Ribbons phase diagram

Fig. 11 Phase diagram of a twisted ribbon solution that forms fibrils. The axes represent relative helix pitch of isolated ribbons and relative stacking attraction of ribbons. Reproduced from Aggeli et al. [20]. Copyright 2001 National Academy of Sciences, USA...

Figure 5.24 Model of hierarchical self-assembly of chiral rodlike monomers.109 (a) Local arrangements (c-f) and corresponding global equilibrium conformations (c -f) for hierarchical selfassembling structures formed in solutions of chiral molecules (a), which have complementary donor and acceptor groups, shown by arrows, via which they interact and align to form tapes (c). Black and the white surfaces of rod (a) are reflected in sides of helical tape (c), which is chosen to curl toward black side (c ). (b) Phase diagram of solution of twisted ribbons that form fibrils. Scaled variables relative helix pitch of isolated ribbons h hh /a. relative side-by-side attraction energy between fibrils eaur/e. Reprinted with permission from Ref. 109. Copyright 2001 by the National Academy of Sciences, U.S.A.

Figure 2 Phase diagram of a solution of twisted ribbons which form fibrils, where the relative helix pitch of isolated ribbons hribbom/a is plotted against the relative side-by-side attraction energy between ribbons "ri/ fibnitTibrii = (27r2b2/a2 ktwist. The areas divided by the thick lines reveal the conditions where ribbons, fibrils, and infinite stacks of completely untwisted ribbons are stable. The dotted lines are lines of stability for fibrils containing p ribbons (p are written on the lines) kbend/ktwist = 0.1 (Aggeli et al., 2001b).

The form of the micelle was found to be close to a hemisphere for y2 = Y3 Variation of the values of 72 and 73 changes the shape of the micelles but the dependence of their size on the length Na and Ng of the blocks remains the same. By direct comparison of the free energies of brush, island and ribbon morphologies a phase diagram was constructed for two different values of 7i, showing the transition between possible morphologies based on Na-Nb variables (see Fig. 5). 

The theoretical results are in good agreement with the experimental observations for PS-fc-P4VP block copolymers. In the experiments a well-defined ribbon morphology was obtained only for Ns/N4vb >2. An experimental phase diagram in a double logarithmic scale is shown in Fig. 6. 

In contrast to PS-fo-P4VP, PS-fo-P2VP block copolymers exhibit only an island-brush transition. Since the exact size and the shape of the ribbon region of the phase diagram depend on the interfacial tension of the involved compounds, the ribbon region can be very small or even vanish. Therefore, the appearance of ribbons in the case of PS-b-P4VP is due to the differences in interfacial tension. 

Figure 4.S Phase diagram of binary water/ intermediate ribbon, distorted lamellar,...

Li Fe + Nd2Fe,4B(Ti) + T2. In the Nd-rich region Tj phase, Tj phase and rich-Nd solid solutions solidify from the liquid at the end point of the liquid. The phase diagram of as-cast buttons and melt-spun ribbons with the composi-... 

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