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.
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机译：我们提出了一种数值自洽场（SCF）方法，该方法描述了应用于稠密接枝聚合物刷的球形单体的自由连接链。我们讨论了Flory-Huggins模型和Carnahan-Starling状态方程，并表明在聚合物体积分数大于10％时，后者在我们的模型中更可取。我们将数值方法的结果与分子动力学（MD）模拟[G.-L.他，H。Merlitz，J.-U。 Sommer和C.-X。 Wu，高分子40，6721（2007）]和分析SCF计算[P. M. Biesheuvel，W。M. de Vos和V. M. Amoskov，Macromolecules 41，6254（2008）]并获得了高达高接枝密度的密度分布之间的紧密一致。与先前对密集接枝聚合物刷的数值和分析研究相反，我们的方法提供了有关链构型的详细信息，包括波动，耗竭和堆积效应。使用我们的模型，我们可以研究最近发现的高密度接枝聚合物刷相对于由波动效应驱动的单个链长的细微变化的不稳定性[H。梅里兹（GL）他，C.-X。吴和J.-U. Sommer，高分子41，5070（2008）。所获得的结果与相应的MD模拟非常吻合。
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