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The ultrasonic relaxation spectrum associated with a three state conformational change of polystyrene in solution
Volume 13, number 5
CHEMICAL PHYSICS LETTERS
THE ULTRASONIC RELAXATION SPECTRUM ASSOCiATED WITH A THREE STATE CONFORMATIONAL OF POLYSTYRENE IN SOLUTION
CHANGE
RASSfNG * Uniccrsit?/ of SalforJ,
The ultrrtsonic rclasation spectrum of ‘solutions of polystyrene in N,Ndimethylfarmsmide has been resolved to five two reiasation times. A two state cwformational model has been propos~vi to explain the data and the kinetics involved in the model have been considered in relation to the relaxation prtranicters.
I. In~od~ction
2. Experimental
Ultrasonic absorption studies of severai synthetic polymers in organic solvents have beer1 reported by many authors f I-81. The polymer that has received most attention is poIystyrene which exhibits a char-
The ultrasonic absorption data for DMF solutions of several poiystyrene samples were measured over the frequency range 1-IO0 MHz using a new resonator I t -25 MHz) and comparison p&se ( 15- 100 MHz) techniques 191. Both techniques measure the
acteristic
single relaxation
in most solvents
centred
around 5-IO MHz.The origir?of the relaxation is thought to be an intramolecuiar process and to our knowledge the only quantitative explanation that has been proposed to date is that of Bauer and coworkers [5,6] in which the relaxation is attributed to a two state conformational change. In this model several segments of the polymer chain ~rldependently undcrgo the conformational change gtgtgtgt . .. =: ... gtgtttgt *..
(11
g and t refer to the guu&e and tram pasirions of nearest neighbouring benzene rings with respect to each other in the polymer chain. where
In this communication we report further ultrasonic measurement of polystyrene solutions in N,N-dime~hy~form~mide (DMFf and an attempt to describe a more detailed mechanism for the conformational change in the polymer chain. + &verhuIme European Visit% C&en&try mark.
Laboratory
Feitow, permaixent address: 11 I, Unfvcrsity of Copenh%$en, Den-
chemicai contribution to the absorption per wavelength cr’h where 01’ is the excess absorption of the solution over solvent at wavelength h. In order to improve the accuracy of the present ultrasonic data we
have used DMF as a solvent because it has a very low background absorption, and a value of (~/f’ = 27 X tOVi7 se$ cm-l compared to 24 X IO-l7 sec2 cm-1 for water and 545 X IO-l7 sec2 cm-l for carbon ~etra~hloride at 25°C. ~~easurements were taken with the apparatus in a d_rybox and also with an open ceil and within the period for 1 experiment (ea. 3 hours) it was found that there were no signif&nt changes in the results. The DMF sample was a cornmercial product carefully purified using the method described by D&ton et al. {IO] . Ttle pofystyrene samples denoted A, B, Ct etc. were obtained from the foliowing sources: A; ‘VW = 44 700, ~~~~~n = 1.16 by courtesy of Dr. C.W. Brown, University of Salford. B;MW = 98200,Al,,,,Mn = 1.02 B.P. Ltd., Sunbury on Th&nes, C ; &ftv + 173000, iM,yji%fn = l-05 Waters Asscuiates, 477
Volume
13, number
1 April 1972
CHEMICAL PHYSICS LETTERS
5
D;M, = 867000,M,/Mn = 1.05 Waters Associates, E;Mii = 867OOO,M~~/M~ = 1.12 Waters Associates, where &,,, is the weight average and M,, the viscosity average molecular weights. All the samples are atactic poiystyrenes; each measurement was repeated several times.
These data indicate that the origin of both processes is intramolecular in nature and the most probable molecular mechanism is associated with conformational changes in the polymer chain. In ultrasonic relaxation studies the simplest way to account for two relaxations is in terms of a three state mechantion.
ism such as k-J 11 kF2 111 >
kl 1 kr,
3. Resu!ts The experimental data for ail the po!ystyrene solutions show the presence of two relaxation times centred at ca. 6 MHz and 75 MHz as shown in fig. 1. The relaxation spectra were all found to be indcpendent of the molecular weight of polymer and also the origin of the individual sample. For a given concentration of polystyrene in DMF (in g/l) the relaxation spectra of al1 the samples are almost identical. The above observations are illustrated in fig. 1 where the solid curves I and II are the computed single relaxation curves from the smoothed out relaxation spectrum (curve III) of ali the polymers at a concentration of 30 g/I. The points are the observed values of 0% for all the polymers and each point represents ar least five independent experimental observations. A summary of the individua! relaxation parameters associated with both relaxations is in table I.
4. Discussion
The data in table I show that the ultrasonic relaxation parameters associated with both the relaxation processes show very similar behatiour. For example, the relaxation times for both high and low frequency relaxation are all independent of aolymer concentration whereas both sets of amplitkie parameters of polymer concentra(“‘xma,) are linear functions
(2)
with the states I, II and III associated with different conformations of the polymer chain and the k’s are the transition probabilities. Following the initial idea of Bauer [5,6] the most convenient way to consider the separate conformations in a vinyl polymer like polystyrene is in terms of the proximity of adjacent benzene
rings with
respect
to each
other.
In order
to
describe three different conformational states we need only consider a maximum of three successive benzene rings at any one time. We can thus define the three states in the following order: State III of highest energy is made up of the energies of all the triads with neighbouring benzene rings in the closest position with respect to each other. State II then folIows and is made up of the energies of all the remaining diads of benzene rings which are in closest position with respect to each other. State I of lower energy which is made up of all the energies of the benzene rings which are atactic with respect to both neighbours. The ezcistence of states 1, II and III in a polystyrene solution has been inferred by Bovey [ 1 I] in relating light scattering, viscosity and NMR data to conformational changes in the molecules. By means of internal rotation about the single bonds in the polymer chain, these states are considered to be in fast dynamic equilibria with each other in such a way that the total number of each state remains constant in a given molecule but their
positions
continually
change
along
the polymer
chain. However, as pointed out by Bauer, a rotation about a single bond in a polymer would force one part of the molecule to have large movement through the solvent. Thus a second rotation about an adjacent bond in the opposite sense is very probable as this only affects a small part of the molecule. It is interesting to note that states I and III in the present model
correspond to the two states considered by Bauer. It has been shown previously [ 121, that the two Fig. 1.
478
relaxation
times associated
with mechanism
(2) are
5.4 5.4 7.3 6.9 5.6 7.6 5.0 5.3 7.2 6.4 6.9 5.0 5.4
300000
44700 98200 173000 300000 411iIoo 867000
300000
3oooo!l 867000
300000
44700 300000
20.0
25.0
30.0
35.0
4010
45.0
50.0
5.7 5.9 4.8 5.4
44700 300000 411000 867000
0.56 0.57
0.63
0.55 0.48
0.40
0.34 0.39 0.38 0.36 0.40 0.36
0.29
0.26 0.24 0.22 0.23
@A)m3xx IO3
Rcl3xation I @ II Relaxation frcqucncy feel X IO+ MI-k
“‘,,,
Molecular wci~llt
gr-’
Polymer cont.
71.0 69.0
94.0
87.0 72.0
74.0
77.0 76.0 75.0 79.0 78.0 75.0
73.0
106.0 86.0 82.0 90.0
Relaxation frcqucncy fcl x 104 Rlllz
1.20 1.13
1.10
0.94 1.05
0.95
0.69 0.69 0.69 0.68 0.68 0.77
0.61
0.50 0.48 0.52 0.50
(a’qnas x lo3
Relaxation II * III
14 13
14
12 11
14
14 10 11 14 10 15
13
L9 15 17 17
Y =fc21fc1
Table 1 Summary of ultrasonic rclaxntion paramctcrs for polystyrene samples in dinletllylfornlarnidc
0.47 0.50
0.57
0.58 0.46
0.42
0.49 0.56 0.55 0.53 0.59 0.47
0.47
0.52 0.50 0.42 0.40
Volume 13, number 5
CHEMICAL
PHYSICS LETTERS
given by the expression
L/*1, 2
=
‘s [z@+4@)“7]
,
(3)
When the two steps in mechanism (2) are not COUpled the expressions (8) and (9) for the relaxation times reduce to
where r1 and r2 are the low and high values of the reIaxation~times and Cpand Z are reiated to the transition probabilities through the following equations_
and
YZ=kl+k2+k_l+k_,,
I/r,
(4)
Q=/ck,k, +/c_,k_;tk,k_,
1
If y = r~/rI, the relaxation pressed% the form l/i1
= [r/(1
(5)
times can now be ex-
+r11c
(6)
and
1 April 1972
I/r1
= k_,(I
+Kr),
(12)
= k-*(1
+KZ) .
(13)
Provided (I$) “* > 1 it also follows from eqs. (1 Cl). (8),(9),(12)and (13) that k_, >k__2,K, 10. Under these conditions eqs. (12) and (13) for the relaxation times are further simplified to give: l/r1
= k, ,
(14)
and
l/T2 = [( 1 +-u)lrl
a/c
.
(7)
From the relaxation parameters in table 1, y = 15 which means that eqs. (6) and (7) are further simplified and reduce to l/T1 = k-,(1
tK,)
t k--,(1
ts,)
,
(8)
I /rx = x-_, .
(15)
From the relaxation data in table 1 the magnitudes of the rate constants k, and k2 are 3.8 X IO7 set-I and 4.7 X 10s set-l respectively and compare well with those found for internal rotation in simple ethanes [ 131.
and 1 + Kl(l
l’r,
ffcz) ’
L (1 tKI)/LQ_2+~)/ic_I
(9)
with K, and k’, being the respective equilibrium constants for the steps I + II and II -+ III. In the present work the two relaxation times are well separated (y = 15) and thus it is reasonable to assume that the two steps in scheme (2) are not coupled. Under these conditions the ratio.of the amplitude parameters can be expressed as
(~‘N,,,(I-w -_
’ =,(‘~‘A)~~~(11+ III)
1+K2 = hKZ( 1 +KI j ’
(10)
where h = Q3/P12 and 2
A study of the two ultrasonic relaxations observed in solutions of polystyrene in DMF indicates that the equilibria being perturbed by the sound wave are associated with conformational changes in the polymer. The simplest way to explain the relaxation times is in terms of a three state conformational mechanism. By considering the kinetics involved in such a mechanism in relation to the observed relaxation data it has been possible to estimate the transition probabilities, which are associated with each step in the mechanism. In addition the relative limits of the equilibrium constants associated with each step have been derived.
.
In eq. (1 I), LL!?$ and AV! are the enthalpy and volume difference between state i and i respectively; Cp is the specific heat of ‘rhe solution at constant pressure, 6 is the coefficient of thermal expansion and V the molar volume. Eq:(lO) predicts that /3 is independent of concentration which can be verified from the data in table 1 where p-== OS. 480,
5. Conclusion
Adrnowledgements J.R. thanks the Leverhulme Trust for a European Visiting Fellowship and professor Orville-Thomas for his hospita%ty. W.L. thanks the S.R.C. and B.P. Ltd., Sunburyan-Thames for a C.A.P.S. award. The S.R.C. aiso provided fi1nd.s to construct the ultrasonic equipment.
Volume 13, number
5
CHEMICAL PHYSICS LETTERS
References [I j R. Cerf, R. Xann and 6. Candau, Compt. Rznd. Aad. Sci. (Paris) 252 (1961) 181, 2229; 2.54 (1962) 106I. f2] C. Tondre and R. Cerf, J. Chim. Phys. 65 (19683 1106. I31 J. Lang, J. Chim. Phys. 66 Ci969) 58. [4] H. Nomura, S. Kato and Y. Xiiyahara, Nippon Kapaku Zasshi 8S (1967) 502; 89 (1968) 149; PO (1969) 250; 91(1970) 1042,837. [5] HJ. Bauer and H. HZ&r, KoIloid 2.230 (1969),194. f6] H.J. Bluer, H. Hisster and M. imme~dorfer, Discussions Faraday Sot. 49 (1970) 238.
I April 1972
[ 7] f&l [9] [ 101
B. Michels and R. Zart?, Kolloid 2. 234 (1969) 1008. J. Rassing, Acta Chem. Stand. 25 (1971) 1506. F. Eggers. private communiirtion. A.E. Colebourne, E. Coliinson and F. Da&on, Trans. Faraday Sot. 59 (IS63) 886. f I I] F.A. Bovey, Polymer mnformation and aonfyuration (Academic Press, New York, 1969) p, 75. [ 12) J. Rassing and E. Wyn-Jokes, Advan. Mol. Rciaration Processes (1971), to be published. [ 131 R.A. Pethrick and E. Wyn-Jones, Quant. Rev. Chem. sot. 73 (1969) 301.
481
CHEMICAL PHYSICS LETTERS
THE ULTRASONIC RELAXATION SPECTRUM ASSOCiATED WITH A THREE STATE CONFORMATIONAL OF POLYSTYRENE IN SOLUTION
CHANGE
RASSfNG * Uniccrsit?/ of SalforJ,
The ultrrtsonic rclasation spectrum of ‘solutions of polystyrene in N,Ndimethylfarmsmide has been resolved to five two reiasation times. A two state cwformational model has been propos~vi to explain the data and the kinetics involved in the model have been considered in relation to the relaxation prtranicters.
I. In~od~ction
2. Experimental
Ultrasonic absorption studies of severai synthetic polymers in organic solvents have beer1 reported by many authors f I-81. The polymer that has received most attention is poIystyrene which exhibits a char-
The ultrasonic absorption data for DMF solutions of several poiystyrene samples were measured over the frequency range 1-IO0 MHz using a new resonator I t -25 MHz) and comparison p&se ( 15- 100 MHz) techniques 191. Both techniques measure the
acteristic
single relaxation
in most solvents
centred
around 5-IO MHz.The origir?of the relaxation is thought to be an intramolecuiar process and to our knowledge the only quantitative explanation that has been proposed to date is that of Bauer and coworkers [5,6] in which the relaxation is attributed to a two state conformational change. In this model several segments of the polymer chain ~rldependently undcrgo the conformational change gtgtgtgt . .. =: ... gtgtttgt *..
(11
g and t refer to the guu&e and tram pasirions of nearest neighbouring benzene rings with respect to each other in the polymer chain. where
In this communication we report further ultrasonic measurement of polystyrene solutions in N,N-dime~hy~form~mide (DMFf and an attempt to describe a more detailed mechanism for the conformational change in the polymer chain. + &verhuIme European Visit% C&en&try mark.
Laboratory
Feitow, permaixent address: 11 I, Unfvcrsity of Copenh%$en, Den-
chemicai contribution to the absorption per wavelength cr’h where 01’ is the excess absorption of the solution over solvent at wavelength h. In order to improve the accuracy of the present ultrasonic data we
have used DMF as a solvent because it has a very low background absorption, and a value of (~/f’ = 27 X tOVi7 se$ cm-l compared to 24 X IO-l7 sec2 cm-1 for water and 545 X IO-l7 sec2 cm-l for carbon ~etra~hloride at 25°C. ~~easurements were taken with the apparatus in a d_rybox and also with an open ceil and within the period for 1 experiment (ea. 3 hours) it was found that there were no signif&nt changes in the results. The DMF sample was a cornmercial product carefully purified using the method described by D&ton et al. {IO] . Ttle pofystyrene samples denoted A, B, Ct etc. were obtained from the foliowing sources: A; ‘VW = 44 700, ~~~~~n = 1.16 by courtesy of Dr. C.W. Brown, University of Salford. B;MW = 98200,Al,,,,Mn = 1.02 B.P. Ltd., Sunbury on Th&nes, C ; &ftv + 173000, iM,yji%fn = l-05 Waters Asscuiates, 477
Volume
13, number
1 April 1972
CHEMICAL PHYSICS LETTERS
5
D;M, = 867000,M,/Mn = 1.05 Waters Associates, E;Mii = 867OOO,M~~/M~ = 1.12 Waters Associates, where &,,, is the weight average and M,, the viscosity average molecular weights. All the samples are atactic poiystyrenes; each measurement was repeated several times.
These data indicate that the origin of both processes is intramolecular in nature and the most probable molecular mechanism is associated with conformational changes in the polymer chain. In ultrasonic relaxation studies the simplest way to account for two relaxations is in terms of a three state mechantion.
ism such as k-J 11 kF2 111 >
kl 1 kr,
3. Resu!ts The experimental data for ail the po!ystyrene solutions show the presence of two relaxation times centred at ca. 6 MHz and 75 MHz as shown in fig. 1. The relaxation spectra were all found to be indcpendent of the molecular weight of polymer and also the origin of the individual sample. For a given concentration of polystyrene in DMF (in g/l) the relaxation spectra of al1 the samples are almost identical. The above observations are illustrated in fig. 1 where the solid curves I and II are the computed single relaxation curves from the smoothed out relaxation spectrum (curve III) of ali the polymers at a concentration of 30 g/I. The points are the observed values of 0% for all the polymers and each point represents ar least five independent experimental observations. A summary of the individua! relaxation parameters associated with both relaxations is in table I.
4. Discussion
The data in table I show that the ultrasonic relaxation parameters associated with both the relaxation processes show very similar behatiour. For example, the relaxation times for both high and low frequency relaxation are all independent of aolymer concentration whereas both sets of amplitkie parameters of polymer concentra(“‘xma,) are linear functions
(2)
with the states I, II and III associated with different conformations of the polymer chain and the k’s are the transition probabilities. Following the initial idea of Bauer [5,6] the most convenient way to consider the separate conformations in a vinyl polymer like polystyrene is in terms of the proximity of adjacent benzene
rings with
respect
to each
other.
In order
to
describe three different conformational states we need only consider a maximum of three successive benzene rings at any one time. We can thus define the three states in the following order: State III of highest energy is made up of the energies of all the triads with neighbouring benzene rings in the closest position with respect to each other. State II then folIows and is made up of the energies of all the remaining diads of benzene rings which are in closest position with respect to each other. State I of lower energy which is made up of all the energies of the benzene rings which are atactic with respect to both neighbours. The ezcistence of states 1, II and III in a polystyrene solution has been inferred by Bovey [ 1 I] in relating light scattering, viscosity and NMR data to conformational changes in the molecules. By means of internal rotation about the single bonds in the polymer chain, these states are considered to be in fast dynamic equilibria with each other in such a way that the total number of each state remains constant in a given molecule but their
positions
continually
change
along
the polymer
chain. However, as pointed out by Bauer, a rotation about a single bond in a polymer would force one part of the molecule to have large movement through the solvent. Thus a second rotation about an adjacent bond in the opposite sense is very probable as this only affects a small part of the molecule. It is interesting to note that states I and III in the present model
correspond to the two states considered by Bauer. It has been shown previously [ 121, that the two Fig. 1.
478
relaxation
times associated
with mechanism
(2) are
5.4 5.4 7.3 6.9 5.6 7.6 5.0 5.3 7.2 6.4 6.9 5.0 5.4
300000
44700 98200 173000 300000 411iIoo 867000
300000
3oooo!l 867000
300000
44700 300000
20.0
25.0
30.0
35.0
4010
45.0
50.0
5.7 5.9 4.8 5.4
44700 300000 411000 867000
0.56 0.57
0.63
0.55 0.48
0.40
0.34 0.39 0.38 0.36 0.40 0.36
0.29
0.26 0.24 0.22 0.23
@A)m3xx IO3
Rcl3xation I @ II Relaxation frcqucncy feel X IO+ MI-k
“‘,,,
Molecular wci~llt
gr-’
Polymer cont.
71.0 69.0
94.0
87.0 72.0
74.0
77.0 76.0 75.0 79.0 78.0 75.0
73.0
106.0 86.0 82.0 90.0
Relaxation frcqucncy fcl x 104 Rlllz
1.20 1.13
1.10
0.94 1.05
0.95
0.69 0.69 0.69 0.68 0.68 0.77
0.61
0.50 0.48 0.52 0.50
(a’qnas x lo3
Relaxation II * III
14 13
14
12 11
14
14 10 11 14 10 15
13
L9 15 17 17
Y =fc21fc1
Table 1 Summary of ultrasonic rclaxntion paramctcrs for polystyrene samples in dinletllylfornlarnidc
0.47 0.50
0.57
0.58 0.46
0.42
0.49 0.56 0.55 0.53 0.59 0.47
0.47
0.52 0.50 0.42 0.40
Volume 13, number 5
CHEMICAL
PHYSICS LETTERS
given by the expression
L/*1, 2
=
‘s [z@+4@)“7]
,
(3)
When the two steps in mechanism (2) are not COUpled the expressions (8) and (9) for the relaxation times reduce to
where r1 and r2 are the low and high values of the reIaxation~times and Cpand Z are reiated to the transition probabilities through the following equations_
and
YZ=kl+k2+k_l+k_,,
I/r,
(4)
Q=/ck,k, +/c_,k_;tk,k_,
1
If y = r~/rI, the relaxation pressed% the form l/i1
= [r/(1
(5)
times can now be ex-
+r11c
(6)
and
1 April 1972
I/r1
= k_,(I
+Kr),
(12)
= k-*(1
+KZ) .
(13)
Provided (I$) “* > 1 it also follows from eqs. (1 Cl). (8),(9),(12)and (13) that k_, >k__2,K,
= k, ,
(14)
and
l/T2 = [( 1 +-u)lrl
a/c
.
(7)
From the relaxation parameters in table 1, y = 15 which means that eqs. (6) and (7) are further simplified and reduce to l/T1 = k-,(1
tK,)
t k--,(1
ts,)
,
(8)
I /rx = x-_, .
(15)
From the relaxation data in table 1 the magnitudes of the rate constants k, and k2 are 3.8 X IO7 set-I and 4.7 X 10s set-l respectively and compare well with those found for internal rotation in simple ethanes [ 131.
and 1 + Kl(l
l’r,
ffcz) ’
L (1 tKI)/LQ_2+~)/ic_I
(9)
with K, and k’, being the respective equilibrium constants for the steps I + II and II -+ III. In the present work the two relaxation times are well separated (y = 15) and thus it is reasonable to assume that the two steps in scheme (2) are not coupled. Under these conditions the ratio.of the amplitude parameters can be expressed as
(~‘N,,,(I-w -_
’ =,(‘~‘A)~~~(11+ III)
1+K2 = hKZ( 1 +KI j ’
(10)
where h = Q3/P12 and 2
A study of the two ultrasonic relaxations observed in solutions of polystyrene in DMF indicates that the equilibria being perturbed by the sound wave are associated with conformational changes in the polymer. The simplest way to explain the relaxation times is in terms of a three state conformational mechanism. By considering the kinetics involved in such a mechanism in relation to the observed relaxation data it has been possible to estimate the transition probabilities, which are associated with each step in the mechanism. In addition the relative limits of the equilibrium constants associated with each step have been derived.
.
In eq. (1 I), LL!?$ and AV! are the enthalpy and volume difference between state i and i respectively; Cp is the specific heat of ‘rhe solution at constant pressure, 6 is the coefficient of thermal expansion and V the molar volume. Eq:(lO) predicts that /3 is independent of concentration which can be verified from the data in table 1 where p-== OS. 480,
5. Conclusion
Adrnowledgements J.R. thanks the Leverhulme Trust for a European Visiting Fellowship and professor Orville-Thomas for his hospita%ty. W.L. thanks the S.R.C. and B.P. Ltd., Sunburyan-Thames for a C.A.P.S. award. The S.R.C. aiso provided fi1nd.s to construct the ultrasonic equipment.
Volume 13, number
5
CHEMICAL PHYSICS LETTERS
References [I j R. Cerf, R. Xann and 6. Candau, Compt. Rznd. Aad. Sci. (Paris) 252 (1961) 181, 2229; 2.54 (1962) 106I. f2] C. Tondre and R. Cerf, J. Chim. Phys. 65 (19683 1106. I31 J. Lang, J. Chim. Phys. 66 Ci969) 58. [4] H. Nomura, S. Kato and Y. Xiiyahara, Nippon Kapaku Zasshi 8S (1967) 502; 89 (1968) 149; PO (1969) 250; 91(1970) 1042,837. [5] HJ. Bauer and H. HZ&r, KoIloid 2.230 (1969),194. f6] H.J. Bluer, H. Hisster and M. imme~dorfer, Discussions Faraday Sot. 49 (1970) 238.
I April 1972
[ 7] f&l [9] [ 101
B. Michels and R. Zart?, Kolloid 2. 234 (1969) 1008. J. Rassing, Acta Chem. Stand. 25 (1971) 1506. F. Eggers. private communiirtion. A.E. Colebourne, E. Coliinson and F. Da&on, Trans. Faraday Sot. 59 (IS63) 886. f I I] F.A. Bovey, Polymer mnformation and aonfyuration (Academic Press, New York, 1969) p, 75. [ 12) J. Rassing and E. Wyn-Jokes, Advan. Mol. Rciaration Processes (1971), to be published. [ 131 R.A. Pethrick and E. Wyn-Jones, Quant. Rev. Chem. sot. 73 (1969) 301.
481