Conformational properties of polymer brushes with aggrecan-like macromolecules under strong stretching conditions on a cubic lattice

The comb-like polymers are used to modify various surfaces due to their branched structure and a number of unique physical and chemical properties. With a sufficiently dense grafting, the macromolecules form a homogeneous polymer brush that completely covers the surface to be modified. Comb-like polymer brushes find applications as biomedical coatings, lubricants, sensors, targeted drug delivery systems, and many others. Given the wide demand for comblike polymer coatings, it is of practical importance to predict their conformational properties as a function of the architecture of the grafted polymers. Сomb-like polymer brushes have been reasonably well studied both theoretically and experimentally at low grafting densities. However, there are no analytical models that quantitatively describe the properties of these brushes under conditions of high grafting densities and near-limit stretching of the macromolecular backbones. To study the conformational properties of planar polymer brushes made of comb-like polymers, two complementary approaches have been applied: analytical and numerical methods of the self-consistent field. The former was used for analytical description of the volume fraction profile of monomeric units of grafted macromolecules under their stretching on a body-centered cubic lattice, and the latter was used for validation of the proposed analytical model by comparing its results with the numerical calculation data on a simple cubic lattice. A universal analytical formula has been obtained that describes the profile of the volume fraction of monomeric units of grafted comb-like macromolecules in a wide range of grafting density values under conditions of athermal low-molecular-weight solvent. The study proceeded with the quantitative estimation of the average thickness of polymer brushes and the average density of monomeric units at different effective grafting densities of comb-like polymers. This was achieved by determining the ratio of the actual grafting density to the maximum possible grafting density of macromolecules with a given architecture as well as at different branching of these macromolecules. It has been demonstrated that, under conditions of athermal solvent, there is an increase in the average thickness of the polymer brush and a decrease in the average density of monomer units, as the branching degree of grafted macromolecules increases at a fixed grafting density and contour length of the main chain of macromolecules. Furthermore, at elevated levels of branching in grafted chains, the observed dependence of the average density on the effective grafting density approaches a linear relationship. The proposed analytical stretching model on a body-centered cubic lattice showed high agreement with the data obtained by numerical simulation on a simple cubic lattice. The findings of this study provide a foundation for predicting the conformational properties of polymer brushes under conditions of high grafting density and the degree of branching of grafted comb-like macromolecules.

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