Debye-Huckel screening

The hydrodynamic radius for each particle was taken to be 0.5 K. q = elementary charge unit. Solvent dielectric e = 80. A time step of 0.001 ps was used k = inverse Debye-Huckel screening length. 

As in the previous chapter on the Smoluchowski theory and its extensions, similar boundary and initial conditions may be used. The reaction of a species A with a vast excess of B (yet still sufficiently dilute to ensure that Debye- HUckel screening is unimportant) can be considered as one where the A species are statistically independent of each other and are surrounded by a sea of B species. An ionic reactant A has a rate of reaction with all the B reactants equal to the sum of the rates of reaction of individual A—B pairs. This rate for large initial separations of A and B is... 

In view of the role one may presume for simple electrolyte - namely, its effect on the Debye-Huckel screening length - a dependence of Ksec on 1-1/2 was anticipated (25). However, the ionic strength was adjusted not by eluant modification, but by varying sample concentration, so the failure of the data for NaPSS eluted in pure H2O to conform to the aforementioned linear dependence is difficult to interpret. 

Fig. 8 Radial monomer density distribution Iot the charge density al( 2neP ap l(ek Tr)) = 3 and the Debye-Huckel screening parameters Kfl = 0.1,0.5,0.8,1.0, and 1.1 (from left to right) [60]...

The second feature is the screening parameter k which appears in the linearized Equation 5.77 and in the solution, Equation 5.79. Its reciprocal Vk is the characteristic range of the screened potential and is sometimes termed the Debye-Huckel screening length. It is composed of the following constants ... 

The electrostatic image treatment of Wagner (1924) was improved by Onsager and Samaras (1934), taking account of Debye-Huckel screening effects (the K parameter) in the ion distribution resulting from repulsive image interactions. They derived the relation for the relative ion... 

This equation cannot actually apply to a polyelectrolyte, but can be used to estimate entropy changes. The two charged segments join together through electrostatic attraction if and only if these come within a distance (say a) less than the Debye-Huckel screening length. The volume (Vj) of closest approach will be Vj X An 13. This leads to Jacobson-Stockmayer equation written for the present system as [20]... 

This theoretical expression was obtained for a charged chain with a Gaussian statistics in a solution with monovalent salt [33]. The chain was assumed to be of infinite length and the electrostatic interactions were treated at a linear level with a Debye-Huckel screened interaction between charges due to the presence of monovalent salts. This treatment neglects non-linear effects connected to counterion condensation, as well as chain-end effects present in our simulations. 

---