Nuclear magnetic resonance study of alkylammonium chlorides. 1. Proton longitudinal relaxation times and linewidths of isotropic micellar medium

Nuclear Magnetic Resonance Study of Alkylammonium Chlorides 1. Proton Longitudinal Relaxation Times and Linewidths of Isotropic Micellar Medium H. NERY, J. P. MARCHAL, AND D. CANET Laboratoire de Chimie Theorique (Equipe de recherche associOe au CNRS No. 22), Universitk de Nancy I, Case Officielle 140, 54037 Nancy Cedex, France AND

J. M. CASES Centre de Recherche sur la Valorisation des Minerais (Laboratoire associ~ au CNRS No. 235), Ecole Nationale SupOrieure de Ggologie, B.P. 452, 54001 Nancy Cedex, France Received July 24, 1979; accepted December 12, 1979 The binary systems D20-n-alkylammonium chloride (with 8, 10, 12, and 14 carbons in the aliphatic chain) have been studied as a function of concentration and temperature. Based on the evolution of proton longitudinal relaxation times (T,) and linewidths, two different aggregates have been characterized. The first one appears at the classical critical micellar concentration (CMC) which is shown to be almost independent of temperature. The concentration at which the second type (presumably rod-shaped micelles) is formed is, on the contrary, strongly temperature dependent. It is demonstrated that forces involved in the formation of these two aggregates are of a different nature. The curves representing T1 variations as a function of concentration are satisfactorily interpreted by assuming a simple mass action law model. It is further shown that the CMC value can be approximated by K t-'/~, where K is the equilibrium constant and n the average number of molecules per micelle. INTRODUCTION

concerning the role of water in such systems. The other NMR parameters of interest are relaxation times, linewidths, and lineshapes. They are related to molecular dynamics and can therefore be very useful in studying surfactant aggregates. Proton longitudinal relaxation times of water and surfactant methylenes were very early investigated by continuous-wave methods (11). More recently, carbon-13 longitudinal relaxation times were measured in order to study segmental motion, local and overall mobility (12, 16), and electrolyte-induced phase transitions (17). On the other hand, proton NMR bandshapes have been related to the type of aggregate and especially to look at the changes from isotropic micellar medium toward liquid crystalline states

NMR techniques are now widely used for studying ionic and nonionic surfactants and especially lyotropic phases formed by these systems in aqueous solutions (1). NMR has proved also to be a valuable technique for determining structural and dynamical properties of isotropic phases involving globular or rod-shaped micelles. Up to the present time, the chemical shift has been the parameter most widely used. Proton (2, 3), fluorine-19 (4, 7), carbon-13 (8, 10), and counterions (9, 25) (23Na, 'a3Cs, 3~C1) were investigated in order to determine critical micellar concentrations and aggregation numbers, to study exchange phenomena among micelles, and to obtain information 174

0021-9797/80/090174-08502.00/0 Copyright © 1980 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 77, No, 1, September 1980

NMR OF ISOTROPIC

MICELLAR

MEDIUM

175

(18, 19). In a similar manner, longitudinal (T1) and transversal (T2) relaxation times and line broadening have been used to monitor the formation of rod-like micelles from spheres (19, 20, 26). Furthermore, it has been extensively shown that the width of counterion resonances (35C1, 81Br, 23Na) may be used for determining, among other things,, critical micellar concentrations (21-25). We wish to present here a systematic study of the system alkylammonium chloride-water as a function of temperature and concentration. The concentration range has been chosen in order to investigate the isotropic micellar systems (relevant work at higher concentrations will be published later). We show in this paper that the longitudinal relaxation time (T~) is particularly well suited for determining the critical micellar concentration. Furthermore, the interpretation of the T1 and linewidth variations leads to additional information concerning in particular the equilibrium constant and the micelle size. It is worth mentioning that proton NMR is fairly easy to perform and allows the investigation of low-concentration solutions. The aim of the present work is to show that NMR might be an interesting alternative to other techniques in determining CMC although it has surprisingly been disregarded; furthermore, owing to the fact that this type of spectroscopy provides information at the molecular level, it is capable of monitoring aggregate and mobility changes in a more detailed and accurate fashion than conventional techniques frequently used in such studies (35).

Paris, France) and recrystallized five times in ether. They were dissolved in D20 at a series of concentrations varying according to k.10 -~, where k is an integer smaller than 10 and 1 is chosen in order to detect the CMC. l is decreased until lyotropic phases appear. NMR proton measurements have been performed at 90 MHz with a Bruker HX90 interfaced to a Nicolet 1080 computer (Centre Rdgional de Mesures' Physiques de l'Acad6mie de Nancy-Metz); 5-mm-o.d. tubes were employed, the deuterium signal of D20 allowing the field frequency stabilization. All the CH2, except those at the extremity of the chain, resonate at approximately the same frequency and yield a single peak whose linewidth is of the order of 5-10 Hz at low concentration. Longitudinal relaxation times and linewidths of this latter resonance have been followed as a function of the concentration for three different temperatures (25, 40, and 70°C), except for the surfactant with 14 carbons whose solubility is insufficient at 25°C. The spectra were recorded in the Fourier transform mode (with a spectral width of 600 Hz). The longitudinal relaxation times are measured according to the well-known inversion recovery method (27) and using experimental procedures previously described (28). An exponential behavior was found in all cases. This may appear surprising since a priori, the proton relaxation time should change from one methylene to the other. Since a single line represents most of the protons of the chain, its recovery should be a sum of exponentials. However, it is well known that a sum of exponentials leads in many instances to the appearance of a single exponential. Furthermore, owing to the complexity of the whole spin system, EXPERIMENTAL dipolar cross relaxation (from which origFour cationic surfactants have been stud- inates the so-called "spin diffusion" pheied. These are n-alkylammonium chlorides nomenon occurring for instance in prowith nc = 14, 12, 10, and 8, nc being the teins (37)) has probably a significant connumber of carbon atoms in the aliphatic tribution and might explain the single-exchain. They have been kindly provided by ponential behavior of the recovery curves. CECA S.A. (16, rue David d'Angers, 75019 Other lines in the spectrum, i.e., those Journal of Colloid and Interface Science, Vol. 77, No. 1, September 1980

176

NERY ET AL.

arising from D20, CH3, and N H +, were disregarded in this study.

c m.1-1) 10.

J

RESULTS

A typical result is presented graphically in Fig. 1. The break in the plot of T~ versus concentration obviously corresponds to the micelle formation. For all systems investigated, except the octylammonium chloride, such an abrupt variation was observed, although less pronounced at high temperatures. For octylammonium chloride, a similar total decrease of TI was observed but over a much larger concentration range (Fig. 2). The linewidths have a distinct behavior. Their variation at the CMC was weak and probably obscured by the broadening due to magnetic field inhomogeneities. The striking feature is the dramatic broadening which

/ 1,0

1 0 -1

/

10 -2

:2

c m.1-1)

-1

\

-2

.2

1'.4

.6

1.

T~(CH~)

1A S.

10.

20. h ~ (CH2)

6.

10.

1'4,

A v (cH,> H z.

FIG. 2. Proton (CH~ of the aliphatic chain) longitudinal relaxation time and linewidth versus amphiphile concentrations (moles per liter) for the system octylammonium chloride/deuterium oxide.

J 10

i.

T~ (CH~) S.

1.0

10

.6

30. H z.

FIo. 1. Proton (CH2 of the aliphatic chain) longitudinal relaxation time and linewidth versus amphiphile concentrations (moles per liter) for the system dodecylammonium chloride/deuterium oxide. Journal of CoUoid and Interface Science, Vol. 77, No. 1, S e p t e m b e r 1980

appeared at higher concentrations and which was not accompanied by a T1 modification (the only exception again concerns the octylammonium chloride for which a simple monotonic increase of linewidths was observed). This behavior will be discussed below and is attributed to the transformation of spherical (or ellipsoidal) micelles to rod-shaped micelles. The concentrations corresponding to the beginning of the breaks in T1 and linewidth plots are reported in Table I. The quoted errors essentially arise from the uncertainties of N M R measurements (of the order 5% for T0. DISCUSSION

We must first explain, at least qualitatively, the behavior of both the longitudinal

177

NMR OF ISOTROPIC MICELLAR MEDIUM

relaxation times and the linewidths. It is well known that these two parameters are directly related to molecular motion. However, it would be illusory here to attempt a quantitative interpretation for the following reasons: (i) The only effective mechanism for proton relaxation is via dipolar coupling. It is impossible to separate the various contributions to this. (ii) The measured quantities represent an average of almost all the methylenes of the aliphatic chain. (iii) As a consequence, a formidable number of parameters including, among others, those related to internal rotation and to

anisotropic overall mobility would be required to properly describe the relaxation behavior in such systems. However, at and above the CMC, rotation around the micelle must contribute to T1 as suggested by Staples and Tiddy (26). Consequently a sharp decrease of T1 is expected. The fact that T1 remains constant above the CMC, while at higher concentration the linewidth increases dramatically, is more intriguing. A similar phenomenon has been observed and discussed by Staples and Tiddy (26) who studied via T1 and linewidth measurements the evolution of micelles induced by addition of sodium chloride. Following this work, there is no

TABLE I Concentrations in Moles per Liter at Which Appear the Two Types of Aggregates under Investigation a 25°C

40°C

70°C

0.25 _+ 0.02 0.039 )b 0.004713

0.25 ± 0.02 (0.039 ~0.004713 )

0.23 ± 0.02 (0.032 \ 0.003867 )

0.055 ± 0.002 0.0095 0.00098) 0.75 -+ 0.03 0.136 0.01406)

0.045 ± 0.003 {0.0088 ~0.00091 ) 1.1 -+ 0.1 [ 0.235 ~0.02428 )

0.055 _+ 0.004 {0.0095 ~0.00098 ) 1.2 ± 0.2 {0.327 ~0.03380 )

0.013 ± 0.001 0.0026 0.00023) 0.27 ± 0.02 0.055 (0.00497)

0.011 ± 0.005 [ 0.0025 \0.00023) 0.50 ± 0.02 [ 0.096 \0.00867 )

0.012 ± 0.001 {0.0025 \0.00023) 1.0 ± 0.2 (' 0.185 (0.01670)

0.0035 _+ 0.0005 0.0008 I 0.00006 ] O. 17 ± 0.03 0.036 / 0.00289 ]

0.0055 ± 0.0005 [ 0.0012 \0.00010 ] 0.35 + 0.05 (0.078 ~0.00625 ]

C8

CMC a

C10

CMC

Rod-shaped micelles

Ca2 CMC

Rod-shaped micelles

Ci4

CMC

Rod-shaped micelles

CMC is the conventional critical concentration referring to globular micelles, b Numbers in parentheses are weight percentages of alkylammonium chloride, and below concentration expressed in mole fraction. Journal of Colloid and Interface Science, Vol. 77, No. 1, September 1980

178

N E R Y ET AL. T A B L E II Coefficients a and b of the Relation In (C) = a n t + b for the Critical Concentrations at Which Appear Globular and Rod-Shaped Miceltes ~ Globular micelles

a b Correlation coefficient

Rod-shaped micelles

25oc

40°c

70°c

-0,755 0.66

-0.72 0.34

-0.62 -0.69

-0.9997

-0.9988

-0.9938

25°c -0.52 0.94

4&c

70°c

-0.53 1.61

-0.42 0.88

-0.9998

-0.9955

a C expressed in mole fraction.

doubt that the rapid increase of linewidth The slopes depend slightly on temperaindicates the formation of larger (rod-like) ture and are in good agreement with results micelles. Further measurements involving previously published (31-33), the value of carbon-13 relaxation, which are being per- a being considered as equal to A g / 2 k T , formed in our laboratory, should provide where Ag represents the energy variation additional information on the dynamics of corresponding to the transfer of a methylene these larger micelles. For the moment, we from the micellar to the aqueous phase (34). just consider this linewidth increase as The concentration at which larger miphenomenologically yielding a second "criti- celles (presumably rod shaped) appear is, on cal concentration." the contrary, strongly temperature deAlso, it must be mentioned that formation pendent. This is not surprising since forces of rod-shaped micelles due to the increase involved in the formation of these agof surfactant concentration or addition of gregates correspond to a move from a nonsalt had previously been detected by NMR aqueous environment to another. of counterions (22, 24), nitrogen-14 NMR It is, however, noteworthy that we obtain (20), carbon-13 relaxation (15, 17), or by again a linear plot of these concentrations other techniques (29, 30). It is, however, as a function of the number of carbons in noteworthy that this type of information, as the aliphatic chain. Furthermore, the slopes evidenced by the present work, can be very of these lines are similar to the ones presimply extracted from proton NMR. viously obtained for the critical micellar We shall now discuss the CMC values. A concentrations (see Table II). This property first remark can be made about their almost might indicate that the transfer energy complete independence on temperature. variation relative to a methylene is approxiThis is in agreement with previous work on mately the same regardless of the conother systems (5, 31), although no satis- sidered phase and confirms what has been factory theoretical explanation can be predicted on the basis of thermodynamical given. It is well known (31, 32) that the considerations (34). The behavior with relogarithm of CMC depends linearly on the spect to temperature then arises from number of carbons of the aliphatic chain. modifications of the external forces. This property is again verified here. The coThe variation of T1 around the CMC efficients a and b, of the equation In (CMC) merits further consideration. In order to fit = a n o + b are reported in Table II, together the experimental data with a theoretical with their correlation coefficients. In this model, let us define K as the equilibrium latter equation, nc is the number of carbons constant between monomeric amphiphile in the aliphatic chain; the CMC must be [X] and small globular micelles [Xn]. K may be written expressed in mole fraction. Journal of Colloid and Interface Science, Vol. 77, No. 1, September 1980

179

NMR OF ISOTROPIC MICELLAR MEDIUM TABLE III

Ris and Rim are determined from the two straight portions of the plot of T1 versus Ct. Combining [1] and [2] and defining x as

Determination of the Quantity K - ~ " from the Experimental T~ Values Octylammonium chloride (Ram = 0.4, Rz~ = 1.54) C M C = 0.25

Decylammonium chloride (Rzm - 0.53, R ~ = 1.611 C M C - 0.0050

Kl[n Ct ~

0.2 0.3 0.4 0.5 0.6 0.8 1 2

R~°

0.43 0.50 0.64 0.72 0.81 0.89 0.91 1.16

0.21 0,29 0,33 0.38 0,41 0,48 0,58 0,70

0.70 0.76 1.14 1.52 1.47 1.64

Ct

R~

0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.3 0.4 0.5 0.6

0.59 0.73 0.85 0.88 0.95 1.08 1.21 1.32 1.41 1.41 1.49

(n = 100)

0.061 0.061 0.060 0.064 0.065 0.078 0.078 0.088 0.078 0.097 0,070

Tetradecylarnmonium chloride (Rm = 0.714, R ~ = 1.780) CMC = 0.0035

0.0108 0.0121 0.0134 0.0102 0.0153 0.0143

4" 10-3 6" 10-3 8" 10-3 10-2

0.750 0.986 1.087 1.316

0.00415 0.00475 0.0055 0.00456

a Ct is the total concentration (moles per liter) in amphiphile. R1 is the inverse of experimental T1.

K -

[Xn] IX]

n

-

CJn (Cm)

;

[1]

n

n is the average number of molecules per micelle, Cs is the concentration of molecules engaged in micelles, and Cm is the concentration of monomers. The observed relaxation rate (the inverse of the longitudinal relaxation time) can be expressed as a function of the relaxation rate of the molecule in the micelles (R~) and of the relaxation rate of the m o n o m e r (Rim). If we denote by Ct the total concentration in surfactant, we obtain C~ Ct - C~ R1 = C t RI~ + Ct Ram ;

R1 - Rim

[3]

Rls - R m

K it,

(n - 100)

Dodecylammonium chloride (R~m = 0.69, R ~ = 1.92) C M C = 0.013

0.01 0.012 0.02 0.03 0.04 0.06

x -

[2]

leads to [ X \-l/n

In principle [4] can be used to determine both the equilibrium constant K and the aggregation number n. Unfortunately, since C~H I ' / i s very close to Ct and since for the values occurring here ( x / n ) 1/, is almost constant and ranges between 0.6 to 0.8, K -~/'~ is the only quantity that we can extract from our experimental data. It must be mentioned that a similar analysis dealing with carbon-13 chemical shifts (8) has apparently yielded both n and K. We have preferred to calculate K -~l" for each concentration corresponding to the transition between the two straight portions of the T1 plot. This is achieved by using Eq. [4] and deducing x from the experimental Ti value. Such results, assuming n = 100 (this value, arbitrarily chosen, although realistic, has in fact very little influence), are reported in Table IlI and have been calculated for experimental data obtained at 40°C. These results show K -~/n to be constant for the decyl-, dodecyl-, and tetradecylammonium chlorides. The slight variations may be attributed to a distribution in micelle size which is concentration dependent (31). For the octylammonium chloride, a somewhat different behavior is observed. K -u" as determined through the application of Eq. [4] is by no means constant over the concentration range of interest regardless of the value of n. This is relevant to anomalies previously noted for small-chain-length amphiphiles (31). As previously noted (32), and as illustrated in Fig. 2, we confirm here Journal of Colloid and Interface Science, Vol. 77, No. 1, September 1980

180

NERY ET AL.

that below a given number of carbons in the aliphatic chain (no = 8) the micellization process extends over a large range of concentrations and is no longer relevant to the relations given above. Finally, by means of some approximations, relations [1] to [4] may be simplified to C~ = C~ - K -1In.

[5]

This suggests that the CMC must be of the order of magnitude of K -1/" which is the value taken by Ct when C~ becomes zero. This is in fact nicely confirmed by the experimental CMC values which have been repeated in Table III. Therefore, in spite of the crude approximations involved in the model used here, it provides a satisfactory description of the whole set of experimental data. It must be further noted that since the CMC is detected by means of an abrupt decrease in T1, the other data are redundant since this concentration can be identified as K -1/n. CONCLUSION

In this paper, we have demonstrated that proton NMR relaxation parameters (T1 and linewidths) are good candidates for determining critical concentrations at which globular or rod-shaped micelles appear. A detailed analysis of the experimental data has yielded two interesting conclusions: processes involved in the formation of these two types of aggregates are different in nature. The conventional critical micellar concentration is close to K -1In (K being the equilibrium constant and n the number of molecules per micelle). NMR seems therefore to be a good tool capable of providing experimental data which can be used in further theoretical and thermodynamical work and which thus leads to a better comprehension of the adsorption phenomena involved in these surfactants. This aspect will be emphasized in a future study involving both proton and carbonJournal of Colloid and Interface Science, Vol. 77, No. 1, September 1980

13 data relevant to the systems investigated here. ACKNOWLEDGMENTS This work has been supported by the D61figation G6n6rale ~. la Recherche Scientifique et Technique Grant 7-77-1556. REFERENCES 1. See, for example, "Lyotropic Liquids Crystals" (S. Friberg, Ed.). Advan. Chem. Ser. 152, Amer. Chem. Soc., Washington, D. C., 1976. 2. Clifford, J., and Pethica, B. A., Trans. Faraday Soc. 60, 1483 (1964). 3. Inoue, H., and Nakagawa, T., J. Phys. Chem. 70, 1108 (1966). 4. Hague, R., J. Phys. Chem. 72, 3056 (1968). 5. MOiler, N., and Birkhana, R. H., J. Phys. Chem. 71,957 (1967); 72, 583 (1968). 6. Bailey, R. E., and Cady, G. H., J. Phys. Chem. 73, 1612 (1969). 7. Mfiller, N., and Platho, F. E., J. Phys. Chem. 75, 547 (1971). 8. Persson, B. O., Drakenberg, T., and Lindman, B. J. Phys. Chem. 80, 2124 (1976). 9. Gustavsson, H., and Lindman, B., J. Chem. Soc. Chem. Commun., 93 (1973). 10. Ulmius, J., Lindman, B., Lindblom, G., and Drakenberg, T., J. Colloid Interface Sci. 65, 88 (1978). 11. Clifford, J., and Pethica, B. A., Trans. Faraday Soc. 61, 183 (1965); 61, 1277 (1965). 12. Alexandre, M., Fouchet, C., and Rigny, P., J. Chim. Phys. 70, 1073 (1973). 13. Roberts, R. T., and Chachaty, C., Chem. Phys. Lett. 22, 348 (1973). 14. Levy, G. C., Komorski, R. A., and Halstead, J. A., J. Amer. Chem. Soc. 96, 5456 (1976). 15. Williams, E., Sears, B., Allerhand, A., and Cordes, E. H., J. Amer. Chem. Soc. 95, 4871 (1975). 16. Henriksson, U., and Odberg, L,, Colloid Polym. Sci. 254, 35 (1976). 17. Kalyanasunderam, K., GrS.tzel, M., and Thomas, J. K., J. Amer. Chem. Soc. 97, 3915 (1975). 18. Lawsort, K. D., and Flautt, T. J., Mot, Cryst. 1, 241 (1966). 19. Ulmius, J., and Wennerstr6m, H., J. Magn. Reson. 28, 309 (1977). 20. Henriksson, U., Odberg, L., Eriksson, J. C., and Westmann, L., J. Phys. Chem. 81, 76 (1977). 21. Lindman, B., Wennerstr6m, H., and Forsen, S., J. Phys. Chem. 74, 754 (1%9). 22. Lindblom, G., and Lindman, B., J. Phys. Chem. 77, 2531 (1973).

NMR OF ISOTROPIC MICELLAR MEDIUM 23, Rosenholm, J. B., and Lindman, B., J. Colloid Interface Sci. 57, 362 (1976). 24. Ulmius, J., Lindman, B., Lindblom, G., and Drakenberg, T., J. Colloid Interface Sci. 65, 88 (1978). 25. Gustavsson, H., and Lindman, B.,J. Amer. Chem. Soc. 97, 3923 (1975). 26. Staples, E. J., and Tiddy, G. J., J. Chem. Soc. Faraday Trans. I, 2530 (1979). 27. Void, R. L., Waugh, J. S., Klein, M. P., and Phelps, D. E., J. Chem. Phys. 48, 3831 (1976). 28. Canet, D., Diter, B., and Marchal, J. P., J. Phys. E. 9, 939 (1976). 29. Kushner, L. M., Hubbard, W. D., and Parker, R. A . , J . Res. Nat. Bur. Stand. 59, 113 (1957). 30. Poukh, I. L., Kucher, R. V., Shevchuck, I. A.,

181

Serdyuk, A. I., Vashun, and L'vov, V. G., Zh. Prikl. Khim. 51, 1045 (1978).

31, Shinoda, K., Makagawa, T., Tamamushi, B. 1., and Isomura, T., "Colloidal Surfactants," p. 43. Academic Press, New York, 1963. 32. Cases, J. M., th6ses, Nancy, p. 80 (1967). 33, Predali, J. J., and Cases, J. M., "VI Internationalen Congress ftir Grenzfl~chenaktive Stoffe," p. 975. Carl Hanser Verlay, 1973. 34. Cases, J. M., Rev. Ind. Mindr. Ser. Mineral. 3, 197 (1979). 35. Mukerjee, P., and Mysels, J. K., Nat. Stand. Ref. Data Ser. Nat. Bar. Stand. No. 36 (1971). 36. Charvolin, J., and Rigny, P., J. Chem. Phys. 58, 3999 (1973). 37. Kalk, A., and Berendsen, J. C., J. Magn. Reson. 24, 343 (1976).

Journal of Colloid and Interface Science, Vol, 77, No, 1, September 1980