Tethered surface

Highly branched polymers, polymer adsorption and the mesophases of block copolymers may seem weakly connected subjects. However, in this review we bring out some important common features related to the tethering experienced by the polymer chains in all of these structures. Tethered polymer chains, in our parlance, are chains attached to a point, a line, a surface or an interface by their ends. In this view, one may think of the arms of a star polymer as chains tethered to a point [1], or of polymerized macromonomers as chains tethered to a line [2-4]. Adsorption or grafting of end-functionalized polymers to a surface exemplifies a tethered surface layer [5] (a polymer brush ), whereas block copolymers straddling phase boundaries give rise to chains tethered to an interface [6],... 

A more accurate analysis of this problem incorporating renormalization results, is possible [86], but the essential result is the same, namely that stretched, tethered chains interact less strongly with one another than the same chains in bulk. The appropriate comparison is with a bulk-like system of chains in a brush confined by an impenetrable wall a distance RF (the Flory radius of gyration) from the tethering surface. These confined chains, which are incapable of stretching, assume configurations similar to those of free chains. However, the volume fraction here is q> = N(a/d)2 RF N2/5(a/d)5/3, as opposed to cp = N(a/d)2 L (a/d)4/3 in the unconfined, tethered layer. Consequently, the chain-chain interaction parameter becomes x ab N3/2(a/d)5/2 %ab- Thus, tethered chains tend to mix, or at least resist phase separation, more readily than their bulk counterparts because chain stretching lowers the effective concentration within the layer. The effective interaction parameters can be used in further analysis of phase separation processes... 

Scheme 12.3 Synthesis of rare-earth metal (Ln) surface complexes, that is, heterogenized Ln single-sites, on silica Do = donor ligands, L = monoanionic ligands and M = Al, Mg, Zr or Si M = Si refers to tethered surface species.

Figure 4. Adsorption of plasma components on (PEO)70o tethered surface. Explanation is given in the text.

W. Norde and R. A. Gage, Interaction of bovine serum albumin and human blood plasma with PEO-tethered surfaces influence of PEO-chain length, grafting density and temperature, Langmuir 20, 4162-4167 (2004). 

Based on the density of grafting, the systems examined are expected to be in the strong brush regime, wherein the chains are strongly stretched away from the tethering surface, even in the absence of any external force. Upon application... 

Recently, Brzozowska et al. used NR and ex situ electrochemical techniques to characterize an innovative type of monolayer system intended to serve as a support for a bUayer lipid membrane on a gold electrode surface [51]. Zr ions were used to noncovalendy couple a phosphate-terminated self-assembled monolayer (SAM) formed on a gold surface to the carboxylate groups of negatively charged phos-phatidylserrne (PS). This tethered surface was then used for the formation of a PS hpid bilayer structure formed by vesicle fusion and spreading. NR studies revealed the presence of an aqueous environment associated with the tether layer which arises from nonstoichiometric water associated with the zirconium phosphate moieties [52]. 

Further improvements in modeling flexible sheet polymers must take into account the molecular connectivity within the membrane. To analyze the shapes of these structures, one discards elasticity theory and finds a more appropriate context in statistical mechanics of random surfaces. A number of approaches have been proposed. For example, the membrane may be (a) represented as a self-avoiding surface,"i2.i99 and its shape characterized by asphericity and radius of gyration,"i2.i99 or (b) viewed as a tethered surface with fixed internal connectivity.200-203 in case (b), nuclei are regarded as hard spheres tethered together by elastic or fluid strings, forming a net with a specified architecture. 

Xu X, Cao D Density functional theory for adsorption of coUoids on the polymer-tethered surfaces effect of polymer chain architecture,/ Chem Phys 130(16) 164901, 2009. 

What is known, of course, is how to solve the free field theory obtained by setting ( = constant. This is quickly found to be totally inconsistent with branched polymers, instead corresponding to an almost tethered surface whose internal connectivity remains that of a flat sheet at all distances. If this result were to carry over to the variable cutoff version of the theory, it would probably spell disaster for all the empirical models discussed earlier. Fortunately, the self-interacting cutoff may provide an escape route by permitting the occurence of localized spikes in the (f) field. In real space these correspond to cylindrical protrusions of the surface, which may signal the onset of a branched polymer instability. Although much work remains before this is firmly established, it looks as if our heuristic assumptions about the structure of fluid films beyond will probably remain intact. 

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