Static properties of end-tethered polymers in good solution: A comparison between different models

Abstract

We present a comparison between results, obtained from different simulation models, for the static properties of end-tethered polymer layers in good solvent. Our analysis includes data from two previous studies--the bond fluctuation model of Wittmer et al. [J. Chem. Phys. 101, 4379 (1994)] and the off-lattice bead-spring model of Grest and Murat [Macromolecules 26, 3108 (1993)]. Additionally, we explore the properties of a similar off-lattice model simulated close to the Theta temperature. We show that the data for the bond fluctuation and the Grest-Murat model can be analyzed in terms of scaling theory because chains are swollen inside the Pincus blob. In the vicinity of the Theta point the structure of the chains is essentially Gaussian in the Pincus blob. Therefore, the data for the second off-lattice model can be compared quantitatively to the self-consistent field theory. Different ways to determine the parameters of the self-consistent field theory are discussed.

Spherical polymer brushes under good solvent conditions: Molecular dynamics results compared to density functional theory

“…22,29,61 Of course in the region where the layering has died out, for flat polymer brushes one observes a decay of ρ(r) roughly compatible with a parabolic decay 21 rather than the Daoud-Cotton power law observed here. For low enough N and/or big enough radius of the internal core, one should expect a crossover to the flat brush limit.…”

Segment Distributions of End-Tethered Polymers in a Good Solvent

“…At larger distances, the influence of the wall should become weaker, and the segment distribution can be expected to approach a maximum value R g N=R g given by the average segment density within the polymer layer whose height is approximately given by the radius of gyration R g of the free, unperturbed chain [6]. The slow increase of the segment distribution close to the substrate, together with its fast decay for distances z R g predicted by renormalization-group (RG) calculations [7] and computer simulations [8], suggests that the segment distribution of an end-tethered polymer in the low-density limit R 2 g 1 is strongly asymmetric, resembling the shape of a mushroom.Although this ''mushroom'' conformation of an isolated end-tethered polymer represents the simplest situation of a broken symmetry for polymer statistics, detailed experimental tests of the theoretical predictions for z in the low-density limit are lacking. Neutron reflectivity measurements on end-adsorbed diblock copolymers confirmed the existence of a depletion layer close to the surface and the RG prediction for the second moment of the segment distribution hz 2 i 2:16R 2 g [9,10].…”

“…At larger distances, the influence of the wall should become weaker, and the segment distribution can be expected to approach a maximum value R g N=R g given by the average segment density within the polymer layer whose height is approximately given by the radius of gyration R g of the free, unperturbed chain [6]. The slow increase of the segment distribution close to the substrate, together with its fast decay for distances z R g predicted by renormalization-group (RG) calculations [7] and computer simulations [8], suggests that the segment distribution of an end-tethered polymer in the low-density limit R 2 g 1 is strongly asymmetric, resembling the shape of a mushroom.…”

“…RG theory and simulations predict that the segment distribution of an isolated end-tethered polymer in a good solvent follows a scaling form~z=R g , the scaling factor being the radius of gyration R g of the free (untethered) chain [7,8]. In order to test this prediction, we measured the intensity-weighted segment distribution S z for endtethered DNA with contour lengths 8:2 m L 59:4 m, corresponding to chains with 20 040 N 0 145 506 basepairs [12].…”

“…proposed by Kreer et al [8] to interpolate between the behavior of end-tethered excluded-volume chains at small and at large distances z. z is related to the propagator of the nth segment of the tethered chain, G n 0; r [14], by z R dxdy R N 0 dnG n 0; r . Equation (1) was shown to be in excellent agreement with RG theory and simulations and allows us to cast all excluded-volume effects into the radius of gyration R g of the free chain.…”