tions that took place after elution, the amount varied between 5 and 10 micrograms. By the combination of thin-layer chromatography with "in situ" microreactions or with reactions carried out after elution (without filtration), satisfactory results were obtained in the identification of 17 alkaloids with different composition and structure (the major compounds contained in opium, tropanic and beta-pyridinic derivatives, as well as lysergic acid). Microreactions "in situ" can also be applied for the obtention of standard substances, directly on the start line of the chromatoplate.
K. Genest, J. Chromatogr., l g , 531 (1965). M. Luchner, K. Winkler, 0. Bessler. J. Hofmann, and W. Poltke, Pharm. Zentralhalle, 103, 484 (1964). D. Neumann and H. B. Schroter. J. Chromatogr., 16, 414 (1964). M. Ikram, 0. A. Mlana, and H. Islam, J. Chromatogr., 11, 260 (1963). St. Enache, T. Constantinescu, and V. Ignat, Farmacia (Bucarest), 15, 723 (1967). St. Enache and T. Constantinescu, Farmacia (Bucharest), 9, 151 (1970). M. Sarsunova, J. Chromatogr., 50,442 (1970). T. Niwaguchi, J. Chromatogr., 59, 127 (1971). R. Fowler, P. J. Gomm, and D. A. Patterson, J. Chromatogr., 72, 351 (1972). S.Ebel, E. Bohr, and E. Plate, J. Chromatogr., 59, 212 (1971). J. H. Knox and J. Jurand, J. Chromatogr., 82, 398 (1973). J. Jane and 8. B. Wheals, J. Chromatogr., 84, 181 (1973). J. R. Broich, S.Goldner, G. Gourdet. S. Andryanskas, V. J. Umberger, and D. B. Hoffmann, J. Chromatogr., 80, 275 (1973). K. K. Kaistha and J. H. Jaffe. J. Chromatogr., 60, 13 (1971). D. J. BerryandJ. Grove, J. Chromatogr., 61, 111 (1971). R. J. Coumbis, C. C. Fulton. P. J. Calise, and C. Rodriguez, J. Chromatogr., 54, 245 (1971). J. R. Broich, D. 8. Hoffmann, S. Andryanskas, L. Galante, and C. J. Umberger, J. Chromatogr., 60, 95 (1971). J. R. Vroich, D. B. Hoffmann, S. Andryanskas, L. Galante, and C. J. Umberger, J. Chromatogr., 63,309 (1971). J. K. Brown, L. Shapazin, and G. D. Griffein. J. Chromatogr., 64, 129 (1972). H. McKennis Jr., L. 8. Burnbull, E. R. Browman. and E. Wada. J. Am. Chem. Soc.. 81, 3951 (1951). T. Constantinescu, hd. Aliment. (Bucarest), 22, 330 (1971). XXX-Tobacco Alkaloids and Related Compounds, Voi. 4, by V. S.Von Euler, Ed., Pergamon Press, Elmsford, N.Y., 1964. G. Baiulescu and T. Constantinescu, Rev. Chim. (Bucarest), 25, 1026 (1974). T. Constantinescu, Lucr. lnst. Cercet. Aliment., 11, 73 (1973). T. Constantinescu, lnd. Aliment. (Bucarest), 20, 379 (1969). T. Constantinescu, Chim. Anal. (Bucarest), 2, 230 (1972). G. Baiulescu and T. Constantinescu, Rev. Chlm. (Sucare$t), 22, 701 (1974). G. J. Kirchner, J. Chromatogr., 62, 31 (1973). G. J. Kirchner, J. Chromatogr., 82, 101 (1973). H. V. Street, J. Chromatogr.. 48, 291 (1970).
LITERATURE CITED (1) I. M. Hais and K. Macek, "Chromatografia pe h h e " . Ed. TehnicB, Bucuresti. 1960. (2) E. Stahl, "Thin-Layer Chromatography", Springer-Verlag, HeidelbergNew York, 1966, pp. 127, 288. 421, 433. 436, 859, 869, 873. (3) D. Waldi, K. Schnackerz, and F. Munter, J. Chromatogr., 6, 6 (1961). (4) W. Debska, Bull. Soc. Amis Sci. Lett. Poznan, Ser. C, 11, 97 (1962); Chem. Abstr., 57, 138869 (1962). (5) M. ikramand and M.K. Bakhsh, Anal. Chem., 36, 111 (1964). (6) A. Kaess and C. Mathis, Ann. Pharm. Fr., 23, 267 (1965). (7) M. Mandek, M. Struhar, and H. Klucarova, Farm. Obzor., 132, 97 (1963); Chem. Abstr., 60, 367g(1964). (8) H. Staub, Helv. Chim. Acta, 45, 2297 (1962). (9) R. A. Heacock and J. E. Forrest, J. Chromatogr., 78, 241 (1973). (IO) I. Bayer, J. Chromatogr., 16,237 (1964). (1 1) R. A. Van Velsum, J. Chromatogr., 78, 237 (1973). (12) E. Brochmann-Hanssen and T. Furnya, J, Pharm. Sci., 53, 1549 (1961). (13) H. Kajita, Seikagaku, 27,456 (1955); Chem. Abstr., 55, 17763(1961). (14) T. Kato, Kagaku Keisatsu Kenkyusho Hokoku, 14, 238 (1961); Chem. Abstr., 56, 7431a (1962). (15) H. Kozuka and M. Motoyoshi, Kagaku Keisatsu Kenkynsho Hokoku, 16, 39 (1963); Chem. Abstr., 59, 1512h(1963). (16) H. J. Kupferberg, A. Burkhalter, and E. L. Way, J. Chromatogr., 16, 558 (1964). (17) G. R. Nakamura, J. Forensic Sci.. 7, 465 (1962): Chem. Abstr., 58, 32721(1963). (18) J. A. Steele, J. Chromatogr., 19, 300 (1965). (19) H. V. Street, J. Pharm. Pharmacol., 14, 56 (1962).
RECEIVEDfor review December 17, 1974. Accepted May 20, 1975.
Gel-Permeation Chromatography Calibration Curve for Asphaltenes and Bituminous Resins Hendrik Reerink and Jan Lijzenga Koninklijke/Shell-Laboratorhm,Amsterdam Shell Research B. V.. Amsterdam, The Netherlands
For the determination of molecular-weight distributions by means of gel-permeation chromatography, one needs a calibration curve which relates molecular weight to elution volume. Such a curve has been constructed for hlgh-molecular bituminous components by comblnlng the chromatograms partly with molecular-weight distributions derived from velocity ultracentrifugation, partly with measured average molecular weights. lt proved possible to calculate the calibration curve for asphaltenes when that for polymers Is known. Benoit's unlversal calibration curve, in which the product of molecular weight and limiting viscosity number Is used as a measure of the hydrodynamic volume, does not apply for asphaltenes.
Recently we have described a method for determining molecular-weight distributions of asphaltenes by means of the ultracentrifuge ( 1 ) . This method is time-consuming and only applicable to rather large molecules (M > lo4). Looking for a technique which does not suffer from these drawbacks, we found that gel-permeation chromatography (GPC) offers good possibilities. 2160
GPC finds increasing application in macromolecular chemistry; it is rapid and fairly simple. Ideally, the molecules are separated according to their "hydrodynamic volume"-which volume depends on both their size and shape. The pore size distribution of the gel has to be adapted to the particle size distribution of the sample. Large and bulky molecules can enter a small fraction of the pores only; they therefore pass quickly through the column; their elution volume is small. Small and compact molecules, on the other hand, can diffuse into all pores of the gel, so that their rate of transport is low and their elution volume large. It is known, however, that GPC of petroleum products is not always ideal. For instance, Oelert ( 2 ) , using Sephadex LH-20 as the gel and chloroform as the solvent, found that the type of hydrocarbon influenced the retention volume. I n a later article, Oelert and Weber ( 3 ) reported that the calibration curve of paraffins and polyaryls differed appreciably from that of catacondensed aromatics. A calibration curve obtained with pericondensed aromatics even had a positive slope (if the molecules are separated according to size, the slope must be negative), which clearly shows that the authors were not dealing with ideal GPC.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
Using a different gelholvent system, we have also found influences of chemical type on GPC separation. For instance, saturates (obtained from bitumens) eluted earlier than more aromatic components of equal molecular weight. Asphaltenes and resins, however, which are known to have similar overall structures, showed very similar elution behavior. This enabled us to determine the molecular-weight distributions of these components by GPC. Even in the ideal case, GPC is not an absolute method, since the rate of transport of a molecule depends on the unknown hydrodynamic volume and the unknown pore-size distribution of the gel. One needs an empirical calibration curve relating molecular size to elution volume. In the polymer field, such a curve is often obtained by means of practically monodisperse polystyrene fractions of known molecular weight. For asphaltenes, this polystyrene curve cannot be used because they have a much smaller hydrodynamic volume than polymer molecules of equal molecular weight, the former having a rather compact, the latter an open coillike structure. In addition, monodisperse asphaltene fractions are not available and very difficult to prepare. Snyder ( 4 ) and Haley ( 5 ) ha.ve constructed GPC calibration curves by plotting number average molecular weights (measured by vapor-phase osmometry) of fractions obtained by GPC vs. the peak elution volumes of these fractions. This is only permissible when the fractions have special molecularweight distributions, or when the distributions are very narrow. We will show that, for our fractions, neither was the case, and also th.at it can be doubted whether it was in the instances reported. One can, however! use known molecular-weight distributions (e.g., determined by the laborious ultracentrifuge method) for the calibration. And, in special cases, one can relate the measured number average molecular weight to the peak molecular weight. In the following, we will describe how the GPC calibration curve is constructed. EXPERIMENTAL Analytical gel-permeation chromatograms were obtained by means of a Waters X-200 chromatograph, equipped with five columns of 120-cm length and 0.95-cm outer diameter, filled with lo4, 3 X IO3, 8 X lo', 2.5 X lo', and 102-8,Styragels, respectively. T h e instrument operated a t ambient temperature, flow rate was 1.0 ml/min, one count equalled 5 ml, a thermostated differential refractometer functioned as the detector. Approximately 2 ml containing 0.5 mg/ml were injected. Tetrahydrofuran ( T H F ) was used as the solvent. Sedimentation experiments were carried out in a Spinco model E analytical ultracentrifuge ( I ) . Toluene or T H F was used as the solvent. Number average molecular weights, M,, were determined by means of a Mechrolab vapor-phase osmometer. Here, too, the solvent was either toluene or T H F . The measurements were done a t 37 "C (in T H F , and preparation No. 1 in toluene) or a t 65 'C (in toluene). GPC and molecular-weight measurements were performed on Basrah and Boscan asphaltenes and on a number of fractions made from Kuwait bitumenj. Some of these fractions have been described earlier ( I , 6 ) , some were made by preparative gel-permeation chromatography over a nonadsorbing silica gel, one (No. 10) by adsorption chromatography; and the resins were made from maltenes by elution of a chromatographic column containing alumina (Peter Spence, type H, 100-200 mesh, dried for 16 hours a t 160 "C) and silica (Davison, grade 923, 100-200 mesh, also dried for 16 hours a t 160 "C) with toluene-ethanol 9O:lO after previous elution with toluene. The following fractions were analyzed: No. 1. Dialysis residue (see Ref. 6). No. 2. Fraction obtained after successive extraction of Kuwait pentane asphaltenes concentrate with n-heptanelbenzene mixtures (FD-6 of Ref. 6). No. 3. Kuwait pentane asphaltenes concentrate (see Ref. 6). No. 4. First GPC fraction ex No. 3. No. 5. Second GPC fraction ex No. 3. No. 6. Third GPC fraction ex No. 3. No. 7 . Fourth GPC fraction ex No. 3.
n-no
r
I
I
25
30
35
40
45
ELUTION VOLUME (COUNTS)
Figure 1.
Correction of GPC chromatograms for tailing
ad-
due to
sorption Table I. Determination of Elution Volumes Corresponding to Number Average Molecular Weights Sample
ups
UA
LA*
VAX
"in,V P O
'peak
1 2 3 7 8 9 11 12 13 14
0.93 1.12 1.05 1.09 1.33 1.26 1.08 1.18 1.08 1.15
1.30 1.57 1.47 1.53 1.86 1.76 1.51 1.65 1.51 1.61
0.26 0.22 0.23 0.22 0.18 0.19 0.23 0.21 0.23 0.21
32.1 32.9 33.6 34.8 35.9 35.3 35.4 35.7 35.0 34.3
5,500 10,800 3,200 2,600 1,550 2,200 1,100 1,400 1,400 2,250
29.0 28.6 29.2 29.5 29.3 29.2 31.5 32.6 30.8 29.7
-
No. 8. Sixth GPC fraction ex No. 3. No. 9. Duplicate of No.8. No. 10. Adsorption-chromatography fraction ex No. 3 (adsorption onto alumina, elution with benzene-ethanol 95:s after previous elution with benzene-ethyl acetate). No. 11. Resins from a strongly blown Kuwait bitumen (see Ref. 1 for some properties of the parent bitumen). No. 12. Resins from a medium-blown Kuwait bitumen (see Ref. I). No. 13. Resins from a lightly blown Kuwait bitumen (Ref. I ) . No. 14. Similar to No. 13, obtained with a less active adsorbent. No. 15. Basrah heptane asphaltenes (see Ref. I ) . No. 16. Boscan heptane asphaltenes (see Ref. 1 ) . The last two preparations were made by precipitation with 10 volumes of degassed n-heptane, centrifuging after cooling, and drying under vacuum at room temperature.
RESULTS A typical GPC diagram is shown in Figure 1, together with the correction made. This was prompted by finding that the concentration of the supernatant of dilute solutions brought into contact with gel material decreased somewhat. The adsorption was estimated to amount t o a few percent under the conditions prevailing in the chromatograph. Washing with T H F resulted in desorption. In agreement herewith, the chromatograms were generally marked by a slight tailing. Ultraviolet spectra indicated that the adsorbed material was not specifically high-molecular. (Measurements on fractions obtained from Kuwait asphaltenes (6) showed that, with increasing molecular weight, the extinction coefficient a t 436 nm increases and the slope of the optical density-wavelength curve decreases.) We therefore assumed that the high-molecular part of the chromatogram was not influenced by the adsorption and corrected for the tailing by making the curve end at M = 200 (which is quite a low value for bitumens, but the amount of the low-molecular material is very small). For a few samples, ultracentrifuge molecular-weight distributions were derived from measurements using both
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
2161
CUMULATIVE WEIGHT FRACTICN
MOLECULAR WEIGHT
*r
f
‘Or
- -- - - -
__ - - - - - -
06
lo5
I
8-
04 -
04
1-
UA
0
5
I
6
6 4-
02-
02
I
ELUTION VOLUME
I
0
2-
2b
20
Flgure 2. (a)Elution volume V. ( b )Molecular weight M
io4-8-
Table 11. Comparison of Number Average Molecular Weights Determined by GPC and by Vapor-Phase Osmometry (VPO) Preparation No.
1 2 3 7 8 9
11 12 13 14
-
M”
G PC
VPO
8600 5500 4200 2800 1850 2200 2000 1750 1600 3000
5 500 10800 3 200 2 600 1550 2 200 1100 1400 1400 2250
T H F and toluene as solvents. These distributions appeared to be practically equal, which result is not unexpected since the concentrations were so low (-0.005%) that association will be virtually absent. In some cases, number average molecular weights were also determined in the two solvents. Those in T H F were approximately 10% lower than those in toluene. This difference which will be due to association in the poorer solvent, toluene, can be neglected for our purpose but we always used the lowest value available. Further results are incorporated in the following sections, with special reference to Tables I and I1 and Figures 3 and 5. CONSTRUCTION OF T H E CALIBRATION CURVE As mentioned in the introduction, we have made use of known molecular-weight distributions. For the high-molecular-weight part of the curve, the distributions were obtained by ultracentrifugation, and the procedure was quite straightforward. The low-molecular-weight part had to be tackled in a different manner. The High-Molecular-Weight Part of the Curve. The experimental gel-permeation chromatogram gives (n - no), the increase of the refractive index with respect to that of the solvent vs. the elution volume, V (see Figure 1).The molecular-weight distributions (MWD’s) determined by ultracentrifugation are slightly in error because we neglected the increase of the extinction coefficient a t 436 nm with increasing molecular weight, M . In the MWD determinations by GPC this error is partly compensated because the refractive index increment per unit of concentration (n - no)/ c, also increases somewhat with M . Disregarding this effect, 2162
6 -
0 I
4-
5 t *t I
10326
28
30
32
34
36
ELUTION VOLUME (COUNTS)
Figure 3. Asphaltenes calibration curve obtained from distributions determined by ultracentrifugation
the chromatograms represent differential weight vs. elution volume. Integration and normalization yield the cumulative weight fraction as a function of V (see Figure 2a). Note that the lower limit of the integral corresponded with the higher elution volume, and vice versa. The cumulative molecular-weight distributions given in Figure 2b were obtained from ultracentrifuge measurements ( I ) . By reading off the molecular weight, M , and the elution volume, V, at equal cumulative weight fractions, indicated in Figures 2a and Zb, the relation between M and V can be found. We have done so for some of the preparations mentioned before. In Figure 3, the values of M are plotted (on a logarithmic scale) vs. V. For each preparation, a smooth curve was obtained. The curves lie close together, but they do not coincide, probably because of errors in the ultracentrifugal molecular-weight distributions, rather than specific interactions between solute and gel during the GPC experiments. An argument for this view is that we see no systematic influence of structure on elution. For instance, the points for the most polar sample (No. 10) lie between those for the GPC fractions (No. 4, 5, and 6) and the dialysis residue (No. 1).Also there is no clear difference between the relatively strongly aromatic Basrah asphaltenes and the other ones. Therefore, and as we aimed a t obtaining a general picture of the MWD’s rather than a high accuracy, we have drawn one average curve. The Low-Molecular-Weight Part of t h e Curve. The ultracentrifuge cannot be used to determine the size distribution of samples containing small molecules because their slow sedimentation is strongly counteracted by rapid diffusion. Therefore, we calibrated the low-molecular end of the GPC curve by means of number average molecular weights, M,, obtained by vapor-phase osmometry. The question is a t which value of the weight fraction, w , the molecular weight is equal to M,,. From the ultracentrifuge work ( I ) , it is known that, for asphaltenes, M , in gen-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
MOLECULAR WEIGHT r
W*
2
t\
105 8 6 4
0 0
05
10
I
I
15
20
I
I
25
30 c
Flgure 4. Cumulative weight fraction, w’, where M equals M,,, as a
function of the standard deviation u for log-normal distribution era1 corresponds approximately to w = 0.25. And this means that, in general, M, does not correspond to the peak in the elution diagram. We have solved this problem by making two assumptions: 1)In the molecular-weight region concerned, the calibration curves (log M vs. V ) for polystyrene and for bituminous products are straight. 2) The molecular-weight distributions are log-normal. Both assumptions are acceptable. The calibration curve for polystyrene for the set of Styragels used in our Waters chromatograph is known to be approximately straight in the low-molecular region; see Figure 6. Theoretical considerations-given later-lead to the conclusion that the calibration curve for asphaltenes is also straight. The actual calibration curve is not straight at high molecular weight (Figure 6), but the curvature has a negligible influence on the calculated number average molecular weight, which quantity will be used in the following. Note that for straight calibration curve and log-normal molecular-weight distribution (MWD), the experimental GPC diagram should by symmetrical. In practice, the diagrams are not in general symmetrical, but have a low-molecular tail (see Figure 1).In agreement herewith, the ultracentrifuge work ( I ) showed that the MWD’s are approximately log-normal, with deviations on the low-molecularweight side. The GPC diagrams of the resins have shapes similar to those of the asphaltenes; consequently their MWD’s are also similar. Since the high-M side of the distribution has a relatively small influence on the value of M,, we have applied the formulas of the log-normal distribution to the low-M side, so as to obtain a relation between M , and the corresponding value of w , which will not be far from the true relation. The two assumptions can be mathematically formulated: In MPS = a p s + bpsV
(la)
hl M A = a A -b bAV Ob) dw 1 1 2 -- -- exp - [-In M/M,) (2) d l n M U& U V 5 Here PS = polystyrene; A = asphaltenes or resins; M, is a parameter equal to .M a t cumulative weight fraction w = 0.5; u is the standard deviation of the distribution. If a log-normal distribution is obtained when combining an experimental GPC diagram with the polystyrene calibration curve, then the distribution would also have been log-normal if the asphaltenes curve had been used. The standard deviations are then related as follows (see Appendix I):
(3)
64-
2-
\ 0
10
26
I
I
I
I
28
30
32
34
‘s“
0
,
36
EWTION VOLUME (COUNTS)
Figure 5. Combination of “high-molecular’’curve of Figure 3 with
“low-molecular’’calibration points Note that this relation contains only the slopes of the curves, and not the values of a p s and a A . The cumulative weight fraction, w * ,where M equals M, is given by (see Appendix I, Equation 1-6) (4)
Values of w * as a function of u are shown in Figure 4. The procedure now is as follows. Using the experimental diagram (Figure l),we calculate the molecular-weight distribution as if the PS calibration holds. We check whether this distribution is approximately log-normal, and-if so-we calculate the standard deviation by means of = ln- M0.50 M0.16 where M0.50 and M0.16 are the molecular weights a t 50 and 16% of the cumulative weight, respectively. The value of UA is obtained by Equation 3 with a value of b A taken from the straight ;high-molecular part of the calibration curve, and that of WA*is read from Figure 4. The corresponding value, V A * , is then taken from the experimental w vs. V curve. This value, in combination with that of M,, gives one point of the calibration curve. The above procedure was applied to ten of our samples. Table I shows the relevant data and also the values of the peak elution volumes. In Figure 5 , values of M,,VPO (determined by vapor-phase osmometry) are plotted vs. VA*;this figure also contaiys the high-molecular part of the calibration curve from Figure 3. The points are reasonably close to the extension of the high-molecular part. This we consider to be evidence corroborating the assumptions made. In Figure 6, the complete calibration curve is compared with the one for polystyrene. ups
ANALYTICAL CHEMISTRY, VOL. 47,
NO. 13,
NOVEMBER 1975
2163
MOLECULAR WEIGHT
‘A
3
2t 1021
26
I
1
28
30
I I J 32 34 36 ELUTION VOLUME (COUNTS)
Flgure 6. Callbration curves for asphaltenes and polystyrene
DISCUSSION Discussion of Results. GPC separation is generally taken to be governed by a hydrodynamically active volume of the molecules. The dilute-solution viscosity also depends on a hydrodynamic volume. Although the volume in the former case need not be equal to that in the latter, the two volumes will be closely related. Measurements showed that the viscosity hydrodynamic volumes of different Kuwait asphaltenes fractions are practically equal a t equal molecular weight (6);we therefore assumed that this also holds for the GPC hydrodynamic volumes. Accordingly, we have represented the high-molecular part of the calibration by one curve, averaging between the curves for the different preparations (see Figure 3). In the low-molecular region, the points show more scatter (compare Figures 3 and 5 ) . This is understandable, since in Figure 5 each point represents one sample, whereas in the high-molecular region (Figure 3) each sample gives a series of points. However, it can also be argued that the “low-molecular” points are less accurate. For instance, the assumption that the refractive index increment, (n - n,)/c, is constant may have introduced some error. In general, the refractive index of bituminous components increases somewhat with increasing molecular weight; the variation in (n - n,)/c, and, consequently, in the error introduced, will therefore increase with decreasing molecular weight. In addition to these systematic errors, there is the normal random inaccuracy of the vapor phase osmometric values, which we believe to have the greatest influence, on the deviations. Second, the number average molecular weight-which we used for the calibration-is very sensitive to errors in the tail of the experimental GPC diagram such as may arise from base-line distortion or from interactions between solute and gel material. 2164
Further, the assumptions of linear calibration curves and of log-normal distributions will not be in full agreement with the actual state of affairs. If we bear these points in mind, the fact that the lowmolecular-weight part of the calibration curve fits the highmolecular part reasonably well is very encouraging and lends support to the assumptions made and the procedure followed. We emphasize that the molecular-weight values obtained from sedimentation measurements are completely independent of those obtained from osmotic pressure. A shape model for the molecules is needed in order to interpret the sedimentation measurements, whereas the osmotic-pressure values are independent of any model. As already mentioned, the molecular-weight distributions (MWD’s) are not as a rule perfectly log-normal; the majority are skewed towards the high44 side. This makes the difference between VA* and the peak-elution volume larger than it would have been for perfectly log-normal distributions. Quite apart from the deviations from log-normality, this difference increases with the calculated u (cf. Table I). The marked difference between VA* and Vpe& demonstrates the importance of the procedure followed. If we had equated M,, to Mpeak, the resultant calibration curve would have been considerably in error in the low-molecularweight part. Molecular weights in that region could amount to about 10%of the values obtained by means of the curve in Figure 5. As a check of the calibration curve, we have converted the experimental chromatograms into molecular-weight distributions and calculated the number average molecular weights (see Appendix 11).In Table 11, the resultant values are compared with those determined experimentally by VPO. The calculated values actually lie much nearer to the calibration curve when plotted VI. VA* in Figure 5. The preparations 1-14 had been obtained in different ways. No. 11-14 are resins which for the greater part are soluble in n-heptane. The others are asphaltenes fractions which are insoluble in this solvent. Most of the latter were obtained by methods which are not related to chemical composition; No. 2 is a high-molecular, strongly polar fraction. The resins are also polar, having been eluted from a chromatographic column by an alcohol-containing solvent. The values of Table I1 reveal no systematic deviations for certain groups, Le., there is no indication that, for instance, resins require a calibration curve different from that for asphaltenes. As we said earlier, the calibration curve for polystyrene will probably differ greatly from that for asphaltenes because of the differences in hydrodynamic volume. The lower the molecular weight, the smaller will be this difference. This expectation is fully borne out by the experiments (see Figure 6). The difference between the two curves will be discussed below. Comparison with Work by Other Authors. Other authors have also made use of polydisperse samples for GPC calibration. Cantow et al. (7), working with polymers, applied a method similar to ours for the high-molecular part of the calibration curve. They compared the integrated GPC diagrams with known molecular-weight distributions, which had been obtained by fractionating polymer samples and determining the molecular weight of the fractions from their limiting viscosity number. The fractions themselves were shown to have sharp distributions. Balke et al. (8)determined various averages of M for two polymer samples. Assuming a linear calibration curve, they used the two constants ( a and b of our Equation 1) as adjustable parameters, and by a least-squares technique min-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
imized the differences between the measured average molecular weights and those calculated from the experimental GPC diagrams. The assumption of a linear curve was based on the fact that often straight lines are found. Actually, however, the curve depends on the pore-size distribution of the gel. In our case, the assumption of a linear calibration curve for asphaltenes was justified by the fact that the experimental polystyrene curve was straight in the region of interest. In addition, it is questionable whether the deviations of different averages may be given equal weight in the least-squares calculation. Depending on the average chosen, errors in the constants a and b will work out differently. Snyder ( 4 ) , Haley ( 5 ) , and Altgelt (9) constructed GPC calibration curves for bituminous products by plotting Mn of GPC fractions made from whole bitumens vs. elution volume. The first two authors did not investigate the fractions separately by repeated GPC which would have given information about the width of the MWD’s of the fractions. Altgelt fractionated three of his GPC fractions further by means of pentane precipitation and chromatography. In one case, he obtained subfractions differing widely in Mn which proves that the original GPC fraction was not monodisperse. In the other two cases, the Mn’s of the subfractions were much nearer to each other. This, however, does not prove that the GPC fractions were monodisperse; each of the subfractions could have had wide distributions with approximately equal Mn values. The fractions made by us by preparative GPC appeared to be far from monodisperse. For instance, the data of Table I show that the GPC fractions 7 and 8 had about the same U-values as the other samples. In addition, we split our sample No. 3 into some 20 GPC fractions using Styragel as the support (see Reference I ) , and these fractions showed much sharper MWD’s than their mother substance had, yet they had U-values of about 0.7, i.e., they were not monodisperse. Haley obtained calibration curves for straight-run bitumens which differed from those for blown bitumens in the high-molecular-weight part. This may be due not only to adsorption phenomena, but also to different widths of the MWD’s of his fractions. Snyder’s results are dealt with below. Relation between the Calibration Curves f o r Asphaltenes a n d f o r Polymers. Following a line of reasoning similar to that of Benoit et al. (IO), we have theoretically calculated the asphaltenes calibration curve, starting from the one for polystyrene. The hydrodynamic volume of a polystyrene molecule is proportional to the cube of the dimensions of the coil, the average shape of which is spherically symmetric: where R = root mean square end-to-end distance of the coil. In polymer physical chemistry, the following relation is well established:
W-rtl = 4R3
(7)
where C$ is a semi-empirical constant, independent of the polymer-solvent system, and [a] is the limiting viscosity number (LVN). Combining Equations 6 and 7 with the well-known Mark-Houwink relation
[VI = K p s M h
(8)
where a and K P S are constants which depend on polymer, solvent, and temperature, we obtain
Table 111. Values of k ~ / k for z Different Elution Volumes Elution volumc, counts
26 27 29 31 33 35 36
MPS
5.5 x 2.8 x 1.0 x 4.3 x 2.1 x 1.1 x 7.5 x
ki f k2
MA
3.8 x 1.7 x 4.3 x 1.4 x 5.0 x 2.0 x 1.3 x
104
io4 104 103 103 103 102
105 105 104 10‘ 103 103 103
0.78 0.95 1.07 1.20 1.20 1.23 1.41
The hydrodynamic behavior of asphaltenes in solution can be described by the model of flat disc-like particles (6). We assume the volume active in GPC to be proportional to the sphere enveloping these particles, i.e.
, (10) where 1 = major axis of the disc. This assumption is based on the conception that a disc-shaped particle will enter a pore of the gel only if it can rotate there freely. Otherwise, the process of entering will be counteracted by a loss of orientation entropy. A plot of the average values of 1 vs. the average M as given in Ref. 6 leads to an empirical relation which shows that 1 is approximately proportional to M0.39.This is equivalent to the relation between limiting viscosity number (LVN) and M derived in Ref. 1; note that the value of 1 is obtained from that of the LVN (by means of a shape model). We assume that this holds for every asphaltene particle, and introduce it into Equation 10: VhA = k2 x 1.73 x 10-24M~1.1s
(11)
We further assume that the hydrodynamic volumes of polystyrene and asphaltenes are equal a t equal elution volume. In formula VhPS = VhA and a = 0.70 Using numerical values, K P S = 1.5 X (derived from Benoit’s data), 4 = 2 X loz3,we obtain log M A
-1.154
+ 1.44 log Mps + 0.85 log k J k p
(13)
Values of the elution volume and corresponding values of MPS and M A were read from the calibration curves (Figure 6). Table I11 shows the values of kllk2 calculated by means of Equation 13. The ratio of k l to kp is nearly constant even for low M , where neither Equations 7 and 8 nor the relation between major axis and M will hold very well. The trend in the values of k J k 2 which seems to exist is probably not meaningful, considering the accuracy of the measurements. Thus, taking k l equal to kp, one can calculate the calibration curve for the asphaltenes with reasonable accuracy when that for polystyrene is known. Also, we note that if the polystyrene calibration curve is a straight line, as is assumed in Equation la, then it follows from Equation 13 that the curve for the asphaltenes is also straight. The ratio of the two slopes, bA/bpS, is found from Equation 13 to be equal to 1.44 while the experimental ratio used in Equation 3 is 1.40.This again demonstrates the good agreement. It is worth observing that the calculated values of Table I11 were obtained without any assumption about the shape of the calibration curve. We will now compare our results with those of Snyder
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
2165
( 4 ) . This author used bitumen fractions as calibration standards. As mentioned above, this is in general only permissible when the fractions have very narrow MWD’s. On similar lines to our treatment, Snyder compared his calibration curve with that for polystyrene and obtained values for the ratio of the molecular weight of the bituminous products, Ma, to the length of the extended polystyrene chain, Lps, ranging from 200 for the lower-molecular-weight components to 460 for the asphaltenes (M in g mol-’ and L in nm). Since MPS = 400 Lps, Snyder’s ratios MAIMPS (at equal elution volume) varied from 0.5 to 1.15. We doubt whether MA can be smaller than MPS since dilute-solution viscosity measurements prove that most bitumen constituents have smaller hydrodynamic volumes than polystyrene (at equal molecular weight). According to Figure 6 and Equation 13, the ratio Ma/Mps in the molecular-weight region concerned lies between 1.5 and 2. The fact that our values for this ratio are 2-3 times as high as those of Snyder, indicates that his fractions did not have very narrow MWD’s. We can explain Snyder’s results when we assume that, for his fractions, the elution volume corresponds to a molecular weight, Mp, which equals two to three times the value of M,. Assuming further that his fractions had lognormal MWD’s, we calculate the standard deviation by means of
M,, = M, exp -u2/2
(14)
where M, was taken to be equal to Mp. In consequence, u = 1.2 to 1.5. These values are of the same order of magnitude as those given in Table I, but seem rather high for GPC fractions. Deviations from log-normality may play a role here, however. From a plot of Snyder’s data of the cumulative weight fraction vs. molecular weight of asphaltenes, we see that his MWD is much narrower than the MWD’s determined by us from velocity ultracentrifugation. The difference is conceivably due to the type of asphaltenes used, but more probably to polydispersity of Snyder’s fractions, viz., to the fact that his higher-molecular-weight fractions had wider distributions than the lower-molecular ones. Benoit’s Concept of a Universal Calibration Curve. In the foregoing, it has been shown that the asphaltenes calibration curve can be calculated to a reasonably good approximation if the curve for a polymer is known and if viscosity data of both types of macromolecules are available. Benoit et al. ( 1 0 ) have shown earlier that the product M[T] can be used as a measure of the hydrodynamic volume of polymer molecules. In a plot of log M[q] for a number of polymers of different conformations vs. elution volume, all points fell on one single curve. In one case, this appeared also to hold for rod-like molecules. The curve thus obtained was called the universal calibration curve. The underlying idea is expressed in our Equations 6 and 7 . Since 4 is a universal constant, the product M[a] will be a universal measure of the hydrodynamic volume of polymers. We have found, however, that the relation between M[a] and V for asphaltenes is different from that for polymers. Corresponding values of V and M, for both asphaltenes and polystyrene, were read from Figure 6. The LVN of polystyrene were calculated by means of Equation 8, using values for KPS and N as given above. The LVN of asphaltenes was obtained by means of numerical tables of Scheraga (11) giving the LVN as a function of the axis ratio, p , of oblate ellipsoids, and a semi-empirical relation between p and the molecular weight. The latter relation was derived similarly to Equation 11 and it shows that p is proportional to M0.l8. The results are given in Figure 7. It is seen that M[v] for asphaltenes is 2-3 times as high as M[a] for polystyrene. 2166
APPENDIX I: THE LOG-NORMAL DISTRIBUTION In this appendix, we have collected a number of relations which have been used in the present paper. The log-normal distribution is given by dw =- 1 exp - (-In 1 MIM,) d l n M uv% 0 4 where w is the weight, normalized to 1,i.e., +-
dw
2
(1-1)
dlnM=l
and u the standard deviation; M, corresponds to the maximum in the differential distribution dwld In M, and to 50% of the cumulative distribution. The moments of the distribution can be calculated by dw d In M = Moa exp (a2u2/2) (1-3) Special cases of Equation 1-3 are: a = 0; YO,total weight = 1,see Equation 1-2 a = 1; Y1, weight average molecular weight Mu = M, exp a2/2
(1-4)
a = -1; Y-1 = reciprocal of number average molecular
weight, leading to M,, = M, exp -a2/2 (1-5) From Equation 1-5, the cumulative weight fraction, w*, where M equals M,, can be obtained dw dlnM= w * = l m dlnM
6
s-“” -m
exp 2 du
(1-6)
in which u = ( l / a) In MIM,. We will now consider gel-permeation chromatography. Suppose we get a log-normal distribution when using a linear calibration curve. In formula In M I = a1
+ blV
(1-7)
will lead to
If we use another linear calibration curve, In M2 = a2 + b2V
(1-9)
then the maxima of the two differential distributions dwld In M correspond to the same elution volume, V,, because the maximum in the distribution corresponds to the maximum in the experimental GPC diagram. Consequently, In M1IM01 = a1 + b l V - (a1 + blV,) = bl(V - V,) (1-10) In M2/M02 = b l (V - V,).
(1-11)
Elimination of (V - V,) yields In MzlM,2 = ( b l l b d In M1/Mol
(1-12)
d In M1 - bl --
(1-13)
and also
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
d In M2
b2
'h
M
.-
71 (ml mole-')
Table 11-1. Values of Parameters ve
Asphaltenes Polystyrene
19.909 22.807
v* 35.489 27.507
C
d
-0.053 -0.011
1.371 2.210
2
26
Figure 7.
V = V,
I
I
28
30
I\
I
I
32 34 36 ELUTION VOLUME (COUNTS)
+ V,
exp c(ln M)d
(11-1)
where V,, V,, c , and d are adjustable parameters. These parameters were computed by a Fortran program, based on an iteration procedure. Since Equation 11-1 is optional and has no physical meaning, extrapolation is not permitted. However, the part of the curve in the interval between the last calibration point at high elution volume and the highest elution volume appearing in the chromatograms is of great importance. This part represents molecular weight values lower than the number average, which contribute greatly to the numerical value of this average. To compute the parameters of the asphaltenes curve, it was therefore necessary to take a point a t high elution volume as input. This point was' chosen in such a way that the curve was extended linearly to V = 45. The numerical values of the parameters pertaining to our columns are given in Table 11-1. The cumulative molecular-weight distribution was calculated by integrating and normalizing the experimental chromatogram and converting the elution volume into the molecular weight according to Equation 11-1. The average molecular weight M , defined as
M,'(so
Comparison of M[q] for asphaltenes and polystyrene
1dw
-1
M)
(11-2)
in which dw equals the normalized differential weight, was calculated with the similar equation We now calculate the second distribution starting from the first by means of -dui - --.- dw d l n M 1 (1-14) dlnM2 dlnM1 dlnMp which is combined with Equations 1-8, 1-12, and 1-13. The result is
--dw d In M2
1 In M2/M02)* (1-15)
1 - --
-
u2\&
where 62
=
(b2/bl)Ul
(1-16)
Equation 1-15 proves that the second distribution is also log-normal. Equation 1-16 has been used to calculate the standard deviations of the asphaltenes distributions; see Equation 3.
APPENDIX 11: CONVERSION OF THE EXPERIMENTAL GPC DIAGRAM INTO MOLECULAR-WEIGHT DISTRIBUTION AND CALCULATION OF AVERAGES As the conversion is performed by a Fortran IV computer program, it is convenient to describe the experimental relation between elution volume and molecular weight by a mathematical function. Cornet and Boerma of this laboratory (private communication) have found that a nonlinear calibration curve can often be rendered by the following equation:
(11-3) Here hi is the recorder response (i.e., n - no)a t elution volume Vi, and Mi the corresponding molecular weight from Equation 11-1.The input is supplied in equal steps in V, in such a way that in one interval in V the chromatogram is approximately linear, since Equation 11-3 may only be used on this condition. In fact, it is sufficient to give 20 values as input ( 12).
ACKNOWLEDGMENT Thanks are due to J. Boerma for carefully performing the GPC experiments. LITERATURE CITED (1) (2) (3) (4) (5)
H. Reerink and J. Lijzenga, J. lnst. Pet., London, 59, 21 1 (1973). H. H. Oelert, Erdol Kohle, 22, 19 (1969). H. H. Oelert and J. H. Weber, ErdolKohle, 23, 484 (1970). L. R . Snyder, Anal. Chem., 41, 1223 (1969). G. A. Haley. "The Blowing of Bitumen", Dissertation, University of New South Wales, Australia, 1972. (6) H. Reerink, lnd. Eng. Chem., Prod. Res. Develop., 12, 82 (1973). (7) M. J. R. Cantow, R. S. Porter, and J. F. Johnson, J. Polym. Sci., Part A - i , 5 , 1391 (1967). ( 8 ) S.T. Balke, A. E. Hamielec, E. P. LeClair. and S. L. Pearce, hd. Eng. Chem., Prod. Res. Develop., 8 , 54 (1969). (9) K. H. Altgelt. Bitumen, Teere, Asphake, Peche, 21, 475 (1970). (10) 2 . Grubisic. P. Rempp, and H. Benoit, Polym. Lett, 5, 753 (1967). (11) H. A. Scheraga, J. Chem. Phys., 23, 1526(1955). (12) A. Lambert, Polymer, 10, 213 (1969).
RECEIVEDfor review February 24, 1975. Accepted July 14, 1975.
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