Free energy total-interaction, electrostatic

Ve = electrostatic free energy of interaction Vw = VDW free energy of interaction VT = total or sum of Ve and Vw free energies v = vesicle volume a = vesicle radius... 

Let AAioc, Aeiec(O), Aeiec(J,nc) denote the free energy associated with moving a counterion to the binding site under standard conditions, the free energy due to electrostatic interactions of the bare polyion, and the free energy of the polyion in the complex Dj(nc), respectively [55], Making use of Eqs. (52)-(54), one can express the total concentration of the complexes mD as [55]... 

Once the system of eqs 3 and 4 is solved under the boundary conditions (7a—d), the total free energy of the system can be calculated by adding the van der Waals interactions between the surfaces to the double layer free energy composed of electrostatic, entropic, and chemical contributions,11 and the stability ratio can be calculated in the usual manner.18... 

Figure 3.12 Typical forms of the total-interaction free energy for (a) electrostatically stabilised systems [curves (i), (ii), and (iii) refer to increasing electrolyte concentration], (b) sterically stabilised systems [curves (i), (ii), and (iii) refer to constant density of polymer chains, but decreasing <5, arising from decreasing values of a].

Figure 24 Total free energy of interaction between solid colloidal panicles inmersed in solution, obtained as a sum of three contributions electrostatic (EL), Lifshitz-van der Waals (LW). and acid-base (AB), following the extended DLVO model, (a) Spherical hydrophilic panicles of radius 2(X) run in 10 M solution of ttidlfferent I. I clcclruiyle and neutral pH potential 22 mV Hamaker constant A 10" J and AC(H ) = 5,. 4 mJ/m (b) Identical hydrophobic particles but in this case AG(ffu) = -.10 mJ/m ...

Ignoring the contribution of the steric stabilization effect at this point, the total Gibbs free energy of interactions between an isolated pair of particles (AG) can be expressed as the sum of the Gibbs free energy of the van der Waals interaction [Eq. (2.9)] and the Gibbs free energy of the electrostatic interaction [e.g., Eq. (2.21)]. 

Biopolymers are, of course, poly electrolytes. This means that electrostatic repulsion between them, as well as the contribution of counterions to the total free energy of the system, are to be included amongst the key factors affecting the character of the biopolymer interactions, and hence the stability of mixed biopolymer solutions with respect to phase separation (Antipova and Semenova, 1997 Grinberg and Tolstoguzov, 1997 Polyakov et al., 1997 Semenova, 1996 Wassennan et al., 1997). For... 

The total free energy of the system is composed of several contributions an electrostatic energy due to the distribution of charges, an energy due to the additional interactions of ions (not included in the mean potential), an entropic term due to the mobile ions, and a chemical free energy which is responsible for the formation of the double layer. 

Consequently, the total electrostatic free energy per unit area (accounting for all the interactions between charges and dipoles) is provided by the expression... 

In summary, the polarization model represents an extended Poisson-Boltzmann approach, in which the hydration and the double layer are not independent interactions, but are intimately coupled to each other, via an electrostatic coupling between the fields ip(z) and m(z). These fields can be calculated by solving Eqs. (2) (3) and (4), and the total free energy of the (5b) system can be obtained by summing up the terms provided by... 

The equilibrium state is determined by a minimization of the free energy. The total interaction in colloidal systems is mainly determined by electrostatic interactions and can be divided in three components. The first component occurs at interactions between net charged molecules or molecules with asymmetric charged distribution. These charge distributions can often be described by multipole expansions, i.e., a combination of monopole, dipole, quadrupole, etc., and is a fruitful approach if each multipole expansion can be described by one or two terms. The interaction is given by the sum of interactions between the terms, where the first contribution is the interaction between ions and is given by Coulomb s law and is the main contribution in systems with... 

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