Abstract
We present Monte Carlo simulations of colloidal particles pulled into grafted polymer layers by an external force. The insertion free energy for penetration of a single colloid into a polymer layer is qualitatively different for surfaces with an ordered and a disordered distribution of grafting points and the tendency of colloidal particles to traverse the grafting layer is strongly size dependent. In dense colloidal suspensions, under the influence of sufficiently strong external forces, colloids penetrate and form internally ordered, columnar structures spanning the polymer layer. The competition between the tendency for macro-phase separation of colloids and polymers and the elastic-like penalty for deforming the grafted layer results in the micro-phase separation, i.e. finite colloidal clusters characterized by a well-defined length scale. Depending on the conditions, these clusters are isolated or laterally percolating. The morphology of the observed patterns can be controlled by the external fields, which opens up new routes for the design of thin structured films.
Highlights
Gra ed polymer layers can prevent the deposition of colloidal particles on solid surfaces, which is exploited in various applications like colloidal stabilization, anti-fouling surfaces[1] and in biomedicine.[2]
We demonstrate that sufficiently strong external forces give rise to collective ordering with a rich variety of morphologies
When many colloids are inserted, the polymers mediate effective many-body interactions among them and the insertion free energy in general depends on the positions of all particles. To explore such multi-particle systems we have performed Grandcanonical Monte Carlo simulations with colloidal particles coupled to a reservoir with a xed chemical potential m at various polymer gra ing densities, chain lengths, particle concentrations and external forces
Summary
We report Monte Carlo computer simulations of polymer-insoluble particles in gra ed polymer layers. The gra ing density ~r 1⁄4 Np/Rg2 determines whether the polymer layer is in the dilute “mushroom” (~r < 1) or in the dense “brush” scaling regime (~r T 3).[20,21] The relevant physical length scale in the mushroom regime is the radius of gyration Rg of the chains, while in the brush regime it is the so-called de Gennes blob: x f rÀ1/2.4 All our simulations are in the intermediate regime where the two length-scales are similar x z Rg. In the following, rather than per Rg2, we will express the gra ing density as the number of anchoring points per colloidal diameter squared, r 1⁄4 ~rRg2/s2. We rst describe the model and simulations on single-colloid insertion, followed by a study of collective ordering in dense colloidal systems
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