4.1. The origin of the coherency
The issue can date back to the previous controversies about “spinodal-assisted crystallization” in bulk polymers. In Ryan et al.'s SAXS experiment (also see in Kaji et al.), they found a fluctuation-induced anomalous scattering at the early-stage crystallization which implies the observation of a spontaneous fluctuation process rather than a sudden nucleation event. The heart of a fierce debate is Ryan et al.’s concept— the ordered and disordered chain conformations are two “thermodynamic phases.” The minutes at the Cambridge meeting on Physical Chemistry in the Mesoscopic Regime in 1999 represent the state of the debates at that time. Leaving the disputes about whether the polymer crystallization is in need for a new theory aside, Ryan et al.’s theory is believed to be out of touch with reality.
In view of this, by taking into account an additional correlation effect induced by topological entanglement of polymers, Muthukumar gives a reasonable overall account of Ryan et al.'s disputed data.5 In his model, however, the nucleation instability is embodied in the
“intrinsic” properties of polymers (entanglement). Just because the nucleation instability is observed “far from equilibrium.,” it does not follow that the universal and fundamental aspect of the metastability should be ignored in the polymer crystallization.
Both Ryan et al.'s thermodynamic theory and Muthukumar’s kinetics model proceed from
“intrinsic” properties and introduce added complexity in the crystallization theory of polymers.
For this issue, our evidence shows another possibility: the “extrinsic” fluctuations can be strong enough to vanish the metastability and then the spinodal crystallization can occur. In other words, we just regard the observed spinodal crystallization as a key feature of the coherency.
The relevant theoretical basis has been developed by Cavagna et al.
4.2. Implication and interpretation of spinodal crystallization
In the first, we would like to draw your attention to some previous controversies about
“spinodal-assisted crystallization” in polymers. Ryan et al.'s SAXS experiment(also see in Kaji et al.) and thermodynamic spinodal-assisted crystallization theoryare in the heart of a fierce debate. The minutes at the Cambridge meeting on Physical Chemistry in the Mesoscopic Regime in 1999 represent the state of the debates at that time.Leaving the disputes about whether the polymer crystallization is in need for a new theory aside, the SAXS experiments clearly demonstrate the existence of a prior density fluctuation (like a split-up of the crystal
order parameter) in polymer crystallization far from equilibrium. Thus, the “spinodal”
concerned here is not the common liquid-liquid phase separation of mixtures through the spinodal decomposition, but is the early-stage crystal nucleation kinetics in terms of a time-dependent “fluctuation” picture. However, since the concept of the conformation-density coupling and the conformation copolymer is not unambiguous, Ryan et al.'s theory is believed to be out of touch with reality. In view of this, Muthukumar brings his kinetics viewpoint.
In Muthukumar’s kinetic theory, owing to the correlation arising from the connectivity of chain molecules, unlike in the classical nucleation theory (CNT) the entropy of the flexible chains connecting different “baby nuclei” also needs to be considered. It is clear that when the topological connectivity is taken into account, the crystal nucleation resembles a cooperative fluctuation of the density waves more than an abrupt change envisioned in the CNT. Certainly, Ryan et al.’s observation has been modeled successfully with Muthukumar’s kinetic theory;
moreover, the simulation picture is in qualitative agreement with several features of Cahn and Hilliards' non-classical model or Binder’s generalized nucleation theory on describing the spinodal nucleation, i.e., the non-localized nucleation with a diffuse-interface. We can summarize further the main ideas—if the nucleation time of polymer crystallization takes place fairly close to the relaxation time of its disentanglement, the process cannot be treated by just the metastable consideration.
However, these are not what the term “spinodal crystallization” is meant to describe. In fact, in spite of the "spinodal nucleation" mentioned above, it should be remembered that the general definition of the polymer crystal model is based on the consideration of the chain self-folding for which the nuclei with diffuse, irregular fold surfaces is still a metastable structure. This also corresponds to the definition initially given by Binder: the spinodal nucleation occurs when the metastability limit (spinodal point) is approached. Nevertheless, a clue to the phenomenon of the spinodal crystallization can be found in following three particular questions.
i. What does happen when at a certain condition the relaxation time of polymer disentanglement exceeds the nucleation time of its crystallization?
ii. As the spinodal nucleation in polymer crystallization is, in fact, observed experimentally and simulationally, is it possible to logically expect that a kinetic metastability limit also exists regardless of whether there is peculiarity (the critical divergence) on crossing the limit?
iii. If it is real, what will be the spinodal structure of the polymer crystal?
Since it is impossible in a brief space to discuss the wide range of phenomena, for first two questions, Cavagna et al.'sand Trudu et al.'sworks have provided some useful information;
whereas for the third question, we would like to draw your attention to the reply in Sec. 4.3.
Having underscored that the thermoreversible gelation is not what should be expected from the superficial morphology, we ought to compare reflections on similarities and differences between the reviewer and us. We all agree that the gelation in fibrillar network systems is not linked with the classical percolation networks but with the self-organizing/assembling processes of long-chain polymers or low-molecular gelators far from equilibrium, although there is considerable argument about the detail of the processes due to the differences in studying object aspects. Reviewer believes that owing to the perturbations far from equilibrium, the interface instability and the secondary nucleation give rise to the fibrillar branch, thereby forming a fibrillar network. But we concerned about whether under certain circumstances there is a further possibility which the effects of the perturbations can be strong enough to make metastable states become unstable and then the fibrillar network can form.
4.3. New Position of FringedMicelle Model
Today we all know very well that the preferred polymer crystal is not that with the lowest free energy (like an extended-chain crystal), but the kinetically dominant metastable crystal (like the chain-folded lamellar crystal). While the definition of metastability is based on the consideration of kinetics, and the perturbation far from equilibrium introduces an added complexity linked with the existence of the metastability limit, it is then entirely reasonable to ask what the spinodal structure of the polymer crystal will be.
For this question, we have no totally new picture but a new interpretation on the almost forgotten fringed-micelle crystal model. It is not hard to imagine that if the chain-folding is a most efficient way of packing polymer chains, the fringed-micelle model is just the opposite.
Since in addition to the high cumulative strain energy in the fringed end (even much higher than the folded surface), the micelle could collapse due to the entropy effect of overhanging loose chains on the sterically nervous transition-interface-layers, such the structure cannot be stable without any stabilizing effect.
Thus, in normal crystallization procedures, the fringed-micelle nucleation is forbidden on the kinetic grounds. However, the fringed-micelle nucleation in thermoreversible gel systems is certainly a different physical process than the metastability as a prerequisite for the nucleation of lamellar crystals in supercooled melt or fibrillar crystals in flowing supersaturated solutions.
This is the reason why we say that the fibrillar network is more like a fibrillar-like, polycrystalline “off-equilibrium” configuration which is frozen into a permanent state by the jamming of polymer chains. By extension, now that the formation of the fringed-micelle crystal does not favor the minimization of the surface energy, the “global entropy maximization” must be the primary to determine its formation. So we believe that our hypothesis of entropy-driven crystallization has certain facts to support it.