Phase coil-globule

The kinetics of emulsion polymerization is complex, involving a large number of species and at least two phases. The first quantitative approach to emulsion polymerization kinetics led to extensions by many others.The important events to consider are 1) the free-radical reactions of chain formation initiation, propagation, chain transfer, and termination and 2) the phase transfer events that control particle formation radical entry into particles from the aqueous phase, radical exit into the aqueous phase, radical entry into micelles, and the aqueous phase coil-globule transition. In free-radical emulsion polymerization, the fundamental steps are shown schematically in Fig. 1... 

Taken together, the experimental observations reported in the previous sections suggest that the formation of colloidally stable particles heated above their phase-transition temperature may be a universal phenomenon, taking place not only in aqueous polymer solutions, but also in solutions of polymers that can undergo a coil-globule transition in organic solvents. 

Partial vitrification may affect kinetic processes during the coil-globule transition. Thus, at very high dilution, macroscopic phase separation well above the LCST might be stopped by partial vitrification of the polymer-rich phase. At this point we can only speculate whether vitrification interferes with the coil-globule transition or not. This problem is open for discussion and needs experimental confirmation. 

Other Phase Transitions of the Coil-Globule Type. 193... 

As we mentioned earlier, I.M. Lifshitz was the first to realize that the coil-globule transition is not just a decrease of the chain size, but a phase transition to a condensed phase. Considering the multiplicity of known and possible condensed states, such a bro ad view on the coil-globule transition opened a perspective for unified understanding of a great number of physical phenomena in a variety of polymer systems. This gave rise to the concept of coil-globule-type transitions. Below we discuss several examples of such transitions. 

Before the volume phase transition was experimentally demonstrated in synthesized gels, its existence was theoretically predicted by Dusek and Patterson [4]. They suggested that the volume phase transition of gels is similar to the coil-globule transition of polymer chains and could be regarded as a first-order phase transition. 

Macrosyneresis, in which the network polymer is contained only in one phase is not the only possibility for phase equilibria in networks. Under favorable conditions two polymer phases can coexist in a network with a diluent phase (50). The two polymer phases in equilibrium differ in the conformations of the network chains. The transition resembles the condensation of a real gas or, in macromolecules, an intramolecular transition due to long-range net attraction between segments in a poor solvent (coil-globule type transition [139)). 

It is known that the coil-globule transition in flexible polymers is well explained by the theory of the type discussed [22]. Note that the chain length and the solvent quality come into the theory in the following combined form x = BN1/2/l3, which is the only dimensionless parameter governing the transition. The presence of the master curve (see Fig. 3.5 below) implies that the phase behavior of the thermodynamic limit with N —> oo is readily discussed from the measurement of shorter chains via finite-size scaling. 

Thus, at T > T3, the long semiflexible macromolecule is in the coil state while at T < T3 it is in the globular state. Consequently, the temperature T3, which is determined by Eq. (3.7), is the temperature of the coil-globule transition for the long freely jointed macromolecule (see Fig. 6). It is clear that this transition is the first order phase transition with a considerable bound of the coil dimensions, it leads simultaneously to the transformation of the coil into the globule and to the formation of the liquid-crystalline ordering in the globule. 

In particular, it is well known that, if the macromolecule is supercooled below the 0 temperature, the phase transition isotropic coil-isotropic globule occurs. We emphasize that for the semiflexible macromolecule this is the peculiar phase transition between two metastable states. It should be recalled that the theory of the transition isotropic coil-isotropic globule for the model of beads is formulated in terms of the second and third virial coefficients of the interactions of beads , B and C24). This transition takes place slightly below the 0 point and its type depends on the value of the ratio C1/2/a3 if Cw/a3 I, the coil-globule transition is the first order phase transition with the bound of the macromolecular dimensions, and if C1/2/a3 1, it is a smooth second order phase transition (see24, 25)). 

The parameters of the effective model of beads for the polymer chain models under consideration (Fig. 7b-d) can easily be found using the methods of Refs.25, 33). We omit here the corresponding trivial analysis and present only the final results for the value of C1/2/a3, which determines the type of the transition isotropic coil-isotropic globule. For the models of Figs. 7 b, d it turns out that at ( > d, always C1/2/a3 coil-globule transition is always of the first order. At the same time, for the model of Fig. 7 c, the type of the transition depends on the ratio da at da 1, this is the first order phase transition and at da S l the transition is of the second order. 

The transition between both globular structures and the coil state turns out to be the first order phase transition. The relation between the free energies of structures A and B depends on the temperature and on the characteristic dimensionless parameter /7a. The latter dependence is manifested already at the temperatures which are much lower than the coil-globule transition temperature, i.e. formally at A > l13. In this region, the following simple result can be obtained ... 

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