When Do Polyelectrolytes Entangle?

Entanglements in polyelectrolyte solutions is a controversial issue in polymer science. Here, we develop an approach based on a scaling relationship between solution correlation length ξ≈lg^ν/B and number of monomers per correlation blob g for polymers with monomer projection length l. Numerical coeffiecients B are obtained from plateaus of normalized specific viscosity η_sp(c)c^α/N as a function of monomer concentration c with degree of polymerization N. Exponent α=1/(1-3ν) describes the concentration dependence of the number of monomers per correlation blob, g∼c^α. Knowledge of B-parameters allow for the universal representation of specific viscosity and relaxation time data in terms of the number of correlation blobs per chain, N/g. Applying this approach to viscosity data for polyelectrolyte solutions, we establish that in solutions of chains with DP up to 10⁴, polyelectrolytes only entangle in the concentrated solution regime. Thus, in order to observe entanglements in polyelectrolyte solutions in a concentration range where their properties are controlled by electrostatic interactions, one has to study polyelectrolyte chains with DP of at least an order in magnitude longer than studied so far.