End‐Anchored Polymers: Compression by Different Mechanisms and Interpenetration of Apposing Layers

Abstract

Summary: This paper presents a systematic study of the compression of end‐anchored polymer layers by a variety of mechanisms. We treat layers in both good and Θ solvents, and in the range of polymer densities that is normally encountered in experiments. Our primary technique is numerical self‐consistent field (NSCF) theory. We compare the NSCF results for the different mechanisms with each other, and with those of the analytic SCF theory. For each mechanism, we calculate the density profiles, layer thicknesses, and free energies, all as functions of the degree of polymerization and surface coverage. The free energy and the deformation of each layer depend on the compression mechanism, and they can be very different from the ASCF theory. For example, the energy of compression can be as much as three times greater than the analytical SCF (ASCF) prediction, and it does not reduce to simple, universal functions of the reduced distance between the surfaces. The overall physical picture simplifies if the free energy is expressed in terms of the layer deformation, rather than the reduced surface separation. We also examine and quantify the interpenetration of layers, discuss why ASCF theory applies better to some compression mechanisms than others, and end with comments on the difficulties in extracting quantitative information from surface‐forces experiments.Comparisons of forces of compression in a good solvent for the three different systems, as functions of D/nb. The lower three curves are for σ* = 3, and the upper three are for σ* = 23.imageComparisons of forces of compression in a good solvent for the three different systems, as functions of D/nb. The lower three curves are for σ* = 3, and the upper three are for σ* = 23.

Grafted Polymer Chains Interacting with Substrates: Computer Simulations and Scaling

“…Descas, J.-U. Sommer, A. Blumen where we have used Equation (14) and (27). Now, the condition for a brush to be formed can be written as…”

“…In Equation (27), the factor four appears because in the simulation method which we use (see Appendix A) a monomer occupies four lattice sites on the adsorbing surface. Since all polymers are grafted to the surface, all monomers contribute to the surface layer.…”

“…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.…”

Neutron reflectometry yields distance-dependent structures of nanometric polymer brushes interacting across water

“…The latter has immediate consequences for the brushes' shear tribological properties, because shear stress between sliding polymer brushes is known to depend on the level of brush interpenetration. 7 The interaction of polymer brushes has been extensively studied theoretically [8][9][10][11] and computationally, 7,[12][13][14] both in terms of pressure-distance curves (i.e., distance-dependent interaction pressures) and in terms of brush conformations. Pressure-distance curves have been determined also experimentally, using amphiphilic multilayers, 15 surface force apparatus (SFA) 16 and atomic force microscopy (AFM).…”

Repulsion Exerted on a Spherical Particle by a Polymer Brush

“…15,16 The second issue is the use of SST for the uniform compression, which makes an unrealistic assumption that the polymer chains are restricted to so-called classical trajectories. Typical experiments [5][6][7][8] come nowhere near the grafting densities required for this assumption, 17 and there is theoretical evidence 18 that this results in considerable inaccuracy.…”