Mavrantzas Vlasis G, Beris Antony N, Leermakers Frans, Fleer Gerard J
Department of Chemical Engineering, University of Patras, Patras, GR 26504, Greece.
J Chem Phys. 2005 Nov 1;123(17):174901. doi: 10.1063/1.2075027.
Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z < or = 2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z = 2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z < or = 2l, continuum for distances z > 2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.
在哈密顿模型的框架下，研究了在静态平衡条件下，稀溶液中的均聚物在相互作用（吸引）表面上的吸附情况。该模型利用链端密度(n(1,e))，并运用描述构象概率的传播子(G)的概念来局部定义聚合物链段密度或体积分数(\phi)；(n(1,e))和(\phi)都进入系统自由能的表达式。传播子(G)服从在自洽势场中行走的爱德华兹扩散方程。通过使系统自由能最小化，得到链端的平衡分布，进而得到链构象概率的平衡分布。这导致了一组模型方程，它们构成了相互作用链吸附的Scheutjens - Fleer（SF）晶格统计理论在连续空间中的精确类似物。由于对于过于靠近表面的距离，连续体公式会失效，所以这里的连续体模型仅用于描述距离表面大于(2l)（其中(l)表示链段长度）的链构象概率；相反，对于距离(z\leq2l)，则使用SF晶格模型。通过这种新颖的公式，(z = 2l)处的晶格解为连续体模型提供了边界条件。通过伪谱配置方法的有效实现，对所得的混合模型（(z\leq2l)时为晶格模型，(z > 2l)时为连续体模型）进行了数值求解。将新模型得到的代表性结果与SF晶格模型的直接应用结果进行了广泛比较，发现在所有研究的情况下，它们实际上是相同的。
