MAY, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
than when grown during seasons of nearly normal rainfall. Sulfur absorption is not reduced during dry seasons, so it is concluded that there is little relation between the absorption of selenium and sulfur by plants. The soil from the plot where sulfur was applied binds selenium as selenite or selenate so that it cannot be completely electrodialyzed from a soil suspension.
Acknowledgment The authors gratefully acknowledge the valuable assistance given by Morris Rhian and Robert Burris in the analysis of the namplea. Literature Cited (1) pnsoc. Official Agr. Chem., Official and Tentative Methods of Anrtlysis, 2nd ed., 1925. (2) 1; qth, 0. A., Eppson, H. F., andGilbert, C. S., Univ. Wyo. Agr. *xpt. Sta., Bull. 206 (1935). (3) BJ em, H. G., U. S. Dept. Agr., Tech. Bull. 482 (1935). (4) Goldschmidt, V. M., and Strock, L. W., Nachr. Ges. Wiss. GCittingen,Math.-phgsik. Klasse I , 123,1935.
595
Hurd-Karrer, A. M., J . Agr. Research, 49, 343-57 (1934). Ibid., 50,413-27 (1935). Hurd-Karrer, A. M., and Kennedy, M. H., Ibid., 52, 9 3 3 4 2 (1936). Knight, H. G., S. Assoc. Oflcial Agr. Chem., 18, 103-8 (1935). Levine, V. E., Am. J. Botany, 12,82-90 (1925). Loddesol, Aasulv, J . Am. SOC.Agron., 24, 74-81 (1931). MacIntire, W. H., J . Assoc. Oficial Agr. Chem., is, 22-33 (1936). Moxon, A. L., and Franke, K. W., IND.ENO.CHEM.,27, 77-81 (1935). Painter, E. P., and Franke, X. W., J . Biol. Chem., 111, 643-51 (1935). Parr Instrument Co., Booklet 113 (March, 1934). Robinson, W. O., Dudley, H. C., Williams, K. T., and Byers. H. G . ,IND. ENG. CHEM.,Anal. Ed., 6,274-6 (1934). Williams, K. T., and Byers, H. G., IND.ENG.CHEM.,28,912-14 (1936).
RECEIVED October 28, 1936. Published with the permission of t h e Director of the South Dakota. Agricultural Experiment Station as communication No. 24 from the Experiment Station Chemistry Department. This paper io Part XVII of a series on “A New Toxioant Occurring Naturally in Certain
Samples of Plant Foodstuffs.”
Mechanism of Thermal Polymerization and Polycondensation Y p’
#Y
H. DOSTAL, H. MARK, AND R. RAFF I. Chemisches Universitats-Institut, Vienna, Austria
EVERAL polymerization and condensation processes have been investigated in the last few years. The products of these processes have some unusual and useful properties. The writers, therefore, began some years ago to measure the kinetics of characteristic polymerization and condensation reactions (6). In this paper only thermal polymerization processes are discussed, and neither photopolymerization nor polymerization under the influence of electric discharges will be taken into account.
The reaction constant of chain growth is, by special time unit, made equal to 1. The corresponding reaction constant for formation of nuclei is called a, which, independent of the time unit, can be regarded as the ratio between both reaction velocities. In every case of polymerization a < 1. By the equation dz
Mdt
(1)
a second time scale, z (with a variable unit l),is introduced. In the first paper (6) z was called Eigenzeit. Now it is possible to show that
Polymerization without Deactivation
m
M,
= ae-*
5
Even when there is no deactivation reaction (that is, when P =n the reaction chains are not broken by special chemical proc(where p = summation index) esses), a definite chain-length distribution occurs, when a given amount of the monomer unif the nuclei are formed monomolecudergoes polymerization (6). . This is larly, and due to the fact that during the polyA survey of the writers’ m e r i z a t i o n process new nuclei are work on the kinetics of some formed and competition occurs becharacteristic polymerizatween the growing chains and the nuclei which are formed as long as tion and condensation reacif the nuclei are formed bimolecumonomeric substance is present. larly. tions is given here so that Therefore this case will be considered From this we can derive for both their results may be at the first as the most simple and fundacases the total amount of monomeric disposal of American and mental one. substance which is bound in chains. English investigators. The In the following formulas the conIn the monomolecular case: centration of molecules a t the time formulas derived to date on aza t = 0 is used as unity. The concen#=as+(3) polymerization and con2 tration of chain molecules with ?a densation processes are also In the bimolecular case: members is represented by M,, and summarized. that of inactive monomer molecules s = 2az az* - aZz4 (of the starting substance) by M . 2 24 (3A) ~
~~
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
596
The amount of unpolymerized monomeric material is given monomolecularly by (4)
and bimonomolecularly by M
= 1
-2
az2
n ~ -2
+ a2z4 24
(4-4)
In these formulas we consider the ratio a as independent of the amount of reaction. In an earlier paper (6) the authors showed that, starting with these formulas, M,, M , and S are derived as fiinctions of time, so that they give a good idea of the whole polymerization process and a possible convenient means of comparing the theoretical results with the experimental measurements. Figure 1 shows a typical case of such an idealized polymerization process. The velocity of the reaction is given by dS/dt. The maximum velocity time can be derived from the condition: d2S/dtZ = 0
The period before the maximum may be called the "induction of the reaction." In the monomolecular case,
VOL. 29, NO. 5
where k and a are constants, or by a similar law. [A reason for refusing (6) would be the suggestion that kj, for very l a r g e values of j, has a c o n s t a n t value greater than zero.] In the case that Equation 5 holds and symbol a belongs to the initial chaing r o w i n g velocity, the quantity of polymer as F I Q U R1.~ POLYMBRIZATION function of time z is apAS A FUNCTION OF TIMEWITHproximately given by OUT DEACTIVATION OR A VARIABLE STERIC FACTOR Nuclei are thought t o be "3rrned mono moleoularly.
instead of S
=
azz 3, where x is the integration variable.
In the same way we can calculate other quantities which are interesting and characteristic of the polymerization process. The formulas show that a shortening of the induction period may occur which would explain the small experimental values of induction.
Polymerization with Deactivation
INFLUENCE OF DEACTIVATION ON LENGTHOF INDUCTION
PERIOD.As we consider now only the beginning of the reThis means that the induction period ends when about 33 per cent of the substance has polymerized. In the bimolecular case,
Here the end of the induction period is reached when 29.3 per cent has polymerized. These formulas hold when deactivation is zero or negligible, and when the ratio a is independent of the chain length. Experiments soon showed that the induction period is nearly always much shorter than these formulas demand. In the case of pure styrene it ends when 5 per cent of the material has polymerized; in the case of indene no induction period could be detected (9). It was therefore necessary to improve the formulas and to find reasons for the shortened induction period. In a series of theoretical investigations several different possibilities were taken into account.
Polymerization without Deactivation but with Decreasing Ratio a Considering the well-known work of Evans and Polanyi (IO), Eyring (II), Bawn (I), and others, it seems reasonable to assume that the chain-formation constant will decrease with increasing length of the chain by the rate of a "steric factor." Without discussing the reason for this behavior, we may consider it as a well-known fact and try to combine this effect with the formulas on the polymerization reactions. When a chain with j members grows into a chain with ( j 1) members by the bimolecular step,
+
Hj f H-+ H j + l
action, we may write
&Wd;
and therefore must not distinguish between the Eigenzeit and the normal time scale. We assume that the deactivation reaction constant is uniform and may be called 2. It is not important whether deactivation is spontaneous, caused by collision with monomer, or due to any other effect. We now consider the chains whose nuclei were formed in the time interval between z = h and z = h dh; their quantity is adh. The rate of deactivation of these chains is given by a factor e-z(z--h),because ( z h) is the "age" of thechains. At the time z =i-, therefore, we still have [adhe-z(r--h)]active chains. During the time from c to (1 d{) the deactivation of a part ldc of these occurs:
+
-
+
(5)
(7)
[udhe-UI - h ) ]Ed!:
The growth, which is prevented, is the cause of a defect in the mass of the polymerized amount of the substance, measured, in these relative units, by formula 7, multiplied by (e By integration from .( = h to 1 = z, the whole defect in mass for this class of chains of equal age is given by
c).
dA =~ ( z h)dh
-
dh [l - e - l ( z - h ) ]
(8)
Withozt deactivation, their mass would be dS' =
U(Z
- h)dh
and hence their actual mass is d S = dS'
the reaction constant kj for this process decreases with increasing j by a law which may (probably) be given by
(6)
z = t
-dA =
-ad h [l 1
- e-lM-h)]
(9)
The whole amount of polymerized substance is found from Equation 9 by the summation over chains of all ages and is represented by Equation 10.
1
INDUSTRIAL AND ENGINEERING CHEMISTRY
MAY, 1937
597
chains is still active when their age is h. As the age, in z units, is identical with the degree of polymerization, n,the distribution of chain length is given by e--km
and from this we derive
The expression is applicable for estimating the degree of curvature of the S-t curve because z = t . The end of the induction period is reached a t the point where the curvature is small in comparison to its initial value-that is, ue-lz
(14)
for chains of equal age. I n the case that the rate of deactivation is so great that the chains are active only during a relatively short time, and the deactivation is caused only
< a or e+ < 1
This point is reached for about Zz = 3, as e-a = 0.0498. Therefore the approximate end of the induction period is given by 20
=
-31 0
5
Substituting this value in Equation 10,
to I S -+t TIME IN HOURS
POLYMERIZATION OF STYRENE,EXPERIMENTALLY AND THEORETICALLY FIGURE3.
This formula holds, of course, only if b is so large that SO becomes small in comparison to 1; otherwise the equation proposed in formula 6 would not be right. If we have, from experimental values, a plot of S as a function of time, we can find the value SO;then we have a relation between a and 6. If we use a general time unit (days, for instance), we have, instead of a and b, three reaction constants kl, kz, and IC3 for formation of nuclei, chain growth, and chain deactivation. Then
by-collisions with monomer, the velocity of deactivation remains proportional for the whole the distribution of size in the whole system of chains is given by expression 14. The mean chain length is then represented by
-
Lmne-"ddn
"I
n e+
which leads from Equation 12 to
As experiments show that in the present cases 80 is not greater than 1/20, the rate of deactivation of every polymerization process is considerable. The effects of shortening the induction period by a steric factor and by deactivation are mathematically similar, and may in actual cases be superposed. INFLUENCE OF DEACTIVATION ON CHAINLENGTH. When we consider chains of equal age, the portion e - l h of these
(15)
dn
This result is but little altered in the case where the steric factor is dependent on chain length. The writers also considered the case where the chains may react with one another and where isomerization and chain growth may be influenced by catalytic processes in earlier publications (4, 5 ) .
Polycondensation Reactions I n the case of polycondensation there is no essential difference between the velocity of formation of nuclei and chain growth. This is the reason why the mathematical treatment must be quite different. The best approach to the solution of the problem is given by a formula of P. J. Flory (5) : II, =
1MOL STYRENE
zp-1
(1
- PI'
(16)
In this formula p is called the "extent of reaction," which means the number of linkages in all chains of the whole system, divided by the number of links in the whole system. m
IT, is the fraction of units present in 2-mers. Therefore Z IT,= 1 1
must hold; this agrees with Equation 16. The dependence of p on time is given by (17)
a0 loo TIMEIN HOURS
10l?0?0w5060
m
because Z (IL,/z) is a measure for the number of molecules
IW,
FIGURE2 . POLYMERIZATION OF STYRENE, PURE AND TOLUENE SOLVTION
1
IN
of ali sizes, and the formation of new linkages is a bimolecular reaction. Of course, a is a reaction constant; the factor
INDUSTRIAL AND ENGINEERING CHEMISTRY
598
FIQURE4. POLYMERIZATION OF INDENE IN TOLUENE SOLUTION '/a is due to the fact that every chain is counted twice in the formula. From Equations 16 and 17 we obtain
and the relative quantity of condensed matter is given by m
11 = Z I I , = 1 2
- rI1
= 1
- (1
- p)2
Where we have a series of products obtained from two kinds of monomer (p-cresol and formaldehyde, for instance), and where only the chains with ends of one type of substance (for example, p-cresol) have stability, Equation 17 must be altered by a factor ( q - p ) , in which the initial quantity of the other substance is measured by q . For (I = 1 (equimolecular system), this leads to
instead of (18) and II=l-(l-p)Z=-
at
1
+ at
(19)
Experiments o n Polymerization The quantitative investigation of polymerization and condensation reactions is not easy. Often catalytic influences, which are difficult to avoid or to keep constant, diminish the reproducibility of the experiments considerably. We find I . ,
0
OBSERVED VALUES.
- THEORETICAL CURVE.
TIME IN MINUTES
FIGGRE5. POLYMERIZATION OF INDENE, EXPERIMENTALLY AND THEORETICALLY
VOL. 29, NO. 5
in the literature several preliminary investigations of the kinetics but no systematic study (14). Therefore experiments were started in this direction, and hydrocarbons especially were found to be relatively insensitive to disturbing influences. Hence styrene (12) and indene (9) were chosen as polymerizing materials, and later vinyl acetate and acrylic ester (2) were included. The velocity of polymerization of styrene and indene is changed by the presence of oxygen, but the material of the wall of the vessel in which the reaction takes place has almost no effect on the polymerization of hydrocarbons. Therefore sufficientlyreproducible values would be obtained under glass in an atmosphere of nitrogen ar in a vacuum. Much more complicated are the conditions with vinyl acetate and acrylic ester, where reproducible results cannot be obtained in glass vessels. It was necessary to work with nickel tubes to obtain fairly reproducible results ( 2 ) . The first problem was to work out the total amount of polymerized material as a function of the time of polymerization. Experiments were carried out with the materials mentioned, in solutions a t different concentrations, in different solvents, and at different temperatures. The reactants were placed in the reaction vessel; the reaction was started and then interrupted after a certain period; the remaining monomeric material was distilled over, and the polymerized matter determined. In several cases the mixture was a n a l y z e d b y means of its refractive index. To prove that during p o 1ym e r i z a t i on very reactive nuclei are present, s u b s t a n c e s w e r e m a d e t o polymerize which do not ordinarily react under the actual 3 6 9 12 15 1& 21
vinyl acetate to polyTHEORETICALLY m e r i z e together with polymerizing styrene, although neither molecule polymerizes alone under the experimental conditions for these two cases. The best results were obtained in the polymerization of styrene. Figure 2 gives the polymerization of styrene in toluene solution at 100" C. at different concentrations. The polymerization curve for the pure substance a t 100" C. is also given for comparison. The experiments in dilute solution give the best opportunity to apply the formulas developed in the preceding paragraphs. From the curve for 1 mole of styrene in 16 moles of toluene, the ratio between the velocities of formation of nuclei and growing of chains was tried and found to be about a = 2 X lo+. The velocity of formation of nuclei has a value of 8 X and the velocity of growing of chains a value of about four units (involving both moles and hours). From the effect of temperature, some preliminary d u e s were derived for the energy of activation for the process of nuclei formation. This energy must lie between 20,000 and 40,000 calories per mole. The curve in Figure 3, which follows the experimental points with good accuracy, is calculated from Equation 10. The close agreement shows that in the case of styrene the breaking of the chains can be seen in the shortening of the induction period, although the induction is still visible. Other conditions are met in the case of indene. In this case polymerization takes place a t much higher temperature, and the average chain length of the polymerized material is remarkably shorter. This may be due to the fact that the
MAY, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
breaking of the chains is much more important a t higher temperatures. But the higher temperature is necessary to activate the double bond of the monomeric substance. We can say, therefore, that indene lies between styrene and ethylone. I n the latter case the activation of the double bond needs such high temperatures that the chain breaking becomes very rapid so that we do not find conditions under which a true polymerization of ethylene takes place. Figure 4 shows the polymerization of indene in toluene solution (at 200" C.). Figure 5 gives a comparison between the experimental values (small circles) and the calculated theoretical curve in the case of indene polymerization in toluene solution a t 200" C. (0.5 mole). The measurements lead to the following constants: 0.92 x 10-4
Velocity of formation of nuclei Sterio factor of the reaction
5.10-10
The following table gives some quantitative results on the polymerization of vinyl acetate in glass tubes under high vacuum:
