Distance between ions

Ion-pair formation (or the formation of triplets, etc.) is a very simple kind of interaction between ions of opposite charge. As the electrolyte concentration increases and the mean distance between ions decreases, electrostatic forces are no longer the only interaction forces. Aggregates within which the ions are held together by chemical forces have certain special features (i.e., shorter interatomic distances and a higher degree of desolvation than found in ion pairs) and can form a common solvation sheath instead of the individual sheaths. These aggregates are seen distinctly in spectra, and in a number of cases their concentrations can be measured spectroscopically. 

Taking the electrostatic energy to be —Ze2/d, where d (p / Amwf13 is the average distance between ions, and the Fermi energy from Eq. (5.43) with EP = p /2me, we have... 

The most important deficiency in the models developed so far concerns the failure to take account of interactions between the mobile ions. As the ionic concentration in polymer electrolytes is frequently greater than 1.0moldm and the mean distance between ions of the order of 0.5-0.7 nm, then relatively stong coulombic interactions exist which must affect ion motion. Ratner and Nitzan have begun to address this problem from a theoretical viewpoint (Ratner and Nitzan, 1989) although it has not been fully developed yet to give a complete description of conduction in ion associated polymer electrolytes. The interactions between ions which lead to ion association are discussed further in the following section. 

Ionic Transport, a. Conductivity The specific conductance of the SPS (Na+ form) membranes is shown in Fig. 8, whose data are summarized in Table II, including values of an apparent energy of activation. An exponential increase in ionic conductance together with a decrease in an apparent energy of activation may be related to a decrease in a "jump" distance between ion-exchange sites as a function of lEC. 

In addition to the Coulombic forces, there is a repulsive force which operates at short distances between ions as a result of the overlapping of filled orbitals, potentially a violation of the Pauli exclusion principle. This repulsive force may be represented by the equation ... 

Zwitterions are stable and can provide a living polymerization, however, at the smaller chain lenght (smaller distance between ions) formation of ylids was noted Q... 

Next let us compute the field at any one ion due to its neighbors when 6 is 0.10. For a square array of ions, the distance between ions occupying available sites is about 20 X 10 cm. The... 

VAN DER WAALS FORCES. Interatomic or intermolecular forces of attraction due to the interaction between fluctuating dipole moments associated with molecules not possessing permanent dipole moments. These dipoles result from momentary dissymmetry in the positive and negative charges of the atom or molecule, and on neighboring atoms or molecules. These dipoles tend to align in antiparallel direction and thus result in a net attractive force. This force varies inversely as the seventh power of the distance between ions. 

Since Na+ is smaller than Cs+ and Cl- is smaller than I-, the distance between ions is smaller in NaCl than in Csl. Thus, NaCl has the larger lattice energy. 

The magnitude of a lattice energy depends directly on the charge on the ions and inversely on the distance between ions (that is, on the radii of the ions). In this instance, all the ions in both drawings are doubly charged, either M2+ or O2-, so only the size of the ions is important. 

The elastic moduli of ionic crystals are also related to the valences and the distances between ions. The force, F = dU/dd, required to separate two ions is proportional to z z2/d2. The stress is a = F/A, where A is proportional to d2. Therefore, Young s modulus, E, of AB compounds is... 

F = force of attraction ex, e2 = charges of the ions r = distance between ions D = dielectric constant... 

The radius of the ionic atmosphere is l//c where is defined in the text. Work out the average distance between ions (d) in terms of the concentration in mol dm . id> Hk, then one is confronting a situation in which the radius of the atmosphere is less than the average distance between ions. Describe what this means. Derive a general expression for at which this problem (coarse grainedness) occurs for a 2 2 electrolyte. Do you think an ionic atmosphere model applies when d> l//c ... 

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