4767
J. Phys. Chem. 1994,98, 4767-4768
COMMENTS Comment on “Refractive Index and Density Variations in Pure Liquids. A New Theoretical Relation”
TABLE 1: Values of d d d d o ) for NondiDolar Liauidsa p(dcldp)p
Z. Niedrich Chehohkiego 21, 60-756 Poznafi, Poland Received: August IO, 1993 There are very important experimental and theoretical results in the current literature which have been omitted in ref 1, giving rise to the wrong conclusion that the density refractive index derivative, anlap, “has never been represented by a good theoretical equation”. Careful measurements of these derivatives were performed in the Koninklijke/Shell Laboratorium in Amsterdam by Coumou et al.,z and it was found that the density derivative at constant temperature, which is theonly one of interest for Rayleigh light scattering, is generally greater than that at constant pressure, (anlap),) (anlap), (seeTable 1). Beforelong, the same conclusion has been reached by Omini3 and N i e d r i ~ h . ~ The theory presented in the paper shows these derivatives to be equal, (dn/ap)T = and therefore, it is in disagreement with experiment. It looks like this disagreement was due to not taking into consideration molecular radial correlations, contrary to what was done in the theories mentioned above. The use of radial correlations may be illustrated by relations from4 t
- 1 = 3r( 1
+ 2 a2 ( -x 6 ) + AaA/a)-2 t3t+ 1
(1) (2)
where e n2, r (4/3).rrpa, TI 1 ap/NR is the internal temperature, a (27/64)(RTc)z/pcisthevander Waalsconstant, p is the number intensity, a is the molecular polarizability, g(x) is the radial correlation function, x is the distance between molecules, A ~ Y A /isC Ythe term dependent on the wavelength X of light, and ‘v is the geometrical volume replacing the effective volume Y in ref 4. Equation 2 finds independent experimental confirmation in the X-ray scattering measurements6 for liquid argon for which (x-6) = 4.5 X 1045 cm4 agrees within the experimental error with (x-6),,, = 4.2 X 1045 cm4. Let us put aside the difference between (an/ap)Tand (anlap), to examine the numerical results of the theory by Proutiere et al.1
p(aE)pk = aP
(t
- 1)[ 1
+ 2(t - 1)2 -1t27t +2
(3)
and by Niedrich4
t(t
- 1[-) t + 0 5 t2
+ 0.5
1
+ 2 3 -L( L
)
2
ddc dp)r= (1IBrkdcldp)r Proutiere Niedrich expt ex t Niedrich eq 3 eq4 (refs 1,2, 8) (ref2) (ref4) (1 /ap)(-dc/dnp
]
(4)
apT, 1 - T/Tl
where ap= (1 / ~ ) ( - 8 p / a T )is~the thermal expansion coefficient, for nondipolar liquids for which experimental data are of better accuracy. In (4) r may be approximated, for unknown a, from the Lorentz-Lorenz formula and (apTl(l - T/T#I’ = 0.43; then (4) reduces to 0022-3654/94/2098-4767%04.50/0
liquid carbon disulfide benzene carbon tetrachloride n-hexadwane cyclohexane n-dodecane n-decane n-nonane n-octane isooctane 1-hexene n-heptane n-hexane n-pentane
2.27 1.54 1.34 1.23 1.20 1.18 1.14 1.11 1.08 1.06 1.04 1.05 1.00 0.93
2.26 1.60 1.42 1.31 1.27 1.26 1.22 1.17 1.16 1.14 1.14 1.12 1.07 1.00
2.24 1.59 1.41, 1.286 1.295 1.27 1.26 1.22, 1.23 1.21 1.16 1.14 1.13 1.15 1.05, 1.10 1.01,0.93b
2.37 1.655 1.455 1.35 1.29 1.26 1.18 1.15 1.075
2.382 1.652 1.458 1.339 1.304 1.28 1.248 1.21 1.187 1.15 1.14 1.14 1.092 1.02
If it is possible, experimental values of p(dc/dp)p and p(dc/dp)rare taken from the same source (ref 2); otherwise, the value of p ( d c / d p ) p is from ref 1, except for n-pentane for which the first value is from ref 8. Doubtful value (see text).
*
with practically unchanged accuracy. From Table 1 it is clear that Proutiere et al.’s theory gives values which are systematically too low (-6% on the average, except for CS2) compared to the experiment while Niedrich’s theory gives values which are for all liquids very well within the experimental error. For the ratios of isotropic Rayleigh light scattering in a liquid RIs = (7$/2X4)l(p dt/ap)? k T /3dl and in a vapor phase RTs = (.rr2/2X4)9r2/pfor equal number density, Proutiere et al.’s theory gives
From Table 2 it is clear that (6) is inconsistent with the experimental data by Coumou.9 It is unreasonable to expect that the theory which is not good even for dispersion interactions (nondipolar liquids) may be good if some perturbation, Le., dipolar or H-bonding interaction, is added. Certainly, because Proutiere et a1.k theoretical results are greater or lower than that in the experiment for dipolar liquids, the mean difference between theory and experiment depends on what kind and number of liquids are under investigation and not on thevalidity of the theory. The experimental results for dipolar liquids should be critically examined first, and only after that modification of existing good theories should be done to include dipolar interactions. In the ref 1 even such simple nondipolar liquid as carbon tetrachloride is given with unacceptable error of -9%, which comes from wrong value of ( a n l a g , = 55 X 10-5 K-I and a, = 1.267 X K-l; meanwhile, generally accepted values are close to (an/aT), = 58.6 X 10-5 K-1 and ap = 1.21 X 10-3
K-1.2
We have therefore shown that there are two aspects in which the theory presented in ref 1 is in disagreement with experiment for nondipolar liquids and a probable reason of this disagreement. We have also shown in one example that there are theories in the literature which are fully in agreement with experiment for 0 1994 American Chemical Society
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The Journal of Physical Chemistry, Vol. 98, No. 17, 1994
TABLE 2: Ratios of Molar Isotropic Scattering Factors in Liquid and in Vapor Phase liquid
Onsager Niedrich Einstein BBttcher (ref 4) 0.225 0.106 0.097 0.083 0.042 0.057 0.067 0.090 0.085
0.206 0.086 0.08 1 0.070 0.037 0.052 0.063 0.084 0.074
0.181 0.093 0.085 0.075 0.038 0.053 0.059 0.082 0.074
expt (ref 9) 0.180 0.094 0.085 0.074 0.039 0.05 1 0.061 0.080 0.070
houtiere et al. A, % 0.164 0.081 0.072 0.064 0.03 1 0.043 0.051 0.068 0.065
-9 -14 -15 -1 3 -20 -16 -16 -15 -15
nondipolar liquids. As for dipolar liquids, modification and
Comments verification of theories may be done only after more critical analysis of experimental data than that in ref 1. References and Notes (1) Proutiere, A.; Megnassan, E.; Huckteau, H. J . Phys. Chem. 1992, 96, 3485.
(2) Coumou, D. J.; Mackor, E. L.; Hijmans, J. Trans. Faraday SOC. 1964,60, 1539, 2244. (3) Omini, M. A. Physica 1976, 83A, 431. (4) Niedrich, Z. Physica 1985, 1288, 69. (5) Bot, A. J . Phys. Chem. 1993, 97, 2804. (6) Buckingham, A. D.; Stephen, M.J. Trans. Faraday SOC.1957,53, 884.
(7) Niedrich, Z . Physica 1987, 1448, 351. (8) Vuks, M. F. Light Scattering in Gases, Liquids and Solutions (in Russian); Leningrad University, 1977; p 124. (9) Coumou, D. J. Trans. Faraday SOC.1969,65, 2654.
