Douglas Jack F, Efimenko Kirill, Fischer Daniel A, Phelan Fredrick R, Genzer Jan
Polymers, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
Proc Natl Acad Sci U S A. 2007 Jun 19;104(25):10324-9. doi: 10.1073/pnas.0703620104. Epub 2007 Jun 12.
Wavefronts associated with reaction-diffusion and self-assembly processes are ubiquitous in the natural world. For example, propagating fronts arise in crystallization and diverse other thermodynamic ordering processes, in polymerization fronts involved in cell movement and division, as well as in the competitive social interactions and population dynamics of animals at much larger scales. Although it is often claimed that self-sustaining or autocatalytic front propagation is well described by mean-field "reaction-diffusion" or "phase field" ordering models, it has recently become appreciated from simulations and theoretical arguments that fluctuation effects in lower spatial dimensions can lead to appreciable deviations from the classical mean-field theory (MFT) of this type of front propagation. The present work explores these fluctuation effects in a real physical system. In particular, we consider a high-resolution near-edge x-ray absorption fine structure spectroscopy (NEXAFS) study of the spontaneous frontal self-assembly of organosilane (OS) molecules into self-assembled monolayer (SAM) surface-energy gradients on oxidized silicon wafers. We find that these layers organize from the wafer edge as propagating wavefronts having well defined velocities. In accordance with two-dimensional simulations of this type of front propagation that take fluctuation effects into account, we find that the interfacial widths w(t) of these SAM self-assembly fronts exhibit a power-law broadening in time, w(t) approximately t(beta), rather than the constant width predicted by MFT. Moreover, the observed exponent values accord rather well with previous simulation and theoretical estimates. These observations have significant implications for diverse types of ordering fronts that occur under confinement conditions in biological or materials-processing contexts.
与反应扩散和自组装过程相关的波前在自然界中无处不在。例如，在结晶和其他各种热力学有序过程、参与细胞运动和分裂的聚合前沿以及更大尺度上动物的竞争性社会相互作用和种群动态中都会出现传播前沿。尽管人们常说，自持或自催化前沿传播可以用平均场“反应扩散”或“相场”有序模型很好地描述，但最近从模拟和理论论证中认识到，较低空间维度中的涨落效应可能导致这种前沿传播与经典平均场理论（MFT）产生明显偏差。本工作在一个实际物理系统中探索这些涨落效应。特别是，我们考虑了一项高分辨率近边X射线吸收精细结构光谱（NEXAFS）研究，该研究涉及有机硅烷（OS）分子在氧化硅晶片上自发前沿自组装成自组装单分子层（SAM）表面能梯度的过程。我们发现这些层从晶片边缘开始组织，形成具有明确速度的传播波前。与考虑涨落效应的此类前沿传播的二维模拟一致，我们发现这些SAM自组装前沿的界面宽度w(t)随时间呈现幂律展宽，即w(t)≈t^(β)，而不是MFT预测的恒定宽度。此外，观测到的指数值与先前的模拟和理论估计相当吻合。这些观测结果对生物或材料加工环境中受限条件下出现的各种类型的有序前沿具有重要意义。
