Size Effects in Interfacial Width

The location of the wetting point Tw also has a direct significance for the phase diagram of a polymer blend confined between antisymmetric surfaces exerting 

As mentioned in Sect. 2.2.2, the effective interfacial width wD characterizing the bilayer structure may be broadened beyond its intrinsic value w, yielded by a mean field theory (Eqs. 10 and 12). This is due to the capillary wave excitations causing the lateral fluctuation of the depth Ie(x,y) corresponding to the midpoint of the internal interface between coexisting phases. This fluctuation is opposed by the forces due to external interfaces, which try to stabilize the position Ie(x,y) in the center of the bilayer [6, 224, 225]. It was suggested recently [121] that the spectrum of capillary waves for a soft mode phase should be cut off by qb and y. This leads to the conclusion that the effective interfacial width wD should depend on the film thickness D as (wD/2)2= b2+ bD/4. Experimental data [121] obtained for olefinic blends (at T close to Tc) indeed show remarkable increase of the measured interfacial width from wd(D=160 nm)=14.4(3) nm to wd=45(12) nm for thickness D-660 nm, where wD levels off (because is comparable with lateral sample dimensions). This trend is in qualitative agreement with the formula due to capillary oscillations in the soft mode phase . However 

Another type of dependence of effective interfacial width wD on film thickness D was observed [130] for immiscible mixture of deuterated polystyrene (dPS) and poly(methyl methacrylate) (PMMA) (at T TC) an increase, from wd=1.8(4) nm for a dPS layer thickness D=6 nm to wd(D=100 nm)=2.5(4) nm, follows the logarithmic dependence wD°clnD (intrinsic interfacial width w= 1.5 nm). This may reflect [6,224] long range forces acting from the external interfaces on the internal interface Ie(x,y). On the contrary, the relation wd D1/2 found for random olefines [121] corresponds [6,224] to short range forces. We note also that capillary waves in dPS/PMMA system were observed [130] already for the thickness-to-intrinsic width ratio D/w 85  

A mean field theory has recently been developed to describe polymer blend confined in a thin film (Sect. 3.2.1). This theory includes both surface fields exerted by two external interfaces bounding thin film. A clear picture of this situation is obtained within a Cahn plot, topologically equivalent to the profile s phase portrait d( /dz vs . It predicts two equilibrium morphologies for blends with separated coexisting phases a bilayer structure for antisymmetric surfaces (each attracting different blend component, Fig. 32) and two-dimensional domains for symmetric surfaces (Fig. 31), both observed [94,114,115,117] experimentally. Four finite size effects are predicted by the theory and observed in pioneer experiments [92,121,130,172,220] (see Sect. 3.2.2) focused on (i) surface segregation (ii) the shape of an intrinsic bilayer profile (iii) coexistence conditions (iv) interfacial width. The size effects (i)-(iii) are closely related, while (i) and (ii) are expected to occur for film thickness D smaller than 6-10 times the value of the intrinsic (mean field) interfacial width w. This cross-over D/w ratio is an approximate evaluation, as the exact value depends strongly on the 

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