2.3 Role of Phase Separations in Gel Formation
The arguments of Sect. 2.2 mean that two specific conditions must be fulfilled in
order for a phase transformation to lead to a macroscopic network of junctions and
thus to a gel [17]: first, the phase transformation must be incomplete and, second, it
must stop wherever connectivity has been established throughout the whole macroscopic sample.
The first condition is driven by thermodynamics, but it is always controlled by
the kinetics of the process through some kind of agency able to create metastability
[25]. Because of this agency, the system fails to attain its ultimate stability
(corresponding to completion of the process) and is arrested in one of the multiple
minima of the free energy profile with respect to the order parameter hΦi (Fig. 3).
The second condition is a geometric factor and it is not related to the process, but
represents the condicio sine qua non for obtaining a gel. It is worth noting that the
connectivity can be established either by individual chain molecules or by a
continuity of microphase separated domains, or by a combination of both kinds
of associations [25]. As a consequence, a large variety of morphologies may be
obtained, depending on the chemical nature of the polymer, the kind of solvent, the
initial polymer concentration, the gelation temperature, the rate of cooling/heating
to this temperature, and so on.
Although application of the above general concepts to understand physical
gelation is, at least on a qualitative ground, straightforward in the case of crystallization, it is more tricky in the case of LL phase separations.
LL phase separation may play a key role in the gelation of some noncrystalline
polymers such as atactic polystyrene (a-PS) [34–36]. For a-PS, the physical junctions are not crystals and there are no specific interchain interactions, yet a-PS can
form gels. Arnauts and Berghmans were the first to explain the gelation of a-PS in
terms of LL phase separation combined with vitrification [36]. In this case, vitrification acts as the agency responsible for arrest of the LL phase separation, and locks
the system in a metastable state.
This mechanism is illustrated in Fig. 4a, where the phase behavior of a polymer
solution featuring an upper critical solution temperature (UCST) behavior at T c is
shown as an example, with T c being the critical temperature. Curve b in Fig. 4 is the
binodal, i.e., the curve delineating the concentration of the polymer-rich and
polymer-poor phases in equilibrium at each temperature. The LL phase separation
occurs at temperatures below the binodal, in any case at temperatures below the T c .
In Fig. 4, the curve s represents the spinodal, which is the ultimate thermodynamic
limit of stability for homogeneous solutions. Below this curve, homogeneous
solutions are unstable and undergo phase separation due to the effect of infinitesimally small fluctuations in composition and density (spinodal decomposition). For
concentrations that fall in the region between the spinodal and binodal, homogeneous solutions are in a (classical) metastable state, that is, they are stable with
respect to concentration and density fluctuations, and undergo phase separation by a
free-energy-activated process involving nucleation and growth. Finally, curve g in
168
C. De Rosa et al.
The arguments of Sect. 2.2 mean that two specific conditions must be fulfilled in
order for a phase transformation to lead to a macroscopic network of junctions and
thus to a gel [17]: first, the phase transformation must be incomplete and, second, it
must stop wherever connectivity has been established throughout the whole macroscopic sample.
The first condition is driven by thermodynamics, but it is always controlled by
the kinetics of the process through some kind of agency able to create metastability
[25]. Because of this agency, the system fails to attain its ultimate stability
(corresponding to completion of the process) and is arrested in one of the multiple
minima of the free energy profile with respect to the order parameter hΦi (Fig. 3).
The second condition is a geometric factor and it is not related to the process, but
represents the condicio sine qua non for obtaining a gel. It is worth noting that the
connectivity can be established either by individual chain molecules or by a
continuity of microphase separated domains, or by a combination of both kinds
of associations [25]. As a consequence, a large variety of morphologies may be
obtained, depending on the chemical nature of the polymer, the kind of solvent, the
initial polymer concentration, the gelation temperature, the rate of cooling/heating
to this temperature, and so on.
Although application of the above general concepts to understand physical
gelation is, at least on a qualitative ground, straightforward in the case of crystallization, it is more tricky in the case of LL phase separations.
LL phase separation may play a key role in the gelation of some noncrystalline
polymers such as atactic polystyrene (a-PS) [34–36]. For a-PS, the physical junctions are not crystals and there are no specific interchain interactions, yet a-PS can
form gels. Arnauts and Berghmans were the first to explain the gelation of a-PS in
terms of LL phase separation combined with vitrification [36]. In this case, vitrification acts as the agency responsible for arrest of the LL phase separation, and locks
the system in a metastable state.
This mechanism is illustrated in Fig. 4a, where the phase behavior of a polymer
solution featuring an upper critical solution temperature (UCST) behavior at T c is
shown as an example, with T c being the critical temperature. Curve b in Fig. 4 is the
binodal, i.e., the curve delineating the concentration of the polymer-rich and
polymer-poor phases in equilibrium at each temperature. The LL phase separation
occurs at temperatures below the binodal, in any case at temperatures below the T c .
In Fig. 4, the curve s represents the spinodal, which is the ultimate thermodynamic
limit of stability for homogeneous solutions. Below this curve, homogeneous
solutions are unstable and undergo phase separation due to the effect of infinitesimally small fluctuations in composition and density (spinodal decomposition). For
concentrations that fall in the region between the spinodal and binodal, homogeneous solutions are in a (classical) metastable state, that is, they are stable with
respect to concentration and density fluctuations, and undergo phase separation by a
free-energy-activated process involving nucleation and growth. Finally, curve g in
168
C. De Rosa et al.