Two dimensional cartoon representation of the fictive mathematical device called a “Lorentz sphere.” The Langevin-Debye model assumes the Lorentz sphere to be homogeneous and isotropic. This assumption implicitly implies that the electric field from the dipoles vanishes inside the Lorentz sphere. The volume of the sphere, represented in the figure by the circle, is large compared to the solvent molecule size. The ovals in the circle represent the polar solvent molecules that can be polarized in two ways: (a) due to the distortion of the charge distribution of the molecules in the presence of an external field and (b) from the alignment by the applied field of the randomly oriented permanent dipole moment of the molecules. These effects are represented by elongation and alignment, respectively.
Permittivity profile. (a) Curves are derived from the Langevin-Debye formalism with the input values for the number density of molecules per (for a molecular weight of and a mass density of for water), optical dielectric constant , static dielectric constant, , and . The black data points correspond to the general solution, whereas the red and green points are obtained for the limiting cases of zero dipole and linear response regime of the solvent, respectively. (b) The radial permittivity following corrections in the LD model due to Onsager (red) and Kirkwood (green). The parameters and are used to give the water dipole moments of and in the gas phase and liquid phase. The inset is a magnified view of region from . (c) The different functional forms used to model the distance dependence of the dielectric constant. The parameters used for each functional form are described in the text. (d) The modified Langevin-Debye model calculated for all the four charges for the atoms of DME. We use the fits from Eq. (14) (long dash – –) and Eq. (15) (short dash - - -) and the parameters in Table I. The curve fits for are displayed. The inset is a magnified view of regions from .
Relative magnitude of nonlinear contribution to the self-energy. The contribution of the nonlinear term to the self-energy of a charge placed in aqueous medium [Eq. (22)]. The grey stars correspond to the three atom types in DME.
Parameters for the functional forms of the distant-dependent dielectric “constant” obtained by fitting to the Langevin-Debye model with corrections due to Onsager-Kirkwood. The magnitudes of the partial charges are those for the atoms in DME. The parameters and are fixed to the static and optical dielectric constants of water, respectively.
Comparison of populations (%) from implicit and explicit solvent simulations for DME. The charge-dependent dielectric model used corresponds to the parameters shown in Table I, while the implicit model uses .
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