Dry brush regime

Finally, for very high coverage o, the N-mer chains stretch to maintain the constant density of the brush layer. In this dry brush regime (marked as III dry in Fig. 35) the brush volume fraction 0=1 and from Eq. (56) stems the brush thickness L ... 

While in the de Gennes-Leibler model the brush anchors are strictly confined at the interface, the SCMF numerical approach by Shull allows for their distribution in a finite region adjacent to the interface. Similar assumption was made in the frame of the SCMF approach by Semenov [235], who derived the analytical expression for the segregation isotherm in the dry brush regime (P>N). 

Another range of matrix molecule sizes P=88-3173 was used in our study [251] on PI (polyisoprene, NA=114)-dPS (N=893) diblock copolymer segregating to interfaces created by polystyrene P-mer with vacuum and silicon substrate. The used PS molecular weights covers the wet and dry brush regime. In Fig. 40a we present typical composition-depth profiles of Pl-dPS obtained at the vacuum ( external ) interface of PS host matrix with P varied (P=88,495, and 3173), but constant bulk diblock concentration < )00=3.2(5)%. The surface peak and a related surface excess z (and coverage a) increases with P. This is even... 

The cases in which one or both of the copolymer blocks form a wet brush are somewhat more complicated and are discussed by Dai et al. (1992). Our discussions in section 6.2 should lead us to suspect that this scaling approach is not likely to be completely accurate - we know from neutron reflectivity measurements (for example those shown in figures 6.14 and 6.20) that, even in the dry-brush regime, there is substantial penetration of the brush by the homopolymer. Nonetheless, the theory does succeed in capturing much of the physics and allows at least semi-quantitative predictions of the interfacial excess and interfacial tension. 

When the homopolymer is comparable in size to the BC the homopolymer will segregate to the middle of the appropriate BC domain and produce a larger interlameUar spacing than the observed-for wet brush regime described previously. In this situation, described as dry brush the brush layer formed by the BC is not interpenetrated by the homopolymer. The latter forms a separate phase. This behavior has been illustrated in different mixtures, such as PS or PMMA homopolymers with symmetric short polystyrene-block-poly(methyl methacrylate) (PS-fc-PMMA) diblock copolymers where the... 

Fig. 35. Schematic conformation diagram (lna/lnN vs InP/InN) for N-mer brush exposed to P-mer chains, structurally identical but with a different isotopic status (%-dependent details of the diagram calculated for the data from [245], describe well the situation also for other experimental reports). The brush height L is described as the power law Lp=oq,with the exponent q characterizing different regimes q=0 (I and II), 1/3 (III wet), 1/2 (III t), 1 (III dry). The cross over between different regions occurs for coverage values o N-1 (I/II), o2=PN 3/2 /(l-2Px) (II/IH wet),o3=(l-2Px)2P 1/2 (HI wet/III t),a4sP 1/2 (III t/III dry),o5=lsr1/2 (II/III dry)...

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