Search for: All records

We introduce a theoretical framework to describe the pH-sensitive phase behavior of polyzwitterion–polyelectrolyte complex coacervates that reasonably captures the phenomenon from recent experimental observations. 

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. 

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. 

Electro-osmotic flow (EOF) is a phenomenon where fluid motion occurs in porous materials or micro/nano-channels when an external electric field is applied. In the particular example of single-molecule electrophoresis using single nanopores, the role of EOF on the translocation velocity of the analyte molecule through the nanopore is not fully understood. The complexity arises from a combination of effects from hydrodynamics in restricted environments, electrostatics emanating from charge decorations and geometry of the pores. We address this fundamental issue using the Poisson–Nernst–Planck and Navier–Stokes (PNP–NS) equations for cylindrical solid-state nanopores and three representative protein nanopores (α-hemolysin, MspA, and CsgG). We present the velocity profiles inside the nanopores as a function of charge decoration and geometry of the pore and applied electric field. We report several unexpected results: (a) The apparent charges of the protein nanopores are different from their net charge and the surface charge of the whole protein geometry, and the net charge of inner surface is consistent with the apparent charge. (b) The fluid velocity depends non-monotonically on voltage. The three protein nanopores exhibit unique EOF and velocity–voltage relations, which cannot be simply deduced from their net charge. Furthermore, effective point mutations can significantly change both the direction and the magnitude of EOF. The present computational analysis offers an opportunity to further understand the origins of the speed of transport of charged macromolecules in restricted space and to design desirable nanopores for tuning the speed of macromolecules through nanopores. 

When very long polymers are trapped into multiple entropic traps created by the meshes of host hydrogels, our recent discovery shows that the guest polymer chains are entropically frozen into a nondiffusive topologically frustrated dynamical state (TFDS) at intermediate confinements. Outside the confinement boundaries of the TFDS, the guest molecules diffuse, whereas in the TFDS regime, the center of mass diffusion coefficient is essentially zero due to the macromolecule being localized into long-lived metastable states with extreme free-energy barriers for the escape of the macromolecule. However, the segmental dynamics of the macromolecule is active with hierarchical dynamics. A key assumption to explain this hierarchical segmental dynamics of the macromolecule in the TFDS regime has been that the number of monomers in the various entropic traps is polydisperse. The validity of this assumption is tested in the present paper by experimentally investigating the segmental dynamics using the ideal tetra-PEG hydrogel as the host matrix and sodium poly(styrene sulfonate) as the guest macromolecule. We find that all features of TFDS previously observed using poly(acrylamide-co-acrylate) hydrogels with the polydisperse distribution of mesh size are recovered in the present system of uniform mesh size as well. Thus, the present study, with the chemical details different from those of our previous systems, adds credence to the universality of the phenomenon of TFDS. Furthermore, the present finding suggests that the polydispersity in the number of monomers in the various entropic traps must arise from conformational fluctuations emanating from the local exchange dynamics of segments among neighboring meshes.