Compressed asymmetric polymer brushes exhibit a symmetric interpenetration zone

The present study investigates the interpenetration properties of two opposing monodisperse asymmetric polymer brushes under external pressure, utilizing a numerical self-consistent field method. The polymer brushes under consideration were composed of chemically identical units, had the same stiffness values, and differed in the grafting density values <i>σ</i>_1,2 and/or in the number of backbone units <i>N</i>_1,2. Both brushes were immersed in an athermal solvent. Contrary to our expectations, the interpenetration zone of various asymmetric brushes always had a symmetrical appearance. We propose an analytical scaling theory rationalizing the symmetry of the interpenetration picture and suggesting how the penetration length scales with the four brush parameters (<i>σ</i>_1,2; <i>N</i>_1,2). Analytical expressions for the interpenetration zone were proposed and verified using numerical SCF calculations. The interpenetration of the two opposing brushes was quantified by two integral parameters: (i) the overlap integral, denoted by <i>Γ</i>, which represents the number of contacts between brushes and (ii) the number of monomer brush units in the foreign half-space, denoted by <i>Σ</i>. We demonstrate that a panoply of curves specifying <i>Σ</i> and <i>Γ</i> as functions of external pressure for different asymmetric brush pairs collapse onto universal master curves once they are rescaled as suggested by the analytical theory.