Investigation of the Effect of Molecular Weight, Density, and Initiator Structure Size on the Repulsive Force between a PNIPAM Polymer Brush and Protein

Abstract

This paper focuses on the effect of degree of polymerization (N), density ( $\sigma$ ), and pattern size ( $x$ ) on the interaction force between a periodically patterned Poly(N-isopropylacrylamide) (PNIPAM) brush and protein. The hydrophobic interaction, the Van der Waals attractive force, and the steric repulsive force were expressed in terms of $N$ , $\sigma$ , and $x$ . The osmotic constant (k1) and the entropic constant (k2) were determined from the fit of the steric repulsive force to an experimentally obtained force distance curve. The osmotic constant was 0.105, and the entropic constant was 0.255. Using these constants, the steric repulsive force was plotted as a function of the separation distance(s) between the substrate and the protein. The forces were determined at a separation distance equal to 0.3 nm, where L0 is the equilibrium thickness of the PNIPAM brush. At this separation distance, the value of the steric repulsive force was much higher than the value of the sum of the hydrophobic interaction and the Van der Waals attractive force for large degree of polymerization ( $N>100$ ) and density ( $\sigma >0.2$ chains/nm2). However, the repulsive force was comparable to the sum of the hydrophobic interaction and the Van der Waals attractive force for a small degree of polymerization ( $N<100$ ) and density ( $\sigma =0.2$ ). Furthermore, the steric repulsive force was plotted as a function of pattern size $x$ . The plot indicated that the steric repulsive force becomes nearly zero for all degrees of polymerization and density when the value of the initiator structure size was less than 200 nm. In addition to the steric repulsive force, the lateral extension of the chains in the periodically patterned PNIPAM brush was calculated by scaling low and compared with the experimental data taken from previously published literatures. The polymer brush structure was modelled as if the immediate bare substrate is so wide that even a stretched polymer segment cannot reach to the next polymer brush structure. In such models, the value of the lateral extension was equal to the thickness of the homogenous brush. It was independent of the pattern size. However, when the polymer brush structure was modelled as if there is another polymer brush structure at a distance half of the size of the period, the lateral extension was found to be dependent on the size of the initiator structure size due to chain bridging. This was witnessed by the patterning of polymer brushes using the interferometric patterning of PNIPAM brushes and an atomic force microscopy imaging of the polymer brush structures both in air and in water. The polymer brush structure resolution in water was much lower than the resolution in air, which indicates the lateral extension of the polymer chains in water. For such kind of periodic polymer brush structures, the gap between them was calculated, and it was found dependent on the degree of polymerization, density, and initiator structure size.