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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
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/
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 rhodaof Rh 101 to mine 101 (Rh 101). Drexhage has found aPF be virtually 100% at room temperat~re,~ which makes this 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
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The Journal of Physical Chemistry, Vol. 84, No. 14, 1980 .lo8
-6 -5
kls-'l
3
4
-----+
5
6
7
T io3 IIC'I
aF
Flgura 1. Temperature dependence of fluorescence quantum yield ((A) Rh B; (0)Rh 101)and of the reciprocal decay time k = 117 ((A) Rh B; (0) Rh 101).
The dyes were purified by thick layer chromatography (EtOH/H,O). All experiments were performed in absolute ethanol solutions of the dyes, with nitrogen being bubbled through the solutions for about 20 min prior to use to avoid degradation by photooxidation. Both dyes proved to be stable under these conditions. The fluorescence emission spectra were corrected with respect to the exciting light intensity and the photomultiplier (GaAs) response. Excitation was carried out at an angle of about 30' to the plane of the cell window by use of a light cable, thus minimizing polarization errors. The increase of density and refractive index of the ethanol solutions of the dyes with decreasing temperature has been ~orrected.~ The fluorescence quantum yield (emitted quanta per absorbed quanta) is given by
$IF(?) @p
d'v
= 1 - 10-ECd
We integrated the fluorescence spectra, which were plotted as relative quanta per wavenumber interval IF('v) vs. 3,and found the above equation to be well fulfilled for both dyes up to concentrations of about 3 X lo4 mol/L. The shape of the emission spectra as well as the quantum yields of both dyes were independent of excitation wavelengths in the range 450-565 nm.6 In Figure 1the fluorescence quantum yields @F and the reciprocal experimental fluorescence lifetimes k = 1,'. (precision for both not better than 10%)of Rh B and Rh 101 are plotted vs. 1/T. Rh 101 exhibits nearly no dependence of aFand k upon temperature. This result
Communications to the Editor
supports Drexhage's value of @F = l.04and is explained by the rigid structure of Rh 101. Accordingly it is not surprising that the fluorescence lifetimes determined from the fluorescence decay curves and the fluorescence lifetimes calculated from the absorption spectrumgagree very well. This is a clear evidence that the fluorescence indeed does not depend on temperature. Hence there is no doubt that @F of Rh 101 approaches 100% at all temperatures. The fluorescence quantum yield @F of Rh B was now determined by using Rh 101 as a reference. It increases by about a factor of 2 between room temperature and 200 K. The corresponding change of k is consistent with the relation @Fk = kF.l0 An Arrhenius plot of In ( l / @ F - 1) vs. 1/T yields an activation energy of 6.6 kcal/mol for Rh B. This energy is most probably due to the torsional motion of the diethylamino groups. At temperatures lower than about 200 K Rh B exhibits GF and k values which appear to be temperature independent. A comparison of properly corrected experimental data shows that the fluorescence quantum yields @F of Rh B and Rh 101 agree within experimental error ( ~ 9 0 %for ) T 200 K. It must therefore be concluded that in this temperature range @F = 100% for both dyes (see above) and that at room temperature @F I50% for Rh B.
References and Notes P. Pringsheim, "Fluorescence and Phosphorescence", Interscience, New York, 1960;C. A. Parker and W. T. Rees, Analyst (London), 85, 587 (1960);H. V. Drushel, A. L. Sommers, and R. C. Cox, Anal. Chem., 35,2166 (1963);J. N. Demas, Ph.D. Dissertation, University of New Mexico, Albuquerque, NM, 1970;B. G. Roberts and R. C. Hirt, Ann. ISA Conf. Proc., 19 (11, 2.2.2.64) (1964);G. Weber and F. W. J. Teale, Trans. Faraday Soc., 53, 646 (1957). J. N. Dernas and G. A. Crosby, J. Phys. Chem., 75, 991 (1971). B. G.Huth, 0. I.Farmer, and M.R. Kagan, J . Appl. Phys., 40, 5145
(1969). K. H. Drexhage, "Structure and Properties of Laser Dyes" in "Topics in Applled physics", Vol. 1, F. P.Schafer, Ed., pp 147-152,171-172, and references cited therein. J. A. Rlddick and W. B. Bungers, "Techniques of Chemistry", Vol. 11, 3rd ed, Wiley-Interscience, New York. aPF of xanthene dyes should be constant down to 250 nm;7 a flat spectral responsivity of f2% has been found in the range 360-590 nm for Rh (a) W. H. Meiuish, J . Opt SOC.Am., 52, 1256 (1962);Rev. Sci. Instrum., 33, 1213 (1962);(b) J. Yguerabide, Rev. Sci. Instrum.,
39, 1048 (1968). D. G. Taylor, and J. N. Demas, Anal. Chem., 51, 717 (1979). J. B. Birks and D. J. Dyson, Proc. R. SOC.London, 275, 135 (1963). Th. Forster, "Fluoreszenz organischer Verbindungen", Vandenhoeck & Rupprecht, Gottingen, 1951.
Philips GmbH Forschungslaboratorium Hamburg 0-2000 Hamburg 54, West Germany
T. Karstens K. Kobs"
Received July 20, 1979; Revised Manuscript Received January 24, 1980
