Debye screening lengths salt concentration

Fig. 3.13. (Top) An electron micrograph of an artificial chromatin model composed of T4 DNA and cationic nanoparticles of diameter 15nm. (Bottom) Typical snapshots of a model DNA (semiflexible polyelectrolyte) complexed with cationic nanoparticles. At low salt concentration (Debye screening length m/a = 1), a beads-on-a-string nucleosome-like structure is observed (left), while locally segregated clusters are formed at higher salt concentrations (rn/a = 0.3) (right) (See [46] for more details)...

The effect of salt on the conformations of a many-arm (osmotic) PE star becomes important when the salt-controlled bulk Debye screening length, given by (33), becomes smaller than the intrinsic screening length, in a salt-free osmotic PE star. This is also true, equivalently, when the concentration of added salt exceeds the intramolecular concentration of counterions in the osmotic star. Clearly, the local electroneutrality in this case is ensured, and the LEA is applicable for analysis of the PE star conformations on a length scale larger than td. 

Thus, the size of the electrostatic blob and the numba of monomas per blob inaease with increasing salt concentration (deaeasing the value of the Debye screening length). 

Thus, in salt solutions, conformations of a polyelectrolyte chain are those of a self-avoiding chain with the excluded volume determined by the electrostatic repulsion between charged monomers. With deaeasing salt concentration, the chain size increases. It becomes comparable with the size of a polyelectrolyte chain in a salt-free solution (see eqn [10]) at salt concentration for which the value of the Debye screening length is equal to ro b up)... 

Fig. 5. Distribution of local concentrations c/cq and corresponding background functions B(t) for monovalent charged ionic spin probes in a dispersion of charged planar platelets in water (simulation based on the Poisson-Boltzmann equation). A concentration of 1.67 mM of a monovalent salt corresponding to a Debye screening length of 7.5 nm was assumed, (a) Local concentration as a function of distance r from the platelet surface for counterions with unlike charge (enrichment near the surface), (b) Dipolar evolution function for counterions with unlike charge (solid line) and fit of the data between t = 1 and 2 ps by an exponential decay (dashed line), (c) Local concentration as a function of distance r from the platelet surface for counterions with like charge (depletion near the surface), (d) Dipolar evolution function for counterions with like charge (solid line) and fit of the data between t = 1 and 2 ps by an exponential decay (dashed line).

Fig. 1 Debye screening length, A[), versus the molar concentration of salt, C, at different volume fractions ip and surface charge densities

At the level of the DH approximation, the interaction energy of segment-coimterion interactions and added salt-imi interactions does not appear explicitly in the formula and enters indirectly via the concentration dependence of the Debye screening length, = tp = where and are the concentrations... 

The dependence of first flash proton uptake on salt concentration is explained by a salt screening effect of the Qb semiquinone electric potential, leading to diminution of the pK shifts of amino acid residues located further from Qb than the Debye screening length in the RC protein. Suppression of the contribution of amino acid residues located far from Qb by the addition of high concentrations of salt reveals the contributions of those amino acid residues which are close to Qb. 

The Debye length decreases with increasing salt concentration. This is plausible, because the more ions are in solution, the more effective is the screening of surface charge. If we quantify all factors for water at 25°C, then for a monovalent salt, the Debye length is... 

Fig. 4.10. Sketch of adsorption of polydisperse particles at (a) low and (b) high salt concentrations. Dotted lines show the effective particle radius (or interaction distance), (c) Surface coverage of the polystyrene particles versus na ( a is a dimensionless screening parameter, where k is the inverse Debye length and a the particle diameter). The more polydisperse particles (41 versus 107nm) have a slightly increased coverage at high na. Solid curves are approximations derived from the effective hard sphere model (see [89] for further details)...

Erom the summary of the theoretical results presented above, it follows that the intramolecular volume of a star-branched PE, with a sufficiently large number of arms, is essentially electroneutral. That is, the bare charge of a star polymer is neutralized by mobile counterions. These counterions are predominantly retained inside the macroion volume, even if the star is immersed in a dilute salt-free solution. Moreover, if the intrinsic Debye length associated with the intramolecular concentration of entrapped counterions, = l paNis used as an upper estimate for the intramolecular electrostatic screening length, one finds that in the osmotic PE star, p a), the electrostatic interactions are screened at... 

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