370
Ind. Eng. Chem. Prod.
Res. Dev. 19Mt 23, 370-374
Statistics of Novolacs Mlrta I. Aranguren, Julio Borrajo, and Roberto J. J. Wllllams' Institute of Materials Science and Technology (INTEMA), University of Mar del Plata and National Research Council, J.B. Just0 4302, (7600) Mar del Plata, Argentina
Statistical quantities such as gel formation, number and weight average molecular weights, and distribution of molecular species were derived for the formation of novolacs, the acid-catalyzed phenol-formaldehyde polymerization products. The approach is an improvement on the previous developments in that while it uses available kinetic information it also takes into account the unequal reactivity and variable substitution effects. This was achieved by a recursive method. The model leads to a reactivity ratio of the internal to external positions close to ' I 3 . Gelation is predicted for a formaldehyde/phenol molar ratio equal to 0.90 at full formaldehyde conversion. The recursive method can be applied to other polymerizations showing the unequal and/or variable parameters.
Introduction
Table I. Reactivity Ratios per Reaction Site
The phenol-formaldehyde condensation is a typical polymerization reaction where the usual simplifying assumptions (i-e.,equal reactivity of functional groups of the same type and absence of substitution effects) do not hold. Drumm and LeBlanc (1972) proposed two different approaches for determining statistical parameters of novolacs, the acid-catalyzed phenol-formaldehyde system. The first one is a kinetic approach involving two reaction steps, addition and condensation, and different reactivity of internal and external positions on the novolac chain. This simplified scheme of novolac chemistry was used by Frontini et al. (1982) for the analysis of batch and continuous reactors and extended by Kumar et al. (1980,1981, 1982),who took into account the existence of five different kinds of reactive sites as well as the possibility of condensation between methylolated species. However, this kinetic approach is still a very rough approximation of novolac chemistry and needs extra hypotheses regarding the distribution of reactive sites among the n-mers. The second approach consists of assigning an effective functionality-less than three-to the phenol molecule. The molecular weight distribution obtained by this approach showed a very good agreement with Stockmayer's weight distribution function (Stockmayer, 1943),when an average functionality f = 2.31 was assigned to phenol. This value was used by Borrajo et al. (1982) to calculate statistical parameters of typical novolacs. Good agreement with experimental data was shown, although the method has no reliable scientific foundation. Our present aim is to derive a model of novolac formation using all available kinetic information and taking both different reactivity of sites and substitution effects into account. A statistical recursive method is to be developed. The major assumption will be that no intramolecular reaction occurs in finite species (absence of loops). This assumption does not exclude the formation of cyclic structures through intramolecular H bonds. Novolac Chemistry Notation. The different possible molecular species are
shown in Figure 1. These molecular species include the monomers and all the possible forms in which the phenolic rings may be present in the reaction mixture (as single species or as part of molecular chains). The para position of the phenolic ring is denoted by 2. The ortho position is denoted by 1when both o and o rpositions are free, and by 1' when one o position is reacted. When two reactive positions of the phenolic ring are used up for methylene bridges, the remaining position is represented by the
o 196-4321/a41 i223-0370$01.50/0 e
r r r r r
( 2 / 1 ) = 2.4 (with B ) (211) = 12 (with any Me) (Me,/Me,) = 2.4 (with any 1 or 2 ) (Me, /B) = 8 (with any 1 or 2) ( i / e )= i, 0 < i < 1
subscript i (internal site). Nineteen molecular species result. Their concentrations are expressed as relative values with respect to the initial phenol concentration A, (Le., A means the ratio between actual and initial phenol concentrations). Kinetic Consideration. Two major steps are involved in the acid-catalyzed formation of phenolic resins. The first one is the addition of formaldehyde to a free reactive position (0,or,or p ) of the phenolic ring to give a methylol. The second one is the condensation of the methylol with a free reactive position of other phenolic ring or with other methylol, to give a methylene bridge (in the condensation of two methylols an ether bridge is first produced). The novolac chemistry is characterized by a high condensation rate with respect to the addition rate (Drumm and LeBlanc, 1972). This implies that concentration of methylol phenols will be low throughout the reaction. Thus, the concentration of the following species: P, Q, R, S, and T, may be neglected. For the same reason, the possibility of condensing two methylols will be deleted in the following analysis. (In resol chemistry this situation is no longer valid). The kinetics related to the formation of dimers under strong acid conditions has been reviewed by Drumm and LeBlanc (1972). The resulting reactivity ratios, per reaction site, are shown in Table I. Internal positions are less reactive than external sites due to steric hindrance. This difference in reactivity is difficult to measure and depends upon the particular species and reaction conditions. Usually an overall effective value is proposed. As there is no agreement in the literature with respect to its value, it will be adjusted by comparing model predictions to known experimental results. All addition and condensation steps are taken as second-order reactions. Specific rate constants may be calculated from the reactivity ratios shown in Table I, taking one of them as a reference value. Table I1 shows the set of specific rate constants corresponding to a novolac prepared under strong acid conditions. Rate Equations
A rate equation for each species was written by summing up all possible steps leading to, or consuming, the par1984 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 3, 1984 371 Table 111. Rate Eauations PHENOLIC RING
0-0
FORMALMHYDE
METHVLOL
Me
I-CH,OHI
‘12 METHYLENE BRIDGE SPECIES
AND
-AW FRAGMENTS
E&> Q R dMt &%L, T k,&,
S
Figure 1. Notation. Table 11. Relative Values of Specific Rate Constants Formaldehyde Additiona k l ~ o / k l o= 0.5 k,,/k,, = 1 . 2
k,~,,/k,, = 0.51’ k z ~ , / k l 0= 1.2i Condensation with External o-Methylols (Me,) k i M e ~ / k i o= 4 kirMe~/kio= 2 kzMel/klo = 24 k , i ~ ~ ~ / =k 2, ,i k 2 ~ e l / k l =o 24i
k,, is a reference value involving two ortho positions and two formaldehyde sites. For the condensation with external p-methylols the values must be multiplied by 2.4; for internal o-methylols the values must be multiplied by i; and for internal p-methylols the values must be multiplied by 2.4i.
ticular species. The complete set is shown in Table 111, expressed as a function of a dimensionless time, t* = kl,,Aot. Then, specific rate constants and concentrations in the rate equations are, respectively, relative values with respect to klo (Table 11), and to the initial phenol concentration, A,,. The set of differential equations was numerically solved with a fourth-order RungeKutta method. After each increment it was verified that the relative concentration of phenolic rings was equal to one A+D+E+F+G+H+Z+J+K+L+M+ N + 0 = 1 (1)
Also, the summation of free formaldehyde, methylols and methylene bridges remained constant and equal to the initial formaldehyde concentration B + Z + J + K + L + M + N + 0 + 2 = &/A0 (2) where 2 = (1/2) [D+ E
+ K + L + M + 2(F+ G + N +
0) + 3Hl (3) is the relative concentration of methylene bridges. The evolution of the different species in the reaction may be expressed as a function of the dimensionless time t* or the degree of formaldehyde conversion (pB) PB = rPA (4)
-dA/dt* = A(2.2B t 14C,) -dB/dt* = B(2.2A t D t 1.7E t 0.5iF t 1.2iG) dD/dt*= 12AC1 t 2.41(C2 t 41)- D(B t 2C,) dE/dt*= 2 A C , t J ( C , + 265)- E(1.7B t 13C,) dF/dt* = 2C,(D t 6 E ) + L(C, t 2L) t 2.4K(C2 t 2K)iF(0.5B t C,) dG/dt*= EC, t M ( C , t 24M)- 1.2iG(B t lOC,) dH/dt* = iC,(F + 12G) t iC,(O t 2.4N) dl/dt*= 1.2AB- U(C, t 1.2C2 t 9.61) dJ/dt* = AB - J(13Cl t C, t 525) dK/dt* = 1.2EB t U(C, t 4.81) - K(C, + 2.4C2 t 4.8K) dL/dt* = BD t 12J(C, t 25)- L(C, t C, t 4L) dM/dt* = 0.5EB t J ( C , t ZI)- M(12C, + C, t 48M) diV/dt* = 1.2iGB t C , K - 2.4iC2N dO/dt* = 0.52% t L(C, t 2L) t 12M(C, t 2M)- iOC, C, = 2(J + L t M t io) t 4.8(1 + K t iN) C, = 2(E + J t K t L t iF)t 24(A + E t J t M t iG) t 4(A t D + I )
is the stoichiometric ratio of functionalities, and pAis the degree of conversion of reactive phenolic positions, given by PA = (1/3)(D + E + I + J) + (2/3)(F G K L M) H N 0 (6)
+ + + +
+ + +
Statistics Statistical parameters were generated from the distribution of molecular species. Three particular parameters were calculated: the number average molecular weight, M,, the weight average molecular weight, M,, and the gelation condition. Number Average Molecular Weight. By definition, it is expressed as
M n= (initial mass mass of produced water)/actual number of moles (7) where initial mass = 94Ao
+ 3oB0
mass of water produced by condensation = 18AJ actual number of moles = Ao(B
+ 1 - 2)
(8)
(9) (10)
The values 94, 30, and 18 correspond to the molecular weights of phenol, formaldehyde, and water, respectively. By replacing eq 8 to 10 in eq 7, we get
M n= [94 + 30(Bo/A,) - l8z]/[B
+ 1 - 21
(11)
A useful approximation may be derived if the concentration of methylolated species (I to 0) is neglected. Then, from eq 2 to 6, it follows 2 = (&/Ao)PB
B = (Bo/Ao) (1 - PB)
(12) (13)
M,, = 194 + (&/A,) (30 - 18P~)]/[l (Bo/Ao) (1 - ~ P B ) ] (14)
Weight Average Molecular Weight. In order to calculate the weight average molecular weight, a recursive method will be used. Let us call Y the average weight hanging from a phenolic ring through a methylene bridge. Then
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 3, 1984
Y = weight of a methylene bridge + C (proportion of methylene bridges associated with a particular molecular species) (weight of the molecular species) (15) The weight of a phenolic ring will be taken equal to the molecular weight of phenol (94), implying that hydrogen atoms belonging to the methylene bridge are considered as still pertaining to aromatic rings. Therefore, the weight of the methylene bridge is taken as 12 units. This leads to Y = 12 + (1/22)[(D + E) 94 + 2(F + G) (94 + Y) + 3H(94 + 2Y) + (K + L + M)124 + 2(N + 0) (124 + Y)l (16) or Y = (106 + (15/Z)[K + L + M + 2(N + O ) ] ) / ( l [F + G + N + 0 + 3H]/2) (17) By definition
+
M, = 3 0 ~MwA(l ~ - wB)
(18)
where WB is the free formaldehyde weight fraction, given by W g = 30E/[94 + 30(&j/Ao) - 1 8 4 (19) and MwAis the weight average molecular weight of all molecular species excluding free formaldehyde, calculated as MwA= 94A (D + E)(94 + Y) + (F + G)(94 2Y) H(94 + 3Y) + 124(1+ J) (K+ L + M)(124 Y) ( N + 0)(124 + 2Y) (20)
+
+ + + +
+
Then, from eq 2, 3, and 18 to 20, we get M, = (900E + (94 + 30[(&/Ao) - E] - 182)(94 + 30[(&/Ao) - E - 4 + 2YZ))/(94 + 30(&/Ao) - 182) (21)
-
Gelation Condition. The novolac gels when M, a. This condition is achieved when Y m, i.e., by setting the denominator of eq 17 to zero 3H = (D + E + K + L + M) (22) +
That is to say, the polymer gels when the number of methylene bridges joined t o triply-reacted phenolic rings (3H) equals the number of methylene bridges joined to terminal phenolic rings (D + E + K + L + M).Note that if all the nineteen species shown in Figure 1are considered in the analysis, the general gelation condition becomes H = (1/3)(D E K L M S Tj (23)
+ + + + + +
Then, the solution of rate equations enables us to determine the reaction extent at which the equality given by eq 23, or its simplified form eq 22, is accomplished. In order to prove the reliability of our statistical analysis it is necessary to show that the general gelation condition leads to known particular cases. (i) Equal Reactivity of Functionalities and Absence of Substitution Effects. In this case, the classical Flory-Stockmayer theory (Flory, 1941; Stockmayer, 1943) holds, leading to PAPBlgel = 1 / 2 Since = PA3PB3 D + E f 3 p ~ p B ( 1- PA)^
(24)
K
+L +M
= ~ P A ' P B-( PA) ~ (1- PB)
and
s + T = 3pA3pB(1- PB)'
(25) replacing eq 25 into eq 23 gives the Flory-Stockmayer relationship. (ii) Reactant A Has Two Types of Sites, Le., 1 and 2, of Different Reactivity. There are two sites of type 1 and one of type 2 per A molecule; both functionalities of reactant B have the same reactivity; there are no substitution effects. In this case, Miller and Macosko (1978) have shown that the gel condition is given by (4qlqz +
= 3/r
(26) where r = pB/pA, and ql, q2 are the degree of reactions of sites 1 and 2, respectively. PA is then given by (27) PA = (2/3)qi + (1/3)qz As in the previous case, the relative concentration of each species may be calculated from the degree of conversions of the different sites. This gives
= ql2q@B3
D = q G B ( 1 - q1l2 E= - ql)(l - q2)PB K + L = 4qlqdl - ql)pB(1 - PB) M 2q12PB(1- PB)(1 - 42)
s = 2ql2q9B(1 - PB)' T = 4i2q2(1- PB)~PB
(28) By replacing eq 28 in eq 23 and taking into account the definition of r, eq 26 is obtained. Results and Discussion Reactivity of Internal Sites. Internal sites of the novolac chains are less reactive than their exterior counterparts. Simplified kinetic approaches have taken r(i/e) = i = 0.125 (Drumm and LeBlanc, 1972; Frontini et al., 1982). However, when comparing experimental and predicted molecular weight distributions, it was stated that increasing the i value was necessary to give a better fit (Drummand LeBlanc, 1972). On the other hand, Kumar et al. (1980,1981,1982)reported on the lack of sensitivity of arbitrarily chosen i values on the resulting molecular weight distribution. In order to clarify this question the better i value was adjusted by comparing model predictions to the experimentally obtained weight average molecular weights, M,, for three novolacs studied by Drumm and LeBlanc (1972). Figure 2 shows the obtained theoretical prediction of M, vs. r(i/e), for the three novolacs (characterized by the formaldehyde/phenol molar ratio, Bo/Ao,and the final formaldehyde conversion, p B ) . The points indicate the corresponding experimental M, values, placed at the r(i/e) value which kept the departure from theoretical curves at a minimum. A satisfactory fitting results for r(i/e) = i = Figure 2 also shows that, for Eo/Aoratios typical of the industrial practice, the predicted M, is very sensitive to the reactivity of internal sites. Only for Bo/AoI0.6 the lack of sensitivity shown by Kumar et al. (1980,1981,1982) does hold. Species Distribution. Figure 3 shows the evolution of the predominant species for a novolac prepared with Bo/Ao = 0.815, as a function of the formaldehyde conversion. This was obtained by solving the equations shown
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 3, 1984 373 Table V. Final Concentration of Major Species (PB= 1) for Different B J A , Ratios A D E F G H 0.600 0.145 0.433 0.092 0.292 0.020 0.015 0.815 0.025 0.346 0.033 0.514 0.023 0.056 0.850 0.015 0.315 0.023 0.552 0.021 0.070
BJA,
Table VI. Comparison between Experimental and Predicted M,,Values
1
'
I
j
O
,
,
T
l2
,
*
%;Oe
ps
0.
0.4
06
:
aa
,
095
1
r(l/e)
method GPCa GPCa GPCa PMRa Cryob
Mn
(B,/A,) 0.60 0.815 0.85 0.85 0.80
P B M,(exptl) (eq 14) E , % 0.95 213 221 3.8 0.94 360 370 2.8 0.94 442 417 -5.7 1 711 695 -2.3 1 557 518 -7.0 Drumm and LeBlanc (1972). Borrajo e t al. (1982).
1
Figure 2. Predicted weight average molecular weight as a function of the reactivity ratio of internal to external sites (points are experimental values).
Figure 4. Predicted number average molecular weight as a function of the formaldehyde conversion (dashed lines represent eq 14 and full lines eq 11).
Figure 3. Evolution of predominant species for a novolac prepared with Bo/Ao = 0.815, as a function of the formaldehyde conversion. Table IV. Relative Concentration of Methylolated Species f o r a Novolac Prepared with B , / A , = 0.815
PB 0.233 0.397 0.593 0.776 0.981
I 0.009 0.006 0.003 0.001
-
J K L M N O 0.018 - 0.005 - - 0.012 0.001 0.009 0.001 - 0.007 0.001 0.011 0.001 - 0.001 0.002 - 0.010 - - 0.003 - - 0.001 - - 0.001
in Table 111, with i = Methylolated species are not shown due to their low concentration. It is seen that the novolac chains are mainly composed of bireacted phenolic rings in o and p positions, and terminal units joined to the chains by p positions. Branching takes place at high conversions but the relative amount of trireacted units remains low, even at full formaldehyde conversions. Also, because of the high reactivity of the p position, both for addition and condensation, the concentration of species with free p positions remains relatively low throughout the polymerization. The concentration of methylolated species as a function of the formaldehyde conversion is shown in Table IV. The very low values are the result of the high condensation rates.
Table V shows the change in the distribution of the major species, at fullformaldehyde conversion, for different initial formaldehyde/phenol molar ratios. A rapid increase in branching (H) with Bo/Aomay be noted. On the other hand, the remaining free phenol decreases significantly when increasing Bo/Ao. Although a decrease is actually what is observed in practice, the predicted concentration is somewhat low when compared with experimental results (Borrajo et al., 1982). Number Average Molecular Weight, M,. Figure 4 shows the evolution of the number average molecular weight, M,,as a function of the formaldehyde conversion. Full lines correspond to the values predicted with eq 11, thus taking into account the concentration of methylolated species. The dashed lines represent eq 14,in which the methylolated species had been deleted. The latter is an excellent approximation, as may be seen from the figure. A comparison between predicted and experimental M, values is shown in Table VI. Experimental values determined with several techniques (gel permeation chromatography, proton magnetic resonance and cryoscopy) correspond to different formaldehyde/ phenol molar ratios and formaldehyde conversions. Very good agreement is obtained, proving that the main assumption stated in our model, namely the absence of loops (intramolecular condensation), is a reasonable hypothesis in the acid-catalyzed phenol-formaldehyde polymerizations. Weight Average Molecular Weight and Gelation Condition. The increase in the weight average molecular weight, M,,during the polymerization is shown in Figure
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 23,No. 3, 1984
2oooc
01 0.6
I
I
0.8
I
PB
’
Figure 5. Evolution o f t h e weight average molecular weight as a function of the formaldehyde conversion (points are experimental values).
5. The points are the experimental results obtained by Drumm and LeBlanc (1972) (also plotted in Figure 2). For Bo/Ao= 0.85 there is a rapid increase in M, toward the end of the polymerization, although the novolac does not gel at pB = 1. The rate equations were solved for different Bo/Ao ratios, looking for the accomplishment of the gelation condition (eq 22). For Bo/Ao= 0.90 this condition was attained at full formaldehyde conversion. Thus,the model predicts gelation of the novolac in the polymerization reactor when Bo/Ao1 0.90. However, well before gelation there is a practical limitation associated with the high viscosity attained by the reaction mixture a t the end of polymerization. A practical operating limit is Bo/Ao= 0.85 (Drumm and LeBlanc, 1972). Conclusions A model capable of predicting the distribution of different species and the statistical parameters characterizing the novolac polymerization under strong acid conditions has been presented. The model started from known rate constants for the formation of dimers and extended their validity for the formation of n-mers. Unequal reactivities
and substitution effects are taken into account. The possibility of forming loops (intramolecular cycles) is neglected. The reactivity of an internal site was shown to be 1/3 of the reactivity of an external site. This result was obtained by fitting experimental values of weight average molecular weights with model predictions, keeping the reactivity ratio of internal to external sites, r ( i / e ) ,as an adjustable parameter. The novolac chain is mainly composed of bireacted phenolic rings in o and p positions and terminal units with free o and 0’positions. The concentration of methylolated species is very low throughout the polymerization; branching begins to be significant for Bo/Ao> 0.8, at high formaldehyde conversions. The number average molecular weight could be expressed as a simple function of the initial formaldehyde/phenol ratio, Bo/Ao, and the formaldehyde conversion, pB (eq 14). Very good agreement with experimental results was shown, reassuring the validity of the absence-of-loops approximation in phenol-formaldehyde polymerizations. Gelation was predicted for an initial formaldehyde/ phenol molar ratio, Bo/Ao = 0.90, at full formaldehyde conversion. A similar analysis may be carried out for novolacs prepared at other conditions (Le., favoring o,o’ substitution), or other polymerizations showing unequal reactivities and substitution effects, provided that the necessary kinetic information is available. Acknowledgment The authors wish to acknowledge a scholarship given to M.I.A. by the Consejo Nacional de Investigaciones Cientificas y TBcnicas, Argentina. Registry No. (Phenol).(formaldehyde)(copolymer),9003-35-4. Literature Cited Borrajo, J.; Aranguren, M. I.; Williams, R. J. J. f o / y m r 1982, 23,263. Drumm, M. F.;LeBlanc, J. R. Klnet. Mech. fo/ym. 1972, 3,157. Flory, P. J. J. Am. Chem. SOC. 1941, 63,3083, 3097. Frontini, P. M.; Cuadrado, T. R.; Williams, R. J. J. f o / y m r 1982, 23,267. Kumar, A.; Kulshreshtha, A. K.; Gupta, S. K. fo/ymer 1980, 27,317. Kumar, A.; Gupta, S.K.; Phuken, U. K. fo/ym. Eng. Sci. 1981, 27,1218. Kumar, A.; Phukan, U. K.; Kulshreshtha, A. K.; Gupta, S. K. fo/ymer 1982, 23,215. Miller, D. R.; Macosko, C. W. Macromolecules 1978, 11, 656. Stockmayer, W. H. J. Chem. fhys. 1943, 1 7 , 45.
Receiued for reuiew October 14, 1983 Accepted F e b r u a r y 10, 1984
