80
R. F. BOYER
A STATISTICAL THEORY OF DISCOLORATION FOR HALOGENCONTAIXING POLYMERS AND COPOLYMERS1 R . F. BOYER Physical Research Laboratory, T h e Dow Chemzcal Company, Midland, Michigan Recezved August 8 , 1946 1P;TRODUCTION
The tendency of halogen-containing polymers to lose a part of their halogen through the catalytic action of light, heat, or chemical reagents has long been recognized. The changes in color and mechanical properties accompanying this degradation reaction were almost sufficient in the early days to militate against the use of such polymers. However, technological advances resulting from better control of the purity of raw materials, improved techniques of fabrication, and the employment of special light- and heat-stabilizing agents have so improved the situation that this problem is now mainly one of academic interest (28). And in proportion, as the practical aspects of the problem were solved, the academic side of the problem received more and more emphasis. In brief, the systematic degradation of halogenated polymers with special reagents has been used to furnish important clues about the structures of high polymers. This field of inquiry is best exemplified by the results of Marvel and coworkers (26,27),who have studied the effects of zinc on polyvinyl chloride and vinyl chloridevinyl acetate copolymers. This experimental work, in conjunction with the theoretical conclusions of Flory (12),Wall (45), and Simha (36), has established, among other things, that polyvinyl chloride possesses a head-to-tail structure. While this technique has not been too successful with copolymers (26), it does constitute an important tool for studying high polymers in general. Other efforts in the same direction include Staudinger and Feisst’s treatment of polyvinylidene chloride with phosphorus and hydrogen iodide in an unsuccessful attempt to obtain a pure, long-chain, soluble, hydrocarbon residue which would offer some clue as to the structure of the original polymer (41). The relationship between formation of hydrogen chloride and electrical conductivity, as well as color in polyvinyl chloride, was reported by Fuoss (15), while Lichtenberger and Naftali (24) described the results of systematic attacks on chlorinated rubber by pyridine. Sumerous other references to the problem have appeared from time to time (33, 40). Ironically enough, this tendency to lose the halogen acids has even been used to advantage. Thus, Dinsmore (8) has shown how vinylidene chloride polymers can be vulcanized, presumably by virtue of the unsaturated system formed on loss of hydrogen chloride. Even prior to this, Ostromysslenskii (34) had prepared rubber-like products by the action of zinc on polyvinyl halides. 1 Presented a t the Twentieth Kational Colloid Symposium, which was held at Madison, Wisconsin, May 28-29, 1046.
DISCOLORATION OF HALOGEN-CONTAINING POLYMERS
81
A more recent ingenious application of degradation has been made by Land and Rogers (22), who found that dehydration of oriented polyvinyl alcohol films caused a slight darkening and the onset of a strong positive dichroism, that is, an ability to polarize light. They postulated the existence of oriented polyene groups, ( 4 H = C H - ) , , to account for this selective absorption of light in a given direction. The present report attempts to extend the theory of such effects by deriving an explicit connection between loss of hydrogen chloride and formation of color in polyvinylidene chloride and its copolymen. The theory should be applicable to other halogen-containing polymers if suitable account is taken of their physical and chemical characteristics. Similarly, it should apply to polyvinyl alcohol which can lose water, and to polyvinyl acetate which can lose acetic acid. Our work is based on the suggestion by Marvel, Sample, and Roy (27) that color formation is the result of polyene structures of the type (-CH=CH-), I where n is an integer, mphich develops on loss of hydrogen chloride. STATISTICAL TREATMENT OF LOSS OF HYDROGEN CHLORIDE
Polyvinylidene chloride might be pictured to have a chain structure of the type:
Hz Clz
Hz Clz
/
c-c
\
c-c
/
c-c
\
c-c
/
Hz Clz
Hz Clz
I1 as indicated from x-ray diffraction studies by Frevel (13), whose principal conclusions have been given by R R i a r d t (35). Because of the disposition of the hydrogen and chlorine atoms, hydrogen chloride will tend to be lost from a monomer unit, and not between two adjacent monomer units. Moreover, after one hydrogen chloride molecule has been removed from a monomer unit, the remaining chlorine atom is stabilized by the double bond (ll), and there should be little tendency for the same monomer to lose a second molecule of hydrogen chloride. Thus a polyvinylidene chloride molecule which has lost hydrogen chloride through exposure to light, heat, or chemical reagents might have a local structure such as:
H CI
/
c=c
\
H
c-c /
C1
c=c
Hz Clz
111
\
c=c /
H CI
82
R. F. BOYER
If this hydrogen chloride is lost a t random along the length of the chain, there will result structures of the type: (--CH=CCl-), IV where n may a w m e integral values. In fact, there should be a distribution of n values given by probability laws and depending on the fraction, p , of all monomer units which have lost a molecule of hydrogen chloride. Briefly, assuming an infinitely long polymer chain with hydrogen chloride lost a t random, the probability that a given unsaturated system is formed consisting of n double bonds in conjugation is: Pn(P)
=
(1 - P W
(1)
This equation follows at once from the theory of probability for successive events (3). n double bonds, each of probability p , must be formed in successive monomer units along the chain, while at each end of this conjugated system is a monomer which has not lost a hydrogen chloride molecule, and for which the probability is (1 - p ) . p is equivalent to the extent of the degradation reaction; thus, if 40 per cent of the original monomers have lost hydrogen chloride, then the probability that any monomer selected at random in the polymer chain is unsaturated is 0.4. Incidentally, the assumption of a finite molecular weight, which would be around 20,OOO for the polymers under consideration, will not greatly alter the results. The exact equation which accounts for chain length will be given later as equation 7a. Figure 1 summarizes some of the pertinent features of equation 1 by plotting the percentage of all double bonds which reside in structures of complexity n as a function of the extent of degradation. In the beginning most of the double bonds are isolated, and it is not until an extensive degree of degradation has occurred that complex double-bond systems occur with appreciable frequency. The probable nature of the double-bond arrangements having been described as a function of the known loss of hydrogen chloride, the next problem is to correlate these structures with color or light absorption. The connection between structure and color in organic compounds has been summarized in excellent reviews by Brode (4) and Lewis and Calvin (23). In particular, both authors treat in detail the extensive and pertinent series of measurements carried out by Hausser, Kuhn, and coworkers on a variety of polyene compounds, R(-C=C-),R’. Of greatest interest are the diphenylpolyenes, which have been studied out t o n = 7 (17). Lewis and Calvin have shown that for these compounds, the square of the wave length of the first absorption maximum increases linearly with n, while the intensity of absorption (as measured by the maximum extinction coefficient) is also a linear function of n. Still other examples of linear conjugated systems are well known; 0-carotene, for example, with its vivid yellow color, has eleven double bonds in conjugation. Sticher
DISCOLORATION OF HALOGEN-CONTAINING POLYMERS
83
and Piper (42) have polymerized phenylacetylene to obtain reddish colored polymers. Tuttle and Jacobs (44) have prepared polymers of phenoxyacetylene possessing a red color with an absorption maximum at 4200 A. They believe this product to be a polyene, since it developed a characteristic blue color.lin the presence of antimony trichloride.
AMONG T H E VARIOUS CONJUGATED
00
P L A T E 0 DdUBLE BONOS,
I
60
6-1 I
I \
20
0
0
20
40
60
[PERCENT OEGRAOATION
FIG.1. Distribution of double bonds among the various conjugated species, (-CH= CH-),, for random loss of hydrogen chloride. TESTISG THE THEORY
Knowing the complexity of double-bond systems which might be expected in a degraded polymer, and knon-ing the general light-absorption characteristics of such polyenes, it should be possible to test the theory. With this end in mind, the following simple experiment was carried out. h vinylidene chloride12 per cent vinyl chloride copolymer was refluxed for 8 hr. in dioxane at atmospheric pressure in the presence of an excess of zinc powder. The zinc had first been treated with hydrochloric acid to remove impurities ( 2 7 ) ,and then washed with TTater and dioxafie. The zinc exerted a catalytic action in removing hydrogen chloride from the polymer, and the boiling solution gradually acquired a yellow color. After 8 hr. the solution was filtered and diluted with an equal volume of water to precipitate the polymer. The dioxane-water mixture was colorless but slightly hazy. The polymer was washed with methanol and
84
R . F. BOYER
acetone. The dried degraded polymer, which now had a brownish color, was redissolved in dioxane to give a 1 per cent solution. Incidentally, this degraded polymer was much more soluble than the original material. The light-absorption curve of this solution for a thickness of 9.5 mm. is plotted in figure 2. The absorption curve is extremely broad and relatively free from any fine details.
3000
€
30
FIG.2. The curve marked p = 0.1 was calculated for a 10 per cent random loss of hydrogen chloride; the curve marked p = 0.05 assumes a 5 per cent non-random loss of hydrogen chloride. c greater than unity implies a preferential building up of long conjugated systems.
This is what might be expected if the absorption resulted not from a single color body but from the superimposed effects of many types of absorbers. The polymer showed chlorine analyses of 71.18 per cent and 69.58 per cent before and after degradation, a result which indicated that the zinc treatment had removed hydrogen chloride from approximately 10 per cent of the monomers. Several words of explanation might be in order at this point concerning the choice of experimental conditions. Marvel, Sample, and Roy (27) had shown
DISCOLORATION OF HALOGES-COSTAIKIXG POLYMERS
85
that the effect of zinc on polyvinyl chloride is to remove chlorine atoms in pairs, with the consequent formation of cyclopropane rings along the polymer chain. Marvel stated that no color developed in the presence of zinc (25). However, on treatment of their polymer with caustic, a reddish brown polymer was formed (27). This action of zinc is what might be expected from the known x-ray structure of polyvinyl chloride (14). H C
H C
v With polyvinylidene chloride, as given by formula 11, it is apparent that this same type of action is not very probable. Thus, the fact that zinc promotes removal of hydrogen chloride from polyvinylidene chloride is at least in agreement with Frevel’s structure. The choice of a vinylidene chloride copolymer was dictated by the following considerations: Melt viscosity studies by McIntire (29) had indicated that polyvinylidene chloride and its copolymers with small amounts of vinyl chloride behaved as linear polymers, whereas polyvinyl chloride seemed to be highly branched. The 12 per cent vinyl chloride copolymer used here was chosen then because it mas believed to be a linear polymer and because it was soluble in dioxane at its boiling point. Pairs of vinyl chloride units along the copolymer chain should be relatively infrequent, and one would not expect much action of the type that occurs between zinc and polyvinyl chloride. It should be stated that measurements of bromine absorption on the degraded polymer indicated that roughly 1 per cent of hydrogen chloride had been lost. Infrared examination of the degraded polymer did not furnish any conclusive results about the amount of unsaturation, although it did reveal considerable C 4 . Assuming that p in equation 1 is 0.1, values of P, 11-ere calculated. The concentration of polymer in the solution measured for light absorption was 10 g. per liter, or approximately 10/90 base moles per liter. The concentration in moles per liter of a conjugated material of complexity n would therefore be lop,/ 90. This value can then be substituted in the expression I = I o 10-eCd 2 30 (2) where c is the concentration in moles per liter, d is the cell thickness, and e is the molar extinction coefficient of the diphenylpolyenes as given by Hausser, Kuhn, and Smakula (17). The calculated optical density at any wave length is:
D A= log,, I o / l =
5 0.10&,Pn n=l
(3)
where the summation includes all polyenes which absorb at that wave length. In this manner the theoretical curve for 10 per cent degradation as shown in
86
R. F. BOYER
figure 2 (with u = 1) was obtained. The general agreement with the observed absorption curveis not too good. In general, theory predicts too much absorption at the shorter IYave lengths, and not enough at the longer wave lengths. There are several principal difficulties with the theory thus far. In the first place, the diphenylpolyenes are likely not good models to use for light absorption. They have terminal phenyl groups which are lacking in the polymer. This would make the agreement even poorer, although our degraded polymer had C=O groups xhich might compensate to some extent for the lack of phenyl
cI. mol. / I i t e r
2000
2400
2800
3200
3600
FIG.3. Light-absorption curves on unsaturated compounds corresponding to the units formed in degraded vinyl chloride and vinylidene chloride polymers and copolymers.
groups. Actually, Kuhn and Grundmann (21) have prepared polyenes of n = 4 and 6 with terminal methyl groups. Such materials absorb in approximately the same spectral region but have smaller extinction coefficients than the corresponding diphenylpolyenes. Thus, the polyene chain itself is apparently much more important than the terminal group when n is large. An even more important difference is that our degraded polymer has chlorine groups spaced regularly along the polyene chains. It might be expected that these chlorine atoms would shift the absorption curve to longer wave lengths (6).
DISCOLORATIOS O F HALOGES-COSTAINING POLYMERS
87
Figure 3, for example, compares the light-absorption characteristics of ethylene (39), vinyl chloride,*butadiene,* and 2-chlorob~tadiene.~Chlorine substitution causes both a shift ton-ard longer wave length and a more intense absorption. Walsh (46), in commenting on the spectrum of vinyl chloride, points out that its ionization limit and electronic levels are at longer wave lengths than for ethylene, despite the high electronegativity of chlorine. His proposed explanation is based on the resonance occurring between the ?r electrons of the C - C double bond and the non-bonding p / r lone-pair electrons on the chlorine atoms. The spectra of the cis- and trans-dichloro-, dibromo-, and diiodoethylenes (18) show a progressive broadening ton-ard longer wave lengths as the weight of the substituent atom increases, even though the position and height of the maxima are roughly the same. Moreover, the various polyene systems in a single polymer chain do not exist as separate molecules, and therefore will have some inductive effect on each other. Brode and Tryon have found that the absorption spectra of non-conjugated, unsaturated fatty acids vary with the number of double bonds present ( 5 ) . Jeffrey (19) has noted from x-ray studies that the single bond midway between the two double bonds in geranylamine hydrochloride is considerably shorter than a normal single bond, and that it behaves as if partly conjugated with the other two double bonds in the molecule. Pertinent ultraviolet-absorption studies have been made by Bateman and Koch (2). Another aspect of this problem is the influence of isomeric structure on the light absorption. Mulliken (32) has calculated, for example, that a polyene in its most elongated form (trans, trans, trans), will shorn greater absorption than the same chain in a more cis-like form. I t is not known, of course, just what shape such partially degraded polymers of the type me are discussing here mould assume, although there would likely be a mixture of isomers present. The coexistence of many values of n and the possibility of mixed isomers for each value of n probably account for the complete lack of detail in the absorption curves of degraded polymers. There is one other possibility, perhaps even more important than any thus far considered,-namely, that the loss of hydrogen chloride along the chain is not completely random. Drake suggested (9) that once a double bond forms anywhere along the chain, a structure of the allyl chloride type results:
I
H C1 H C11 H -C+C-C=c-c-c H j C1 jH
--
C1 C1
VI
'
The light-absorption data on vinyl chloride and butadiene were obtained from L. G. Reinhardt, Spectroscopy Division, The Dow Chemical Company. * The light-absorption curve on 2-chlorobutadiene was furnished through the courtesy of Dr. J. B. Iiichols, Experimental Station, E . I. du Pont de Iiemours & Co., Wilmington, Delaware.
88
R. F. BOYER
The chlorine atom of allyl chloride is quite labile because of the inductive effect of the double bond. Conant, Kirner, and Hussey reported, for example, that in a reaction with sodium iodide, allyl chloride was seventy-nine times more reactive than n-propyl chloride (7). While the structure pictured above is complicated by extra chlorine atoms, it might be anticipated that an adjacent double bond would form more quickly than would an isolated bond. The theory for such a non-random loss of hydrogen chloride follows: 50 0-= I
40 -
P e r c e n t of Toto1 N u m b e r of Double 8 o n d s Residinp in Structures of C o m p l e x i t y , __ R , f o r Non R a n d o m Loss
of HCI
-
I
FIG.4. Distribution of conjugated systems for 20 per cent loss of hydrogen chloride with increasing degrees of departure from random 1055 of hydrogen chloride (increasing values of u ) .
If u is the relative reactivity of an adjacent hydrogen chloride molecule, so that u p is the probability of forming a double bond in conjugation to an existing double bond, then the probability, P n ( p , a ) , of obtaining ri double bonds in conjugation is: Pn(p,.) = [(I -
oP)2/Ul(UP)"
(4)
89
DISCOLORATIOS O F HALOGEN-CONTAINING POLYMERS
Actually, this inductive effect is unidirectional but the net result is that a conjugated system would tend to propagate itself at the expense of isolated double bonds. Figure 4 illustrates calculations based on equation 4,when p is 0.2 and u assumes various values. I t is readily apparent that long conjugated systems can form quite readily. Figure 5 is a plot of the number-average value of 12 as a function of the extent of reaction, p , for several values of u. This number
1
1 Extent
of Reaction, p
0.5
0.6
.7
.8 .9
0
b
FIG.5 . Number-average length of conjugated systems as a function of the fraction of available hydrogen chloride lost for several values of C .
average, n, is an expression of the complexity of the conjugated double-bond systems, and is given by it = l/ln+ ( u p ) (5) Color calculations based on equation 4 for p = 0.05 and u = 6 are shown in figure 2. For this case we included in the calculations an assumed light-absorption curve for diphenylpolyene corresponding to n = 8. A somewhat similar light-absorption curve would appear in figure 2 for p = 0.01, u = 50. NO special significance other than that of curve fitting can be attached to these
90
R. F. BOYER
latter two results. One reason why the calculated absorption curves end abruptly at 5200 A. is the lack of absorption data on the diphenylpolyenes for n greater than 7. Kuhn (20)reports absorption maxima at 5300, 4930, and 4620 A. for the n = 11 diphenylpolyene, but does not give an absorption curve. He also reports n = 15 with an absorption maximum at 5700 A., which might account for the observed absorption of figure 2 out to 6000 A. Positional isomerization of double bonds is another reaction which can increase the degree of conjugation. Isolated double bonds along the chain would conceivably migrate and either form a conjugated system or extend an existing one. Such reactions usually require catalytic conditions (38), but might proceed under ultraviolet light. This predilection for isomerization might cause the hydrogen chloride on a monomer adjacent to an existing double bond to be more readily removed. Any such isomerization tendency would increase the average length of the polyene systems. It would act in both directions along the chain, whereas the allyl chloride effect should be unidirectional. Asinger (l), incidentally, recommends the use of silver stearate for cleaving halogen acids from alkyl halides of high molecular weight without shifting of the double bond. In the case of exposure to light, it will be precisely those regions of the chain which have already developed unsaturation and conjugation that will absorb radiant energy most strongly and over a progressively widening spectral band. This localization of absorbed energy may then promote unsaturation in adjacent monomers, again promoting the formation of long conjugated systems. Thus, in concluding this section, one can say that probability theory coupled with the known absorption spectra of long conjugated polyene compounds can account for the general nature of color formation in degraded polyvinylidene chloride. Chemical and isomeric differences between the studied polyenes and the degraded polymers, inductive effects of one conjugated system upon another one along the same polymer chain, and the influence of unsaturation in promoting loss of hydrogen chloride from an adjacent monomer unit (allyl chloride effect) are all unknown factors. These three factors acting concurrently should serve to extend the calculated absorption further toward the red end of the spectrum, and hence into better agreement with observation. Incidentally, this method of calculating the color of degraded polymers gives a n interesting interpretation of two important characteristics of vinylidene chloride and vinyl chloride polymers. The first question is: Why should these materials darken in sunlight since they do not contain chromophoric groups which would be expected t o absorb radiant energy present in sunlight (wave lengths longer than 2900 A,)? A simple calculation, based on equation 1 and the known light absorption of polyenes, shows that if a chlorinated polymer loses only a few hundred parts per million of hydrogen chloride during manufacture and processing, then the observed light absorption of freshly molded polymer, as reported by Matheson and Boyer (28), is readily explained. Such a loss of hydrogen chlorideis not unreasonable with commercial molding and extrusion temperatures in excess of 100°C. 1
DISCOLORATION OF HALOGEN-CONTAINING POLYMERS
91
The second point is this: Matheson and Boyer (28) have suggested that esters of maleic and aconitic acid stabilize vinylidene chloride polymers by undergoing @ Diels-Alder condensation with conjugated double-bond systems formed in the degraded polymer. The solid polymer contains 1700/97 moles per liter of monomer units, and therefore the total number of pairs of double bonds would be (1700/97)(P,
+ pa + 2P4 + 2P6 f 3pS ++)
(6)
where the P’s are probabilities given by equation 1. For a polymer which has lost 10 per cent of hydrogen chloride, the above equation predicts a requirement of 0.15 mole or 3 weight per cent of tributyl aconitate. This is the correct order of magnitude for the amount of such stabilizer described in one patent (16). This does not prove the proposed mechanism and may merely be a coincidence. Actually, the unsaturated ester would have to react with only an occasional pair of conjugated double bonds to lessen the color markedly. COPOLYMERS OF HALOGENATED WITH YON-HALOGENATED MONOMERS
We wish now to extend the results of the previous section to the case of copolymers between halogenated and non-halogenated monomers. In general, the second monomer should be one that does not lose hydrogen chloride, acetic acid, water, hydrogen cyanide, or in any way develop unsaturation. Ideal comonomers for this purpose would be ethylene, isobutylene, styrene, the acrylates, and the methyl methacrylates. I t is immediately evident on qualitative grounds that such neutral monomers interspersed at random along a polymer chain will have several important effects on the discoloration resulting from the loss of hydrogen chloride. In general, they will prevent the formation of certain long conjugated systems that might otherwise occur, they will limit the maximum size of long conjugated systems, and they will tend to inhibit inductive action between adjacent conjugated systems. Thus, for a given loss of hydrogen chloride, such a copolymer should not develop as deep a red color as the pure halogenated polymer. The hydrogen chloride which is lost is channeled, so that short conjugated systems should form with greater ease. Figure 6 shows light-absorption curves on a series of unstabilized vinylidene chlorideethyl acrylate copolymers which were exposed in the form of 0.007-in. films to a Fadeometer for 24 hr. The beneficial action of the neutral comonomer is readily apparent. Figure 7 is a calculated plot of the average length of the uninterrupted vinylidene chloride chains as a function of the mole fraction of vinylidene chloride in the copolymer. Identical results hold for all other copolymer systems which are ideal. The ethyl acrylate copolymer was chosen for study because it is believed to be ideal, that is, the copolymer formed has approximately the same composition as the monomer mixture, and is independent of the per cent yield. As figure 7 indicates, a fairly large proportion of the neutral comonomer is necessary to reduce the average length of the vinylidene chloride chains to a safe level as regards the possibility of developing long unconjugated systems. Moreover, these are number-average values, and while there will be many
92
R. F. BOYER
shorter chains, there will also be an appreciable number of chains up to five times the average length. Figure 7 was calculated by using an expression given by Stockmayer (43). If the copolymer is not ideal, and, for example, vinylidene chloride monomer enters the copolymer more rapidly than the acrylate does, the
30
/
J
ETHYL ACRYLATE COPOLYMERS
/
I
20 Film Thi:kness
=0.007 IO
2 4 Hours Fadeometer
Exposure
0
400
500 700
WAVELENGTH IN MILLIMICRONS
FIG.6. Beneficial effect of increasing amounts of neutral comonomer (ethyl acrylate) on the light stability of vinylidene chloride-ethyl acrylate copolymers. These films did not contain a light stabilizer.
average length of vinylidene chloride chains will be even longer, as shown by the upper curves of figure 7. In general, as the proportion of acrylate in the copolymer increases, there will exist long runs of acrylate chains which do not contribute their maximum possible amount to the desired stabilizing action except by acting as a diluent. A desired copolymer would be one containing exactly one or two acrylates
DISCOLORATION O F HALOGEN-COSTAINING POLYMERS
93
between every three to four vinylidene chloride units along the chain. The precise effect of the neutral monomer on double-bond formation will be apparent from quantitative calculations to be given later.
0
0.2
0.4
0.6
0.8
1.0
FIG. i . Effect of monomer composition on the average length of the vinylidenc chloride sequences. CI measures the preferential tendency of a vinylidene chloride nionomer to add onto a copolymer chain which has an active vinylidene chloride group at the growing end of the chain.
In attempting to develop a statistical theory4 for the loss of hydrogen ellloride from such copolymers, we have made the following simplifying assumptions, some of which are admittedly artificial: The author is indebted to R. Simha for the derivation of equations 7-12, as well as equations 15-18.
94
R. F. BOYER
(1) The copolymer is ideal in that the two monomers enter the chain at random. (2) All copolymer chains have the same length or degree of polymerization, L. (3) Hydrogen chloride is lost at random. (4) Only one hydrogen chloride molecule can be removed from each vinylidene chloride monomer. If z is the mole fraction of vinylidene chloride units in the copolymer, the acrylates will divide these chlorides up into runs of length t . Simha (37) has shown that
N(t) = N(1 fort j L
-
- x)x'[2 + ( L - t -
1)(1 -
.)I
(7a)
1, and
N ( L ) = NxL
(7b)
for t = L , where N ( t ) is the number of runs of consecutive vinylidene chlorides of length t , L is the degree of polymerization of the copolymer chain, and N is the total number of such chains. From now on the acrylates can be ignored, and httention focused only on polyvinylidene chloride chains possessing a distribution of chain lengths as defined by equations 7a and 7b. From these vinylidene chloride polymers a fraction, p , of the hydrogen chloride is removed by some physical means. p is defined as the ratio of the total number of hydrogen chloride molecules removed (or the total number of unsaturated monomers formed) to the total number of vinylidene chloride monomers present. This action is equivalent to forming a new copolymer, so to speak, between vinylidene chloride and its unsaturated product, -CH=CCI-. What is now required is the number, M,(t, p ) , of runs of conjugated chains of length, n, as a function of t and p . By analogy with equations 7a and 7b,
M4t, p )
=
NMl
- p)pn[2 + ( t - n -
1)(1
- p)l
(84
for n = t . However, runs of conjugated double bonds of length n can exist in vinylidene chloride chains of lengths tl, g . . . t L , so that, following Montroll (30), the total number, M , ( p ) , of conjugated systems of length n as a function of the degree of unsaturation, p , is given by
=
N(n)p"
(1 0 4
95
DISCOLORATION OF HALOGEN-CONTAINING POLYMERS
Expression 10a refers to a run of n double bonds for t = n ;expression 1Oc refers to a run of n double bonds in pure polyvinylidene chloride; and expression lob covers all intermediate cases. N(n)p" in equation loa is, from equation 7a:
+ ( L - n - 1)(1 - x)]
X ( n ) p n = N ( 1 - z)snpn[2
(11)
Equation 10b is obtained by substituting equation 7a in equation 8a, whence L-1
t=n+1
L-1
- r)(l - p)p"
;M,(t, p ) = N(l
r'[2 1 -%+I
+ ( L - t - 1)(1 -
.[2
+
(t
-n
2)1
- 1)(1 - p)l
(12)
The quantity within the summation sign can be expanded and then summed according to methods given by Montroll and Simha (31). However, the final expression appeared at first to be extremely awkward for purposes of calculation, and quite sensitive to small arithmetical errors. Fortunately, these calculations could be carried out rather conveniently with punched-card computing machines (lo), and this has been done: using standard IBM (International Business Machine) equipment. L , the degree of polymerization, was taken as 100, corresponding to a molecular weight of approximately 10,OOO. The actual molecular weight for copolymers of vinylidene chloride and ethyl acrylate is probably several times this value. However, with L greater than 100 the work on the machines would have multiplied many fold, and the final answers would not have been greatly different. Calculations were completed for the following conditions:
x
=
0.98, 0.95, 0.90, 0.85, 0.75, 0.65
p = 0.05, 0.15, 0.30, 0.45, 0.60 n = 1, 3, 5, 7, 9
The IBM machines also handled the calculations for equation 11. The three terms which were finally added up to give the total number of conjugated systems of length n are, of course, equations lOc, 11, and 12. Thus, calling M , ( p ) the total number of conjugated systems of length n when the extent of degradation is p , we have M,(p)
=
equation 10c
+ equation 11 + equation 12
(13)
The logarithm of M , ( p ) plotted against n for n equal to 1, 3, 5, 7, and 9 gave straight lines. Thence, values of M , ( p ) for n equal to 2, 4,6, 8, 10, 11, and 12 could be obtained very readily. The complete set of values of M , ( p ) is listed in table 1. Figure 8 is a plot showing the individual contributions of the three terms in equation 13 to M , ( p ) for the particular case where p = 0.30 and n = 1. Similar results would hold for other values of p and n. The extension of this curve to values of x smaller than 0.65 was obtained by the use of equations 15 and 16, The writer is indebted to John Milliman and D. B. Ovait, who interpreted this problem for use on the IBM machines and then carried out the calculations.
96
R. F. BOYER
DISCOLORATION OF HALOGEN-CONTAINING POLYMERS
98
R. F. BOYER
given in the appendix. The over-all behavior shown in figure 8 is what would be expected according to the distribution of chain lengths in a copolymer, as defined by figure 7. Figure 9 shows how the distribution of conjugated systems changes for three different copolymers (r = 1.0, 0.85, and 0.65) for p = 0.60. It is very evident
0
FIG.8. Top curve is total number of isolated double bonds (n = 1) for 30 per cent loss of hydrogen chloride as a function of copolymer composition. The t = L curve gives the number of double bonds occurring in pure polyvinylidene chloride; t = n is the number of double bonds which occur in single vinylidene chloride monomers isolated between comonomer units. The remaining curve gives the number of double bonds occurring in all other sequences of vinylidene chloride units.
that increasing amounts of the neutral comonomer shift the distribution in favor of shorter conjugated systems, and hence at the expense of those long conjugated systems which cause a more intense visible color. Qualitatively, the theory is in accord with experimental results of the type shown in figure 6. It does not appear worthwhile to attempt any calculations of the actual color, or light transmission, of degraded copolymers in view of the moderate success obtained on pure polymers. Most of the factors, such as the allyl chloride
99
DISCOLORATION OF HALOQEN-CONTAIA-ING POLYMERS
effect, influence of chlorine atoms on light absorption, isomerization, and inductive effects, would be operating in copolymers, although to a lesser extent. It being assumed that visible coloration arises from values of n greater than 3, figure 10 shows the per cent of all double bonds which would occur in conjugated structures of n greater than 3 for different amounts of degradation and different amounts of neutral monomer. Figure 11 is a similar plot for n greater than 5.
I
2
3
4
5
6
?
8
9
FIQ.9. Distribution of conjugated systems for 60 per cent loss of hydrogen chloride at three different mole fractions, z,of vinylidene chloridc. Random loss of hydrogen chloride. The per cent values given on the ordinates of figure 10 were obtained from the values in table 1 by performing the operation:
Figure 12 gives the percentage of all double bonds which are found in conjugated structures longer than a given value of n for values of n from 3 to 10. p was taken as 0.60. The increasing slope of these lines as n is made greater emphasizes in still another way the pronounced rdle of a neutral comonomer in reducing the number of long conjugated systems.
100
R. F. BOYER
One might summarize these results by pointing out that there are three different ways in which a neutral comonomer will benefit the light and heat stability of a copolymer. ( 1 ) With increasing amounts of neutral monomer present, the number of active (vkylidene chloride) monomers per chain decreases, and is given by Lz. Therefore, when several copolymers with different values of z are subjected to
FIG.10. Per cent of all double bonds found in conjugated structures longer than ~t= 3, for hydrogen chloride losses ranging from 5 to 60 per cent. The smaller the ordinates, the smaller would be the visible discoloration of the copolymer. Random loss of hydrogen chloride.
the same light or heat source, or to the Same concentration of reagent, there will be fewer double bonds formed because of the law of mass action. In other words, p will decrease as z decreases, the exact relationship depending on the order of the reaction. (8) Even when the reaction conditions for several copolymers are varied until p is the same in each case, the total number of double bonds will be smaller the
101
DISCOLORATIOS OF HALOGES-COSTAIhXNG POLYMERS
smaller the value of x. This total number of double bonds, given by equation 17, is Lpx per copolymer chain. (3) Finally, for the same extent of degradation, p, the number of long conjugated systems is greatly reduced, as shown by table 1 and figures 9 to 12. However, when the extent of degradation is increased so as to give the same value of Lpx for two copolymers, then the conjugated systems formed in each copolymer are identical. Thus, pure polyvinylidene chloride degraded 10 per cent (px = 0.10), should possess the same conjugated groups as a 10 per cent
0
.05
.IO
.I5
.20
.25
.30
. 5
FIG.11. Per cent of all double bonds found in conjugated systems longer than n = 5 . The hydrogen chloride loss (from 15 to 60 per cent) is assumed to occur a t random.
vinylidene chloride-90 per cent ethyl acrylate copolymer which has been fully degraded (px = 0.10). In the former case, even though space is available, long conjugated systems do not form frequently because of the small probability for their occurrence. In the latter case, the probability of a large number of double bonds in conjugation is high, but there is no place for them to form. Hence, their net frequency is again small. As equation 1 B will emphasize, the only factor governing the nature of a conjugated system is the product (px). Even when the conjugated systems are identical in theory, they need not be so
102
R. F. BOYER
in practice; and the color of the two copolymers would almost certainly be different. For small values of z (say less than 0.10), it will not be possible to realize large values of p z even when the copolymer is fully degraded. Table 2 presents some numerical examples chosen to illustrate the three principles outlined above. Results are listed on the number of active monomers, the number of degraded monomers, and the number of conjugated systems of
various lengths, n , for z = 1.0, 0.90, and 0.45, with p = 0.30 and 0.45. All quantities are given for a single copolymer chain. Comparison of columns (a), (b), and (c) with one another and comparison of columns (d), (e), and (f), as a second group, shows the marked decrease in the longer conjugated systems as z decreases. However, comparison of column (b), for which L p z = 27, with column (f), for which L p z -- 29.25, shows approximately the same number of conjugated systems, even though z has decreased from 0.90 to 0.65. Thus far, nothing has been said about the theory of non-random loss of
103
DISCOLORATIOK O F H d L O G E K - C O K T A l h l X G POLYMERS
hydrogen chloride in copolymers. By analogy, one might guess that a very good first approximation could be obtained by using in the copolymer equations a modified value, p', for the degradation, where p' = up. p is the actual degradation and u is again a measure of the tendency for conjugated chains to propagate themselves. The values of M J p ) thus obtained should be divided by u to yield the desired answer. double'bonds and the number of !ymer
0.90 Sumber of degraded monomers, Lpz, per chain: p = 0.30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . p = 0.45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30 45
0.65
90
65
27 40.5
19.5 29.25
14.47 1.03 0.00737 0.00529 0.000374
12.70 0.472 0.0175 0.000620 0.oooO250
(C
(e)
14.51 2.33 0.374 0.0602 0.00965
~
,
1
(1)
14.80 1.236 0.103 0.00863 0.000716
Various side reactions, such as chain scission, cross-linking, and oxidation, have been ignored, except to point out the presence of some C=O groups in one experimental sample. While these factors are important commercially where one is dealing with a molded sample, they can be reduced in importance in a laboratory study by working at sufficient dilution with inert atmospheres. SUMMARY
Starting with the assumption of Marvel, Sample, and Roy that discoloration in degraded polyvinyl halides arises from polyene structures of the type I 4 H = CH-),, a statistical calculation has been made of the expected distribution of n values, both for random and for non-random loss of hydrogen chloride. Next, using the known light-absorption characteristics of polyene compounds, the expected color or light transmission curve of a degraded polymer is computed. Comparison of theory with an experiment on vinylidene chloride-vinyl chloride copolymer indicated fair agreement.
104
R. F. BOYER
Next, the theory was extended to cover copolymers between a reactive monomer (vinylidene chloride) and a stable monomer (ethyl acrylate), where the presence of a neutral group in the copolymer chain greatly reduced the number of long conjugated systems. No color calculations were attempted with copolymers, although a number of quantities related to color were presented in graphical form. The important parameter for copolymers is pz, the product of fraction of hydrogen chloride removed and mole fraction of chlorine-containing monomer. All degraded copolymers for which px is the same should have the same distribution of conjugated systems, although not necessarily the same color. It will be realized that the results presented here on chlorine-containing polymers and copolymers are applicable to polyvinyl acetate, polyvinyl alcohol, and other polymers which can lose molecules to form double bonds along the chain. This material was first presented in part before a Colloquium at the Department of Physics, Case School of Applied Science, in the Spring of 1942, and in part before the Midland Section of the American Chemical Society on April 1, 1943. I should like to express appreciation first to Professor H. Mark, who called our attention to the Marvel, Sample, and Roy theory of discoloration in polyvinyl halides, and second, to Dr. R. Simha for his help on the mathematical equations used in the copolymer section, as well as for a critical reading of the manuscript. I am also indebted to Dr. L. K. Frevel, Dr. L. A. Matheson, and Mr. R. C. Reinhardt for stimulating discussions concerning this material. REFERENCES (1) ASINGER,F.: Ber. 76B, 660 (1942). (2) BaTEMAN, L., AND KOCH,H. P.: J. Chem. soc. 1946,216. (3) BOND,W. N.:Probability and Random Errors, Edward Arnold and Company, London (1935). The type of statistics employed is identical with that used by Flory (J. Ani. Chem. Soo. 68, 1877 (1936)) for calculating molecular-size distributions in linear
condensation polymers. (4) BRODE, W. R . : Chemical Spectroscopy, particularly Chap. VII. John Wiley and Sons, Inc., New York (1939). (5) Reference 4, figure 7.21. (6) BRODE, W . R.: J. Applied Phys. 10, 758 (1939). (7) CONANT, J. B., KIRNER, W. R., AND HUSSEY,R . E.: J. Am. Chem. Soc. 47, 488 (1925). (8) DINSMORE, R. P.: Modern Plastics 21, 88 (December, 1943); see also Canadian patent 433,186. (9) DRAKE,L. R . (The Dow Chemical Company) : Private communication. This same
(10) (11) (12) (13)
effect was subsequently noted by C. S. Marvel and E. C. Homing, Chap. 8, “Synthetic Polymers”, p. 754 in Vol. I , 2nd edition of Organic Chemistry, an Advanced Trealise, Henry Gilman (Editor), John Wiley and Sons, Inc., New York (1943). ECKERT, W. J. : Punched Card Methods i n Scientific Computation. Thomas J. Watson Astronomical Computing Bureau, Columbia Univefsity, New York (1940). FIESER A N D FIESER: Organic Chemistry, p. 152. D. C. Heath and Company, Boston, Massachusetts (1944). FLORY, P. J.: J. Am. Chem. SOC.61, 1518 (1939). FREVEL, L. K . (The Dow Chemical Company) : Cnpublished observations.
105
DISCOLORATION OF HALOGEN-CONTAINING POLYMERS
(14)FULLER, C. S.:Chem. Rev. 26, 161 (1940). (15) Fuoss, R. M.: Trans. Electrochem. SOC.74, 110 (1938). A. W., AND GOCGIN, W. C.: U.S. patent 2,273,262(February 17, 1942). (16)HANSON, (17)HAUSSER, K.W., KUHN,R., AND SMAKULA, A,: Z. physik. Chem. B29, 384 (1935). (18)International Critical Tables, Vol. V, p. 368, fig. 43. McGraw-Hill Book Company, Inc., New York (1929). (19) JEFFREY,G. A.: Proc. Roy. SOC.(London) A183 (1945);see also BATEMAN, L., AND JEFFREY, G. A,: J. Chem. Soc. 1946, 211. (20) KUHN,R.: Angew. Chem. 60,707 (1937). (21)KUHN,R., AND GRUNDMANN, C.: Ber. 71A, 442 (1938). (22) LAND,E. H . , AND WEST, C. D . : "Dichroism and Dichroic Polarizers" i n Vol.'VI of Colloid Chemistry, Jerome Alexander (Editor). Reinhold Publishing Corporation, New York (1946). (23) LEWIS,G. N.,AND CALVIN, M.: Chem. Rev. 26, 273 (1939). J., AND KAFTALI,M.: Rub. Chem. Tech. 13, 133 (1940);original in (24) LICHTENBERCER, Bull. soc. ind. Mulhouse 116, 169 (1939). (25)MARVEL, C. S.:Private communication. See also MARVEL, C. S., AND RIDDLE, E. H. : J. Am. Chem. Soc. 62, 2666 (1940),where i t is shown that zinc removes hydrogen bromide from polyvinyl bromide. (26)MARVEL, C. S.,JONES, G. D., MASTIN,T . W., AND SCHERTZ, G. L.: J. Am. Chem. Soc. 64, 2356 (1942). (27)MARVEL, C. S.,SAMPLE, J. H., AND ROY,M. F.: J. Am. Chem. SOC.61,3241 (1939). (28)MATHESON, L. A., AND BOYER,R. F.: Manuscript in preparation. (29)MCINTIRE, 0. R . (The Dow Chemical Company) : Unpublished observations. (30)MONTROLL, E.: J. Am. Chem. SOC.63, 1215 (1941),Equation (14). (31)MONTROLL, E., AND SIMHA,R.: J. Chem. Phys. 8,721 (1940),especially the appendix. (32) MULLIHEN, It.: J. Chem. Phys. 7, 570 (1939). (33) OSTROYISSLENSHII, I.: J. Russ. Phys. Chem. SOC.44, 204, 210 (1912). (34) OSTROMISSLENSKII, I.:German patent 264,123(1913);Chem. Zentr. 84,II. 1187 (1913). (35)REINWRDT,R . C.: Ind. Eng. Chem. 36,422 (1943). (36)SIMHA,R . : J. Am. Chem. SOC.63, 1479 (1941). (37)Reference 36, Equation (la). (38)SLOBODIN, YA. M: J. Gen. Chem. (U.S.S.R.) 6, 129 (1936). (39) SNOW,C. P., AND ALLSOPP,C. B.: Trans. Faraday SOC. SO, 93 (1934). (40) STAUDINGER, H., BRUNNER, M., AND FEISST,W.: Helv. Chim. Acta 13, 805 (1930). (41)STAUDINGER, H., AND FEISST, W.: Helv. Chim. Acta 13, S32 (1930). J., AND PIPER, J. D.. Ind. Eng. Chem. 33, 1567 (1941). (42)STICHER, (43)STOCKYAYER, W. H.: J. Chem. Phys. 13, 199 (1945). (44) TUTTLE,W. P., JR., AND JACOBS, T . L.: Abstracts of papers presented a t the Buffalo Meeting of the American Chemical Society, Sept. 7-11, 1942, Page 13M. (University of California, Los Angeles.) (45)WALL,F. T . : J. Am. Chem. Soc. 82, 803 (1940);63, 821 (1941). (46)WALSH,A. D.: Trans. Faraday SOC.41, 35 (1945).
APPENDIX After the machine calculations on copolymers were completed, Simha4derived several pertinent equations which mould serve to simplify any further calculations. The summation in equation 12 can be written as:
- X'[(L - n
+ 1) - p ( L -
11.
- l)])
(15)
106
R. F. BOYER
The complete expression for M,(p), which is the sum of equations 10c, 11, and 12, is given by
M d p ) = N(1 for n = L - 1 and by
- pz)(pz)"[2
+ (L - n - 1)(1 - pz)l
(16a)
for n = L. The similarity in form between this equation and equation 7, which holds for the degradation of pure polymer, is rather surprising. Moreover, one can see at once from equation 16 why a plot of log M,(p) should be linear with respect to n. Next, two expressions connected with the total number of double bonds are useful : L
nM,(p) = N L p x n-1
This is, so to speak, the normalization equation which accounts for all of the double bonds regardless of the complexity of the structures in which they reside. The total number of double bonds up to a certain length, n = k, of the conjugated chains is: n-k "-1
+
nM,(p) = N(Lpz - (p~)~+l[L k(L
- 1 - k)(l - ps)]}
(18)
These results can be extended one step further to yield two useful equations. The ratio of equation 18 to equation 17, called f , is the fraction of all double bonds contained in structures up to size n = k.
+
f = 1 - ( p x ) k [ L k(L - 1 - k)(l - pz)l/L (19) The fraction, F , of all double bonds contained in structures for n greater than k is, of course, given by
F(n
> k)
= 1 - f(n
5 12)
(20)
It is evident from equations 19 and 20 why the semilogarithmic plots of figures 10 and 11 should be very nearly linear.
