No abstract

The development of predictive equations of state for nanoparticle−surfactant or −polymer mixtures is of extreme importance in nanotechnology and fabrication of advanced materials. Of particular interest is modeling the transitional regime between entropy-controlled (depletion, repulsive interactions) vs enthalpy-controlled physics (adsorption, attractive interactions). In this paper, the perturbed Lennard-Jones chain (PLJC) equation of state (EOS) for polymer−solvent mixtures is modified and extended to calculate the chemical potentials in nanoparticle−polymer mixtures. The EOS predictions are compared to Monte Carlo simulations that use the same LJ molecular model over a wide range of polymer concentrations approaching the semidilute regime, 0.15 < c p/c p* < 0.8. The original PLJC equation, with one adjustable parameter, predicts the nanoparticle chemical potential very well for the enthalpy-dominated strong adsorption regime, e.g., LJ energy parameters εcp > εpp, where εcp = colloid−polymer and εpp = polymer−polymer. However, for LJ parameters leading to weak polymer adsorption or depletion, εcp < εpp, the PLJC could not predict simulation results without further modification. We introduced a semiempirical term that corrects for the polymer−colloid excluded volume. The correction introduces one additional adjustable parameter, but this parameter remained essentially unchanged for all particle compositions, sizes, and εcp values studied. These results illustrate that a polymer equation of state, when corrected for the polymer−particle excluded volume, holds promise in modeling the effects of attractive polymeric modifiers on nanoparticle dispersions.