J. Phys. Chem. B 1999, 103, 7747-7750
7747
Closed-Looped Micelles in Surfactant Tetramer Solutions Martin In,*,† Olivier Aguerre-Chariol,‡ and Raoul Zana§ Complex Fluids Laboratory, CNRS-Rhodia, Prospect Plains Road, Cranbury, New Jersey, 08512, Centre de Recherches d’AuberVilliers, Rhodia, 52, rue de la Haie coq, 93308 AuberVilliers, France, and Institut Charles Sadron, 6 rue Boussingault, 67000 Strasbourg, France ReceiVed: June 17, 1999; In Final Form: August 3, 1999
Formation of a dominant population of closed loops in wormlike micellar systems, theoretically predicted but never reported so far, is achieved with a new cationic surfactant tetramer. The contour length distribution N(L) of the closed-looped micelles is determined by transmission electron microscopy at cryogenic temperature. At large contour lengths, the distribution observed scales as N(L) ∝ L-5/2, as expected from ring-chain equilibrium polymerization theory. At small contour lengths, the rigidity-dependent ring closure probability provides a direct estimate of the persistence length. These results re-emphasize the new possibilities offered by surfactant dimers (gemini) and oligomers in obtaining new morphologies in self-assemblies.
In aqueous solutions, surfactants self-assemble into micelles whose size and shape are determined by packing constraints resulting from a balance between attractive hydrophobic interactions and repulsive interactions between the hydrophilic headgroups.1 Since one micellar dimension must be close to the surfactant length, growth starting from a small spherical micelle can take place in one or two dimensions only. In each case, the topology of the aggregates is essentially determined by the balance between the conformational entropy and the excess energy coming from the rim of the aggregate, as in, for example, the end caps of wormlike micelles. As a result of the above, growth in one dimension leads mainly to open wormlike micelles, while growth in two dimensions leads mainly to closed bilayer membranes (vesicles).2 Under specific conditions that enhance the rigidity of the bilayer, disklike micelles have, however, been observed.3 In this report, a newly synthesized cationic surfactant tetramer is shown to fulfill the rather stringent conditions necessary to obtain wormlike micellar solutions containing a dominant fraction of closed rings. These conditions are now explained further. The one-dimension growth of surfactant micelles provides a well-studied example of equilibrium polymerization:4 it is a reversible aggregation phenomenon resulting in an equilibrium distribution of micellar lengths that is determined by state variables such as concentration and temperature. The length distribution is exponential:1,2
N(L) ∝ exp(-L/〈L〉)
(1)
as is the distribution of polymerization degree in linear polymeric systems:5
N(x) ∝ px
(2)
N is the number of micelles (respectively polymers) of length L (respectively degree of polymerization x). 〈L〉 is the average * Author to whom correspondence should be addressed. † Complex Fluids Laboratory, CNRS-Rhodia. ‡ Centre de Recherches d′Aubervilliers, Rhodia. § Institut Charles Sadron, CNRS.
Figure 1. Chemical structure of the surfactant tetramer 12-3-124-12-3-12.
micellar length and depends on the concentration c as 〈L〉 ∝ xcexp(Ec), where Ec is the end cap energy (expressed in units of kT). Ec corresponds to the excess chemical potential of the surfactants constituting the two end caps of a wormlike micelle, as compared to the chemical potential of the surfactants residing in the cylindrical body. The end cap energy expresses the tendency of the micelle to grow and can be related to the extent of reaction p, i.e., the fraction of reacted functions, in a polymer system: p = 1 - xexp(-Ec). Under equilibrium conditions, the closed ring/open chain competition most often favors the open chains.2,6 On one hand, the intramolecular reaction leading to the formation of a loop brings an enthalpic gain (formation of a bond) without cost in mixing entropy (no reduction of the number of molecules). On the other hand, the number of conformations for a closed ring is strongly reduced compared to that of an open chain. The conformational entropy cost is actually the dominant parameter and increases very rapidly with the degree of polymerization x.7 The resulting ring size distribution reads:6
Nloop(x) ∝ (p′)xx-5/2
(3)
Nloop(x) is the number of loops corresponding to a polymerization degree x. p′ is the extent of reaction in the population of open chains only. The weight fraction of rings wr relates p and p′ as
10.1021/jp9919922 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/27/1999
7748 J. Phys. Chem. B, Vol. 103, No. 37, 1999
Letters
Figure 2. Cryo-TEM micrographs of a vitrified 1% aqueous solution of 12-3-12-4-12-3-12 showing many closed-loops coexisting with open wormlike micelles. The bottom left picture shows one of the biggest loops (800 nm). Loops containing a branching point (lasso) or more are also present but are not taken into account in the distribution presented in Figure 3.
follows: (1 - p′) ) (1 - p)/(1 - wr) and is given by
wr ∝
1
∞
p′xx-3/2 ∑ c x)1
(4)
where c is the concentration. Comparing eqs 3 and 2, it can be seen that, due to the x-5/2 factor, the population of large loops is drastically depleted as compared to the population of open chains. Therefore, in most situations of equilibrium polymerization, rings are always present, but in such low amounts that they are not expected to influence the properties of the systems, i.e., to be experimentally observable. Equation 4 also expresses the intuitive fact that very low concentrations favor intramolecular reactions and thus loop formation. Therefore, a large fraction of loops can be obtained if one can considerably reduce the concentration and at the same time maintain a high extent of reaction. In fact, when the reaction is brought to completion (p ) 1), there exists a critical concentration below which the system contains 100% rings.4,6 This explains why the dilution technique has been widely used to prepare cyclic macromolecules.8
Applying the concepts of equilibrium polymerization to wormlike micellar systems, the formation of a significant amount of closed-looped micelles would require a surfactant with a very low critical micelle concentration (cmc) and a high end cap energy Ec.2,9 For the latter, the spontaneous curvature of the surfactant assembly has to be reduced to about 1/l (where l is the surfactant length and 1/l the mean curvature of a cylinder of radius l) but not much further as to prevent two-dimensional growth. Hence a very fine-tuning of the packing parameter is needed, which is difficult to achieve with conventional surfactants (single alkyl chain with a polar headgroup). As a consequence observations of rings have been rather scarce in wormlike micelle systems.10 Such a fine-tuning can, however, be achieved with surfactant dimers (gemini) or oligomers.11 A newly synthesized cationic surfactant tetramer,12 referred to as 12-3-12-4-12-3-12 (Figure 1), fulfills the above conditions and gives rise to a large fraction of closed-looped micelles. This surfactant can be considered as the tetramer of the dodecyltrimethylammonium bromide (DTAB). It is a higher homologue of the surfactant dimer (gemini) 12-3-12 and trimer 12-3-12-3-12 which have been previously studied.11
Letters
J. Phys. Chem. B, Vol. 103, No. 37, 1999 7749
(
P(Lr) ∝ L-5 r exp
-7.027 + 0.492Lr Lr
)
(5)
where Lr ) L/2lp, lp being the persistence length. The loop size distribution is obtained by introducing a factor qLr (where q < 1) as in eq 2, and dividing by Lr, so that:
(
Nloop ) ALr-6 exp -
Figure 3. Loop size distribution in 1% aqueous solution of 12-312-4-12-3-12 (histogram) and best fit with eq 6 (curve). The mode of the distribution corresponds to twice the persistence length (lp ) 75 nm). The decreasing part of the distribution scales as L-5/2 as expected from the ring closure probability for Gaussian polymers.
The cmc of the surfactant tetramer has been found to have the very low value of 0.06 mM using the electrical conductivity method (for comparison, DTAB cmc ) 15 mM). Its end cap energy has not been determined, but is likely to be extremely high in view of the rapid increase of Ec in going from the monomer DTAB (Ec ≈ 0 kT) to the dimer 12-3-12 (Ec ≈ 40 kT) and trimer 12-3-12-3-12 (Ec ≈ 80 kT).13 The surfactant tetramer thus appears to be an ideal candidate for the formation of closed-looped micelles. A 1 wt % solution of 12-3-12-4-12-3-12 was examined by transmission electron microscopy at cryogenic temperature14 (Figure 2). The low concentrations combined with the smaller (one-half) mean square radius of gyration of a ring with respect to an open linear chain, results in a decrease in the overlap of micelles. In this respect, intermicellar electrostatic repulsion also probably plays a role, since the micelles are fairly regularly spaced, about 50 nm apart. A clear observation of many closedlooped micelles coexisting with some open wormlike micelles is thus possible. The contour lengths L of about 400 closed-looped micelles have been determined (Figure 3). The distribution is monomodal and positively skewed: average (200 nm) > median (170 nm) > mode (150 nm). An important feature is the broad range of sizes observed, going from 70 to 900 nm. The decreasing part of the distribution is very close to the power law (L-5/2) established for long loops (it actually decreases somewhat faster, as expected from the p′x factor in eq 3). This is quite satisfactory because this means that sample preparation for cryo-TEM observation disturbed little if at all the size distribution of the closed-looped micelles. The confinement of the surfactant solution in two dimensions may have induced a new equilibrium distribution: the power law distribution L-5/2 generalized for any space dimension reads L-(d/2+1),4 where d is the spatial dimensionality. In two dimensions it would have resulted in a L-2 dependence. The presence of a peak in the distribution means that the wormlike micelles formed by the surfactant tetramer have an intrinsic rigidity that prevents the formation of small rings. The ring closure probability for long flexible polymers obeying Gaussian statistics7 is not valid for short semi-flexible ones. For these latter, it is given by ref 15:
)
7.027 + 0.492 Lr qLr Lr
(6)
The experimental loop size distribution is very well described by eq 6, when the persistence length is set equal to 75 nm (Figure 3). Usually, the persistence length of wormlike micelles is determined by a combination of dynamic and static light scattering or by small angle neutron scattering. In analyzing scattering data to determine a persistence length, it is critical to take into account growth, polydispersity, and intermicellar interactions.16 The values obtained for either neutral or screened wormlike micelles range from about 20 to 50 nm, in agreement with theoretical predictions.17 Several theoretical models account for the electrostatic contribution to the rigidity of polyelectrolytes18 and it has been clearly demonstrated with wormlike micelles by mixing ionic and neutral surfactants.19 The rather high value of 75 nm found for the cationic surfactant tetramer can be attributed to electrostatic interactions and to the oligomeric nature of the surfactant. Finally, since the bending energy of a closed micelle of one persistence length is 2π2kT, the observation of several rings of contour length as small as 60-80 nm, confirms that Ec . 20kT. In conclusion, aqueous solutions of a newly synthesized cationic surfactant tetramer were shown to contain a large proportion of closed-looped micelles coexisting with open wormlike micelles. The distribution of contour lengths of the loops, Nloop(L), determined from cryo-TEM observation, presents a maximum at L ) 2lp and at large L values decreases as L-5/2, in agreement with theoretical treatment of the ring closure probability of Gaussian polymers. The formation of a dominant population of closed-looped micelles, which has never been reported so far in any surfactant systems, relies upon the very low critical micelle concentration and proper packing constraints of the surfactant tetramer used. These results emphasize the new possibilities offered by surfactant oligomers in obtaining organized assemblies with novel architectures. Acknowledgment. We thank Dr. J. Chang and Dr. S. Ranganathan for careful reading of the manuscript and Dr. O. Anthony for his help in editing the pictures. References and Notes (1) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans 2 1976, 72, 1525. (2) Porte, G. J. Phys. Chem. 1983, 87, 3541. (3) Zemb, Th.; Dubois, M.; Deme´, B.; Gulik-Krzywicki, Th. Science 1999, 283, 816. (4) Petschek, R. G.; Pfeuty, P.; Wheeler, J. C. Phys. ReV. A 1986, 34, 2391 and references therein. (5) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, 1953; Chapter 8. (6) Jacobson, H.; Stockmayer, W. H. J. Chem. Phys. 1950, 18, 1600. (7) The conformational entropy lost corresponds to the loss of accessible volume for the tethered chain ends. For an open chain, one of the chain ends is randomly distributed in a volume of the order of R3, surrounding the other chain end (R2 ) mean square end-to-end distance of the chain). If the polymer conformation obeys Gaussian statistics, R2 is proportional to the degree of polymerization x. The ring closure probability, i.e., the probability of the two chain ends coinciding with each other, is inversely proportional to the accessible volume lost, and scales therefore as x-3/2. At
7750 J. Phys. Chem. B, Vol. 103, No. 37, 1999 equilibrium, the distribution is further reduced by a factor x, since a ring may reopen at any point of its contour.2,6 (8) Cyclic Polymers; Semlyen, J. A., Ed.; Elsevier Applied Science Publishers: London, 1986. (9) van der Schoot, P.; Wittmer, J. P. Submitted (available on the web: cond-mat/9808175). Kroger, M. Macromol. Symp. 1998, 113, 101. (10) Clausen, T. M.; Vinson, P. K.; Minter, J. R.; Davis, H. T.; Talmon, Y.; Miller, W. G. J. Phys. Chem. 1992, 96, 474. Lin, Z.; Scriven, L. E.; Davis, H. T. Langmuir 1992, 8, 2200. Danino, D.; Talmon, Y.; Le´vy, H.; Beinert, G.; Zana, R. Science 1995, 269, 1420. (11) Talmon, Y.; Zana, R. Nature 1993, 362, 624. Danino, D.; Talmon Y.; Zana, R. Langmuir 1995, 10, 1448. Zana, R.; Benrraou, M.; Rueff, R. Langmuir 1991, 7, 1072. Zana, R.; Le´vy, H.; Papoutsi, D.; Beinert, G. Langmuir 1995, 11, 3694. (12) This surfactant has been synthesized from spermine NH2(CH2)3NH(CH2)4NH(CH2)3NH2, by permethylation of the amino groups (Giumanini, A. G.; Chiavari, G.; Scarponi, F. L. Z. Naturforsch. 1975, 30b, 820), followed by quaternization of amino groups with bromododecane in acetonitrile. The crude product has been purified by recrystallization from a mixture of acetone and ethanol. The purity of the surfactant has been checked by 13C NMR and elemental analysis. (13) In, M.; Warr, G. G.; Zana, R. Phys. ReV. Lett. 1999, in press.
Letters (14) Crystalline powder of surfactant was dissolved in water at 70 °C. After complete dissolution the solution was kept at room temperature for 15 h or 11 days before observation. A small droplet of the solution was then applied to a 3 mm copper grid, coated by a perforated carboned plastic film made hydrophilic by glow discharge in 0.1 Torr air, and blotted with a filter paper to reduce the thickness of the liquid film down to about 30200 nm, forming menisci in the holes. The grid is then immediately plunged in liquid ethane at its freezing temperature. Blotting and plunging are performed in a continuous stream of air saturated with water to prevent evaporation. This ultrafast cooling allows complete vitrification of the specimen. The grids are transferred, on a GATAN 626 cryo-specimen holder, using a cryo-transfer device. The TEM used is a JEOL 1200 EX II equipped with a low-dose facility which reduces electron damage. Specimens were equilibrated at about -160 °C in the microscope column, and examined at 120 kV with a direct magnification not greater than 35000 times. (15) Shimada, J.; Yamawaka, H. Macromolecules 1984, 17, 689. (16) Magid, L. J. J. Phys. Chem. B 1998, 102, 4064. (17) May, S.; Bohbot, Y.; Ben-Shaul, A. J. Phys. Chem. B 1997, 101, 8648. (18) Barrat, J. L.; Joanny, J. F. AdV. Chem. Phys. 1995, 94, 1. (19) Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Langmuir 1998, 14, 6013.
