Department of Physics, Cornell University, Ithaca, NY 14853, USA.
Proc Natl Acad Sci U S A. 2013 Jun 4;110(23):9301-4. doi: 10.1073/pnas.1221529110. Epub 2013 May 20.
In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropy-driven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substrate-mediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate.
在异质外延中，沉积材料与衬底之间的晶格失配强烈影响成核和生长过程。在生长动力学通常由键合过程主导的原子中，失配对成核和生长过程的影响已经得到了很好的研究，这些原子的相互作用长度约为一个晶格间距。相比之下，对于失配对较大颗粒（如球状蛋白和纳米颗粒）的结晶过程的影响，人们了解得较少，这些较大颗粒的颗粒间相互作用能量通常与热涨落相当，且相互作用范围较短，仅延伸到颗粒尺寸的一小部分。在这里，我们使用胶体实验和模拟发现，具有短程吸引力相互作用的颗粒在各向同性应变的晶格上形成晶体，其晶格间距明显大于相互作用长度尺度。通过测量单层增加单轴应变时二聚体形成的自由能成本，我们表明，基础失配衬底介导了一种熵驱动的吸引力相互作用，其延伸范围远远超过相互作用长度尺度。值得注意的是，由于这种相互作用是由热涨落引起的，降低温度会导致这种由衬底介导的吸引力晶体溶解。这种违反直觉的结果强调了在这个技术上重要的范围内，熵在异质外延中的关键作用。最终，晶格失配晶体生长的这种熵成分可用于开发用于同质成核和单晶生长的独特方法，其应用范围从蛋白质结晶到控制纳米颗粒组装成有序、功能超结构。特别是，具有空间调制应变分布的衬底的构建将利用这种效应来指导自组装，从而通过对衬底的修改直接控制成核位点和由此产生的晶体形态。
