Smeared charge distribution

However, these studies predicted larger polyion sizes and smaller electrostatic potentials than experimentally measured [85]. These discrepancies primarily arise from the assumption of smeared charge distributions in the polyion domain, whereas the potential around the polyion actually varies strongly with distance from the polyion. 

For the sake of discussion, let us consider the smeared charge distribution so that Eq. (6.76) can be written as... 

In Eq. (6.86), the Q s are the partition functions of individual components in the presence of a field. Explicitly, for the polyelectrolyte chain with smeared charge distribution along the backbone, single chain partition function is given by... 

Thermodynamic properties of polyelectrolyte solutions are mostly determined by ionic distribution around the polyion skeleton. To explain thermodynamic properties, therefore, the rod-like model may be effective. It is assumed that the polyion is a rod of infinite length and has smeared charges distributed uniformly over the surfaces of the rod. That is, a real polyion chain consists of a series of discrete charges and each charge is surrounded by its own ionic atmosphere. If the radius of ionic atmosphere is... 

Wave-like properties cause electrons to be smeared out rather than localized at an exact position. This smeared-out distribution can be described using the notion of electron density Where electrons are most likely to be found, there is high electron density. Low electron density correlates with regions where electrons are least likely to be found. Each electron, rather than being a point charge, is a three-dimensional particle-wave that is distributed over space in... 

If <72 is smeared out into a continuous charge distribution over volume v2 at charge density p2 and at an average distance r 2 from qi, then... 

Figure 2.1 Charge distribution and surface dipole at a metal surface. For simplicity the positive charge residing on the metal ions has been smeared out...

In a simple model for sp metals known as jellium the ionic charge is smeared out into a constant positive background charge (see also Fig. 1.2). If the metal occupies the region —oo < z < 0, the positive charge distribution is given by ... 

We have also to say a few words about a smeared out analogue utilized in our consideration to represent the surface charge distribution. There was an indication in the literature that the image interaction within this adsorption layer may influence the interaction on a macroscopic scale, i.e., which is being commensurate with the range of colloidal forces [29]. However, later results... 

One typical consequence is that we refrain from considering smeared out distributions, as In the Polsson-Boltzmann model. Another implication is that image charges have to be taken into account. 

The radius of charge distribution of the hydrated electron has been estimated by several methods. The values obtained from hydration energies, encounter radius, i.e. the radius required to account for experimental diffusion controlled rate coefficients, and Jortner s cavity-continuum model are all in the range 0.25—0.30 nm [33]. This clearly indicates that the electron is not associated with a single water molecule only, but rather that the charge of the electron is smeared out over 3—4 water molecules. 

Equation (14.79) has a simple physical interpretation. Let us imagine the electrons smeared out into a charge distribution whose density is —ep(x, y, z). The force on nucleus 8 exerted by the infinitesimal element of electronic charge —ep dx dy dz is [Eq.(6.56)]... 

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