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J. Phys. Chem. B 2000, 104, 8782-8791
A Proton Nuclear Magnetic Resonance Relaxation Study of C12E6/D2O E. E. Burnell,*,† D. Capitani,‡ C. Casieri,§ and A. L. Segre‡ Institute of Nuclear Chemistry of CNR, Area della Ricerca di Roma, M.B. 10, Monterotondo Staz., Rome, Italy, Physics Department, UniVersity of L’Aquila, 67100 L’Aquila, and INFM, Italy, and Department of Chemistry, UniVersity of British Columbia, 2036 Main Mall, VancouVer, B.C., V6T 1Z1, Canada ReceiVed: February 18, 2000; In Final Form: May 22, 2000
Aqueous solutions of the nonionic surfactant, n-dodecylhexaoxyethylene glycol [C12H25(OCH2CH2)6OH], termed C12E6, form various phases at room temperature: there is a micellar phase at high water content, hexagonal, cubic, and lamellar mesophases at intermediate water contents, and an isotropic phase at very low water content. Proton nuclear magnetic resonance (NMR) T-1 1 relaxation rates have been measured for the C12E6/D2O system as a function of composition, spectral frequency, and temperature. The results are interpreted in terms of the possible molecular motions for the C12E6 molecule in the different phases. A review of relaxation theory is presented with special attention to molecular exchange between sites that are associated with different relaxation rates.
1. Introduction Lyotropic liquid crystals are a rich and fascinating class of systems.1 Often they are used as models for biological membranes because they form phases similar to those found in biologically important assemblages.2 The rich variety of phases formed is interesting in its own right, and a detailed understanding of this fascinating and important class of liquid crystal is not yet available. A particularly interesting series of lyotropic liquid crystals is that formed by the neutral oxy ethylene glycol derivatives. Many other lyotropic systems consist of long-chain hydrocarbons with a charged headgroup, a counterion, and water. The CxEy/water mixtures consist of a hydrocarbon chain with an uncharged but polar headgroup plus water. The phases formed by these materials are quite similar to those formed by their charged cousins and those formed by two-chain phospholipid/ water dispersions. The C12E6/water system (the phase diagram from ref 3 is shown in Figure 1) has attracted particular interest, and some fascinating phenomena have been suggested to rationalize experimental observations. For example, at higher water content, the lamellar phase consists of planar regions that contain embedded cylinders.4,5 These cylinders do not appear to exist in the lower water content lamellar phase. It is interesting to ask whether such fascinating structures have any consequence for nuclear magnetic resonance (NMR) relaxation measurements. In this paper we report proton NMR T-1 1 relaxation rates for C12E6/D2O as a function of composition, spectral frequency, and temperature. The results are interpreted in terms of possible molecular motions for the C12E6 molecules. 2. Review of Relaxation Theory NMR relaxation measurements provide a powerful method for investigating molecular motions in anisotropic systems. In * Author for correspondence. E-mail:
[email protected]. † Department of Chemistry. ‡ Institute of Nuclear Chemistry of CNR. § Physics Department.
Figure 1. Phase diagram of C12E6/D2O (from ref 3).
particular, when several different motions are present, NMR measurements made as a function of frequency can in principle give information about the amplitudes and characteristic times for each of the motions. For this to be the case, each motion must modulate some part of the spin Hamiltonian. This modulation is possible as long as faster motions do not average the Hamiltonian to its isotropic value, such as would be the case for the intramolecular part of the Hamiltonian averaged over random molecular tumbling in an isotropic fluid. For each motion i it is helpful to divide the Hamiltonian into time-average 〈H〉i and time-dependent or fluctuating (H(t) 〈H〉i) parts:
H(t) ) 〈H〉i + (H(t) - 〈H〉i)
(1)
where 〈H〉i is the average Hamiltonian that remains after the motion; for isotropic motion, 〈H〉i ) 0. It is the time-fluctuating term (H(t) - 〈H〉i) that gives rise to relaxation. Consider a molecule for which the only nuclei that have spin are protons (I ) 1/2). The spin-lattice relaxation rate T-1 1
10.1021/jp000691l CCC: $19.00 © 2000 American Chemical Society Published on Web 08/24/2000
Proton NMR of C12E6/D2O
J. Phys. Chem. B, Vol. 104, No. 37, 2000 8783
associated with the modulation of the intramolecular dipolar interactions that results from the random tumbling of the molecules in an isotropic fluid can be written as follows:6
1/T1 ) K(j(ω0) + 4j(2ω0))
(2)
2 3 γ4h2 1 K ) M2 ) 3 5N 4π2 i
