Energy of dipoles

Complete and Incomplete Ionic Dissociation. Brownian Motion in Liquids. The Mechanism of Electrical Conduction. Electrolytic Conduction. The Structure of Ice and Water. The Mutual Potential Energy of Dipoles. Substitutional and Interstitial Solutions. Diffusion in Liquids. 

In this case the interaction between neighbouring molecules is not only stronger but also orientation dependent. The mean statistical energy of dipole-dipole interactions 0dd also decreases with r 6, but depends on i2 (p dipole moment) according to 3>... 

Figure 5.3. The classical picture the energies of dipoles varies continuously from parallel alignment with the applied magnetic field (-m-B) to antiparallel (+m-B). On the right is shown the distribution of molecules that results and the lower mean energy of the ensemble relative to the field-free environment.

As mentioned above, the energy of dipole-dipole interactions in this system also proves to be small enough. 

An important point to note is that, like the potential energy of dipole-dipole interactions between rotating molecules, the potential energy of the London interaction also decreases very rapidly with distance (as 1/r6 see Fig. 5.1). 

The energy (81a) of order 1 is simply that of electrostatic intoraction of the permanent dipole moment p(0) and a uniform electric field. The energies of order 2 and upward are energies of the inductional kind, that is to say, energies of interactions between successivdy induced dipole momoits and a uniform electric field. We thus can quite graerally write, for the iw-th order energy of dipole-uniform field interaction ... 

The average energy of dipole-dipole interaction (see Chapter i8) is given by... 

If molecules of a crystal have no inversion center, the static dipole moments of a molecule in the ground and in the excited states are usually not equal to zero. In this case and in the dipole-dipole approximation for the expression (15.16) can be reduced to the interaction energy of dipoles Ps and Ps<... 

The reaction between RCV and a monofunctional compound may be taken as the reaction for comparison. In this case, AG will be the difference between AG for two and polydipole systems, i.e. the free energy of dipole—dipole interaction in multidipole systems. The value of AG may... 

Later work on more carefully prepared samples indicated, however, that both the activation energy of dipole rotation and the relaxation time are independent of concentration (II, 12, 39). 

E activation energy of dipole rotation in NH4F ice (1.7-5.7 kcal./mole) E activation energy of dipole rotation in pure ice (13.2 kcal./mole) a 550 cal. 

These values permit us to estimate the mean distances between both isolated complexes and partieles which form a cluster fjsoi > 22 A, rci s 6.8-9 A. As the energy of dipole-dipole interactions at a distance of 7-10 A is much less than kT, we can suppose that for cluster formation it is not the dipole-dipole interactions themselves that are important but a favorable spatial location of V(IV) ions. Cluster formation seems to occur aroimd a VCI4 molecule which joins two polymer chains. This increases the probability of coordination of other VCI4 molecules nearby. For vanadium ions in a coordination environment of six such a hypothetical model can be represented as shown in Fig. 3-6. 

The energy of dipole interactions, ( k) can be calculated from the equation [1] ... 

Activation Energy of Dipole-Dipole (E, jj,) and Spin-Rotational H Atom Interaction for Liquid TBP and Supported on TVEX (50%TBP)... 

The activation energy of dipole-dipole and spin-rotational interaction between carbon atoms for both liquid TBP and supported TVEX resins are collected in Table 8.3. The lower difference on the activation energy of spin-rotational interaction E(,(sj) for the C-4 atom of TBP in TVEX matrix compared with C-4 atom of 100% TBP is connected with effect of polymer matrix on mobility of extractant butyl chains. Increase of activation energy of dipole-dipole interaction for carbon C-3 and C-4 atoms of tri-butylphosphate in TVEX (as compared with liquid TBP) is caused by change of TBP conformation composition due to influence of TVEX matrix. 

Activation Energy of Dipole-Dipole E,.(dd) and Spin-Rotational E, Interaction between Carbon Atoms in Extractant Molecules for Liquid TBP and TVEX-TBP... 

With electric or magnetic fields present, additional energy contributions must be taken into account. To be more precise, the free energy of dipoles in external fields is to be considered, e.g., the free energy density due to magnetization in a magnetic field... 

Dipole j, in turn, gives rise to the field pf Tji at position i.e. the energy of dipole i is changed by an amount... 

We reobtain the classical induction energy (1.5). The permanent dipole p at particle 1 polarizes particle 2, the induced field lowers the energy of dipole pi, and vice versa. 

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