Ind. Eng. Chem. Res. 1987, 26, 1072-1079
1072
Subscripts oil = at incipient oil entrainment air = at incipient air entrainment
McDuffie, N. G. AICHE J . 1977, 23, 37. Neale, G.; Hayduk, W. Can. J . Chem. Eng. 1980,58, 129. Toyokura, T.;Akaike, S. Bull. SOC.Mech. Eng. (Jpn.) 1970,13, 373. Wong, C. F.; Hayduk, W. Ind. Eng. Chem. Res. 1987, in press.
Literature Cited Received f o r review December 16, 1985 Accepted January 21, 1987
Chiou, C. S.; Gordon, R. J. AICHE J . 1976, 22, 947. Lubin, B. I.; Springer, G. S. J . Fluid Mech. 1976, 29. 385.
Application of a Nonlinear Group-Contribution Model to the Prediction of Physical Constants. 1. Predicting Normal Boiling Points with Molecular Structure W.Y. Lai and D. H.Chen* Department of Chemical Engineering, Lamar University, Beaumont, Texas 77710
R. N. Maddox School of Chemical Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
A nonlinear group-contribution model was developed t o predict normal boiling points of organic compounds by using only the structural information. Extensive structural corrections which take care of the size/shape and polar effects are provided. With the proposed method, normal boiling points have been calculated for 1169 organic compounds, and when compared with experimental data, this method produced an average absolute error of 1.29%. Therefore, the proposed method has proved t o be the best general method for predicting the normal boiling point of a n organic compound. A comparison with five other methods available in the literature is also presented. The normal boiling point is one of the few physical constants known for most chemical compounds due to the ease of measurement. Still, a certain estimation technique for the normal boiling point is necessary when experimental data are not readily available. This situation arises (1)when new compounds are involved, (2) when literature data are not at hand, or (3) when the actual normal boiling point does not exist but is required by a particular correlation. If prediction is necessary, only very poor or limited methods can be employed (Reid and Sherwood, 1966). The situation is particularly severe when, for whatever reason, the boiling point has to be estimated, and this calculated value is, in turn, used to predict other physical properties. Also in a simulation package, it is advisable to provide a standby estimation method for each physical constant which is required as an input. There are a number of prediction methods, all empirical, existing in the literature: the methods of Watson (1931), Burnop (1938), Kinney (1938, 1940), Meissner (1949), Lydersen (1955), Forman and Thodos (1958,1960), Ogata and Tsuchida (1957), Somayajulu and Palit (1957), Stiel and Thodos (1962), Purarelli (1976), and Miller (Lyman et al., 1982). Most of them involve group-contribution techniques which are devised for homologous series with no more than one functional group attached to a hydrocarbon framework (Reid and Sherwood, 1966). Reid and Sherwood (1966) and Lyman et al. (1982) have presented major reviews of the methods available, each with a detailed analysis of the methods evaluated. Development of a Nonlinear Group-Contribution Model When the normal boiling points of n-alkanes are plotted against the number of carbon atoms, a smoothed curve can be produced as shown in Figure 1. The curve shows that the difference in the normal boiling points between suc-
cessive members of n-alkanes is not constant and falls off continuously. The methylene (or methyl) group contributions to the normal boiling points of n-alkanes are shown in Figure 2. From this observation, an appropriate model which can represent this specific trend should be preferred. Chen (1981) and Chen and Maddox (1982) proposed a nonlinear group-contribution model, which is a generalization of the classical group-contribution concepts. In this new approach, the natural trend of contribution declining for successive methylene (or methyl) groups is closely followed. The model, however, was only applicable to paraffins and compounds with one functional group. In this work, the nonlinear group-contribution model has been extended to be valid for a general compound. The model proposed by Chen (1981) and Chen and Maddox (1982) assumes that each methylene (or methyl) group contribution differs from the preceding one by a constant ratio rc (decay ratio) so that the total n methylene (or methyl) group contributions amount to the partial sum of the first n terms of the geometric series. For normal alkanes, the model to predict the normal boiling points is Tb = CZ + bc(l - rcn),/(l - rC) Tc # 1 (1) where Tb = the normal boiling point; n = the number of carbon atoms; and a, b,, and r, = the characteristic constants where the subscript c indicates a carbon (methylene or methyl) group. Note that in the classical group-contribution model, r, = 1 and Tb = a + nb,. Equation 1 allows a nonlinear function for T b . Figure 3 shows the group-contribution model for the n-alkane series. As another example, Figure 4 shows that the contribution of the nth methylene (or methyl) group in the normal alcohol series also, in general, declines as n increases. Thus, for a homologous series with a functional group such as n-alcohol series, the group-contribution model is
Tb = *To whom all correspondence should be addressed.
(+ a
bc-
:I;;)
+
0888-5885/87/2626-1072$01.50/0 0 1987 American Chemical Society
(
bf + ffCZ) (2)
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1073
, ,, ,
, I
5
I ,
, , ,
10
I IS
, , , ,
W B E R OF CARBON PTMIS.
,
, , , , 20
.
, , ,
25
I , 10
,
,
,
,, ,,
I 0
35
1
100
I
Q
#
S
I
,
I
t
,
,
,
10
S
I
,
,
,
is
. 20
n ILMBER OF CARBON &TOYS. n
Figure 1. Boiling points of normal alkanes (smoothed curve).
Figure 5. Illustration of the group-contribution model for the nalcohol series. 1
I
LEGEND t
B P
Conpound
Propane
5
IS
10
21
20
30
4 2 0,
sn s
n P ~ o p v lChloride
46 1 2
1 3 Dichlaropiopane
120 d
- 3 88
1 2 3 Tnchloroprapane
1 5 6 8s
JL 4 s
* boiling poinf ~n 2
(1
Contribution
Oc
4"
15
n l l l CARBOL &TOM
Figure 2. Contribution of the nth methylene (or methyl) group to normal boiling points of n-alkanes.
mm
CI CROUP
Figure 6. Contribution of the mth C1 group to normal boiling points for alkyl chlorides (carbon number = 3).
100
1
0
,
,
,
,
1
10
5
hUUBER OF CARBON AT'OWS,
1
1
1
1
1
15
1
1
1
1
20
n
Figure 3. Illustration of the group-contribution model for the nalkane series. I
2
,
4
5
6
7
n t h CARBON ATOM
Figure 4. Contribution of the nth methylene (or methyl) group to normal boiling points of n-alcohols.
where bf and bfc= characteristic constants of the functional group and T b , a, b,, r,, and n are defined in eq 1. In Figure
5, the group-contribution model for n-alcohols is shown. The n-alkane contributions are also depicted (note that they are exactly the same as given by eq 1). As can be seen, the hydroxyl group contribution varies with n and is described by the combination of an increment bf and an interaction term bfc(l - r c n ) / ( l- r,). The contribution declining of successive functional groups is also obvious. Figure 6 shows the mth chlorine group contribution in C1-containing compounds for which the carbon number is equal to 3. Naturally, the model has to take this trend into consideration. Compounds with more than one functional group can be classified into two types: homogeneous multifunctional groups and heterogeneous multifunctional groups. For example, ethylene glycol and glycerol have two and three hydroxyl groups, respectively; dibasic acids such as oxalic acid and succinic acid have two carboxylic groups. These compounds can be termed as having homogeneous multifunctional groups. On the other hand, some compounds containing two or more different types of functional groups, such as mixed halides and amino acids, are said to have heterogeneous multifunctional groups. For compounds with homogeneous multifunctional groups such as glycols and chlorides, eq 2 can be modified as
(3)
where rf = decay ratio of the functional group; m = number of the particular functional group; and T b , a , b,, r,, n, b f , and bf, are defined in eq 2. The group-contribution model for compounds with homogeneous multifunctional groups is illustrated in Figure 7.
1074 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table I. Characteristic Constants Groupsa functional series group OH alcohols 0 ethers C(=O) ketones carboxylic acids C(=O)OH C(=O)H aldehydes C(=O)O esters amines primary NHZ secondary NH tertiary N amides 1 C(=O)NHZ 2 C(=O)NHR C (=O)NRR' 3 nitriles CN nitros NO2 SH thiols S sulfides halides F fluorides c1 chlorides Br bromides I iodides
bf 179.75 72.83 126.16 235.91 119.29 124.51
bfc
rf
-15.35 -6.98 -10.17 -16.64 -9.32 -10.39
0.88 0.93 (0.83) (0.84) (0.84) (0.83)
109.52 86.20 60.94
-6.81 -7.27 -4.51
0.94 (0.94) 0.55
361.4 325.41 276.30 171.31 222.34 139.04 133.38
-35.80 -30.32 -28.91 -12.57 -16.08 -8.73 -7.47
(0.76) (0.78) (0.63) (0.77) 0.70 (0.81) (0.82)
49.05 108.14 135.23 178.36
-3.42 -6.76 -8.61 -9.79
0.83 0.75 0.83 0.77
*IMBER
= a = 103.59; b, = 44.34; r, = 0.94 in this method. An rf value inside parentheses is predicted.
In compounds with heterogeneous multifunctional groups, the interaction between different types of functional groups is taken into account by adding an additional term bfifj to eq 3, that is,
where bfi, rfi, and bfi, = characteristic constants of the functional groups of the ith type; mi = number of functional groups of the ith type; 1 = number of functional group types; bfifj = interaction parameter between functional groups of the ith type and the j t h type, i < j ; and Tb,a, b,, r,, and n are defined in eq 2. For instance, in 2,3-dibromo-l-propanol, 1 = 2, ml = 2, m2 = 1,and n = 3, the bromine groups are designated as the type 1functional groups, and the hydroxyl group is designated as the type 2 functional group. The nonlinear least-squares regression method proposed by Marquardt (1963) was used to determine the optimal constants in this study. The predictive constants for group
0 NH2 NH CN NO*
c1 Br
(-28.53) -14.88 4.18 -4.26 (-21.98) (-40.27) -30.97 -39.75
(-14.08) (-15.84) (-13.97) (-40.83) (-53.17) -27.26 -31.71
Values in parentheses are estimated.
(-6.02) (-5.20) (-14.37) (-18.70) -13.16 -16.26
OF CARBOY
ATOMS, P
Figure 7. Illustration of the group-contribution model for alkyl chlorides.
contributions and interaction parameters are given in Tables I and 11, respectively.
Structural Corrections The above derivations are applicable to straight-chain compounds (in terms of groups); no structural corrections are included. For compounds with other geometric shapes (branched, alicyclic, aromatic, etc.) and other specific structures (double bond, cis, trans, etc.), certain types of structural corrections are necessary. Due to the fundamental differences in structural corrections, the organic compounds are classified into two categories: non-hydrogen-bonding compounds and hydrogen-bonding compounds. In this work, a quite sophisticated system of structural corrections has been developed. Structural variables which account for the size/shape and polar effects are proposed. Although the structural contributions are generally small (less than 10% of the value of the normal boiling temperature), it is this system (of structural corrections) that makes this method powerful. Interested readers are referred to the work of Lai (1984) and Yang (1986) for detailed explanations. A. Structural Corrections for Functional Group Positions. Non-Hydrogen-Bonding Compounds. For non-hydrogen-bondingcompounds, the effect of functional group positions is considered by adding an additional term af to eq 4. Functional groups may be linked to the main chain at various locations. For instance, the carbonyl group may be attached to the 2-position or 4-position along the main chain as in 2-heptanone or 4-heptanone. The effect of the functional group positions along the main chain will be considered. For compounds with multifunctional groups, where several functional groups may be linked to a carbon atom, the structure is identified as a coposition structure of functional groups. For instance, 1,l-dichloroethane has a coposition structure because two chlorine groups are
Table 11. Values of interaction Parameter between Different Functional GroupsD group A group B OH C(=O)OH 0 NH2 NH OH C(=O)OH
I
I
of t h e Functional
(-5.87) (-17.73) (-23.10) (-16.93) (-13.37)
(-15.05) (-19.60) (-14.02) (-11.38)
CN
NO2
c1
(-51.26) -9.86 (-27.61)
-36.00 -32.58
-23.66
Br
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1075 attached to the same carbon. The coposition structure also has a significant effect on physical properties. The combination of the above-mentioned functional group position effects gives the correction term up That is, I
Uf
=
c
m, CUij
i = l j=1
+ TCOf
Table 111. Characteristic Constants of Functional Group Position Correctionsa A. hydrogen-bonding functional groups group
(5)
-14.75 NH2 NH 7.40 B. non-hydrogen-bonding functional groups
__
and arl, . =
i tj
Pij - 2 Eij
= (MC
+ 1)/2 - 2
MC - Pjj - 1 5ij
= (MC
+ 1)/2 - 2
[or =
Xitij’l
if Pij I (MC
if Pij > (MC
(6)
+ 1)/2
+ 1)/2
(7) (8)
where X i = characteristic constant of the function group of the ith type; T = characteristic constant associated with coposition structures of functional groups; ti; = 1- [y; MC = number of groups in the main chain; Pij = position of the j t h functional group of type i along the main chain; Cof = CmkC2 = C ( m k ) ! / [ ( m-k2)!2!], copoqition number where mk is the number of copositioned functional groups (all types) a t the kth coposition structure of functional groups, for instance, Cof = 6 for both CC14 and CC12F2;and 1 and mi are defined in eq 4. Parameter tijis the relative position of an end-based functional group along the main chain. For example, the carbonyl group (in ketones) and the chlorine groups (in chlorides) are end-based functional groups. In other words, tij = 0 if the functional group is located at the end of the main chain (e.g., 1-chloroheptane) or a t the 2-position of the main chain (e.g., 2-chloroheptane), and tij = 1 if the functional group is located at the center of the main chain (e.g., 4-chloroheptane). If MC = 3 and Pij = 2, tijis defined as 0. On the other hand, parameter ti: is the relative position of a center-based functional group such as the -0- group (in ethers) and the -N< group (in tertiary amines). If MC = 3 and Pij = 2, ti/is equal to 1. In Table I, except -0-, -NH-, -Ne, and -S-, all functional groups are end-based. As an example to determine ti/, for n-butyl ethyl ether, MC = 7, Pll = 3, and f l l ’ = 0.5 (i = 1, j = 1). Another example is given here to clarify the calculation of Cop Consider 1,1,1,3,3-pentafluoropropane, 2 Cof = ,EmiC2 = -3!+ - = 42! 1=1 2!1! 2!0! Hydrogen-Bonding Compounds. If the end-based hydrogen-bonding functional groups (e.g., OH groups) move from the main chain (primary positions) to side-chain positions (secondary or tertiary positions), the correction is
If the center-based hydrogen-bonding functional groups (e.g., NH groups) move away from the central position, the effect is given by
In eq 9 and 10, uiand Xi = characteristic constants of the ith type hydrogen-bonding functional group, 1‘ = number of hydrogen-bonding functional group types, m[ = number of hydrogen-bonding functional groups of type i and ti, and ti; are defined in eq 7 and 8. For example, in 1-hexanol, no correction for OH group position is needed. In 2-hexanol, tll = 0 and ahf = u1 0’ = 1,i = 1, designated to OH).
A, -0.39 -3.91
ui -19.90
OH
group 0 O=C< COO S
A, -3.13
-14.70 -9.01 -10.60
Ai
group
SH CONRlRz
F C1
A, -3.90
group
Br I
-5.10
3.51
NO2
-9.01 2.85
-7.00 -11.32
= -11.03 for non-hydrogen-bonding compounds. - -: value
not applicable.
In 3-hexanol, tll = 0.67 and a h f = u1 + 0.67X1. Position corrections for non-hydrogen-bonding functional groups can be ignored when dealing with a hydrogen-bonding compound. General Comments on Functional Group Position Corrections. A functional group (hydrogen-bonding or non-hydrogen bonding) located at the open end of a side chain does not require a position correction if it is an end-based functional group, such as the chlorine group in 4-chloromethyloctane (synonym: 4-(a-chloromethyl)octane) . Note that the main chain is defined as the longest chain (in terms of number of groups) in a molecule for a nonhydrogen-bonding compound and as the longest chain including (or linked to) a hydrogen-bonding functional group for a hydrogen-bonding compound. In the following structural diagrams, each main chain is labeled by a frame, c c c c (1)
e c-c-c-c-c
(2)
c-c-c-c-c-c-CI
c c
c
C
I
c
C O H
The predictive constants for the corrections of functional group positions are shown in Table 111. B. Structural Corrections for Branched Side Chains. Non-Hydrogen-BondingCompounds. The effect of branched side chains can be adequately described by the following correction term for non-hydrogen-bonding compounds: nip
n,
where tT/ and t+j’= center-based relative positions of the ith three-way branch and the j t h four-way branch, respectively; lTi and 1, = numbers of groups on the ith three-way branch and the j t h four-way branch, respectively; nT and n+ = numbers of three-way branches and four-way branches, NE = structural variable for the neighboring effect; and a , p, A, 6, t = constants. (MC + 1 ) / 2 - P ET/ (or t+:) = (MC + 1)/2 - 2 if P 5 (MC + 1 ) / 2 P - (MC + 1 ) / 2 ET[ (or E+:) = (MC + 1)/2 - 2 if P > (MC + 1)/2
1076 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table IV. Neighboring Effects Employed in the Proposed Group-Contribution Model” no. of no. of structural group NE structural group NE R -- C
-C -R ‘
R,
R3
I
!
P3
R1
I
1
I
R -- C -C - R‘
I
1
R2
R4
R,
A3
I
I
1
Table V. Association Center of Hydrogen-Bonding Compounds series association center alcohols COH primary amines CNH, secondary amines NH C (=O) OH carboxylic acids amides C (=O) NH,; C (=O) NRH
at the far end of the split chain. If SCk = 2 and Qk, = 1, VTkj or q + k j is defined as zero. The following examples I I illustrate the structural variables in eq 12. In 2-ethylR2 R4 hexanol, SC1 = 5 , Qll = 1, qTll = 0; in 2,6-dimethyl-3“ R , R’, Rl, R,, R3, R4 = alkyl, aryl, alicyclic, or functional heptanol, SCl = 2, Ql1 = 1, 7 ~ 1 1= 0,SC2 = 4,Q21 = 3, vTZ1 groups. = 1; in 2,5,5-trimethyl-3-ethyl-3-heptanol, MC = 7, P,, = 3, (11 = 0.5, h i = 1, SC1 = 2, Qii = 1, ~ ~ = 10 , 11+21 = 2, P = branched chain position, P = PT,and P = P+,for En’ SC2 = 4,Q21 = 2, q+21 = 0.5, 1,- = 2. and E+,’ calculations, respectively. When branch corrections are carried out in a hydroFor instance, in 3-ethyl-4,4-dimethyl-5-chloroheptane, gen-bonding compound, all functional groups except the IT1 = 2, PT1 = 3, [TI’= 0.5, MC = 7 , lT2 = 1,PT2 = 5,ET2/ one in the current association center are considered as if = 0.5, 1+, = 2, P+l= 4,and E+1’ = 0. they were carbon groups. For example, the bromine group The structural effect, increase of the normal boiling is considered as a carbon group when the branch correction point due to neighboring side chains, is defined as the is made with respect to the association center, COOH, in neighboring effect in this study. The neighboring side a-bromopropionic acid. chain structures and the associated NE’S are listed in Table General Comments on Branched Side Chain CorIV. The neighboring effect structural variable, NE, rerections. It should be noted that the branched side chain flects the relative contribution of a neighboring side chain corrections can be applied only to the nonring portion of structure to the normal boiling point. Again in 3-ethyla compound. 4,4-dimethyl-5-chloroheptane, NE = 2 + 2 = 4. C. Structural Corrections for Cyclic (NonaroWhen dealing with esters, for the structural corrections matic) Rings. Non-Hydrogen-BondingCompounds. of either functional group positions or branched side For non-hydrogen-bonding compounds with cyclic (nonchains, consider COO as a carbon group (because COO is aromatic, may be fused) rings, the correction term a, takes regarded as a single group). For instance, MC is equal to the form 7 for isopropyl n-valerate. Hydrogen-Bonding Compounds. The branch cora, = a,’ + ac/ (13) rections with respect to a hydrogen-bonding association where center (functional group plus, in case of alcohols and primary amines, the nearest carbon group) can be expressed as n, ahh,,
=
2
2
nTk
C(aiqTkj h=l]=l
a,‘ =
+ @!jhj1’* + n+k
rclco
C ( 6 r q + k ~+ c i ) l + k j (12) + h=l]=l
where VTk, (or v+kJj = (Qk, - l)/(SCk- 21, relative position of the j t h brallch along the kth split chain; Qkl = the j t h branch position on the kth split chain; l,, = number of groups of the split chain (other than the split chains constituting the main chain) copositioned with the hydrogen-bonding functional group, e.g., in 3-ethyl-3-pentano1, l,, = 2; sck = the kth split chain length, number of groups on the kth split chain which emerge from the association center; n, = number of the split chains emerging from the association center; oh,p,, A,, 6,, and t, = characteristic constants of the ith association center; lTkl and l + k ] = three-way and four-way branch chain lengths; and nTk and n+k = numbers of three-way and four-way branches on the kth split chain. The branch corrections for the entire hydrogen-bonding compound becomes 1=1
+ A”Co
C, = ring size (e.g., C1 = 5 for cyclopentane); n, = number of nonaromatic cyclic ring units (may be fused); NE = structural variable for neighboring effect on a nonaromatic cyclic ring as defined in Table IV (except that in this case R and R’ are connected to form a ring structure); Co = number of coposition structures (e.g., Co = 1 for 1, l-dimethylcyclohexane);fcl = degree of fusion for the j t h ring unit (e.g., fcl = 2 for decahydronaphthalene); and a”, pl’, A“, Y,, and e = characteristic constants. For example, in 1,1,3,4-tetramethylcyclohexane, Cl = 6, Co = 1,fcl = 1,and NE = 1. Hydrogen-Bonding Compounds. For hydrogenbonding cyclic (nonaromatic) rings, the following corrections with respect to the ith association center are proposed (14) ahc,i = ahr,i’ + ahc,i’ where ne
ahr,lf=
n,
where n A = number of association centers in the compound of interest. Table V shows the association centers of hydrogenbonding compounds. Notice that three-way and four-way branch corrections are applied to each split chain. VTk, (or q+kl) is taken as zero for the branch position closest to the association center and taken as one for the branch position
pl’NE
a,”CfclYCcJe‘ ]=l
= A,”Co; a,”, A;’, vcr, and e, = characteristic constants; and C,, Co, f c l , n, are defined in eq 13. The cyclic (nonaromatic) ring corrections for the entire hydrogen-bonding compound become
ahc,,’
where nA is defined in eq 12’.
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1077
D. Structural Corrections for Aromatic Rings. Non-Hydrogen-Bonding Compounds. For non-hydrogen-bonding compounds with aromatic ring structures, the correction term a, is expressed as a, = a,’ + a,’ (15) where
a,’ = plNE
+ y’o + 6’mt + e’p
nB = number of hydrocarbon aromatic ring units (may be fused with the benzene ring as the basic unit); f b , = degree of fusion for the j t h hydrocarbon aromatic ring unit; NE = neighboring effect in an aromatic ring structure; 0,mt, and p = numbers of ortho, meta, and para structures in a six-membered ring, respectively; nH = number of heterocyclic aromatic ring types; Hk = number of the kth-type heterocyclic aromatic rings ( H , is for thiophene ring or furan ring; H 2 is for N-methylpyrrole ring); and a’, p’, A’, 6’, e‘, ffk“‘, and Vb = characteristic constants. For example, fbl = 1, o = 1, mt = p = 0, and NE = 1 for 1,2-dimethylbenzene, and f b l = 2 for naphthalene. Hydrogen-Bonding Compounds. For aromatic structures in hydrogen-bonding compounds, the correction term with respect to the ith association center is
where
aha,i
= p/c
+ y[o + 6;”t + ei’p
a / , p i , y[,
v/, e[, Ubi, and (Yki”’ = characteristic constants; nB,0,mt, p , H k , and nH are defined in eq 15 (H3 is for pyrrole ring); and c = direct connection between the hydrogen-bonding functional group and the hydrocarbon aromatic rings (e.g., c = 1 for phenol and c = 0 for benzyl alcohol). The aromatic ring corrections for the entire hydrogenbonding compound become
fb,,
n.4
aha
=
(16’)
Caha,i/nA i=l
where nAis defined in eq 12’. General Comments on Aromatic Ring Corrections. Note that 0, mt, and p corrections are valid only for a six-membered ring. In general, for a ring structure with k 1 substituents, k corrections (0 mt + p = k ) are needed to determine the relative positions of these substituents. For instance, p = 1 (for the main chain), o = 2 (for two side chains), NE = 3, f b l = 1, and nB = 1 for 1,2,3,4-tetramethylbenzene. The distinction between the ortho correction and the neighboring effect should be made clear here. The ortho correction is used to describe the relative position between two substituents. The neighboring effect is determined according to neighboring structures as outlined in Table IV. E. Miscellaneous Structural Corrections. NonHydrogen-Bonding Compounds. Some structural corrections including double-bond, triple-bond, and cis and trans corrections are combined in a,: a , = I’,d + r 2 d , + rrt + &is + qtra (17)
+
tra = number of cis and trans structures, respectively; and rl,rZ,ir, 4, and = characteristic constants. Hydrogen-Bonding Compounds. No miscellaneous structural corrections are proposed for hydrogen-bonding compounds. F. General Comments on Structural Corrections. In summary, to estimate the normal boiling point of a given compound, the group contributions are calculated first. After that, various structural corrections should be estimated and added up. The summation of the group contributions and the structural contributions is the estimated
+
Tb*
Note that a compound may need different types of structural corrections in different portions of the compound simultaneously. For instance, in tetralin, the aromatic correction should be made on the aromatic portion and the alicyclic correction on the nonaromatic portion. Another example is for isopropylbenzene; the branched side chain correction is needed in the aliphatic portion and the aromatic ring correction needed in the aromatic portion. A cyclic unit (aromatic or nonaromatic) can be considered as a C-membered straight chain when relative position is to be calculated or when the main chain is to be determined. A cyclic unit (aromatic or nonaromatic) on a branched side chain should be corrected as an equivalent branched straight chain plus a ring formation correction. Hence, there is one three-way side chain correction (lT1 = 4) and one four-membered ring formation correction for the cyclobutyl group in 6-cyclobutylundecane. For tertiary amines, branched side chain corrections are always required due to the branched structures of this type of compounds. Predictive constants for branched side chain corrections, cyclic (nonaromatic) ring corrections, aromatic ring corrections, and miscellaneous structural corrections are given in Table VI. The structural corrections for which the predictive constants are not available from the tables should be assigned a value of zero in actual predictions. Any structural features not discussed heretofore should also be ignored.
Illustrative Examples A complete flow chart is shown in Figure 8 to explain the procedure of implementing the proposed method. Two examples are given below to demonstrate the procedure. Example 1: Estimate the Normal Boiling Point for 2’-Methyl-l,l-diphenylethane. (1)Structural Diagram.
+
where d = number of double bonds; t = number of triple bonds; d, = number of conjugated double bonds; cis and
(2) Group Contributions. Since only carbon groups are present, eq 4 reduces to n = 15 G.C. = a + b,(l - rcn)/(l - r,)
(3) Structural Corrections. Aromatic ring corrections, from eq 15, are n6
a, = a ’ C f b j ” b j=1
+ p ” E + 7’0
= 2 and f b l = ffb2 = 1 (two benzene rings) and NE = 1 and o = 1 (two side chain substituents on one of the benzene rings). Branched side chain corrections, from eq 11, are nb
ab
= (aFT1’ +
P)lTll’’
1078 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table VI. Predictive Constants for Branched Chain Corrections, Cyclic (Nonaromatic) Ring Corrections, Aromatic Ring Corrections, and Miscellaneous Structural Correctionsa non-hydrogen-bonding compds hydrogen-bonding compds with hydrocarbons others OH COOH NH, NH -3.71 -0.60 2.50 0.07 1.16 5.57 -11.44 -4.34 -7.46 -7.90 -10.80 -9.50 __ _. 4.10 3.95 -12.54 -9.87 1.92 -5.81 6.29 -2.77 0.01 -15.05 -2.28 -10.74 -8.63 -11.21 -10.91 __ __ 29.94 20.07 1.28 6.00 __ -_ __ 1.46 (1.46) ... -12.87 (-12.87) (-16.00) -16.00 ... ... -1.55 -0.38 0.90 -0.38 ... ... 3.32 ... 7.92 5.01 24.00 25.00 5.01 2.45 15.80 0.00 25.00 15.00 -10.66 -14.00 -10.28 -6.51 (-10.00) ... 0.91 -6.24 (-7.00) -3.00 -7.28 3.68 -3.00 -10.28 -7.69 (-10.00) ... ... 1.94 2.50 __ __ __ __ -2.16 5.42 __ __ __ 6.65 ... __ __ -_ 9.46 ~~
...
__
...
...
... ... ... ...
...
...
__
...
...
__
"Values in parentheses are estimated. - - : value not applicable. value not available. ol"' = -9.29, ai'' = 41.76, and ai'' = 66.17. 6 = 2.19 for aromatic hydrocarbons, -2.53 for cyclic (nonaromatic) hydrocarbons, and 11.65 for aliphatic hydrocarbons. 6 values for nonhydrocarbons are not available. # = 10.70 for aromatic hydrocarbons, -6.90 for cyclic (nonaromatic) hydrocarbons, and 10.42 for aliphatic .e.:
hydrocarbons. # values for non-hydrocarbons are not available.
Table VII. Average Deviations in the Estimation of Normal Boiling Pointsu data AAPE, S.D., confidence limit,b MAPE % series pts [el, % be, % e f u, (1.961, % 1.49 hydrocarbons 240 1.19 -0.01 f 2.92 6.32 1.81 7.87 0.03 f 3.54 alcohols 130 1.29 1.85 5.53 -0.92 f 3.62 ethers 45 1.47 42 1.35 1.69 5.39 -0.38 f 3.30 ketones 0.74 2.70 1.05 f 1.45 carboxylic 42 1.15 acids 0.20 i 2.02 2.22 aldehydes 32 0.93 1.03 3.46 0.23 f 1.88 esters 78 0.75 0.96 amines 1.61 -0.15 f 3.16 6.02 primary 65 1.11 1.74 4.85 -0.21 f 3.40 secondary 50 1.34 2.35 5.45 0.55 i 4.60 tertiary 46 1.88 1.00 amides 19 0.71 2.56 0.02 f 1.96 1.58 -0.08 i 3.10 5.34 nitros 38 1.04 1.54 5.09 0.43 f 3.02 nitriles 30 1.07 45 1.23 1.58 3.86 -0.04 f 3.10 thiols 0.77 2.28 0.59 i 1.51 sulfides 35 0.84 2.56 fluorides 61 2.24 5.85 -0.74 f 5.01 2.05 6.37 -0.87 f 4.01 chlorides 75 1.67 2.04 bromides 60 1.68 5.94 -0.62 i 4.00 36 1.02 1.28 4.33 0.45 f 2.51 iodides -0.03 f 3.06 7.87 total 1169 1.29 1.56 "AAPE = average absolute percent error. MAPE = maximum absolute percent error. S.D. = standard deviation. 95% reliability limit.
Figure 8. Flow chart of the proposed method
MC = 14, P T 1 = 7, lT1 = 1, tTl' = 0.091 (methyl group as a branched side chain located at the seventh position of the main chain whose chain length is 6 + 1 + 6 + 1 = 14),
and S.C. = a, + a b (other corrections need not be considered). (4) Tb Value. The value is derived from
Table VIII. Summary of Results for Estimating Normal Boiling Points av absolute percent error ( % ) for method compd class proposed Meissner Lyderson et al. Miller Purarelli hydrocarbons (20)b 1.22 3.17 11.53 8.28 4.48 sulfur-containing organics (11) 0.71 2.10 3.68 5.52 nitrogen-containing organics (12) 1.16 4.40 5.42 6.95 19.92 oxygen-containing organics (16) 0.82 3.66 5.90 7.23 8.92 halogen-containing organics (13) 1.35 7.11 11.93 6.04 10.38 multihetero-containing organics (10) 1.54 4.67 8.46 7.60 12.94 total 1.12 4.10 8.83 6.83 9.70 a
The Stiel and Thodos method is applicable only to paraffins.
Stiel and Thodos 1.04
Values in parentheses are the number of compounds tested
1.04"
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1079
Th = G.C. + S.C. 1 - 0.9415 + 2 X 7.92 15.80 = 103.59 44.34 1 - 0.94 10.66 (-3.71 X 0.091 - 4.34) = 566.77 K
+
+
+
The measured normal boiling point is 562.2 K. Thus, the error is 0.81%. Example 2 Estimate the Normal Boiling Point for 4-Chloro-2-methyl-2-butanol. (1)Structural Diagram. OH
I I
CI-e-C-e-e
C
(2) Group Contributions. From eq 4, with m, = 1 (for OH), m2 = 1 (for Cl), 1 = 2, n = 5, and i = 1for OH, and i = 2 and j = 2 for C1,
(bf, +
h-)
+ bflf2
(3) Structural Corrections. Functional group position corrections, from eq 9, with 1‘ = 1, ml’ = 1, i = 1, and j = 1(refer to the OH group) are aM= g1 + MC = 5, Pll = 2, and tl1= (2 - 2)/(3 - 2) = 0. Branched side chain corrections, from eq 12 and 12’, are ahb = n l , (nA= 1, only one association center; although the compound has three split chains, no branched side chains exist on each split chain. However, 1, = 1 due to the copositioned methyl group in this tertiary alcohol) and S.C. = ahf+ ahb (no other structural corrections are needed). (4) T b Value. The Tb value is derived from Tb = G.C. S.C. 1 - 0.945 = 103.59 + 44.34 - o.94 179.75 -
+
+
1 - 0.945 15.35 1 - 0.94
+ 108.14 - 6.76 11-- 0.945 - 30.97 0.94
The experimental value of -2.93%.
Tb
19.90 - 12.54 = 426.66 K is 439.2 K. The error is
Results and Comparisons Normal boiling points were calculated for 1169 organic compounds (including those with multifunctional groups, hydrogen-bonding, and complex structures) with an average absolute percent error of 1.29% by using the proposed method. In this study, data were taken from API Research Project 44 (1975) tabulations, Lunge’s Handbook of Chemistry (1979), Dictionary of Organic Compounds (1982), and CRC Handbook of Chemistry and Physics (1984). No other physical constants are used as inputs; only chemical structure is needed. Table VI1 shows the detailed analysis including number of data points, average absolute percent error (AAPE), standard deviation, confidence limit of the prediction, and maximum absolute percent error (MAPE). Note that among the 1169 compounds, 79 compounds are not included in the regression. Comparison of the proposed method with other methods is shown in Table VIII. The average absolute percent error (1.12%) based on a sample of 82 compounds is considerably more accurate than those obtained from the methods of Lydersen et al. (8.83%), Meissner (4.10%), Miller (1.83%), and Purarelli (9.70%). The Purarelli method produces poor estimation although it is somewhat easier to use. The Stiel and Thodos method can be applied
only to paraffins. Even in this category, the proposed method has an AAPE of 0.93% compared favorably to the AAPE of 1.04% of the Stiel and Thodos method.
Conclusions The nonlinear group-contribution model, which is a generalization of the classical group-contribution concepts, has been successfully applied to the estimation of the normal boiling points. Extensive structural corrections which account for the sizelshape and polar effects are provided. The proposed method can predict the normal boiling points of 1169 compounds with an average deviation of 1.29%. Based on a sample of 82 compounds, the comparison clearly shows that the proposed method is considerably more accurate than others. The proposed method is general enough to be applicable to compounds with high molecular weight, multifunctional groups, and complex structures and does not require any other physical constants as inputs. It is worthwhile to mention that the nonlinear groupcontribution model is a generally valid procedure. It can be used to develop predicting methods for other physical constants (e.g., T,, P,, and V,) and other temperaturedependent physical properties (e.g., viscosity and thermal conductivity). In other words, the same structural information or input procedure can be used to estimate a series of properties. An interactive program will be written in order to computerize the proposed method. Acknowledgment This work was presented at the American Chemical Society Annual Meeting, Division of Industrial & Engineering Chemistry, Sept 8-13, 1985, Chicago, IL.
Literature Cited API Research Project 44,1975; Thermodynamics Research Center, Texas A&M University, College Station. Burnop, V. C. E. J . Chem. SOC.1938, 826-829. Chen, D. H. Ph.D. Dissertation, Oklahoma State University, Stillwater, 1981. Chen, D. H.; Maddox, R. N. FPRI Internal Report, 1982, Fluid Properties Research, Inc., Stillwater, OK. CRC Handbook of Chemistry and Physics, 64th ed.; Weast, R. C., Ed.; The Chemical Rubber Co.: Cleveland, OH, 1984. Dictionary of Organic Compounds, 5th ed.; Buckingham, J., Ed., Chapman and Hall: New York, 1982. Forman, J. C.; Thodos, G. AIChE J. 1958, 4, 356. Forman, J. C.; Thodos, G. AIChE J . 1960,6, 206. Kinney, C. R. J . A m . Chem. SOC.1938,60, 3032. Kinney, C. R. Ind. Eng. Chem. 1940, 32, 559. Lai, W. Y., M.S. Thesis, Lamar University: Beaumont, TX, 1984. Lange’s Handbook of Chemistry, 12th ed.; Dean, J. A., Ed.; McGraw-Hill: New York, 1979. Lydersen, A. L. “Estimation of Critical Properties of Organic Compounds”; Engineering Experimental Station Report 3, 1955; University of Wisconsin, Madison. Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H. Handbook of Chemical Property Estimation Methods; McGraw-Hill: New York, 1982. Marquardt, D. W. J . S I A M 1963, 11, 431. Meissner, H. P. Chem. Eng. Prog. 1949,45, 149. Ogata, Y.; Tsuchida, M. Znd. Eng. Chem. 1957,49, 415. Purarelli, C. Chem. Eng. 1976, 83(18), 127. Reid, R. C.; Sherwood, T. K. T h e Properties of Gases and Liquids-Their Estimation and Correlation, 2nd ed.; McGrawHill: New York, 1966. Somoyajulu, G. R.; Palit, S. R. J . Chem. Soc. 1957, 2540. Stiel, L. I.; Thodos, G. AIChE J . 1962, 8, 527. Watson, K. M. Ind. Eng. Chem. 1931, 23, 360. Yang, C. Y. D.E. Dissertation, Lamar University, Beaumont, TX, 1986.
Received for review January 24, 1986 Accepted January 29, 1987
