Phase first-order collapse

For an athermal case, the continuous deswelling of the network takes place (Fig. 9, curve 1) which in the result of compressing osmotic pressure created by linear chains in the external solution (the concentration of these chains inside the network is lower than in the outer solution, cf. Ref. [36]). If the quality of the solvent for network chains is poorer (Fig. 9, curves 2-4), this deswelling effect is much more pronounced deswelling to strongly compressed state occurs already at low polymer concentrations in the external solution. Since in this case linear chains are a better solvent than the low-molecular component, with an increase of the concentration of these chains in the outer solution, a decollapse transition takes place (Fig. 9, curves 2-5), which may occur in a jump-like fashion (Fig. 9, curves 3-4). It should be emphasized that for these cases the collapse of the polymer network occurs smoothly, while decollapse is a first order phase transition. 

When Co grows, the network volume slightly decreases and the concentration of surfactant q within the network increases. When cjj, exceeds a critical concentration of micelle formation (at this point cq = c, see Figs.14,15), the network collapses because the surfactant molecules aggregated in micelles cease to impose osmotic pressure which causes additional expansion of the network. At relatively small values of the ratio Vf/V, the collapse is continuous (Figs. 14, 15), so that the number of surfactant molecules in micelles increases from zero starting at the concentration c. However, when the ratio Vf/V is sufficiently large, a discrete first-order phase transition takes place. 

A characteristic manifestation of the coexistence of two gel phases and hence of the first-order phase transition in a swollen network consists of the van der Waals loop which appears in the dependence of the swelling pressure P (or of the chemical potential of the solvent plf see Eq. (1)) on 0. The composition of coexisting gel phases at the collapse (values

2) is given by the condition of equality of the chemical potentials of the solvent px and polymer p2 in both phases... 

The polyelectrolyte regime (cti < Fig. I, curve 1). In this regime, the collapse of tl network occurs always as a first order phase transition. The jump of the itetwork volume takes (dace somewhat below the 6-temperature ... 

From a comparison of Eqs. 25 and 26 one could conclude that the osmotic pressure actually leads to a much higher swelling than electrostatic interaction. Since in poor solvent the value of the subchain size does not depend on the value of fi, the amplitude of the collapse transition in the case of j8 = 0 is higher than in the case of fi = 1. It was also shown that the transition point between the swollen and collapsed states of the chain and the character of this transition depends essentially on whether the counterions are inside the polymer coil or whether they have moved for the outer solution region. The coil-globule transition for fi = 0 in most cases is the first-order phase transition. The sharpness of this transition decreases with an increase in fi. In some cases the character of this transition for fi 0 becomes continuous in contrast to a jump-like first-order phase transition for fi = 0 (Figure 5). 

For /3 = 0, the contraction of the macromolecule to a state close to the state of the electroneutral molecule takes place at higher salt concentration and the transition is less sharp. It is interesting to note that in some cases the transition of a macromolecule to the globular state is a first-order phase transition for /3 0 and a continuous transition for /3 = 0. Thus in the case of a single molecule immersed in salt solution the coil-globule transition is sharper than in the case of a polyelectrolyte gel, whereas in the case of the salt-free solution the collapse transition of a single macromolecule is vice versa expected to be less sharp than the transition of the polyelectrolyte gel. 

The temperature dependence of the internal magnetic field in europium metal shows a sudden collapse at 88-5 K where a first-order phase transition causes the field to fall from 40% of the saturation value to zero [51]. 

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