通过干燥烧结的二氧化硅纳米球的高度多孔层：从珠粒到宏观机械性能的弹性性能的按比例放大
Highly porous layers of silica nano-spheres sintered by drying: Scaling up of the elastic properties from the beads to the macroscopic mechanical properties
摘要：
通过干燥二氧化硅球的胶体分散体获得的层被发现是一个很好的基准测试多孔介质的弹性行为，在具有挑战性的情况下，高孔隙率和纳米尺寸的微观结构。经典的用于这些系统，肯德尔的方法明确地考虑了表面粘附力对颗粒之间的接触面积的影响。这种方法使用单个可调节参数（粘附能）提供杨氏模量，但不提供关于张量性质和弹性的可能各向异性的进一步信息。另一方面，均匀化方法（例如，规则的混合物，Eshelby，Mori-Tanaka和自洽计划），连续介质力学和渐近分析的基础上，提供的刚度张量的孔隙率和弹性常数的珠子的知识。在此，自洽方案准确地预测体积和剪切模量，没有可调参数，提供的孔隙率小于35%，由直径小至15 nm的颗粒组成的层。相反，肯德尔的方法被发现在整个孔隙率范围内预测的杨氏模量。此外，肯德尔模型中的粘附能必须调整到颗粒材料的断裂能的数量级的值。这表明干燥过程中的烧结导致颗粒之间形成共价硅氧烷键。
英文摘要：
Layers obtained by drying a colloidal dispersion of silica spheres are found to be a good benchmark to test the elastic behaviour of porous media, in the challenging case of high porosities and nano-sized microstructures. Classically used for these systems, Kendall's approach explicitely considers the effect of surface adhesive forces onto the contact area between the particles. This approach provides the Young's modulus using a single adjustable parameter (the adhesion energy) but provides no further information on the tensorial nature and possible anisotropy of elasticity. On the other hand, homogenization approaches (e.g. rule of mixtures, Eshelby, Mori-Tanaka and self-consistent schemes), based on continuum mechanics and asymptotic analysis, provide the stiffness tensor from the knowledge of the porosity and the elastic constants of the beads. Herein, the self-consistent scheme accurately predicts both bulk and shear moduli, with no adjustable parameter, provided the porosity is less than 35%, for layers composed of particles as small as 15 nm in diameter. Conversely, Kendall's approach is found to predict the Young's modulus over the full porosity range. Moreover, the adhesion energy in Kendall's model has to be adjusted to a value of the order of the fracture energy of the particle material. This suggests that sintering during drying leads to the formation of covalent siloxane bonds between the particles.
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