By K. Binder (auth.), S. Granick, K. Binder, P.-G. de Gennes, E. P. Giannelis, G. S. Grest, H. Hervet, R. Krishnamoorti, L. Léger, E. Manias, E. Raphaël, S.-Q. Wang (eds.)
The rapidly-developing box of restrained polymers is reviewed during this quantity. certain emphasis is given to polymer facets of this interdisciplinary challenge. Taken jointly, the contributions provide considerable facts of the way the sector of polymer technology maintains to adapt with the passage of time. the subjects revolve round the tendency of surfaces to bog down chain rest and to stimulate new kinds of chain association. those were implicated in numerous magnificent phenomena. here's a directory of authors and affiliations: okay. Binder (Johannes Gutenberg-Universität Mainz, Germany); P.-G. de Gennes (College de France, France); E.P. Giannelis, R. Krishnamoorti, and E. Manias (Cornell collage and college of Houston, USA); G.S. Grest (Exxon learn and Engineering Co., USA); L. Leger, E. Raphael, and H. Hervet (College de France, France); S.-Q. Wang (Case Western Reserve college, USA).
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Example text
Plot of the amplitude (envelope) function B(Z) vs Z, for a planar interface between coexisting disordered (Z®¥) and lamellar (Z®–¥) phases of block copolymer melts in the bulk. The midpoint of the profile (Z,B)=(0,1/2) is denoted by an open circle, while the inflection point (solid circle) is at [--(1/2) ln(3/2), 1/Ö3]. From Fredrickson and Binder [234] The solution of Eq. (78) with these boundary conditions is [234] B(ᐎ) =[1+3 exp(2ᐎ)]–1/2 (81) Since there is no symmetry between the ordered and disordered phases of block copolymers, this profile is not antisymmetric around its midpoint.
3 ˜ ¬© +1 1 ¹ © +2 2 ¹ ¼ ¿ 3 ±° mP ª 2º ª 2 º ½ ±À (95) Phase Transitions of Polymer Blends and Block Copolymer Melts in Thin Films 41 One finds [36] that the vertical morphology is favored over the horizontal anti-symmetric morphology when ( )k (d2 - d1) / (2n + 1) > 0 l˜3 - 3l˜ + 2 + -1 (96) which is always true if k=1, while for k=2 there exists now a region where the anti-symmetric structure (Fig. 4a) is the stable one. e. the same condition as Eq. (90) when we interpret d as the average of d1 and d2 .
This transition may persist in a thin film (b), but the distinction is that this surface order transition line will meet the line ct(D), where the thin film exhibits a first-order transition to the ordered phase, at a triple point (H1trip (D), c trip (D)) where ms is still finite. Case (c ) draws the analogous phase diagram of a polymer mixture in thin film geometry that has a prewetting transition in semi-infinite geometry (Fig. 6a). 37 Phase Transitions of Polymer Blends and Block Copolymer Melts in Thin Films + D /2 ò y(z )dz = 0 , which in discuss in detail the complications due to the constraint -D /2 the above linear treatment we have taken into account by introducing a suitable phase f.