Flory-Huggins interaction parameter phase diagrams

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

Figure 3. Phase diagram including the hockey puck and lamellae phases. The phases are (I) bilayer lamellae, (II) monolayer lamellae, (III) bilayer hockey pucks, (IV) mono-layer hockey pucks, and (V) incomplete monolayer lamellae. Log(v3x) is plotted against X. X = <-/>/( 1 — ) where is the volume fraction of the coil, v = k/X and k = Na -ZL2 where the coil part is assumed to consist of Nsegments with a mean-square separation between adjacent segments of 6a2, and L is the rod length. % is the Flory—Huggins interaction parameter.

It is worth bearing in mind that all the interactions between the two polymeric blocks A and B are considered at the molecular level, so phase separation operates at molecular and/or nanometre scales. Here we will use the copolymer polystyrene-co-polyisoprene, ie, PS-co-PI, to illustrate how to form a phase separation diagram. The solubility parameters of PS and PI are 9.2 and 8.1 (cal/cm ), respectively (Brandrup and Immergut, 1989). By using Eq. (7.12), a first approximation of the Flory—Huggins interaction parameter is found to be xab = 0.086. Based... 

Li et al., from a knowledge of the phase diagram for PCL/polystyrene blends, determined a value of the Flory-Huggins interaction parameter x for this polymer pair of 0.061-i-150(RT) J moL [81], while Watanabe et al. quoted a value of x=(-469/32) (1 -2.46x1 O /T) [82 ]. 

Pajula K, Taskinen M, Lehto VP, Ketolainen J, Korhonen O (2010) Predicting the formation and stability of amorphous small molecule binary mixtures from computationally determined Flory-Huggins interaction parameter and phase diagram. Mol Pharm 7 795-804 Pajula K, Lehto VP, Ketolainen J, Korhonen O (2012) Computational approach for fast screening of small molecular candidates to inhibit crystallization in amorphous drugs. Mol Pharm 9 2844-2855... 

Figure 2.30 Schematic phase diagram for a diblock copolymer. Here fis the volume fraction of one of the blocks, x is the Flory-Huggins interaction parameter and N is the degree of polymerization...

Figure 6.45 Schematic drawing showing phase diagram of rigid-rod polymer mixed with solvents of different solvent power expressed in the Flory—Huggins interaction parameter (Xiz)- Drawn after Donald and Windle (1992).

Fig. 17 Schematic phase diagram for a dibiock copoiymer. F=voiume fraction of one of the biocks, x= Flory-Huggins interaction parameter, and N = degree of poiymerization. (From Ref. 65.)...

However, in practice, to fit experimental phase diagrams, one has to make x a more complex (often, non-monotonic) function of T. Sometimes, researchers use a concentration-dependent Flory-Huggins interaction parameter - while this is clearly contrary to the spirit of the original Flory-Huggins theory, it can be useful to successfully fit experimental diagrams (see, e.g.. Reference [38]). For more detailed discussion see, for example. References [38-40]. 

For various elasticity theories, the qualitative phase diagrams have been constructed as functions of the Flory-Huggins interaction parameter (Fig. 13) [93]. Case a describes simultaneously cross-linked IPNs from the point of view of James-Guth theory, case b from the point of view of Flory theory, while case c relates to sequentially cross-linked IPNs using Flory theory. 

Figure 1 shows a comparison between the latest SOFT predictions for an AB diblock copolymer and experimental results obtained for a particular block copolymer S3tstem poly (isoprene-b-ethylene oxide) (PI-b-PEO). The y-axis of these phase diagrams shows the productxabN, which is a measure for the degree of segregation between the two blocks. It contains the Flory-Huggins interaction parameter, xabi derived from a lattice model ... 

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