A terminally anchored polymer chain in shear flow: Self-consistent velocity and segment density profiles

The behavior of a terminally anchored freely-jointed bead-rod chain, subjected to solvent shear flow, was investigated via Brownian dynamics simulations. Previous calculations have been improved by computing the segment density and fluid velocity profiles self-consistently. The segment density distributions, components of the radius of gyration, and chain attachment shear and normal stresses were found to be sensitive to low values of shear rate. Additionally, it was found that the thickness of a model polymer layer was a strong function of the shear rate, and that the functional dependence on shear rate changed dramatically as the chain length increased. For the longest chains studied, the thickness of the model polymer layer first increased as the shear rate increased, passed through a maximum, and then decreased at high shear rates, in accordance with experimental results in theta solvents. These results suggest that a dilute or semi-dilute layer model may explain hydrodynamic behavior previously thought to be due to the entanglements that occur in dense surface bound polymer layers.Nomenclature a_i acceleration of bead i - b radius of the beads - d length of the rods connecting the chain beads - d_i vector from bead i to bead i + 1 - F_i external force applied to bead i - F_i^b external force on bead i due to Brownian motion of surrounding fluid - F_i^h external force on bead i due to viscous drag - F_i^s external force on bead i due to surface interactions - f Stokes drag coefficient - Boltzmann's constant - L_h effective hydrodynamic thickness - m_i mass of bead i - N number of beads on a model chain - n number of chains anchored to the surface per unit surface area - P segment density distribution P pressure - Q flow in a tube with no surface bound polymer layer - Q_a flow in a tube with a surface bound polymer layer - R_g vector representation of the radius of gyration - R tube radius - r radial coordinate in the tube geometry - S_ij pair hydrodynamic interaction tensor for beads i and j - T_i internal chain force in rod i connecting beads i and i + 1 - T_X component of the surface attachment force in the direction of the fluid flow - T_y component of the surface attachment force perpendicular to the surface - T temperature - v_i velocity of the center of mass of bead i - V_if average fluid velocity at the location of bead i - v_if⁰ fluid velocity in the absence of a polymer chain - v_if perturbation to the fluid velocity due to hydrodynamic interactions - V_b bead volume = 4 b³/3 - scalar fluid speed in the axial direction down the tube - x axial coordinate in the tube geometryGreek symbols _w apparent shear rate - fluid viscosity - polymer layer permeability - volume fraction of space occupied by chain beads - (_w)_a chain attachment stress perpendicular to the surface - (_w)_a chain attachment stress in the plane of the surface and in the direction of fluid flow