(Color online) Depict the picture of long chain molecules on interface. (a) Long chain alkanes are considered as Gaussian chains. Each molecule has and only has one terminal group on the boundary plane. Meanwhile, other monomers are forbidden to reach the plane. is the height of molecules on boundary immerse into bulk, is mean diameter of molecule spreads in the direction parallel to the boundary plane(more details of and are presented in text. (b) The coordinate employed in our calculations. is perpendicular to the interface, and are parallel to the boundary plane.
(Color online) Typical features of heat capacity and entropy of on interface are illustrated by and . Solid line displays specific heat and the dash line is the entropy. It is clearly shown that there are two singularities for each . The first transition temperature, is higher than the bulk transition temperature while the second one is lower. In the calculations, we let .
(Color online) Phase transition temperatures as a function of degree of polymerization. Only the higher theoretical transition temperature on interface is shown in the figure. The results from both theory and experiment (Ref. 7) show that the surface transition temperatures are higher than the bulk transition temperatures. Since long chain approximation is introduced, there are considerable deviations when is small.
(Color online) According to the theoretical calculations, there are two transitions for each on interface. Solid phase I is the monolayer and solid phase II is the perfect solid in which both positional and orientation orders are acquired.
Four parts of contributions to free energy. The dash line is the contribution of entropy; solid line is the contribution of van der Waals interaction. The chain outside of the boundary will be “frozen” at higher temperature. Meanwhile, the monomer on boundary will be frozen at lower temperature.
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