According to de Gennes, the density profile for homopolymers adsorbing onto planar surfaces is characterized by a proximal, central and distal region. We have used self-consistent field calculations and focused on the central region in the limit of very long chain lengths. Our results complement earlier predictions for comparatively low molecular weights that basically only revealed a mean field scaling exponent of −2 for the power-law decay of the density. For very long chains, however, a more rich picture emerges. Apart from an inner sub-region where the loop conformations dominate and still the mean field exponent is found, there exists an outer sub-region where the tail conformations dominate with excluded volume scaling of ‒4/3. It is shown that the outer region grows logarithmically with chain length and only will exceed the decade when the length of the polymer chains exceeds N ≈ 3 × 10⁷. We argue that ‘inner-adsorption blobs’ are visited twice by loop conformations (loops by definition return to the surface) and hence become overcrowded giving rise to mean field scaling. The ‘outer-adsorption blobs’ are visited just once by tails (tails do not need to return to the surface) and therefore provide the expected excluded volume scaling.

根据de Gennes的观点，均聚物吸附到平面表面上的密度分布的特征是近端，中央和远端区域。我们使用了自洽场计算，并在非常长的链长范围内将重点放在中心区域。我们的结果补充了对相对较低分子量的早期预测，该预测基本上仅揭示了密度幂律衰减的平均场比例指数为-2。但是，对于很长的连锁店，就会出现更加丰富的情况。除了一个内部子区域，其中环构象占主导地位，并且仍然找到平均场指数，还有一个外部子区域，其中尾部构象占主导，排除体积比例为scaling4 / 3。Ñ ≈3×10 ⁷。我们认为“内部吸附斑点”通过回路构象（根据定义，回路返回表面）被访问两次，因此变得人满为患，导致平均场缩放。“外部吸附斑点”仅被尾巴访问一次（尾巴无需返回表面），因此可提供预期的排除体积缩放。