Quantifying the effects of neglecting many-body interactions in coarse-grained models of complex fluids

We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solution of star polymers. In the latter case, coarse-graining to an effective fluid described by pair potentials is found to neglect important aspects of the true behavior.

Figure 1

(a) Snapshot of a highly size- asymmetrical mixture of spheres. The effective one-component model is realized by integrating out the small sphere degrees of freedom. (b) A snapshot of three star polymers. The big spheres represent a coarse-grained model in which each polymer is replaced by a single effective particle. In both (a) and (b) simulation measurements are also shown for the structural quantity $g_3^{\prime }\left(r_{\min }\right)$ discussed in the text, whose asymptote (dashed) yields information on the third virial coefficient.

Figure 2

Comparison of $B_3^{\mathrm{eff}}\left({\eta }_s^r\right)$ and $B_3^{\mathrm{dep}}\left({\eta }_s^r\right)$ for the AO model with size ratios $q=0.5,0.25,0.154$. Lines are guides to the eye and statistical uncertainties are smaller than the symbol sizes. To aid visibility, the curves for $q=0.25$ and $q=0.5$ have been shifted vertically by $0.5$ and $1.0$, respectively.

Figure 3

Estimates of the dimensionless third virials $B_3^{\mathrm{pmf}}/B_2^2$ and $B_3^{\mathrm{star}}/B_2^2$ vs functionality for various chain lengths $n$. Volumes ranged from $V={\left(20\sigma \right)}^3$ to $V={\left(40\sigma \right)}^3$, large enough to access the limiting behavior of $g_3^{\prime }\left(r_{\min }\right)$. Bonded monomers interact via a FENE potential with parameters $K=30.0\epsilon /{\sigma }^2,R_0=1.5\sigma$ [34]. The LJ potential was truncated and shifted at $r=2.5\sigma$. In all cases $T$ is chosen to yield $B_2=-3321{\sigma }^3$. Errors are comparable with symbol sizes.