J. Phys. Chem. 1981, 85, 1943-1947
done, the values of T~ are similar to those found for solutes in isotropic media of the same viscosity. In this sense, the influence of static order on reorientational motion is small. (2) Profound effects of long-range order are revealed by measurements of Jl(wo). As long as the nuclear Larmor frequency is significantly below the cutoff frequency for order director fluctuations (wo I1/50c), ODF will yield large contributions to Jl(wo). Similar contributions to relaxation of solvent spins are often masked by the reorientational terms, but this is less likely for solutes since TR is relatively short. Armed with a more extensive set of measurements of viscosities, diffusion coefficients, and elastic constants for binary nematic solutions (together with a modest increase in precision of the relaxation measurements), it appears feasible to use measured J1 values to explore refined aspects of ODF theory. This could lead to a reasonably precise value of the cutoff frequency as well as a test of the “one-constant
1943
approximation” for K, 7,and D. (3) Very slow processes, with correlation times longer than -0.1 ps, contribute to Jo(0)but not to spectral densities evaluated in the MHz range. Translational diffusion of the solute, accompanied by small fluctuations in the relevant spin interaction strengths, provides a physically plausible explanation. Acknowledgment. We thank David Jaffe for writing some highly useful fitting programs for relaxation measurements, Harry Dickerson for the measurement of the capillary viscosity of Phase 5, Dr. Michael Moseley for measuring the diffusion coefficients of chloroform in Phase 5, and Drs. H. Lopes Cardozo and C. Maclean for providing us with the results of their twist viscosity measurements prior to publication. Support of this work was provided by grants from the National Science Foundation (CHE77-22164and CHE76-05890) and the Public Health Service (RR-708).
Effect of the Charge Density of Linear Polyelectrolytes on Their Orientation in an Electric Field. A Study of Poly(rA)*Poly(rU) and Poly(rA)*SPoly(rU) D. Balasubramanlant and Elllot Charney’ Laboratoty of Chemical Physics, National Institute of Arthritis, Metabolism and Digestlve Diseases, National Institutes of Heakh, Bethe&. Maryland 20205 (Received: November 2 1, 1980; I n Final Form: March 17, 198 1)
The electric field induced dichroism of two polynucleotide complexes, poly(rA).poly(rU)and poly(rA).2poly(rU), which differ in the linear density of their formal charges by the ratio 1:1.4 is compared to that predicted on the basis of the expected contributions of condensed counterions and of the diffuse ion atmosphere. The experimental dichroism at low fields is shown to differ in the ratio 1.25 f 0.20 compared to predicted values of -1.0 and 1.2 for the respective contributions. Additionally, an experimental examination of the strong ionic strength dependence which is predicted by a Debye-Huckel treatment of the diffuse ion-atmospherepolarization, but not by counterion-condensation theory, shows that an ionic strength independent component of the polarization exists.
The description of linear polyelectrolytes in solution in terms of their fixed-charge distribution and the variablecharge distribution in their ionic atmosphere is a subject of intense current interest.’-l0 These charge distributions determine many of their physical and chemical properties. The recognition that single-stranded polynucleotides and DNA, and their helical complexes, are good candidates for experimental observations on polyelectrolytes because of their high charge density, and the importance relegated to their dynamic behavior and structure has generated a number of attempts to analyze their polyelectrolyte proper tie^.^ In several recent papers from this laboratory,l&14we have discussed the extent to which their orientation in electric fields, as measured by linear dichroism, is consistent with a description of the polyelectrolytes as more or less linear macroions of high charge density surrounded by a polarizable sheath of condensed counterions. Still more recently, a general expression for the orientation energy in the field has been obtained by treating the field-induced steady-state flow of the diffuse ion atmosphere of the solvent surrounding the polyion in the Debye-Huckel approximation.15 When, as in the work re-
’
School of Chemistry, University of Hyderabad, “Golden Threshold”, Hyderabad 50001,India
ported in this paper, there is only one charge type of counterion in solution, the treatments yield equivalent results for the dependence of the field-induced polarization (or lack thereof) on the charge density of the polyion. However, these treatments do not predict the same dependence of the polarization on the ionicity of the solvent, condensation theory predicting that the polarizability is virtually independent of the solvent ionic strength, and (1)R. W. Wilson, D. C. Rau, and V. A. Bloomfield, Biophys. J.,30, 317 (1980). (2)G.S.Manning, Acc. Chem. Res., 12,443(1979);Q. Rev. Biophys., 11, 179 (1978). (3)M. Fixman and J. Skolnick, Macromolecules, 11, 863 (1978). (4) M. Fixman, J. Chem. Phys., 70,4995 (1979). (5)M. Gueron and G. Weisbuch, Biopolymers, 19,353 (1980);J . Phys. Chem., 7 5 , 1991 (1979). (6)J. A. Schellman and D. Stigter, Biopolymers, 16, 1415 (1977). (7)D.Soumpasis, J. Chem. Phys., 69,3190 (1978). (8)K.Iwasa, Biophys. Chem., 9,397 (1979). (9)M. T.Record, Jr., C. F. Anderson, and T. M. Lohman, Q. Reu. Biophys., 11, 103 (1978). (10)E. Charney and J. E. Milstien, Biopolymers, 17, 1629 (1978). (11) E.Charney, Biophys. Chem., 11, 157 (1980). (12)E.Charney, K.Yamaoka, and G. S.Manning, Biophys. Chem., 11, 167 (1980). (13)E.Charney and C-H. Lee, Macromolecules, 13, 66 (1980). (14)E.Charney and H. H. Chen, manuscript in preparation. (15)D. C. Rau and E. Charney, Biophys. Chem., in press.
This article not subject to US. Copyright. Published 1981 by the American Chemical Society
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The Journal of Physical Chemistty, Vol. 85, No. 13, 1981
the Debye-Huckel treatment predicting a significant dependence on the Debye-Huckel screening parameter K and therefore on the ionic strength. In the present work, the polynucleotides poly(rA) and poly(rU) have been used to form helical rodlike complexes with formal negative charge densities which differ in approximately the ratio 2:3 as the result of the formation of double helices poly(rA)-poly(rU) and triple helices of poly(rA).2poly(rU). The axial polarizability of the polyion obtained from both counterion condensation theory and the diffuse ion-atmosphere treatment of the surrounding charge distribution are parametrically dependent on the linear charge density (the formal charge per unit distance as projected on the axis of the polyion). Thus the relative electric field orientation of these two species in the same ionic environment are explicit in the theories. The orientational energy is predicted to be substantially identical for the two species in both theories. In condensation theory, the counterions condense on a highly charged POlyion (intercharge separation less than one per 7.1 A) to reduce the effective charge-density parameter of the theory to unity2 while in the Debye-Huckel ion-atmosphere treatment, under the conditions of the presence of only one type of counterion charge, the dependence on the formal, but not on the effective, charge density disappears completely from the orientational energy.15 I t is the purpose of this investigation to determine the adequacy of these theoretical descriptions for the polarization of linear polyelectrolytes by an electric field, with respect to their predictions of the effect of variations of the formal charge density (the density prior to counterion condensation). Since, for practical reasons related to the ability to establish the necessary field strengths ( of the order of several kV/cm) across the solution, it was necessary to work a t low ionic strengths, it became necessary first to establish that the poly(rA).poly(rU) systems could be separately maintained a t ionic strengths corresponding to NaCl concentrations (or equivalent MgC12concentrations) of 1 or 2 mM or less. Earlier work161a had established that these complexes are stable at higher ionic strengths, but as the well-known double helical hemi-protonated complex of poly(rA) becomes increasingly stable with decreasing ionic strength, it was necessary to establish that the poly(rA)-poly(rU)and poly(rA)-2poly(rU)species could be obtained as stable complexes a t the low ionic strengths necessary for the electrooptic experiments. The conditions under which these stable complexes exist, with Mg2+as the counterion, have been established and are specified in the Experimental Section.
Experimental Section Stevens and Felsenfeld16have described the temperature and ionic strength (NaC1) conditions for the formation of the double-stranded poly(rA)-poly(rU) and the triplestranded poly(rA).2poly(rU) helices obtained by the stoichiometric mixing of the two polynucleotides. The detailed phase diagram relating the transition temperatures corresponding to the transitions from the triple to double, and triple (or double) to single strands has also been published by Fresco, as a function of Na+ counterion concentration in the millimolar to molar range.17 Extrapolation of these data to submillimolar range (necessary for the electric dichroism measurements) suggests that the (16)C. L. Stevens and G. Felsenfeld, Biopolymers, 2, 293 (1964). (17) J. R.Fresco in "Informational Macromolecules" H. J. Vogel, V. Eryson, and J. 0. Lampen, Ed., Academic Press, New York, 1963,p 121. (18) H. T. Miles and J. Frazier, Biochem. Biophys. Res. Commun., 14, 21 (1964).
Balasubramanian and Charney
triple helix would be stable only well below 0 "C. A similar difficulty is encountered even if KC1 were to be used instead of NaC1.lg Hence we have had to look for other possible salts wherein the double- and triple-stranded complexes can be independently obtained at convenient temperatures, e.g., 2-5 "C. Based on the earlier work and the suggestion of Dr. H. T. Miles, Laboratory of Molecular Biology, National Institutes of Health, that the magnesium ion might be several-fold as effective as Na+ or K+ as a condensing counterion toward polynucleotide chains, we have tried MgClz in submillimolar concentrations as the salt medium to generate poly(rA).poly(rU) and poly(rA).2poly(rU) with success. Poly(riboadeny1icacid) (poly(rA), Lot No. 441102, 7.2 f 0.7) and poly(ribouridy1ic acid) (poly(rU), Lot No. 444401, S20,w6.1 f 0.1) were obtained from P. L. Biochemicals, and were used as aqueous solutions in deionized, glass-double-distilled and N2-purged water containing the desired molarity of MgC12 (ranging from 0.125 to 1.000 mM). The pH of the unbuffered solutions so prepared were around 6.8. The concentrations of the polymers were adjusted to be in the range of 0.5 X to 1.0 X M by dilution from stock solutions using the molar extinction coefficients at the absorption maxima (around 260 nm) as 10.4 X lo3 for poly(rA) and 0.99 X lo4 for poly(rU). Circular dichroism (CD) spectra ensured that the individual solutions of poly(rA) and poly(rU) at these pH and salt conditions were single stranded, in agreement with published data.20 For the preparation of the poly(rA).poly(rU) and poly(rA).Bpoly(rU)complexes, individual solutions of the above two polynucleotides were mixed in the necessary stoichiometric ratios at 4 "C, and the presence of the complexes monitored by following the CD spectra and the optical density a t 260 and at 280 nm as a function of temperature (thermal melting curves). The CD spectra of the 1:l mixtures of poly(rA) and poly(rU) were in excellent agreement with that of the double-helix poly(rA).poly(rU), and those of the 1:2 mixtures were also identical with that of the triple-helix poly(rA).2poly(rU) reported by Brahms20 in all details. That the desired complexes are formed was confirmed by the optical density and melting profile data. Addition of an equimolar poly(rA) solution to poly(rU) resulted in a hypochromism of about 4090,already at 4 "C, compared to the value expected if no interaction were to occur. Again, the addition of poly(rA) to poly(rU) in the 1:2 ratio resulted in a hypochromism of over 55% of the 260-nm band under similar conditions. These reductions in the optical density are in accord with earlier observations16 for poly(rA).poly(rU) formed upon mixing the two polynucleotides a t higher molarities of NaC1. When the 1:l mixtures in 1mM MgClz was heated from the initial temperature of 2 "C, the optical density at 260 nm showed a sharp increase at about 65 "C, suggesting a melting transition a t this temperature. No change was seen in the 280-nm region during the heating; a change in the absorbance at 280 nm is indicative of the presence of the triple helix.16 Alteration of the MgClz concentration from 0.125 to 1 mM did not cause a significant change in the T, value. When poly(rA) and poly(rU) solutions in 1mM MgC1, were mixed in the molar ratio of 1:2, and heated from 4 "C onward, a sharp transition was seen at around 67 "C in the optical density values at 260 nm as well as at 280 nm. The hyperchromism a t 260 nm was about thrice that at 280 nm. Again, the T, values of the 1:2 mixture were not very sensitive to the (19)H.Krakauer and J. M. Sturtevant, Biopolymers, 6 , 49 (1968). (20)J. Brahms, J.Mol. Biol., 11, 785 (1965).
Effect of Charge Density on Polyelectrolyte Orientation
variation in the MgC12 concentration between 0.125 and 1mM. These results, interpreted along the lines of Stevens and Felsenfeld, would suggest that (1)mixing of equimolar solutions of poly(rA) and poly(rU) dissolved in submillimolar MgC1, in water (pH 6.8) at 4 OC produces the double-helix poly(rA).poly(rU), which melts upon heating to produce single chains without any evidence for intermediate conversion to the triple helix and poly(rA); (2) mixing solutions of poly(rA) and poly(rU) in the 1:2 molar ratio under the above conditions generates the triple-stranded complex poly(rA)-2poly(rU),which melts upon heating directly to the single chains with no evidence for any intermediate disproportionation into poly(rA).poly(rU) and poly(rU); and (3) variation of the MgC12 concentration in the range of 0.125 to 1 mM does not markedly alter the melting profile or the T, values of the complexes. We are also attempting to obtain independent infrared spectral evidence for the double- and triple-stranded complexes, and for any disproportionation reactions of these, but, at the concentrations used, this is an elusive problem; generally polynucleotide concentrations 100- to 1000-fold higher than the present ones are used in these studies.ls Thus, while the CD melting temperatures and hyperchromicities all point to the clear predominance of the double- or triple-stranded species under the appropriate conditions, the existence of several percent of the other species is not precluded. Thermal melting studies were conducted by using a Cary 14 spectrophotometer with 1-cm pathlength thermojacketed cells. CD spectra were run by using a Cary 60/6001 spectropolarimeter with cells of appropriate pathlengths and thermojacketing. The electric dichroism apparatus has been described elsewhere,21along with the detailed procedures for measuring and calculating the reduced dichroism. Single square-wave pulses of 100 ps were used and at least six measurements were made at each field strength. The data were stored and analyzed by using a Hewlett Packard data processing system, using the program developed by Dr. C-H. Lee. All measurementa were made at 2 "C with the polymer concentrations in the range of 10" to M. The concentrations of MgC12used were 0.125, 0.250, 0.375, and 0.500 mM, since higher concentrations prevented measurements at high field strengths.
Discussion and Results Counterion Condensation. A number of the physical properties of the polynucleotide complexes are well modeled by the assumption that they are smoothly charged rods with intrinsic negative charge densities corresponding approximately to the projection of their discrete charges on the rod axis. At charge densities greater than about one charge per 7.1 A,"condensation theory" predicts that sufficient counterions will condense along the surface of the polyion to reduce the value of the net charge to a fixed value, almost independently of the ionic strength of the surrounding solution over quite a wide range of ionic strengths below a few tenths molar.2 On this basis, Manningzzhas calculated the axial polarizability of such a polyelectrolyte and we have recently determined that the orientation of DNA and of poly(rA) at low electric fields in solution containing only Na+ or only Mg2+as counterions are consistent with this model. In these studies,'@12 the principal parameter tested was the ionic strength dependence which enters through the Debye-Huckel screening parameter K . The expression for the orientation dependence on the charge type Z (=1for Na+, = 2 for (21)K.Yamaoka and E. Charney, Macromolecules, 6 , 66 (1973). (22)G.S. Manning, J. Chem. Phys., 51, 924 (1969).
The Journal of Physical Chemistry, Vol. 85, No.
73, 7987 1945
Mg2+)of the counterion, and on the charge density parameter, t = e2/c k T b is given by12 (2 - t-') NezL2E2 (1) 1 - 2 ( 2 t - 1) In Kb 1 8 0 k 2 p
'
The formal charge density is specified in eq 1, both in 5 and directly by the value of b, which represents the separation of charges in their projection on the rod axis. For example, for native DNA, b = 1.7 A, one-half of the interbase separation, because there are two bases in the double helix each with a repeat distance of 3.4 A. In eq 1,N is the total number of charges on the rod of length L, and e , E, k , and T are, respectively, the electronic charge, the magnitude of the electric field, the Boltzmann constant, and the absolute temperature. With the poly(rA)-poly(rU) and poly(rA).2poly(rlJ) system, we may test the effect of the charge separation since the projection of the intrinsic charges on the axes of these complexes differs markedly. Using the data of Arnott et al.,23924 we obtained values of b for the poly(rA). poly(rU) and oly(rA)-2poly(rU)systems of, respectively, 1.4 and 1.01 At 2 "C, the temperature of the electric field dichroism measurements, the resultant charge density parameters are E(A-U) = 5.00 and t(A.2U) = 6.94. Note that these values differ slightly from the values used by Record, Woodbury, and Lohman (Biopolymers, 15, 893 (1976)) which, however, are based on earlier less-refined X-ray diffraction models of the poly(rA).poly(rU) and poly(rA).2poly(rU)structures. For the poly(rA).poly(rU) and poly(rA).2poly(rU) systems, one must also account for the fact that, for species of the same degree of polymerization, the total number of formal charges N(A.U) = 2/JV(A.2U). The charge-dependent part of the orientation factor, @', of eq 1 is c#J(N,L,E)/(e2L2E2/1SOk21'?: (2 - E1)N c#J' = (2) 1 - 2(ZE - 1) In Kb
1.
The orientation factor, or its dependence on K , b, and 2, may be obtained from measurements of the dichroism associated with an optical transition of the polymer when the latter is oriented by an electric field. The dichroism induced by the electric field may be specified in terms of the difference between the absorbance measured parallel to the field direction, All, and the isotropic absorbance in the absence of a field, Ao, as the product of the orientation factor and an optical factor, f ( 8 ) , which depends on the direction, 8, that the optical molecular transition moment at the wavelength of the radiation makes with the principal molecular orientation a ~ i s . ~ ~ p ~ ~
1 -4 - _--All - A0 - 4 f(8) A0 A0
(3)
A t low electric fields where eq 1 is expected to hold, the degree of orientation is not large and the influence of the field on the structural parameters which determine f(8) are nil or negligible. The 258-nm transition of poly(rA). poly(rU) and poly(rA).2poly(rU)lies approximately in the plane of the bases whose angular relation to the axes of the helical complexes are almost identical (with respect to their effect on the dichroism). Thus, we may use the dichroism of the two species as a measure of their orientation at low field strengths. Using the values of the pa(23)S. Arnott, D.w. L. Hukins, and S. D. Cover, BBRC, 48,1392 (1972). (24)S. Arnott, P.J. Bond, E. Selsing, and F. J. C. Smith, Nucl. Acids Res., 3 , 2459 (1976). (25)K.Yamaoka and E. Charney, J.Am. Chem. Soc., 94,8963(1972). (26)T. C. Troxell and H. A. Scheraga, Macromolecules, 4,519(1971).
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The Journal of Physical Chemistry, Vol. 85, No. 13, 1981
0.10 r
Balasubramanian and Charney
/ .08
0.08
c I
/t
h
n
-
0.06
yi
0.04 0.02
* .
a
0 0
0.2
0.4
0.8
0.6
1
I
I
20
10
I
I
30
08 r
E*x lO-'(V/cm)* Figure 1. The experimental dichroism of poly(rA).poly(rU) ( 0 )and of poly(rA).2poly(rU) (0)in 0.125 mM MgC1, solution.
TABLE I --In I
6.0
0.125 0.250 0.375 0.500
338 227 181 153
0.14 0.11 0.07 0.06
0.13 0.11 0.05 0.04
1
1
7.0
I
I
80
Flgwe 2. The dependence of the experimental dichroism at E = 2200 V/cm on the ionic strength, I, and on the Debye-Huckel shielding parameter, K , in solutions of 0.125, 0.250, 0.375, and 0.500 mM MgCI,: poly(rA).poly(rU) (0);poly(rA).2poly(rU) (0).
1.1 1.0 1.4 1.5
rameters specified above at ionic strengths specified by K , one can predict the relative orientations of poly(rA). poly(rU) and poly(rA).2poly(rU)of the same length to be nearly identical. When the L2 dependence (eq 1) is accounted for, the predicted orientation ratios (A-U/A.BU) vary from 0.9 to 1.0 in the ionic strength range of the experiments reported here. This prediction may be compared to the observations by comparing the slopes of the dichroism curves (see Figure 1where, as an example, the data obtained in 0.125 mM MgC12 are plotted). In Table I, the values of the slopes at four concentrations of MgC12 are given. The ratio of the experimental slopes vary from 1.0 to 1.5 with an average value of 1.25 f 0.20. Ion-Atmosphere Polarization. In the foregoing discussion, the orientation is assumed to originate solely in the moment induced in the polyion and its condensed counterion. In the ion-atmosphere treatment additional induced polarization results in the polarization of the surrounding noncondensed solvent ions. In this case the axial polarizability that determines the orientation factor at low fields is given by (4)
where Q = l / b and F(KL)is independent of charge type and Z is the charge of the counterions in the ion atmosphere. If the charge on the rod, assumed to be a smoothly charged cylinder, consists of the inherent or formal charges and a condensed counterion layer of charge, and only one charge type of counterion is present then in the symbolism of Manning2 (5) where Z'is the charge of the condensed counterions. Since only one type of counterion is present in these experiments, Z = 2' and the polarizability becomes, as noted above, essentially independent of the formal charge density of the polyion. The length dependence of F(K,L)in this treatment varies with KL,but is approximately quadratic under the experimental conditions. Once again, accounting for this on the basis of contour lengths calculated from the in-
terbase separation, the ratios of the slope of poly(rA). poly(rU) to poly(rA).2poly(rU) are predicted to be 1.21 which is well within the experimental f0.20 distribution of the observed average value, 1.25. If the polydispersity of the samples and the small uncertainties in composition are not serious determinants, the data of Table I can be assessed still more quantitatively than by the use of an average value for the ratio of the slopes of the reduced orientational energies. In the ion-atmosphere treatment the function F(KL)of eq 4 is found to be increasingly proportional to a higher power of L and as a consequence in accord with the observations, the ratio of the slopes for the A-U/A.BU system should decrease as the ionic strength decreases. Ionic Strength Dependence. While the lack of, or low sensitivity to, the formal charge density is a feature of both treatments, there is a difference in their analysis of the ionic strength dependence. We have previously shown that condensation theory predicts that the orientation of the polyions should be almost independent of the ionic strength of the solvent in this range.12 There are solutions of polyelectrolytes where this appears to be true, but under conditions equivalent to those of the experiments reported here, the orientation of polyelectrolytes, DNA in unbuffered or phosphate buffer solutions for example, has been shown to have a strong dependence on ionic strength.'lv2' Unlike the condensation theory, the diffuse ion-atmosphere treatment predicts a strong dependence on ionic strength, I , which is of the order of K - ~ .under ~ ~ these conditions. The . ~ ~ experimental data are plotted in Figure 2 against K - ~ and against In I (for comparison to other work). It is quite clear that this prediction is born out; an important component of the orientation energy is ionic strength dependent. While only limited significance can be attributed to the magnitude of the difference because of uncertainties in the size and compositional distributions in the samples, the data indicate that the two species exhibit a different response to the ionic strength as their parallel displacement from each other on logarithemic and exponential plots dictate. The parallelism of these plots implies the presence of a source of polarization that is independent of ionic (27)M.Hogan, N.Dattagupta, and D. M. Crothers, Proc. Natl. Acad. Sci. U.S.A., 75, 195 (1978).
J. Phys. Chem. 1981, 85,1947-1951
strength and therefore the contention that counterion condensation does provide a component of the polarization. This same behavior has been observed in DNA, where, however, the observations are made by varying the effective charge density by adjusting the concentration of Mg2+ under conditions where the ion atmosphere is held constant with an excess of Na+.15128 In the experiments on the A-U and A.2U species, the only significant counterion present is Mg2+.
Conclusions The results of these experiments, therefore, demonstrate the following: (1) The insensitivity of the polarization energy of linear polyelectrolytes in an electric field to the formal charge density as predicted for the contributions (28)D.C. Rau and E. Charney, manuscript in preparation.
1947
of both the condensed counterion layer and the diffuse ion atmosphere, and (2) the existence of a strong dependence of the polarization energy on the ionic strength of the diffuse ion atmosphere as predicted by the Debye-Huckel treatment.15 The observation that the dichroism of the two species of poly(rA) and poly(rU) complexes is not linearly displaced (the parallelism of the exponential curves of Figure 2) is new evidence for the existence of a component of the polarization which is independent of ionic strength.1°J2 Because of uncertainties in the compositional dependence of the A.U and A-2U samples on ionic strength, the existence of this component of the polarization, due largely to the condensed counterions, can only be cautiously inferred from the present data. Acknowledgment. We thank H. T. Miles and D. C. Rau for very helpful discussions.
Refractive Indices of Molten KN03-NaN02 Mixtures and Electronic Polarizabilities of Potassium and Nitrite Ions Y. Iwadate, K. Kawamura,' Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, O-okayam, Meguro-ku, Tokyo 152, Japan
and J. Mochlnaga DepartImnt of Synthetic Chemistry, Faculty of €nglnwrlng, Chlba Unlverslty, Yayokho, Chlba 260, Japan (Received: December 29, 1980; In Flnal Form: March 11, 1981)
Refractive indices of the binary molten KN03-NaN02mixtures were measured with visible light at 12 wavelengths with the goniometer method. The refractive indices of these molten mixtures were represented by empirical formulae as functions of both temperature and wavelength. The molar refractivities were calculated from these data. The refractive indices at infinite wavelength were estimated by use of Cauchy's approximate relation for dispersion, from which it was found that Fajans' theory was not applicable to the description of the electronic polarizabilities of these molten mixtures or to the molar refractivities. The electronic polarizabilities of K+ and NOz- at 340 "C were calculated to be 1.03 X and 3.24 x cm3, respectively.
Introduction Measurement of the refractive indices is one of the useful and convenient approaches for an estimation of the electronic polarizabilities of molecules or ions in a medium. The electronic polarizabilities of individual ions have so far been evaluated in various states such as gases,lS2 aqueous solution^,^-^ organic solutions~'crystals,g1oand liquid crystals.'l Numerous investigations on the refractive indices of molten salts have been performed and these results have been summarized.12 In recent years, excellent accurate (1)L. Pauling, Proc. R. SOC. London, Ser. A, 114,181 (1927). (2)M.Born and W. Heisenberg, 2.Phys., 23,388 (1924). (3)C.J. F. Bottcher, Recl. Trau. Chim. Pays-Bas., 62,325,503(1943); 65,19,91 (1946). (4)K. Fajans and G. Joos, 2.Phys., 23, 1 (1924). (5)J. K. Baird, H. R. Petty, J. A. Crumb, V. E. Anderson, and E. T. Arakawa, J. Phys. Chem., 81,696 (1977). (6) C. J. F. Bottcher, Physica, 9,945 (1942). (7)J. D. Olson and F. H. Horne, J. Chem. Phys., 58, 2321 (1973). (8)A. R. Ruffa, Phys. Rev., 130, 1412 (1963). (9)E.Kordes, 2.Elektrochem., 59, 551 (1955). (10)J. R. Tessman, A. H. Kahn, and W. Shckley, Phys. Reu., 92,890 (1953). (11)P. Adamski and A. D. Gromiec, Mol. Cryst. Liq. Cryst., 35, 337 (1976). (12)G. J. Jam, "Molten Salb Handbook, Academic Press, New York, 1967, p 89. 0022-365418112085-1947$01.25/0
measurements of the refractive indices of molten salts have been carried out by Gustafsson et al.,13-15in which the refractive indices have been measured up to seven significant figures with wave-front shearing interferometry. Nevertheless, few data on the refractive indices of molten salts are available to estimate the refractive indices extrapolated to infinite wavelength by which the electronic polarizabilities of ions in molten salts can be determined. The purpose of this work is to obtain the temperature coefficients of the refractive indices needed to estimate the thermal conductivities of these molten ionic mixtures by wave-front shearing interferometry16-18and, at the same time, to measure the electronic polarizabilities of ions in ionic melts. In the present work, the refractive indices of molten KNO3-NaNOZmixtures were measured with visible light (13)L.W. Wendelov, S.E. Gustafsson, N. Halling, and R. A. Kjellander, 2.Naturjorsch. A, 22, 1363 (1967). (14)S.E. Gustafsson and E. Karawacki, Appl. Opt., 14,1105 (1975). (15)E.Karawacki and S. E. Gustafsson, 2.Naturforsch. A, 31,956 (1976). (16)0.Odawara, I. Okada, and K. Kawamura, J. Chem. Eng. Data, 22, 222 (1977). (17)S. E.Gustafsson, 2.Naturforsch. A, 22, 1005 (1967). (18)S. E.Gustafsson, N. 0. Halling, and R. A. E. Kjellander, Z. Nuturforsch. A, 23,44,682 (1968).
0 1981 American Chemical Society
