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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. 

We present a general theory of the phase behavior of concentrated multicomponent solutions of charged flexible heteropolymers with specific chemical sequences. Using a field theoretic formalism, we have accounted for sequence specificity, electrostatic and van der Waals interactions among all constituent species, and topological correlations among all heteropolymer chains in the system. Our general expression for the Helmholtz free energy of the system is in terms of density profiles of the various components and is an explicit function of the sequence specificity of the heteropolymers, polymer concentration, salt concentration, chemical mismatch among the various monomers and solvent, and temperature. We illustrate our general theory in the context of the self-assembly of intrinsically disordered proteins by considering solutions of sequence-specific charged-neutral heteropolymers. For the heteropolymers under consideration, the system exhibits microphase separation. The boundaries of order–disorder transition and the relative stabilities of the canonical microphase-separated morphologies (lamellar, cylindrical, and spherical) are presented in the weak segregation limit as functions of sequence, polymer concentration, chemical mismatch parameters, and salt concentration. Unique mapping between heteropolymer sequence and morphology diagram is presented. The derived general theory is of broad applicability in addressing sequence effects on the thermodynamic behavior of any multicomponent system containing flexible heteropolymers. 

Using fluorescence microscopy and single-particle tracking, we have directly observed the dynamics of λ-DNA trapped inside poly(acrylamide-co-acrylate) hydrogels under an externally applied electric field. Congruent with the recent discovery of the nondiffusive topologically frustrated dynamical state (TFDS) that emerges at intermediate confinements between the traditional entropic barrier and reptation regimes, we observe the immobility of λ-DNA in the absence of an electric field. The electrophoretic mobility of the molecule is triggered upon application of an electric field with strength above a threshold value Ec. The existence of the threshold value to elicit mobility is attributed to a large entropic barrier, arising from many entropic traps acting simultaneously on a single molecule. Using the measured Ec which depends on the extent of confinement, we have determined the net entropic barrier of up to 130 kBT, which is responsible for the long-lived metastable TFDS. The net entropic barrier from multiple entropic traps is nonmonotonic with the extent of confinement and tends to vanish at the boundaries of the TFDS with the single-entropic barrier regime at lower confinements and the reptation regime at higher confinements. We present an estimate of the mesh size of the hydrogel that switches off the nondiffusive TFDS and releases chin diffusion in the heavily entangled state.