Weak polyelectrolytes tethered to cylindrical surfaces are investigated using a molecular theory. These polymers form a model system to describe the properties of aggrecan molecules, which is one of the main components of cartilage. We have studied the structural and thermodynamical properties of two interacting aggrecans with a molecular density functional theory that incorporates the acid-base equilibrium as well as the molecular properties: including conformations, size, shape, and charge distribution of all molecular species. The effect of acidity and salt concentration on the behavior is explored in detail. The repulsive interactions between two cylindrical-shaped aggrecans are strongly influenced by both the salt concentration and the pH. With increasing acidity, the polyelectrolytes of the aggrecan acquire charge and with decreasing salt concentration those charges become less screened. Consequently the interactions increase in size and range with increasing acidity and decreasing salt concentration. The size and range of the forces offers a possible explanation to the aggregation behavior of aggrecans and for their ability to resist compressive forces in cartilage. Likewise, the interdigitation of two aggrecan molecules is strongly affected by the salt concentration as well as the pH. With increasing pH, the number of charges increases, causing the repulsions between the polymers to increase, leading to a lower interdigitation of the two cylindrical polymer layers of the aggrecan molecules. The low interdigitation in charged polyelectrolytes layers provides an explanation for the good lubrication properties of polyelectrolyte layers in general and cartilage in particular.
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