Formation and Propagation of Cracks in Colloidal Packings

我们最近的工作为控制固定固结和开裂的力学提供了坚实的理解，即紧密堆积的胶体分散体由于接触或界面力而非线性和粘弹性变形。我们的模型根据适当的无量纲群确定了空气-水、聚合物-水或聚合物-空气界面能足以形成均匀的无空隙或多孔膜的条件，因为水分散体的薄层在刚性基底上干燥。该模型还预测，当变形太慢而跟不上蒸发速度时，当裂缝打开时恢复的弹性能超过额外消耗的表面能时，在毛细压力以上，裂缝变得有利。在压力过滤池中对聚合物晶格和无机氧化物胶体进行补充实验，可以直接测量开裂所需的负毛细压力，证明许多填料直到毛细压力显著超过预测的无限裂纹的最小值才会开裂。进一步的实验和理论证实了缺陷对成核裂纹的重要性，就像在张力作用下的线弹性固体一样。这项工作为解决剩下的难题和两个相关的挑战提供了基础。首先，在薄膜干燥锋之后的裂纹尖端形成了一个特征间距，并且经常以粘滑的方式在毛细管压力梯度的方向上前进。这表明了一个额外的动力学过程，这在一定程度上归因于水在毛细管压力梯度的驱动下流过颗粒填料。为了阐明模式选择过程，我们提出了两种具有控制梯度传播的实验几何，并通过扩展现有模型对动态过程进行了分析。一个薄的矩形通道将蒸发限制在开放的一端，并允许裂纹从末端传播，通过显微镜通过平面观察。或者，上面提到的压力过滤单元可以稍微倾斜，以产生具有自由表面的薄层的厚度梯度，但没有由不均匀蒸发引起的横向流动。随着毛细管压力的增加，裂纹在厚边由缺口成核并向薄边扩展。其次，一些技术需要高度多孔的薄膜，这些薄膜不能干燥到理想的厚度而不开裂，这就提出了如何保持毛细管压力高于薄膜表面半月板所能达到的开裂压力的问题。为此，我们建议研究由胶体棒形成的薄膜，其中随机填充产生的孔隙大于棒的直径，从而降低相对于相同直径的球体的随机紧密填充的最大毛细压力。成功与否将取决于控制裂缝的填料的有效模量是否下降到足以抵消效益。在压力过滤池中对薄水铝石胶体棒进行实验，无论是裸的还是用二氧化硅涂层稳定的，将确定临界毛细管压力作为膜厚度的函数，以评估潜力。第三，我们打算探索硬球和软球二元混合物的压力过滤池中的膜形成和开裂，通过相互作用将硬相的渗透延迟到尽可能高的体积分数。这项工作使用与上述相同的实验工具，将以正在发展的理论为指导，以理解最近发现的“光晕”。由于小的高电荷聚合物晶格和较大的电中性无机球之间的静电吸引而产生的效应。智力上的价值在于创造了一个坚实的理解基础，并利用它来设计技术的新途径。成功地理解这些现象将有利于干燥工艺，这对从传统的（但不断改进的）建筑涂料，到制造陶瓷基材和多层器件的胶带铸造工艺，再到精心定制的喷墨纸颗粒涂料等技术都很重要。该研究通过为研究生和本科生在化学及相关行业的职业生涯提供一个激励的工具，提供了更广泛的影响。

CBET-0754078, Russel Our recent work offers a solid understanding of the mechanics controlling consolidation and cracking of immobilized, i.e. close packed, colloidal dispersions that deform nonlinearly and viscoelastically due to contact or interfacial forces. Our model identifies, in terms of appropriate dimensionless groups, the conditions under which air-water, polymer-water, or polymer-air interfacial energies suffice to form homogeneous void-free or porous films as thin layers of aqueous dispersions dry on a rigid substrate. The model also predicts the capillary pressure above which cracking becomes favorable, when deformation is too slow to keep up with evaporation, as the elastic energy recovered when a crack opens exceeds the additional surface energy expended. Complementary experiments with polymer latices and inorganic oxide colloids in a pressure filtration cell permit direct measurement of the negative capillary pressures required for cracking, demonstrating that many packings do not crack until the capillary pressure exceeds significantly the minimum predicted for an infinite crack. Further experiments and theory establish the importance of flaws to nucleate cracks, as for linearly elastic solids under tension. This work provides a foundation for addressing a remaining puzzle and two related challenges. First, crack tips following a drying front in a thin film develop a characteristic spacing and often advance in the direction of the gradient in capillary pressure in a stick-slip fashion. This suggests an additional dynamical process, which some attribute to the flow of water driven through the particle packing by gradients in the capillary pressure. To elucidate the pattern selection process we propose two experimental geometries with controlled propagation of gradients, complemented with analysis of the dynamic process through an extension of the existing model. A thin rectangular channel confines evaporation to the open ends and allows cracks propagating in from the ends to be viewed through the flat faces via a microscope. Alternatively, the pressure filtration cell mentioned above can be tilted slightly to create a gradient in thickness of a thin layer with a free surface but without the lateral flows caused by nonuniform evaporation. Cracks nucleated by notches at the thick edge then should propagate toward the thin edge with increasing capillary pressure. Second, some technologies require highly porous films that cannot be dried at the desired thickness without cracking, raising the question of how to maintain capillary pressures for cracking above those attainable with menisci at the surface of the film. For this purpose we propose to study films formed with colloidal rods for which random packing creates pores larger than the rod diameter, thereby reducing the maximum capillary pressure relative to random close packing of spheres of the same diameter. Success will depend on whether the effective modulus of the packing, which controls cracking, does not fall enough to negate the benefit. Experiments with colloidal rods of boehmite, either bare or stabilized with a silica coating, in the pressure filtration cells will determine the critical capillary pressures as a function of film thickness to assess the potential. Third, we intend to explore film formation and cracking in the pressure filtration cell for binary mixtures of hard and soft spheres with interactions tuned to delay percolation of the hard phase to as high a volume fraction as possible. This effort, using the same experimental tools as above, will be guided by theory being developed to understand the recently discovered ?halo? effect due to electrostatic attractions between small highly charged polymer latices and larger electrically neutral inorganic spheres. The intellectual merit lies in the creation of a solid fundamental basis of understanding and using that to devise new avenues for the technology. Success in understanding these phenomena should benefit drying processes important to technologies ranging from conventional (but always improving) architectural coatings, through tape casting processes for fabricating ceramic substrates and multilayer devices, to carefully tailored particulate coatings for inkjet papers. The research provides broader impact by posing a stimulating vehicle for educating graduate students and undergraduates for careers in the chemical and related industries.