KNOCK RESISTANCE OF PURE HYDROCARBONS Correlation with Chemical Structure H. K. L I V I N G S T O N E. 1. du Pont de Nemours & Co., Wilmington, Del.
A
method of correlating the octane numbers of pure hydrocarbons with chemical structure is needed to provide a workabIe method for predicting the octane numbers of hydrocarbons that have not yet been obtained in pure form. A correlation based on current theories of engine knock and hydrocarbon oxidation has been obtained. Predicted knock ratings are consistent with known research octane ratings for almost all the 108 pure hydrocarbons for which octane data are available. The resistance of hydrocarbons to knock is a function of structural factors that depend on electronic effects contributed by the following retarding groups: methyl, tert-alkyl, vinyl, methylene (in ring compounds), and phenyl. The relative effects of these groups have been summarized by eight rules that permit calculation of “structural retardation factors” for hydrocarbons from chemical structure alone. The success of the structural retardation factor method of predicting octane numbers emphasizes the importance of the initial oxidation reaction in the series of reactions that eventually lead to knock and provides a basis for further study of electronic and structural effects in hydrocarbon oxidation.
HROUGH the efforts of the American Petroleum Institute, there has been made available a large body of knock ratings of pure hydrocarbons (4). Although it is known that these rat,ings correlate in a general way with certain structural factors, such as the centralization of the hydrocarbon molecule (4, no detailed correlation between knock resistance and chemical structure has ever been presented. It is the purpose of the present paper to present such a correlation and explore its implications in terms of current theories of engine knock and hydrocarbon oxidation. I n developing this detailed correlation, reliance was placed on t,hree postulates. , 1. The knock resistance of a hydrocarbon as judged by its octane number, O N , is a direct function of its oxidation resistance as judged by the standard oxidat,ion temperature, SOT. That is
T
ON =
$
(SOT)
(1)
There are many reasons for believing that the knock resistance of hydrocarbons is a function of their resistance to low temperature oxidation. This idea was first proposed by Prettre (27) in 1932. The best evidence in its support may be obt.ained from the oxidation studies of Maman @ I ) , Ivanov (16), and Edgar and coworkers (1, 26, 26). These authors passed stoichiometric hydrocarbon-air mixtures through tubes at progressively increasing temperatures and noted the temperature a t which significant oxidation occurred. It appears that the best criterion of significant oxidation is the formation of measurable amounts of carbon monoxide. These temperatures, designated the standard oxidation temperature (SOT) as obtained from their dat,a, are s!rmmarized in Table 1. Aplot of standard oxidation temperature
against research octane number, shown in Figure 1, shows that a valid correlation exists within the accuracy (of the order of 1.25’ C.) of the SOT data. Research octane numbers were chosen in preference to motor octane numbers because the low temperature and slow engine speed of the research octane rating conditions (ASTM Method D 908-48T) would be expected to give a better correlation with oxidation performance than the more severe motor rating conditions (ASTM Method D 357-47) which favors hydrocarbon pyrolysis.
Table I. Standard Oxidation Temperatures of Hydrocarbons RepoGed SOT, C. 316 265 250 280
Hydrocarbon n-Heptane 2-Methylhexane n-Octane
276
260 295 275 312
2-Methylheptane 3-Methylheptane
290
4-Methylheptane 3-Ethylhexane
Reference Maman ( 2 1 ) Beatty ( 1 ) Ivanov (16) Ivanov (16) Maman (81) Pope Maman j81) 26) Pope
($6) Maman %aman ((11) 81)
Average SO?’, 0 @. 275 280 265 295 295
290 280 Pope (26) 295 314 Maman (ti) 331 2.2-Diiiiethglhexnrre Maman (82) 330 326 2,3-Dimerbylhexane Maman ($1) 325 319 2.&Dimethylhexane Maman (81) 320 275 Pope (86) 2,5-Dimethglhexane 295 305 Maman (82) 300 Pope (26) 2-Methyl-3-ethylpentane 320 344 Maman ($2) 446 2,2.3-Trimethylpentane RIaman (11) 445 465 Maman (81) 46P 2,2,4-Trimethylpentane 520 Pope (26) 440 Maman (21) 2,3,4-Trimetbylpentane 440 483 Maman (81) 485 Tetramethylbutane 315b Beatty (1) 315 1-Heptene 316b 315 Beatty ( I ) 3-Heptene a As the other data for trimethylpentanes were taken from Xaman, only Mnrnrtn’s da.trt were considered in obtaining this average. n Beatav and Edear were based on t h e teinuerature n.t which
In considering correlations between knock resistance and other fuel characteristics, it is preferable to use the standard compression ratio-i.e., the compression ratio of the CFR engine at standard knock intensity-as determined by the CFR engine guide curves for micronieter setting as a function of octane number. The standard compression ratio has the advantage that it is a continuous function of knock resistance, whereas the octane number scale is limited to values bekeen 0 and 100. For fuels pith knock resistance greater than iso-octane, the discontinuous z nil. of tetraethyllead per gallon’’ is used scale of “iso-octane in the American Petroleum Institute tables of octane ratings. In the present work, these ratings have been converted to standard compression ratios, using guide curves obtained in the Du Pont Petroleum Laboratory. h simple equation that expresses the relation of octane numher, O N , to standard compression ratio, SCR, with good accuracy is
+
100
0’538 4.85
O x i = XCR 2834
-
+ 0.830
December 1951
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
This equation is of the form given by Kobayashi (ZO), but different constants have been derived so as to fit the American CFR engine data.
P
I
3. A logical combination of the above two postulates leads to a third-namely, that the knock resistance of a hydrocarbon is a direct function: of the structural retardation factor, SRF. The equation is
I
I
I
ON = + ( S R F )
I
2 450-
28353
(3)
An attempt to apply this correlation, using Hinshelwood's methyl retardation factors, has shown that general agreement exists, but the correlation is not uniformly satisfactory (Figure 4). This is to be expected, since Hinshelwood's method of calculating MRF values was derived for simple hydrocarbons and does not take into account three complications.
+ W
400-
0
75 RESEARCH OCTANE NUMBER 25
50
100
Figure 1, Correlation between Standard Oxidation Temperatures and Research Octane Numbers
There is an approximate straight-line relation between standard compression ratio, SCR, and standard oxidation temperature, SOT, as shown by the data in Figure 2. The equation of the straight line is
SOT
36
=
+ 50 (SCR)
Oxidation may occur on several or all carbon atoms, thougb Hinshelwood's method yields a value based on the most oxidizable hydrocarbon only. Special retardin effects would be exerted by tert-alkyl groups in highly branchecf hydrocarbons such as iso-octane. To be applicable to all hydrocarbons, the method must also take into account the retarding effects due to vinyl groups (in olefins), ring methylene groups (in naphthenes), and phenyb groups (in aromatics).
(1B)
2. The standard oxidation temperature, SOT, is a direct function of the structural retardation factor, SRF. That is
SOT
=
+ (SRF)
(2)
0
P
a
+ v,
300ke/" 250
METHYL RETARDATION FACTOR (MRF) I 2 3
Figure 3. Correlation of Oxidation Temperature with Methyl Retardation Factors of Hydrocarbons
STANDARD COMPRES3K)N RATIO FOR RESEARCH OCTANE RATING CONDITIONS
Figure 2. Correlation of Oxidation Temperatures with Knock Resistance of Hydrocarbons
A similar correlation was made by Hinshelwood (f6),who pointed out that the rate of oxidation of hydrocarbons, as determined by Cullis and Hinshelwood (@, decreased in a regular fashion as the amount of methyl retarding effect on the most oxidizable hydrocarbon increased. Hinshelwood postulated that methyl groups had a strong retarding effect on oxidation, which decreased rapidly as carbon atoms became further removed from the methyl group, and that the great change in oxidation rate with chemical structure among isomeric hyrdocarbons could be predicted from this principle. Hinshelwood msde his original correlation with oxidation rate, but the same correlation can be made with the minimum oxidation temperature under standard conditions. A plot of standard oxidation temperature, using the data of Table I, against his methyl retardation factor, MRF, shows that a satisfactory correlation exists for the simpler parafEnic hydrocarbons. This plot is given in Figure 3. The approximate equation expressing this correlation is
SOT = 250
+ 100 ( M R F )
(24
I n order t o place the correlation predicted in Equation 3 OD a quantitative basis, it was decided to accept the knock resistance of pure hydrocarbons, as given in the American Petroleum Institute tables, as the best available source of hydrocarbon oxidation data (by Equation 1, knock resistance is a function of oxidation resistance) and use the American Petroleum Institute data to modify Hinshelwood's method of calculating oxidation resistances into the simplest possible form that would yield accurate correlations. RULES FOR C A L C U L A T I N G STRUCTURAL R E T A R D A T I O N FACTORS
Eight rules have been devised. 1. Each carbon atom in a hydrocarbon offers a possible site for oxidation, so the structural retardation factor, SRF, is the resultant of individual retardation factors. The retardation factor for the most oxidizable carbon atom is arbitrarily considered to have twice the significance of the other factors. The structural retardation factor is the sum of the individual factors, Thug
where j = the individual retardation factors, listed in order from the smallest VI) to the largest (ft).
INDUSTRIAL AND ENGINEERING CHEMISTRY
2836
2. The oxidizability increases with the number of possible sites for oxidation-Le., number of carbon atoms. The octanes will be taken as reference hydrocarbons, and all other hyrocarbons will have factors added equal to one for each carbon atom less than eight or factors subtracted equal to one for each carbon atom more than eight.. Thus
SRF = 2f1
+
i fi
+
(8
-
i)
z
= 2(0.70)
+ 0.90 + 1 + 1 + 1 + 1 f 1 + (8 - 7 ) = 8.30
Therefore, 8.30 is the unique value of the structural retardation factor of 2,3-dimethylpentane.
5. Empirical tests indicate that the retarding effect of the tertiary alkyl groups is approximately three times that of the methyl g r o u p i . e . , k = 1.50 for tertiary alkyl retardation. This rule is applied only to all highly methylated tert-alkyl groups, e.g.
1
where i = total number of carbon atoms.
x"'
CHs-
I
-,
CHI
I
I
I
I
2 (&F)
3
I
I
CHaCHp
1
CHaCHI
Br
T
! i
CH+2--CH2--CH--CHI
@ Trirubrtiluted butanes and pentanes
7-
3. The retarding effects of oxidation retarding groups will be assumed to decrease with TL, the number of the carbon atoms between the retarding group and the carbon atom in question. Derick's rule of place factor decay (IO), which states that f = k(1/3"), will be taken to express the decay of individual retarda' tion factors with distance from the retarding group. Derick's rule was employed successfully by Hinshelwood (15) in calculating methyl retardation factors. The maximum value for any retarding group will be taken to be unity. Thus j
71
where,f is the individual factor for any carbon atom, k is the maximum retarding effect of the j retarding group, and TZ is the number of carbon atoms between the j retarding group and the carbon atom for which f is being calculated. But no matter how many retarding groups are involved or how large the individual (k/3n) factors are, f cannot exceed unity. The minimum value offis, of course, zero. 4. The most common retarding groups in hydrocarbons are methyl groups, for which k = 0.45. The methyl groups themselves are considered to have the maximum oxidation resistance, so that for every methyl group, the assignment f = 1 is made for the individual factor of the methyl carbon atom. EXAMPLE.2,3-Dimethylpentane.
/
CHs 8+(!X3
fa = 1 = 1 fr = 2(1.50/3O)~ (0.45/3)0 4- (0.45/3), = 1.80 (By Rule 3, f-, = 1) (0.45/3')8 (0.45/3'), = 1.80 f8 = Z(1.50/3)~ (By Rule 3, fa = 1) ff = 1
j.,
fr f, f8
+ +
+
= 1 = =
1 1
XRF = 2(1)
+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + (8 - 8) = 9.00
Therefore, 9.00 is the unique value of the structural retardation factor of iso-octane. 6. Vinyl groups are themselves more oxidizable than methyl groupa, having individual factors of 0.90 to 1.00, but the vinyl retarding effect is slightly greater than methyl retardation and extends three times as far. That is, k = 0.50 for vinyl groups, but TZ = number of trimethylene units between the retarding group and the carbon atom in question. Assignments made for the individual factors of carbon atoms in vinyl groups are
. , . ..
CHFCH-
f=0.95 f=O.95
. . .f. -CH=CH-. . . .. = 0.95 f = 0.95 . , . . . -CH=C-RI f
k
=
0.95 f = 1.0
. . . .-++, *
I . .
1
1
R R
f = 0.90 f fa
fs
=
1
++ ++
+
+
(0.45/3')a (0.45/3'){ (0.45/3), (0.45/3')e = 1.10 (By Rule 3, fa = 1) (0.45/3)r (0.45/3O)q (0.45/3)e = 0.90 fr = (0.45/3)a fa = (0,45/32)a (0.45/3')r (0.45/3), (0.45/3'). = 0.70 fe = 1 fr = 1 fll
=
= 1
++
++
I
I
S+CHi
0 All other hydrocarbon$
(kd3"'); f 5 0; f
I
or CHI-C-C-
I
All carbon atoms in the group are considered to have the maximum oxidation resistance, so that for all these carbon atoms, the assignment for the individual factors is f = 1. Quaternary carbon atoms-Le., those with no carbon-hydrogen bonds-are assigned individual factors o f f = 1. EXAMPLE. 2,2,4-Trimethylpentane.
Figure 4. Relationship between Hinshelwood'r Methyl Retardation Factor, MRF, and Standard Compression Ratio, SCR, under Research (F-I) Conditions
f=
CHBCH,
1
CH,-CH-C-,
CHa
4'
Vol. 43, No. 12
EXAMPLE. 2-Methyl-1-heptene.
= 0.90
,
December 1951
2837
INDUSTRIAL AND ENGINEERING CHEMISTRY
'
j2 =
fa =
j;
= 1.0
SRF
=
2(0.60)
f4
+ 0.62 + 0.67 + 0.67 + 0.95 + 1.0 + 1.0 + 1.0 + (8 - 8)
7.11
Therefore, 7.11 is the unique value of the structural retardation factor of 2-methyl-1-heptene. 7. Ring methylene groups have a retarding effect on adjacent carbon atoms somewhat smaller than the methyl retarding effect. Empirical tests indicated k = 0.38 as the best value for fivemembered rings and k = 0.31 for six-membered rings. This retarding effect is limited to the cycloalkane ring itself and does not extend to side chains. Furthermore, substitution in the ring prevents the methylene retarding effects from passing through the substituted carbon atom. Thus, in cyclohexane, retarding effects on the starred carbon atom are received from the left and from the right, each of the five unstarred carbon atoms contributing twice.
=
Left %(0.45/36)y= 0.82
0.75 = fa fa = f2 = 0.48 ja = 0.45/3 = 0.15 fs = 0.45/3O = 0.45 fr = 1.0 ' SFR = 2(0.15) 0.45
f6
+
+ 0.48 f 0.48 + 0.75 + 0.75 + 0.82 + 0.95 + 1.0 + (8 - 9) = 4.98
8. Phenyl retardation is recognized as the strongest retarding effect known. The carbon atoms in the phenyl group itself as well as side-chain carbon atoms a t least as remote as the 8-carbon atom are assigned individual factors of f = 1, the maximum value. EXAMPLE, Propylbenzene.
a
B
r
4 . 1 1
CH2-CH2-CHz
*
/
1-c 2+H6 3 + H CI/ 4-CH
1
= 1
f4
=
f6
= 1 = 1
fa
= 1
SFR = 2(1)
*
\ /
fa = 1
fl
But in methyl cyclohexane the only methylene retarding effects are received from the left side of the starred carbon atom;
bH+6 h H t 5
f6
fa =
fa fr
1
= 1 = 1
+ 1 + 1 + 1 + 1 + 1 + 1 + 11 ++ (8 - 9) = 9.00
CORRELATION OF STRUCTURAL RETARDATION FACTORS WITH KNOCK RESISTANCE
Application of the eight rules given above to 108 different hydrocarbons has led to the compilation of structural retardation factors which is summarized in T?ble I1 together with the research octane numbers for these hydrocarbons. The eight rules were designed to yield structural retardation factors that correlate with the'known knock resistance of hydrocarbons. Obviously a perfect correlation could be obtained by devising sufficient rules to fit each individual case, but with only eight rules the correlation is certain to be less than perfect. The objective is to obtain the best possible correlation with the
the methyl substitution on the a-carbon to the right blocks all methylene effects from this direction. The a-carbon itself, being no longer a methylene (-CHz-), contributes no retardation, though methyl retardation from the methyl group exerts the conventional effect (f = 0.45/3) on the starred carbon atom. EXAMPLE. Propylcyclohexane.
.;gJ
1+H
dCH3Hs-CHJ
d'
2 4 H2 CHa+6 3+CHa I &H2+5
ji = (0.45/3')~
+
4
-+ \ / CH2
d l
+
0
2(0.31/3')2 (0.31/3)0 (031/3')4 Left (0.31/3*)~f 2(0.31/34)6 f Z(0.31/3°)s (0.31/3)s f Right (0.31/32)r (0.31/33)s (0.31/34)z = 0.95
+
+
+
Figure 5.
IO
I
20
1
1
1
1
1
I
30 40 50 60 70 80 RESEARCH OCTANE NUMBER
Correlation
I
90
I
I 1
100 110
of Structural Retardation Factors with
Knock Resistance of Pure Hydrocarbons
Points Identifled bv number refer to hydrocarbons listed in Table 111
INDUSTRIAL AND ENGINEERING CHEMISTRY
2838 Table
II.
Hydrocarbon Rfethane Ethane Propane Butane Isobutane Pentane Isopentane Keopentane Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane Heptane 2-Methylhesane 3-LIethylhexane 3-Ethylpentane 2,Z-Dimethylpentane 2,3-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane Triptane Octane 2-RIethylheptane 3-Rfethylheptane 4-WIeth lheptane 3-Ethyl%esane 22-Dimethylhexane 2,3-Dimethylhesane 2,4-Dimethylhexane 2,5-Dimethylhexane 3,3-Dimethylhexane 3 4-Dimethylhexane 2’Methyl-3-ethylpentane 3-Methyl-3-ethylpentane 2,2,3-Trimethylpentane Iso-octane 2 3 3-Trimethylpentane 2:3:4-Trimethylpentane 2,2,3,3-Tetramethylpentane 2 ,2-Dimethyl-3-ethylpentane 2,4-Dimethyl-3-ethylpentane 2 2 3 3-Tetramethylhexane E’td;iene Propylene 1-Butene 2-Butene Isobutvlene 1-Pentkne 2-Methyl-I-butene 2-Methyl-2-butene 1-Hesene 2-Hesene 3-Hexene 2-Methyl-1-pentene 2-Methyl-2-pentene 2-Methyl-3-pentene 2-Methyl-4-pentene
Structural Retardation Factors and Knock Resistances of Pure Hydrocarbons Structural Retardation Factor, SRF 9.00 9.00 8.80 7.80 9.00 6.60 8,50 9.00 5.54 7.40 7.70 9.00 9.00 4.44 6.26 6.49 6.55 8.90 8.30 8.20 8.40 9.00 3.41 5.16 5.38 5.51 5.36 7.89 7.14 7.31 7.08 7.34 7.61 7.40 7.80 9.00 9 .00 9.00 9.00 9,00 9.00 8.08 8.90 8.85 8.85 8.70 8.85 8.90 8.25 8.90 8.85 7.60 8.15 8.76 8.55 8.75 8.88 8.50
Research Octane N0.a 107.5 107.1 105.7 93.6 101.1 61.7 92.3 85.5 24.8 73.4 74 5 91.8 101.7 0.0 42.4 52.0 65.0 92.8 91.1 83.1 80.8 105.7 Below 0 21.7 26.8 26.7 33.5 72.5 71.3 65.2 55.5 75.5 76.3 87.3 80.8 104.5 100,o 102,9 101.3 106.9 105.7 102,6 105.8 100.2 101.4 07.4 99.6 101.5 90.9 101.3 97.3 76.4 92.7 94.0 95.1 97.8 99.3 95.7
Hydrocarbon 3-llethvl-1-pentene 2-Ethyi-I-butene 2,3-Dimethyl-2-butene 2,2-Dimethyl-3-butene 2-Methyl-2-hesene 2,3-Dimethyl-2-pentene 2,4-Dimethyl- 1-pentene 2 4-Dimethyl-2-pentene 2:2-Dimethyl-4-pentene 2,2,3-Trimethyl-3-butene 1-Octene 2-Octene
a
3.. O. C. t , P-”.-P
4-Ootene 2-Xethyl-I-heptene 2-Methyl-2-heptene 2-Methyl-5-heptene 2-RIethv1-6-heutene 2,3-Din&hyl-i-hexene 2,2,3-Trimethy1-3-pentene 2 2,4-Trimethyl-3-pentene 2:2,4-Trimetbyl-4-pentene 2.3,3-Trimethyl-l-pentene 2,3,4-Trimethyl-3-pentene Nethylcgolopentane 1 1-Dimethylcyolopentane Ethvlcvclooentane
Table 111. Exceptional Hydrocarbons Designated in Figure S R F Too High S R F Too Low 2
Neopentane 2 2-Dimethylbutane
3 2’2-Dimethylpentane
4 2’2-Dimethylbesane 1 3 3’3-Dimethylpentane 14 2:5-Dimethylhexane 15 2-Methyl-5-heptene
Structural Retardation Factor, SRF 8.85 8.90 8.70 8.85 8.20 8.70 8.85 8.90 8.85 8.90 5.73 6.76 7.55 7.75 7.11 7.65 7.90 7.38 8,65 8.90 8.90 8.90 8.90 8.70 8.02 8.55 6.92 5.67
1,2-Dimethylcyclohexane 1,3-Dimethylcyoiohexane 1,4-Dimethylcyolohexane Ethvlcvclohexane
n-Butylcyclohexane Isobutylcyclohexane sec-Butylcyclohexane tert-Butvlcvclohesane 1-hIethj.1-4-isopropylcyclohexa.ne 4-Methyl-1-cyclohexene 3,3,5-Trimethyl-l-cyclohesene 3,5,5-Trimethyl-l-cyolohesene Toluene Ethylbenzene Propylbenzene Isopropylbenaene
Research Octane N0.Q
8.30 7.25 7.54 6.52 6.55 6.26 4.98 6.98 7.06 3.98
96.0 98.3 97.4 105.4 90.4 97.5 99.2 100.0 102.2 102.6 28.7 56.3 72.5 73.3 70.2 75.9 71.3 63.8 96.3 101.7 101.7 102.9 102,9 96.9 91.3 92.3 67.2 31.2 Below 0 83.0 74.8 80.9b 69.3b 67.8b 46.5 17.8 62.8 81.3 Below 0
6.15 8.63 6.28 8.16 8.56 8.78 9 .oo 9.00 9.00 9.00
51.0 98.5 67.3 84.1 96.5 95.5 107.2 103.6 105.1 105.9
4.58
5.84
33.7
0 Data for CI t o C4 hydrocarbons from Puokett ( 2 8 ) ; all others from published data of A.P.I. Project 46 (taken from the Eleventh Annual Report of t h e Project ( 4 ) or from monthly reports published during 1949-50). Octane numbers over 100 calculated from the standard comuression ratios bv Eouation 1A. b Average of octane numbers of the cis- and $Tans-isomers. “
minimum number of rules. The degree of correlation obtained with the structural retardation factors summarized in Table I1 is illustrated by Figure 5 . The solid line drawn in Figure 5 represents Equation 4. The dotted lines indicate a probable uncertainty of k0.33 unit in structural retardation factor above 40 octane number, and a somewhat larger uncertainty a t lower octane numbers. All but 15 of the 108 points in Figure 5 fit Equation 4 within these tolerances. The 15 exceptional hydrocarbons are listed in Table 111. O - 0.58 ( S F R ) - 2.12 _X (4) 100 3.50 -0 ,057 (SFR)
P
Vol. 43, No. 12
5
5 1 3-Dimethylcyclohexane 6 1:4-Dirnethylcyclohexane 7 1 1 3-Trimethylcyclohesane 8 l~l\iethyl-4-isopropyloyclohexane 9 Butane 10 Pentane 11 3-Ethylpentane 12 2-Methyl-3-ethylpentane
SIGNIFICANCE OF RESULTS
It has been demonstrated that the knock resistance of hydrocarbons can be correlated with structural factors within the individual hydrocarbon molecules. This result is of considerable importance in several different phases of combustion research.
1
DEVELOPNEXT OF A CHEMICAL MECHANISM OF THE KXOCK PROCESS. The actual knock process in internal-combustion engines occurs a t high pressures and temperatures near the end of the combustion process and undoubtedly results from an extraordinary increase in reaction rate owing to chain-branching reac. tions ( I d ) . The results presented above suggest very strongly, however, that the controlling steps in the chemical reactions lead. ing to knock occur early in the combustion process a t the relatively low temperatures and pressures a t which the hydrocarbons begin to oxidize. The fact that Hinshelwood’s oxidation theory, based on initial oxidation studies, can be used to predict the knock resistance of hydrocarbons is indirect evidence for this conclusion. Better evidence can be obtained from the direct correlation between octane number and oxidation temperature expressed by Equation l. Data eimilar t o those given in Table I can be obtained from the work of other investigators. The fact that preliminary oxidation reactions resembling those observed in tube and bomb oxidation studies occur in engines during the compression stroke is now well established (9, 23, 24, $9). In tube, bomb, or engine the products of oxidation include peroxides, which are generally believed to enter into chain-branching reactions leading t o knock (8, 6, 1 1 , l a ) . The particular contribution of the methyl retardation factor s to offer a basis for predicting, from structural considerations, how readily a hydrocarbon will oxidize.
December 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
PREDICTION OF OCTANEKUMBERS. The general structural factors governing the knock resistance of hydrocarbons are known-the octane number generally increases with centralization and with unsaturation of the hydrocarbon molecule. There has been heretofore no basis for quantitative prediction of the effect of structural changes, except for the empirical schemes proposed bv Kobayashi (17-19) and Mibashan ($2) for paraffin and olefin hydrocarbons. The structural retardation factor method of predicting octane numbers represents an empirical approach based on accepted oxidation theory and 1s applicable to all common types of hydrocarbons. This method is far superior to that of Kohayashi and significantly better than Mibashan's method in degree of correlation with known octane number data. I t was found that in a comparison of predicted and observed octane numbers for 51 hydrocarbons for which all three methods were applicable the present method gave a standard deviation of predicted from observed values of 1.94, as compared with 2.92 for Mibashan's method and 7.28 for Kobayashi's method. The structural retardation factor can be used to evaluate the effect on octane number of typical refining processes, such as alkylation, cyclization, hydrogenation, and the like, by consideration of the generalized effect of the process on methyl or other retarding effects. The possibility of predicting octane numbers from structural retardation factors has been examined in the case of several hydrocarbons for which octane ratings were recently published by the American Petroleum Institute Project 45 (4)-the publication having occurred after the eight rules for determining SRF values had been formulated. The results, summarized in Table IV, show that the predictions were reasonably accurate.
Table
IV. Prediction of Octane Numbers of Novel Hydrocarbons
Structural Retardation Hydrocarbon Factora 2-Methyl-1-pentene 8.55 2-Methyl-Cpentene 8.50 1,l-Dimethylcyclopentane 8.55 4-Methyl-1-cyclohexene 8.16 3,3,5-Trimethyl-l-cyclohexene 8.56 3,5,5-Trimethyl-l-cyclohexene 8 78 a From Table 11. b From Equation 4. C As published by A.P.I. Project 46.
Predioted Research Octane N0.h 94.4 93.0 94.4 86.5
Experimental Research Octane NO.^ 95.1 95.7 92.3 84.1
94.5
96.5
99.0
95.6
RECOGNITION OF IRREGULARITIES IN OCTANE DATA. Whenever physical data have been collected for a considerable number of compounds, correlation with chemical structure offers a highly desirable method of recognizing irregularities in the physical data. These irregularitiefi may result from improper determination of the data or from novel factors influencing the correlation. Many examples of this method of treating collections of data are known. A typical case was the application of Sugden'f parachor to collected surface tension data (SO). Some erroneous measurements were discovered; more important, special factors affecting surface tension, such as hydrogen bonding, were discovered by inspection of the common features among those compounds that did not show the expected surface tension-parachor correlation I n the same way, those hydrocarbons for which the octane number data do not correlate well with the methyl retardation factors should be the subject of special study. As the octane number data were all obtained under the most careful conditione, it is unlikely that errors in measurement are responsible for the irregularities. Therefore the compounds for which correlation is poor are probably those for which the eight rules for calculating methyl retardation factors are not sufficient to account for all the important retarding effects. The hydrocarbons for which major deviations from the average correlation were observed are listed in Table 111. Four main classes of compounds can be recognized.
2839
1. Neoalkanes. Compounds 1, 2, 3, and 4 are all 2,2-dimethylalkanes-commonly called neopentane, neohexane, neoheptane, and neo-octane, respectively-that do not have the high octane number predicted from the structural retardation factors, apparently because other effects, possibly ease of pyrolysis to more oxidizable fragments, reduce the octane numbers below the high value to be expected from oxidation resistance. 2. Di- and trialkylcgclohexanes. Although most cyclohexanes have octane numbers in agreement with the SRF valuea obtained by Rule 7, this rule undervalues the retarding effect of the alkyl groups in 1,3-dimethylcyclohexane (Compound No. 5 ) , 1,4-dimethyl cyclohexane (Compound KO. 6), 1,lJ3-trimethylcyclohexane (Compound No. 7), and l-methyl-4-isopropy1cyclohexane (Compound No. 8). The assumption that methylene retardation is interrupted by alkylation (see Rule 7) is apparently not completely valid for these compounds. 3. %-Alkanes. Compounds 9 and 10 (butane and pentane) have SRF values that are too low to agree with their known octane numbers. The error is particularly large for butane. All other nalkanes have SRF values that are in accord with their octane ratings. No reason for this anomaly can be offered a t present. 4. 3-Ethyl 'compounds. Some 3-ethylalkanes-specifically 3ethylpentane (Compound No. 11) and 3-ethyl-2-methylpentane (Compound No. l2)-are unusually oxidation resistant as judged by their octane ratings, as though the R group had
somewhat the same oxidation retarding effect as a tert-alkyl group. Table I shows Compound No. 12 to be actually rather easily oxidizable, and in Figures 1and 2, it is this hydrocarbon (at a SOT value of 320" C.) that shows the greatest disagreement betx-een oxidation resistance and knock resistance values. I t is possible that hydrocarbons with this particular six-carbon group behave anomalously in engines, in that they resist knock even though they are readily oxidizable. More information about these compounds will be needed. 5 . Miscellaneous. The SRF values calculated by the prexent method were approximately 0.4 unit high for 3 3-dimethylpentane (Compound No. 13), 2,5-dimethylhexane (dompound No. 14), and 2-methyl-5-heptene (Compound S o . 15). Yo explanation can be offered for these anomalies. DEVELOPMENT OF HYDROCARBON OXIDATION THEORY.One of the factors limiting the development of a complete theory of hydrocarbon oxidation is the scarcity of oxidation data obtained under comparable conditions. Cullis and Hinshelwood (8) have recently presented data for relative oxidation rates of 11 hydrocarbons, referred to a standard static oxidation apparatus a t 202" C., 250 mm. oxygen pressure, and a total pressure of the order of 500 mm., but many more hydrocarbons would have to be studied for this collection of data to he representative of all important hydrocarbons. An attempt has been made to correlate Cullis and Hinshelwood's relative oxidation rates with octane number data (Figure 6 ) . The rate increases with decreasing octane number, but the data are rather scattered, probably because of the extrapolations involved in referring the rate data to standard conditions. The theory of structural retardation factors in oxidation gives in quantitative terms the relative importance of methyl groups, tert-alkyl groups, vinyl groups, and cyclic structures in retarding oxidation. From these observations it should be possible to identify the electronic effects that are important in retarding oxidation. Hinshelwood (14) has emphasized the great importance of structure in hydrocarbon oxidation, as contrasted to the relatively mild effect of structure in pyrolysis or sulfurization. I n this connection, he has referred to the hyperconjugation effects associated with methyl groups, represented schematically by writing the methyl group as HazC-, as the possible explanation for methyl retardation in saturated hydrocarbons (15). Ubbelohde ( S I ) suggests that the ability of the initial hydrocarbon oxidation products to exist in the excited state increases with the number of carbon-carbon bonds capable of entering into vibration in a polymethylene chain, so that oxidizability in-
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INDUSTRIAL AND ENGINEERING CHEMISTRY
creases with “excitability,” u hich increases with chain length. These effects are peculiarly important in oxidation since the oxygen-oxygen (peroxide) bond is more excitable if carbon-carbon bonds are numerous. Double bonds (C=C) interrupt vibration along the chain. No such effect appears in sulfurization (in-
Vol. 43, No. 12
oxidizability in the gas phase. It is irequmtly assumed [see, for example, chapter 3 of Goldstein’s xcent book (13)] that gasphase oxidation, like liquid-phase oxidation, occurs preferentially o n the tertiary carbon atom. This is not in accord wit,h the lacts of knock resistance or low temperature osidation resistanccconsider, for. example, the extremc repistance of iso-octane and t,riptane to either oxidation or knock. h r i alternate approach has been made by Boord (3) in which the knock resistance asdociated with tertiary carbon a t o m s is corwlated with the greater tendency to form ket,ones, rathcr than aldehydes, on chain osidation. LITERATURE CITED
.20.I
0
20
I
40 60 80 lor) RESEARCH OCTANE NUMBER
Figure 6. Relation of Relative Oxidation Rates to Octane Numbers of Pure Hydrocarbons Oxidation rater horn Cullis and Hinshelwood (8)
volving sulfur-sulfur bonds) (15) because the bond vibration frcquemies of sulfur-sulfur are different from the carbon-carbon frequency. It seems likely that detailed treatments of the rlectronic effects in oxidation could be developed from a coneideration of the eight rules of methyl retardation developed here. It is extremely important to recognize that tertiary carbon atoms do not increase the gas-phase oxidizability of hydrocarbons. Sttack on tertiary carbon atoms is typical of free-radical rpactions and Cullis ( 7 ) has shown that it occurs in gas-phwe hydrocarbon oxidation, but only as a secondary factor during the latrr stages of ixaction. The structural effects in gas-phase oxidation show very clearly that ovidixability increases with the number of secondary carbon atoms in the molecule. Both primary and tertiary carbon atoms make little contribution to Ion teniperaturc
B e a t t y a n d Edgar, J . Am. C h n . Sx.,56, 107 (1934). Bennett and Mardles, J . Clion. Scc., 1927, 3155. Boord, “Third Symposium on Conihustion a n d Flame and Explosion Phenomena,” p. 416, Baltimore, Williams & Wilkins Co., 1949. Boord et al., American Petroleum Iiijtitiite Research Project 46, Elmenth Annual RepoTf (1950). Boyd, O i l Gas J., 2 9 , No. 42, 147 (1931). Callendar, Engineering, 123, 147, 182, 210 (1927). Cullis. Trans. Faraday Sac., 45, 709 (1949). Cullis and Hinshelwood, Disc?issioiis Pa,uday Soc., No. 2, 117 (1947). Damkohler and Egpersgluas, Z. phi/si/:. C h i . . 51B, 157 (1942). Derick, J . Am. Chern. Soc., 3 3 , 1181 (1911). Insi. PetroleiivL Techno!,, 13, 281 (1927). ND. ENG.C ~ M .29, , 551 (1937). Goldstein, “The Petroleum Chcniicals I n d u s t r y , ” New Y o l k , John n l l e y & Sons, 1950. Hinshelwood. Diseussio~~u FamdriU Hinshelmood, J . C ~ E VSac., I . 1948, 5 Ivanov, Acfa Physl‘coct im. U.R.S.S., 9, 421 (1938), Kobayashi, J . Soc. Chenn. I n d . , J a p q n . 40, Suppl. binding 153 (1937). Z M . , SuppI. binding 219. Itid., Suppl. binding 317. Kobayashi, Y a m a o k a , Koguchi, and Ishizaki, Ibid., 4 9 , 75 (1946). >laman. Pub. sei. et tech. ministkre n i i (It’mnce). Bull. semiccs lech., 91, 33 (1940). Mibashan, Petyoleum Refine?, 22, 195 (1943) Pastell, S A E Quarterly Tram., 4, 571 (1050) Peletier. v Hoogstraten, Smittenbeig and K o o ~ j r n a r Cholezir ~, d5 Ind., 20, 120 (1939). Pope, Dykstra, and Edgar, J . Am. Ciion. aSor.., 51, 1875 (1929). Ibid., 11. 2203. Prettre, Bull. sac. chem., 51, 1132 (1932). P u c k e t t , J . Research Xatl. B u r . S t m d a r d s . 35, 273 (1945). Schmidt a n d Miihlner, Schriften deulsdi. d a d . Indljahrtforsdl., 54, 28 (1941). Sugden, “ T h e Parachor a n d Valency,“ Inndon, G . Itoutledge and Sons, 1930. Ubbelohde, Rev. inst. franc. pelrole ci Au/:, combrtstiblm l i p i d e a , 4, 488 (1949).
ko.
~ i E C E i Y E n hlar 1. 1951. Contribution 99 du Pont de K‘emours 8: Co.
irolil
J a c k - o n Laboratory,
E. I.
