Langmuir, Vol.20, No.4, 1501-1510, 2004
Nanoscale colloids in a freely adsorbing polymer solution: A Monte Carlo simulation study
A key issue in nanoscale materials and chemical processing is the need for thermodynamic and kinetic models covering colloid-polymer systems over the mesoscopic length scale (similar to1-100 nm). We have applied Monte Carlo simulations to attractive nanoscale colloid-polymer mixtures toward developing a molecular basis for models of these complex systems. The expanded ensemble Monte Carlo simulation method is applied to calculate colloid chemical potentials (mu(c)) and polymer adsorption (Gamma) in the presence of freely adsorbing Lennard-Jones (LJ) homopolymers (surface modifiers). Gamma and mu(c) are studied as a function of nanoparticle diameter (sigma(c)), modifier chain length (n) and concentration, and colloid-polymer attractive strength over 0.3 < R-g/sigma(c) < 6 (R-g is the polymer radius of gyration). In the attractive regime, nanocolloid chemical potential decreases and adsorbed amount increases as sigma(c) or n is increased. The scaling of Gamma with n from the simulations agrees with the theory of Aubouy and Raphael (Macromolecules 1998, 31, 4357) in the extreme limits of R-g/sigma(c). When R-g/sigma(c) is large, the "colloid" approaches a molecular size and interacts only locally with a few polymer segments and Gamma similar to n. When R-g/sigma(c) is small, the system approaches the conventional colloid-polymer size regime where multiple chains interact with a single particle, and Gamma similar to sigma(c)(2), independent of n. In contrast, adsorption in the mesoscopic range of R-g/sigma(c) investigated here is represented well by a power law Gamma similar to n(p), with 0 < p < 1 depending on concentration and LJ attractive strength. Likewise, the chemical potential from our results is fitted well with mu(c) similar to n(q)sigma(c)(3) where the cubic term results from the sigma(c) dependence of particle surface area (similar tosigma(c)(2)) and LJ attractive magnitude (similar tosigma(c)). The q-exponent for mu(c) (mu(c) similar to n(q)) varies with composition and LJ attractive strength but is always very close to the power exponent for Gamma (Gamma - n(p)). This result leads to the conclusion that in attractive systems, polymer adsorption (and thus polymer-colloid attraction) dominates the mu(c) dependence on n, providing a molecular interpretation of the effect of adsorbed organic layers on nanoparticle stability and self-assembly.