Polymer Engineering and Colloid Science Lab, Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Soft Matter. 2023 Apr 26;19(16):2949-2961. doi: 10.1039/d3sm00016h.
We carry out coarse-grained Brownian dynamics simulations of shearing flow of a colloidal suspension bridged by telechelic polymers with "sticky" end groups and vary sticker strength over a range from 3 to 12 in units of , motivated by an interest in simulating the rheology of latex paints. The most extensive results are obtained for dumbbells, but the trends are confirmed for 3-bead trumbbells and chains of up to 11 beads. The numbers of colloids and of polymers are also varied over a wide range to confirm trends established for smaller, more computationally affordable, systems. The dynamics are the result of an interplay of the shear rate and three different times scales: the time for a sticker on a bridging chain to be released from a particle surface, which scales as exp(0.77), the time for the polymer chain to relax, , which scales as the square of polymer chain length, and the time for a colloid to diffuse a distance comparable to its own radius, , which scales as . The scalings of the bridge-to-loop and loop-to-bridge times namely ∝ exp (0.75) and ∝ exp (0.71), are similar to those of , for values above around 5 , because of the relatively short chains considered here (, 60 Kuhn steps). However, becomes more dominant for longer chains, as shown by Travitz and Larson. The zero-shear viscosity is estimated from the Green-Kubo relation, and found to scale as exp (0.69), similar to that of . A weak influence of on is observed, with the influence expected to become stronger when becomes larger, as shown previously by Wang and Larson. At shear rates in the nonlinear regime, shear-thinning is found with exponents ≈ -0.10 to -0.60, and the first normal stress difference is positive, consistent with some of the experimental data of Chatterjee on model latex paint formulations. The weakness of the shear thinning, relative to that of hydrophobically modified ethoxylated urethane (HEUR) solutions without colloids, is likely due to the observed insensitivity of the loop-to-bridge and bridge-to-loop transition times to the imposed shear rate. This preliminary study provides the first mesoscale simulations of these suspensions, useful for assessing and improving both more accurate multi-scale models and eventually constitutive equations for these complex suspensions.
我们进行了粗粒化布朗动力学模拟，研究了由具有“粘性”端基的端接聚合物桥接的胶体悬浮液在剪切流动中的情况，端基强度在 3 到 12 的范围内变化，这是为了模拟乳胶涂料的流变学。最广泛的结果是针对哑铃型的，但对于 3 珠哑铃型和长达 11 珠的链型，趋势也得到了证实。胶体和聚合物的数量也在很宽的范围内变化，以确认在更小、更具计算成本效益的系统中建立的趋势。动力学是剪切速率和三个不同时间尺度相互作用的结果：桥接链上的一个粘性标签从粒子表面释放的时间 ，其标度为 exp(0.77)，聚合物链松弛的时间 ，其标度为聚合物链长度的平方，胶体扩散距离与自身半径相当的时间 ，其标度为 。桥到环和环到桥的时间标度分别为 ∝ exp (0.75)和 ∝ exp (0.71)，与 相似，对于大于约 5 的 值，因为这里考虑的链相对较短（ ，60 个库恩步骤）。然而，正如 Travitz 和 Larson 所展示的那样，对于更长的链， 变得更为主导。零剪切粘度 是从格林-库伯关系估计的，发现其标度为 exp (0.69)，与 相似。观察到 对 的弱影响，Wang 和 Larson 之前曾表明，当 变大时，这种影响预计会更强。在非线性剪切率下，发现剪切稀化具有指数 ≈ -0.10 到 -0.60，第一法向应力差为正，与 Chatterjee 对模型乳胶涂料配方的一些实验数据一致。与不含胶体的疏水性改性乙氧基化脲（HEUR）溶液相比，剪切稀化较弱，这可能是由于观察到环到桥和桥到环的转变时间对施加的剪切率不敏感。这项初步研究提供了对这些悬浮液的首次介观模拟，有助于评估和改进更准确的多尺度模型，并最终为这些复杂悬浮液建立本构方程。
