Interconnected Networks: Structural and Dynamic Characterization of

Sep 11, 2008 - Aqueous dispersions of the phospholipid dioctanoylphosphatidylcholine (diC8PC) phase-separate below a cloud-point temperature, dependin...
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J. Phys. Chem. B 2008, 112, 12625–12634

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Interconnected Networks: Structural and Dynamic Characterization of Aqueous Dispersions of Dioctanoylphosphatidylcholine Pierandrea Lo Nostro,*,† Sergio Murgia,‡ Marco Lagi,† Emiliano Fratini,† Go¨ran Karlsson,§ Mats Almgren,§ Maura Monduzzi,‡ Barry W. Ninham,| and Piero Baglioni† Department of Chemistry and CSGI, UniVersity of Florence, Via della Lastruccia 3, 50019 Sesto Fiorentino, Firenze, Italy, Department of Chemistry and CSGI, UniVersity of Cagliari, Cittadella UniVersitaria Monserrato, S.S. 554 BiVio Sestu, 09042 Monserrato, Cagliari, Italy, Department of Physical and Analytical Chemistry, Uppsala UniVersity, Uppsala SE-751 23, Sweden, and Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Institute of AdVanced Studies, Australian National UniVersity, Canberra, Australia 0200 ReceiVed: May 6, 2008; ReVised Manuscript ReceiVed: July 24, 2008

Aqueous dispersions of the phospholipid dioctanoylphosphatidylcholine (diC8PC) phase-separate below a cloud-point temperature, depending on lipid concentration. The lower phase is viscous and rich in lipid. The structure and dynamics of this system were explored via cryo-transmission electron microscopy (cryo-TEM), small-angle X-ray scattering (SAXS), and NMR. The lower phase comprises a highly interconnected tridimensional network of wormlike micelles. A molecular mechanism for the phase separation is suggested. Introduction That an aqueous dispersion of dioctanoylphosphatidylcholine (diC8PC) phase-separates on cooling has been known for 30 years.1-3 The system has an upper consolute critical temperature (Tc). The coexistence curve as a function of the lipid mole fraction is shown in Figure 1. At the cloud point, the solution becomes translucent, and eventually the system separates into two clear, isotropic phases (see Figure 1). The upper phase comprises a diluted micellar solution of diC8PC, while the bottom phase contains about 99% of the surfactant and is highly viscous. The phase separation is reversible, with the cloud-point temperature lower than the reclarification temperature by 0.5 K. This behavior contrasts with that of nonionic poly(oxyethylene) surfactants, which phase-separate upon heating, with a lower consolute temperature.4 The nature of the solvent affects the cloud-point temperature in both systems. Typical are effects induced by deuterium oxide,5 urea,6 and monovalent electrolytes7 on the phase separation of aqueous dispersions of diC8PC. This is to be expected since modifications of solvent will alter solute association free energies, headgroup curvature of aggregates via intramolecular interactions, and interaggregate interactions. However, the mechanisms that drive such phenomena are still uncertain and debated. For any given surfactant, the packing parameter P is defined as VH/(lmaxap), where VH is the volume occupied by the hydrophobic tails, lmax is the length of the hydrocarbon chains in their fully stretched state, and ap is the area per polar heagroup. Depending on the value of P, surfactants form nearly spherical (for P < 1/3), or cylindrical aggregates (for 1/3 < P < 1/ ).8 V 2 H and lmax can be obtained according to Tanford’s formulas:9 * Corresponding author: fax +39 (055) 457-3036; e-mail [email protected]. † University of Florence. ‡ University of Cagliari. § Uppsala University. | Australian National University.

VH ) 27.4 + 26.9(n - 1)

(1)

lmax ) 1.54 + 1.265(n - 1)

(2)

where n is the number of carbons in the hydrophobic tail. According to Sarmiento and co-workers,10 the value of ap for diC8PC at pH ) 5.8 and 25 °C is about 69 Å2; therefore, for this lipid we estimate P ) 0.60. For the shorter diC6PC and diC7PC we obtain similar values of P, and for the nonionic surfactants C12E4 and C12E5 the packing parameters come out to be 0.46 and 0.41, respectively. This result indicates that both short-chain lecithins (zwitterionic) and these CiEj nonionic surfactants promptly form rodlike aggregates above the critical micelle concentration (cmc) in aqueous dispersions. In the case of CiEj, the dispersion separates upon heating (lower consolute separation temperature); thus micelles have to grow with increasing temperature, at fixed concentration. This is possible if P increases; that is, if ap decreases. NMR data actually show that the polar headgroups dehydrate, giving up two H2O molecules per EO unit, at the cloud point. Furthermore, the net interactions between the large cylindrical structures change from repulsive to attractive, and then the aggregate keeps growing until phase separation occurs. For lecithins, the situation is different because the polar headgroup is zwitterionic (large permanent dipole), there are two aliphatic chains, and the aqueous dispersion separates upon cooling. In this case the phase separation process is presumably driven mainly by the dehydration of the polar heads as temperature lowers.11 The long-range permanent dipolar attractive fluctuation forces between aggregates take over to cause the transition. These effects are clearly modified by neutral solutes and salts.7 Basically, there are different hypotheses for the interpretation of temperature-induced phase separation: (a) Micelles grow indefinitely, until the system phase separates. This hypothesis is the basis of the BlankschteinThurston-Benedek (BTB) theory,12-14 which basically provides a fitting procedure of the coexistence curve from which the chemical potential gain of the micellar growth and the intermicellar interaction coefficient are evaluated.

10.1021/jp803983t CCC: $40.75  2008 American Chemical Society Published on Web 09/11/2008

12626 J. Phys. Chem. B, Vol. 112, No. 40, 2008 (b) Intermicellar interactions become stronger and stronger while cooling, until the assemblies get together and eventually separate.15 (c) According to Talmon and co-workers,16 network entropy alone can justify the micellar growth, phase separation, and critical behavior in nonionic surfactant-based systems. This is based on the fundamental work of Safran and co-workers.17,18 For colloids this proposition is true for the original theories of Langmuir (clays, plates), Onsager (tobacco mosaic virus, cylinders), and spherical and cylindrical colloids that rely on the competition of electrostatic interactions, entropy, and packing alone.19-22 But this cannot be the whole story. This is exemplified in Hofmeister, specific ion dependence of cloud points of nonionic PEO surfactants.23,24 Similar changes occur due to ion adsorption at the micellar interface, which also affects curvature and interactions, and the consequent variations of phase volumes due to these and other solute effects. As a matter of fact, Hofmeister effects reflect specific ion-surface interactions that give rise to specific ion adsorption and are relevant in phaseseparation processes.7 Such ion-surface interactions can be described in terms of ionic dispersion potentials.25,26 It is known that, under some circumstances, micelles can grow dramatically to form giant cylindrical aggregates that resemble polymer solutions in their rheological properties.27 However, equilibrium or living polymers are macromolecules that break and recombine continuously.28 Their molecular weight distribution depends strongly on the surfactant concentration, and covalent linkings of the true polymers are replaced by weak interactions, precisely as for random connected cylinders that form in microemulsions.29 To the best of our knowledge, the molecular mechanism that controls the liquid-liquid phase separation in aqueous dispersions of diC8PC has not been clarified in detail. Therefore, we undertook a detailed investigation on the structure of the two phases, and particularly of the lower, viscous, and lipid-rich phase, through cryogenic transmission electron microscopy (cryo-TEM), small-angle X-ray scattering (SAXS), and nuclear magnetic resonance (NMR) experiments. Materials and Methods 1,2-Dioctanoyl-sn-glycero-3-phosphocholine (dioctanoylphosphatidylcholine, diC8PC) was obtained from Avanti Polar Lipids Inc. (Birmingham, AL) in powder form. The purity was stated to be greater than 99%, and the lipid was used without any further purification. Bidistilled water was purified with a Millipore water purification system to remove ionic impurities (resistivity >18 MΩ · cm). Samples were prepared by weighing the required amounts of lipid and solvent (either H2O or D2O) directly in a glass tube, in order to obtain a solution with the desired lipid mole fraction (xL). After the preparation, the sample was kept in a refrigerator at 277 K, until a clear and foam-free solution was formed, before the experiments proceeded. Cryogenic Transmission Electron Microscopy. Thin sample films (typically 10-500 nm) of the lower phase were prepared at a controlled temperature (298 K) and relative humidity (between 98% and 99%) in a custom-built environmental chamber. The films were then vitrified by quick freezing in liquid ethane and transferred to a Zeiss EM 902A transmission electron microscope for examination. Samples were protected against atmospheric conditions, and the temperature was kept below 108 K during both transfer and examination. A zeroenergy loss bright-field mode was used, and the accelerating voltage was 80 kV. The electron exposures ranged between 5 and 15 e-/Å2, depending on the thickness of the vitrified sample

Lo Nostro et al. layer. The extent of underfocus varied approximately between 1 and 3 µm. The details of the procedure have already been described.30 Small-Angle X-ray Scattering. SAXS measurements were performed on a Hecus SWAX instrument (Kratky camera) with a position-sensitive detector (OED 50 M, 1024 channels of width 54 mm). A Seifert ID-3003 X-ray generator provided Cu KR radiation (λ ) 1.542 Å). A 10 mm thick nickel filter was used to remove the Cu Kβ radiation. The sample-to-detector distance was 281 mm. The volume between the sample and the detector was kept under vacuum (P < 1 mbar) during the measurements to minimize scattering from the air. The lower phase was transferred into a 1 mm quartz capillary by use of a syringe. Measurements were performed at 298 K on a sample at xL ) 1.5 × 10-3. All scattering curves (slit-smeared data) were corrected for the background contribution (quartz capillary filled with water) and slit-desmeared by a direct method.31 Nuclear Magnetic Resonance. Samples for NMR analysis were prepared in deuterated water (99.9% from Cambridge Isotope Laboratories, Inc.) or in distilled water (Millipore MilliQ) by weighing the required amounts of diC8PC, H2O, and 2H2O in NMR tubes and mixing with a vortex mixer. Biphasic samples were stored for at least 72 h before the NMR experiments were run, in order to achieve a complete phase separation. 1H NMR experiments were performed on a Bruker Avance 300 (7.05 T) spectrometer, operating at a frequency of 300.131 MHz, and equipped with a Bruker field gradient probe DIFF30 that can reach field gradients up to 12.0 T · m-1. The temperature was controlled and kept constant within (0.1 °C by a gradient cooling system, and calibrated with 80% glycol in DMSO-d6 (Bruker temperature-calibration sample). In order to extract self-diffusion coefficients from NMR experiments, great care must be taken to avoid a number of sources of artifacts that can severely affect the accuracy of the measurements. Among the different sources of error are (i) radiation damping, (ii) the “meniscus effect” (background gradients caused by magnetic susceptibility differences at the sample interfaces),32 and (iii) convection due to small temperature gradients inside the sample.33 Of these, the first two were minimized by use of small amounts of sample (∼250 µL) in a capillary NMR tube (Wilmad 518, inner diameter ) 1.96 mm) that was inserted in a 5-mm NMR tube. Above 298 K, convection effects were circumvented by use of the convectioncompensated double stimulated echo sequence (DSTE) followed by a longitudinal eddy current delay (LED)34 rather than the classical stimulated echo sequence (STE), which was, instead, used for the measurements carried out at 298 K. Sine-shaped gradients were used to further decrease the effects of eddy currents. In both cases, self-diffusion coefficients were obtained by varying the gradient strength (g) while keeping the gradient pulse length (δ) and the gradient pulse intervals constant within each experimental run. The data were fitted according to the Stejskal-Tanner equation:

I δ ) exp -Dq2 ∆ I0 3

[

(

)]

(3)

I and I0 are the signal intensity in the presence and absence of the applied field gradient, respectively. q ) γgδ is the so-called scattering vector (γ being the 1H gyromagnetic ratio), t ) (∆ - δ/3) is the diffusion time, ∆ is the delay time between the encoding and decoding gradients, and D is the self-diffusion coefficient to be extracted. To investigate the time-scale dependence of the diffusion processes, ∆ was varied between 0.05 and 1.6 s, while δ was

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Figure 1. Coexistence curve for diC8PC in H2O. The pictures show the sample at three different temperatures in the monophasic region and after phase separation.

always kept at 1 ms. Typically, the maximum g was varied between 1 and 12 T · m-1 depending on the ∆ value used. The efficacy of the DSTE versus the STE sequence at high temperature was tested via 1H NMR experiments at 318 K, with a 2H2O sample in a 5-mm NMR tube. Although for both sequences a monoexponential attenuation of the signal intensity was detected, with the DSTE sequence the calculated selfdiffusion coefficient for the residual 1H2O (D ) 2.94 × 10-9 m2 · s-1) was only 3% different from that reported by Mills35 (3.03 × 10-9 m2 · s-1), while the value obtained with the STE sequence was significantly different (8.37 × 10-9 m2 · s-1). This difference confirms the inadequacy of the STE sequence and the effectiveness of the DSTE sequence when NMR selfdiffusion experiments are run more than a few degrees away from room temperature. The 1H resonance intensity of the methyl groups of the phospholipid acyl chains was used to evaluate the lecithin selfdiffusion coefficients, and identical results (within the experimental error) were obtained from the 1H resonance intensity of the methylene groups. Experimental errors on the self-diffusion coefficients were estimated to be 5% of the measured value. Results and Discussion Figure 2 shows the minimized Corey-Pauling-Koltun (CPK) model of diC8PC. The aqueous dispersions of this zwitterionic surfactant undergo a phase separation upon cooling. When the separation temperature is plotted versus the lipid mole fraction, an asymmetric coexistence curve is obtained (see Figure 1), with an upper consolute temperature (UCST) below which samples separate into an upper phase (with a diluted dispersion of lecithin) and a lower, diC8PC-rich phase. The effect of D2O, salts, and neutral cosolutes (urea), as well as that of dissolved gases, on the phase behavior of diC8PC has been the object of some studies.5-7,10,36 Cryogenic Transmission Electron Microscopy. Cryo-TEM images show that the lower phase is composed of a dense network of wormlike micelles. The high concentration of lipid in the lower phase (about 0.16 M) makes it difficult to ascertain the structure of the micelles for two reasons: (i) the thick films

Figure 2. CPK (Corey-Pauling-Koltun) model for diC8PC. Carbons are shown in green, oxygens in red, phosphorus in purple, and nitrogen in deep blue. Hydrogens are omitted for clarity.

contain lots of micelles that scatter the electrons and decrease both contrast and resolution, and (ii) in the thick films the micelles overlap. The best possibility to observe individual micelles is given in the thin part of the vitrified film where the network starts to grow up from the area that is void of micelles. Just at the border between the empty area and the network, only one layer of micelles should be present. In the thicker areas the network appears denser, because of overlap, and portions of micelles extended in the direction of the electron beam are imaged as black spots. When Figure 3 is examined closely, a few protruding micelles can be identified. Some of these are long and without any clearly visible branch (open arrows); others have a branched appearance (solid arrows). The micelles making the border are curled and appear to have branches and loops, but unfortunately the contrast and acuity are too low to allow definite conclusions. The length of the wormlike micelles that extend from the network can be estimated from Figure 3 (100-300 nm); however, it is not possible to ascertain if these are typical lengths. The average micellar radius measured from the photos, about 2 nm, corresponds approximately to the diC8PC monomer length (18 Å). Figure 4 shows cryo-TEM micrographs taken on a sample conditioned at 43 °C. Again we have chosen the thinnest areas

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Figure 3. Cryo-TEM images of the bottom phase: Solid arrows indicate branch points, and open arrows (in panel a) indicate long micelles, without branches, protruding from the network into the thin part of the vitrified film. The scale bar is 100 nm.

Figure 4. Cryo-TEM images from the sample at 43 °C. Arrows indicate branching points. The scale bar is 100 nm.

where the network starts to grow up. The border seems to be built of branched micelles (Y-junctions, solid arrows), possibly also with loops. From the cryo-TEM images the micelles appear as branched structures (with Y-junctions) rather than just entangled objects (with X-junctions), although the low contrast prohibits a definitive statement. Due to the high density of aggregates, the contrast was too low. This is an intrinsic limit in our system, as the lower phase concentration is determined only by temperature. Although it is quite clear that the lower phase structure is a network of giant micelles, cryo-TEM results need to be confirmed by other experimental findings.37 Small-Angle X-ray Scattering. The SAXS pattern for the lower phase shows a broad band centered at 0.186 Å-1 (see Figure 5): the spectrum was fitted with a core-shell cylindrical form factor P(q):38

P(q) )

K Vparticle

∫0π⁄2 F(q, R)2 sin R dR + background

(4)

where K is a scale factor, F(q, R) is the scattering amplitude, and the integral averages the form factor over all possible orientations for the cylinder (R is the angle between the cylinder axis and the scattering vector, q); the form factor is then normalized by the total particle volume. In particular,

J1(qr sin R) + qr sin R J1[q(r + t) sin R] 2(Fshell - Fsolvent)VshellJ0[q(H + t) cos R] (5) [q(r + t) sin R]

F(q, R) ) 2(Fcore - Fshell)VcoreJ0(qH cos R)

where J0(x) ) (sin x)/x, Vcore ) πr2l, and Vshell ) π(r + t)2(l + 2t). r and l are the radius and the length of the core of the

Figure 5. Experimental (desmeared) SAXS spectrum in quartz capillary and fitting curve (solid line) for the lower phase.

cylinder, respectively. t is the shell thickness, F indicates the scattering length densities, and J1(x) is the first-order Bessel function. After the spectrum was desmeared, the values obtained for the fitting were r ) 9.4 Å, t ) 8.8 Å, and l ) 20.6 nm. The first two parameters are in agreement with cryo-TEM data (the diC8PC length being given by r + t ) 18.2 Å), with the length of the hydrocarbon chain in its fully stretched conformation according to Tanford’s rule (10.4 Å), and with literature data (t ) 8.4 Å).39

Interconnected Networks of DiC8PC

Figure 6. Stack plot of the 1H NMR signals belonging to the choline methyl groups recorded at 298 K in the diluted phase of freshly prepared (biphasic) diC8PC/2H2O sample at xL ) 1.9 × 10-3 while the gradient strength is varied in the STE experiment.

Nuclear Magnetic Resonance. Two biphasic samples with a lecithin mole fraction xL ) 1.9 × 10-3 were prepared in H2O and 2H2O, respectively. The 1H NMR acquisition performed on the two separated phases of both samples confirmed that the surfactant is mostly present in the bottom phase. However, in the diluted upper phase of the diC8PC/2H2O sample, a doublet rather than the expected singlet (due to the choline methyl groups) was observed around 3.3 ppm. In addition, and contrary to the lecithin-rich bottom phase, all the NMR signal decays obtained through STE experiments were found to be biexponential. The best fit for the data provides self-diffusion coefficients of about 3 × 10-10 and 1 × 10-11 m2 · s-1. Figure 6 reports a stack plot of the NMR signals at about 3.3 ppm for increasing values of the gradient strength, g. Since the monomer aggregate-solution exchange occurs on a rapid time scale with respect to the NMR experiment, this spectral and diffusion evidence is determined by a massive phase separation and represents a clear indication that the sample, although optically isotropic, is not at equilibrium yet. Indeed, it takes about 72 h for a complete phase separation. After this lapse time, the NMR signal decay observed for the upper phase becomes monoexponential with a measured self-diffusion coefficient of 3.52 × 10-10 m2 · s-1, in excellent agreement with a molecular dispersion of diC8PC. Therefore, NMR data were acquired at least 72 h after the preparation of the samples at 298 K. NMR investigations on the diC8PC/H2O sample gave essentially the same results, but it was not possible to extract the monomer self-diffusion coefficient in the dilute phase, because of the unfavorable signal-to-noise ratio in the 1H NMR spectrum. Since this value is essential for calculation of the micellar selfdiffusion coefficients in the diC8PC/H2O system (see the Appendix and the discussion below), it was obtained from the Stokes-Einstein equation Dmon) kBT/(6πηRh) by use of the lecithin self-diffusion coefficient measured in the upper phase of the diC8PC/2H2O biphasic sample and with the (reasonable) assumption that the hydrodynamic radius (Rh) of the monomer is identical in the two solvents. The calculated self-diffusion coefficient for the surfactant monomer in the diC8PC/H2O system was 4.48 × 10-10 m2 · s-1 (with 1.132 and 0.890 mP · s for the viscosities of 2H2O and H2O, respectively). In heterogeneous systems, the translational motion is often strongly affected by the structure of the sample and typically

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Figure 7. Normalized signal attenuations recorded at 298 K in the concentrated phase of both diC8PC/D2O (blue circles) and diC8PC/ H2O (red triangles) samples at xL ) 1.9 × 10-3, with increasing gradient strength in STE NMR experiments performed at different diffusion times (∆ ) 0.05, 0.1, 0.2, 0.4, 0.8, and 1.6 s) and during a period of 2 weeks.

Figure 8. (a) Lecithin self-diffusion coefficients at different sample compositions, corrected for water viscosity and temperature, recorded at (×) 298 and (O) 323 K. (b) Lecithin self-diffusion coefficients for the same samples as in panel a, also corrected for the free surfactant diffusion (all samples), along with the concentration effects (only for samples before the minimum; see text).

depends on the observation time; therefore STE NMR experiments were performed on the concentrated phase of both samples and repeated at different diffusion times over a period of 2 weeks, in order to check any evolution in the sample composition. The results are shown in Figure 7. The signal decays are monoexponential, independent of the diffusion time, and do not change upon sample aging. This means that no structural change in the samples has occurred during the whole period of observation. Fitting the data yields lecithin selfdiffusion coefficients of 0.75 × 10-11 and 0.91 × 10-11 m2 · s-1 for samples prepared in H2O and 2H2O, respectively, with an error of (1%. Figure 8a shows the surfactant NMR self-diffusion data collected at 298 and 323 K on diC8PC/H2O samples at different lipid volume fractions (φL) corrected for water viscosity and temperature. φL values were obtained from the surfactant volume

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TABLE 1: Surfactant Mole (xL) and Volume Fractions (OL), Volume Ratios between Lecithin-Poor (Vup) and Lecithin-Rich (Vdown) Phases in Biphasic Samples, and Observed and Corrected Self-Diffusion Coefficients at 298 and 323 Ka T ) 298 K xL × 103 Vdown/Vup 0.177 0.353 1.020 1.900 3.940 9.300 a

1/9 1/3 2/3 1 phase 1 phase

φL 0.08 0.08 0.08 0.115 0.241

T ) 323 K

Dobs × 1011 (m2 · s-1) Dcorr × 1011 (m2 · s-1) 0.78 0.79 0.75 0.86 1.00

0.76 0.77 0.73 0.84 0.99

φL 0.005 0.009 0.027 0.051 0.115 0.241

Dobs × 1011 (m2 · s-1) Dmic × 1011 (m2 · s-1) Dcorr × 1011 (m2 · s-1) 5.79 3.80 2.07 1.80 2.00 2.65

4.72 3.34 2.10 1.69 1.95 2.63

The error on Dobs is (1%, while that for Dmic and Dcorr is (5%.

(766 Å3)5 and the concentration (in molar units) of the lipid dispersions. Since at 298 K the diC8PC/H2O dispersion phase separates for lipid volume fractions smaller than 0.077 (indicated by the vertical line in Figure 8a), NMR experiments on such biphasic samples were carried out on the lower phase. In these samples most of the surfactant collects in the lower phase; therefore the φL values were recalculated to take into account the volume of that phase. According to the lever rule, an increase of the lipid amount causes growth of the lower phase at the expense of the upper phase, so that φL in the concentrated phase remains unchanged for the different samples. Table 1 reports surfactant mole fractions, volume ratios between lower and upper phases (of the biphasic samples), and calculated φL and self-diffusion coefficient values for each investigated sample. The experiments performed at the higher temperature will be analyzed first. The occurrence of a minimum in the observed self-diffusion coefficients (Dobs) as a function of the surfactant concentration is typical of wormlike micellar systems. In order to investigate the mechanisms involved in diC8PC diffusion, the Dobs values recorded at 323 K were adjusted by removal of the contribution due to free surfactant diffusion (Dmon), according to eq A1 (see Appendix). In addition, the data for φL < 0.077 due to the interacting but still disentangled micelles were analyzed with eq A2 to get an accurate value for the micellar self-diffusioncoefficient,Dmic,withtheremovalofparticle-particle and hydrodynamic interactions. The corrected data are plotted in Figure 8b. The data were fitted with a power law in φL (Dcorr ) CφLx, where C is a constant), and the calculated scaling exponents were -0.42 and +0.28, respectively. Therefore, in the dilute regime the obtained Dmic values closely follow the power law in φL that is expected for wormlike micellar diffusion (-0.35; see Appendix). In the semidilute regime, the scaling exponent is in good agreement with a wormlike micellar model where surfactant self-diffusion is regulated by a mechanism that involves intermicellar connections (theoretical value of +0.25; see Appendix). NMR studies on wormlike micellar systems have recently pointed out that the mean square displacement (msd) of surfactants that diffuse in a monodimensional curvilinear way along the micellar contour actually scales with t1/2 rather than simply obeying the linear form of the Einstein equation (〈z2〉 ) 2Dt).40 However, in the presence of intermicellar connections, and if the density of the branches is large enough for the surfactant molecules to cross several branch points during the experimental time, then a Gaussian behavior is recovered. In Figure 9 the log-log plot of diC8PC msd at different lecithin concentrations versus the experimental time ∆ is reported. Fitting the data to the 〈z2〉 ) 2Dtx equation gave scaling exponents x spanning between 1.06 and 0.91, meaning that the surfactant molecules experience normal (Gaussian) diffusion in

Figure 9. Plot of a representative selection, for samples having different compositions, of lecithin mean square displacements at 323 K fitted according to 〈z2〉 ) 2Dtx. (O) φL ) 0.009; (0) φL ) 0.051; (]) φL ) 0.241. (∆ ) t are as in Figure 7.)

the investigated concentration range. While such behavior was expected for samples in the dilute regime, here it may represent additional evidence for the building up of a tridimensional network in the semidilute concentration regime. In conclusion, from the self-diffusion data analysis and the calculated scaling exponents with φL at 323 K, the presence of linear wormlike micelles emerges straightforwardly. When the lipid volume fraction increases, for φL> φL*, the aggregates start to interconnect. The average micelle length (L) in the sample at φL ) 0.027 was determined at different temperatures (see eq A5 in the Appendix). Here, since there is no reason for the micelle to swell, the diameter of the wormlike aggregate was used as a constraint and fixed to 4 nm, according to the structural parameters of diC8PC determined via SAXS measurements and cryo-TEM observations (this work). The results are reported in Table 2 together with the diffusion coefficients of the wormlike micelle translational motions in the parallel and perpendicular directions with respect to the rod main axis (D| and D⊥; see eqs A6 and A7 in the Appendix), and an estimate of the Kuhn length (LK) obtained from equation eq A8. Kuhn lengths as high as those obtained in the present study (about 100-340 nm) are reported in the literature.41 It is interesting to note that Kuhn lengths having the same size of the micellar lengths were also found in the lecithin-bile salt wormlike micellar system.42 Some important conclusions can be obtained from these data. The Kuhn length reduces when temperature is increased, indicating an increase in the flexibility of the micelles at higher temperatures. However, since LK is always comparable to the micellar size, the wormlike aggregates can basically be considered as rigid rods and, consequently, eqs A5-A8 hold. From the power law fitting of the average micellar length L versus φL (Figure 10), for samples examined before the minimum in Figure 8a, the scaling exponent for φL was calculated to be +0.7, in good agreement with the value predicted by the formula L

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TABLE 2: Translational Diffusion Coefficients,a Average Micellar Lengths and Kuhn Lengths, Critical Micelle Concentration,b and Water Viscosityc T (K) 298 318 323 328 333

η (mP · s)

cmc × 106

Dmic × 1011 (m2 · s-1)

D| × 1011 (m2 · s-1)

D⊥ × 1011 (m2 · s-1)

L (nm)

LK (nm)

0.890 0.596 0.546 0.504 0.466

1.61 2.46 2.74 2.89 3.12

1.75 2.10 2.65 3.40

2.26 2.69 3.36 4.23

1.50 1.81 2.30 2.96

171 153 126 101

340 252 166 99

Dmic, D|, and D⊥ were obtained from Broersma’s equations. The error on Dmic is (5%. b Expressed as lipid mole fraction; data from ref 7). For the diC8PC/H2O sample with φL ) 0.027 at different temperatures. a

c

Figure 10. Log-log plot of the average micellar lengths for samples having different lecithin concentrations at 323 K. The solid line is the best fit to a power law.

Figure 11. Arrhenius plot of the micellar lengths versus 1/T for the diC8PC/H2O sample with φL ) 0.027.

) φ0.5 L exp (Es/2kBT) where Es is the scission energy, that is, the energy required to create two endcaps from a semi-infinite cylinder (see Appendix). It is not surprising that this exponent is somewhat higher than the expected value (+0.5). In fact, for charged cylindrical micelles the usual exponent in the growth law for the average micelle length should increase at low (or zero) added salt, because of the extra contribution to the free energy of an endcap due to Coulomb interactions.43 The Arrhenius plot obtained from the L versus T-1 graph (see Figure 11) provides a value for the scission energy Es of about 60 kJ/mol. Characteristic values reported in the literature (see ref 44 and references therein) vary approximately between 50 and 170 kJ/mol. Therefore, the Es found in this work can be considered as a low-range value. It is interesting to recall here that, according to the BTB model, the value of ∆µ (which reflects the chemical potential gain of the uniaxial micellar growth along the main axis) is about 74 kJ/mol for diC8PC.7 Wormlike micelles were seldom observed in pure binary systems when either ionic or nonionic surfactants were used.45,46 Instead, they are usually obtained from cationic surfactants, after replacement of the hydrophilic counterions (like Br-) with more lipophilic species such as alkyl sulfonate or salicylate.47 Actually, the one-dimensional growth that leads to these large

anisotropic aggregates in aqueous solutions is typically provoked by adding cosurfactants or salts,7 depending on the nature of the surfactant.48 Such additives produce an increment in the surfactant packing parameter, and consequently a decrease in the interfacial curvature of the aggregate. Since in a wormlike micelle the curvature at the endcaps is higher than the spontaneous curvature in the cylindrical central portion, such additives definitely produce an increase in the scission energy that, in turn, represents the driving force for the huge linear micellar growth. Hence, a low scission energy is expected in the case of surfactants that bear a short hydrophobic tail (smaller value of the packing parameter) and, for a specific system, in the absence of any additive. The zwitterionic lipid examined in this work complies with both these requirements and this justifies the low value of Es calculated from the Arrhenius plot. Accounting for the formation of a three-dimensional network in the analysis of data for the semidilute concentration regime seems to be a more complicated task. Indeed, in aqueous systems, connections are negatively curved and are usually found when high salt concentrations give rise to a strong screening of the electrostatic repulsions between the polar heads of ionic surfactants. In this way the scission energy becomes much larger than the energy of formation of a 3-fold cross-link, which is actually favored. Therefore, the same structural features of the diC8PC molecule that provide the rationale for the low value of Es should, in principle, work against the building up of intermicellar connections. The high stiffness of the wormlike micelles can account for the observed behavior of the system under study. In fact, beyond the overlap concentration, the micelles could rearrange into an energetically favored interconnected system. In order to allow both endcaps and branch points, we have to consider that the endcap energy (half of the scission energy) is rather high, and the junctions have lower mean curvature than the cylinder (and negative Gaussian curvature). However, the energy difference between endcaps and junctions may not be prohibitively large, and the entropy of the junctions is much more favorable since they can exist everywhere. Moreover, the unavoidable polydispersity in surfactant chain length can lead to local phase separation within aggregates that favors locally reversed curvature regions, that is, junctions. On the other hand, the calculated packing parameter P is just an estimate. It is affected by changes in solution conditions (temperature, solute adsorption, concentration, interaggregate interactions) that determine curvature. Cubic phases of zero average curvature can pack at surfactant parameters around and above 0.8, and cylinders with junctions probably correspond to the onset of connected random disordered phases. These are ubiquitous in cationic microemulsions where curvature is a delicate balance of oil penetration into surfactant tails.29,49,50 Finally, there are two further mechanisms that promote the formation of branchpoints: (i) this process requires a partial dehydration of the polar headgroups and some hydrating water

12632 J. Phys. Chem. B, Vol. 112, No. 40, 2008

Lo Nostro et al.

molecules are pushed back into the bulk aqueous phase (with an increment in entropy), and (ii) when the concentration of branches increases, the semispherical endcaps can fuse together to form a continuous cylindrical bridge that connects different rods. In the present system, the formation of connections is strongly suggested by the following experimental observations: (1) Gaussian diffusion is observed for all NMR experiments performed in this work. An anomalous non-Gaussian diffusion should be detected in the case of living polymers or for living networks with a low connectivity degree. (2) The exponent found for the power law that fits the data for φL > φL* is very close to the value expected for wormlike systems in the presence of intermicellar connections. (3) The cryo-TEM micrographs are similar to what has been observed in other systems with connected networks16 and give some evidence for the presence of three-way Y junctions. A last remark can be made on the basis of the scaling exponent with φL (+0.25) obtained for samples at 298 K (whose compositions, calculated in the lower concentrated phase, always lie above the φL* threshold). Independently of the phaseseparation process, the microstructure in the diC8PC concentrated phase is retained. Therefore, previous conclusions drawn for the sample investigated at 323 K are also valid for the concentrated phase of the biphasic samples at 298 K. Of course, a noticeable difference must be underlined: as indicated by the constant Dobs values and by visual inspection of the sample, an increase in the surfactant concentration causes the bottom diC8PC-rich phase to grow at the expense of the top diC8PCpoor phase rather than a change in the microstructure of the sample. Conclusions The bottom, lipid-rich phase formed after the liquid-liquid phase separation in a water dispersion of diC8PC is composed of wormlike micelles (polymerlike or giant micelles). CryoTEM images clearly show rods with a length of 300 nm or more. These micelles have a cross-section radius of about 18 Å (as detected from SAXS) and, as ascertained mainly through NMR analysis, are entangled in a dense tridimensional interconnected network. The mechanism of the temperature-dependent phase transition involves a conversion of the prolate micelles from a homogeneous starting dispersion to rodlike aggregates, which segregate in the bottom phase. Upon cooling, rods keep growing and the onset of several branch points leads to the formation of a tightly packed interconnected structure, where dehydration of the polar headgroups and entropy play the major roles. Acknowledgment. Partial financial support from Consorzio Interuniversitario per lo Sviluppo dei Sistemi a Grande Interfase (CSGI, Italy) and Ministero dell’Universita` e della Ricerca is gratefully acknowledged. Appendix For surfactant solutions above the critical micelle concentration (cmc), the measured self-diffusion coefficient (Dobs) is a combination of the self-diffusion coefficient of the micellarbound (Dmic) and that of the free surfactant monomers (Dmon). Therefore, according to the two-site fast-exchange model, we have φ Dobs ) pDmic + (1 - p)Dmon

(A1)

where p is the fraction of surfactant in the micellar state, given by p ) (Ctot - cmc)/Ctot, and Ctot is the total surfactant

concentration. The superscript φ indicates that the micellar displacements are reduced because of both interparticle collisions and hydrodynamic effects (the viscous shear wave generated by a moving particle).51 In order to obtain the micellar self-diffusion coefficient free of such concentration effects, we make use of the following equation:52

9φ 32 φ φ 1 + H(φ) + 1φg φg 1-

φ Dmic ) Dmic

( )(

)

(A2)

-2

where φ represents the micellar volume fraction, and φg ≈ 0.57185 is the colloidal-glass transition volume fraction. H(φ) is related to the many-body static effects due to hydrodynamic interactions and is given by

H(φ) )

2b2 6bc c 2bc 1+ 1 - b 1 + 2c 1 - b + c 1 - b + c + 4bc

(

[

bc2 2bc + 1+ 1 - b + c + 2bc (1 + c)(1 - b + c)

)

]

3bc2 bc2 (A3) (1 + c)(1 - b + c) - 2bc2 (1 + c)(1 - b + c) - bc2 where b(φ) ) (φ/φc)1/2, c(φ) ) 11φ/16, and φc is the closest packing volume fraction. Wormlike micellar aggregates consist basically of semiflexible rodlike micelles whose static and dynamic behaviors at equilibrium resemble those of polymers, the main differences being (i) the reversible scission these micelles undergo, (ii) the concentration dependence of the micellar length, and (iii) the possibility for these aggregates to form an interconnected network (living network) rather than simply an entangled network (living polymer). As the volume fraction of the surfactant is increased, micelles grow, andsdepending on the value of the scission energy Es (i.e., the energy required to create two endcaps from a semiinfinite cylinder)smay become very long. While growth proceeds, above a surfactant volume fraction (φL*), micelles will entangle and eventually interconnect.53 In this kind of system, Dobs results from different contributions. Here only a brief summary of the various diffusion mechanisms concerning wormlike micelles will be presented. A more complete discussion can be found in the literature (ref 54 and references therein). A major distinction can be made between mechanisms that rule the material transport before and after φL*, that is, the volume fraction threshold between the diluted (φ < φL*) and the semidiluted regimes (φ > φL*). Upon increased surfactant concentration in the diluted regime (before φL*), theory predicts that the aggregates’ growth will produce a decrease in the micellar self-diffusion coefficient (Dmic) up to a concentration where the wormlike micelles begin to overlap (at φL*). Once the contributions to Dobs due to free (molecular) surfactant diffusion along with interparticle collisions and hydrodynamic interactions are removed, and since in this regime the surfactant diffusion within the aggregate is limited by the diffusion of the micelles, Dobs will be equal to Dmic and scales with φ-0.35. In particular, the average micellar length (L) depends on φ according to55

L ) φL0.5 exp(Es/2kBT)

(A4)

Very different behavior is expected for Dobs when φL > φL*. In this concentration range (semidilute regime) the micellar

Interconnected Networks of DiC8PC

J. Phys. Chem. B, Vol. 112, No. 40, 2008 12633

motion can be described by a pure reptation mechanism, and scission/recombination processes must be taken into account if the micelle’s lifetime (the time before a micelle disrupts) is smaller than the reptation time (the time a micelle requires, by curvilinear diffusion along its own contour, for complete disengagement from a tubelike environment). According to these diffusion mechanisms and whether the reversible scission is included or not, Drep should scale with φ-1.71 or φ-3.05, respectively. Although micellar and molecular diffusion occur simultaneously, let us focus now, for the semidilute regime, only on the surfactant monomers’ diffusion in the aggregates and neglect for the moment the micellar diffusion. There are two opposite possibilities: (i) the surfactant molecules freely diffuse over the whole micelle before it breaks, or (ii) the micelle falls apart before the monomer diffuses on its surface. Then, Dsurf is expected to be an increasing or a decreasing function of the surfactant concentration, scaling as φ0.97 or as φ-0.23, respectively. In any case, if intermicellar connections are taken into account, the surfactant diffusion should lead to an increase of Dsurf scaling with φ0.25, while the reptation of branches between connections should be a decreasing function of φ, with Dbranch scaling with φ-0.75. As suggested by Schmitt and Lequeux,54 if these diffusion mechanisms are combined together, the only explanation for the minimum in the Dobs/φL plot would be a crossover between the micellar diffusion regime in the dilute concentration range and a diffusion regime where the surfactant diffusion in the absence of scission or, alternatively, in the presence of intermicellar connections, is the dominant and fastest mechanism. The average length L of the wormlike aggregate can be obtained from self-diffusion measurements according to Broersma’s equations, that are valid for rigid rodlike particles in solution with a length-to-diameter ratio larger than 5:56,57

kBT (σ - γ) 3πη0L

(A5)

D| )

kBT (σ - γ|) 2πη0L

(A6)

D⊥ )

kBT (σ - γ⊥) 4πη0L

(A7)

Dmic )

Here D| and D⊥ represent the diffusion coefficients for parallel and perpendicular displacement with respect to the rod axis, respectively, and

σ ) ln

( 2Ld )

γ| + γ⊥ 2 0.15 13.5 37 22 γ| ) 0.807 + + 2 - 3+ 4 σ σ σ σ 0.15 8.1 18 9 γ⊥ ) -0.193 + + 2 - 3+ 4 σ σ σ σ γ)

By use of the following formula:58

[

( )]

D| - D⊥ 3 L ) 1 - 0.5 Dmic 4 LK

1⁄4

(A8)

the Kuhn length (LK) of a rigid rod can be obtained from its diffusion coefficients. The Kuhn length is twice the persistence length (Lp) and gives an estimate of the micellar flexibility. At

a length scale equal to or smaller than Lp, wormlike micelles behave as rigid rods. In turn, this length is related to the micellar bending modulus k:

Lp )

k kBT

(A9)

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