amphiphilic mesophases. The previous studies of the inverted hexagonal, H_II, and inverted micellar cubic, Q_II, phases considered the amphiphilic monolayers to be homogeneously bent. In contrast, we assume a unit cell of an inverted mesophase to consist of flat fragments of monolayer. Hence, the unit cells of the H_II and Q_II phases are represented by a hexagonal rod and a polyhedron, respectively. Our model is motivated by Turner and Gruner's X-ray diffraction reconstruction of structure of the H_II phase. The only deformation of the amphiphilic monolayers we consider is tilt of the hydrocarbon chains with respect to the monolayer surface, determined by the packing constraints imposed in the mesophases. Applying our recent model for the elastic energy of tilt in liquid membranes [#!ref23!#], we show that: i) tilt accounts in a natural way for the frustration energy of mesophases resulting from filling by the hydrocarbon chains the corners of the unit cells, ii) the energy of tilt variation along the membrane surface is analogous to the bending energy. We compute the energetics of the H_II, Q_IIsc and Q_IIfcc phases and obtain a hypothetical phase diagram in terms of the elastic constants of monolayers. Moreover, we calculate the structural dimensions of the mesophases. We verify the model showing that the obtained phase diagram describes the recent data for the glycolipids/water systems; the predicted dimensions of the Q_II phase are in accord with the measured values; the model treats quantitatively the structural features observed for the H_II phase. Received: 9 February 1998 / Revised: 4 June 1998 / Accepted: 3 July 1998     

脯氨酸聚酯的单链力学性质

脯氨酸聚酯(PPEs)是一类分子量较高且分子量分布较窄的新型可降解脂肪族聚酯,有巨大的应用潜力.然而,还没有关于PPEs力学性质的报道.本工作使用基于原子力显微镜的单分子力谱(AFM-based SMFS)实验技术和熵焓弹性耦合模型研究了PNC 12PE(一种PPEs)在极性有机溶剂中的力学性质.熵焓弹性耦合模型对PN...     

靶向淋巴系统造影剂的制备及其动物实验

采用两种方法,一种方法是以右旋糖酐（Dextran）和DTPA的二酐为原料,DMAP为催化剂,另一种是以右旋糖酐和DTPA为原料,采用DMAP及EDC.HCl为联合催化剂,合成造影剂Dextran-DTPA-Gd.通过比较产物的水溶性及Gd含量确定了最佳制备条件,得到了钆含量为16.1%、水溶性好的高分子造影剂;通过FTIR、粒度分析表征了Dextran-DTPA-Gd的结构及其分子粒径大小（分布范围为100～150nm,平均值为130nm）;动物实验中,以钆喷酸葡胺注射液（Magnevist）为阳性对照,通过对比家兔腿部磁共振成像图,绘制腿部淋巴系统信号增强率-时间曲线,证明Dextran-DTPA-Gd具有更高的信号增强效果（最高值为314%）及淋巴系统选择性的特点,为其进一步应用奠定了基础.     

Circumferential buckling instability of a growing cylindrical tube

A cylindrical elastic tube under uniform radial external pressure will buckle circumferentially to a non-circular cross-section at a critical pressure. The buckling represents an instability of the inner or outer edge of the tube. This is a common phenomenon in biological tissues, where it is referred to as mucosal folding. Here, we investigate this buckling instability in a growing elastic tube. A change in thickness due to growth can have a dramatic impact on circumferential buckling, both in the critical pressure and the buckling pattern. We consider both single- and bi-layer tubes and multiple boundary conditions. We highlight the competition between geometric effects, i.e. the change in tube dimensions, and mechanical effects, i.e. the effect of residual stress, due to differential growth. This competition can lead to non-intuitive results, such as a tube growing to be thinner and yet buckle at a higher pressure.     

Non-local continuum modeling of carbon nanotubes: Physical interpretation of non-local kernels using atomistic simulations

The longitudinal, transverse and torsional wave dispersion curves in single walled carbon nanotubes (SWCNT) are used to estimate the non-local kernel for use in continuum elasticity models of nanotubes. The dispersion data for an armchair (10,10) SWCNT was obtained using lattice dynamics of SWNTs while accounting for the helical symmetry of the tubes. In our approach, the Fourier transformed kernel of non-local linear elastic theory is directly estimated by matching the atomistic data to the dispersion curves predicted from non-local 1D rod theory and axisymmetric shell theory. We found that gradient models incur significant errors in both the phase and group velocity when compared to the atomistic model. Complementing these studies, we have also performed detailed tests on the effect of length of the nanotube on the axial and shear moduli to gain a better physical insight on the nature of the true non-local kernel. We note that unlike the kernel from gradient theory, the numerically fitted kernel becomes negative at larger distances from the reference point. We postulate and confirm that the fitted kernel changes sign close to the inflection point of the interatomic potential. The numerically computed kernels obtained from this study will aid in the development of improved and efficient continuum models for predicting the mechanical response of CNTs.     

Curvature-dependent surface energy and implications for nanostructures

At small length scales, several size-effects in both physical phenomena and properties can be rationalized by invoking the concept of surface energy. Conventional theoretical frameworks of surface energy, in both the mechanics and physics communities, assume curvature independence. In this work we adopt a simplified and linearized version of a theory proposed by Steigmann–Ogden to capture curvature-dependence of surface energy. Connecting the theory to atomistic calculations and the solution to an illustrative paradigmatical problem of a bent cantilever beam, we catalog the influence of curvature-dependence of surface energy on the effective elastic modulus of nanostructures. The observation in atomistic calculations that the elastic modulus of bent nanostructures is dramatically different than under tension – sometimes softer, sometimes stiffer – has been a source of puzzlement to the scientific community. We show that the corrected surface mechanics framework provides a resolution to this issue. Finally, we propose an unambiguous definition of the thickness of a crystalline surface.     

Nonlocal vibration of carbon nanotubes with attached buckyballs at tip

Nonlocal longitudinal vibration of single-walled-carbon-nanotubes (SWCNTs) with attached buckyballs is considered. Attached buckyball at the tip of a SWCNT can significantly influence the resonance frequency of the vibrating system. Closed-form nonlocal transcendental equation for vibrating system with arbitrary mass ratio i.e. mass of buckyball to mass of SWCNT is derived. Nonlocal elasticity concept is employed to develop the frequency equations. Explicit analytical expressions of axial frequencies are proposed when mass of the attached buckyball is larger than the mass of SWCNT. Nonlocal longitudinal frequencies are validated with existing molecular dynamic simulation result. For arbitrary mass ratios, the frequency shifts in SWCNT due to (i) added buckyballs and (ii) nonlocal-effects are investigated. The present communication may be useful when designing tuneable resonator in NEMS applications.