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13C relaxation measurements of molecular motion in micellar solutions
Volume
22, number
2
CHEMICAL
PHYSICS
1 October
LETTERS
1973
13C RELAXATION MEASUREMENTS OF MOLECULAR MOTION IN MICELLAR SOLUTIONS R.T. ROBERTS and C. CHACHATY Service de Chimie-Physique, Centre d’Etudes Nuckaires 91- Gif-sur- Yvette, France
Received
de Saclay,
23 July 1973
Measurements have been made of the 13C nuclear magnetic resonance longitudinal relaxation time T1 in micellar of added sodium chloride. The purpose of the exsolutions of sodium kauryl sulphate with different concentration periment was to see what effect added electrolyte had on the motion of the paraffin chains. It is shown that the methylene group next to the polar head gains more freedom as the electrolyte concentration is increased. The molecular motions inside the micelle do not change.
1. Introduction The electric double layer around aggregations of colloidal surfactants plays an important role in the mechanism of aggregation. It can be said that the mechanism of micelle formation is a balance between the hydrocarbon forces of the interior and the electrical forces at the surface. Many measurements have been made on the micelle interior and it is now generally accepted that the hydrocarbon chains exhibit a liquid like character, the terminal methyl group having a completely liquid environment, with a motional gradient along the chain to the polar head group which remains on a surface. Nuclear magnetic resonance measurements on soap-water systems [ 1] and 13C measurements on phospholipid [2] support this idea. It has only recently been reported, however, that the translational motion, the diffusion of a single molecule within the micelle, is rapid [3,4], and also that this diffusion changes dramatically with the ionic strength of the polar head group [4]. The purpose of our experiment was to see what effect changes in the structure of the electric double layer had on the motion of the hydrocarbon chain. It is known from light scattering measurements [5] that added salt changes the aggregation number at a given surfactant concentration. The critical micelle 348
concentration is lowered on addition of salt, so the aggregation number at a given concentration is respectively greater. Geometrical calculations on spherical and ellipsoidal micelles [6] show that on increasing the aggregation number, the surface per polar head group gets smaller. Whilst this may be true when the aggregation number increases with increasing concentration, it need not be the case when salt is added.
2. Method and results The sodium lauryl sulphate (SLS) and sodium chloride used were analytical grade and obtained from Prolabo, Paris. The samples were made in quantities no less than 50 ml, to reduce weighing errors. The 13C relaxation measurements were made on a Varian XL1 00-l 2WG spectrometer at a frequency of 25.2 MHz (see fig. 1). The spectrometer was equipped with a 1 kW pulse amplifier (V 4420) allowing a 90” radio frequency pulse of 16 bsec. Two methods have been used for measuring the relaxation time, firstly the method of progressive saturation [7], that is, 90”. t, 90”, with 0.2 < t < 10 set and secondly, for relaxation times shorter than 1 set, the inversion recovery method [8] as modified by Freeman and Hill [7]. This method involves the sequence . . . 90:) T > T, ,
Volume
1 October 1973
CHEMICAL PHYSICS LETTERS
22, number 2
3-6
50
30
0 PPM
Fig. 1. 13C NMR spectrum of sodium lauryl sulphate at 25.2 MHz, with assignment of lines.
13C spin-lattice SO4 o (ppm from TMS) SLS 0.86 mole P-’ SLS 0.43 mole P-l SLS 0.43 mole Q-’ NaClO.15 mole P-’ SLS 0.43 mole P-l NaClO.30 mole P-’
Table 1 relaxation time (set) of sodium lauryl sulphate
CH2
CH2
CH2CH2CH2CH2
CH2CH2
CH2
CH2
CH2
CH3
69.86
26.16
30.52
30.1s
29.67
32.63
23.50
14.44
0.35 0.35
0.35 0.37
0.38 0.39
0.43 0.41
0.35 0.41
0.55 0.66
1.20 0.75
2.20 2.10
0.53
0.37
0.35
0.45
0.48
0.60
0.90
2.00
0.70
0.40
0.40
0.40
0.48
0.50
0.85
2.20
180”, t, 90,” . . . with, in our case 0.1 < t < 1 set and T = 2 sec. The results are shown in table 1. It can be safely assumed in our case that the relaxation mechanism of the 13C is dipolar coupling to the adjacent protons. In this case, fhe correlation time of the motion can be easily computed from the formula
is the carbon-hydrogen
bond length, and r, is then
the effective correlation time. For the carbon atoms adjacent to the polar head group, this correlation time has been calculated and it is found that: set
for
SLS 0.43 M P-‘, zero NaCl
re = 3.02 X 10. ” set
for
SLS 0.43 M Vp1,0.3M NaCI.
re = 6.04 X lO_” and
where N is the number of effective protons, yH and rc are the gyromagnetic ratios of the proton and carbon nuclei, respectively, ti is Planck’s constant, rCH
Since the molecule can be assumed to time, this effective be the correlation
is aggregated into a micelle, that have a much longer reorientation correlation time can be assumed to time for internal motion.
349
Volume 22, number 2
CHEMICAL PHYSICS LETTERS
3. Discussion The results shown in table 1 can be briefly summarized as follows. On addition of salt, to a solution of sodium lauryl sulphate at a given concentration, it is found that the longitudinal relaxation time (T1) of the carbon next to the polar head group increases. The increase within experimental error is proportional to the molar concentration of salt. From light scattering measurements [S] it is known that for the maximum concentration of added salt, in our case 0.3 M, the aggregation number of the micelle has nearly doubled. This is equivalent, for our solution of 0 3 M 9-l to a concentration increase up to 0.86 M !Z-P . Measurements on a solution of 0.86 M II-’ showed that the T, of the carbon next to the polar head group remained the same as its value at 0.43 M II-I. The fact that the relaxation time has increased on adding salt shows that this carbon, and in consequence the polar head group, has greater freedom of movement. To explain this effect one must look at the structure of the electric double layer at the micelle surface. The electric double layer can be divided into two regions. A compact inner region, the Stern layer, in which a close association with the fixed micellar ions is maintained, and within which a considerable fraction (60 to 805%) of the counter-ions is found, and a more distant dissociated region, the Guoy-Chapman layer in which the counter-ions are distributed according to the Poisson-Boltzmann relation to form a poorly screening ion atmosphere. Some points about the Stern layer can be made. From capacitance studies of charged double layers [9] it has been necessary to attribute a lower dielectric constant to the Stern layer than that of the bulk solution and a certain degree of structuring and rigidity has been associated with the Stern layer. Grahame [lo] described the Stern layer around the mercury electrode under certain conditions as being ice-like, but Robb [ 1 l] disputes this view in his study of counter-ion binding. However, on the question of effective dielectric constant of the Stern layer the result of Giese et al. [ 121 should be noted. These authors studied the dielectric relaxation behaviour of aqueous electrolyte solutions and interpreted their results for Na+ as indicating that the water molecules in the Na+ hydration layer are sufficiently orientated to prevent
3.50
1 October 1973
rotation of the dipole. Hence, the Stern layer possibly contains fully hydrated sodium ions. In explaining our relaxation resuIts we must consider what could cause an increase in the freedom of motion of the polar head group on the addition of salt. If one accepts that the sodium ions that are present in the Stern layer in the absence of added electrolyte have an atmosphere of water that is orientated then one can speak of an ice-like structure for this region and so accept that the polar head groups are restrained in their movement. We would then propose that adding counter-ions to the solution dehydrates the Stern layer. This does not dramatically affect the electrical forces between adjacent polar head groups, and so does not necessarily change the surface per polar head group, but it does, by reducing the amount of water within the Na+ hydration layer, allow a greater freedom of movement for the polar head group. It is interesting to note that the relaxation times of other carbons along the length of the chain do not change on adding salt. The relaxation time of the terminal methyl group is the same with and without electrolyte and at higher surfactant concentration. Thus, it can be assumed that the density of the hydrocarbon interior remains constant. The fact that the relaxation time of the carbon next to the polar group does not change on doubling the concentration without added electrolyte could be taken as further evidence of the degree of hydration of the double layer. In this case, at 0.86 M 12-l we know that the aggregation number has also nearly doubled [S] and so would expect a smaller surface area per polar group [6] . This, in turn, would lead one to expect a decrease in the relaxation time of the carbon. The fact that this is not the case could be taken as evidence that it is the electrical forces that govern the mobility of the polar group and its neighbouring carbon, and that the motion is independent of the exact surface area per polar group.
Acknowledgement We should like to thank Dr. Rigny and Mr. Alexandre for helpful discussions. One of us (R.T.R.) would like to thank the S.R.C. for a fellowship held during the course of this work.
Volume 22, number 2
CHEMICAL PHYSICS LETTERS
References [ 1 ] J. Charvolin and P. Rigny, to be published. 121 A.G. Lee, J.M. Birdsall, Y.K. Levine and J.C. Metcalfe, Biochim. Biophys. Acta 255 (1972) 43. [3] H.M. McConnell and P. Devaux, J. Am. Chem. Sot. 94 (1972) 447.5. [4] R.T. Roberts, Nature, to be published. [5] H.V. Tartar and A.L.M. LeLong, J. Phys. Chem. 59 (1955) 1185.
1 October 1973
[6] H.V. Tartar, f. Phys. Chem. 59 (1955) 1195. [7] R. Freeman and H.D.W. Hill, J. Chem. Phys. 54 (1971) 3367. [8] R.L. Void, J.S. Waugh, M.P. Klein and D.E. Phelps, J. Chem. Phys. 48 (1968) 3861. 191 D.C. Grahame, Chem. Rev. 41 (1947) 441; J. Am. Chem. Sot. 80 (1958) 4201. [lo] D.C. Grahame, J. Chem. Phys. 23 (1955) 1725. [ll] I.D. Robb, J. Colloid Sci. 37 (1971) 521. [ 12 1 K. Giese, U. Kaatze and R. Pottel. J. Phys. Chem. 74 (1970) 3718.
351
22, number
2
CHEMICAL
PHYSICS
1 October
LETTERS
1973
13C RELAXATION MEASUREMENTS OF MOLECULAR MOTION IN MICELLAR SOLUTIONS R.T. ROBERTS and C. CHACHATY Service de Chimie-Physique, Centre d’Etudes Nuckaires 91- Gif-sur- Yvette, France
Received
de Saclay,
23 July 1973
Measurements have been made of the 13C nuclear magnetic resonance longitudinal relaxation time T1 in micellar of added sodium chloride. The purpose of the exsolutions of sodium kauryl sulphate with different concentration periment was to see what effect added electrolyte had on the motion of the paraffin chains. It is shown that the methylene group next to the polar head gains more freedom as the electrolyte concentration is increased. The molecular motions inside the micelle do not change.
1. Introduction The electric double layer around aggregations of colloidal surfactants plays an important role in the mechanism of aggregation. It can be said that the mechanism of micelle formation is a balance between the hydrocarbon forces of the interior and the electrical forces at the surface. Many measurements have been made on the micelle interior and it is now generally accepted that the hydrocarbon chains exhibit a liquid like character, the terminal methyl group having a completely liquid environment, with a motional gradient along the chain to the polar head group which remains on a surface. Nuclear magnetic resonance measurements on soap-water systems [ 1] and 13C measurements on phospholipid [2] support this idea. It has only recently been reported, however, that the translational motion, the diffusion of a single molecule within the micelle, is rapid [3,4], and also that this diffusion changes dramatically with the ionic strength of the polar head group [4]. The purpose of our experiment was to see what effect changes in the structure of the electric double layer had on the motion of the hydrocarbon chain. It is known from light scattering measurements [5] that added salt changes the aggregation number at a given surfactant concentration. The critical micelle 348
concentration is lowered on addition of salt, so the aggregation number at a given concentration is respectively greater. Geometrical calculations on spherical and ellipsoidal micelles [6] show that on increasing the aggregation number, the surface per polar head group gets smaller. Whilst this may be true when the aggregation number increases with increasing concentration, it need not be the case when salt is added.
2. Method and results The sodium lauryl sulphate (SLS) and sodium chloride used were analytical grade and obtained from Prolabo, Paris. The samples were made in quantities no less than 50 ml, to reduce weighing errors. The 13C relaxation measurements were made on a Varian XL1 00-l 2WG spectrometer at a frequency of 25.2 MHz (see fig. 1). The spectrometer was equipped with a 1 kW pulse amplifier (V 4420) allowing a 90” radio frequency pulse of 16 bsec. Two methods have been used for measuring the relaxation time, firstly the method of progressive saturation [7], that is, 90”. t, 90”, with 0.2 < t < 10 set and secondly, for relaxation times shorter than 1 set, the inversion recovery method [8] as modified by Freeman and Hill [7]. This method involves the sequence . . . 90:) T > T, ,
Volume
1 October 1973
CHEMICAL PHYSICS LETTERS
22, number 2
3-6
50
30
0 PPM
Fig. 1. 13C NMR spectrum of sodium lauryl sulphate at 25.2 MHz, with assignment of lines.
13C spin-lattice SO4 o (ppm from TMS) SLS 0.86 mole P-’ SLS 0.43 mole P-l SLS 0.43 mole Q-’ NaClO.15 mole P-’ SLS 0.43 mole P-l NaClO.30 mole P-’
Table 1 relaxation time (set) of sodium lauryl sulphate
CH2
CH2
CH2CH2CH2CH2
CH2CH2
CH2
CH2
CH2
CH3
69.86
26.16
30.52
30.1s
29.67
32.63
23.50
14.44
0.35 0.35
0.35 0.37
0.38 0.39
0.43 0.41
0.35 0.41
0.55 0.66
1.20 0.75
2.20 2.10
0.53
0.37
0.35
0.45
0.48
0.60
0.90
2.00
0.70
0.40
0.40
0.40
0.48
0.50
0.85
2.20
180”, t, 90,” . . . with, in our case 0.1 < t < 1 set and T = 2 sec. The results are shown in table 1. It can be safely assumed in our case that the relaxation mechanism of the 13C is dipolar coupling to the adjacent protons. In this case, fhe correlation time of the motion can be easily computed from the formula
is the carbon-hydrogen
bond length, and r, is then
the effective correlation time. For the carbon atoms adjacent to the polar head group, this correlation time has been calculated and it is found that: set
for
SLS 0.43 M P-‘, zero NaCl
re = 3.02 X 10. ” set
for
SLS 0.43 M Vp1,0.3M NaCI.
re = 6.04 X lO_” and
where N is the number of effective protons, yH and rc are the gyromagnetic ratios of the proton and carbon nuclei, respectively, ti is Planck’s constant, rCH
Since the molecule can be assumed to time, this effective be the correlation
is aggregated into a micelle, that have a much longer reorientation correlation time can be assumed to time for internal motion.
349
Volume 22, number 2
CHEMICAL PHYSICS LETTERS
3. Discussion The results shown in table 1 can be briefly summarized as follows. On addition of salt, to a solution of sodium lauryl sulphate at a given concentration, it is found that the longitudinal relaxation time (T1) of the carbon next to the polar head group increases. The increase within experimental error is proportional to the molar concentration of salt. From light scattering measurements [S] it is known that for the maximum concentration of added salt, in our case 0.3 M, the aggregation number of the micelle has nearly doubled. This is equivalent, for our solution of 0 3 M 9-l to a concentration increase up to 0.86 M !Z-P . Measurements on a solution of 0.86 M II-’ showed that the T, of the carbon next to the polar head group remained the same as its value at 0.43 M II-I. The fact that the relaxation time has increased on adding salt shows that this carbon, and in consequence the polar head group, has greater freedom of movement. To explain this effect one must look at the structure of the electric double layer at the micelle surface. The electric double layer can be divided into two regions. A compact inner region, the Stern layer, in which a close association with the fixed micellar ions is maintained, and within which a considerable fraction (60 to 805%) of the counter-ions is found, and a more distant dissociated region, the Guoy-Chapman layer in which the counter-ions are distributed according to the Poisson-Boltzmann relation to form a poorly screening ion atmosphere. Some points about the Stern layer can be made. From capacitance studies of charged double layers [9] it has been necessary to attribute a lower dielectric constant to the Stern layer than that of the bulk solution and a certain degree of structuring and rigidity has been associated with the Stern layer. Grahame [lo] described the Stern layer around the mercury electrode under certain conditions as being ice-like, but Robb [ 1 l] disputes this view in his study of counter-ion binding. However, on the question of effective dielectric constant of the Stern layer the result of Giese et al. [ 121 should be noted. These authors studied the dielectric relaxation behaviour of aqueous electrolyte solutions and interpreted their results for Na+ as indicating that the water molecules in the Na+ hydration layer are sufficiently orientated to prevent
3.50
1 October 1973
rotation of the dipole. Hence, the Stern layer possibly contains fully hydrated sodium ions. In explaining our relaxation resuIts we must consider what could cause an increase in the freedom of motion of the polar head group on the addition of salt. If one accepts that the sodium ions that are present in the Stern layer in the absence of added electrolyte have an atmosphere of water that is orientated then one can speak of an ice-like structure for this region and so accept that the polar head groups are restrained in their movement. We would then propose that adding counter-ions to the solution dehydrates the Stern layer. This does not dramatically affect the electrical forces between adjacent polar head groups, and so does not necessarily change the surface per polar head group, but it does, by reducing the amount of water within the Na+ hydration layer, allow a greater freedom of movement for the polar head group. It is interesting to note that the relaxation times of other carbons along the length of the chain do not change on adding salt. The relaxation time of the terminal methyl group is the same with and without electrolyte and at higher surfactant concentration. Thus, it can be assumed that the density of the hydrocarbon interior remains constant. The fact that the relaxation time of the carbon next to the polar group does not change on doubling the concentration without added electrolyte could be taken as further evidence of the degree of hydration of the double layer. In this case, at 0.86 M 12-l we know that the aggregation number has also nearly doubled [S] and so would expect a smaller surface area per polar group [6] . This, in turn, would lead one to expect a decrease in the relaxation time of the carbon. The fact that this is not the case could be taken as evidence that it is the electrical forces that govern the mobility of the polar group and its neighbouring carbon, and that the motion is independent of the exact surface area per polar group.
Acknowledgement We should like to thank Dr. Rigny and Mr. Alexandre for helpful discussions. One of us (R.T.R.) would like to thank the S.R.C. for a fellowship held during the course of this work.
Volume 22, number 2
CHEMICAL PHYSICS LETTERS
References [ 1 ] J. Charvolin and P. Rigny, to be published. 121 A.G. Lee, J.M. Birdsall, Y.K. Levine and J.C. Metcalfe, Biochim. Biophys. Acta 255 (1972) 43. [3] H.M. McConnell and P. Devaux, J. Am. Chem. Sot. 94 (1972) 447.5. [4] R.T. Roberts, Nature, to be published. [5] H.V. Tartar and A.L.M. LeLong, J. Phys. Chem. 59 (1955) 1185.
1 October 1973
[6] H.V. Tartar, f. Phys. Chem. 59 (1955) 1195. [7] R. Freeman and H.D.W. Hill, J. Chem. Phys. 54 (1971) 3367. [8] R.L. Void, J.S. Waugh, M.P. Klein and D.E. Phelps, J. Chem. Phys. 48 (1968) 3861. 191 D.C. Grahame, Chem. Rev. 41 (1947) 441; J. Am. Chem. Sot. 80 (1958) 4201. [lo] D.C. Grahame, J. Chem. Phys. 23 (1955) 1725. [ll] I.D. Robb, J. Colloid Sci. 37 (1971) 521. [ 12 1 K. Giese, U. Kaatze and R. Pottel. J. Phys. Chem. 74 (1970) 3718.
351