Effective dielectric responses of graded composites of the particles with a general power-law gradation profile

The effective dielectric response of graded spherical composites having general power-law gradient inclusions is investigated under a uniform applied electric field, where the dielectric gradation profile of the spherical inclusions is modeled by the equation epsilon(i) (r) = c(b+r)(k). Analytical solutions of the local electrical potentials are derived in terms of hyper-geometric function and the effective dielectric response of the graded composites is predicted in the dilute limit. From our result, the local potentials of graded spherical composites having both simple power-law dielectric profile epsilon(i)(r) = cr(k) and linear dielectric profile epsilon(i) (r) = c(b+r) are derived exactly by taking the limits b --> 0 and k --> 1, respectively. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded spherical composites, and it is shown that the DEDA is in excellent agreement with exact result. (C) 2005 Elsevier B.V. All rights reserved.

Effective AC response of nonlinear spherical coated composites

Under alternating current electric field, effective response of granular nonlinear composites with spherical coated inclusions is investigated in the dilute limit by using the perturbation approach. For an external sinusoidal applied field with finite frequency omega, the local fields and potentials of composites in general consist of components at all harmonics for cubic nonlinear constitutive relationships. We derive the local potentials of spherical coated composites at harmonics. Moreover, we give the formulae of the nonlinear effective AC susceptibility at the third harmonic frequency.

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency omega. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.

Dielectric responses of graded cylindrical composites

The effective dielectric responses of linear composites with graded cylindrical particles are investigated under an external uniform electric field. As an example, with the Kummer function, we have obtained the analytical solutions of electric potentials of graded composites with a cylindrical inclusion particle of dielectric function profile epsilon(i) = cr(k)e(betar), where r is the inside distance of a point in cylindrical particle from the original point of cylindrical coordinates. In the dilute limit, the effective dielectric response is derived by means of the mean field method. For larger volume fraction, we have estimated the dielectric response of the graded composites with an effective medium approximation. Furthermore, from our results, we have discussed the effective responses of graded composites for power-law and exponential dielectric function profiles, respectively. (C) 2004 Elsevier B.V. All rights reserved.

Effective ac response in weakly nonlinear composites

The perturbation method is developed to deal with the problem of determining the effective nonlinear conductivity of Kerr-like nonlinear media under an external ac electric field. As an example, we have considered the cylindrical inclusion embedded in a host under the sinusoidal external field E-1 sin(omegat) + E-3 sin(3omegat) with frequencies omega and 3omega. The potentials of composites at higher harmonics are derived in both local inclusion particle and host regions. The effective responses of bulk nonlinear composites at basic frequency and harmonics are given for cylindrical composites in the dilute limit. Moreover, the relationships between the nonlinear effective responses at the basic frequency and the third harmonics are derived.

Effective dielectric response of composites witli graded material

The effective dielectric response of linear composites containing graded material is investigated under an applied electric field Eo. For the cylindrical inclusion with gradient dielectric function, epsilon(i)(r) = b + cr, randomly embedded in a host with dielectric constant epsilon(m), we have obtained the exact solution of local electric potential of the composite media regions, which obeys a linear constitutive relation D = epsilonE, using hypergeometric function. In dilute limit, we have derived the effective dielectric response of the linear composite media. Furthermore, for larger volume fraction, the formulas of effective dielectric response of the graded composite media, are given.

Effective dielectric response of graded spherical composites

The effective dielectric response of composites containing graded material is investigated when an external uniform electric field E-0 is applied to it. For a spherical particle with gradient dielectric constant, epsilon(i) (r) = b + cr, randomly embedded in a host with dielectric constant epsilon(m), we have obtained the exact solution of local electric potential in the composite media regions, which obey a linear constitutive relation D = epsilonE, using hypergeometric function. In dilute limit, the effective dielectric response of the linear graded composite media is derived. Furthermore, for larger volume fraction, we have given an effective medium approximation to estimate the effective dielectric response of the graded composite media. (C) 2003 Elsevier B.V All rights reserved.

Effective properties of graded elliptical cylindrical composites

The effective property has been investigated theoretically in graded elliptical cylindrical composite's consisting of inhomogeneous graded elliptical cylinders and an isotropic matrix under external uniform electric field. As a theoretical model, the dielectric gradient profile in the elliptical cylinder is modeled by a power-law function of short semi-axis variable parameter (xi(2) - 1) in the elliptical cylindrical coordinates, namely epsilon(i)(xi) = c(k) (xi(2) - 1)(k), where c(k) and k are the parameters, and xi is the long semi-axis space variable in an elliptical cylindrical inclusion region. In the dilute limit, the local analytical potentials in inclusion and matrix regions are derived exactly by means of the hyper-geometric function, and the formulas are given for estimating the effective dielectric responses under the external lfield along (x) over cap- and (y) over cap -directions, respectively. Furthermore, we have demonstrated that our effective response formulas can be reduced to the well-known results of homogeneous isotropic elliptical cylindrical composites if we take the limit k -> 0 in graded elliptical cylindrical composites. (c) 2006 Elsevier B.V. All rights reserved.

Effective properties of spherically anisotropic piezoelectric composites

Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions (i.e., piezoceramic material) in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease (increase) as the inclusion elastic (piezoelectric) constants increase.

Effective AC and DC responses of nonlinear composites at higher concentration

For higher concentration of inclusions, an effective medium approximation (EMA) method is used to investigate the bulk effective response of weakly nonlinear composites, which are subject to the constitutive relation of electric displacement and electric field, D-alpha = epsilon E-alpha + chi(alpha)|E|(2) E. As an example of three dimensions, under the external AC and DC electric fields E-app = E-a (1 + sin omega t), we have derived the general effective nonlinear response of composites by the EMA method for higher concentration of spherical inclusions. Furthermore, the effective nonlinear responses at harmonics are predicted.

Dielectric response of spherically anisotropic graded piezoelectric composites

A graded piezoelectric composite consisting of a spherically anisotropic graded piezoelectric inclusion imbedded in an infinite nonpiezoelectric matrix, with the physical properties of the graded spherical inclusion having a power-law profile with respect to the radial variable r, is studied theoretically. Under an external uniform electric field, the electric displacement field and the elastic stress tensor field of this spherically anisotropic graded piezoelectric composite are derived exactly by means of displacement separation technique, based on the governing equations in the dilute limit. A piezoelectric response mechanism, in which the effective piezoelectric response vanishes along the z direction (or x,y directions), is revealed in this kind of graded piezoelectric composites. Furthermore, it is found that the effective dielectric constant decreases (or increases) with the volume fraction p of the inclusions if the exponent parameter k of the grading profile is larger (or smaller) than a critical value. (C) 2007 American Institute of Physics.

基于介电泳的电极阵列电场仿真研究

介电泳方法被广泛地应用于微纳颗粒的分离和操纵中,实现介电泳操作的关键是设计满足所需电场分布的电极阵列。针对目前在微电极阵列设计中尚缺乏简单有效的电场解析方法的现状,提出一种基于格林公式的电极阵列电场的解析方法。首先介绍了传统介电泳和行波介电泳的概念和计算模型,分析了介电泳过程与电极上所施加的交变电压的频率和幅度的关系,然后在确立电极电势的边界条件的基础上,采用基于格林公式的电场解析方法,建立了非均匀电场的解析模型,得出不同条件下的电极阵列电场分布的仿真结果,最后利用FEMLAB有限元仿真软件对解析模型进行了对比仿真,验证了该解析模型的可行性。基于格林公式的电场解析求解方法能够有效地提高电极阵列设计中的针对性以及缩短电极设计的时间。

面向微粒操纵的介电泳芯片系统研究

针对目前在纳米器件及传感器的制造中尚无对大量粒子进行有效操纵的方法,我们利用介电泳方法对大量微粒进行定位和传输操纵,介绍了利用MEMS工艺进行介电泳芯片加工的过程以及整个观测与实验系统的建立,通过有限元软件对传统介电泳和行波介电泳中电极阵列的电场分布进行求解,并在该实验系统下实现了对微通道中的悬浮高度和微粒的运动速度的测量.该实验系统的研究为液体环境下微纳颗粒的装配和分离提供了一条有效的技术路径.

纳电子器件制备的单根碳纳米管精确装配与电连接研究

目前,利用单根碳纳米管进行纳电子器件的研制成为纳电子学界研究的前沿与热点,但在纳电子器件研制过程中,如何实现单根碳纳米管与微电极的精确装配与电连接成为关键技术难题之一。为探索实现此关键技术的新方法,本文尝试将介电电泳与具有实时力/视觉反馈的原子力显微镜操作方法相结合,从而结合粗、精两级操作方式,来实现单根碳纳米管的精确装配与电连接。单根多壁碳纳米管的精确装配与电特性测试实验验证了该方法的有效性,从而为装配研制基于单根纳米管/线的纳电子器件提供了一种新颖可行的方法。

基于机械力与电场的AFM纳米操作/加工研究

纳米技术是在纳米尺度上研究物质的特性和相互作用，以及利用这些特性的多学科交叉的新兴科学技术。纳米加工技术是对纳米技术的重要应用，它使人类在纳米尺度上进行结构和器件的制造成为可能。基于原子力显微镜(AFM)的纳米加工是近20年来发展的技术，由于AFM具有许多新颖的技术特点(如高分辨率，可操控等)，因而基于AFM的纳米加工技术成为纳米科学研究的新热点。 本论文以纳米制造为背景，围绕基于AFM的纳米加工技术所涉及的科学问题，重点开展了基于机械力的AFM纳米操作和基于电场的AFM纳米加工的理论方法和实现技术研究。在这些研究的基础上，开展了基于纳观机械力的刻划、纳米颗粒的排列、碳纳米管的装配实验研究，开展了基于微观电场的氧化点、氧化线、氧化文字的加工实验研究，以及微观电场氧化切割、焊接加工方法的研究。 本文的主要内容包括：交互式纳米操作系统的构建，基于机械力的AFM纳米操作研究，基于电场的AFM纳米加工研究，基于机械力与电场的AFM纳米操作/加工实验研究。具体如下： 在商用AFM的基础上，研究并搭建了具有力觉与视觉反馈的交互式纳米操作系统。通过该系统操作者可以实时感觉到操作中作用在AFM针尖的纳观力并控制针尖的运动，还可以实时观察到模拟出的针尖操作过程，因而显著提高了纳米操作的直观性、可靠性及效率。 在基于机械力的AFM纳米操作研究方面，为了理解纳观环境下普遍存在的黏附力特性，对AFM的力曲线进行了分析并给出了详细解释；通过研究探针悬臂的形变，提出了探针所受三维作用力的建模方法，以此模型获得了操作中的纳观力信息；基于多刚体动力学理论提出了碳纳米管的二连杆动力学建模方法，并对碳纳米管在操作中的弯曲特性进行了仿真分析。这些研究为基于机械力的AFM纳米操作提供了理论指导。 在基于电场的AFM纳米加工方面，研究了微观电场在样本表面的分布，建立了电场氧化加工中电场分布模型，以此模型分析了氧化物特性与电场分布的关系；对氧化加工中氧化物生长过程进行了动力学分析，得到了氧化物生长的理论模型；系统地研究了氧化加工中各因素(偏压，加工速度，针尖－样本距离等)对氧化结构生成的影响，总结了氧化物的生成与各因素的关系，验证了理论分析的结果，提高了电场氧化加工的重复性及可控性。这些研究为基于电场的AFM纳米加工提供了理论及实验依据。 在基于机械力与电场的AFM纳米操作/加工理论研究的基础上，进行了相关的实验研究。通过基于机械力的AFM纳米操作方法实现了在样本表面刻划文字，纳米颗粒的排列，碳纳米管的操作及装配；通过基于电场的AFM纳米加工方法实现了在样本表面加工氧化点，氧化线及氧化文字等纳米结构。利用电场氧化加工方法还实现了对碳纳米管的定点切割与焊接，拓展了AFM纳米加工的应用领域。这些实验研究验证了系统的操作及装配性能，证明了电场加工的有效性及具有潜在的应用前景。 本文的研究工作为制造纳米结构、纳米器件提供了一条可行的技术途径，对AFM纳米加工技术的进一步发展具有一定的理论参考及实践指导意义。