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J. Phys. Chem. 1980, 84, 1870-1871
Some Considerations on the Application of the London Model for Calculating Boiling Points Publication costs assisted by Conselo Nacional de Investigaciones Cienfiflcas y T h i c a s , Argentina
Sir: Myers has proposed,' recently, a model for calculating boiling points (Tb) from molar refraction (RM),ionization potential (I), and molecular size by applying London's theory. Myers has developed the corresponding relations for spherical, cylindrical, and flat molecules as follows: for spherical molecules
applied to nonspherical molecules: (1)If the molecules are cylindrical, then L/ v b = molecular cross-sectional area must be nearly constant, as known from experimental data in related molecules.2 (2) In the case of flat molecules, A / Vb = "thickness" of the molecule must also be nearly constant. This can be easily observed from van der Waals radii of atoms or group of atoms, which are almost of the same ordera3 If we consider now that L/ v b and A/ V, are constant, Tb1I2 must be proportional to RMP/'. For the substances reported in ref 1, we can obtain the following linear regression: for cylindrical molecules Tbli2
for cylindrical molecules
= 11.11
+ 0.07563RM1'/2
with a correlation coefficient of 0.9906 for flat molecules for flat molecules Tb1l2e= 12.99 Tb1I2 a F = RMI'/'(A/V~)~
where v b is the molar volume at T b , L is the molecular length, and A is the molecular cross-sectional area. When S,F , and C are plotted against Til2,it is possible to obtain linear correlations between these quantities. The correlation coefficient for spherical molecules ranges between 0.9729 and 0.9968, while for cylindrical molecules it is 0.9976. Nevertheless, regarding flat molecules, the correlation coefficient is 0.798, provided benzene is included among these molecules, or 0.975, if this substance is excluded. His model presents, however, weak points when
Fig. la. ~2 v s
+ 0.07122R~I~1~
with a correlation coefficient of 0.9834, including benzene. Furthermore, if we consider that the ionization potentials are very similar, we can simplify the model, obtaining, thus, Tb1I2 cc RM. Calculation shows in this instance the following correlation coefficients: for cylindrical molecules, 0.988, and for flat molecules, 0.968 (including benzene). These calculations were performed by employing the data reported by Myers. In the case of spherical molecules, the model appears to be reasonably because of the nature of the model itself. However, if we wish to extend this treatment to nonspherical molecules, serious errors will be
R, I I for
cylindrical molecules
I
Fig.Ib.
T;
vs
R,I'
For
f l a t molecules.
Figure 1.
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0 1980 American Chemical Society
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J. Phys. Chem. 1980, 84, 1871-1872
introduced in the model. Strictly speaking, the heat of vaporization cannot be explained only in terms of London forcesS4 In Figure 1,RMP/2 vs. Tb1i2is plotted for hydrocarbons from ethane to tetradecane; the data for several alkenes are included. If we take into account the fact that Myers considers that the heat of vaporization is proportional to the London dispersion energy, then the linear regression must go through the origin. With this reasoning and from Figure 1, we see that the linear correlation does not exist, except if we consider a very reduced number of compounds. The data used for Figure 1have been taken from several In short, Myers’ model can be applied to spherical molecules. For nonspherical molecules, this is not a realistic approach for calculating boiling points. The model itself appears to be very simple when it (comesto describing molecular forces only in terms of London forces.
be nearly constant, but this constant will be a definitely smaller number than for the hydrocarbons. There is another complexity about which Mor6 and Capparelli could not have known. In the case of spherical molecules the lines are actually straight. However, it has been found that for the alkanes the graph of RMI1l2(L/ vb)3/2 vs. Tb1/2 curves upward. The apparently good linear fit of the simplified equations is somewhat deceptive. The reason for the curvature will be discussed in a forthcoming paper. R. Thomas Myers
Department of Chemistry Kent State University Kent, Ohio 44242 Received September 20, 1979
References and Notes (1) R. T. Myers, (J. Phys. Chem., 83, 294 (1979). (2) See, for example, S. Glasstone, “Treatise on Physical Chemistry”, 2nd ed, Van Wostrand. Princeton, N.J., 1946. (3) A. Hopfinger, “Conformational Properties of Macromolecules”, Academlc Press, New York, 1973. (4) C. J. Bottcher, “Theory of Electric Polarization”, Elsevier, New York, 1973. (5) ”International (CriticalTables”, Vol. 111, McGraw-Hill, New York, 1928. (6) ”Landolt-Bornstein, Zahlenwerte und Funktionen aus Physlk, Chemie Astronomie, Geophysik und Technik”, Voi. I, Springer Verlag, West Berlln, 1951, Parts 2 and 3. (7) “Handbook of Chemistry and Physics”, 57th ed, Chemical Rubber Co., Cleveland, 1976-1977. Instituto de Investdgaciones Fislcoquimicas Te6ricas y Aplicadas Casilla de Correo ‘76 1900 La Plata, Argentina
A. Mor6 A. L. Capparelli”
Received August 27, 1979
Rhodamine B and Rhodamine 101 as Reference Substances for Fluorescence Quantum Yield Measurements
Sir: The xanthene dye rhodamine B is frequently used as a fluorescence standard (e.g., in the method of Parker and Reed) for determining absolute fluorescence quantum yields @F. A measured fluorescence quantum yield is only as good as that determined for the standard, assuming that the experimental errors are similar. The fluorescence quantum yield values reported in the literature for rhodamine B (Rh €3) range from 0.41 to 0.97.l In their review of the measurement of photoluminescencequantum yields Demas and Crosby claimed @F = 0.71 at room temperature for Rh B to be the safest value.2 However, Huth et al.3 concluded from their measurements that @F = 0.45-0.50 at 293 K. We have measured the fluorescence emission of Rh B
A Simplified Forms of the Myers-London Model for Intermolecular IForces in Liquids
/
/
Publication costs assisted by Kent State University
Sir: The suggestions of Mor6 and Capparelli for simplifications of my equations derived for cylindrical and flat molecules are very useful, and welcome. These equations give the effect of intermolecular London forces of attraction on the boiling point. It is true that 1, is approximately proportional to molar volume, but this, is only roughtly true, because there is a 16.2% decrease in the ratio L/ v b in going from ethane to octane. If one wishes to accept this degree of deviation then one can also assume that RM, for hydrocarbons, is approximately proportional to length. (Each time a CH2 group is added the length will increase the same amount, and RMwill increase by 4.62 mL.) We then find that Tb1l2= 0.267511/2L-k 9.979 correlation coefficient = 0.9905 The next approximation of nearly constant I works just as well in this context. The principal difficulty with this sort of approximation comes when one changes from one class of compound to another. For example, for the polysilanes L/ v b will also
rhodamine 13
rhodamine 101
at different temperatures and exciting wavelengths. In addition, we also determined the temperature dependence of the reciprocal decay time k = 1 / r of Rh B. For comparison we carried out the same experiments with rhodamine 101 (Rh 101). Drexhage has found aPF of Rh 101 to which makes this be virtually 100% at room temperat~re,~ dye an interesting candidate for a standard. We hesitated to use the well-known standard quinine bisulfate in 0.1 N sulfuric acid2 because its spectral range (200-400 nm) differs too much from that of the xanthene dyes (250-590 nm).
0022-3654/80/2084-1871$01.00/00 1980 American Chemical Society
