Two types of bonding in supramolecular telechelic blends. Homobonding is shown schematically on the left in (a), linking similar homopolymers with affinity , which is the gain in free energy in creating this bond. Homobonding also allows for the linking of -homopolymers (not shown), which is mediated by the affinity . On the right in (b), heterobonding is depicted, where dissimilar links bond with the affinity . A mixed bonding blend has both varieties of bonding produced by a set of affinities with similar values.
The phase diagram on the isopleth for the reacting system with only homobonding. The abscissa is the temperature-independent bond strength and the vertical scale is the temperaturelike coordinate . Both - and -chains are equally reactive with and . The disordered homogeneous phase is denoted as DIS, while the region of two-phase coexistence is denoted as 2 phase. The liquid-liquid critical line approaches the Flory–Huggins critical value in the limit of weak bonding.
The average number of links per chain for the two trajectories shown in the inset phase diagrams, which is the homobonding melt phase diagram of Fig. 2. Both (a) upper and (b) lower panels show the average length of chains that initiate with either -chains or -chains, labeled and , across the critical transition from the DIS phase to the two-phase region. Only lengths for the -rich phase are shown in the two-phase region (the -rich phase is the same with the species indices permuted). The upper panel (a) shows the lengths for a trajectory of continuous increase in bond strength across the transition. The lower panel (b) shows a cooling trajectory of decreasing . In both cases, the longer -chains are preferentially located in the -rich phase, mixing with some shorter -chains and largely expelling the longer -chains into their own phase.
The phase diagram of a melt of a reactive heterobonding chains on the isopleth. Starting from the upper left, where bonding is weak, there is a fluid-fluid critical line near , which corresponds to a mostly unbonded blend of incompatible and links (homopolymers). As the bond strength increases, the fluid-fluid critical line is depressed with the growing influence of copolymers, and it terminates at a Lifshitz point (LS) below a reentrant 2 phase nose. At the Lifshitz point the fluid-fluid critical line becomes a finite-wavelength critical line, which for larger bond strengths approaches the limit, shown with a dashed line, of long alternating block copolymers. Note also the reentrant lamellar (Lam) phase for temperatures below that of the Lifshitz point.
The characteristic length of chains (number average of number of links) with a terminal -block in the heterobonding melt shown for an “isothermal” cut along . The trajectory in the phase diagram for these chains is shown in the inset; note that this is a magnified portion of Fig. 4 below the Lifshitz point. Plotted in the 2 phase region on the left are both phases, labeled for their dominant composition in the legend. Vertical lines delineate the phase boundaries.
The volume fraction of segments of type contributed by copolymers in the 2 phase region along the trajectory of Fig. 5 in the -rich phase. At lower bond strengths, the volume fractions of - and -segments in the copolymers are small and nearly equal, so that these copolymers on average have roughly the same block content, i.e., they are predominantly diblock copolymers. As the bond strength increases, the -segment content from copolymers grows faster than the -segment composition, which can be interpreted as more triblocks present in the -rich phase.
A phase diagram of a reactive melt with mixed bonding. Homobonding is maintained with bond strengths , and the heterobond strength varies along the abscissa. Weak bonding in the upper left corner corresponds to a (polydisperse) blend of nearly all homopolymers, some of which are bonded homopolymers. Copolymer influence, the reentrant phase sequences, and expected regions of emulsion (in the neighborhood of the Lifshitz point LS) are all similar to those encountered in the heterobonding model phase diagram, Fig. 4, but these features are pushed out to greater heterobond strengths, .
The number average length of chains with terminal links for a trajectory in the mixed bonding phase diagram, Fig. 7. This is a cooling trajectory, shown in the inset, with the bond strength maintained at . In the two-phase region, 2 phase, the characteristic length of chains with terminal -links is shown for both phases in the blend. The phases are labeled by majority composition and vertical lines mark the phase boundaries.
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