Polyelectrolyte concentration potential

Morishima et al. [75, 76] have shown a remarkable effect of the polyelectrolyte surface potential on photoinduced ET in the laser photolysis of APh-x (8) and QPh-x (12) with viologens as electron acceptors. Decay profiles for the SPV (14) radical anion (SPV- ) generated by the photoinduced ET following a 347.1-nm laser excitation were monitored at 602 nm (Fig. 13) [75], For APh-9, the SPV- transient absorption persisted for several hundred microseconds after the laser pulse. The second-order rate constant (kb) for the back ET from SPV- to the oxidized Phen residue (Phen+) was estimated to be 8.7 x 107 M 1 s-1 for the APh-9-SPV system. For the monomer model system (AM(15)-SPV), on the other hand, kb was 2.8 x 109 M-1 s-1. This marked retardation of the back ET in the APh-9-SPV system is attributed to the electrostatic repulsion of SPV- by the electric field on the molecular surface of APh-9. The addition of NaCl decreases the electrostatic interaction. In fact, it increased the back ET rate. For example, at NaCl concentrations of 0.025 and 0.2 M, the value of kb increased to 2.5 x 108 and... 

The solution must be electrically neutral (unless a large external electrostatic potential gradient is applied). If the molar polyelectrolyte concentration is m, and the average valence is z, there must be mz counterions (of unit valence) in solution, for instance Na+ ions for a polyacid. 

Another consequence of the Donnan effect is that it is difficult, if not impossible, to calculate ionic strength and composition of a solution of polyelectrolytes and salts, especially if the polyelectrolyte concentration is high. One should try to separate a portion of the salt solution from the mixture, without applying a substantial chemical potential difference. This can be done, for instance, by ultrafiltration. The ultrafiltrate then contains, ideally, no polyelectrolyte, but all the salts. It can be chemically analyzed, and from the result the ionic composition can be calculated (Section 2.3.3). 

The BaS04 suspension was then titrated stepwise with polyelectrolyte and allowed to equilibrate for about 30 minutes after each addition. The zeta potential of the resulting suspension was then determined by Doppler electrophoretic light scattering analysis using a Coulter Electronics DELSA 440. BaS04 suspensions were titrated to a toti polyelectrolyte concentration of 100 mg polyelectrolyte/m BaS04. 

An early theoretical depletion interaction study with polyelectrolytes as depleting agents was made by Bohmer et al. [78] who used the self-consistent field method of Scheutjens and Heer. For high salt concentrations, the polymer concentration dependence of the depletion layer thickness matches with that of an uncharged polymer in solution. Below a salt concentration of 1 mol/L the depletion layer thickness starts to decrease with increasing polyelectrolyte concentration at lower polymer concentration. At low salt concentrations a significant repulsive barrier in the potential between two uncharged parallel flat plates was found. 

At the certain concentration the ( -potential levels off and the polyelectrolyte is mostly adsorbed on the particles depleting the bulk from the majority of polyelectrolyte molecules. The further increasing of bulk polyelectrolyte concentration does not influence on i -potential and amount of polyelectrolyte on the particles. Thus, the layer-by-layer assembling of the polyelectrolytes onto colloidal particles can be performed in two different ways [28-30]. Either the concentration of polyelectrolyte added at each step is just sufficient to form a saturated layer or adsorption is curried on at excess of polyelectrolyte concentration. (Fig. 2.3). 

For low-polyelectrolyte concentrations, R 00 and Eqs. [304] and [305] give the standard bulk Debye-Hiickel solution for the potential near an ion of radius a... 

The interactions between bare mica surfaces in 10 and 10 M KNO solutions were determined at pH = 3.5. In both cases an exponential type relation F(D) = 0-lcD was indicated, with decay lengths 1/k = 1.4 nm and 8 nm for the two salt concentrations, respectively, but with an effective surface potential tp = 40 mV, considerably lower than its value at the higher pH used in the PEO experiments (figure 6a, curve (a)). The lower value of p is probably the result of a lower net degre of ionization of the mica surface in the presence of the large H1" concentration (the low pH was used to ensure full ionization and polyelectrolyte). 

Since the polyelectrolytes contain only one type of mobile ion, the interpretation of conductivity data is greatly simplified. Polyelectrolytes have significant advantages for applications in electrochemical devices such as batteries. Unlike polymer-salt complexes, polyelectrolytes are not susceptible to the build up of a potentially resistive layer of high or low salt concentration at electrolyte-electrolyte interfaces during charging and discharging. Unfortunately flexible polyelectrolyte films suitable for use in devices have not yet been prepared. 

A polyelectrolyte solution contains the salt of a polyion, a polymer comprised of repeating ionized units. In dilute solutions, a substantial fraction of sodium ions are bound to polyacrylate at concentrations where sodium acetate exhibits only dissoci-atedions. Thus counterion binding plays a central role in polyelectrolyte solutions [1], Close approach of counterions to polyions results in mutual perturbation of the hydration layers and the description of the electrical potential around polyions is different to both the Debye-Huckel treatment for soluble ions and the Gouy-Chapman model for a surface charge distribution, with Manning condensation of ions around the polyelectrolyte. 

Thin-film ideal or Nemstian behavior is the starting point to explain the voltammetric behavior of polyelectrolyte-modified electrodes. This condition is fulfilled when (i) the timescale of the experiment is slower than the characteristic timescale for charge transport (fjD pp, with Ithe film thickness) in the film, that is all redox within the film are in electrochemical equibbrium at any time, (ii) the activity of redox sites is equal to their concentration and (iii) all couples have the same redox potential. For these conditions, anodic and cathodic current-potential waves are mirror images (zero peak splitting) and current is proportional to the scan rate [121]. Under this regime, there exists an analytical expression for the current-potential curve ... 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

A related phenomenon occurs when the membrane in the above-mentioned experiment is permeable to the solvent and small ions but not to a macroion such as a polyelectrolyte or charged colloidal particles that may be present in a solution. The polyelectrolyte, prevented from moving to the other side, perturbs the concentration distributions of the small ions and gives rise to an ionic equilibrium (with attendant potential differences) that is different from what we would expect in the absence of the polyelectrolyte. The resulting equilibrium is known as the Donnan equilibrium (or, the Gibbs-Donnan equilibrium) and plays an important role in... 

Figure 3.1a shows a membrane that is permeable to water and K+ and Cl - ions but impermeable to colloidal electrolytes (polyelectrolytes such as charged proteins). Let a denote the interior of the cell and (3 the extracellular region. In the absence of the poly electrolyte, water, K + and Cl" partition themselves into the two sides such that the chemical potentials of each species are the same inside as well as outside, as thermodynamics would demand. Moreover, the requirement of electroneutrality in both ot and (3 demands that the concentrations of each species K + and CP be the same on either side of the partition. 

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