Mixtures Between Two Interfaces

So far we have described separately the segregation phenomena occurring at both surfaces of thin films composed of binary polymer mixtures. Now we dis- 

Consider a binary polymer mixture confined in a thin film of thickness D with both surfaces, left (L) and right (R), exerting specific short-ranged surface fields. Related bare surface contributions to free energy are denoted by fsL(( sL) and fsR( t)sR). The overall free energy F (per site volume Q and area A normal to the surface) is expressed on the analogy of Eq. (24) as [6,60,177,219,222]  

A closely related form has been used earlier [93,221 ] within Landau theory. A solution to this variational problem is given by a differential equation describing the profile (z) and two surface boundary conditions. The equation defining the trajectory -2kV([ vs is given on the analogy of Eq. (25)  

Here the parameter Af(( %,Ap,( b), defined by Eq. (8), describes the excess free energy needed to create a (local) unit volume of a blend with composition from a reservoir with a flat profile (V(( (z)=0) kept at composition ( b. For symmetric profiles ( b corresponds directly to the concentration in the middle of the thin film ( (z=D/2). The chemical potential difference Ap, bounded by the relation Ap=9AFM/3( (( 0J for a semi-infinite mixture ()b= t)00, may be varied now. 

Surface concentrations ( SL and (( SR, determined by conditions (51), as well as the trajectory -2kV ( (Eq. 50), specify the overall thickness D of the profile  

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The form of Eq. (54) allows us to have better insight into the problem it reflects scaling properties of a mixture between two interfaces. The behavior of such a blend is best characterized by a set of scaling parameters defined by... 

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