Simulations were performed on a triangular fcc lattice. The simulation box consisted of 100x100x100 beads. The layers x = 1 and 2 were immobilized and represented a hard flat surface. A random selection of the beads in these layers were set as initiators until the assumed grafting density (GD) was attained. The first polymer segment was thus usually in the layer no 3.

Periodic boundary conditions were used in all directions, so immobilized layers no. 1 and 2 acted as a reflecting surface in the x-direction.

The dynamics of all system elements (chain fragments, monomer and solvent) was provided by the dynamic lattice liquid model (DLL). This Monte Carlo model of molecular movement of elements is based on generally accepted view of translational dynamics in simple and complex liquids. One element typically represents group of atoms such as a polymer repeating unit, monomer or solvent molecule. In a classical molecular dynamics simulation, one can observe three major diffusion regimes in various time scales: ballistic diffusion, slowed diffusion due to caging effect of neighbors and Fickian diffusion in long time scales.

The caging stage is realized as element oscillation around mean position represented by lattice site. The basic diffusion move is realized as translation to the neighboring lattice site. The DLL model is based on the assumption that in a dense system, a translational move is possible only by cooperative movement of a group of elements.

Macromolecules such as polymer chains are represented in the DLL model as a set of elements, reflecting polymer segments, connected by non-breakable and inextensible (over length of one lattice constant) bonds. The DLL model fulfills the continuity condition and provides the correlated movements of elements as in a real liquid. The excluded volume is preserved for each element due to an assumption that only one molecule at a time can be present on a specific lattice site. Excluded volume is also preserved for bonds because elements are forbidden to move through the bonds. It is assumed that each element possesses some free excess volume to vibrate around its temporal position. The ‘vibratory’ movement of an element is represented by a random attempt of a movement to one of the neighboring lattice sites. A set of possible vectors of movement attempts is equal to lattice coordination number, for simplicity. If a local group of elements possesses vectors of movement attempts that sums to zero, the movement of those elements is allowed – excluded volume is not violated.