Entropy of Polymer Brushes in Good Solvents:  A Monte Carlo Study

Abstract

Entropy of polymer brushes composed of monodisperse flexible polymer chains regularly grafted on a flat substrate plane with an equal “spacing” is numerically studied in the good solvent limit. We consider systems of not only a free polymer brush but also a compressed polymer brush and two polymer brushes facing each other at a “distance”. The total number of configurations, entropy, and force are calculated for various chain lengths and graft densities by means of Monte Carlo simulations using an efficient enrichment algorithm on a simple cubic lattice. We demonstrate that the effect of excluded volume plays an essential role. We find that the entropy of a free polymer brush falls as −ΔS ∼ (spacing)-2.4±0.1, while the entropy of a compressed polymer brush and two polymer brushes agrees very well with the analytical SCF theory by Milner, Witten, and Cates [Macromolecules 1988, 22, 2610−2619]. The resulting interlayer force agrees also excellently well with the recent experiments by Yamamoto et al. [Macromolecules 2000, 33, 5602−5607].

Grafted Polymer Chains Interacting with Substrates: Computer Simulations and Scaling

“…We now turn to study the scaling behavior of M according to Equation (9) and (10). The expected asymptotic power laws correspond in a double logarithmic representation to straight lines, as indicated in Figure 2 and 5.…”

“…However, the situation there is different due to the lack of attractive monomer/surface interactions. [9,10] A more formal, analytical approach to the problem of polymer adsorption uses field theoretic methods, in particular renormalization group techniques. Now, the presence of the surface converts the infinite space surrounding polymers in solution to a problem in semiinfinite space: it turns out (as in the case of restricted geometries) that the field theoretic methods work less well in the semi-infinite than in the infinite geometry.…”

“…We mention here that for end-anchored chains without attraction to the surface there are other interesting features which appear. [25] In this case, much recent attention was devoted to the compression of the end-grafted layers by different mechanisms; [10,26,27] one also studied entanglements in polymer brushes. [28,29] The influence of the end-grafted chains on the adsorption of simple fluids and of spherical molecules on surfaces has been investigated using density functional approaches and computer simulations.…”

Changes in the structure of tethered chain molecules as predicted by density functional approach

“…The studies included scaling theories [13][14][15], classical self-consistent field methods [16,17], single chain mean-field methods [18], density functional theories [18][19][20][21][22] and computer simulations [23][24][25][26][27][28][29][30][31][32][33][34]. In our opinion, particularly important for further theoretical studies of systems involving tethered chains is the development of density functional theory (DFT) [20,21,[35][36][37][38][39][40][41][42] that is based on the approach proposed by Yu and Wu [43].…”

Confinement and compression of an oligomer brush

“…19,22,23 Simple behavior of compressed SAMs can be understood using scaling arguments, 8 creation of gauche defects, 24 geometrical models ͑cooperative tilting͒, 25 or cubic lattice models. 26 However, these models neglect polymer-specific characteristics that can result in unexpected behavior. For example, attractive electrostatic forces in polyelectrolyte brushes lead to a first order phase transition ͑collapse͒ unparalleled in neutral SAMs.…”