缺陷单层和双层石墨烯的拉曼光谱及其激发光能量色散关系

拉曼光谱作为一种无破坏性、快速且敏锐的测试技术已经成 为表征石墨烯样品和研究其缺陷的最重要的实验手段之一. 本论文用离子注入在单层和双层石墨烯中产生缺陷, 并利用拉曼光谱研究了存在缺陷时单层和双层石墨烯的一阶和二阶拉曼模, 单层石墨烯的D模为双峰结构, 而双层石墨烯的D模具有四峰结构. 同时, 利用四条激光线系统地研究了本征和缺陷单层和双层石墨烯的拉曼峰频率的激发光能量依赖关系, 并基于石墨材料的双共振拉曼散射机理指认了离子注入后样品各拉曼峰的物理根源. 关键词： 石墨烯 缺陷 拉曼光谱 能量色散关系     

单层MoS_2的热弹耦合非线性板模型

单层二硫化钼(MoS_2)是有广泛应用前景的二维纳米材料,但其力学性质还没有被深入研究,特别是其热弹耦合力学行为迄今还没有被关注到.本文首次提出了考虑热应力影响的单层MoS_2的非线性板理论,并对比研究了其与石墨烯的热弹耦合力学性质.对于不可移动边界,结果显示:1)有限温度产生的热应力降低了MoS_2的刚度,但提高了石墨烯的刚度; 2)在相同几何尺寸和温度条件下,变形较小时MoS_2的刚度大于石墨烯,但伴随变形的增大,MoS_2的刚度将小于石墨烯.研究结果表明,边界预加轴向外力和环境温度可以调节单层二维纳米结构力学性质.本文建立的热弹耦合板模型,可以推广至其他单层二维纳米结构.     

单层石墨烯杨氏模量的理论模型

石墨烯力学性能的研究对其在半导体技术中的应用是十分重要的,本文基于半连续体模型并结合石墨烯纳米结构特性,通过对原子的描述构建了石墨烯形变分量和位移分量的新关系,从而给出了单层石墨烯结构形变能,并计算了不同尺寸单层石墨烯的杨氏模量值.通过对不同方向杨氏模量的分析,讨论了单层石墨烯的手性行为.结果表明:随着尺寸的增加,单层石墨烯两个方向的杨氏模量分别趋于0.746 TPa和0.743 TPa,当尺寸相同时,两方向杨氏模量的最大差值不超过0.003 TPa,此结果与文献报道结果相符.在小应变情况下,单层石墨烯薄膜呈各向同性,且薄膜尺寸变化对该特性影响不大.该计算结果对研究石墨烯的其它力学特性提供一定的参考价值.     

氧化石墨烯褶皱行为与结构的分子模拟研究

应用反应力场分子动力学方法,模拟了单层氧化石墨烯在径向压缩作用下的褶皱过程,研究了含氧基团(羟基、环氧基)对氧化石墨烯褶皱行为以及褶皱球结构稳定性的影响.当石墨烯仅含羟基时,该类氧化石墨烯呈现出"推进式"的褶皱行为,而当石墨烯仅含环氧基时,该类氧化石墨烯则呈现出片层与片层"贴合式"的褶皱行为.褶皱行为的不同决定了氧化石墨烯最终褶皱球结构的差异.通过分析原子级势能增量分布与C—C成、断键位置之间的关系,发现氧化石墨烯上C—C成、断键主要发生在变形较为严重的区域,且相较于羟基,环氧基对与其连接的C—C键具有更强的削弱作用.为了研究氧化石墨烯褶皱球的结构稳定性,模拟了其在无约束条件下的释放过程.发现氧化石墨烯褶皱球的结构稳定性取决于其中C—C成、断键数量,即C—C成、断键的数量越多,结构越稳定,且在同一氧化率下,褶皱球的结构稳定性随环氧基比例的增大而提高.本研究表明,通过改变氧化石墨烯片层上含氧基团的相对比例,可实现对其褶皱球稳定性的控制.     

石墨烯的三阶非线性和光双稳态调控特性

研究单层石墨烯的三阶非线性和光双稳态效应。通过理论分析和数值模拟,改变单层三阶非线性石墨烯的费米能级、弛豫时间、双光子吸收系数及温度条件,调制单层三阶非线性石墨烯光双稳态的阈值大小。单层三阶非线性石墨烯的费米能级越大,温度越高,则光双稳态的阈值越大;双光子吸收系数越大,双稳态的低阈值越大;弛豫时间和双光子吸收系数会明显地改变石墨烯结构的光透射率,而光透射率则对石墨烯材料自身温度不敏感。该结论可为设计各类微纳结构的光子器件如光开关和光传感等提供理论依据。     

范德华力的广义参变本构模型及其在碳纳米管计算中的应用

提出了处理非成键原子间范德华力的广义参变本构模型以及基于此进行碳纳米管结构力学行为数值模拟的数学规划算法.纳米管中原子间短程力作用采用分子结构力学模型来模拟，而作为长程力的范德华力用杆单元来模拟，这类杆单元有着特殊的非线性本构关系.对于这种非线性问题的处理，建立了广义参变本构模型与参数二次规划求解算法.与一般的数值方法相比较，本方法不需要传统的冗长的、反复的迭代，并具有非常好的收敛性，因此为碳纳米管结构力学行为的有效预测提供了保障.数值结果证明了这种方法的正确性和有效性. 关键词： 广义参变本构模型 数学规划算法 分子结构力学 有限元法     

单层与双层石墨烯的光学吸收性质研究

采用紧束缚模型分别描述单层、双层石墨烯的能带结构, 利用光子-电子相互作用的二阶微扰理论分别计算单光子和双光子吸收系数.计算结果表明: 单层石墨烯单光子吸收系数为常数, 约为6.8×10⁷ m^-1, 即单层石墨烯对入射光的吸收率约为2.3%; 双层石墨烯的单光子吸收比单层石墨烯的单光子吸收强, 且随入射光波长呈分段性变化.单层石墨烯的双光子吸收系数与波长λ⁴成正比; 双层石墨烯双光子吸收系数在红外波段(～ 3100 nm处)有一个很强的共振吸收峰. 研究结果可为石墨烯材料在光电子器件的研究和制作方面提供指导. 关键词： 石墨烯 光学吸收 紧束缚模型     

类石墨烯结构二维层状碳化硅的非线性二次谐波特性的第一性原理研究

二维层状碳化硅（two-dimensional layered silicon carbide,2d-SiC）是一种类石墨烯结构的半导体,在非线性光学频率转换上具有潜在的应用.本文基于第一性原理高精度全电子势线性缀加平面波结合态求和方法研究了层叠和拉伸下类石墨烯2d-SiC结构的非线性二次谐波系数.非线性过程物理源分析表明,三带项构成的单粒子跃迁过程是2d-SiC结构的二次谐波过程的主要微观跃迁机制,电子的带间运动显著受到带内运动的调谐,π电子离域带对非线性过程有重要贡献.理论上给出了2d-SiC结构的二次谐波系数的角度依赖,为实验研究提供理论参考.拉伸可导致不同频率的二次谐波增强.     

高质量大面积石墨烯的化学气相沉积制备方法研究

石墨烯因其奇特的能带结构和优异的物理性能而成为近年来大家研究的热点, 但是目前单层石墨烯的质量与尺寸制约了其实际应用的发展. 本文采用常压化学气相沉积(CVD)方法, 基于铜箔衬底, 利用甲烷作为碳源制备了高质量大面积的单层与多层石墨烯. 研究发现: 高温度、稀薄的甲烷浓度、较短的生长时间以及合适的气体流速是制备高质量、大面积石墨烯的关键. Raman光谱, 扫描电子显微镜、透射电子显微镜等表征结果表明: 制备的石墨烯主要为单层, 仅铜箔晶界处有少量多层石墨烯. 电学测试表明CVD制备的石墨烯在低温时呈现出较明显的类半导体特性; 薄膜电阻随外界磁场的增大而减小.     

石墨烯/柔性基底复合结构双向界面切应力传递问题的理论研究

界面力学性能是影响石墨烯/柔性基底复合结构整体力学性能的关键因素,因此对该结构界面切应力传递机理的研究十分必要.考虑了石墨烯和基底泊松效应的影响,本文提出了二维非线性剪滞模型.对于基底泊松比相比石墨烯较大的情况,利用该模型理论研究了受单轴拉伸石墨烯/柔性基底结构的双向界面切应力传递问题.在弹性粘结阶段,导出了石墨烯双向正应变和双向界面切应力的半解析表达式,分析了不同位置处石墨烯正应变和界面切应力的分布规律.导出了石墨烯/柔性基底结构发生界面滑移的临界应变,结果表明该临界应变低于利用经典一维非线性剪滞模型得到的滑移临界应变,并且明显受到石墨烯宽度尺寸以及基底泊松比大小的影响.基于二维非线性剪滞模型建立有限元模型(FEM),研究了界面滑移阶段石墨烯双向正应变和双向界面切应力的分布规律.与一维非线性剪滞模型的结果对比表明,当石墨烯宽度较大时,二维模型和一维模型对石墨烯正应变、界面切应力以及滑移临界应变的计算结果均存在较大差别,但石墨烯宽度很小时,二维模型可近似被一维模型代替.最后,通过与拉曼实验结果的对比,验证了二维非线性剪滞模型的可靠性,并得到了石墨烯/聚对苯二甲酸乙二醇酯(PET)基底结构的界面刚度(100 TPa/m)和界面剪切强度(0.295 MPa).     

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.     

Optical Two-Photon Surface Nonlinear Waves

A theory of the optical surface two-photon small-amplitude breather in a multilayer system of the isotropic and anisotropic left-hand metamaterials, when there are a graphene monolayer (graphene-like twodimensional material) and a transition layer with impurity optical atoms (semiconductor quantum dots), is constructed. It is shown that the system of constitutive equations for two-photon transitions and wave equation for a surface plasmon–polariton TM mode are reduced to the nonlinear Schrödinger equation with damping. Explicit analytical expressions for a surface two-photon small-amplitude self-induced transparency breather (0π-pulse) are obtained. It is shown that the optical conductivity of graphene leads to the exponential damping of intensity of a surface two-photon nonlinear wave during the propagation. One- and two-photon small-amplitude breathers in graphene are compared, and it is shown that differences between their parameters are substantial.     

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr?dinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.     

Optical solitons for non-Kerr law nonlinear Schrödinger equation with third and fourth order dispersions

In this paper, we obtain optical soliton solutions for non-Kerr law nonlinear Schrödinger equation (NLSE) with third order (3OD) and fourth order dispersions (4OD). We will use two integration schemes, namely sin-cosine method and Bernoulli’s equation approach with five laws of nonlinearities. Sine-cosine method is applicable to Kerr, power and anti-cubic laws, this method provides bright soliton solutions. The second method is applicable to parabolic and cubic quintic laws, this method generates dark soliton. The results may be used in discussing the propagation of optical solitons in highly dispersive media with Kerr, power, anti-cubic, parabolic and cubic quintic law nonlinearities.     

Lax Pairs and Integrability Conditions of Higher-Order Nonlinear Schrödinger Equations

We derive the Lax pairs and integrability conditions of the nonlinear Schrödinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrödinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrödinger equation.     

Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity

Explicit expressions are given to study the biaxial buckling of monolayer graphene sheets. Based upon the continuum mechanics, a plate model is adopted in which the small length scale effect is incorporated into the governing equation through the nonlocal elasticity theory of Eringen. By employing the Galerkin method, analytical expressions are derived which allow quick and accurate calculation of the critical buckling loads of monolayer graphene sheets with various boundary conditions from the static deflection under a uniformly distributed load. The effectiveness of the present study is assessed by molecular dynamics simulations as a benchmark of good accuracy.     

Exact self-similar wave solutions for the generalized (3 + 1)-dimensional cubic–quintic nonlinear Schröinger equation with distributed coefficients

In this paper, a similarity transformation is presented to reduce the generalized (3 + 1)-dimensional cubic–quintic nonlinear Schrödinger equation with distributed coefficients to the related constant-coefficients one. Then a number of spatiotemporal self-similar wave solutions are constructed. Under the specific choice of the dispersion, cubic and quintic nonlinearities, phase modulation and the gain/loss, we investigate the dynamical behaviors of those spatiotemporal self-similar waves in an inhomogeneous optical fiber media.     

Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium

In the present paper, the sinusoidal shear deformation plate theory (SDPT) is reformulated using the nonlocal differential constitutive relations of Eringen to analyze the bending and vibration of the nanoplates, such as single-layered graphene sheets, resting on two-parameter elastic foundations. The present SDPT is compared with other plate theories. The nanoplates are assumed to be subjected to mechanical and thermal loads. The equations of motion of the nonlocal model are derived including the plate foundation interaction and thermal effects. The governing equations are solved analytically for various boundary conditions. Nonlocal theory is employed to bring out the effect of the nonlocal parameter on the bending and natural frequencies of the nanoplates. The influences of nonlocal parameter, side-to-thickness ratio and elastic foundation moduli on the displacements and vibration frequencies are investigated.     

Nonlocal plate model for nonlinear bending of single-layer graphene sheets subjected to transverse loads in thermal environments

This paper investigates the nonlinear bending behavior of a single-layer rectangular graphene sheet subjected to a transverse uniform load in thermal environments. The single-layer graphene sheet (SLGS) is modeled as a nonlocal orthotropic plate which contains small scale effect. Geometric nonlinearity in the von Kármán sense is adopted. The thermal effects are included and the material properties are assumed to be size dependent and temperature dependent, and are obtained from molecular dynamics (MD) simulations. The small scale parameter e ₀ a is estimated by matching the deflections of graphene sheets observed from the MD simulation results with the numerical results obtained from the nonlocal plate model. The numerical results show that the temperature change as well as the aspect ratio has a significant effect on the nonlinear bending behavior of SLGSs. The results reveal that the small scale parameter reduces the static large deflections of SLGSs, and the small scale effect also plays an important role in the nonlinear bending of SLGSs.     

Localized and periodic wave patterns for a nonic nonlinear Schrödinger equation

Propagating modes in a class of ‘nonic’ derivative nonlinear Schrödinger equations incorporating ninth order nonlinearity are investigated by application of two key invariants of motion. A nonlinear equation for the squared wave amplitude is derived thereby which allows the exact representation of periodic patterns as well as localized bright and dark pulses in terms of elliptic and their classical hyperbolic limits. These modes represent a balance among cubic, quintic and nonic nonlinearities.