Spherical polyelectrolyte

Muller M, Reihs T, Ouyang W (2005) Needlelike and spherical polyelectrolyte complex nanoparticles of poly(L-lysine) and copolymers of maleic acid. Langmuir 21 465 -69... 

Phenylation of styrene, acrylic esters, and acrylamide with Ph3Bi(02CCF3)2 was examined using palladium nanoparticles immobilized in spherical polyelectrolyte brushes (Pd SPB) (Scheme 7) [21], The reaction can be conducted under air, and... 

Ballauff M (2007) Spherical polyelectrolyte brushes. Progr Polym Sd 32 1135-1151... 

Fig. 2 TEM-image of spherical polyelectrolyte block copolymer micelles (PB-P2VP.MeI). The pronounced contrast of the polyelectrolyte shell is due to the counterions (I-) [19]...

Wittemann A, Haupt B, Ballauff M (2003) Adsorption of proteins on spherical polyelectrolyte brushes in aqueous solution. Phys Chem Chem Phys 5 1671-1677... 

Mei Y, Lu Y, Polzer F, Ballauff M, Drechsler M (2007) Catalytic activity of palladium nanoparticles encapsulated in spherical polyelectrolyte brushes and core-shell microgels. Chem Mater 19 1062-1069... 

Sharma G, Mei Y, Lu Y, Ballauff M, Irrgang T, Proch S, Kempe R (2007) Spherical polyelectrolyte brushes as carriers for platinum nanoparticles in heterogeneous hydrogenation reactions. J Catal 246 10-14... 

Schrinner M, Polzer F, Mei Y, Lu Y, Haupt B, Ballauff M, Goldel A, Drechsler M, Preussner J, Glatzel U (2007) Mechanism of the formation of amorphous gold nanoparticles within spherical polyelectrolyte brushes. Macromol Chem Phys 208 1542-1547... 

Schrinner M, Proch S, Mei Y, Kempe R, Miyajima N, Ballauff M (2008) Spherical polyelectrolyte brushes synthesis, characterization and application for the oxidation of alcohols. Adv Mater 20 1928-1933... 

Mei Y, Sharma G, Lu Y, Drechsler M, Ballauff M, Irrgang T, Kempe R (2005) High catalytic activity of platinum nanoparticles immobilized on spherical polyelectrolyte brushes. Langmuir 21 12229-12234... 

Lu Y, Wittemann A, Ballauff M (2009) Supramolecular structures generated by spherical polyelectrolyte brushes and their application in catalysis. Macromol Rapid Commun 30 806-815... 

When fl = 0, in particular, the polyelectrolyte-coated particle becomes a spherical polyelectrolyte with no particle core. In this case, Eq. (6.171) tends to... 

Figure 6.8 shows as a function of the ratio dia of the polyelectrolyte layer thickness d to the core radius a for two values of Q (5 and 50) at = 10 . Note that as dIa tends to zero, the polyelectrolyte-coated particle becomes a hard sphere with no polyelectrolyte layer, while as dia tends to inhnity, the particle becomes a spherical polyelectrolyte with no particle core. Approximate results calculated with Eq. (6.155) for Q = 5 (low charge case) and Eq. (6.168) for Q = 50 (high charge case) are also shown in Fig. 6.8. Agreement between exact and approximate results is good. For the low charge case, the surface potential is essentially independent of d and is determined only by the charge amount Q. In the example given in Fig. 6.8, for the high charge case, the particle behaves like a hard particle with no polyelectrolyte layer for dia 10 and the particle behaves like a spherical polyelectrolyte for dia 1.

In this chapter, we give approximate analytic expressions for the force and potential energy of the electrical double-layer interaction two soft particles. As shown in Fig. 15.1, a spherical soft particle becomes a hard sphere without surface structures, while a soft particle tends to a spherical polyelectrolyte when the particle core is absent. Expressions for the interaction force and energy between two soft particles thus cover various limiting cases that include hard particle/hard particle interaction, soft particle/hard particle interaction, soft particle/porous particle interaction, and porous particle/porous particle interaction. 

Note that the following exact expression for the electrostatic interaction between two porous spheres (spherical polyelectrolytes) for the low charge density case has been derived [5,6] (Eq. (13.46)) ... 

If we further take the limit Kd 1 in Eq. (15.61), then we obtain the electrostatic interaction energy for the case where sphere 1 is a spherical polyelectrolyte and sphere 2 is a hard sphere, namely. 

We derive an approximate expression for the electrophoretic mobility of spherical polyelectrolytes for the case of low potentials. In this case, the equilibrium potential i/ ° (r) is given by... 

This is the required expression for the mobility of spherical polyelectrolytes in concentrated suspension for low potentials. 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

That is, in this limit the conductivity equals that in the absence of the particles so that spherical polyelectrolytes do not contribute to the conductivity. 

In the limit a 0, we have that 0 and soft particles become spherical polyelectrolytes. In this limit, Eq. (24.37) tends to... 

In this section, we treat the practically important case where potential is not very high so that dynamic relaxation effect is negligible. In this case, we have <5pei(T) = 0 or 5rij(r) = 0. Consider first the case where potential is low and a —> 0 and where Pflx = constant, which corresponds a uniformly charged spherical polyelectrolyte of radius b. 

We thus obtain the following expression for the dynamic mobility of a spherical polyelectrolyte ... 

We shall consider in this section a rigid spherical polyelectrolyte. According to the Debye-Huckel theory, the potential of average force between the polyelectrolytes may be approximated as follows ... 

Grohn, F., and Antonietti, M. Intermolecular structure of spherical polyelectrolyte mi-crogels in salt-free solution. 1. quantification of the attraction between equally charged polyelectrolytes. Macromolecules, 2000,33, No. 16, p. 5938-5949. 

Wall, T.F., and Berkowitz, J. Numerical solution to the Poisson - Boltzmann equation for spherical polyelectrolyte molecules. Journal of Chemical Physics, 1957, 26, p. 114-122. 

These problems have been solved for the rod-like polyelectrolytes under consideration here [19] and for spherical polyelectrolytes [23], For details of the procedures the reader is referred to these original papers. 

Fig. 14 Schematic representation of a spherical polyelectrolyte brush prepared by the photoemulsion grafting from technique (details see text). The brush consists of a solid polystyrene core and surface-attached strong (PSS) or weak (PAA) polyelectrolyte brush shell (Reprinted from Ref. [71] with permission from the American Physical Society)...

Antonietti M. Structure and viscosity of spherical polyelectrolyte microgels a model for the polyelectrolyte effect Polymer and Colloid NATO ASI, Les Houches, Sept 14-24, 1999. 

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