Department of Mechanical Engineering, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands.
Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands.
Phys Rev E. 2017 Dec;96(6-1):062611. doi: 10.1103/PhysRevE.96.062611. Epub 2017 Dec 18.
Diffusing-wave spectroscopy (DWS) extends dynamic light scattering measurements to samples with strong multiple scattering. DWS treats the transport of photons through turbid samples as a diffusion process, thereby making it possible to extract the dynamics of scatterers from measured correlation functions. The analysis of DWS data requires knowledge of the path length distribution of photons traveling through the sample. While for flat sample cells this path length distribution can be readily calculated and expressed in analytical form; no such expression is available for cylindrical sample cells. DWS measurements have therefore typically relied on dedicated setups that use flat sample cells. Here we show how DWS measurements, in particular DWS-based microrheology measurements, can be performed in standard dynamic light scattering setups that use cylindrical sample cells. To do so we perform simple random-walk simulations that yield numerical predictions of the path length distribution as a function of both the transport mean free path and the detection angle. This information is used in experiments to extract the mean-square displacement of tracer particles in the material, as well as the corresponding frequency-dependent viscoelastic response. An important advantage of our approach is that by performing measurements at different detection angles, the average path length through the sample can be varied. For measurements performed on a single sample cell, this gives access to a wider range of length and time scales than obtained in a conventional DWS setup. Such angle-dependent measurements also offer an important consistency check, as for all detection angles the DWS analysis should yield the same tracer dynamics, even though the respective path length distributions are very different. We validate our approach by performing measurements both on aqueous suspensions of tracer particles and on solidlike gelatin samples, for which we find our DWS-based microrheology data to be in good agreement with rheological measurements performed on the same samples.
扩散波光谱学（DWS）将动态光散射测量扩展到具有强多重散射的样品。DWS 将光子在浑浊样品中的传输视为扩散过程，从而可以从测量相关函数中提取散射体的动力学。DWS 数据分析需要了解光子在样品中传播的路径长度分布。虽然对于平板样品池，可以很容易地计算出此路径长度分布并以解析形式表示；但对于圆柱样品池，没有这样的表达式。因此，DWS 测量通常依赖于使用平板样品池的专用设置。在这里，我们展示了如何在使用圆柱样品池的标准动态光散射设置中进行 DWS 测量，特别是基于 DWS 的微流变测量。为此，我们进行了简单的随机行走模拟，得出了路径长度分布作为传输平均自由程和检测角的函数的数值预测。该信息用于实验中提取材料中示踪粒子的均方位移以及相应的频率相关粘弹性响应。我们方法的一个重要优点是，通过在不同的检测角度下进行测量，可以改变样品中的平均路径长度。对于在单个样品池上进行的测量，与传统的 DWS 设置相比，可以获得更广泛的长度和时间尺度。这种角度依赖的测量还提供了一个重要的一致性检查，因为对于所有检测角度，DWS 分析都应该产生相同的示踪剂动力学，即使各自的路径长度分布非常不同。我们通过在示踪粒子的水悬浮液和类似固体的明胶样品上进行测量来验证我们的方法，对于这些测量，我们发现我们的基于 DWS 的微流变数据与在相同样品上进行的流变测量非常吻合。
