一维纳米结构力学性能尺寸效应的实验及理论研究
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摘要
随着纳米技术的迅速发展,纳米结构力学性能的实验测量和建模引起了广泛的关注。本文针对一维纳米结构的弹性模量,尤其是尺寸效应相关的问题进行了实验和理论建模研究。本文对纳米结构的研究主要集中在中等尺寸聚合物纳米纤维,直径100～1200纳米和超细金属纳米杆,直径小于10纳米.直径大于1200纳米的“宏观”纤维中,没有显示出明显的尺寸效应。
实验部分,本文采用静电纺丝技术制备了不同直径的PCL纳米纤维,并对单根PCL纳米纤维进行了轴向拉伸、静态弯曲和动态弯曲三种类型的实验。实验中发现纳米纤维的横截面积是椭圆形,影响了分析结果的精度。本文分别利用AFM和SEM的测量数据,引入垂直直径和水平直径,对结果进行了修正。为研究纳米纤维的尺寸效应,对直径变化范围在100～1200纳米的纳米纤维的力学性能进行了实验研究。实验研究结果显示,在纳米纤维弯曲实验中,纤维弹性模量随纳米纤维直径的变化呈现相反的变化趋势,即直径越小,弹性模量越大,但对纤维拉伸实验的统计结果没有显示出尺寸效应。
为了分析纳米纤维的尺寸效应,本文对应变梯度理论进行了部分的改进,发展了应变梯度弹性理论的动力学模型。该模型能描述纳米纤维弯曲时出现尺寸效应,而拉伸时无尺寸效应的情况,并且模型与实验数据符合良好。本文发展的应变梯度理论模型还预测了纳米纤维固有频率的尺寸效应变化趋势。
为了进一步分析超细纳米杆的尺寸效应,本文发展了晶格理论的原子模型。晶格模型适应于解释超细纳米杆在拉伸情况下的微小的尺寸效应,这一结论好像与中等尺寸纳米纤维在拉伸加载情况下不显示尺寸效应的结论相矛盾,本文对于这一矛盾的解释是:超细尺度下的一维纳米结构,厚度仅有几层原子,结构变形时,表面能量的影响起主导作用。本文利用其它的原子模型即分子动力学模型对提出的晶格尺寸效应理论模型进行了检验,两种模型得到一致的结论。因此,我们认为一维纳米结构的拉伸也包含尺寸效应,但与中等尺寸纳米纤维弯曲时的尺寸效应相比,拉伸尺寸效应在更细的尺度,即一维超细纳米结构上表现出来。
With the rapid advancement of nanotechnology there is considerable interest in the measurement and modeling of the mechanical properties of nanostructures. Therefore, this dissertation is concerned with the experimental measurements and computational modeling of the elastic modulus of 1-dimensional nanostructures, with a special emphasis on the size-dependent phenomenon. The nanostructure studied in my research consists of moderately-fine polymeric nanofibers with diameters between 100 and 1200 nm, and ultra-fine metallic nanowires with diameters up to 10 nm. Macro fibers have diameters exceeding 1200nm and they do not exhibit the size-dependent trend.
In the experimental measurements, a series of tests involving a single-strand, electrospun PCL nanofiber is conducted. Three kinds of test are carried out; uniaxial tensile, static bending and dynamic bending. Further, since the cross-section of the nanofiber is generally ellipsoidal in shape, it is necessary to correct for the lack of circularity. The analytical correction is performed using data from vertical and horizontal diameters provided by the AFM and SEM measurements, respectively. To study the size-dependent response, measurements on nanofibers of varying diameters that range from 100-1200 nm are carried out. The results on the elastic modulus clearly depict an inverse size-dependent trend with the fiber diameter; the smaller the diameter, the higher the elastic modulus is elevated. This is particularly pronounced in the results of the moderately-fine nanofibers for both the bending tests, but appears to be statistically unchanged for the tensile test.
To analytically investigate size-dependency in moderately-fine nanofibers, a strain-gradient (SG) model based on a dynamics formulation is developed. Application of the SG model to the moderately fine nanofibers produces a size-dependent behavior under bending loads and an absence of size-dependency under tensile loads. These predictions are consistent with the results of the experimental tests on the moderately-fine nanofibers. Further, our SG model shows a size-dependent trend in the natural frequency of the nanofibers.
To study size-dependency in ultra-fine nanowires an atomic model consisting of lattice cells is developed. Our lattice model predicts a smaller-scale size-dependent trend in ultra-fine nanowires under tension. This result seems to contradict that of the tensile-loaded, moderately-fine nanofibers that do not exhibit size-dependency. Our explanation of this apparent contradiction is that at the ultra-fine scale, the nanowires are a few atom layers thick, making the surface energy predominate over the core energy. Our lattice model size-dependent predictions are checked against those of another atomic model - that of the molecular dynamics simulation, and the two results are consistent with each other. Therefore, we feel confident that ultra-fine nanowires do exhibit size-dependency, albeit at a much small scale compared to bending size-dependency in the moderately-fine nanofibers.
实验部分,本文采用静电纺丝技术制备了不同直径的PCL纳米纤维,并对单根PCL纳米纤维进行了轴向拉伸、静态弯曲和动态弯曲三种类型的实验。实验中发现纳米纤维的横截面积是椭圆形,影响了分析结果的精度。本文分别利用AFM和SEM的测量数据,引入垂直直径和水平直径,对结果进行了修正。为研究纳米纤维的尺寸效应,对直径变化范围在100～1200纳米的纳米纤维的力学性能进行了实验研究。实验研究结果显示,在纳米纤维弯曲实验中,纤维弹性模量随纳米纤维直径的变化呈现相反的变化趋势,即直径越小,弹性模量越大,但对纤维拉伸实验的统计结果没有显示出尺寸效应。
为了分析纳米纤维的尺寸效应,本文对应变梯度理论进行了部分的改进,发展了应变梯度弹性理论的动力学模型。该模型能描述纳米纤维弯曲时出现尺寸效应,而拉伸时无尺寸效应的情况,并且模型与实验数据符合良好。本文发展的应变梯度理论模型还预测了纳米纤维固有频率的尺寸效应变化趋势。
为了进一步分析超细纳米杆的尺寸效应,本文发展了晶格理论的原子模型。晶格模型适应于解释超细纳米杆在拉伸情况下的微小的尺寸效应,这一结论好像与中等尺寸纳米纤维在拉伸加载情况下不显示尺寸效应的结论相矛盾,本文对于这一矛盾的解释是:超细尺度下的一维纳米结构,厚度仅有几层原子,结构变形时,表面能量的影响起主导作用。本文利用其它的原子模型即分子动力学模型对提出的晶格尺寸效应理论模型进行了检验,两种模型得到一致的结论。因此,我们认为一维纳米结构的拉伸也包含尺寸效应,但与中等尺寸纳米纤维弯曲时的尺寸效应相比,拉伸尺寸效应在更细的尺度,即一维超细纳米结构上表现出来。
With the rapid advancement of nanotechnology there is considerable interest in the measurement and modeling of the mechanical properties of nanostructures. Therefore, this dissertation is concerned with the experimental measurements and computational modeling of the elastic modulus of 1-dimensional nanostructures, with a special emphasis on the size-dependent phenomenon. The nanostructure studied in my research consists of moderately-fine polymeric nanofibers with diameters between 100 and 1200 nm, and ultra-fine metallic nanowires with diameters up to 10 nm. Macro fibers have diameters exceeding 1200nm and they do not exhibit the size-dependent trend.
In the experimental measurements, a series of tests involving a single-strand, electrospun PCL nanofiber is conducted. Three kinds of test are carried out; uniaxial tensile, static bending and dynamic bending. Further, since the cross-section of the nanofiber is generally ellipsoidal in shape, it is necessary to correct for the lack of circularity. The analytical correction is performed using data from vertical and horizontal diameters provided by the AFM and SEM measurements, respectively. To study the size-dependent response, measurements on nanofibers of varying diameters that range from 100-1200 nm are carried out. The results on the elastic modulus clearly depict an inverse size-dependent trend with the fiber diameter; the smaller the diameter, the higher the elastic modulus is elevated. This is particularly pronounced in the results of the moderately-fine nanofibers for both the bending tests, but appears to be statistically unchanged for the tensile test.
To analytically investigate size-dependency in moderately-fine nanofibers, a strain-gradient (SG) model based on a dynamics formulation is developed. Application of the SG model to the moderately fine nanofibers produces a size-dependent behavior under bending loads and an absence of size-dependency under tensile loads. These predictions are consistent with the results of the experimental tests on the moderately-fine nanofibers. Further, our SG model shows a size-dependent trend in the natural frequency of the nanofibers.
To study size-dependency in ultra-fine nanowires an atomic model consisting of lattice cells is developed. Our lattice model predicts a smaller-scale size-dependent trend in ultra-fine nanowires under tension. This result seems to contradict that of the tensile-loaded, moderately-fine nanofibers that do not exhibit size-dependency. Our explanation of this apparent contradiction is that at the ultra-fine scale, the nanowires are a few atom layers thick, making the surface energy predominate over the core energy. Our lattice model size-dependent predictions are checked against those of another atomic model - that of the molecular dynamics simulation, and the two results are consistent with each other. Therefore, we feel confident that ultra-fine nanowires do exhibit size-dependency, albeit at a much small scale compared to bending size-dependency in the moderately-fine nanofibers.
引文
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