Numeric SCF model

We emphasize that in both models discussed here, the free ends of the branches are fixed at the external boundary of the corona. Relaxation of this constraint is possible in the numerical SCF model of Scheutjens and Fleer. It is therefore instructive to compare the predictions of the analytical theory to the more accurate results obtained by means of the numerical SF-SCF computations. 

The thermodynamic model of micellization, presented here, describes the association of any amphiphilic molecules, including low molecular weight surfactants or polymeric amphiphiles. The physical origin of the minimum in the free energy, as a function of p, is specified by the molecular architecture and the interactions between amphiphilic molecules involved in the assembly, and will be discussed in the corresponding sections. An extension of the model for the case of a continuous distribution of micelles with respect to aggregation number (polydispersity of the aggregates) involves the value of d Fp/dp. If this quantity is small in the vicinity of p = Po, then the micelle distribution is wide, and vice versa [37]. The approximation of micelle monodispersity is essential for application of the numerical SCF model which is discussed in Sect. 9. 

Below, we begin with a brief description of the numerical SCF model. In prior studies, we used this method to determine the free energies as a function of surface separation for polymer-coated surfaces in solution. Here, we describe our findings for die interactions between solid surfaces immersed in (1) a singlecomponent melt and (2) a melt that contains polymers with surface-active end-groups We also introduce an analytical SCF model for the melt containing end-functionalized chains and present the results from this theory. Comparisons are made between the numerical and analytical SCF results and die implications of these findings are discussed furdier in the Conclusions section. 

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