Nanoscale colloidal particles display fascinating electronic, optical and reinforcement properties as a consequence of their dimensions. Stable dispersions of nanoscale colloids find applications in drug delivery, biodiagnostics, electronics, and polymer nanocomposites.  In many experimental approaches to dispersion and self-assembly of nanoscale colloids, surfactants or polymers are added to control the onset of self-assembly. However, robust molecular models of the effects of organic modifiers are not generally available. We have developed a novel application of the expanded ensemble Monte Carlo simulation method to calculation of the chemical potential (m_c) of nanocolloidal particles in the presence of polymeric surface modifiers.

            We present results of extensive calculations of colloid chemical potential and polymer adsorption in LJ colloid-polymer systems as a function of nanocolloid size and concentration, polymer chain length (molecular weight) and concentration, and colloid-polymer interaction strength. Based on the results, a simple model for the physical dependence of chemical potential on contributions from particle size and modifier chain length is developed. The dependence of chemical potential on polymer chain length and colloid diameter was found to be represented well by a power scaling law of the form bm_c^ex ~ s_c^3.0n^b .We observe that the chain adsorption and configurations near the particle dominate the dependence of chemical potential on chain length. In addition, the net force between colloidal particles in a dilute polymer solution is calculated as a function of colloid size and modifier chain length.