Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC H3A 0C3, Canada.
Soft Matter. 2017 Oct 11;13(39):7112-7128. doi: 10.1039/c7sm00911a.
We present theoretical and experimental descriptions of the elasticity of cylindrical micellar filaments using micro-mechanical and continuum theories, and atomic force microscopy. Following our micro-mechanical elasticity model for micellar filaments [M. Asgari, Eur. Phys. J. E: Soft Matter Biol. Phys., 2015, 38(9), 1-16], the elastic bending energy of hemispherical end caps is found. The continuum description of the elastic bending energy of a cylindrical micellar filament is also derived using constrained Cosserat rod theory. While the continuum approach provides macroscopic description of the strain energy of the micellar filament, the micro-mechanical approach has a microscopic view of the filament, and provides expressions for kinetic variables based on a selected interaction potential between the molecules comprising the filament. Our model predicts the dependence of the elastic modulus of the micellar filaments on their diameter, which agrees with previous experimental observations. Atomic force microscopy is applied to estimate the elastic modulus of the filaments using force volume analysis. The obtained values of elastic modulus yield the persistence length of micellar filaments on the same order of the previously reported values. Consistent with previous studies, our results indicate that semi-flexible linear micelles have a relatively large local strain energy at their end points, which explains their tendency to fuse to minimize the number of end caps at relatively low total surfactant volume fractions. Also, the elastic modulus of micellar filaments was found to increase when the indentation frequency increases, a finding which agrees with previous rheological observations on the bulk shear modulus of micellar solutions.
我们使用微机械和连续体理论以及原子力显微镜，对圆柱形胶束纤维的弹性进行了理论和实验描述。根据我们之前提出的胶束纤维微机械弹性模型[M. Asgari, Eur. Phys. J. E: Soft Matter Biol. Phys., 2015, 38(9), 1-16]，得到了半球形末端帽的弹性弯曲能。还使用受约束的卡塞格林棒理论，推导出了圆柱形胶束纤维的弹性弯曲能的连续体描述。虽然连续体方法提供了胶束纤维应变能的宏观描述，但微机械方法则从微观角度观察纤维，并基于纤维分子之间的选定相互作用势能，为动力学变量提供了表达式。我们的模型预测了胶束纤维弹性模量与直径的依赖关系，这与之前的实验观察结果一致。通过力体积分析，应用原子力显微镜来估计纤维的弹性模量。得到的弹性模量值与之前报道的胶束纤维的持久长度相当。与之前的研究一致，我们的结果表明，半柔性线性胶束在其端点处具有相对较大的局部应变能，这解释了它们在相对较低的总表面活性剂体积分数下倾向于融合以最小化末端帽数量的原因。此外，当压痕频率增加时，胶束纤维的弹性模量也会增加，这一发现与之前关于胶束溶液体剪切模量的流变学观察结果一致。
