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Raman band intensities in binary liquid solutions
JOI:RNAL
OF MOLECL~LAR
SPEC’TROSC’OPY
8,
164-166
(196,2)
Raman Band intensities in Binary Reliable int,ensity data for Raman bands of liquids ))irrsrJ- solutions, it might be expected the intensity of linearly with concentrat.ion. Rea,‘s (I) data show this No satisfactory explanation for t,he observed behavior be quantitatively described b)- a simple kinetic schernr. Thcl following symbols are defined: 14, .11:
: nlolecule : molecule
of the component of t,he component
Liquid Solutions are only recently :~vailitble (1 I. In :I band of a component, wo111tl vxr~ expectation to be false, in grner:d. has been given. The deviatiorls can
with its first absorption band nearest the visil)lc, with its first nbsorpl,ion band farthest, in the
ult r:I
violet., U” : photon .M,‘: vi,-.lll X2’: u,-.U, .11,‘: 31, in .Il:“: JI, in Y’: vu-energy
Y”:
of the esrit,ing radiation (:wumecl t.o be rnonochromatir), coniples, complex, an excited vibratioll-rotxt,ion level, an excited vibration-rotation level, required to excite 31, , v,,energ>-required to escite -II:!
Ttw following
processes
are :rssluned AI,
to occur: +
V,I -‘“+ P
.11,-,
(Ii
I
.11,-
-~ + .II, + vi1,
(21
ill1-
--/i3
I31
JI, + v’ ,
M,f + AI? 22 + 31, + ‘I~?+, .lls
+
k, vi, - +
.lI
151 iCi)
RI:-
-LJ4
.II:,+v”,
!ll,+
LL+
jf,”
‘-5
1111+
NI?-
+
Ml
i-l1
+
/,
iii
N,-.
(Si
In the ideal case, t)here is no interaction between molecules complexes. In this case, the usual steady st.ate treatment results for the intensities of the Ramnn lines:
and the photorl-molwulr in the expressions below
LETTER
TO THE
EDITORS
165
In these expressions, lo is the intensity of the exciting radiation, Zlcare is the ideal intensity for a Raman line of Mi , and Z&r. is the ideal intensity for a Raman line of 1cZg. These expressions correctly describe the ideal case. By assumption, Mi has its first absorption band nearer the visible than M2 , and it seems reasonable to assume (II,+ has a higher steady state concentration than Mn+.Presumably, the photon-molecule interactionis stronger as the photon wavelength becomes more nearly equal to the wavelength of an absorption maximum. With this assumption, process (8) can be ignored; and the following expressions for the intensities of the Raman lines can be derived, for the nonideal case:
02) The ratios of the nonideal
and ideal line intensities
are: (13)
(14) These ratios are required for comparison wit,h the experimental data, If it is now assumed the individual rate constants do not vary appreciably between the individual rotational lines of a given vibration-rotation band, then these functjions correctly describe the observed behavior. The data of Ref. 1 and of Evans and Bernst,ein (2) were plotted according to (13) and (14). The experiment,al points lie on straight lines. Thus, all the available experimental data are fitted by this scheme. The fraction of photon transfer is small compared to Rayleigh and Raman scattering. Equation (13) has precisely the form of Stern-Volmer law for the quenching of fluorescence (3). The “excited” molecule in this paper is, however, a photon-molecule complex rather than a molecule in an upper electronic state. The general features of the hypot.hesis bear other resemblances to fluorescence. The depolarization ratios of the bands of solutions do not appear to he a strong function of concent,ration, based on limited data (2, 4). On the basis of a simple linear addition of the intensity of the transferred radiation (assumed completely depolarized) to the natural intensity of the hand, there should be a large change in the depolarization ratio. A seemingly artificial assumption is required t,hat t.he transfer process does not result in depolarization of the emitted radiation. The assumption of independent probabilities for quenching and depolarization in energy transfer has heen made for fluorescence spectra. The probability for depolarization is greater than that for quenching (Ref. S, p. 352). The photon-molecule complex is root an excited state of the molecule. The lifetime of this complex must be longer than the time between collisions C-10-” second). If t,he concept of intermediate states employed in second-order perturbation theory is accepted, then the lifetime is very much shorter t,han this, if the conventional interpretation is adaccording to time-dependent perhered to. Energy is not conserved in these transitions, turbation theory (5). The uncertainty principle has been invoked as an explanation of t)his concept (6). However, a conceptual difficulty is immediately apparent. No measurement is being performed on the molecule or on the photon when they collide. Supposedly, the un-
166
LETTER
TO
THE
EDITORS
certainty principle applies in situations where measurements are being made. :\ simpk~ way out of these difficulties is to assume the existence of a photon-molecule complex. This assumption admits an experimental test, namely, measurement of the time delay in Rayleigh scattering. Presently available photomultipliers do not have adequate time resolutiori for such a measurement. However, photomultipliers with time resolution in the naighbol~hood of a few picoseconds have been reported (7). Measurements in this time range would definitely establish if the time de1a.v is longer or shorter than the intermolecular collision time. If t,he time delay is less than the intermolecular collision time, then this kinetic. tnec*h:misnl must be discartlcd. For the present, it is :L simple way of accounting for tht, ot)rervcltl behavior of Raman bands of tjinary solutions.
I)r. 1). G. Rea made his original notebooks nvailahle to me and obtained arl(lition:il data on the C8?-CCI, and benzene-CCl, syskms. This aid and enlightening ronversatiorl:: cottcrrning the concepts srt forth here are gratefttll>~ acknowledged. Helpftll cwntttcttts ott :t ttt~tn~wr of points were given me hy Professor R. C. 1,ord.
I. Il. ti. REA, b. Xol. Spect/Wcopj/ 4, 50? (19ciO). ‘2. .I. C. IGVANS AXU H. J. BERMTEIX, (‘rr,a. J. C’hetn. 34, 1127 (1956). 5. I’. I%IS(;SIIEIM, “Fluorescence and Phosphorescence,” 1). 90. Interscience, Ye\\- 1’orli, 1949. 4, 1). (:. REA (private communicatiorl). 5. W. HEITLER, “The Quantum Theor)- of Radiation, ” 2nd rd., p. 131. L’niv. Press, I,ondon and Sew York, 194-1. 6. I,. It. I!%.F:I,TON, ” Introductory Nuclear Throq.,” p. 181. Isaac I’it,nntn and Sons, I,ondon, 195!). 7. (:. A. ~fl)RTON, Physir.s Today 11, No. 5, 22 (1958).
OF MOLECL~LAR
SPEC’TROSC’OPY
8,
164-166
(196,2)
Raman Band intensities in Binary Reliable int,ensity data for Raman bands of liquids ))irrsrJ- solutions, it might be expected the intensity of linearly with concentrat.ion. Rea,‘s (I) data show this No satisfactory explanation for t,he observed behavior be quantitatively described b)- a simple kinetic schernr. Thcl following symbols are defined: 14, .11:
: nlolecule : molecule
of the component of t,he component
Liquid Solutions are only recently :~vailitble (1 I. In :I band of a component, wo111tl vxr~ expectation to be false, in grner:d. has been given. The deviatiorls can
with its first absorption band nearest the visil)lc, with its first nbsorpl,ion band farthest, in the
ult r:I
violet., U” : photon .M,‘: vi,-.lll X2’: u,-.U, .11,‘: 31, in .Il:“: JI, in Y’: vu-energy
Y”:
of the esrit,ing radiation (:wumecl t.o be rnonochromatir), coniples, complex, an excited vibratioll-rotxt,ion level, an excited vibration-rotation level, required to excite 31, , v,,energ>-required to escite -II:!
Ttw following
processes
are :rssluned AI,
to occur: +
V,I -‘“+ P
.11,-,
(Ii
I
.11,-
-~ + .II, + vi1,
(21
ill1-
--/i3
I31
JI, + v’ ,
M,f + AI? 22 + 31, + ‘I~?+, .lls
+
k, vi, - +
.lI
151 iCi)
RI:-
-LJ4
.II:,+v”,
!ll,+
LL+
jf,”
‘-5
1111+
NI?-
+
Ml
i-l1
+
/,
iii
N,-.
(Si
In the ideal case, t)here is no interaction between molecules complexes. In this case, the usual steady st.ate treatment results for the intensities of the Ramnn lines:
and the photorl-molwulr in the expressions below
LETTER
TO THE
EDITORS
165
In these expressions, lo is the intensity of the exciting radiation, Zlcare is the ideal intensity for a Raman line of Mi , and Z&r. is the ideal intensity for a Raman line of 1cZg. These expressions correctly describe the ideal case. By assumption, Mi has its first absorption band nearer the visible than M2 , and it seems reasonable to assume (II,+ has a higher steady state concentration than Mn+.Presumably, the photon-molecule interactionis stronger as the photon wavelength becomes more nearly equal to the wavelength of an absorption maximum. With this assumption, process (8) can be ignored; and the following expressions for the intensities of the Raman lines can be derived, for the nonideal case:
02) The ratios of the nonideal
and ideal line intensities
are: (13)
(14) These ratios are required for comparison wit,h the experimental data, If it is now assumed the individual rate constants do not vary appreciably between the individual rotational lines of a given vibration-rotation band, then these functjions correctly describe the observed behavior. The data of Ref. 1 and of Evans and Bernst,ein (2) were plotted according to (13) and (14). The experiment,al points lie on straight lines. Thus, all the available experimental data are fitted by this scheme. The fraction of photon transfer is small compared to Rayleigh and Raman scattering. Equation (13) has precisely the form of Stern-Volmer law for the quenching of fluorescence (3). The “excited” molecule in this paper is, however, a photon-molecule complex rather than a molecule in an upper electronic state. The general features of the hypot.hesis bear other resemblances to fluorescence. The depolarization ratios of the bands of solutions do not appear to he a strong function of concent,ration, based on limited data (2, 4). On the basis of a simple linear addition of the intensity of the transferred radiation (assumed completely depolarized) to the natural intensity of the hand, there should be a large change in the depolarization ratio. A seemingly artificial assumption is required t,hat t.he transfer process does not result in depolarization of the emitted radiation. The assumption of independent probabilities for quenching and depolarization in energy transfer has heen made for fluorescence spectra. The probability for depolarization is greater than that for quenching (Ref. S, p. 352). The photon-molecule complex is root an excited state of the molecule. The lifetime of this complex must be longer than the time between collisions C-10-” second). If t,he concept of intermediate states employed in second-order perturbation theory is accepted, then the lifetime is very much shorter t,han this, if the conventional interpretation is adaccording to time-dependent perhered to. Energy is not conserved in these transitions, turbation theory (5). The uncertainty principle has been invoked as an explanation of t)his concept (6). However, a conceptual difficulty is immediately apparent. No measurement is being performed on the molecule or on the photon when they collide. Supposedly, the un-
166
LETTER
TO
THE
EDITORS
certainty principle applies in situations where measurements are being made. :\ simpk~ way out of these difficulties is to assume the existence of a photon-molecule complex. This assumption admits an experimental test, namely, measurement of the time delay in Rayleigh scattering. Presently available photomultipliers do not have adequate time resolutiori for such a measurement. However, photomultipliers with time resolution in the naighbol~hood of a few picoseconds have been reported (7). Measurements in this time range would definitely establish if the time de1a.v is longer or shorter than the intermolecular collision time. If t,he time delay is less than the intermolecular collision time, then this kinetic. tnec*h:misnl must be discartlcd. For the present, it is :L simple way of accounting for tht, ot)rervcltl behavior of Raman bands of tjinary solutions.
I)r. 1). G. Rea made his original notebooks nvailahle to me and obtained arl(lition:il data on the C8?-CCI, and benzene-CCl, syskms. This aid and enlightening ronversatiorl:: cottcrrning the concepts srt forth here are gratefttll>~ acknowledged. Helpftll cwntttcttts ott :t ttt~tn~wr of points were given me hy Professor R. C. 1,ord.
I. Il. ti. REA, b. Xol. Spect/Wcopj/ 4, 50? (19ciO). ‘2. .I. C. IGVANS AXU H. J. BERMTEIX, (‘rr,a. J. C’hetn. 34, 1127 (1956). 5. I’. I%IS(;SIIEIM, “Fluorescence and Phosphorescence,” 1). 90. Interscience, Ye\\- 1’orli, 1949. 4, 1). (:. REA (private communicatiorl). 5. W. HEITLER, “The Quantum Theor)- of Radiation, ” 2nd rd., p. 131. L’niv. Press, I,ondon and Sew York, 194-1. 6. I,. It. I!%.F:I,TON, ” Introductory Nuclear Throq.,” p. 181. Isaac I’it,nntn and Sons, I,ondon, 195!). 7. (:. A. ~fl)RTON, Physir.s Today 11, No. 5, 22 (1958).