Energy & Fuels 2001, 15, 1123-1128
1123
Hydrodynamic Properties of Coal Extracts in Pyridine Verina J. Wargadalam, Koyo Norinaga, and Masashi Iino* Institute for Chemical Reaction Science, Tohoku University, Katahira 2-1-1, Sendai 980-8577 Received January 4, 2001. Revised Manuscript Received March 20, 2001
Hydrodynamic properties, such as solution viscosity and diffusivity, were measured at 298 K to investigate the solution state characteristics of coal extracts in pyridine obtained from Upper Freeport (UF) and Illinois No. 6 (IL) coals. The solvation constants obtained by applying the Pal-Rhodes equation to the viscosity of the extracts in pyridine are 2.9 and 4.6 for the UF and IL extracts, respectively. A larger content of acidic hydroxyl groups in IL extract than UF extract make pyridine solvate IL extract more extensively than UF extract. However, the solvation constant of the O-methylated IL extracts is 9.3, unexpectedly larger than that of the original IL extract. To have further insight into this observation, the change in the molecular shape of the extracts by the O-methylation were examined, using the combination of intrinsic viscosity and diffusion coefficient. The shapes of the coal extracts have been found to be prolate ellipsoids with axial ratio of 6.5 and 4.0 for UF and IL extracts, respectively. The axial ratio of the O-methylated IL extract is 13.1, suggesting that the elimination of the hydrogen bonds or the steric effect of added methyl makes the shape of IL extract stretched out. This deformable nature of coal extracts makes the interpretation of the solvation constants from Pal-Rhodes equation inaccurate, as it assumes that the particles are monodispersed hard spheres.
Introduction Coal-derived materials such as coal extracts and liquefaction products are known to readily associate and form aggregates or micelles in organic solvents, through hydrogen bonds, ionic attraction, interaction between aromatics, and so forth.1 However, their association behaviors are not still well-known. One of the reasons to delay the elucidation of the aggregations is that sizes and shapes of coal aggregates and molecules in solvents are not known. These have been extensively studied for petroleum-derived asphaltenes,2 but little for coalderived materials. In this work we studied the size and shape of coal extract particles in pyridine. Here, we define “particle” as a general term for a dispersed phase, aggregate, or molecule, in solution, and “elemental particle” denotes unit particles which form aggregates. The viscosity-concentration relationship for Newtonian systems, developed by Einstein,3 is expressed as
η ) ηr ) 1 + 2.5φ ηs
(1)
where η, ηs, and ηr are the solution, the solvent, and the relative viscosity, and φ is the volume fraction of the particle in solution. This equation is based on the assumptions that the dispersed particles are hard spheres and unsolvated, and have a uniform size; and also there is no interaction among particles. * Author to whom all correspondence should be addressed. Fax: +81-22-217-5655 (1) Stenberg, V. I.; Baltisberger, R. J.; Patal, K. M.; Raman, K.; Woolsey, N. F. Coal Science; Gorbaty, M. L., Larsen, J. W., Wender, I., Eds.; Academic Press: New York, 1983; Chapter 2. (2) Baltus, R. E. Structure and Dynamic of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds; Plenum Press: New York, 1998; Chapter 10. (3) Einstein, A. Ann. Phys. 1911, 34, 519.
In coal molecular solutions, dispersed particles can be polydispersed aggregates in size and structure. For such complex systems, the Einstein equation is no longer adequate. Thus, several modified Einstein equations have been proposed to account for those effects. 4-6 The parameters obtained from those viscosity equations are often very difficult to interpret, since these parameters often depend on more than one physical property, and represent a combining effect. The Pal-Rhodes equation6 (eq 2) is simple, and it accounts for the effect of interaction among particles and with the solvent,
ηr ) [1 - Kφ] -2.5 or
(1/ηr)0.4 ) 1 - Kφ
(2)
K is the solvation constant and K ) 1 for unsolvated particles. This equation is based on the assumptions that elemental particles are monodispersed hard spheres and allowed to form the aggregates with sphere shape and size polydispersity. Sheu et al.7 investigated the rheological properties of Ratawi vacuum residue in solution up to 45 wt % concentration. It showed that the concentration dependencies of the solution viscosity were well explained by Pal-Rhodes equation over the wide concentration range measured. However, it was noted that the solvation constant obtained from this analysis could not be used to evaluate the degree of (4) Roscoe, R. B. J. Appl. Phys. 1952, 3, 267. (5) Mooney, M. J. Colloid Interface Sci. 1951, 6, 162. (6) Pal, R.; Rhodes, E. J. Rheolog. 1989, 33, 1021. (7) Sheu, E. Y.; De Tar, M. M.; Storm, D. A. Fuel 1991, 70, 1151.
10.1021/ef0100045 CCC: $20.00 © 2001 American Chemical Society Published on Web 07/12/2001
1124
Energy & Fuels, Vol. 15, No. 5, 2001
Wargadalam et al.
Table 1. Elemental Analysis of Coal Extracts (wt %) coal extract
C
H
N
S
Oa
UFPS ILPS methylated-ILPS
86.0 80.0 77.8
5.8 5.9 6.1
1.9 1.9 1.2
1.7 1.3 0.9
4.6 10.9 14.0
a
By difference. Table 2. Physical Properties of Coal Extracts
coal extract
Mwa
density [η]c 106Dd Mnb Mw/Mn (g/cm3) (cm3/g) (cm2/s)
UFPS 1774 1116 ILPS 1083 664 methylated-ILPS 1061 619
1.5 1.6 1.7
1.217 1.224 1.171
5.6 5.2 16.6
2.66 3.12 2.45
a Weight averaged molecular weight. b Number averaged molecular weight. c Intrinsic viscosity. d Diffusion coefficient.
Dispersion method.13 The capillary tube was 4000 cm in length with 0.05 cm inside diameter and wound as a helical coil with diameter of 19 cm. It was positioned in the temperaturecontrolled chamber. HPLC grade pyridine was pumped through the capillary tube by Tosoh pump model DP-8020, and a steady flow of 5.5 × 10-4 cm3/s was maintained. The concentration of the extract solution is 0.1 g/L, and after the filtration through a 20 µm filter the solutions were injected to the capillary by a six-port valve with a 100 µL sample loop. The injection period was 100 s, giving the injected volume of 0.055 cm3. The elution profiles of the samples were monitored using a variable wavelength UV detector (Hitachi 655A). The diffusion coefficients, D, were determined from the variance of the eluted peak, which is expected to be a normal distribution, using the following equations:
s2 )
solvation, since the elemental particles here are deformable and polydispersed in size, unlike the assumption for eq 2. Therefore, to know the detailed structure and fractal dimensions of deformable particles of coal exrtracts, a complimentary information of viscosity is necessary. For this objective, in this study, diffusivity was measured, and combined with intrinsic viscosities to estimate the size and shape of particles. Several works have been performed using this method to characterize the size and shape of petroleum-derived components.8,9 In the present work, coal extracts, obtained from Upper Freeport (UF) and Illinois No. 6 (IL) coals, in pyridine were investigated. In addition, the effect of hydrogen bonding on the shape and size of the particles was investigated through the O-methylation treatments of the coal extracts. Experimental Section Sample Preparation. Pyridine-soluble fractions of UpperFreeport (UFPS) and Illinois (ILPS) coals were prepared from the extraction and solvent fractionation by the same procedure described elsewhere.10 O-methylation of ILPS was carried out by the procedure reported by Liotta.11 Table 1 shows the results of the elemental analysis of those extracts. The densities of the coal extracts were determined by the extrapolation of their solution densities data measured by pycnometer. The molecular weights and distribution of the extracts were measured by laser desorption-ionization mass spectrometry (LD/MS) using Thermoquest Co. Ltd. Vision 2000 with the same procedure described elsewhere.12 These properties of the samples were summarized in Table 2. Viscosity Measurements. The viscosity was measured using a capillary viscometer of Ubbelohde type mounted in a temperature-controlled water bath. The concentration of the solutions measured was ranged up to 30 g/L. The volume fraction of the extract in pyridine was calculated from its density and weight concentration. The solutions of the extract were prepared for various concentrations by dissolving it in pyridine and ultrasonic irradiation for 30 min. The solution preparation conditions such as temperature and time were carefully kept the same for all sample solutions. Diffusion Coefficient Measurements. The diffusion coefficient measurements were carried out using the Taylor (8) Sakai, M.; Yoshihara, M.; Inagaki, M. Carbon 1983, 21 (6), 593. (9) Nortz, R. L.; Baltus, R. E.; Rahimi, P. Ind. Eng. Chem. Res. 1990, 29, 1968. (10) Iino, M.; Takanohashi, T.; Oshuga, H.; Toda, K. Fuel 1988, 67, 1639. (11) Liotta, R.; Brown, G.; Isaac, J. Fuel 1983, 62, 781. (12) Norinaga, K.; Iino, M. Energy Fuels 2000, 14, 929.
a 2L 24Du jo
(3)
where a is the capillary tube radius, L is the length of the capillary tube, and uo is the mean velocity of the solvent, while s is calculated from
s)
t1/2 (8 ln 2)1/2
(4)
where t1/2 is the width of the peak at half-height. We have confirmed that the injected solute concentrations below 0.5 g/L were well within the Beer’s law region. The Reynolds number, Re, was 1.5, indicating that laminar flow conditions were maintained. The Peclet number, Pe, of 3.0 × 108 satisfied the assumption of negligible axial diffusion.14 The L2/a2 of 2.6 × 1010 eliminates the radial concentration gradients. The De2Sc < 20, where De and Sc are Dean and Schmidt numbers, shows the deviation of the secondary flow15 is less than 0,05%. Those conditions ensured that the assumptions of an ideal Taylor Dispersion method in our experiments were satisfied. The apparatus was examined by carrying out several experiments on monodispersed standard polystyrenes in cyclohexane. The diffusion coefficient of polystyrene (MW ) 2100) in cyclohexane at 298 K was 1.95 × 10-6 cm2/s, in good agreement with the reported value16 of 2.23 × 10-6 cm2/s determined by a similar procedure.
Results and Discussion Viscosity Measurements. Figure 1 shows the solution viscosity of the UFPS, ILPS, and O-methylated ILPS at 298 K as a function of concentration. The inflection point (C*) was observed at about 15 g/L and 10 g/L for UFPS and ILPS, whereas it was not found for O-methylated ILPS within the range of concentration measured. In petroleum asphaltene/ toluene solution, the similar inflections were observed at concentration of 17 and 36 g/L.17 They ascribed those phenomena to the appearance of small aggregates for the first inflection and the appearance of larger aggregate for the second one, following the aggregation mechanism proposed by Andersen and Birdi.18 For our case also at concentrations above C* the aggregation of (13) Taylor, G. Proc. R. Soc. London, Ser. A 1953, A219, 186. (14) Baldauf, W.; Knapp, H. Chem. Eng. Sci. 1983, 38, 1031. (15) Alizadeh, A.; Nieto de Castro, C. A.; Wakeham, W. A. Int. J. Thermophys. 1980, 1, 243. (16) Barooah, A.; Chen, S. H. J. Polym. Sci.: Polym. Phys. 1985, 23, 2457. (17) Mohamed, R. S.; Ramos, A. C. S.; Loh, W. Energy Fuels 1999, 13, 323. (18) Andersen, S. I.; Birdi, K. S. J. Colloid Interface Sci. 1991, 142, 497.
Hydrodynamic Properties of Coal Extracts in Pyridine
Figure 1. Plot of viscosity of UFPS (b), ILPS (9), and methylated-ILPS (2) in pyridine at 298 K vs concentration.
coal particles was enhanced extensively, yielding a significant increase in viscosity by increasing the concentration. A lower C* of ILPS compared to UFPS suggests a stronger tendency of ILPS to aggregate compared to UFPS. The viscosity of ILPS is higher than UFPS, where the difference increases with increasing concentration and become larger at concentrations above C*. This suggests that the aggregation in ILPS is more strongly accelerated by the increase in concentration than UFPS. In the case of methylated-ILPS, phenolic hydroxyl, which is responsible for the hydrogen bonding, was eliminated.11 Since hydrogen bonding is known as one of the most important intermolecular (particle) attractive forces, the absence of an inflection point can be considered due to the elimination of hydrogen bonding. However, a higher viscosity of the O-methylated ILPS solution compared to the original ILPS solution is an unexpected result. One possible explanation for that is that the elimination of phenolic hydroxyls makes Omethylated ILPS less polar compared to the original one, thus, the solubility of the O-methylated ILPS in polar pyridine becomes lower and more aggregations occur. Cody et al.19 reported using the small-angle neutron scattering (SANS) analysis, that the alkylation of ILPS promotes the aggregation. We applied the Pal-Rhodes equation to UFPS and ILPS data in the range of concentration below C* and to the O-methylated ILPS data in the entire range of concentration measured. Figure 2 shows the plot of (1/ ηr)0.4 against φ, and the linear relationships were obtained. Based on the assumption of eq 2, it suggests that the particles of UFPS, ILPS, and O-methylated ILPS are approximately spheres. The solvation constant, K, estimated from the slope of the plot, represents the ratio of the solvated volume to the nonsolvated volume of the aggregate. K values of UFPS, ILPS, and O-methylated-ILPS are 2.9, 4.6, and 9.3, respectively (19) Cody, G. D.; Thiyagarajan, P.; Botto, R. E.; Hunt, J. E.; Winans, R. E. Energy Fuels 1994, 8, 1370.
Energy & Fuels, Vol. 15, No. 5, 2001 1125
Figure 2. Plot of the Pal-Rhodes equation for UFPS (b), ILPS (9), and methylated-ILPS (2) in pyridine at 298 K. Table 3. Physical Parameter for Coal Extract in Pyridine Obtained by Assuming Sphere Shape at 298 K solute
ava (nm)
adb (nm)
Kc
UFPS ILPS methylated-ILPS
1.00 0.82 1.18
0.91 0.78 1.00
2.9 4.6 9.3
a Sphere equivalent radius derived from intrinsic viscosity. Sphere equivalent radius derived from diffusion coefficient. c Solvation constant obtained from the Pal-Rhodes equation. b
as listed in Table 3. A higher K value of ILPS than UFPS, shows a stronger interaction between ILPS and pyridine. This can be attributed to a larger content of phenolic hydroxyls in ILPS compared to UF,20 whereby pyridine is known having a strong interaction with such polar functional groups.21 In the case of O-methylated ILPS, the interaction with pyridine would be less than the original ILPS, thus the K value would be smaller. Unexpectedly, K of O-methylated ILPS was found to be much greater than that of the ILPS. As mentioned earlier, K obtained from the Pal-Rhodes equation is affected not only by the degree of solvation but also by the detailed structure and fractal dimensions of the aggregate that cannot be obtained from viscosity data alone. When the Pal-Rhodes equation was applied to the entire range of concentration measured for UFPS and ILPS, linear relationships of Pal-Rhodes equation were not obtained, suggesting that at concentrations higher than C* the assumptions of the equation cannot be applied. Diffusion Coefficient Measurements. First, the applicability of the Taylor dispersion technique for complex mixtures of coal extracts with strong polydispersity in chemical structures and sizes was checked. The effect of polydispersity of particles (solutes) on diffusion coefficient, D, from the Taylor method has been investigated by Mes & co-worker,22 who reported that (20) Norinaga, K.; Iino, M. Energy Fuels 2000, 14, 1121. (21) van Krevelen, D. W. Coal; Elsevier: Amsterdam, 1960. (22) Mes, E. P. C.; Kok. W. Th.; Poppe, H.; Tijssen, R. J. Polym. Sci.: Polym. Phys. 1999, 37, 593.
1126
Energy & Fuels, Vol. 15, No. 5, 2001
Wargadalam et al.
Figure 4. Plot of ηsp/c of UFPS (b), ILPS (9), and methylatedILPS (2) in pyridine at 298 K vs concentration.
Figure 3. Elution profile of UFPS as a function of time detected by UV wavelength at 310 nm (a) and 350 nm (b): experimental (s), calculation (- - -).
the effect of polydispersity on the diffusion coefficient is relatively small. The deviation is about 8% for a solute with polydispersity index (Mw/Mn) of 2. Table 2 shows that the indexes for UFPS and ILPS are 1.5 and 1.6. The presence of UV-sensitive low molecular weight materials is known to be considerably disturbed when UV was used as the concentration monitor. When a system has aconsiderable amount of small molecules with high extinction coefficients, D measured should be higher than a true average D, since the contribution of small molecules with high D to the UV profile is overestimated. To overcome this lack of reliability the fractionation to narrow molecular weight distribution samples has often been carried out. In this work the extract fraction were not fractionated, instead, the most appropriate UV wavelength was chosen in order to minimize the disturbance from UV-sensitive low molecular weight materials. Figure 3 shows the eluted peak of UFPS at UV wavelengths of 310 and 350 nm, respectively. At 310 nm, the Gaussian peak (dotted line) which was calculated on the basis of the variance of the experimental peak is not fitted well with the experimental peak (solid line). This disagreement may be due to the UV-sensitive low molecular weight materials, and would yield a higher D than an actual average value. At 350 nm the agreement between the experimental and the calculated peak is better. Furthermore, when the wavelength was increased to 370 nm, the elution peak was nearly equivalent in shape with the peak observed at 350 nm. Therefore, the UV-wavelength of 350 nm was chosen in this work. Table 2 shows that the diffusion coefficient, D, of UFPS, ILPS, and O-methylated ILPS in pyridine at 298 K are 2.66 × 10-6, 3.12 × 10-6, and 2.45 × 10-6 cm2/s,
respectively. Nortz et al.9 measured the diffusion coefficients of asphaltene from Athabasca vacuum residue in 1-methyl-naphthalene by the Taylor method. They found that D values of the asphaltenes (Mn ) 650-1000) at 323 K are in the range of (1.5-1.1) × 10-6 cm2/s. From our own measurements, the D value of Kafji petroleum asphaltene (Mn ) 1780) in pyridine at 298 K is 2.07 × 10-6 cm2/s, a value similar to the D value for the coal extracts. Combination of Viscosity and Diffusivity Data. The intrinsic viscosity, [η], is defined by considering the concentration dependence of the solution viscosity:
ηr ) 1 + [η]c + kc2 + ...
(5)
where c is the solute concentration and k is a constant. For low concentrations, the series expansion in c can be truncated, and eq 5 is rearranged as
ηr - 1 ) [η] + kc c
(6)
The intrinsic viscosity, then can be obtained from the intercept of (ηr - 1)/c vs c plot. Linear relationships are observed for the plots below C* as shown in Figure 4. Table 2 shows that the [η] of UFPS and ILPS solutions are nearly the same, whereas it is much greater for the O-methylated ILPS. D for the extracts in pyridine was measured at very low concentration (the injected solution is 0.1 g/L) and [η] is also the value extrapolated to zero concentration. At infinite dilute solution, the intrinsic viscosity, [η], can be written23 as
[η] )
νNA V M e
(7)
where ν is the shape factor, NA is the Avogadro number, and M and Ve are the molecular weight and the effective (23) Scheraga, H. A.; Mandelkern, L. J. Am. Chem. Soc. 1953, 75, 179.
Hydrodynamic Properties of Coal Extracts in Pyridine
Energy & Fuels, Vol. 15, No. 5, 2001 1127
Table 4. Physical Parameter for Coal Extract in Pyridine Obtained by Assuming Prolate Ellipsoids Shape at 298 K solute
b/aa
Veb (nm3)
aec (nm)
bd (nm)
ae (nm)
UFPS ILPS methylated-ILPS
6.5 4.0 13.1
1.33 1.20 0.85
0.68 0.66 0.59
2.38 1.68 3.27
0.37 0.41 0.25
a Axial ratio. b Effective volume determined by eq 7. c Effective hydrodynamic radius. d Equatorial radius. e Semi axis of revolution.
volume of particles. ν depends on the shape of particles, and for a sphere, ν is 2.5, and for ellipsoids ν is higher than 2.5. At the condition of infinite dilute concentration, particles are considered to exist as molecules, not aggregates. If we assume the shape of particles as a sphere, the effective hydrodynamic radius, ae, can be determined from ae ) (3/4π)1/3 Ve1/3 using Ve in eq 7, or from eq 8.
fo ) 6πηsae )
kT D
(8)
where fo is the friction factor of a sphere of radius ae, k is a Boltzman constant, T is the temperature, and ηs is the solvent viscosity. fo can be determined from the diffusion coefficient, D. ae obtained from [η] and D is referred to av, and ad, respectively. As listed in Table 3, av is larger than ad for all extracts, indicating the deviation from the assumption that the particles are spheres. Next, we assume ellipsoid shape for the extract molecules. The friction factor of ellipsoid particle developed by Perrin, 24 is given as follows:
f ) fo/F
(9)
where
F)
)
p2/3
x1 - p2 p2/3
x1 - p2
ln
1 + x1 - p2 p for prolate ellipsoids (p < 1)
tan
-1
xp2 - 1 for oblate ellipsoids (p > 1)
f is the mean friction factor, and is equal to fo if the particle is a sphere; p is the axial ratio, i.e., b/a (a is the semi axis of revolution and b is the equatorial radius). f can be determined from D ) kT/f, where k is a Boltzman constant, and T is the temperature. By inputting the value of p and ν from p-ν relationship25 into the eqs 7 and 9, and solving these equations simultaneously, ae can be obtained when we assumed prolate shape, as shown in Table 4. Table 4 shows that the effective volume of UFPS and ILPS is similar, while the O-methylated ILPS is smaller than ILPS. The effective radius, ae, of the UFPS, ILPS, and O-methylated ILPS molecules are 0.71, 0.67, and 0.55 nm, respectively. These values are about 10 times smaller than the aggregate radius of ILPS or O-methylated (24) Perrin, F. J. Phys. Radium 1936, 7, 1. (25) Scheraga, H. A. J. Chem. Phys. 1955, 23 (8), 1526.
ILPS obtained from SANS analysis.19 It supports our assumption that in the analysis using the combination of [η] and D we may deal with the particle as a single molecule. The deviation from spherical shape is increased with axial ratio (b/a), i.e., 4.0, 6.5, and 13.1 for ILPS, UFPS, and O-methylated ILPS, respectively. The axial ratio of O-methylated ILPS is higher than the original ILPS. This may be due to the drastic change in the conformation of the ILPS particle by the elimination of hydroxyls, resulting in the stretched prolate shape. The steric effects of the added methyl groups would also contribute to the conformation changes. It may result in a simple interpretation of the K obtained by Pal-Rhodes equation impossible, since it assumes that the elemental particles are monodispersed hard spheres. When we assumed oblate shape for the extracts, no definite ae was obtained. When a coal molecule dissolves in solvent, its effective size may increase, due to solvation. Therefore, since the intrinsic viscosity is determined using solution concentration predicted from the dry mass of coal extract (which we found there is no alternative approach to this measurements), the actual effective volume of coal molecule can be larger than the value obtained from eq 7. The same deviation may also come from a polydisperse solution where its effective solute size is an average size. However, this possible erroneous does not shift the conclusion derived from our results. The application of the Pal-Rhodes equation suggests the particles as approximately spherical, whereas from the combination of [η] and diffusion coefficient data the particle can be modeled as ellipsoids. This difference can be attributed to the different extents of aggregation, i.e., they were obtained from the data at dilute solutions where the associations occur, and at infinite dilute solutions where the associations hardly occur, respectively. Accordingly, it suggests that the shapes of coal particles were changed from ellipsoids at nonaggregation states to spheres at higher aggregation states. Conclusion The characteristics of the coal extracts, obtained from Upper Freeport (UF) and Illinois No. 6 (IL) coals, in pyridine at 298 K can be concluded as follows: • The concentration dependencies of the solution viscosity can be explained by the Pal-Rhodes equation, for the concentration range up to 15 and 10 g/L for UFPS and ILPS, respectively. • A stronger interaction between pyridine with ILPS compared with UFPS was responsible for a higher solvation constant obtained, due to a higher acidic hydroxyl groups content of ILPS. • The analysis using the combination of intrinsic viscosity and diffusion coefficient at very diluted solution suggests that the particles can be modeled as prolate ellipsoids. The difference from the shape suggested by the Pal-Rhodes equation is attributed to a different aggregation state in both analyses, i.e., nonaggregated and aggregated state for prolate ellipsoids and spheres, respectively. • The elimination of the hydrogen bonding and/or the steric effects of added methyl stretch the prolate ellipsoid shape of the ILPS, increasing the axial ratio.
1128
Energy & Fuels, Vol. 15, No. 5, 2001
Acknowledgment. The authors are grateful to Dr. Hiroyuki Seki of Petroleum Energy Center for providing molecular weight distribution data of the extracts. This work was supported by a Research for the Future
Wargadalam et al.
Project grant from the Japan Society for the Promotion of Science (JSPS). EF0100045
