Grafting distance

Fig. 11 Experimentally determined grafting distance b as function of degree of polymerization of insoluble block for polyelectrolyte block copolymer micelles at different salt concentrations salt free, o 0.3mol/l, 1 mol/1. Reprinted with permission from [15]. Copyright (2004) Springer... 

Important parameters that control the size of micelles are the degree of polymerization of the polymer blocks, NA and NB, and the Flory-Huggins interaction parameter %. The micellar structure is characterized by the core radius Rc, the overall radius Rm, and the distance b between adjacent blocks at the core/shell-interface as shown in Fig. 1. b is often called grafting distance for comparisons to polymer brush models, b2 is the area per chain which compares to the area per head group in case of surfactant micelles. In the case of spherical micelles, the core radius Rc and the area per chain b2 are directly related to the number of polymers per micelles, i.e., the aggregation number Z=4nR2clb2. 

Fig. 4 Experimentally determined grafting distance b as a function of the degree of polymerization of the insoluble block for polyelectrolyte block copolymers at different salt concentrations [49] ( ) salt free, (O) 0.3 mol/l, ( ) 1 mol/1...

From the measured core radii the grafting distance b can be calculated. Its variation as a function of added salt concentration is shown in Fig. 6 a. In the osmotic brush regime at low added salt concentrations the grafting distances are practically constant. At concentrations above c s 0.05 mol/1 ( salted brush ) the grafting distances decrease with increasing salt due to screening of the repulsive interactions between the corona chains [49]. 

Fig. 6 Experimentally determined grafting distance b (a) and shell thickness D (b) as a function of NaCl-concentration for PEE-PSSH. Different behavior at low salt ( osmotic brush ) and high salt concentration ( salted brush ) can well be distinguished [49]...

The average distance, d, between PEG surface grafting sites determined from the optically measured adsorbed mass (200 100 ng/cm ) is = 1.4 0.4 nm. Because this optically determined 4i is clearly smaller than the random coil size, Ir-p = 6.8 nm, we conclude that the chains are extended with respect to their Gaussian dimension. The length, L, of such a bmsh can be predicted qualitatively from this grafting distance and the known number of monomer units. Using the scaling relation proposed by Alexander (1977) we have ... 

Extensive experimental characterization has been carried out by many groups in order to determine how the characteristic dimensions of block copolymer micelles depended on the composition of the starting copolymers. TEM and SAXS were two of the mainly used methods for the determination of Rc and R - These results have been rationalized by Forster et ah, who found that, in the case of uncharged block copolymers, the grafting distance was depending on the soluble block length as with bo I nm and... 

Figure 1. Schematic cross sections in brushes immersed in good (a) and poor (b) solvents. In the good solvent case the blob size is set by the grafting distance. The solvent quality determines the blob size in a precipitant.

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