Chains anchor

Fig. 6 Simulation results for the normalized monomer number density, p(z)Rf/Np y as a fimction of the scaled distance from the grafting surface z/fip for anchored chains of length N = 50 and grafting densities p a = 0.02, 0.04, 0.06, 0.09, and 0.17 (from top to bottom). Note thatfip is determined within the simulation for a single, free polymer chain...

Schlesinger, P.H., Djedovic, N.K., Ferdani, R., Pajewska, J., Pajewski, R. and Gokel, G.W. (2003) Anchor chain length alters the apparent mechanism of chloride channel functions in SCMTR derivatives, Chem. Commun. 308-309. 

The second repulsive energy (referred to as steric repulsion) is produced by the presence of adsorbed surfactant layers of nonionic surfactants, such as alcohol ethoxylates or A-B, A-B-A block, or BA graft copolymers, where B is the anchor chain and A is the stabilizing chain [mostly based on polyethylene oxide (PEO) for aqueous systems]. When two droplets or particles with adsorbed PEO chains of thickness 5 approach a separation distance h such that h < 28, repulsion occurs as a result of two main effects. The first arises as a result of the unfavorable mixing of the PEO chains, when these are in good solvent conditions. This is referred to as Gm x and is given by the following expression ... 

Fig.1. Dry thickness h0 of various PDMS layers irreversibly adsorbed on the silica surface of a silicon wafer, as a function of the scaling variable Nm 0m. N is the polymerisation index of the surface anchored chains and(])0 is the polymer volume fraction in the incubation bath. The triangles correspond to 4>0=1, i.e., to the maximum surface density of anchored chains for the particular molecular weight. The range of molecular weights used is 29.6 kg mol-1

In order to investigate the internal organization of the surface-anchored chains, we now consider the concentration profile of the layers when swollen by a good solvent. Such concentration profiles have been investigated in details theoretically, since the Alexander-de Gennes model, and we can hope to be able to dis-... 

Interdigitation Between Surface-Anchored Chains and a Polymer Melt... 

In order to understand the role played by surface-anchored chains in adhesion and friction, it is essential to understand under which conditions a surface layer, when in contact with a melt, is penetrated by free chains. The question has been addressed theoretically mostly for polymer brushes, and more recently for Guiselin s pseudo-brushes. We want to review here some of these analysis, and compare the predictions of the models with the available experimental data. 

Fig. 11. Normalised enhanced adhesive strength wyw as a function of the surface density, a, for two PDMS elastomers in contact with silicon wafers covered with irreversibly adsorbed chains. Wis the thermodynamic work of adhesion, W=2y, with ythe surface tension of PDMS, 7=21.6 mN m"1 at 25 °C. The filled symbols correspond to a molecular weight between crosslinks in the elastomer Mc=24.2 kg mol-1 while Mc=10.2 kg mol-1 for the open symbols. The adhesive strength, G, has been measured by peel tests performed at a very low velocity of the propagation of fracture, 0.17 im/s. The molecular weight of the surface anchored chains is Mw=242 kg mol-1...

Such behavior has been interpreted in terms of a molecular model proposed by Brochard-Wyart and de Gennes [143] and further refined [145,146]. The first version of these models considers a solid surface bearing a few end grafted polymer chains, with a surface density, G, below the onset of the mushroom regime gAT<1, with N the polymerization index of the anchored chains). The melt chains have a polymerization index P. Both N and P are assumed to be much larger than Ne, the average number of monomers needed to form an entanglement. Thus the... 

When the slip velocity is further increased, the Rouse friction [148] finally becomes dominant, for Vs>V ocN l. A linear friction regime is then recovered, with a constant extrapolation length, b much larger than b0 and comparable to what would be observed on an ideal surface without anchored chains [139]. 

Besides the essential possibility of controlling the surface friction by changing the surface density of anchored chains all other parameters being kept constant, the value of V (Eq. 26) can also be adjusted by changing the molecular weight of the anchored chains [150,152,154]. 

These surface-anchored layers can be used as adhesion promoters to enhance elastomer-solid adhesive strength. We have shown that there is then an optimum surface density of surface anchored chains to do so. At high coverage of the surface, the layers lose their efficiency, a tendency which can be rationalized in terms of interdigitation between the elastomer and the surface chains. A full characterization of the different regimes of adhesion enhancement associated with the different regimes of interdigitation between the surface chains and the elastomer is a difficult experimental task, not fully accomplished to date. 

An important question is now to understand how these two effects, adhesion enhancement and adjusted friction, can interplay. For example, when peel tests are used to estimate the adhesive strength, the curvature of the peeled ribbon implies a fracture advancing through both modes I and II of opening [72,155]. This means that in the presence of surface anchored chains, the connector... 

The distribution of products of a FTS of hydrocarbons can be derived in the following way [12-14]. Let us call a fraction of products with i carbon atoms < )j. Now, if a product with nC appears in the gas phase, its fraction, is a measure of termination of the anchored chain growth (by addition of CH units) at the nC-containing hydrocarbon. At the same time, all products with i > n taken together, are the measure of propagation of the growth. If the probability of growth is a and that of termination is (1 - a ). 

Fig. 26. Conformation of terminally anchored chains (a) Isolated coils at low coverages (de Gennes, 1980) (b) high stretched chains at high coverages (Milner et al., 1988). The distance between graph points scales as...

Fig. 27. Effect of solvent quality and graft density on layer thickness for terminally anchored chains from Eq. (112).

Comparison of these potentials with those for the terminally anchored chains shows the interaction to be relatively weak. For example, experiments with polystyrene in cyclohexane, which does not adsorb on mica, yielded no detectable forces between mica surfaces because of the polymer (Luckham and Klein, 1985). Indeed, estimates of the potential from Eq. (130) at the experimental conditions fall several orders of magnitude below the detection limit for the instrument. 

Fig. 32. E>elineation of regimes for interaction between free polymer at bulk concentration /3pb and terminally anchored chains of graft density l2a for n = 5000, p = 500, and v/l3 = 1 (Gast and Leibler, 1986) 1, Negligible interpenetration and layer thickness unaffected by free polymer 11, slight interpenetration, but layer significantly compressed by free polymer III, complete interpenetration and relaxed layer.

The two primary features of the phenomena are the layer thickness necessary to provide stability and the conditions at which the dispersions flocculate. The first can be quantified by generalizing the potential for terminally anchored chains to interactions between spheres via the Deijaguin approximation, adding the attractive dispersion potential, and then assessing the layer thickness necessary to maintain —fl>mi /fcT < 1 — 2. To illustrate this, consider the small overlap limit of Eq. (122), which transforms into... 

Results for surfaces with a low density of surface anchored chains ... 

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