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ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
(10) J. R. Van Wasser, "Phosphorus and Its Compounds", Vol. 1, Interscience Publishers, New York, N.Y., 1958, pp 452-459. (1 1) R. P. Mitra, H. C. Malhatra, and D.V. S. Jaln, Trans. Faraday SOC.,62, 167 (1966). (12) D.0. Campbell and M. L. Kllpatrick, J. Am. Chem. Soc., 76, 893 (1954). (13) J. P. Crouther and A. E. R. Westman, Can. J. Chem., 32, 42 (1954). (14) G. A. Abbott, J . Am. Chem. Soc., ;I,763 (1909). (15) K. B. Yatslmirskii and V. P. Vasii'ev, Instability Constants of Complex Compounds", Van Nostrand, Princeton, N.J., 1966, pp 99-101, 106-108. (16) J. I.Watters, E. D. Loughan, and S.M. Lambert, J . Am. Chem. Soc., 7 8 , 4855 (1956). (17) J. I. Watters, P. E. Sturrock, and R. E. Simonaites, Inorg. Chem.,2 , 765 (1963).
L. G. Sillen and H. E. Martell, "Stability Constants of MetaCIon Complexes", Special Pub. No. 17, The Chemical Society, Burlington House, London, 1964; Supplement I,Spec. Publ. No. 25 (1971). J. I.Watters and R. Macle;, J . Inorg. Nucl. Chem., 3 0 , 2163 (1968). , G. Schwarzenbach in Advances in Inorganic Chemistry and Radiochemlstry", Vol. 3, H. L. Emeleus and A. G. Sharpe, Ed.,Academic Press, New York, N.Y., 1961, pp 257-285. (21) H. Irvlng and R. J. P. Williams, J . Chem. Soc., 3192 (1953). I
RECEIVED for review April 16, 1976. Resubmitted January 16, 1978. Accepted May 8, 1978.
Structure Parameter Analyses of Asphalt Fractions by a Modified Mathematical Approach Huynh Hon Klet, Shadi La1 Malhotra, and Louls-Philippe Blanchard" D6partement de G6nie Chimique, Facult6 des Sciences et de Ggnie, Universit6 Laval, Q d b e c , Out$.,Canada, G7K 7P4
A modlfled mathematical approach has been developed and applled to the asphalt model proposed by Haley. Various structure parameters have likewlse been derlved using analytical data obtained by element analyses, nuclear magnetic resonance and Infrared spectroscopy and Mw molecular weights calculated from gel permeation chromatograms (using vapor pressure osmometry, Mn values, and vlscosity measurements). The results obtained with this approach and those obtained by experiment agree well indicatlng its validity and the exactness of the method of resolution. Analyses of structure parameters suggest that although all asphalt fractions are built up of aromatic and naphthenic rlngs, the ones having low molecular weights have few aliphatic chalns attached to them. Using the structure parameters, molecular weights were computed for the various asphalt fractlons and were found to agree wlth their Mw (GPC)values.
Dickie and Yen ( 1 ) who studied asphaltenes originating from different sources, proposed that their macrostructure is composed of individual sheets which associate to form unit cells and larger associated micelles. Speight (2) used element analyses and nuclear magnetic resonance spectroscopy (NMR) in his study on the structure analyses of Athabasca asphaltenes to show that individual condensed aromatic sheets vary from six-ring to fourteen-ring and larger units. Hirsch and Altgelt (3)developed mathematical equations based on the concept of floating parameters to calculate the average structural parameters of petroleum heavy ends. Their method provides rigorous relations among the structure parameters but requires data from element analyses, NMR, and infrared (IR) spectroscopy as well as density and molecular weight determinations. The structures of Kuwait and Arabian asphalts were determined by Haley ( 4 ) and Dickinson ( 5 ) . The equations which they proposed, are simpler and easier to apply than those of Hirsch and Altgelt (3). Recent studies by Zalka and Mandy (6),by Yen (7), and by Katayama et al. (8) have led to the suggestion of more complex structures which even take into account the interactions between various elements such as carbon, hydrogen, sulfur, oxygen, and nitrogen. In the present study, the equations proposed by Haley ( 4 ) have been reinvestigated. Changes, required to adapt them to the experimental results obtained in this work, were made 0003-2700/78/0350-1212$01 .OO/O
and a novel mathematical approach involving an IBM 370/158 computer was used to solve the resulting simultaneous equations. The details of this study form the subject of the present paper.
EXPERIMENTAL The data on the origin of the asphalt, its separation into various fractions by preparative gel permeation chromatography (GPC) and their characterization by analytical GPC, vapor pressure osmometry (VPO), NMR, IR, and element analyses has b e e n presented elsewhere (9). THEORETICAL In Figure 1is shown a schematic diagram of asphalt where the carbon atoms are classified into various types (3). The structure shown has its origin in the results of numerous studies on the composition of asphalts using a variety of techniques. It is based on a number of assumptions where: the structure is believed to be built u p of hydrogen and carbon atoms only ( 3 ) ; the amount of aliphatic and naphthenic carbon in t h e form of tertiary atoms is negligible; the amount of P-methylene hydrogen occurring in the a-hydrogen band is also negligible; the aromatic carbon is hexagonally pericondensed with more than three rings and no aromatic rings are joined by single bonds; the naphthenic carbon is attached to the aromatic ring; the paraffinic chains are attached to aromatic or naphthenic ring; only one pericondensed aromatic system occurs per molecule. The different subscripts used for various positions of carbon atoms signify ( 4 ) the following: 1. Aliphatic Carbons Relative to an Aromatic Ring (a) CA(CH~, C H ~ CH3) , - (CH, CH2, CH3) alpha (b) CB(CH~, CH - (CH, CH2) beta or farther removed (c) CB(CH~) beta CGCH~ - CH3 gamma or farther removed (d) 2. Naphthenic Carbons Relative to an Aromatic Ring (a) CAN(CH~, CH~) (CH, C H J alpha CBN(CH~, C H ~) (CH, CH2) beta or farther removed (b) 3. Aromatic Carbons Relative to Other Carbon Atoms CRIaromatic internal carbon, each bonded to three (a) other aromatic carbon atoms 0 1978 Amerlcan
Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
n
1213
position 6 , and methyl protons in position y t o an aromatic ring respectively. HT represents the total number of protons as calculated from N M R with HT = Ha Hp H7 Ha7. the percentage of naphthenic carbon ( C N % ) from (3) N M R (9) calculated with the relation in (IO);%CN = 54.3(Ha/H, 0.10). the atomic ratio of hydrogen t o carbon of t h e (4) methyl and methylene groups (MMHC) using the Haley equations ( 4 ) . (Results are presented in Tables I to 111). the weight average molecular weight (Mw) (9). (5) In the analysis input data for his computer program (FORTRAN), Haley (4) used criteria 1to 4 listed here along with data on aromatic hydrogen, HA. In the present study, HA data was not used but additional information concerning the Mw of asphalt fractions was added for the IBM 370/158 computer system used. Analysis O u t p u t D a t a a n d Related Equations. The different carbon types shown in Figure 1and defined in the text can be evaluated quantitatively by solving a series of equations, relating them to the given input information. Haley (4) proposed 14 such equations relating them with the structural parameters. All of these equations have been retained in the present study. Based on these, the molecular weight Mw of the asphalt fractions were calculated using the following derived expression (1):
+
+
+
+
RPH
W
v /v W
Figure 1. Classification of carbon atom types in asphalts
Table I. IR Absorptivity Values (L g-l cm-') for Methylene and Methyl Groups Calculated from the Slopes of Absorbance vs. Concentration Curves ( 4 ) wavenumber CH, + CH, + CH, CH3 CH, CH3 (1460 (1380 (2850 (2920 fract. cm-l) cm-') cm-l) cm-') no. 0.29 0.10 0.60 5 0.81 0.30 0.11 0.61 6 0.87 0.33 0.13 0.66 7 0.97 0.31 0.11 0.54 8 0.69 0.32 0.14 0.52 9 0.88 0.30 0.13 0.46 10 0.62 0.29 0.14 0.46 11 0.60 0.30 0.12 0.41 12 0.54 0.33 0.14 0.32 13 0.46 0.25 0.12 0.23 14 0.38 0.24 0.10 0.20 15 0.34 (b) (c)
CRPc aromatic peripheral carbon, each bonded to two other aromatic carbon atoms and one aliphatic or naphthenic carbon atom CRpH aromatic peripheral carbon, each bonded to two other carbon atoms and one hydrogen atom
CALCULATIONS Analysis I n p u t Data. The information required as input data for use in the calculation of structural parameters was derived from element analyses, NMR, IR, VPO, and GPC in the following form: C/H atomic ratio from element analysis (9). (1) Ha*,Hp*,H,* where Ha* = H,/HT, Hp* = H,/HT and (2) H,* = H7/HT. Subscripts a, ,d, and y represent: methine, methyl, and methylene protons in position a, methyl, methylene, and methine protons in
Mw =
12(CRI
+
CRPC
)+
13(CACHl
+
CBCH
+ CANCH, ) + I4(CACH, + C A N C H , + CBCH, + C B N C H , ) + 1 5 ( C A C H , -k CBCH,+ CGCH,) (11 CRPH
+
CBNCHl
Equation 1 serves to verify the exactness of solutions for the system equations; this, however, does not intervene in their resolution. Resolution of System Equations. In Haley's (4) system of equations, only one (see Equation 2 of the present text) out of 14 equations relating CRI,CRPC,and CRpH is nonlinear and has been developed from a pericondensed aromatic ring system.
~ C R-I ( C R +~ C R P H )+~ S ( C R P C -k 12=0
CRPH)-
CH, (1380cm-') 59.8-38.5 42.2-27.2 34.0-21.9 23.1-14.9 25.7-16.6 19-9-12.8 20.1-13.0 15 -2-11.O 17.2-11.1 16-0-10.3 13.5-8.7
(2)
A system of 14 equations can generally be solved by using nonlinear resolution methods; however, this was not adequate in the present study. To obtain an optimum solution, an alternate approach had to be developed. Equation 2 may be expressed in a different form by combining it with another Equation (3) relating C R ~and C C ~ H via a floating parameter V , in the following way: CRPC
-
V5(CRPH)
(3)
=
Table 11. Number of Carbon Atoms in the Form of Methyl and Methylene Groups ( 4 ) fract. no. 5 6 7 8 9 10 11 12 13 14 15
+
CH, (2920cm-') 70.8-61.6 48.0-41.8 36.5-31.8 21.5-18.7 23.7-20.7 14.2-12.4 12.3-10.7 11.3-9.8 8.4-7.3 7.4-6.5 6.7-5.8
CH, + CH, 130.6-100.1 90.2-69.0 70.6-53.8 44.6-33.7 49.5-37.3 34.1-25.2 32.4-23.7 26.5-20.8 25.6-18.4 23.4-16.8 20.2-14.6
CH, + CH, (2850cm-') 141.9-118.2 90.4-75.3 67.0-55.9 45.4-37.8 31.6-31.4 28.3-23.6 25.7-21.4 22.9-19.1 15.7-13.1 12.3-10.2 10.5-8.7
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
Table 111. Relative Weights of Methyl and Methylene Hydrogen as well as the Ratio of Methyl plus Methylene Hydrogens to Carbon ( 4 ) )for Various Asphalt Fractions fract. no. WCH, WCH, MMHC 5 718 850 2.44 576 2.45 6 507 2.46 7 408 438 2.50 8 277 258 9 199 248 2.43 148 2.49 10 154 2.53 11 155 129 12 132 118 2.51 88 2.68 13 133 14 124 78 2.60 15 105 70 2.58
0.14
0.18
FLOATING
0.14
VARIABLE
240
0.18
(VI )
Flgure 3. Variation of structure parameters in Fraction 9 as a function
of v , 3
20
S I
-20
W m J 3
0.8
8
w K 1100
3
20
700
K
O
Y
II
s
a
2
0.3
60
-20
W
300 7
1
0
4
7
1
zoo
K $
4
0.08
7
1?0
0
CRPH 140
Figure 2. Variatlon of structure parameters in Fraction 9 as a function of Cwn FLOATING
Substituting the value of C R ~from C Equation 3 in Equation
2:
VARIABLE ( V e )
Figure 4. Variation of structure parameters in Fraction 9 as a function
of v*
The transformation of Equation 2 into Equation 4 permits the calculation of the parameter CRI from the variable V5 and an assumed value for CRPH.The system becomes linear with 13 remaining equations which may be solved by the usual methods. The method used in this study allowed the control of the algorithm and consequently produced a solution having some physical significance. To begin, the values of C R p c , CRI, CBCHa, CACH,, CACK, and may be calculated as a function of the five floating variables V1, V2, V,, V4, V5,and the parameter CRPHusing Equations 3 to 8 (4). 2
CGCHs I
(7)
Equations 3 to 8 can be solved by assuming arbitrary values for the floating variables and the parameter CRPH;however, erroneous assumptions for any of these can result in negative solutions or can give rise to molecular weights which are far from the true values. I t is necessary therefore to study the behavior pattern of each structural parameter as a function of all five floating variables as well as the parameter C R p H . This allows the adjustment of the values of these variables in order to arrive a t an optimum solution. B e h a v i o r - P a t t e r n of S t r u c t u r e - P a r a m e t e r s as a Function of Floating Variable Values. The input data for
1
I
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
058
i
w 3
0.5
3
0.3
0.05
3
0.03
i
____L
CACHz 4-3
IL W
2
\! 208
IL
3
I
(d)
17
a
9
EO4
CANCH;
I
054
058
FLOATING
Figure 6.
of v,
0.54
VARIABLE
058
0.7
(V,l
Variation of structure parameters in Fraction 9 as a function
Table IV. Structure Parameter Behavior as a Function of Floating Variables
0.0
0.7
0.8
F L O A T lN G
VARIABLE
(V51
Flgure 7. Variation of structure parameters in Fraction 9 as a function of v,
which the structure parameters behave under varying conditions, one is referred to Table IV where ( 9 ) indicates an increase, (I) a decrease and (-) no change in the structure-parameters. After studying the behavior of the structure-parameters as a function of the floating variables and CRPH(Figures 2 to 7), the structure-parameters CRI,CRPC,CBCH~, CACH~, CACH~ and CBCH, were calculated by using Equations 3 to 8. The remaining seven structure-parameters, viz., C*cH2, C A N C H ~ , CANCH~, CBCH~, CBNCH,,CBNCH~, and CGCH~ were calculated with Equations 9 to 16 using the root mean square method.
(CIH- ~ ) ( C A C H+, CBCH,+ CRPH+ CBNCH,+ CANCH , ) + (2CIH - ~ ) ( C A C H+, CANCH,+ CBCH,+ CBNCH,) + (3CIH- ~ ) ( C A C H+, CBCH,+ C G C H , ) -CRI - CRPC= 0 (9)
( H a* - ~ ) ( C A C H+, CANCH, 1 + (2Ha * 2)(CACH, + CANCH,) + ( 3 H ~ * 3)(cACH3) + Ha *(CBCH, + C B N C H , + CRPH + 2 C B C H , + ZCBNCH, + 3CBCH, + 3CGCH,) = 0 (10) W o * - ~ ) ( C B C H+, CBNCH,) + (2Hp*+
2)(cBCH,
CBNCH,)
+
(3Ho*
- 3)(cBCH3)
f
H~*(~A + CANCH, c H , + CRPH+ ~ C A C H+, 2CANCH,
+
Q C A C H , -k 3 C G C H , ) =
(11)
(3Hy* - 3 ) ( C G C H , ) + H y * ( C A C H , + CANCH, + CBCH,+ CBNCH,+ ~ C A C H+, ~ C A N C H +, 2CBCH,
+
2CBNCH,
+
QCACH,
+
0 (12) ~)(CANCH + ,CANCH,+ CBNCH,+ CBNCH,) + (CN %)(CACH,+ CACH,+ CACH,+ CBCH,+ CBCH, + CBCH,+ CGCH,+ CRI + CRPC+ CRPH1 = 0 (13) (MMHC - ~ ) ( C A C H+, CANCH,+ CBNCH,+ C B C H , ) + (MMHC - 3 ) ( C A C H , + CBCH, + CGCH,)=0 (14) CRPC- CACH,- CACH,- CACH,- CANCH,CANCH,= 0 (15) 3CBCH,
in part b; CGCH~, C A N C H ~ ,CBNCH,, CBCH2, in part c and Mw in part d. The following important conclusions were drawn from the results of these studies: (a) As the structure parameter C R p H increases, the other structure parameters, viz., CACH,, CACHs, Cwc, CBCH3, and CBCH, increase linearly; CRI, C A N c H 1 , CACH2, and C B N c H z follow a parabolic trend (with a minimum) and the rest of the structure parameters CBCH2, CBNCH1, CANCH2, CGCH3 and Mw follow a similar parabolic trend (but with a maximum in this case, see Figure 2). (b) The variation of structure parameters is nonlinear with V , but more or less constant with V,. (See Figures 4 and 5). (c) The variation of structure-parameters becomes linear as the values of VI, V,, and V , increase (See Figures 3 , 6 and 7). In order to obtain a better appreciation of the manner in
+
CRPH ) =
and
CACH,+ CBCH,+ CGCH,+ CANCH,- CACH,CBCH,- CRPC- C B N C H , = 0 (16)
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
Table V. Values of the Floating Variables variable fract. no. V, v* v3 v, 5
I 9 10
11 13
0.20 0.20 0.25 0.14 0.25 0.25
0.28
0.4
0.91
0.34
1.0
0.83
0.50 0.27
1.0 2.1 1.0 1.0
0.66 0.50 0.80 0.67
0.33 0.50
v, 1.00 0.83 0.83 0.83
1.00 0.83
This method of linear regression is based on the algorithm of Gaussian reduction and on the orthogonal decomposition proposed by Householder (11,12). The search for the solution of all structure-parameters follows many steps and these are shown in Figure 8 where a flow diagram covering all stages of the calculations is presented.
RESULTS AND DISCUSSION From the structure-parameters behavior as a function of the floating variable study, (Figures 3 to 8 and Table IV), an optimum solution was obtained which was further adjusted by bringing the values of the structure-parameters to the nearest integer. With these values, the floating variables were then recalculated. The results obtained are presented in Table V. The values of VI, V,, V,, V,, and V5are 0.40 f 0.25, 0.40 f 0.13, 1.5 f 0.5, 0.66 f 0.17, and 0.83 indicating that these fall into a narrow range. The floating variable V5 defined as degree of substitution has the most effect on the solution. VI, V,, and V , are also important variables; however, these are not as important as V,. Variable V , has no significant effect on the solution. Using the variables in Table V, the structure-parameters and the total number of carbon atoms for fractions 5 , 7,9, 10, 11, and 13 were calculated and these are presented in Table VI. The most pronounced trend in this table is the decrease in the values of the structure-parameter CBCHz with decreasing molecular weight of the asphalt fraction. The NMR analyses (9) of these fractions had also indicated that the content of the paraffinic carbon is quite important in the medium molecular weight fractions (5, 7 , S I I ) . On the other hand, the low values of CACH~ and CACH~ indicate that the number of aliphatic chains attached to the aromatic rings is quite low and even negligible as is the case for CACH~. If, at all, the aliphatic chains are attached to the aromatic rings, these must, in all probability, be terminated by a methyl group in the p position (CBCHJ which leads to the suggestion that these chains are not very long. This is further supported by the presence of methine groups in the p position CBcHl and methyl groups in the alpha position CACH3. Low values for CACH~ and CBCH~ were also found by Haley ( 4 ) and Hirsch and Altgelt ( 3 ) in their respective works. The values of CANCHz were found to be very low, however those of C w c H 1 , CBNCH1, and CBNCHBwere relatively high. This has lead to the suggestion that the naphthenic rings are attached to other naphthenic rings forming a condensed system. It could also be that these are attached to aliphatic chains. Contrary to what was observed in the case of aromatic rings, the naphthenic rings carry longer aliphatic chains attached to them. This is supported by the high values of CBCH~ and CGCH~ (in the latter case the chains are terminated by methyl groups). The low molecular weight fraction 13 was found to have a high degree of aromaticity from its low CBCHz values when compared to corresponding values in the higher molecular weight fractions, and to the other types of carbon in fraction 13. The naphthenic carbons CBNcH1, CBNCHz, and the aromatic carbons CRI, CRpC, and CRpH constitute a large proportion
n
w 0
8 mrlriorlr
uF9
$ 0
4
u
B w 0
oooooc
ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
1217
Table VII. Comparison of Mw, %CN, %Cp,, and % C AObtained ~ from Structure Parameter and Experimental Data fract. no. Mwa M W b %CNa %CN %Cp,ra %cpub %CAra %CArb 5 7 9 10 11 13 a
2755 1150 865 76 0 677 61 5
2950 1290 860 740 650 590
Structure-parameter values.
27 25 22 28 24 28
22.3 23.3 22.8 28.2 27.1 29.3
42 53 50 40 46 30
54.7 61.7 58.2 46.8 50.9 37.7
31 22 28 32 30 41
23 15 19 25 22 33
Experimental values using GPC calibration curve (9). The validity of the system equations used in the present study was further verified by using these to calculate molecular weights Mw (Equation l),percentages of naphthenic carbon % C N (Equation 17), paraffinic carbon % C ,, (Equation 18) and aromatic carbons C A (Equation ~ 19) of various fractions and comparing them with the experimentally obtained data.
EXPERIMENT INPUT DATA C/H,H.,HB,HI,CN%,MMHC, MW OF A FRACTION
C ~ p nAND FLOATING VARIABLES VI >VP # V 3,v,
%CN =
,v,
4
CN =
CT
I
CALCULATION OF PARAMETERS IR C CRPC , c s c n 3 , ~ A c ~ , . ~ A, C c sHc n~ I ACCORDING TO EQUATIONS 1350 81
1
CALCULATION OF PARAMETERS Cacn2 C A N C H , . ~ A N CCHB~C~H ~ " % N C H ~ , C ~ N C ,HC ~G C H ~BY SOLVING A SYSTEM OF 8 EQUATIONS WITH LEAST SQUARES METHOD
CACH,+ CACH,+ CACH,+ CBCH,+ CBCH,+
CHANGING ASSUMED
I
In Table VI1 are shown the results obtained using Equations 1,17,18, and 19 along with the experimental data. The values calculated by the two different approaches are not far removed from each other, thus reflecting on the reliability of the set of equations used in the present study.
PRINTING OUTOF VALUES FOR 14 PARAMETERS, WITH THOSE OF
CONCLUSION V I , V ~ , V ~ , V ~ ,AND V ~ CRPH MOLECULAR WEIGHT CLOSEST TO EXPERIMENTAL INPUT DATA
1
REJECTALL NEGATIVE V A L U E S , OPTIMUM SOLUTION WITH POSITIVE INTEGER OR ZERO VALUE FOR T H E STRUCTURAL PARAMETERS
1
Flgure 8. Flow diagram of various steps followed for the computation of the 14 structure parameters
(65%) of the total carbons. Furthermore, the sum of aromatic carbons ( C R I + C R p C + CRpH) together represents 41% of the total carbons. These results agree with the earlier study reported from this laboratory (9). Based on these results, if one were to imagine a structure for the low molecular weight asphalt fractions, it would have to be a combination of aromatic and naphthenic rings with no long aliphatic chains (low values of CAcH1, CAcH2, &HI) but short chains in the form C B C H ~alpha ) of single methyl groups in the position (CARH~, to the aromatic ring alone (low CBCH2). The structure of the higher molecular weight asphalt fractions, however, is not the same.
(1)The advantage of the proposed model lies in its simplicity and ease of application. Furthermore, the method of resolution used permits a better control on the algorithm and thus yields a more precise solution. (2) The results obtained using this mathematical model agree well with those obtained experimentally, thus indicating its validity and the exactness of the method of resolution. (3) The analyses of structure-parameters in the present study suggest that all asphalt fractions of intermediate molecular weights are built up of aromatic and naphthenic rings. The aliphatic chains attached to the aromatic rings are short whereas those attached to the naphthenic ring are longer. In the case of asphalt fractions having low molecular weights, these appear to be made up of aromatic and naphthenic rings with no or very little aliphatic character in them. This observation was also pointed out in an earlier study (9),where, like the model aromatic compounds, the low molecular weight asphalt fractions did not follow the universal calibration curve. (4) The results obtained are comparable to those in the literature ( 4 ) although the two approaches used are considerably different. Haley ( 4 )however calculated the molecular weights of asphalt fractions using the structure-parameters and compared them with their unit sheet weights, whereas in the present study, these are compared to their weight average molecular weights Mw and this is closer to reality. Further studies on the characterization of asphalts by studying their glass transition temperatures are being carried
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
out and will be reported on in due course.
(9) H. H. Kiet, L. P. Blanchard, and S.L. Malhotra, Sep. Sci., 12, 607 (1977). (IO) R. B. Williams, “Symposium on Composition of Petroleum Oil”, ASTM
ACKNOWLEDGMENT The authors are indebted to T o Xuan Ky for many helpful discussions in carrying out the computer analyses.
Spec. Tech. Publ., 224, 168 (1958). (1 1) R. M. Calla, “Introduction to Numerical Method and Fortran Programming”, John Wiley, New York, N.Y., 1967. (12) C. Lanzos, “Applied Analysis”, Prentice-Hall, New York, N.Y., 1956.
LITERATURE CITED
RECEIVED for review December 27, 1977. Accepted April 24, 1978. The authors gratefully acknowledge the financial assistance received from B. P. Canada Limited, from the National Research Council of Canada, and from the Department of Education of the Government of Quebec. The work described in this paper forms part of the general research program undertaken by the “Groupe de Recherches en Sciences Macromol6culaires” a t Lava1 University.
(1) J. P. Dickie and T. F. Yen, Anal. Chem., 39, 1847 (1967). (2) J. G. Speight, Fuel, 50, 102 (1971). (3) E. Hirsch and K. H. Altgelt, Anal. Chem., 42, 1330 (1970). (4) G . A. Haley, Anal. Chem., 44, 580 (1972). (5) E. J. Dickinson, Proc. Assoc. Asphalt Paving Techno/.,43, 132 (1974). (6) L. Zalka and T. Mandy, Acta Chim. Acad. Sci. Hung., 79, 375 (1973). (7) T. F. Yen, Energy Sources, 1, 447 (1974). (8) Y. Katayama, T. Hosoi, and G. Takeya, Nippon Kagaku Kaishi, I , 127
(1975).
CORRESPONDENCE Comparison of Radiant Power of the Eimac Xenon Arc Lamp and Hollow Cathode Lamp Sources Sir: Lately there has been considerable interest in the use of the Eimac pre-focused xenon arc lamp as a source in atomic absorption in (1-3),atomic fluorescence ( 4 , 5 ) ,and molecular luminescence spectrometry (6). Recently, this lamp has been characterized with respect to its power output, noise spectrum, and optical properties (7). Most workers find that the Eimac lamp provides significantly higher radiant power than other commonly used continuum sources of comparable power input (6, 7). We and others (2, 3, 8 ) have been interested in this lamp as a primary source in atomic absorption. In this application, an obvious question which arises is how the radiant power of the Eimac lamp compares with the hollow cathode lamps ordinarily used in commercial atomic absorption instrumentation. The purpose of this paper is to provide some data to answer this question. At the outset we must decide exactly which intensity measure we wish to compare, i.e. radiant power (watts), radiance (watts sr-l m-2), irradiance (watts m-2), etc. The objective of such a comparison is to tell which source would be “more intense” for a particular application, in this case atomic absorption spectrometry. Greater intensity is desirable in this application for three reasons; first, to reduce the influence of thermal emission signals originating from analyte emission, flame background, or graphite furnace blackbody emission; second, to reduce the effect of photon shot noise; and third, to avoid difficulties from photomultiplier dark noise. The first of these benefits requires greater source radiance, while the latter two require greater radiant power a t the photodetector. Thus, we wish to compare the two sources both on the basis of radiance, which is a function of the sources themselves, and on the basis of radiant power a t the detector, which is also a function of the spectrometer and entrance optics. What one actually measures, of course, is the photoanodic current of the detector, which is a measure of, and directly proportional to, the radiant power emerging from the exit slit. Moreover, the photocurrent is proportional to the radiance of the source, as well as to the detector sensitivity, the transmission factor of the spectrometer and the entrance optics, the width and height of the slits, and the solid angle of radiation collected from the source by the spectrometer. Thus, one may also compare the relative radiances of two 0003-2700/78/0350-1218$01.00/0
sources by keeping constant all terms associated with the entrance optics, spectrometer, and photodetector; thus, the ratio of measured photoanodic current would be equal to the ratio of radiances. Although the comparison of radiant power a t the detector is straightforward, a comparison of radiance is complicated by the fact that the Eimac lamp contains an internal parabolic reflector which is an integral part of the lamp. Other sources, i.e., conventional Xenon arc lamps and hollow cathode lamps, do not have such a reflector. The problem is, do we consider the reflector as a part of the lamp itself or as a part of the entrance optics of a spectrometer? If the latter, then the radiance comparison is not straightforward. We will try to avoid this problem by measuring only the relative radiant powers a t the detector, but we will do so for two different experimental designs, In the first design, the photocurrents will be compared when all optical parameters external to the lamps are held constant, i.e., same detector sensitivity, spectrometer slit widths, external entrance optics, and position of source. This essentially provides a comparison of the relative irradiance (watts m-2) a t the entrance slit, providing that the fraction of light passing through the entrance slit which is actually collected by the collimating mirror in the spectrometer is the same for both sources. In any case, this experiment will allow a comparison of the sources on the basis of the first of the aforementioned three benefits of greater intensity, i.e., reduced effect of atomizer emission. In the second experiment design, we acknowledge the fact that in atomic absorption measurements, a continuum source like the Eimac would ordinarily be used with a very high resolution spectrometer (like the echelle spectrometer used in this work), while a line source could be used with a conventional medium-resolution monochromator with much larger slit area and possibly greater acceptance angle. Thus it would be of practical interest to compare the radiant power emerging from the exit slits of these two lamp-spectrometer systems, because it has a bearing on the relative influence of photon shot noise and dark current noise of the detector. The comparison of the radiant powers of line and continuum sources must of course take into account the very different spectral distributions of the two sources. In conventional atomic absorption instruments, the hollow cathode 0 1978 American
Chemical Society
