NOTES
4418
/I
an appreciable discrepancy in the chemical shift values, our values for a 10% solution being consistently to lower field by 0.28 to 0.32 p.p.m. Independent spectra were obtained on two different Varian A-60 spectrometers. The chemical shifts of the 9,lO-protons agreed satisfactorily ( f 0.02 p.p.m.) with our other results, lending credence to their accuracy. It may be noted that the low-field resonance lines are broader than the others. This might be the result either of long-range coupling or of a short relaxation time for the 4,5-protons. No significant narrowing of these lines was observed during spin-decoupling experiments in which the 9,lO-proton resonance was irradiated.
I Figure 1. Observed and calculated proton n.m.r. spectra of phenanthrene at 60 Me.
the procedure and iterative computer program described by Swalen and re ill^.^ A variety of different line assignments was tested corresponding to different chemical shift assignments and relative signs for the coupling constants. Only one assignment gave satisfactory agreement for both the line positions and the line intensities. The observed and calculated spectra for a 13% solution are given in Figure 1. The analysis was checked by comparing the observed 100-Me. phenanthrene spectrum with that calculated from the parameters determined at 60 Mc., and good agreement was found. The coupling constants showed no significant variation with concentration over the range studied. The chemical shifts did vary, and values were extrapolated to infinite dilution. The results, together with values from the previous study, are shown in Table I.
Acknowledgment. We wish to express our appreciation to Varian Associates for supplying 60- and 100-Me. n.m.r. spectra of phenanthrene, to Dr. E. Wadsworth of San Diego State College for making an A-60 spectrometer available for our use, and to the National Science Foundation for partial support of this work as well as for a grant-in-aid assisting the purchase of the n.m.r. spectrometer used in these studies. (4)J. D. Swalen and C . A. Reilly, J. Chem. Phys., 37, 21 (1962).
Logarithmic Distribution Functions for Colloidal Particles by E. P. Honig Philips Research Laboratories, N . V. Philips’ Glosilampenfabrieken, Eindhoven, The Netherlands (Received August 91, 1966)
Table I: Chemical Shifts and Coupling Constants for Phenanthrene - 6 ~ ~ 8
- &$I,
~ J . j j0.p.8.,
p.p.m.-
This
10% in
Inf. dil. in CDClsb
i
CDClP
(k0.006)
CJ’
Ref. 3
(*O.OS)
1 2 3 4 9
8.125 7.825 7.883 8.933
7.855 7.570 7.612 8.648 7.702
12 13 14 23 24
8.4 1.6 0.5” 7.3 1.6 8.4
8.11 1.31 0.66 7.20 1.24 8.40
work
34
Recently, Espenscheid, Kerker, and Matijevi6I stated that a set of different logarithmic distribution functions p,(r) was obtained by varying a parameter n of the “general” logarithmic distribution function (eq, 21 of their paper), characterized by the three parameters n, r,, and a, P,(T>
a
See ref. 3.
This work.
Assumed.
The coupling constants found here are generally similar to those reported earlier,3 but some differences do occur, It should be pointed out that the previous analysis was based on an interpolation procedure, and JI4 was assumed to be 0.5 C.P.S. There is also The Journal of Physical Chernistru
=
rnexp [- (In T - In rn)2/2an2] 2/2?ra,rnn+lexp[(n 1>zan2/2]
+
(1)
However, it will be shown now that all distribution functions (1) can be reduced to the logarithmic normal distribution function, containing only two parameters: r, and a., (1) W. F. Espenscheid, M. Kerker, and E. MatijeviO, J . Phys. C h m . , 68, 3093 (1964).
NOTES
4419
Equation 1 can be rewritten as
only; hence a new parameter r,,, may be substituted, defined by
In r,
In r n
+ (n + 1)un2
(3)
so or
or
exp The term In r,
[hr
- { l n r , + (n + 1).n2]12 2un2
C!)
+ (n + l)un2 contains parameters
The distribution function (1) is thus reduced to the logarithmic normal distribution function (4), where a single parameter rm replaces the two parameters r, and n. From an experimentally determined distribution curve only the parameters r,,, and u, can be evaluated. In order to determine r, and n separately, one must think of an experiment where rn and n are connected by a relationship other than eq. 3; however, this does not seem possible because r, and n have no physical significance. Hence, there is no reason to introduce a set of logarithmic distribution functions (by variation of the parameter n), and it is sufficient to deal with the logarithmic normal distribution function.
Volume 69, Number 19 December 1966
