Ultrasonic absorption studies of aqueous solutions of nonionic

Mar 27, 1987 - Instituí Charles Sadron (CRM-EAHP) and Greco Microemulsion, CNRS, ... The ultrasonic absorption of aqueous solutions of three nonionic...
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J. Phys. Chem. 1987, 91, 5957-5960


Uitrasonlc Absorption Studies of Aqueous Solutions of Nonionic Surfactants in Relation with Critical Phenomena and Micellar Dynamics Arun Borthakurf and Raoul Zana* Institut Charles Sadron (CRM-EAHP) and Greco Microemulsion, CNRS, 67000 Strasbourg, France (Received: March 27, 1987: In Final Form: June 15, 1987)

The ultrasonic absorption of aqueous solutions of three nonionic surfactants, C6E3, C6E5, and CsEs, has been investigated in the megahertz range as a function of temperature T, concentration C, and ultrasonic frequency. The data show no evidence of a contribution of the critical fluctuations of the micellar concentration to the absorption of the system even at a temperature only 0.1 OC below the critical temperature Tc. This result appears to be due to the fact that (i) the changes of the thermodynamic state of the surfactant upon micelle clustering close to Tc are very small and (ii) the ultrasonic frequency range investigated is well above that characteristic of the fluctuations. The ultrasonic absorption of the nonionic surfactant solutions investigated appears to arise mostly from the perturbation by the sound waves of the surfactant exchange equilibrium between micelles and bulk. For C6E3the rate constants characterizing this process have been found to be close to those for ionic surfactants of comparable cmc, and the micelle polydispersity is small. These results are the first ones reported for a nonionic surfactant far from its critical temperature. Finally the volume change upon association of a surfactant to the micelles is +2.9 cm3/mol. The results also show the existence of a high frequency relaxation process the origin of which is discussed.

Introduction Critical phenomena in aqueous solutions of nonionic surfactants of the C,E, type (n is the number of carbon atoms of the alkyl chain; m is the number of the ethylene oxide E groups of the hydrophilic head group) have recently attracted considerable attention.'-' In view of the extreme sensitivity of ultrasonic absorption to critical phenomena, particularly in fluids,8-13it was felt worthwhile undertaking ultrasonic absorption studies of aqueous solutions of nonionic surfactants in relation with their critical behavior. Recall that the ultrasonic absorption of classical binary liquid mixtures shows a very steep increase at the approach of the critical point. This effect arises from the coupling between the pressure and temperature changes associated with the propagation of ultrasounds and the fluctuations of concentration taking place in the system, which are characterized by an extended spectrum of relaxation frequencies. In binary mixtures ultrasonic absorption is capable of detecting critical concentration fluctuations already at temperatures some 20 O C below the critical temperature TC.l1-l3 Nevertheless our first ultrasonic absorption study of nonionic surfactant solutions which involved C I ~ Efailed ~ ' ~to reveal any absorption associated with critical effects, even close to Tc. To explain this result as well as qualitatively similar ones found for various microemulsion systems14 we argued that the characteristic frequency f associated with the concentration fluctuations was much too small with respect to the ultrasonic frequency at which the measurements were performed (4-20 MHz). This explanation appeared to be supported by an order of magnitude estimate off based on data reported for micro emulsion^.^^ These estimates, however, have been reconsidered in view of recent data for nonionic surfactant solutions (see below).' There was another reason for which an ultrasonic absorption study of nonionic surfactant solutions appeared worth undertaking. Indeed ultrasonic absorption has proved to be a useful tool for gaining information on the dynamics of the exchange of surfactant between micelles and the bulk in the case of ionic N o such studies have been performed yet for nonionic surfactants and no experimental data are available for the rate constant for the exit of a nonionic surfactant from, or its association to, the micelles. The present study involved ultrasonic absorption measurements on aqueous solutions of three nonionic surfactants: C&3, C6ES, and C8E6. These surfactants were selected because they have fairly large critical micellization concentrations (cmc) and critical concentrations (Cc, see Table I) contrary to C1&,.l The fairly 'On leave of absence from the CSIR, Regional Research Laboratory, Petroleum and Natural Gas Division, Jorhat (Assam), India.

TABLE I: Values of the Cmc, Critical Concentration, and Critical Temperature of the Investigated Surfactants M,," dmol cmc, M C," M Tp,b O C C6E3






0.1 O C

0.600*d 0.606 0.215

-0.16 0.0099c

0.178 =iO.l86*g 0.191

44.7*d 44.8e 47.8e 75*c 86e 71-76*' 74.8e

Molecular weight. bThe values with an asterisk represent the critical concentration and critical temperature reported in the corresponding references. The other Tc values are the cloud temperature at the listed concentration. CFromref 1. dFrom ref 3b. #Obtainedas part of this work. fProbably slightly larger than 0.10 M, from trends in Table 1 in ref 1 . gOn the basis of the C, values reported for CBE4(ref 3a) and C8E5(ref 2). low value of the critical temperature of C6E3(see Table I) makes ultrasonic measurements possible even very close to Tc with our setup. Moreover, the large Cc values help our understanding of the ultrasonic absorption behavior of nonionic surfactants close (1) Degiorgio, V. Physics of Amphiphiles: Micelles Vesicles and Microemulsions; Degiorgio, V., Corti, M., Eds.;North Holland: Amsterdam, 1985 and references therein. (2) Zulauf, M.; Rosenbuch, J.-P. J . Phys. Chem. 1983,87, 856. Zulauf, M.: Havter. J. Colloid Polvm. Sci. 1982. 260. 1023. Zulauf. M.: Weckstrom. K.; HGter, J.; Degiorgid, V.; Corti, M. J . Phys. Chem. 1985, 89, 3411. (3) (a) Corti, M.; Degiorgio, V.; Zulauf, M. Phys. Rev. Lett. 1982, 48, 1617. Corti, M.; Degiorgio, V. Surfactants in Solutiotu; Mittal, K., Lindman, B., Eds.; Plenum: New York, 1984; p 471. (b) Corti, M.; Minero, C.; Degiorgio, V. J. Phys. Chem. 1984, 88, 309. (4) Magid, L.; Triolo, R.; Johnson, J. J. Phys. Chem. 1984, 88, 5730. (5) Kato, T.; Seimiya, T. J . Phys. Chem. 1986, 90, 3159. (6) Zana, R.; Weill, C. J . Phys. Lett. 1985, 46, L-953. (7) Di Meglio, J.-M.; Paz, L.; Dvolaitzky, M.; Taupin, C. J. Phys. Chem. 1984, 88, 6036. (8) Fixman, M. J . Chem. Phys. 1962, 36, 310, 1957. (9) Kawasaki, K. Phase Transitions and Critical Phenomena; Domb, C., Green, M. S.,Eds.; Academic: New York, 1976. (10) Blandamer, J.; Waddington, D. Adu. Mol. Relaxation Processes 1970, 2, 1 . (11) Labowski, M. Acousr. Lert. 1978, 2, 130; 1979, 3, 37. (12) Anantaraman, A.; Walters, A.; Edmonds, P.; Pings,C. J. Chem. Phys. 1966, 44, 2651. (13) D'Arrigo, G.;Sette, D. J . Chem. Phys. 1968, 48, 691. (14) a n a , R.; Lang, J.; Sorba, 0.; Cazabat, A. M.; Langevin, D. J . Phys. Lett. 1982, 43, L-829(15) Graber, E.; Lang, J.; Zana, R. Kolloid Z . Z . Polym. 1970, 237,470. Graber, E.; Zana, R. Kolloid Z . Z . Polym. 1970, 237, 479. (16) Zana, R.; Yiv, S. Can. J . Chem. 1980, 58, 1780. (17) Kaneshina, S.; Ueda, I.; Kamaya, H.; Eyring, E. Biochim. Biophys. Acta 1980, 603, 237.

0022-365418712091-5957$01.50/0 0 1987 American Chemical Society


Borthakur and Zana

The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 ~ 1 0Y ' ~ d l f ' i l c " ~ '~ l







Ti'C)~ I























Figure 1. Variation of the ultrasonic absorption of a 0.606 M C6E3 solution with temperature at 3.96 (X); 6.49 ( 0 ) ;9.06 (0); and 11.65 (+)

Figure 2. Variation of the ultrasonic absorption of a 0.215 M C6E3 solution with temperature at 3.96 (X); 6.49 (0);9.06 (0); and 11.65 (+)



to Tc (see below). Finally, our previous studies of ionic surfactant solutions'5,16show that large cmc values are usually associated with exchange processes with relaxation frequencies in the megahertz range investigated in the present study.

Experimental Section The samples of C6E3, C6ES,and CsE6 were gifts from Drs. Platone and Cesari (Eniricerche, San Donato Milanese, Italy). These compounds were purified by molecular distillation. Some of their characteristics are listed in Table I. It can be seen that the cloud temperatures measured as part of the present work agree well with the reported ones.' The ultrasonic absorption measurements were performed by the standard pulse techniquel4-I6 at 3.96, 6.49, 9.06, and 11.65 MHz. Results and Discussion I . Ultrasonic Absorption and Critical Effects in Aqueous Micellar Solutions of Nonionic Surfactants. The ultrasonic absorption of two C6E3solutions was measured as a function of T u p to the phase separation temperature where the solutions were extremely cloudy but still monophasic. A contribution of critical fluctuations of the micelle concentration to the measured ultrasonic absorption should show as an increase of the ultrasonic absorption a/f ( a is the absorption coefficient in m-l; f i s the ultrasonic frequency in Hz) with T, becoming very steep at T close to Tc.11-13 Clearly, the results plotted in Figures 1 and 2 do not show this behavior. Thus for the 0.215 M solution a/f goes through a maximum and then decreases monotonously as T increased to Tc. For the 0.606 M solution which nearly corresponds to the critical concentration (see Table I) a/f decreases continuously as T i s increased: the absorption is the largest at the lowest T investigated, some 30 OC below Tc. At such low T the contribution of critical fluctuations, if any, would be extremely small. Thus our results show no evidence of a contribution of critical effects in the investigated frequency range. These results confirm and extend those for CI2E6l4(the only example of such study to our knowledge). Recall that the characteristic frequency f* associated with the dominant concentration fluctuation of correlation length is given

f* = k ~ / 1 2 ~ , { 3


where 7 is the solution viscosity, which is typically about 2 In our earlier estimate off*, 5 was taken as 40 nm14 and resulted inf* N 0.3 kHz." Since then, however, values of 5 have been reported for nonionic surfactant solution^.'^^^ Thus for C6E3,{ = 4.5 nm at 3 "C below TC,3bleading t o p = 0.2 MHz. This ~~~

(18) Aniansson, E. A. G . ;Wall, S. J . Phys. Chem. 1974, 78, 1024; 1975, 79, 857.

Figure 3. Effect of the surfactant concentration on the ultrasonic absorption of C6E3solutions at 3.96 (X); 6.49 (0);9.06 (0); and 11.65 (+) MHz and 25 OC.

value is about 20 times lower than the lowest frequency at which our measurements were performed. Nevertheless any contribution of critical fluctuations to the absorption of the solutions should have still been measurable, particularly for the 0.606 M C6E3 solution (this concentration is very close to the critical concentratiodb), in view of data reported for binary mixture^.^^-'^ The absence of any measurable effect suggests that the critical concentration fluctuations in nonionic surfactant solutions are not well coupled to the sound waves. Recall that the amplitude A of the ultrasonic relaxation (see below) involves the correlation length of the fluctuations and also the changes of thermodynamic parameters associated with the fluctuations. If these changes are small, A is also small. In nonionic surfactant solutions, the fluctuations of the micelle concentration responsible for the critical behavior' do not affect the environment of the surfactant, as it remains in the micelles, and therefore do not affect its thermodynamic properties. (This is well documented for the surfactant molar volume.") The same reasoning holds for the recently evidenced processes by which nonionic micelles collide and merge temporarily upon c ~ l l i s i o n .From ~ ~ ~ the above it would appear that no contribution of critical effects to the absorption of the solutions is detected in the megahertz range mainly because the changes of thermodynamic parameters associated with micelle concentration fluctuations and micelle collisions with merging are very small. The fact that the frequency range investigated is well above the evaluated characteristic frequency f* for the micelle concentration fluctuations probably also contributes to the failure to observe an absorption due to critical effects. Measurements at frequencies down to 0.2 MHz are planned in future work. 2. Ultrasonic Absorption and Micelle Formation. For C6E3 and C6E5solutions the a/p vs. concentration C curves in Figures 3 and 4 show a sharp break and a nearly linear increase which,

The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 5959

Ultrasonic Absorption of Nonionic Surfactants

005 -+ o

l 0


0 0.15

C i M 0.20 kJ L

Figure 4. Effect of the surfactant concentration on the ultrasonic absorption of C6E5solutions at 6.49 (0);9.06 (0); and 11.65 (+) MHz and 25 OC. f IMHrl I





1 8 9 1 0 12

Figure 6. Effect of the frequency on the ultrasonic absorption of 0.215 M (-- -) and 0.606 M (-) C6E3solutions at 15 OC ( 0 ) ;25 OC (+); and 45 OC (0).

3. Preliminary Quantitative Analysis of the C& Absorption Data in Terms of Surfnctant Exchange. The surfactant exchange process can be represented as














C I M / fII 010


Figure 5. Effect of the surfactant concentration on the ultrasonic absorption of C8E6solutions at 6.49 (0);9.06 (0); and 11.65 (+) MHz and 25 OC.

when extrapolated to low concentration, yields the cmc values 0.14.105 M for C6E3and 0.115 M for C6ES. Our value for C6E3 is in excellent agreement with that listed by Degiorgio.’ No cmc value has been reported for C6ES. However our value, about 10% larger than for C6E3,is in line with what can be expected when considering the reported 15% increase of cmc in going from C8E4 to C8Es’ The results in Figure 3 for CsE3are qualitatively similar and quantitatively close to those previously obtained for alkali metal decanoates, which also have a cmc close to 0.1 M.15 Thus, the a/f vs. C curve goes through a maximum at low frequency (3.96 MHz), and this maximum is shifted to higher concentrations as the frequencyfis increased. For C6ESthe maximum was not observed because the measurements did not extend to sufficiently high concentration and also because the lowest frequency was 6.49 rather than 3.96 MHz. The a/f vs. C curves of Figure 5 for C8E6yield apparent cmc’s ranging from 0.016 to 0.019 M, that is larger than the reported value’ of 0.01 M. This difference arises from the fact that the measurements of Figure 5 were performed at too high a frequency, owing to experimental constraints. Recall that the ultrasonic absorption studyI4J5of alkali metal carboxylates has shown that cmc’s as low as 0.01 M can be obtained from the a/f vs. C plots only if the measurements are performed at sufficiently low frequency, say 1 MHz. However, the absorption of the C8E6solutions was too low to be measured a t such frequency with the pulse method used in the present work and this resulted in large apparent cmc’s. Finally, the comparison of the results for C6E3(and C6ES)and C8E5shows that the values of a/f are generally much larger for the hexyl surfactants, except at concentrations close to the cmc, in the frequency range investigated. Again a similar result has been found for the alkali metal soaps.1s The analogy between the ultrasonic absorption behaviors of the investigated nonionic surfactants and alkali metal soapsIs as far as the concentration and surfactant chain length dependences of the ultrasonic absorption are concerned leads to the conclusion that this absorption probably arises from the perturbation of the surfactant exchange equilibrium between micelles and the bulk by the ultrasonic waves.17

where S is a monomeric surfactant and Si and Si-1 two micellar species of aggregation numbers i and i - 1. Within the approximations of Aniansson and Wa1118 treatment of micellar kinetics, the relaxation frequencyfR and the ultrasonic relaxation amplitude A are given uz C - cmc

A = 0.05

dv Avoz k-- (C - cmc) RT fRZ N



where k- is the rate constant for the exit of a surfactant from the micelle having the average aggregation number N determined by classical methods; AVOis the volume change associated with this reaction; u characterizes the width of the micelle size distribution curve which is assumed to be Gaussian;18 d is the density of the solution; v is the velocity of ultrasound in the solution, T the temperature, and R the gas constant. A is expressed in m-’ s2. Moreover, the rate constant k+ for the association of a surfactant to the micelle is given byz1 k+ = k-/cmc


Finally, the concentration C, where the a/f vs C curve goes through a maximum is given by16

Equations 3-5 permit the determination of k-, k+, u, and AVOfrom the values of A , fR, N , and cmc. The values of A and fR can be obtained from the fit of the a / f vs. f data to the relaxation equation a



+ (f/fR)’

+ B


where B is a constant. Such a fitting procedure requires a/f data (19) In ref 14, f* was incorrectly given as 1.2 kHz. (20) Teubner, M. J . Phys. Chem. 1979, 83, 2917. (21) Aniansson, E. A. G.; Wall, S.;Almgren, M.; Hoffmann, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J . Phys. Chem. 1976, 80, 905.


The Journal of Physical Chemistry, Vol. 91, No. 23, 1987

TABLE II: Values of A , B , and f, for C& Solutions at Various Temperatures T, OC 10"A, m-I s2 fn, MHz 10l5B,m-] sZ


C = 0.215 M 4530 f 1500 2.1 f 0.5 4500 f 1200 2.3 f 0.5 2500 f 500 2.7 f 0.5

60 f 20 70 f 20 75 f 20

15 25 45

C = 0.606 M 3200 f 1000 5.2 f 0.5 1800 f 400 6.15 i 0.6 1210 f 300 5.7f 0.7

300 f 80 250 f 80 175 f 50

15 25

in a wide frequency range. This is clearly not the case for the data obtained in the present study, shown in Figure 6. Nevertheless these results are sufficient for a preliminary analysis of the surfactant exchange in C6E3solutions. The values OffR and A have been obtained by plotting the quantity (a/f - B)-' vs. f . B was adjusted as to obtain linear plots, from whichfR and A were determined. The results are listed in Table 11. The errors are fairly large but it can be seen that fR increases with the surfactant concentration Cas predicted by eq 3 and increases little with T, whereas A decreases much as T increases. Similar results have been reported for ionic surfactants.22 In what follows only the results at 25 OC are analyzed as neither the cmc nor the N values have been reported a t 15 and 45 O C . The N value at 25 O C has not been reported either. Therefore, for the evaluation of the rate constants, N was taken as 40 on the basis of the reported value2 of 70 f 5 for C8E5,and on the assumption that N w , / N c g E , = (6/8)2. Assuming further a linear increase offR with c (see eq 3) in the C range investigated, we obtained

k- = (2.5 f 1) X lo8 s-' k+ = (2.5 f 1)


lo9 M-Is-l

(r=6f2 The average residence time of C6E3in the micelle is thus TR = N / k - = 0.15 ps. The value of k- for C6E3 is close to that for sodium nonyl sulfate2' or potassium decanoate15which have nearly the same cmc as C6E3. Also k+ is large, close to the diffusioncontrolled value as for ionic surfactants.2' Finally the micelle polydispersity is very low, as for ionic surfactants not too far from the cmc2' Indeed the polydispersity index, the ratio of the weight average and number average aggregation numbers, is N,/N, = 1 d / h R a! 1.02. Equation 6 permits a test of the self-consistency of the experimental results. Inserting the values of k-/N and k-/$ obtained from thefR vs C plot yields C, = 0.52 f 0.12 M for the concentration where the absorption is maximum at 3.96 MHz, while the experimental value is seen to be 0.38 f 0.05 M in Figure 3. Thus as far as k+, k-, and a values are concerned the nonionic surfactant C6E3behaves very similarly to ionic surfactants having the same cmc. For the time being, however, this conclusion is restricted to a temperature some 20 OC below Tc, that is, far from Tc. However, one cannot exclude that close to Tc the dynamic behavior of nonionic surfactants would become different from that of ionic surfactants of comparable cmc. The values of k-/N,fR, and A have been used to evaluate AVO from eq 4, taking d = 1 g/cm3 and u = 1.5 X lo5 cm/s. We thus found AVO= 3.1 f 0.5 and 2.7 f 0.5 cm3/mol at C = 0.215 and 0.606 M, respectively, that is, an average value of 2.9 f 0.5 cm3/mol. There has been no report for the value of the volume change upon micellization of C6E3. However, the above value appears reasonable in view of the following results. (i) Volume changes of about 3 cm3/mol have been reported upon micellization of three nonionic surfactants with a hexyl chain:


(22) Rasing, J.; Sams, P.; Wyn-Jones, E. J . Chem. SOC.,Faraday Trans. 2 1973, 69, 180.

Borthakur and Zana C6H13SO(CH2),0H,with i = 2, 3, and 4.23 (ii) The volume change upon transfer of 1-hexanol from the aqueous phase to sodium decyl or dodecyl sulfate micelles is of about 2.6 ~ m ~ / m o l . ~ ~ One last point deserves discussion. The B values in Table I1 are significantly larger than the a/f value for pure water (21 X 10-15 m-l s2 at 25 "C). The differences reveal the existence of a second relaxation process taking place at a frequency higher than the surfactant exchange process. Recall that ionic surfactant solutions also show a second ultrasonic relaxation process which is faster than the surfactant exchange and which is detected only at fairly large concentration^.'^^^^^^ This faster relaxation process has been shown to be sensitive to the micelle shape15and has been attributed in separate studies to a dynamic equilibrium between "surfactant-bound" water molecules and free water moleculesZ5 and to a fast equilibrium between micelle-bound counterions and free counterions in ionic surfactant solutions.26 In view of the fact that this fast relaxation process is observed with both ionic and nonionic surfactant solutions, the second assignment may not be correct. At this stage it is noteworthy recalling that there has been numerous ultrasonic absorption investigations of aqueous solutions of alcohols (1-propanol, 2-propanol, 2-butanol, 1-butanol, ...)27+28 as well as butoxyethanol (C4E1, see above)29and diethylene glycol monobutyl ether (C4E2):30 These systems have some ultrasonic absorption charactenstics similar to those of the nonionic surfactants investigated in this work and of ionic surfactants. In particular a second relaxation process is very often observed, which takes place at high frequencies and which has been attributed to water-alcohol interactions (hydration). Such a process may be responsible for the high-frequency relaxation characterizing the nonionic surfactant solutions investigated.

Conclusions The present study did not reveal any contribution of critical fluctuations of the micelle concentration to the ultrasonic absorption of aqueous solutions of C6E3close to its critical temperature at frequencies above 3.9 M H z in contradistinction of classical binary mixtures close to the critical point. The measured ultrasonic absorption appears to arise essentially from the perturbation by the sound waves of the surfactant exchange equilibrium between micelles and the bulk. From the data it has been possible to estimate the rate constants for the association of C6E3to, and its exit from, the micelles, as well as the width of the micelle size distribution curve and the volume change upon association of one surfactant to the micelles. The rate constants are close to those for sodium decanoate, which has the same cmc as C6E3. The micelle polydispersity is small. These results show that far from Tc nonionic surfactants behave very much like ionic surfactants having the same cmc. Acknowledgment. A.B. thanks the C N R S for financing his stay in Strasbourg under the CSIR-CNRS exchange program. We thank Drs. Platone and Cesari from Enirecerche (Italy) for generously donating the samples of nonionic surfactants used in the present investigation. Registry NO. C&3,25961-89-1;C&, 86674-95-5; CsE6,4440-54-4. (23) Corkill, J.; Goodman, J.; Walker, T. Trans. Faraday SOC.1967, 63, 768. (24) Manabe, M.; Kikuchi, S.; Katayama, S.; Tokunaga, S.; Koda, M. Bull. Chem. SOC.Jpn. 1984,57, 2027. Manabe, M.; Shirahama, K.; Koda, M. Bull. Chem. SOC.Jpn. 1976, 49, 2904. Vikingstad E. J . Colloid Interface Sci. 1979, 72, 75. (25) Tiddy, G.; Walsh, M.; Wyn-Jones, E. J. Chem. Soc., Faraday Trans. 1 1982, 78, 389. (26) Diekmann, S. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 528. (27) Blandamer, M.; Hidden, N.; Symons, M.; Treloar, N. Trans. Faraday SOC.1968, 64, 3242 and references therein. (28) Nishikawa, S.; Mashima, M.; Yasunaga, T. Bull. Chem. SOC.Jpn. 1976, 49, 1413. Tamura, K.; Maekawa, M.; Yasunaga, T. J . Phys. Chem. 1977, 81, 2122 and references therein. (29) Kato, S.; Jobe, D.; Rao, N.; Ho, C.; Verrall, R. J . Phys. Chem. 1986, 90, 4167. (30) Nishikawa, S.; Shibata, M. Bull. Chem. SOC.Jpn. 1984, 57, 2357.