Refractive index and density variations in pure liquids: a new theoretical relation

Abstract

3485 4 r l l r : l 3 1 ' \ ' \ ' \ ' \ T Figure 4. Temperature dependencies of the normalized rotation relaxation time, 7iR at a given frequency; y = 2R'kTIw/p2. The temperatures TIL&) and T2*(L2) are the transition temperatures in eq 36 for the pores with different sizes, L, > L2; To = I , cI = 1, cb = 80, w i = 0.1, c. = 3. Curves 1 and 1' are obtained at R / & = IO; curves 2 and 2' at R / & = 4.interval around the transition point, T*(L), the dielectric friction and correspondingly the orientational relaxation time change from the value €6") to the value €6")' determined by eq 29b. The temperature and size dependencies of the rotational relaxation time at different values of parameters are shown in Figure 4. It should be emphasized, however, that eqs 36-39 present an example rather than an analysis of a real system. A different temperature dependence will be obtained using the same methodology but assuming different behaviors of A and T .In conclusion, we have studied the role of a boundary in modifying the relaxation behavior of a dipole embedded in a liquid. The formalism presented here which is based on the continuum approach extends previous works by introducing a nonlocal dielectric description of the liquid. Although the relaxation may be nonexponential in time we have calculated the dielectric friction for a given frequency as a function of zo, the distance of the dipole from the boundary. The effect of the boundary has been shown to be small unless the properties of the liquid itself are drastically changed due to the presence of the interface. The nonlocal nature of dielectric function modifies the dielectric friction derived within the local approximation and allows to introduce temperature dependence into the relaxation process through the characteristic length, AppendixIn order to calculate the dielectric friction in the bulk liquid we will follow the cavity approach.12J6q'8 Consider a dielectric sphere of radius R and dielectric constant el at the center of which a dipole is located. Outside the sphere there is a liquid with dielectric function e(k,w), eq 1. For this model the electrostatic potential, 4, can be written by expanding the solution of the Laplace equation in spherical coordinates. The potential in the liquid, r > R , should vanish at infinite distance, and the homogeneous part of the potential inside the sphere, r < R , has to be analytic at the origin. The nonhomogeneous part of the potential in the sphere arises from the point dipole with the dipole moment p at the center. Thus we have =('42) The coefficients A, B, and C are obtained from the boundary conditions at r = R which are similar to the conditions 8,9, and 10 used for the plane interface. As a result the field induced at the surface of dielectric sphere, r = R, has the form € I ) 4 R/ A) I I) (A3 1 withf(R/A) given by eq 28.A similar approach for the calculation of the dipole damping in the liquid (with the same boundary conditions) was adopted by van der Zwan and Hynes in ref 12. Our results, however, differ from theirs.A ...

Scattering by pure seawater: Effect of salinity

“…Table 1 lists the details of these parameters including their estimates and the associated errors. Theoretical calculation using the model that we proposed for estimating the density derivative of the refractive index ( 2 ( ) n ρ ρ ∂ ∂ ) [3] agrees with Morel's measurements within the experiment error (2%) with an average difference ranging from -0.67% to 1.97% for values of δ varying from 0.039 to 0.051 [4].…”

Light scattering by pure water and seawater: the depolarization ratio and its variation with salinity

“…Jonasz and Fournier [29] recommended a value of 0.039, also measured by Farinato and Rowell [4] but after removal of stray light using a filter with a half power band width of only 0.46 nm. Using the latest thermodynamic data of water and improved estimates of the density derivative of the refractive index of water [30][31][32], Zhang and Hu [33] were able to model the scattering by pure water that agrees with the Morel [26,34] measurements within 2% using either value of 0.051 or 0.039, but a better agreement was obtained when the value of 0.039 was used. Recently, the ocean optics community seems to have converged on recommending using 0.039 as the depolarization ratio for pure water [1].…”

Estimating scattering of pure water from density fluctuation of the refractive index

“…, M is the molar mass and N A the Avogadro number. Proutiere et al [16] pointed out that since the classic equations (such as Lorentz-Lorenz or Laplace) are only approximations, they may fail to give accurate values for the derivatives, such as 2 n ρ ρ ∂ ∂ . By imposing the same approximations but only after differentiating n 2 in Eq.…”

“…In the meantime, several theoretical relationships between refractive index and density for liquid water have been developed and verified with experimental measurements [14][15][16]. Given the inherent uncertainties associated with determining ( ) T n P ∂ ∂ experimentally, it is of great interest to re-evaluating the scattering of pure water directly from its underlying physics: density fluctuation of the refractive index.…”