We use Brownian dynamics (BD) simulations
resolved at the level
of a Kuhn step to calculate the rate at which a telechelic polymer
with surface-adhering endcaps transitions from a bridge between two
flat surfaces to a loop on a single surface. We then use self-consistent
field theory to obtain the equilibrium ratio of bridges to loops and
apply the principle of detailed balance to obtain the slower loop-to-bridge
times from the faster bridge-to-loop times. The bridge-to-loop transition
time has two scaling regimes: one where it is approximately equal
to the time for a lone hydrophobic particle to desorb from a surface,
and the other where it is dominated by the retraction time of the
polymer; approximate formulas for both times are given. The results
are important for interpreting the dynamics and rheology of latex
coating fluids, in which colloidal particles are dynamically bridged
by telechelic rheology-modifying polymers.
We combine the self-consistent field
theory and the Derjaguin approximation
to predict the polymer-induced colloidal interactions and the nonuniform
distributions of the loops and bridges of telechelic polymers adsorbed
onto particle surfaces when the polymers are compressed or stretched
as a function of interparticle distance. We validate our approach
by comparing its predictions to those of Brownian dynamics simulations.
We also determine the dependence of intercolloidal interactions on
particle size and surface coverage as well as the molecular structures
of telechelic polymers, including chain length and missing associating
ends, which are important parameters in the design of commercial latex
coatings. By mapping the predicted interparticle interaction strengths
to Baxter temperatures, we can quantitatively predict the phase behaviors
of the mixtures of colloids and telechelic polymers.
We investigate the transition between the overdamped and underdamped regimes in Langevin dynamics simulations with significant conservative forces by comparing direct simulations with theories of Kramers, Mel'nikov and Meshkov (MM), and Larson and Lightfoot (LL). The need for clarification is made evident by noting that the most commonly cited theories of Kramers and MM do not apply in the overdamped limit to escape times from a Lennard-Jones (LJ) potential, because Kramers and MM do not account for the flatness of the LJ potential at the escape position, which allows for a region of nearly free Brownian diffusion near the escape position. While the little-known LL approach does consider an LJ potential, it does not properly consider the underdamped regime, and so a complete description is only achieved by combining the LL and MM results into a single general equation, which we validate for the first time by an explicit comparison with Langevin simulations.
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