Solution Properties of Asphaltenes | Langmuir

In the case of anisotropic particles, analytical expressions of form factors are ... a power law relation between the measured aggregate parameters, n...
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Langmuir 2008, 24, 3709-3717


Solution Properties of Asphaltenes Loı¨c Barre´,* Se´bastien Simon, and Thierry Palermo Institut Franc¸ ais du Pe´ trole (IFP), 1&4 AVenue du Bois-Pre´ au, 92852 Rueil-Malmaison, France ReceiVed August 23, 2007. In Final Form: January 14, 2008 Ultracentrifugation has been used to produce asphaltene fractions of reduced polydispersity. The structure of these asphaltene fraction solutions has been investigated using viscosity and X-ray scattering (SAXS) measurements as a function of concentration. The relative viscosities of the solutions were found to be fraction-dependent: intrinsic viscosities, radii of gyration, and second viriel coefficients followed a power law with molar mass Mw. A flat disc model succeeded in describing scattering data but failed to take viscosity data into account. By contrast, a fractal model has been found to be consistent with dependence of all measured parameters. Asphaltene-in-toluene solutions were found to form nanometric mass fractal aggregates of fractal dimension 2.1, which in consequence trapped solvent. When, instead of concentration, effective volume fractions are used, the relative viscosities of fractions merge on a master curve which can be fitted by a hard sphere model. In addition, the reduced osmotic moduli deduced from scattering measurements of the different solutions, when expressed as a function of a concentration adimensional parameter, merge again on a master curve which is in accordance with the hard sphere behavior. The viscosities of solutions can be fully predicted from structure considerations if the ratio of hydrodynamic to gyration radius is taken as 0.6. This ratio is found consistent with the fractal description of the aggregates.

I. Introduction Heavy crude oils are defined by their high densities.1 They present peculiar properties such as a large amount of high molecular mass compounds (resins and asphaltenes) and very high viscosities typically in the range 100-10 000 cP at room temperature.2 This viscosity leads to difficulties, for instance, in their transport by pipelines. Several processes to improve flow properties, such as dilution of heavy crude oils with less viscous hydrocarbons,3 are used or are in development. In order to optimize these methods, a better understanding of the origin of the large viscosity of heavy crude oils is required. From an academic viewpoint, the rheological behavior of heavy crude oil can also be used to provide insight into its colloidal state. Since the pioneering work of Mack,4 several studies have shown that asphaltenes are responsible for the very high viscosity of heavy crude oils.5-10 They are the most polar part of a crude oil1 and are defined as the fraction of petroleum insoluble in an alkane such as n-heptane (NF-T60-115 method) but soluble in toluene. The definition of this fraction implies that asphaltenes are not a pure material but a mixture of molecules. At the molecular level, conventional models11 based on powder X-ray diffraction show that they are composed of aliphatic/naphthenic moieties * Corresponding author. Tel.: + 33 1 47 52 73 10, Fax: + 33 1 47 52 70 25, E-mail address: [email protected] (1) Speight, J. G. The Chemistry and Technology of Petroleum, 2nd ed.; Marcel Dekker: NewYork, 1991. (2) Sanie`re, A.; He´naut, I.; Argillier, J. F. Oil Gas Sci. Technol. 2004, 59, 455-466. (3) Gateau, P.; He´naut, I.; Barre´, L.; Argillier, J. F. Oil Gas Sci. Technol. 2004, 59, 503-509. (4) Mack, C. J. Phys. Chem. 1932, 36, 2901-2914. (5) Reerink, H. Ind. Eng. Chem. Prod. Res. DeV. 1973, 12, 82-88. (6) Altgelt, K. H.; Harle, O. L. Ind. Eng. Chem. Prod. Res. DeV. 1975, 14, 240-246. (7) Evdokimov, I. N.; Eliseev, N. Y.; Eliseev, D. Y. J. Pet. Sci. Eng. 2001, 30, 199-211. (8) He´naut, I.; Argillier, J. F.; Barre´, L.; Brucy, F.; Bouchard, R. SPE International Symposium on Oilfield Chemistry, February 13-16, 2001, Houston, TX; SPE 65020. (9) Angle, C.; Lue, L.; Dabros, T.; Hamza, H. Energy Fuels 2005, 19, 20142020. (10) Luo, P.; Gu, Y. Fuel 2007, 86, 1069-1078. (11) Yen, T. F.; Erdman, J. G.; Pollack, S. Anal. Chem. 1961, 33, 1587-1594.

surrounding cores of polynuclear aromatics. This structure, thought to remain in solution, might be responsible for aggregation observed at very low concentration.12,13 These entities associate in turn into structures of larger scale referred to as aggregates in this paper. Most of the asphaltene solution studies involving viscosity measurements have been undertaken in the frame of the colloidal approach:4-10,20,26,28-30 asphaltenes are considered solute particles, possibly solvated and/or anisotropic, dispersed either in maltenes or in simple solvents to mimic crude oil behavior. The viscosities of asphaltene solutions present a nonlinear “exponential-like” increase as a function of the asphaltene concentration. Small-angle neutron and X-ray scattering have been widely used to probe the aggregate structure of heavy crude oils and asphaltene solutions.14-25 Different intraparticle structure factors (spheres, oblate or prolate cylinders, mass fractal aggregates, and so forth) have been applied to scattering spectra, and most of the studies converge on characteristic aggregate sizes of 3 to (12) Andreatta, G.; Goncalves, C.; Buffin, G.; Bostrom, N.; Quintella, C.; Arteaga-Larios, F.; Pe´rez, E.; Mullins, O. Energy Fuels 2005, 1282-1289. (13) Goncalves, S.; Castillo, J.;, Fernandez, A.; Hung, J. Fuel 2004, 18231828. (14) Fenistein, D.; Barre´, L.; Broseta, D.; Espinat, D.; Livet, A.; Roux, J.-N.; Scarcella, M. Langmuir 1998, 14, 1013-1020. (15) Roux, J.-N.; Broseta, D.; Deme´, B. Langmuir 2001, 19, 5085-5092. (16) Spieker, M.; Gawrys, K.; Kilpatrick, P. J. Colloid Interface Sci. 2003, 267, 178-193. (17) Gawrys, K.; Kilpatrick, P. J. Colloid Interface Sci. 2005, 288, 325-334. (18) Gawrys, K.; Blankenship, G.; Kilpatrick, P. Langmuir 2006, 22, 44874497. (19) Sheu, E. J. Phys.: Condens. Matter 2006, 18, S2485-S2498. (20) Storm, D.; Sheu, E.; DeTar, M. Fuel 1993, 72, 977-981. (21) Sheu, E. Phys. ReV. A 1992, 45, 2428-2438. (22) Sheu, E.; Liang, K.; Sinha, S.; Overfield, R. J. Colloid Interface Sci. 1992, 153, 399-410. (23) Mason, T.; Lin, M. Phys. ReV. E 2003, 050401-1-050401-4. (24) Tanaka, R.; Sato, E.; Hunt, J.; Winans, R.; Sato, S.; Takanohashi, T. Energy Fuels 2004, 18, 1118-1125. (25) Fenistein, D.; Barre´, L. Fuel 2001, 80, 283-287. (26) Wargadalam, V.; Norinaga, K.; Lino, M. Fuel 2002, 1403-1407. (27) Nortz, R.; Baltus, R.; Rahimi, P. Ind. Eng. Chem. Res. 1990, 29, 19681976. (28) Pierre, C.; Barre´, L.; Pina, A.; Moan, M. Oil Gas Sci. Technol. 2004, 59, 489-501. (29) Bardon, C.; Barre´, L.; Espinat, D.; Guille, V.; Li, M. H.; Lambard, J.; Ravey, J. C.; Rosenberg, E.; Zemb, T. Fuel Sci. Technol. Int. 1996, 14, 203-242. (30) Sheu, E. Energy Fuels 2002, 16, 74-82.

10.1021/la702611s CCC: $40.75 © 2008 American Chemical Society Published on Web 03/04/2008

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Figure 1. Diagram of separation of asphaltenes A in toluene into three fractions by using two successives ultracentifugations; proportion of each obtained fraction are given in mass. Table 1. Elemental Analysis (by Weight) of Asphaltenes A (Not Separated by Ultracentrifugation) A











10 nm, depending on asphaltene and solvent nature, and on thermodynamic conditions. These studies pointed out the large size polydispersity of these aggregates. Coupling viscosity measurements to determine size, mass5-7,14,26-29 or surface tension30 measurements have been used to gain insight into aggregate structure. In spite of these efforts, there are still open questions concerning the nanometric organization of the aggregates, with results being likely obscured by size polydispersity effects. We present in this paper a combination of scattering and viscosimetric experiments on asphaltene fractions obtained by ultracentrifugation. This fractionation technique allows enough material of reduced polydispersity and varied mass to be obtained to study concentration dependence of viscosity and X-ray scattering. Different structure-dependent parameters, namely, intrinsic viscosity, packing limit volume fraction, radius of gyration, “aggregate” weight, fractal dimension, and second viriel coefficient, are inferred from these measurements. Possible interpretations, discussed in the framework of solvated particle suspension, are proposed. Finally, a structural model, consistent with all the measured parameters, is discussed; this model can fully predict the solution viscosities from microscopic considerations. II. Experimental Section II.A. Asphaltene Sample Preparation and Characterization. Asphaltenes were prepared by precipitation in an excess of heptane (NF-T60-115 method) from an asphaltene-rich vacuum residue coming from a Saudi Arabian field. Mass balances were performed to ensure complete solvent removal. This sample is named A, and Table 1 presents its composition in terms of carbon, hydrogen, nitrogen, oxygen, and sulfur. The asphaltenes A are afterward separated into three fractions of different sizes by ultracentrifugation. This procedure and the proportion of each fraction obtained are summarized in Figure 1. The experimental procedure is the following: the asphaltenes A are solubilized in toluene at a volume fraction φ ) 0.03. Then, a first ultracentrifugation (35 000 rpm for 4 h 30 min at 20 °C; 147 000 g) using a Beckman L8 ultracentrifugation apparatus fitted with a SW 50.1 metallic rotor inside a cell under vacuum allows two fractions to be obtained from asphaltenes A: a supernatant and a pellet. While this latter is dried and set apart for study (sample named AP), the supernatant is once again separated into two fractions: a second pellet (sample ASP) and a second supernatant (ASS), which both will be studied.

This protocol yields three fractions of lower polydispersity than asphaltenes A and varied molar masses (as shown in Table 2) in sufficient amounts. The original asphaltene powder and the fractions were diluted at the desired weight concentration in rectapur grade toluene (VWR International), used as received without further purification, and allowed to stand overnight before any experiment to avoid any kinetic effects. Prior to experiments, solutions were observed using an optical microscope to ensure that the whole sample of asphaltene was dispersed at submicrometer size. The specific gravity of each asphaltene fraction has been determined by measuring specific gravity of asphaltene solutions at 25 °C using an Anton Paar DMA5000 densitometer. Indeed, the specific volume of the solutions versus mass fraction of asphaltene showed a linear behavior, in the range 1-25 wt %, which permits an extrapolation at null dilution. The volume fraction of asphaltene φ is deduced from the mass fraction of the solutions and from the specific gravity. II.B. Viscosity Measurements. The viscosities reported are the zero shear rate viscosities determined in the first Newtonian domain of asphaltene solutions using a Contraves LS30 viscometer at 25 °C. The relative viscosities (ηrel; see below) of asphaltene solutions are accurately determined with an error estimated at (2%, because of the viscometer sensitivity. The study of relative viscosity enables information to be obtained on shape, solvation, polydispersity, and interactions of particles suspended in a liquid. The relative viscosity ηrel, defined as the ratio of the suspension viscosity η to that of the pure solvent η0, increases as a function of volume fraction of particles φ due to creation of further drag force. The relative viscosity can be expressed by a virial expansion.31,32 ηrel )

η ) 1 + [η]φ + k[η]2φ2 + ... η0


To obtain the k and [η] parameters, eq 1 can be rearranged to yield ηred )



ηspe 1 η ) - 1 ) [η] + k[η]2φ + ... φ φ η0


where ηred and ηspe are, respectively, the reduced and specific viscosities. Equation 2 predicts that a plot of ηspe/φ versus φ should yield a straight line where the intercept is defined as the intrinsic viscosity [η] and the slope is related to k, known as Huggins’ constant. The first-order development of eq 1, in the case of rigid, spherical particles, much larger than solvent molecules and sufficiently distant (diluted) to consider their actions as simply additive, is the wellknown Einstein equation,33 in which the intrinsic viscosity is 5/2. Different expressions are obtained with other hypotheses. For anisotropic particles such as ellipsoids defined by two axes R and L, Simha,34 Layec,35 and Wolff36 give formulations of the zero shear intrinsic viscosity, always higher than 5/2, as a function of the particle shape and the axis ratio p ) L/R. For oblate ellipsoids (0 < p e 1), Wolff36 gives 5 1-p 32 1 5 [η]ell ) + - 1 - 0.628 ) + g(p) (3) 2 15π p 1 - 0.075p 2



For solvated particles or aggregates, the hydrodynamic “swollen” volume fraction φeff, often called “effective” volume fraction, is (31) Huggins, M. L. J. Am. Chem. Soc. 1942, 64, 2716-2718. (32) Liu, S.; Masliyah, J. H. AdV. Chem. Ser. 1996, 251, 107-176. (33) Einstein, A. Ann. Phys. 1911, 34, 519. (34) Simha, R. J. Phys. Chem. 1940, 25-34. (35) Layec, Y.; Wolff, C. Rheol. Acta 1974, 13, 696-710. (36) Wolff, C.; Dupuis, D. “Viscosite´ ” Techniques de L’Inge´ nieur doc. R 2 350, Editions Techniques de l’Inge´ nieur, 1994.

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Table 2. Features of Asphaltenes Fractions in Dry State (Density) and Solubilized in Toluenea fraction

density (T ) 25 °C)

Mw (g.mol-1)

V (Å3)

Rg (Å)

A2 (mol cm3 g-2)



Rh (Å)


1.12 1.15 1.15 1.09

198 000 666 000 584 000 79 000

2.9 × 105 9.6 × 105 8.4 × 105 1.2 × 105

100 160 151 63

1.88 × 10-5 7.5 × 10-6 9.78 × 10-6 2.5 × 10-5

7.0 12.5 10.6 5.0

1.2 1.6 1.6 1.6

56 98 88 37

0.58 0.61 0.58 0.61


a Molar masses Mw, radii of gyration Rg, and second viriel coefficient A2 as determined by SAXS on one hand, and intrinsic viscosity [η], Huggins coefficient k as determined by viscosity measurement on the other hand. Please note that these values correspond to asphaltene aggregated form since measured above the “critical nanoaggregate concentration”.12

different from the “dry” solute volume fraction φ. The ratio of these quantities defines a solvation constant kS kS )

φeff nVeff Veff ) ) φ nV V


where n is the number of aggregates per unit volume, Veff is the hydrodynamic volume of a solvated aggregate (solute plus solvent trapped in the aggregate), and V the volume of a “dry” aggregate (solute only). So, for a dilute system of spherical solvated aggregates, eq 3 can be combined with the general eq 1 η 5 5 ηspe ) - 1 ) φeff + ... ) ksφ + ... ) [η]φ + ... η0 2 2 or φeff )

[η] φ (5) 2.5

and alternatively for swollen ellipsoids ηspe )

[25 + g(p)]φ


+ ... )

[25 + g(p)]k φ + ... ) [η]φ + ... s

or φeff )

[η] φ (6) 2.5 + g(p)

These latter equations supply practical ways to convert nominal volume fractions into effective ones. When particle concentration increases, their action is no longer only additive and particle pair interactions have to be considered. The Huggins coefficient k is a measure of both hydrodynamic and “thermodynamic” interactions between particles. For monodispersed hard sphere systems, Batchelor37 found a value of 1.2. This second-order coefficient takes suspension viscosity behavior into account up to φ ) 0.15. For more concentrated systems, eq 1 loses its interest because of the difficulties in evaluating the higher-order coefficients. Instead, semiempirical models such as Eiler,38 Mooney,39 Krieger and Dougherty,40 and Quemada41 have been developed. They predict the viscosity divergence when the particle volume fraction approaches the dense random packing limit fraction φm. The Quemada equation, based on dissipated energy minimization by viscous effects, is frequently used because of its simplicity


ηrel ) 1 -

φ φm




Polydispersity can also have a significant effect on the rheological behavior of suspensions. For spheres, in the moderate regime of concentration, theoretical studies32 revealed that the Einstein constant remains constant whereas second-term coefficient k (eq 2) decreases when the polydispersity degree increases. In the concentrated regime, the maximum packing fraction φm increases from about 0.63 for the monodisperse case up to values close to unity for large polydispersity systems (small spheres can fill the gap between the large ones in (37) Batchelor, G. K.; Green, J. T. J. Fluid Mech. 1972, 56, 275. (38) Eiler, H. Kolloid Z. 1941, 97, 313. (39) Mooney, M. J. Colloid Sci. 1951, 6, 162. (40) Krieger, I. M.; Dougherty, T. J. Trans. Soc. Rheol. 1959, 3, 137. (41) Quemada, D. Rheol. Acta 1977, 16, 82-94.

contact). Consequently, for a same volume fraction a suspension of polydisperse spheres will exhibit a lower viscosity than the monodisperse one, especially at higher fractions (see eq 7). The description of polymer solution rheology in the moderate regime of concentration is not basically different from the swollen particle approach. Intrinsic viscosity values have been widely used for a rapid and convenient characterization of polymer molecular weight M using the Mark-Houwinck-Sakurada equation42 [η] ) k1MR


where R depends on the polymer solvent interaction. In the general case where the polymer is described in terms of coils of fractal dimension df, the expression of R depends, in addition, on df.42 R)

3 -1 df


When the coils are no longer isolated, differences appear between polymer and particle rheology due to the entanglement of chains. II.C. Small-Angle X-ray Scattering (SAXS). II.C.1. Equipment. An in-house experimental setup was used: a copper rotating anode generator (Rigaku RU200), operating at 1 kW, provides an X-ray beam which is reflected on a parabolic multilayer mirror Xenocs. The reflected monochromatic beam (λ ) 1.54 Å) is collimated by two pairs of crossed slits whose parasitic scattering is removed by another pair of crossed slits located just before the sample. The asphaltene solutions were loaded in 2 mm glass capillaries. A linear position-sensitive detector Elphyse, located 0.8 m from the sample, collected the scattering intensity. The range of scattering angles 2θ enables a range of the wave scattering vector q, defined as q ) 4π sin θ/λ, of 1 10-2 to 0.22 Å-1 to be covered. After normalization with respect to thickness, transmission, and measuring time, the solvent signal was subtracted from the sample signal, and the raw intensities were converted to the scattering cross section I(q) in absolute scale (cm-1). All the present experiments were conducted at 25 °C. II.C.2. Dilute Systems. The scattered intensity I(q) probes the correlations between asphaltene-rich regions on a scale of the order of q-1. For a particle in a solvent system, a general expression of I(q) can be derived43 I(q) ) φ(1 - φ)Ie∆F2 F(q) S(q)


with the following: φ the particle volume fraction; Ie∆F2 the contrast term; Ie is the intensity scattered by one electron and ∆F is the electronic density difference between particles and solvent, determined from density and chemical composition of solvent and particles; F(q), the form factor which is a function of shape, size, and polydispersity of particles; F(0) is normalized to the volume V of a scattering particle; and S(q), the structure factor which depends on the interparticle interactions. For solutions that are dilute and without interparticle interactions (S(q) ) 1), in the so-called Guinier region (at scales larger than the (42) Tirrell, M. Fundamentals of Polymer Solutions. In Interactions of Surfactants with Polymers and Proteins, Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, 1992; Chapter 3. (43) Espinat, D. ReVue de l’Institut Franc¸ ais du Pe´ trole 1990, 45, 595-820.

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typical size of particles), the Zimm approximation44 can be used to determine the scattering cross section at zero angle I(0) and the radius of gyration Rg of the particles


q2Rg2 1 1 1+ + ... ) 3 I(q) I(0)


for qRg < 1


The validity of eq 11 can be extended for swollen particles.15 For polymers, Burchard46 consider the Zimm approximation valid up to qRg ) 2. From eq 10, I(0) takes a simple form for dilute solutions from which the particle volume V can be extracted

∑ mM i

I(0) φ∆F

where A2 is the second virial coefficient. Positive values of A2, signifying repulsive interaction between objects, lead to a lowering of the I(q)/φ ratio at small q values as the concentration increases. This relation holds up to concentrations where interactions are described by pair interactions. The left-hand part of eq 19 can be used to define an “apparent” mass Mapp which tends toward the real one at low concentration. II.C.4. Polydispersity. For polydisperse systems such as asphaltene solutions,22,25 SAXS measurements give the weight-average molecular weight of aggregates MW and the z-average radius of gyration RgZ defined by the following expressions:

)V 2


Mw )

The “molar mass” M can be derived by using the usual expression M ) dNaV



c c 1 )K ) M I(0) I(0) d Na w

F(q) ) πR2(2h)



2 sin2(qh cos R) 4J1 (qR sin R)

(qh cos R)2

(qR sin R)2

sin R dR (15)



2 2

2 qh exp 3 (qRD)2

for qh e 1; qRD . 1


Determination of 2h is straightforward: a plot of ln[q2I(q)] versus q2 gives a slope related to the height of cylinder. Moreover, the radius of gyration of such an object is a function of dimensions and axis ratio of the cylinder 2

Rg2 )

RD (2h) + 12 2



II.C.3. Interactions. For moderate concentrations c of particles, interparticle interactions have to be taken into account, and the previous equations are modified through a virial expansion to give Ie∆F2 c 1 ) d2Na I(q) Mw





q2Rg2 + 2A2Mwc + ... for 3 A2Mwc < 0.25 (18)

This equation can be simplified in the Guinier region to yield Ie(∆F2) c 1 1 ) (1 + 2A2Mwc) ) for 2 I(0) M M Nad w app qRg < 1 and A2Mwc < 0.25 (19) (44) Zimm, B. H. J. Chem. Phys. 1948, 16, 1093-1099. (45) Liu, Y.; Sheu, E.; Chen, S.; Storm Fuel 1995, 74, 1352-1356. (46) Burchard, W. AdV. Polym. Sci. 1999, 113-194.


2 i gi


(21) miMi


with mi, Mi, and Rgi the mass, molar mass, and radius of gyration of the ith fraction, respectively. For polydisperse discs (RD, 2h) described by a Schulz distribution of radius17,18 f(R) )

In the flat disc limit (2h , RD), this expression has a simple form at large q values17,18,43 F(q) ∝

RgZ )


It is worth noting that expressions 11-14 are model-independent. In the case of anisotropic particles, analytical expressions of form factors are available. We consider here the expression of cylinders (radius R, height 2h)17,18,43


∑ mMR



(20) mi


with d the specific gravity of the solute and Na the Avogadro number. Combining eqs 11, 12, and 13 and considering concentration c in grams per unit volume, one obtains Ie∆F



( ) z+1 〈R〉



Rz exp -

〈Rg〉2 )


( )

(z + 1)R 〈R〉 1 ; z) σ 〈R〉 Γ(z + 1)

(2h)2 〈R〉2 (z + 6)(z + 5) + 3 2 (z + 1)2


-1 (22) (23)

II.C.5. Fractal Aggregates. Asphaltene particles have been frequently described as mass fractal aggregates of dimension df.8,14,15,18,25,28,30 In this case, on a much smaller scale than the typical size of aggregates, a simple expression of the scattering cross section is expected I(q) ∝ q-df for qRg > 1


Furthermore, a power law relation between the measured aggregate parameters, namely, radius of gyration, second viriel coefficient, and molar mass, should be observed for these aggregates46 Rg ) k2Mw1/df


A2 ) k3Mw-[(3/df)-2]


It should be noted that, for homogeneous thin discs of equal thickness, the combination of eqs 17 and 13 yields Rg ∝ M1/2


III Results III.A. Ultracentrifugation. The densities of the different fractions are given in Table 2. The densities of opposite fractions are similar, suggesting a separation by mass rather than by density. This point will be discussed later with the SAXS results. III.B. Viscosity Measurements. Figure 2 shows the variations of viscosity of asphaltene solutions as a function of the asphaltene volume fraction for all the investigated systems. We note that the four curves have similar aspects, namely, an “exponential-

Solution Properties of Asphaltenes

Langmuir, Vol. 24, No. 8, 2008 3713

Figure 2. Variations of relative viscosity of asphaltene solutions as a function of volume fraction φ for samples A, AP, ASP, and ASS in toluene (T ) 25 °C).

Figure 3. Determination of intrinsic viscosities and Huggins’ coefficients for samples A, AP, ASP, and ASS in toluene (T ) 25 °C).

like” increase in relative viscosity with the asphaltene volume fraction. Moreover, samples do not have the same viscosimetric properties. The order of variation of these viscosimetric properties follows the sedimentation ones

when concentration increases, a decrease of intensity at small q values, significant of repulsive interactions, is observed. On the contrary, the high q region is superimposed, indicating that the small length scale of these aggregates does not depend on concentration. Indeed, a scaling behavior in q-2.1 is observed. The variations of 1/Mw app versus asphaltene concentration c are represented in Figure 5. The range of validity of eq 19, corresponding to the condition A2Mwcmax < 0.25, is represented by the linear bold line from which, according to eq 19, true “aggregate weight” Mw and A2 are deduced. These parameters are given in Table 2. The “dry” volume of aggregate deduced from eq 13 is also reported. As expected, values of the initial asphaltene are intermediate between those of fractions. Moreover, the Mw dispersion indicates a large polydispersity of the nonseparated asphaltene aggregates likely at the origin of separation rather than density variations. This conclusion is strengthened by the fact that molar masses and radii of gyrations of the different fractions present large variations whereas their densities are quite similar. The centrifugation conditions are proven to be discriminative to produce fractions with marked mass and size differences. These well-defined fractions can help us to separate size, polydispersity, and interaction contributions to asphaltene solution viscosity. The positives values of A2, significant for repulsive interactions between aggregates, are consistent with the absence of large aggregates, as observed on long-term aging solutions using optical microscopy. III.D. Scaling Laws Between Measured Parameters. We first consider the radius-mass dependence of aggregates as measured by SAXS (Figure 6). Despite the small amount and

ηrel(AP) > ηrel(ASP) > ηrel(A) > ηrel(ASS) and the asphaltene concentration at which the viscosity diverges follows the opposite trend. We also note that unfractionnated solution A has a viscosity intermediate between those of the P and S fractions. Figure 3 shows the variations of the reduced viscosities as a function of asphaltene volume fractions for all the investigated samples. The values of intrinsic viscosities and Huggins constants, using eq 2, are reported in Table 2. The intrinsic viscosities of asphaltene solutions are all superior to the 2.5 value of hard sphere dispersions as already reported by several authors.5,6,9,14,20,26,29,30 Concerning the Huggins constants, we note that they are all greater than 1 and are nearly constant (1.2-1.6) considering the experimental uncertainties. All these values will be discussed later. III.C. SAXS. In Figure 4 are represented the variations of I(q)/φIe∆F2 as a function of the wave scattering vector q for solutions of asphaltenes ASP in toluene at different volume fractions. All the curves present similar aspects, i.e., a plateau for the low q (Guinier) region followed by a decrease of the normalized scattered intensity for higher q values. The Rg values, deduced from the fit of the 1/I(q) versus q2 plot, in the range qRg < 2 and for the most diluted case, are given in Table 2. Moreover,

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Figure 4. Variations of I(q)/φIe∆F2 as a function of the wave scattering vector q for solutions of asphaltenes in toluene at different volume fractions. Solid lines represent Zimm eqs 11.

limited range of data, a regression analysis yields the following relationship:

Rg ) 0.43Mw0.45


The variations of the intrinsic viscosity as a function of the molar mass of the asphaltenes in toluene are also plotted in Figure 6. Again, despite the small amount and limited range of data, a regression analysis yields the following relationship:

[η] ) 0.049Mw0.41


Finally, the dependence of A2 versus the “aggregate” weight is plotted in Figure 6. In spite of more scattered data, the log-log representation exhibits a reasonable linear behavior from which the following relation is extracted:

A2 ) 0.0129Mw-0.55


IV. Discussion IV.A. Comparison Between Disc and Fractal Model. The scaling dependence in q-2.1 of I(q) at large q values can be interpreted as the result of either scattering by thin homogeneous discs (eq 16) or scattering by mass fractal aggregates (eq 24), corresponding to an aggregate fractal dimension df of 2.1. These two models have been proposed in the literature and will be considered in the following. IV.A.1. Disc Model. For all fractions, the plot of ln[q2I(q)] versus q (eq 16) leads to similar slopes from which thickness 2h of discs can be extracted (Table 3).

Figure 5. Variations of the apparent molar mass (a) of asphaltenes A, AP, ASP, and ASS in toluene as a function of asphaltene concentration. Bold lines represent the range where eq 19 is valid.

For monodisperse discs, the radius of the disc can be estimated from eq 17 and the aspect ratio p ) h/R as well as the volume VD ) 2hπRD2 can be calculated. The comparison with the dry volume of aggregates V (Table 2) enables us to estimate the solvation constant kSD. Finally, the intrinsic viscosity [η]D of such anisotropic and swollen object can be estimated using expressions 3, 4, and 5. Differences between flat disc and oblate ellipsoid are neglected, which is expected for small aspect ratio values (p ) h/R ) L/R , 1). For polydisperse discs, the same approach has been used with expressions 22 and 23; for these calculations, we choose, according to the results of Gawrys17,18 a value of polydispersity σR/〈R〉 close to 0.31. All the calculated parameters are gathered in Table 3. Similar thicknesses 2h on the order of 10 Å have been found for all the fractions. On the other hand, significant variations of the radius R or mean radius 〈R〉 can be observed. Therefore, asphaltenes can be seen as flat discs of constant thickness and a radius related to the molecular weight. Such a description is consistent with the scaling dependence between R and M (exponent of 0.45 in eq 28 to be compared with 0.5 in relation 27). However, in this case, the scaling dependence between [η] and M should be the same as that between [η] and the axis ratio p. Layec et al.35 reported an exponent value close to 1 for oblate ellipsoids. This value strongly differs from the experimental value (0.41 in eq 29). Moreover, comparison between measured (Table 2) and calculated (Table 3) values of the intrinsic viscosity shows significant discrepancies.

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Figure 6. Relations between the intrinsic viscosity [η], the radius of gyration Rg, the second viriel coefficient A2, and the molar mass Mw of the asphaltenes in toluene at 25 °C. Figure 8. Variations of relative viscosity of asphaltene solutions as a function of effective volume fraction φeff for samples A, AP, ASP, and ASS in toluene (T ) 25 °C). The curves represent the predictions of the Quemada model (eq 7) for values of φm of 0.6 and 0.7.

Figure 7. Variations of reduced viscosity as a function of effective volume fraction φeff for samples A, AP, ASP, and ASS in toluene for moderate volume fractions (φeff e 0.15) (T ) 25 °C).

Therefore, we should note that a description of asphaltenes as flat discs is consistent with SAXS results but does not take viscosity measurements into account. IV.A.2. Fractal Model. The fractal dimension of the aggregates can be deduced from the scaling law between the measured parameters Mw, Rg, [η], and A2.46 The exponent value 0.45 of the scaling law between Rg and Mw (relation 28) is first considered. Similar values of this exponent have been reported in the literature using scattering techniques,14,15,18,25 or a combination of vapor-phase osmometry (VPO) and diffusivity.27 Such a value, close to 0.5, may be related

to mass fractal aggregates. Identification of eq 20 with the general eq 25 gives a fractal dimension dfRg of 2.2. The exponent value 0.41 of the scaling law between [η] and Mw (relation 29) is in good agreement with the value determined by Baltus (0.44).27,47 In this study, the authors have used numberaverage molar masses of asphaltenes (determined by VPO) in the Mark Houwink relation and not the weight-average molar mass as in our own work. Moreover, this exponent is also a measurement of the fractal dimension df of aggregates. The application of eqs 8 and 9 leads to a fractal exponent df[η] of 2.13 in good agreement with the value of 2.2 deduced from the massradius relationship. Finally, the identification of eq 30 with the eq 26 leads to a fractal dimension dfA2 of 2.07. The closeness of the different independent determinations of fractal dimension, dfRg ≈ df[η] ≈ dfA2 ≈ dfI(q), close to 2.1, is a very strong indication of the fractal nature of asphaltene aggregates. It can be concluded that asphaltene solutions in toluene are described as a polydispersion of solvated aggregates of fractal dimension close to 2.1. Moreover, their viscosities at very low concentrations are controlled by size, mass, and fractal structure of the aggregates. The consequence of the swollen nature of aggregates has to be taken into account for both viscosity and scattering properties. (47) Baltus, R. E. In Structures and Dynamics of Asphaltenes, Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: London, 1998; Chapter 10, pp 303-335.

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Barre´ et al.

Table 3. Estimation of Intrinsic Viscosities [η]SAXS from Scattering Data for Models of Monodisperse (RD, 2h) or Polydisperse (〈R〉, σR, 2h) Discsa polydisperse discs (〈R〉, σr, 2h)

monodisperse discs (R, 2h) fraction A AP ASP ASS a

2h (Å) 10 12 9 10

RD (Å) 141 226 214 89

p ) h/RD

VD (Å3)

0.035 0.027 0.022 0.058

2.5 × 7.9 × 106 5.4 × 106 1.0 × 106 106

kSD 8.5 8.2 6.4 8.5

[η] saxs 174 215 205 110

〈R〉D (Å) 97 156 147 61

p ) h/〈R〉D

〈V〉D (Å3)


[η] saxs

0.051 0.039 0.032 0.084

1.2 × 3.7 × 106 2.6 × 106 4.9 × 105

4.0 3.9 3.0 4.0

59 72 68 38


Dimensions (2h, R, 〈R〉), volumes (VD, 〈V〉D), and solvation constants (kSD, kSDσ) of the discs are deduced from scattering curves.

IV.B. Viscosity. For swollen particles, the pertinent parameter which takes into account the concentration of aggregates entrapping solvent is the effective volume fraction φeff. The relative viscosities are plotted versus this parameter using eq 5 to convert nominal in effective volume fractions. IV.B.1. Moderate Regime of Concentration (φeff e 0.15). For moderate effective volume fractions, the variations of the reduced viscosity are plotted as a function of the volume really occupied by aggregates (Figure 7). All the data merge approximately on a master curve up to φeff ) 0.15. This means that after concentration renormalization, all the measurements correspond roughly to the same model. Moreover, all the fraction measurements lie on a same line representing the following equation:

η ) η0(1 + 2.5φeff + 10φeff2) ) η0(1 + 2.5φeff + 1.6‚2.52 φeff2) (31) The coefficient 10, slightly higher than the value found by Batchelord37 for monodispersed hard sphere indicates, for a fraction of reduced polydispersity, moderate interactions between aggregates. The measurements for the unfractionnated solution are slightly lower than for fractions leading to the equation

η ) η0(1 + 2.5φeff + 7.6φeff2) ) η0(1 + 2.5φeff + 1.2‚2.52 φeff2) (32) The differences between second-order coefficients (7.6 vs 10) may be ascribed to polydispersity effects, since k decreases when the polydispersity degree increases.32 IV.B.2. Concentrated Regime. For more concentrated regimes, the relative viscosity is plotted as a function of effective volume fraction (Figure 8). The same trends as in diluted regime are observed, namely, the same general behavior for all fractions and a lowering of viscosimetric properties for unfractionnated asphaltene. Moreover, the Quemada eq 5 has been applied to these data in order to extract the dense random packing limit fraction φm, a physically meaningful parameter. We find a value of 0.6 for fractions and of 0.7 for the unfractionnated asphaltene. These values are consistent with both monodisperse (0.63) and polydisperse (0.63 < φeff < 1) values for hard spheres.32 In conclusion, the viscosities of asphaltene aggregate dispersions, by considering their solvation, are well-described by a hard sphere approach in the dilute regime. We must point out that these results do not mean that asphaltenes are hard spheres, but that the hard sphere model appears to describe the viscosity of the investigated samples well. Polydispersity and probably interactions have to be taken into account for viscosity modeling in a more concentrated regime. IV.C. Scattering. As for viscosity measurement, scattering data can be rationalized by considering the so-called “reduced osmotic modulus” which is the real to apparent “aggregate” weight ratio of different fractions. This reduced osmotic modulus

Figure 9. Variations of the reduced osmotic modulus as a function of the reduced parameter A2Mwc ) φ/φm. The solid line represents the behavior of hard spheres and the dotted line that of flexible chains.46

represents the interparticle interaction contribution by which the true “aggregate” mass is modified to yield the measured apparent “aggregate” mass Mapp(c) which is a function of the concentration.46 The concentration has to be expressed also in a scaled form, and X ) A2Mwc is used as the reduced concentration. The plot of reduced osmotic modulus versus the reduced concentration is shown in Figure 9 for all the fractions and concentrations. Again, all the data merge on a single curve, which means that concentration and mass act in the same way. Moreover, this master curve can be compared to two limiting case models: the hard spheres and the flexible chains ones. Despite a limited range of concentrations, the experimental data, when renormalized for the swollen nature of aggregates, are in favor of hard sphere interactions. This result is different from previous conclusions obtained by Fenistein14,15 who considered the possibility of overlapped aggregates.

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IV.D. The Rh/Rg Ratio. The hydrodynamic radius Rh can be estimated by combining eqs 4 and 5 4 /3πRh3dNav [η] Vh ) ) 2.5 V Mw


Numerical values as well as the ratios Rh/Rg are reported in Table 2. This ratio is expected to depend only on the structure of the aggregates and to be constant for all the investigated systems. The reported values, 0.6 on average, are reasonably constant. Moreover, this Rh/Rg ratio is close to the value of 0.72 found by Wiltzius48 for silica mass fractal aggregates of fractal dimension 2.13. Burchard47 also found similar values (0.58) for randomly branched polymers. This ratio is again consistent with a model of swollen mass fractal aggregates.

V. Conclusion Relevant structural parameters on asphaltene fractions have been extracted from viscosity and small-angle X-ray scattering (48) Wiltzius, P. Phys. ReV. Lett. 1987, 58, 710-713.

measurements. Data have been analyzed using fractal and disc models. We have shown that, even if disc model is consistent with SAXS results, it failed to take viscosity data into account. By contrast, using the fractal model, asphaltenes were found to form nanometric aggregates, and the scaling behavior of all these parameters are consistent with a mass fractal description of these aggregates, which in consequence trapped solvent. The fraction and concentration dependence of the viscosity solution can be fully predicted if solvation and fractal character of aggregates are taken into account. The high-concentration SAXS behavior seems to indicate that aggregates do not overlap. The hydrodynamic to gyration radius ratio is found to be consistent with a fractal description of the aggregates. Acknowledgment. We are grateful to R. Nageotte (Institut Pasteur, Paris, France) for ultracentrifugation experiments, and D. Frot (IFP) for helpful discussions. The viscosity measurements were carried out with the help of V. Blard and A. Morisset (IFP). We thank D. Espinat (IFP) and J. Jestin (LLB) for critical reading of the manuscript. LA702611S