Polyelectrolytes coupling

The tilt angle derived from a detailed analysis of the peaks as a function of pressure is given in Fig. 11. In the absence of polymer one observes the reduction of t to zero whereas for PDADMAC t>25° even at the highest pressure. For comparison we also include the tilt angle measured for PAH in the subphase. The binding of this cationic polyelectrolyte apparently has only a minor influence on monolayer structure. The polyelectrolyte coupling may be best understood looking at the model of Fig. 12 which should hold specif-... 

X (q) is the q-dependent polyelectrolyte coupling constant discussed earlier in this section (Eq. 2.18). 

Water-soluble polymers and polyelectrolytes (e.g., polyethylene glycol, polyethylene imine polyacrylic acid) have been used success-hilly in protein precipitations, and there has been some success in affinity precipitations wherein appropriate ligands attached to polymers can couple with the target proteins to enhance their aggregation. Protein precipitation can also be achieved using pH adjustment, since proteins generally exhibit their lowest solubility at their isoelectric point. Temperature variations at constant salt concentration allow for frac tional precipitation of proteins. 

In the following paper, the possibility of equilibration of the primarily adsorbed portions of polymer was analyzed [20]. The surface coupling constant (k0) was introduced to characterize the polymer-surface interaction. The constant k0 includes an electrostatic interaction term, thus being k0 > 1 for polyelectrolytes and k0 1 for neutral polymers. It was found that, theoretically, the adsorption characteristics do not depend on the equilibration processes for k0 > 1. In contrast, for neutral polymers (k0 < 1), the difference between the equilibrium and non-equilibrium modes could be considerable. As more polymer is adsorbed, excluded-volume effects will swell out the loops of the adsorbate, so that the mutual reorientation of the polymer chains occurs. 

The Dependencies of Radius of Gyration Rg, Static Correlation Length Hydrodynamic Screening Length Viscosity r, Self-Translational Diffusion Coefficient D, Cooperative Diffusion Coefficient Dc, Coupled Diffusion Coefficient Df, and Electrophoretic Mobility p on c and N for Various Regimes of Polyelectrolyte and Salt Concentrations... 

Therefore, remarkably, the coupled diffusion coefficient becomes independent of N and c in the Rouse regime of salt-free polyelectrolyte solutions. This is to be... 

But p decreases with salt concentration with an apparent exponent of k which changes from 0 at low salt concentration to — at high salt concentrations. The N-independence of p arises from a cancellation between hydrodynamic interaction and electrostatic coupling between the polyelectrolyte and other ions in the solution. It is to be noted that the self-translational diffusion coefficient D is proportional to as in the Zimm model with full... 

We have identified three diffusion coefficients. These are the self-translational diffusion coefficient D, cooperative diffusion coefficient Dc, and the coupled diffussion coefficient fly. fl is the cooperative diffusion coefficient in the absence of any electrostatic coupling between polyelectrolyte and other ions in the system, fly is the cooperative diffusion coefficient accounting for the coupling between various ions. For neutral polymers, fly and Dc are identical. Furthermore, we identify fly as the fast diffusion coefficient as measured in dynamic light scattering experiments. The fourth diffusion coefficient is the slow diffusion coefficient fl discussed in the Introduction. A satisfactory theory of flj is not yet available. 

By accounting for the coupling between the dynamics of polyelectrolyte chains and their counterions and salt ions and assuming that small ions relax faster than polyelectrolyte chains, we have derived Df to be... 

Although the coupling of counterion dynamics and polyelectrolyte dynamics has been accounted for at the mean field level, the relaxation of counterion cloud needs to be included in comparing with experimental data. 

As discussed extensively in this chapter, most of the surprising properties of polyelectrolyte dynamics are due to the coupling of counterion dynamics with polymer dynamics. But, there is no adequate understanding of how much of the counterions are mobile and how much are effectively condensed on polymer chain backbone. Theoretical attempts [77, 78] on counterion condensation need to be extended to concentrated poly electrolyte solutions. 

Although the majority of chiral CEC—MS applications still involve packed columns, few reports on chiral OT-CEC-MS are found in recent literature. The feasibility of coupling OT-CEC (using a short Chirasil-Dex-coated capillary column) to MS and MS/MS for trace analysis of hexobarbital enantiomers in biological fluids was reported by Schurig and Mayer. More recently, Kamande et al. investigated polyelectrolyte multilayer (PEM) coating as a new medium for the separation of chiral analytes, and PEM-coated capillaries were successfully coupled to ESI/MS for the stereoselective analysis of five /1-blockers. 

Coulombic, van der Waals, entropic and osmotic forces are coupled in a nontrivial way and give rise to important charge regulation in polyelectrolyte systems. The salt concentration is also an important factor to define the structure and thermodynamic properties of polyelectrolyte solutions. In weak polyelectrolytes the ionization equilibrium is also coupled to these interactions and thus the pKof ionizable groups depends on the organization of the interface and differs from that for the isolated molecule. 

The third approach has been to graft the redox couple by means of a covalent bond to the polyelectrolyte backbond as described early in 1965 in the book of Cassidy and Run [20]. Several of these systems are charged polymers in at least one oxidation state, like poly(viologen), poly(vinylferrocene), and so on. Examples of polyelectrolytes like polyacrylic acid with covalently bound viologen were reported by Fernandez, Katz and coworkers [21], hydroquinone [22] and Anson et al. with bound ferrocene [23]. 

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 ... 

Due to the presence of interactions, the apparent redox potential of a redox couple inside a polyelectrolyte film can differ from that of the isolated redox couple in solution (i.e. the standard formal redox potential) [121]. In other words, the free energy required to oxidize a mole of redox sites in the film differs from that needed in solution. One particular case is when these interations have an origin in the presence of immobile electrostatically charged groups in the polymer phase. Under such conditions, there is a potential difference between this phase and the solution (reference electrode in the electrolyte), knovm as the Donnan or membrane potential that contributes to the apparent potential of the redox couple. The presence of the Donnan potential in redox polyelectrolyte systems was demonstrated for the first time by Anson [24, 122]. Considering only this contribution to peak position, we can vwite ... 

When the characteristic time for charge diffusion is lower than the experiment timescale, not all the redox sites in the film can be oxidized/reduced. From experiments performed under these conditions, an apparent diffusion coefficient for charge propagation, 13app> can be obtained. In early work choroamperometry and chronocoulometry were used to measure D pp for both electrostatically [131,225] and covalently bound ]132,133] redox couples. Laviron showed that similar information can be obtained from cyclic voltammetry experiments by recording the peak potential and current as a function of the potential scan rate [134, 135]. Electrochemical impedance spectroscopy (EIS) has also been employed to probe charge transport in polymer and polyelectrolyte-modified electrodes [71, 73,131,136-138]. The methods... 

From a theoretical point of view, charge propagation in films containing space-distributed redox centers can be achieved either by the physical displacement of the sites or by the transference (hopping) of electrons from neighboring reduced to oxidized sites or by the combination of both processes. In the case of free diffusing couples immobilized in oppositely charged polyelectrolytes, both processes occur and an apparent diffusion coefficient can be defined and measured [136, 142, 143] ... 

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