Leibniz Institute of Polymer Research Dresden e. V., 01069 Dresden, Germany.
J Chem Phys. 2012 Jan 28;136(4):044903. doi: 10.1063/1.3676657.
We present a numerical self-consistent field (SCF) method which describes freely jointed chains of spherical monomers applied to densely grafted polymer brushes. We discuss both the Flory-Huggins model and the Carnahan-Starling equation of state and show the latter being preferable within our model at polymer volume fractions above 10%. We compare the results of our numerical method with data from molecular dynamics (MD) simulations [G.-L. He, H. Merlitz, J.-U. Sommer, and C.-X. Wu, Macromolecules 40, 6721 (2007)] and analytical SCF calculations [P. M. Biesheuvel, W. M. de Vos, and V. M. Amoskov, Macromolecules 41, 6254 (2008)] and obtain close agreement between the density profiles up to high grafting densities. In contrast to prior numerical and analytical studies of densely grafted polymer brushes our method provides detailed information about chain configurations including fluctuation, depletion, and packing effects. Using our model we could study the recently discovered instability of densely grafted polymer brushes with respect to slight variations of individual chain lengths, driven by fluctuation effects [H. Merlitz, G.-L. He, C.-X. Wu, and J.-U. Sommer, Macromolecules 41, 5070 (2008)]. The obtained results are in very close agreement with corresponding MD simulations.
我们提出了一种数值自洽场（SCF）方法，用于描述应用于密集接枝聚合物刷的自由连接链状单体。我们讨论了 Flory-Huggins 模型和 Carnahan-Starling 状态方程，并表明在我们的模型中，当聚合物体积分数高于 10%时，后者更可取。我们将我们的数值方法的结果与分子动力学（MD）模拟[G.-L. He、H. Merlitz、J.-U. Sommer 和 C.-X. Wu，Macromolecules 40，6721（2007）]和解析 SCF 计算[P. M. Biesheuvel、W. M. de Vos 和 V. M. Amoskov，Macromolecules 41，6254（2008）]的数据进行了比较，并在高接枝密度下获得了密度分布的密切一致。与先前关于密集接枝聚合物刷的数值和分析研究相比，我们的方法提供了有关链构象的详细信息，包括涨落、耗尽和堆积效应。使用我们的模型，我们可以研究最近发现的密集接枝聚合物刷由于涨落效应而对单个链长的微小变化的不稳定性[H. Merlitz、G.-L. He、C.-X. Wu 和 J.-U. Sommer，Macromolecules 41，5070（2008）]。得到的结果与相应的 MD 模拟非常吻合。
