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We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid–liquid, liquid–gel, and gel–gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.
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Dipole Theory of Polyzwitterion Microgels and Gels
The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins.
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- Award ID(s):
- 2309539
- PAR ID:
- 10544365
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Gels
- Volume:
- 10
- Issue:
- 6
- ISSN:
- 2310-2861
- Page Range / eLocation ID:
- 393
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/gels10060393
