Activation energy, spatial confinement, and mean first passage and escape times of a tracer in a wormlike micellar fluid: an effective potential approach

Abstract

Wormlike micelles are long semiflexible cylindrical polymer structures formed by amphiphiles. In solution, these linear micelles percolate in multiconected entangled networks, where cross-links can break and recombine dynamically. Technological applications of wormlike micellar fluids include tunable encapsulation/delivery of molecules or colloids in biomedicine, oil industry, and/or cleaning processes. In this work, we propose that the experimental activation energy, the spatial confinement, and the mean first passage and escape times of a spherical tracer immersed in wormlike micellar network, in which caging effects are observed, can be estimated from economic Brownian dynamics simulations of a single particle interacting with an effective one-dimensional cosine-like potential of amplitude U0 and periodicity L. The proposed one-fitting parameter method has been used to characterize the long-time dynamics of wormlike micellar solutions formed by the self-assembly of a mixture of zwitterionic and anionic surfactants at several temperatures and different concentrations of surfactant and brine. The amplitude U0 has displayed a good agreement regarding the corresponding experi- mental activation energy at different temperatures. The periodicity L has shown to be an upper bound of the mesh size ξ and of the same order of magnitude regarding the entanglement length le, obtained from rheology and microrheology experiments. The escape time of the tracer in the effective potential τescape and the time t∗, at which a change of curvature in the mean square displacement occurs, are upper and lower limits, respectively, of the experimental relaxation time. Our method is simple and fast, and we foresee that it should be applicable to model the long-time behaviour of tracers in other polymer systems, in which caging effects are present.

Special issue on soft matter research in Latin America

“…The mobility of polymers at high concentrations depends on a number of factors, including the size of the polymer, the interaction between the monomers and the particular concentration. Guerrero-García et al [33] proposed that the activation energy and other dynamic quantities of a spherical tracer immersed into a wormlike micellar network can be described by a Brownian dynamics simulations of a single particle interacting with an effective potential. The method applies for systems in which caging effects are present.…”