The slowly formed Guiselin brush

– We study polymer layers formed by irreversible adsorption from a polymer melt. Our theory describes an experiment which is a “slow” version of that proposed by Guiselin (Europhys. Lett., 17 (1992) 225) who considered instantaneously irreversibly adsorbing chains and predicted a universal density profile of the layer after swelling with solvent to produce the “Guiselin brush”. Here we ask what happens when adsorption is not instantaneous. The classic example is chemisorption. In this case the brush is formed slowly and the final structure depends on the experiment’s duration, tfinal. We find the swollen layer consists of an inner region of thickness z∗ ∼ t−5/3 final with approximately constant density and an outer region extending up to height h ∼ N which has the same density decay ∼ z−2/5 as for the Guiselin case. Introduction. – Several years ago, Guiselin [1] proposed an experiment to study irreversible polymer adsorption. In its simplest form, a melt is exposed to a surface so attractive to the polymer chains that they adsorb instantaneously and irreversibly. This freezes in melt chain configurations, including the size distribution of surface loops (see fig. 1(a)). The adsorbed layer is then swollen with solvent, washing away unattached chains. Guiselin predicted that the resulting interfacial structure, which has come to be known as the “Guiselin brush”, has a universal density profile, c(z) ∼ z−2/5 in good solvent. Neutron scattering [2, 3] and neutron reflectivity [4, 5] studies have indicated density profiles both consistent [3, 5] and inconsistent [4] with this prediction. In this letter we study the same irreversible melt adsorption processes as did Guiselin, but we ask: what replaces the Guiselin brush if the adsorption is not instantaneous? The most important example of this is chemisorption where functionalized chains develop polymer-surface bonds which are usually irreversible. This arises in various technologies where polymers are attached to solid surfaces to permanently modify surface properties [6–8] (fig. 1(a)). For example, in fiber-reinforced thermoplastics, strong polymer-fiber interfaces are frequently created by chemisorption of polymers onto the fibers after functionalization of fiber surfaces with coupling agents [8–10]. Another related class involves reinforcement of immiscible polymer interfaces by chemical reactions between multi-functionalized chains at the interfaces [11]. Unlike the physisorption processes studied by Guiselin, chemisorption is extremely slow (microscopically speaking) in that 2 mutually reactive groups must collide millions of times,