End-grafted chains

The first case concerns particles with polymer chains attached to their surfaces. This can be done using chemically (end-)grafted chains, as is often done in the study of model colloids. Alternatively, a block copolymer can be used, of which one of the blocks (the anchor group) adsorbs strongly to the particles. The polymer chains may vary from short alkane chains to high molecular weight polymers (see also section C2.6.2). The interactions between such... 

K. O Connor, T. McLeish. Entangled dynamics of heahng end-grafted chains at sohd/polymer interface. Faraday Discuss Chem Sci 95 67-78, 1994. 

With respect to SCF models that focus on the tail properties only (typically densely packed layers of end-grafted chains), the molecularly realistic SCF model exemplified in this review needs many interaction parameters. These parameters are necessary to obtain colloid-chemically stable free-floating bilayers. A historical note of interest is that it was only after the first SCF results [92] showed that it was not necessary to graft the lipid tails to a plane, that MD simulations with head-and-tail properties were performed. In the early MD simulations (i.e. before 1983) the chains were grafted (by a spring) to a plane it was believed that without the grafting constraints the molecules would diffuse away and the membrane would disintegrate. Of course, the MD simulations that include the full head-and-tails problem feature many more interactions than the early ones. 

We emphasize at the outset that this article deals with flexible linear chains only, neither branched polymers [54,159] nor the packing of stiff chains near surfaces [52,53] will find much attention. However, we also shall not cover films formed by end-grafted chains ( polymer brushes [160-172]), although in brushes formed from two different types of chains A,B interesting phase separation behavior can occur [165,166] that is related to the phase separation in non-grafted films as treated here. Also films formed from strictly two-dimensional chains in a plane [173-175] are outside of our attention.,... 

Over the last 10 years there have been a large number of experimental, theoretical and numerical simulations on the properties of polymer brushes. The static properties of polymer brushes are now very well understood and have been reviewed extensively elsewhere [26-29]. In this article I will concentrate on more recent results for polymer brushes in a shear flow. Accordingly, the next section on the static properties will be brief. In Section III, the hydrodynamic penetration depth for the solvent into the brush will be discussed for shear flow past the brush and for two surfaces approaching each other. In Section IV, the normal and shear forces between two surfaces bearing end-grafted chains will be discussed. Two processes, interpenetration and compression, are found to occur concurrently. The origin of the reduced friction observed in recent SFA ex-... 

Fig. 4. Penetration of the velocity field (solid line) in a simple shear flow adjacent to a surface bearing end-grafted chains. The mer density p(z) is the dashed curve. The velocity profile v(z) outside the brush extrapolates to zero at the penetration depth (dotted curve), (a) Illustrates the parabolic brush and (b) the corresponding result for an Alexander-de Gennes brush. Here fi/ 0=30, where 0 is the correlation length at the grafting surface. From Milner [55].

Strictly speaking, the force between two surfaces each bearing end-grafted chains is not always the same as the force between two surfaces, one bare and the other bearing end-grafted chains, after one scales the distance D by ns. This is true only if the force between monomers on the chain is comparable to that between a monomer and the... 

Fig. 9. Concentration profiles determined by neutron reflectivity for three end grafted PDMS layers in contact with PDMS melts. The molecular weight of the grafted chains is mN= 92 kg mol-1 for all the layers. Curve a surface density in the layer o= 0.011, molecular weight of the melt mP=90 kg mol-1 curve b o=0.01, mP=360 kg mol-1 curve c o= 0.015, mP= 17 kg mol-1. The layer contracts more and more when exposed to a melt of larger molecular weight. In all cases the melt chains penetrate down to the surface, as demonstrated by the volume fraction of end grafted chains which always remains much lower than one...

Fig. 12. Schematic representation for an elastomer/solid interface strengthened by the addition of end-grafted chains...

The experimental data obtained at low surface densities, for end grafted chains, are in very good agreement with these theoretical predictions, not only for the overall evolution of the slip velocity vs the shear rate or of the slip length vs the slip velocity as shown in Fig. 19, but also for the molecular weight dependence of the critical velocity V which do follow exactly the laws implied by... 

Fig. 2. Schematic of connecting chains at an interface, a diblock copolymers, b end-grafted chains, c triblock copolymers, d multiply grafted chain, and e random copolymer...

These questions have been addressed mainly for the case where the connecting chains are diblock copolymers or end-grafted chains. In this case, each chain... 

Two examples are shown in Figs. 25 and 26, where Qc and Ojlhrij are plotted as a function of 2. In the first case we compare interfaces between an epoxy and either PS or high-impact PS, where both interfaces have been reinforced with the same deuterated end-grafted chain, while, in the second case, we compare interfaces between polyamide 6 (PA-6) and either polypropylene (PP) or a PP-based alloy with a PP matrix and 70% EPDM rubber particles, where both interfaces have been reinforced with the same type of grafted PP chains. Two observations can be made ... 

Fig. 32. Maximum achievable fracture toughness of interfaces between A and B polymers reinforced with block copolymers or end-grafted chains as a function of the degree of polymerization N of the reinforcing block. (A) PS-b-PMMA between PPO and PMMA ( ) dPS-COOH chains in a HIPS matrix grafted on an epoxy interface ( ) dPS-COOH chains in a PS matrix grafted at an epoxy interface (O) PS-b-PVP chains at the interface between PS and PVP. Data from [22,36,38,40]...

Fig. 50. Possible mechanism by which chains with multiple reactive sites can graft to an interface. This example, which would be typical of a maleic anhydride functionalized polymer reacting on a polyamide, shows on one side end-grafted chains and on the other side of the interface, a loop structure. The effect of this loop structure on the mechanical strength of the interface is not fully clear but loops that are too short will weaken the interface...

Figure 6.7. Segment density profiles for end-grafted chains in a good solvent calculated by Hirz using self-consistent mean-field theory, for four values of the grafting density o ( , 0.25 A, 0.12 o, 0.08 and A, 0.04). The solid lines are the parabolic profiles predicted by equation (6.1.15). After Milner et al. (1988).

Fig. 16 Physisorbed polymers with trains, loops and tails, and end-grafted chains at the sur ce.

The ATRP fabrication of polyacrylonitrile (PAN), poly (2-(dimethyl-amino)ethyl methacrylate), and polystyrene end-grafted chains on the inner walls of ordered mesoporous silica [31]... 

Figure 1.9 Thermal desorption of carboxydecyl chains, (a-b) Variation in the IR absorbance associated with the corresponding species (CO from acid groups, CO from anhydrides, and CH). Note the increased stability of the hydrocarbon skeleton as compared to decyl monolayers (dotted line in (b)). (c) Simulated desorption of the CHs, assuming that 80% of the chains undergo end-coupling, which leads to increased thermal stabiUty (the dashed lines indicate the simulated desorption curves for one-end and two-end grafted chains). Note the similarity with the experimental results in (b). Reprinted with permission from Ref. [168]. Copyright (2007) by American Chemical Society.

We report the investigation of the forces between smooth solid surfaces bearing end-grafted chains in good solvent conditions. The forces are raonotonically repulsive with a range about twice that for corresponding adsorbed chains. We observe no evidence of bridging attraction at low... 

---