Shear Swelling of Polymer Brushes Grafted onto Convex and Concave Surfaces

Abstract

The shear response of polymer brushes is explored as a function of grafting surface curvature using the Alexander-deGennes ansatz, where the free ends of the chains are localized at the tip of the brush and all tethered chains in the brush are stretched equally. Brushes adsorbed onto the concave and convex surfaces of a cylinder are found to swell to a maximum of 35% of their nonsheared brush height in good solvent, larger than the predicted maximum shear swelling of planar brushes of the same grafting density. For significantly convex surfaces, increased surface curvature increases the maximum amount of shear swelling. In contrast, brushes grafted onto concave surfaces with the same grafting density show diminished shear swelling as the grafting surface becomes more concave. The shear response of nonplanar brushes is important in a variety of possible applications, including the fabrication of pressure-sensitive microvalves and dynamic membranes and an understanding of the rheological behavior of hairy-rod polymers or molecular bottlebrushes.

Simulation of Copolymer Bottle‐Brushes

“…[8] On a surface of a cylinder of radius r and length L there should then be p blobs, each of crosssectional area j 2 (r) (geometrical factors of order unity are ignored throughout). Since the surface area of the cylindrical segment is Lr, we must have [8,9,15] …”

“…[4] In the present work, we focus on the following two problems: (i) the conformation of a side chain of one-component bottle-brush polymers, where the backbone is treated as a rigid straight line or thin cylinder, [5][6][7][8][9][10][11][12][13][14][15][16] and (ii) the phase separation of copolymer bottle-brushes with a rigid backbone, where two types (A,B) of flexible side chains are grafted with one chain end to the backbone in an alternating way. In problem (i), the stretching of the side chains in the radial direction in the case of sufficiently high grafting density was mostly discussed in terms of a scaling description, [5][6][7][8][9][13][14][15] extending the Daoud-Cotton [17] ''blob picture'' [18][19][20] from star polymers to bottlebrush polymers. If one uses the Flory exponent [21,22] n ¼ 3/5 in the scaling relation for the average root mean square endto-end distance of a side chain in a radial direction, R eÀe / s ð1ÀnÞ=ð1þnÞ N 2n=ð1þnÞ , where s is the grafting density and N is the number of effective monomeric units of a side chain, one obtains R eÀe / s 1=4 N 3=4 .…”

Inwardly curved polymer brushes: concave is not like convex

“…where ψ(y) = x * 4 ) (21) In the entire regime 2, equation (17) shows that the normalized brush height x * increases when the curvature R * /R increases, until it reaches x * = 1 for R = R * ( Figure 6). In other words, the brush height increases when the interface is curved more strongly, as long as there is some free solvent in the center.…”

“…To our knowledge, only two theoretical papers have addressed this problem [16,17], one in the context of the study of the elastic properties of polymer-decorated membranes [16] and the second one in the context of shear swelling of polymer brushes grafted onto convex and concave surfaces [17]. However, these authors described the chain conformation and the free energy of the brush on the concave side of the interface incorrectly, since they essentially used the classical Daoud-Cotton scaling approach [18] which correctly describes brushes anchored on the convex side of interfaces but not on concave side, as we will show bellow ; in the DaoudCotton approach the structure of the brush is self-similar and scales linearly with the distance from the center of curvature (Figure 1).…”

Bioinspired synthesis of optically and thermally responsive nanoporous membranes

“…Assuming simple Hagen-Poiseulle flow, however, is inaccurate because the thickness of surface-grafted polymer layer in a cylindrical conduit is flow-rate dependent. Except for very low flow rates, we assume the polymer layer either swells due to shear 33 or flattens if the order of the polymer brush is not very high and not all chains are pointing toward the flow (incomplete grafting). 34,35 Additionally, if we assume that the polymer graft is a continuous gel with viscoelastic properties, which could be induced by embedding gold nanoparticles into the polymers, instabilities at the interface can develop even at very low Reynolds numbers.…”