A Many-Body Hamiltonian for Nanoparticles Immersed
in a Polymer Solution
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Abstract
We developed an analytical theory
for the many-body potential of
mean force (POMF) between <i>N</i> spheres immersed in a
continuum chain fluid. The theory is almost exact for a Θ polymer
solution in the protein limit (small particles, long polymers), where <i>N</i>-body effects are important. Polydispersity in polymer
length according to a Schulz–Flory distribution emerges naturally
from our analysis, as does the transition to the monodisperse limit.
The analytical expression for the POMF allows for computer simulations
employing the <i>complete N</i>-body potential (i.e., without <i>n</i>-body truncation; <i>n</i> < <i>N</i>). These are compared with simulations of an explicit particle/polymer
mixture. We show that the theory produces fluid structure in excellent
agreement with the explicit model simulations even when the system
is strongly fluctuating, e.g., at or near the spinodal region. We
also demonstrate that other commonly used theoretical approaches,
such as truncation of the POMF at the pair level or the Asakura Oosawa
model, are extremely inaccurate for these systems