Macroions, electrostatic

Again, in contrast to radical polymerization, there is no chain termination by combination, since the growing chains (macroions) repel each other electrostatically because of their like charges. Chain termination occurs only by reaction of... 

The cell model is a commonly used way of reducing the complicated many-body problem of a polyelectrolyte solution to an effective one-particle theory [24-30]. The idea depicted in Fig. 1 is to partition the solution into subvolumes, each containing only a single macroion together with its counterions. Since each sub-volume is electrically neutral, the electric field will on average vanish on the cell surface. By virtue of this construction different sub-volumes are electrostatically decoupled to a first approximation. Hence, the partition function is factorized and the problem is reduced to a singleparticle problem, namely the treatment of one sub-volume, called cell . Its shape should reflect the symmetry of the polyelectrolyte. Reviews of the basic concepts can be found in [24-26]. 

As already indicated in Sect. 2, the osmotic coefficient 0 provides a sensitive test for the various models describing the electrostatic interaction of the counterions with the rod-like macroion. It is therefore interesting to first compare the PB theory to simulations of the RPM cell model [26, 29] in order to gain a qualitative understanding of the possible failures of the PB theory. In a second step we compare the first experimental values 0 obtained on polyelectrolyte PPP-1 [58] quantitatively to PB theory and simulations [59]. 

An important effect not taken into account by the various models discussed in Sect. 2 is the specific interactions of the counterions with the macroion. It is well-known that counterions may even be complexated by macroions and these effects have been discussed abundantly in the early literature in the field [24]. From the above discussion it now becomes clear that these effects must be traced back to specific effects which are not related to the electrostatic interaction of counterions and macroions. Hence, hydrophobic interactions related to subtle changes in the hydratation shell of the counterions could be responsible for this small but significant discrepancy of the electrostatic theory and experiment. Further studies using the PPP-polyelectrolytes will serve for a quantitative understanding of these effects which are outside of the scope of the present review. 

Mechanical work done on the macroionic phase is stored as electrostatic energy in that phase. So, in the system under consideration, the Gibbs, Helmholtz and electrostatic energies are related by... 

Hribar, B., and Vlachy, V. Evidence of electrostatic attraction between equally charged macroions induced by divalent counterions. Journal of Physical chemistry B, 1997, 101, No. 18, p. 3457-3459. 

However, if a sufficiently high number of charges per unit length are affixed to a polymeric chain, a highly charged macroion results [2, 3], As a consequence of this, the electrostatic energy of a counterion near to such a... 

Figure 3a shows separately the electrostatic (DLVO-like) and excluded volume contributions to the effective interaction potential between two macroions, W (r). The electrostatic contribution is all the way repulsive and decays mono-... 

For low surfactant concentration case, the difference in the him thickness between the hlms containing three and two micellar layers is about 15.8 nm. The experimentally observed height of the step-wise thickness transition is about 15.3 nm. For high surfactant concentration, the difference in the him thickness for the hlms with three and two micellar layers is about 8.6 nm (see Table 2) while the experimentally observed height of the step-wise thickness transition is about 10.1 nm. The increased deviation between simulation predicted hlm-thickness difference and the measured value of the step-wise thickness transition at a high surfactant concentration is probably due to the fact that our present modelling does not account for the contributions of the finite size of the small electrolyte ions as well as the solvent molecules to the electrostatic part of an effective interaction W(r) between the pair of micellar macroions. Our present model accounts for the contributions of the finite size of the electrolyte ions and the solvent molecules to the excluded volume interaction only. 

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