Self-consistent field approach is used to model a single end-tethered polymer chain on a substrate subject to various forces in three dimensions. Starting from a continuous Gaussian chain model, the following perturbations are considered: (i) hydrodynamic interaction with an externally imposed shear flow for which a new theoretical framework is formulated; (ii) excluded volume effect in a good solvent, treated in a mean field approximation; (iii) monomer-substrate repulsion. While the chain stretches along the flow, the change of the density profile perpendicular to the substrate is negligible for any reasonable simulation parameters. This null effect is in agreement with multiple neutron scattering studies.
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