中文摘要：

应用自洽场理论（SCFT）研究了受限于球内的高分子溶液的结构,重点关注高分子链在受限壁附近的行为.根据自洽场理论数值计算结果,讨论了球半径、高分子与球限制壁的相互作用、高分子平均浓度等因素对球内高分子浓度分布的影响.从高分子浓度分布和吸附/排空层厚度可以发现,在一定的条件下,受限的高分子在受限壁上会发生吸附/排空转变.吸附/排空转变与受限球大小、高分子链长和平均浓度,以及高分子链与受限壁之间相互作用都有关系.理论预测发生吸附/排空转变时的高分子与球限制壁的临界相互作用参数与链长的倒数成线性关系,且斜率与球半径有关.限制球越小,要发生吸附/排空转变,需要高分子与球之间有更大的临界吸引能.

英文摘要：

The present study applies the numerical self-consistent field theory（SCFT） to the polymer solution confined in a sphere, which is relevant for many technological and biological applications. This paper focuses on the adsorption/depletion transition of the polymer chains near the inner surface of the confining spherical shell. Dependence of the density profiles of the confined polymers on the radius of the confining wall, the polymer-wall interaction, and the mean polymer concentration are analysed from the numerical results of SCFT. It is found that the polymer segments distribute uniformly near the centre of the confining sphere and inhomogeneously near the confining shell. When the radius of the confining sphere is large enough, the confined polymers behave similarly to those near a flat plane. The lower the mean concentration of the confined polymer segments is, the more sensitive the thickness of the adsorption or depletion layer is to the sphere radius. The density profiles of the polymers and the thickness of the adsorption or depletion layer indicate that the adsorption/depletion transition can take place under specified conditions. The transition depends on the dimension of the confining sphere, the polymer chain length, the mean concentration, as well as the polymer-wall interaction. A linear relationship between the critical polymer-wall interaction parameter at the transition point and the reciprocal value of the chain length is observed from the numerical results of SCFT. Similar behaviour has also been found in the polymer chains near a flat plane. However, the slope and the intercept of the linear relationship here are functions of the radius of the sphere when the confining effect comes into play. It is found that higher critical attraction energy between the polymers and the wall is needed for adsorption/depletion transition to occur for smaller confining sphere. In other words, it is more difficult for the adsorption/depletion transition to occur.