Arindam Kundagrami

Charge regularization in phase separating polyelectrolyte solutions

Theoretical investigations of phase separation in polyelectrolyte solutions have so far assumed that the effective charge of the polyelectrolyte chains is fixed. The ability of the polyelectrolyte chains to self-regulate their effective charge due to the self-consistent coupling between ionization equilibrium and polymer conformations, depending on the dielectric constant, temperature, and polymer concentration, affects the critical phenomena and phase transitions drastically. By considering salt-free polyelectrolyte solutions, we show that the daughter phases have different polymer charges from that of the mother phase. The critical point is also altered significantly by the charge self-regularization of the polymer chains. This work extends the progress made so far in the theory of phase separation of strong polyelectrolyte solutions to a higher level of understanding by considering chains which can self-regulate their charge.

Continuum theory of polymer crystallization.

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.

Kinetics of swelling of polyelectrolyte gels: Fixed degree of ionization

The swelling kinetics of uncharged and charged polymer (polyelectrolyte) gels in salt-free conditions is studied in one dimension by solving the constitutive equation of motion (Newtons law for the elementary gel volume) of the displacement variable by two theoretical methods: one in which the classical definition of stress is used with the bulk modulus taken as a parameter, and the other in which a phenomenological expression of the osmotic stress as a function of polymer density and degree of ionization is taken as an input to the dynamics. The time-evolution profiles for spatially varying polymer density and stress, along with the location of the gel-solvent interface, are obtained from the two methods. We show that both the polymer density (volume fraction) and stress inside the gel follow expected behaviours of being maximum for the uniformly shrunken gel, and relaxing slowly to the lowest values as the gel approaches equilibrium. We further show that, by comparing the temporal profiles of the gel-solvent interface and other variables between the two methods, one may attempt to assign an effective bulk modulus to the polyelectrolyte gel as a function of the degree of ionization and other parameters of the gel such as hydrophobicity, cross-link density, and the temperature. The major result we get is that the effective bulk modulus of a polyelectrolyte gel increases monotonically with its degree of ionization. In the process of identifying the parameters for a monotonic swelling, we calculated using a well-known expression of the free energy the equilibrium results of two-phase co-existence and the critical point of a polyelectrolyte gel with a fixed degree of ionization.

Charge-regularized swelling kinetics of polyelectrolyte gels: Elasticity and diffusion

We apply a recently developed method [S. Sen and A. Kundagrami, J. Chem. Phys. 143, 224904 (2015)], using a phenomenological expression of osmotic stress, as a function of polymer and charge densities, hydrophobicity, and network elasticity for the swelling of spherical polyelectrolyte (PE) gels with fixed and variable charges in a salt-free solvent. This expression of stress is used in the equation of motion of swelling kinetics of spherical PE gels to numerically calculate the spatial profiles for the polymer and free ion densities at different time steps and the time evolution of the size of the gel. We compare the profiles of the same variables obtained from the classical linear theory of elasticity and quantitatively estimate the bulk modulus of the PE gel. Further, we obtain an analytical expression of the elastic modulus from the linearized expression of stress (in the small deformation limit). We find that the estimated bulk modulus of the PE gel decreases with the increase of its effective charge for a fixed degree of deformation during swelling. Finally, we match the gel-front locations with the experimental data, taken from the measurements of charged reversible addition-fragmentation chain transfer gels to show an increase in gel-size with charge and also match the same for PNIPAM (uncharged) and imidazolium-based (charged) minigels, which specifically confirms the decrease of the gel modulus value with the increase of the charge. The agreement between experimental and theoretical results confirms general diffusive behaviour for swelling of PE gels with a decreasing bulk modulus with increasing degree of ionization (charge). The new formalism captures large deformations as well with a significant variation of charge content of the gel. It is found that PE gels with large deformation but same initial size swell faster with a higher charge.