Properties of a Two-Dimensional Asphaltene Network at the Water

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Properties of a Two-Dimensional Asphaltene Network at the Water-Cyclohexane Interface Deduced from Dynamic Tensiometry Patrick Bouriat,* Nabil El Kerri, Alain Graciaa, and Jean Lachaise Laboratoire des Fluides Complexes, UMR5150, Universite´ de Pau, 64013 Pau Cedex, France Received April 19, 2004 Static and dynamic tensiometries show that a newly prepared water/asphaltenated cyclohexane interface behaves as expected: the mean area occupied per asphaltene molecule is 2 nm2, and variations of interfacial tension and dilatational elastic modulus with time indicate that equilibrium is reached more slowly than that for usual surfactants. The use of the time/temperature superposition principle allows a detailed rheological study of a 2 day old interface of the same type which has reached equilibrium. It is found that the two-dimensional asphaltene network exhibits a glass transition zone, behaves as a gel near its gelation point, and is built by a universal process of aggregation.

Introduction Industrial dewatering of crude oils is rendered difficult by the fact that the water-in-crude emulsions they form spontaneously are very stable. This stability is principally attributed to the presence of an asphaltene film at the oil/water interface. Asphaltenes are surface active molecules naturally present in the crude oils.1 They are defined as their most polar and heaviest compounds. They are composed of several polynuclear aromatic sheets surrounded by hydrocarbon tails, forming particles whose molar masses are included between 1000 and 10000 g. Those particles exhibit colloidal properties since asphaltenes can also associate themselves into larger three-dimensional (3D) structures whose sizes are strongly dependent on their solubility in the oil phase.2 Many authors3-5 observed that the interfacial film formed by asphaltenes at the oil/water interface presents a highly viscoelastic behavior. This behavior, strongly dependent on the solubility of asphaltene in oil, was attributed to physical cross-links between asphaltenic aggregates.6-8 Another characteristic property of water-in-crude emulsions is that their stability increases with time.9 This fact is confirmed by rheological measurements: Mohammed et al. have shown a slow increase in film compliance with aging.10 They attributed this slow film build up to further adsorption and rearrangement of indigenous materials * Corresponding author. E-mail: [email protected]. (1) Yarranton, H. W.; Hussein, H.; Masliyah, J. H. J. Colloid Interface Sci. 2000, 228, 52. (2) Speight, J. G. In Asphaltenes and asphalts, 1; Yen, T. F., Chilingarian, G. V., Eds.; Elsevier Science: New York, 1994; Chapter 2. (3) Strassner, J. E. J. Pet. Technol. 1968, 20, 303. (4) Bhardwaj, A.; Hartland, S. Ind. Eng. Chem. Res. 1994, 33, 1271. (5) Acevedo, S.; Escobar, G.; Gutie´rrez, L. B.; Rivas, H. Colloids Surf., A 1993, 71, 65. (6) McLean, J. D.; Kilpatrick, P. K. J. Colloid Interface Sci. 1997, 196, 23. (7) Singh, S.; McLean, J. D.; Kilpatrick, P. K. J. Dispersion Sci. Technol. 1999, 20, 279. (8) Ese, M. H.; Yang, X., Sjo¨blom, J. Colloid Polym. Sci. 1998, 276, 800. (9) Jones, T. J.; Bleys, G.; Joos, P. J. Can. Pet. Technol. 1978, AprilJune, 100. (10) Mohammed, R. A.; Bailey, A. I.; Luckham, P. F.; Taylor, S. E. Colloids Surf., A 1993, 80, 237.

present in the crude oil. Studying the slow decrease of interfacial tension between water and crude oil both with dynamic tensiometry and videography, Bhardwaj and Hartland concluded that aging consists of a slow transportation of the natural surfactants present in crude oil to the crude oil/water interface, followed by some steric rearrangements within the interfacial film.4 Considering the bulk diffusion coefficient of asphaltenes, Jeribi et al. concluded that aging was due to a slow reorganization of the interface rather than continuous adsorption.11 Reorganization and aging are two phenomena related to colloidal aggregation. Such a process could explain why an asphaltene film at the oil/water interface, initially fluid, tends to become increasingly viscoelastic. The purpose of this work is to verify this assumption. To get a better understanding of the extent of asphaltenic cross-linking at the water/oil interface, it is of interest to investigate the film properties by means of a detailed 2D rheological study. We used a poor solvent for asphaltene dissolution to favor asphaltene adsorption and film buildup at the oil/water interface. Interfacial tension and dilatational elasticity measurements were carried out with an interfacial drop tensiometer. First of all we present the materials and methods used. Then we perform a conventional study of both the interfacial tension and dilatational elastic modulus of a newly prepared water-asphaltened cyclohexane interface in order to compare the interfacial behavior of asphaltenes with that of usual surfactants. Finally we proceed to a detailed study of the rheological properties of a 2 day old water-asphaltened cyclohexane interface in order to obtain information on the asphaltene organization at this interface. Materials and Methods The water used is ultrapure grade from a Milli-Q plus system (Millipore). Cyclohexane (99.9% HPLC grade) and pentane (99% HPLC grade) were purchased from Sigma-Aldrich. Vic-Bilh crude oil extracted in France was furnished by Total. The asphaltenes used in this study are extracted from crude oil by adding pentane at a 1/5 volume crude/pentane ratio. The mixture is shaken and allowed to rest at ambient temperature for 24 h in order to favor asphaltene precipitation. Supernatant (11) Jeribi, M.; Almir-Assad, B.; Langevin, D.; He´naut, I.; Argillier, J. F. J. Colloid Interface Sci. 2002, 256, 268.

10.1021/la049017b CCC: $27.50 © 2004 American Chemical Society Published on Web 07/29/2004

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is then eliminated by filtration. The residue is abundantly washed with pentane until a colorless solution is obtained. The solid fraction is dried under vacuum. The obtained fraction thus represents 9.25 wt % of the crude initially used. This fraction is generally called asphaltenes by petroleum engineers, although chromatography measurements show that it contains a significant quantity of resins (30%). The last stage of this preparation consists of diluting the so-called asphaltenes in a poor solvent in order to favor asphaltene adsorption and film buildup at the oil-water interface. We chose cyclohexane because its refractive index, n0 ) 1.426, is very close to the refractive index of solvent mixtures at the onset of asphaltene precipitation (approximately 1.44).12 We fixed the asphaltene concentration at 100 g/L because that is their approximate concentration in crude oil. This solution was preserved in a closed opaque recipient in order to avoid any action of oxygen or light. Dynamic interfacial tension was measured with a drop tensiometer (Tracker, IT Concept, France). A rising drop of cyclohexane with asphaltenes is maintained vertically in a thermostated cell full of pure water by means of a microsyringe. The shape of the droplet is recorded in real time with a video camera. A computer calculates the drop area and interfacial tension from the Laplacian shape of the drop. To evaluate the dilatational elastic modulus, the apparatus is designed to program sinusoidal variations of the drop area. Chosen amplitude and frequency of the sinusoidal variations are applied to the syringe piston by computer-controlled servomotors. The relative area variation imposed by the apparatus and the interfacial tension response are recorded in order to evaluate the complex dilatational interfacial elasticity E* with eq 1

E* )

dγ* d ln A*

(1)

where A* is the complex area of the drop and γ* is the complex interfacial tension, assuming that the interfacial area response is sinusoidal. Then one can evaluate the real part ′ and the imaginary part ′′ of the complex dilatational interfacial elasticity

E* ) ′ + j′′

(2)

with j ) x-1. The real elasticity ′ characterizes the conservative behavior of the interface while the imaginary part ′′ is related to dissipative interfacial phenomena. Dilatational elastic modulus is given by 2

2 1/2

E ) (′ + ′′ )

(3)

and loss angle by

φ ) tan-1(′′/′)

(4)

To evaluate the complex dilatational interfacial elasticity E* with eq 1, one has to be sure that the interfacial tension response to the sinusoidal stretch of the area has a sinusoidal form. This linear response regime is obtained by imposing small area amplitude variations on the drop. For a wide range of asphaltene concentrations and oscillating periods, it appears that plots representing γ ) f(ln A) for cyclohexane/water interfaces generally present hysteresis centered on the equilibrium values of area and tension attained before oscillations. As expected, providing that surface variation is sufficiently small (less than 7%), hysterese all have an elliptic shape indicating the validity of eq 1 for the determination of E*. The drop tensiometer also allows the determination of the relaxation modulus E(t). At t ) 0, a sudden small increment of area ∆A is applied to the drop initially having an interfacial tension γeq and an area A. The instantaneous interfacial tension response γ0 and the further relaxing interfacial tension γ are recorded. The elastic modulus is calculated with the Gibbs equation: E ) dγ/(d ln A) which becomes in this case

A(γ - γeq) γ - γeq E(t) ) ) E(0) ∆A ∆γ with ∆γ ) γ0 - γeq and E(0) ) A∆γ/∆A.

(5)

Figure 1. Interfacial tension of water/asphaltenated cyclohexane versus asphaltenes concentration (T ) 25 °C).

Results and Discussions 1. Newly Prepared Interface. Figure 1 displays, at equilibrium, interfacial tensions between water and asphaltene solutions for asphaltene concentrations ranging between 0.1 and 100 g/L in cyclohexane. It appears that asphaltene behavior at the water/oil interface is very similar to that of usual surfactants. Interfacial tension decreases as asphaltene concentration increases until a critical concentration (about 17.5 g/L) beyond which it remains constant. This concentration plays the same role as the critical micelle concentration (cmc) of ordinary surfactants: the interface is saturated above this concentration. Observation of one cmc for asphaltenes has already been reported by other authors, for various solvents.13,14 The values of the cmc that they reported range between 1 and 30 g/L, depending on the solvents used for asphaltene precipitation and their redissolution. Available interfacial area A0 by a unit of asphaltenic compounds at the oil/water interface can be deduced from the negative slope of the linear variation of γ below the cmc by means of the Gibbs equation

kBT dγ )d ln c A0

(6)

where c is the asphaltene concentration in cyclohexane, T is the temperature, and kB is Boltzmann’s constant. A0 is found to be about 2 nm2. This value, in agreement with the values given in refs 13 and 14 (ranging from 1 to 4 nm2), is plausible for compounds whose mean molar weights are included between 1000 and 10000. Thus, one can conclude that asphaltene molecules or particles, but not aggregates, are principally adsorbed at the water/ cyclohexane interface. Typical variations of interfacial tension with time are shown in Figure 2. At t ) 0 the oil drop is created in deionized water and is allowed to relax in interfacial tension. As expected, the kinetics increase with asphaltene concentration but are very slow in comparison with those commonly expected for most of the surfactants with similar molecular weight in this concentration range. Equilibrium is reached after 50 min for 100 g/L, after 14 h for a more diluted solution (0.1 g/L). Jeribi et al attributed such slow kinetics to a molecular reorganization process at the interface, because the (12) Buckley, J. S.; Hirasaki, G. J.; Liu, Y., Von Drasek, S.; Wang, J. W.; Gill, B. S. Pet. Sci. Technol. 1998, 16, 251. (13) Loh, W.; Mohamed, R. S.; Ramos, A. C. S. Pet. Sci. Technol. 1999, 17, 147. (14) Rogel, E.; Leon, O.; Torres, G.; Espidel, J. Fuel (Guildf.) 2000, 79, 1389.

Asphaltene Network

Figure 2. Variation of interfacial tension with time for water/ asphaltenated cyclohexane interface at two different concentrations of asphaltenes: 0.1 and 100 g/L (T ) 25 °C).

Figure 3. Evolution with time of the dilatational elastic modulus of water/asphaltenated cyclohexane (100 g/L) interface at 25 °C. The frequency of the measurements is fixed at 0.1 Hz.

diffusion process would lead to much smaller relaxation times.11 To study the evolution of these relaxation times as a function of the asphaltene mass fraction, these authors treated the interfacial tension as decreasing monoexponentially. In fact, a careful examination of the relaxations drawn in Figure 2 shows that they are not monoexponential but are multiexponential over several decades. The shortest relaxation times correspond to the diffusion process of the asphaltenes from the bulk to the interface; the longer times are related to the rearrangement of the asphaltene molecules at the interface to form the film. To follow the formation of this film, the evolution with time of the dilatational elastic modulus of a water/oil interface is presented in Figure 3. The concentration of asphaltenes in cyclohexane, fixed at 100 g/L, is representative of asphaltene concentration in crude and allows the surface tension to reach equilibrium after a relatively short time. Although the age of the drop is greater than the time necessary to reach the end of the asphaltene adsorption, the elastic modulus still increases with time. This augmentation confirms that asphaltenes, yet adsorbed at the interface, reeorganize themselves at the interface over long periods of time. One can assume that this organization consists of associations of asphaltene molecules located at the interface in order to form two-dimensional aggregates. This assumption corroborates results reported in the introduction of this paper: with aging, the initially fluid interface tends toward a permanent viscoelastic state. 2. Two Day Old Interface. A 2D Network Exhibiting a Glass Transition Zone. To obtain more detailed information on the type of organization of the asphaltene

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Figure 4. Elastic modulus of the interface between water/ asphaltenated cyclohexane (100 g/L) plotted against pulsation at six temperatures as indicated. Aged 48 h at 25 °C.

molecules, a complete analysis of the viscoelastic properties of the interface must be performed as a function of pulsation. Unfortunately, the device used can explore only two decades of pulsations ranging between 0.01 and 1 rad/s at the very most. We then decided to conduct those experiments at different temperatures hoping that a shift in temperature implies a shift in pulsation; i.e., the observed phenomenon presents a master curve. Figure 4 presents experimental data relative to a water/ asphaltenated cyclohexane (100 g/L) interface for temperatures ranging from 15 to 55 °C. The drops used were maintained during 48 h at ambient temperature, then brought to the chosen temperature before measurements. ′′ versus ′ relative to all temperatures and pulsations can be reported in one single Cole-Cole diagram. This means that the contributions of all temperatures studied form a single continuous curve. Thus, on the experimental domain, it is verified that a shift in temperature involves a shift in pulsation and vice versa. It is then possible to apply the time/temperature superposition principle in order to extend artificially the pulsation gap at a given temperature.15 The curves presented in Figure 4 were shifted horizontally by a quantity log[a(T,T0)] relative to an unshifted curve obtained at a reference temperature T0 in order to form a master curve. Moreover, with the same shift factors a(T,T0), another continuous master curve was obtained for the loss angle φ. Experimental evolutions of shift factors with temperature are plotted as circles in Figure 5. In this semilogarithmic diagram, the plot does not follow Arrhenius law but a more substantial variation indicating glass transition. To ensure that the material present at the interface exhibits glass transition in this temperature interval, we verified that the temperature shift factors obey the Williams, Landel, Ferry equation16

ln a(T,T0) )

-C1(T - T0) C2 + (T - T0)

(7)

On Figure 5, we can see that the shift factors follow the WLF equation (represented by a solid line). This indicates both that the time/temperature superposition principle is valid and that the asphaltene film present at the interface behaves like a material near its glass transition temperature. (15) Ferry, J. D. J. Am. Chem. Soc. 1950, 72, 3746. (16) Williams, M. L.; Landel, R. F.; Ferry, J. D. J. Am. Chem. Soc. 1955, 77, 3701.

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Figure 5. Temperature dependence of the shift factor a(T,T0) used to construct a master curve with experimental data plotted in Figure 4. Solid line is obtained from eq 7 with T0 ) 30 °C, C1 ) 6.2, and C2 ) 30 K.

Figure 7. Measured normalized stress relaxation modulus at T ) 30 °C (circles) for the system which obeys the master curve presented in Figure 6. Solid line is obtained using eq 10.

< 1 is a relaxation exponent. A gel with n approaching 1 is purely viscous whereas for n approaching 0 it is purely elastic. The loss angle φ is related to n by

φ)n

Figure 6. Composite curves of the elastic modulus and loss angle obtained from the same series of measurements as the data of Figure 4 and reduced to T0 ) 30 °C.

A 2D Gel near Its Gelation Point. The master curve, relative to the reference temperature: T0 ) 30 °C, obtained by shifting the experimental data of Figure 4 with the shift factors presented in Figure 5, is presented in Figure 6. Two zones can be identified. Above ωa(T,T0) ) 1, the plot is typical of a glass transition zone: the phase angle decreases and the elastic modulus levels off and tends toward a constant value. The interface no longer exhibits a viscoelastic behavior and tends to behave as a Hookean solid. Below ωa(T,T0) ) 1, the system presents a characteristic viscoelastic behavior. For a wide range of pulsations between 0.001 and 10 rad/s, the log-log plot of the dilatational elastic modulus E is a straight line while the loss angle remains constant. Winter and Chambon17,18 have shown that for a crosslinking polymer system near its gelation point, the loss and storage modulus are congruent (i.e., parallel) at the gel point with a pulsation dependence of

′ ∼ ′′ ∼ ωn

(8)

where ω is the pulsation of the measurement and 0 < n (17) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367. (18) Chambon, F.; Winter, H. H. J. Rheol. 1987, 31, 683.

π 2

(9)

Figure 6 shows that the value in degree of loss angle corresponding to the linear plot of elastic modulus is equal to 25. This corresponds to a relaxation exponent n equal to 0.277. On Figure 6 a slope of 0.277 is also represented, and we observe that it is parallel to the linear part of the elastic modulus plot. This confirms that oscillating drop measurements can be used to assert that adsorbed asphaltenes self-aggregate in order to form an interfacial structure which presents all the characteristics of a gel near its gelation point. Furthermore Winter and Chambon have shown that at the gel point, the relaxation elastic modulus, corresponding to stress relaxation experiments, relaxes with time according to the power law

E(t) ∼ t-n

(10)

Equation 10 was verified as follows. A drop of asphaltenated cyclohexane was allowed to age for 48 h in water. The value γeq of the interfacial tension between water and asphaltenated cyclohexane (100 g/L) at aquilibrium was recorded. Then the volume of the drop was suddenly increased by a small amount and both the corresponding increment of interfacial tension, ∆γ, at this time and the following interfacial tension decrease with time, γ, were recorded. Figure 7 presents the time evolution of (γ γeq)/∆γ which is equal to the normalized relaxation modulus E(t)/E(0), according to eq 5. This normalized relaxation modulus appears to obey eq 10 with n ) 0.277 corresponding to the value deduced from loss angle via eq 9 and from the slope of the linear part of the elastic modulus plot via eq 8. As the system obeys eqs 8, 9, and 10, it satisfies the gelation criteria as defined by Winter and Chambon for substances near their gelation point. A Power Mass Distribution of 2D Aggregates. The experimental results presented in Figures 6 and 7 show undoubtedly that at the water/cyclohexane interface, the interfacial network constituted by asphaltene naturally self-organizes in order to form a 2D membrane which exhibits the same viscoelasticity as a gel near its gel point.

Asphaltene Network

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2D gelation was observed by Naumann and co-workers for lipopolymers at the air/water interface.19, These authors observed a rheological transition from viscous to elastic behavior of the monolayer when it was compressed by means of a Langmuir balance. The substantial increase in the storage modulus induced by this transition was attributed to the increase in the density of networkforming physical junction points. This network structure was not attributed to entanglement effects because the lipopolymers used were too short. Moreover, they showed that gel formation proceeds in two steps: micellelike structures (called spherical nanoclusters) are formed by alkyl chain condensation induced by interfacial compression, then neighboring clusters are attracted by H-bond bridges between polymer moieties and mediated by water molecules.20 Asphaltene aggregation at the water/cyclohexane interface presents at least one similarity with lipopolymer gelation in the sense that an adsorbed asphaltene (about 2 nm2 per adsorbed molecule) is equivalent in size to the nanometric surface micelles of the lipopolymers mentioned above. This nanometric size, which confers colloidal properties on the solution, is a common feature for 3D physical gel formation of star, diblock, and triblock polymers as noted by Foreman et al.20 This is probably why 2D asphaltene condensation naturally occurs while for lipopolymers, gelation is induced by surface compression responsible for the formation of nanometrical surface micelles. One unanswered question remains: why do asphaltenes at the water/cyclohexane interface constitute a 2D network which tends naturally to reach its gel point? It has been shown by Krotov and Rusanov21 that a multielement model such as the parallel coupling of continuous Maxwellian blocks of relaxation times τ and elasticity k(τ) was able to describe efficiently the dilatational rheology of a surface layer. In such a model, the relaxation modulus is calculated by

E(t) )

∫0∞ k(τ)e-t/τ dτ

(11)

and the complex dilatational elasticity E* by

E* )

∫0∞ k(τ) 1 +iωτiωτ dτ

(12)

The fact that E(t) ∼ t-n and E* ∼ ωneinπ/2 implies that the distribution function of the relaxation time is of the form

k(τ) ∼ τ-(n+1)

(13)

i.e., it obeys a power law too. As, in a general way, the relaxation time τ(M) is linked to each aggregate of mass M by27 τ(M) ∼ MR, a power law for the relaxation time distribution, as is the case for this system, implies that the mass distribution of the asphaltene aggregates on the interface follows a power law and then a scaling law. Fractal-like structures of asphaltene aggregates, which also follow scaling law, have been observed by various authors in oil phases.22-24 Using small-angle neutron (19) Naumann, C. A.; Brooks, C. F.; Fuller, G. G.; Knoll, W.; Frank, C. W. Langmuir 1999, 15, 7752. (20) Foreman, M. B.; Cauffman, J. P.; Murcia, M. J.; Cesana, S.; Jordan, R.; Smith, G. S., Naumann, C. A. Langmuir 2003, 19, 326. (21) Krotov, V. V.; Rusanov, A. I. In: Physicochemical hydrodynamics of capillary systems: Imperial College Press: London, 1999; Chapter 4. (22) Park, S. J.; Mansoori, G. A. Energy Sources 1988, 10, 109. (23) Janardhan, A. S.; Mansoori, G. A. J. Pet. Sci. Eng. 1993, 9, 17.

scattering (SANS)25 and small-angle X-ray scattering (SAXS),26 Fenistein et al have shown that asphaltene aggregates in the toluene have a self-similar structure of fractal dimension close to 2 and that their mass distribution follows a power-law shape, with exponent τ ) 1.66, from the mass of a monomer to the maximum measurable value: 1500000 g. Moreover they made the assumption that the self-similar structure of aggregates was probably the consequence of a colloidal aggregation phenomenon. Different models such as percolation27 and diffusionlimited28 and reaction limited29 colloid aggregation (DLCA and RLCA) describe aggregation of colloidal particles depending on the type of their mutual interactions. All these models predict self-similar structures for colloid aggregates obeying laws of universal class. Fenistein et al. pointed out that both the fractal dimension value and the mass distribution exponent of asphaltene aggregates are similar to those predicted by the RLCA model, DF ) 2.1 and τ ) 1.5, respectively, and concluded that asphaltenes should exhibit a potential of the DLVO type, attributing the short-range attraction to the aromatic sheets and the repulsive barrier to their aliphatic chains.26 As our measurements prove that interfacial asphaltene aggregate mass distribution follows a scaling law, it is reasonable to assume that a similar universal process, such as that encountered in oil phases, takes place at the water/cyclohexane interface. A final remark concerns the explanation of the apparent “glass transition” observed on such an asphaltene film. During the interfacial colloidal aggregation, more and more aggregates are present at the interface. This progressively reduces the number of degrees of freedom of the aggregates present at the interface. When the interface is sufficiently old, the consequence is the prevention of any aggregate-aggregate bond. This “quasifrozen” state should explain both why after a long aging time the interfacial film does not transit to a postgel state and why it behaves as if it was near a glass transition. To our knowledge, the fact that an interface naturally tends to a near critical gel which exhibits a behavior similar to a glass transition has never been reported elsewhere. Our results on the interfacial aggregation of asphaltenes favor the RLCA or the percolation model rather than the DLCA model because the latter model predicts a bellshaped mass distribution while our results give a power law shaped distribution as predicted by the two former ones. Direct measurements of interfacial mass distribution of aggregates would make it possible to select between RLCA or percolation, the most suitable model for the description of asphaltene interfacial aggregation. Conclusions The mean available interfacial area of an adsorbed asphaltenic compound is found to be 2 nm2 indicating that it is asphaltene molecules (or small particles) but not large aggregates (previously formed in the bulk phase) which principally adsorb on the interface. Moreover, the very low kinetics observed, several hours, is attributed to rearrangement with time of the adsorbed material. The (24) Liu, Y. C.; Sheu, E. Y.; Chen, S. H.; Storm, D. A. Fuel 1995, 74, 1352. (25) Fenistein, D.; Barre´, L.; Broseta, D.; Espinat, D.; Livet, A.; Roux, J. N.; Scarsella, M. Langmuir 1998, 14, 1013. (26) Fenistein, D.; Barre´, L. Fuel 2001, 80, 283. (27) Adam, M.; Lairez, D. In Physical properties of polymeric gels; Cohen Addad, J. P., Ed.; Wiley: New York, 1996; Chapter 4. (28) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. Rev. Lett. 1984, 53, 1657. (29) Meakin, P.; Family, F. Phys. Rev. B 1987, 31, 564.

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time/temperature superposition extends artificially, but successfully, the pulsation interval of the oscillations and allows a detailed rheological study of a 2 day old interface on which the rearrangement of the adsorbed entities can be considered as finished. We have found that temperature shift factors follow the Williams-Landel-Ferry equation, which means that the 2D asphaltene network exhibits a glass transition zone. This 2D network behaves as a gel

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near its gelation point because both its complex elastic modulus and its relaxation modulus follow scaling laws. Furthermore asphaltenes form interfacial aggregates whose mass distribution follows a power law which indicates that the 2D network is built by a universal process of aggregation, as percolation or RLCA. LA049017B