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

Abstract

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 behaviour.Many-body forces occur when the net interaction between two particles is not simply pairwise additive, but depends on the presence of other particles. They appear in a wide range of physical systems including dense phases of noble gases [1], molecular systems [2], nuclear matter [3], superconductors [4] and complex fluids such as polymers [5], lipid membranes [6,7] and colloidal dispersions [8][9][10][11]. In seeking to make theoretical and computational progress with such systems one often attempts to simplify matters by "coarse-graining" ie. integrating over the degrees of freedom on small length or times scales. This leads to a description of the system in term of an effective Hamiltonian describing the interactions among the remaining degrees of freedom. These interactions are inherently many-body in character, even if the original system involves only pairwise interactions.To appreciate how many-body interactions arise in coarse-grained (CG) representations of complex fluids, consider the case of colloids dispersed in a sea of much smaller polymers. This system is commonly modelled as a highly size-asymmetrical mixture of spheres as shown in the simulation snapshot of Fig. 1(a). However, since dealing with components of disparate sizes is theoretically and computationally problematic, one typically seeks to integrate out the polymer degrees of freedom to yield an effective one-component model. But the colloidal interactions arise from the modulation of the polymer density distribution by all the colloids, and consequently, the effective one-component description is many-body in form. A second example is shown in Fig. 1(b) which depicts three star polymers in solution. A common CG model replaces each star by a single effective particle. However, the net interaction between two polymers depends on the proximity of a third, and hence the effective Hamiltonian has a many-body character [12].Computer simulation is a powerful route for designing CG models for complex fluids, which is currently receiving considerable attention. Indeed, in principle it can be used to determine a many-body potential for the CG coordinates which is consistent with the underlying atomistic model [13,14]. But implementing such approaches (Color online).(a) Snapshot of a highly siz...

Three-body critical Casimir forces

“…This procedure, however, often generates many-body forces, beyond the linear superposition of basic pairwise forces. This kind of nonadditivity is present in various systems such as colloidal suspensions [1][2][3][4][5][6][7][8], systems governed by quantum-electrodynamic Casimir forces [9][10][11][12][13][14], polymers [15][16][17][18][19], granular systems [20][21][22], nematic colloids [23], and noble gases or nanoparticles with van der Waals forces acting among them [24][25][26][27][28][29][30][31],…”

Tuning the phase diagram of colloid-polymer mixtures via Yukawa interactions

“…Note how the (local) attractive or repulsive nature of U T sensitively depends on the key parameters {q D ,φ R d ,q Y , }. It should be also clarified that this pair potential does not account for the multibody nature of the depletion interaction [21,28,52,53].…”

“…It is noted that this method does not account for multiple overlap of depletion zones [20,28], which becomes especially relevant for q D > 0.4 [21]. Using the same approach done with the analytical FVT phase diagrams but in a canonical ensemble, colloidal G-L and F-S coexistence points are calculated from the simulation data (see Sec.…”

“…The thermodynamical consequences of assuming pair-wise addition in the latter case have been analyzed and discussed in detail [20,21]. Describing the mixture by an effective pairpotential approach has been widely applied [21][22][23][24][25][26][27]. Contrary to the usually complex or computationally based approaches followed, the method reported here is simple, yet accurate, and constitutes a systematic tool for predicting phase diagrams of colloid-polymer mixtures.…”

Supramolecular polyelectrolyte complex (SPEC): pH dependent phase transition and exploitation of its carrier properties

“…Systems such as soluble polymercolloid dispersion mixtures show a rich phase behaviour [11][12][13][14][15][16][17] and may serve as an interesting model system as they provide a window to evidence emergence of new materials at molecular as well as mesoscopic length-scales. [18][19][20][21][22][23][24] Such polymeric materials have been moulded into materials with nanoscopic morphologies and have been used in nano-lithography, organic photovoltaics, batteries, etc. 25 Thus understanding the phase behaviour of soluble polymers and polymer-colloids has received immense importance.…”