1838
R. W. KILB
struction of O2 entirely via (c), that is, no considerable reaction between 0 2 and any hydrocarbon or hydrocarbon radical at all, would be consistent with our results and with other observations on hydrocarbon flames. For it O2 reacts only with H atoms, the large amount of CO formed in CH2 flames would have to arise by reactions of 0, OH, H2O with species such as CHI, CH2, etc. But then all plausible reactions which form CO would also destroy free valences and the formation of CO and H2 from the hydrocarbon fuel should have to be considered a chain terminating process which was fed by free radicals generated in reaction (c). This view would account for the fact that flames rich enough to contain hydrocarbon in the products possess only about the equilibrium [HI in the post flame gas, while fuel lean hydrocarbon flames or either rich or lean H2 flames contain so many free radicals that [HI in the post flame gas is many times the concentration appropriate to the
Vol. 63
equilibrium H2 = 2H. It would also agree with experiments on the slow CH,, O2 reaction in static systems at 900°K. or higher, where CH, inhibits its own oxidation presumably by the destruction of radi~a1s.l~A destruction of O2 only via reaction (c) would require that reactions between 0 2 and hydrocarbon or hydrocarbon radicals, such as are presumed to occur in low temperature oxidations and in cool flames, be irrelevant to the main course of the reaction in hot flames; but many persons have believed the low temperature mechanisms to be irrelevant to hot steady flames. It must be pointed out, however, that our data are not sufficiently precise to exclude some reaction of O2 in other ways than via reaction (c). All we can claim is that (c) is more important than any other way. (15) M. Vanpee and F. Grard, “5th Symposium on Combustion,” Reinhold Publ. Corp., New York, N. Y., 1955, p. 484; D. E. Hoare and A. D. Welsh, ibid., p. 474; and references cited by these authors
THE EFFECT OF SIMULTANEOUS CROSSLINKING AND DEGRADATION ON THE INTRINSIC VISCOSITY OF A POLYMER BYR. W. KILB General Electric Research Laboratory, Schenectady, New York Received March 86, 1060
The change in intrinsic viscosity [q]is studied for a process during which a polymer is simultaneous1 degraded and crosslinked. An example of such a process is irradiation of polymers. It is possible to determine the rerative amount of degradation and crosslinking by following the change of [ q ] during the process. Qualitative agreement of theory with experiment is good. Quantitatively the method is limited to the range unity to ten for the ratio of degradations to crosslinks. outside these limits the shape of the [ q ]curve is insensitive to this ratio. It is found that the best sensitivity is obtained when [ q ]is determined in e solvents. By followin the change in osmotic and li ht scattering molecular weight for silicone irradiated by an electron source, the ratio of degrafations to crosslinks was f o u n t t o be less than 0.5.
During certain processes, polymer molecules are simultaneously crosslinked and degraded. Typical examples are irradiation and oxidation. This leads to a polymer with long chain branching and either increased or decreased molecular weight, depending on the degree of degradation. We are interested here in determining the relative amount of crosslinking and degradation from a study of the change in intrinsic viscosity of the polymer. This problem has been treated in an approximate manner by Shultz, Roth and Rathmann.’ Although most of their results are qualitatively correct, their quantitative calculations are inexact because of their use of the Stockmayer and Fixman2 approximation for the effect of branching on the intrinsic viscosity of a polymer. Recently Zimm and Kilb* have shown that previous theories seriously overestimate the effect of branching on intrinsic viscosity, and proposed a new theory which is in good agreement with the available data. We propose to use this theory in the present study. The quantitative results of Shultz, et aE., also suffer to some extent from the lack of use of a definite molecular weight distribution. (1) A. R. Shultz, P. I. Roth and G. B. Rathmann, J. Polymer Sci., 22, 495 (1956). (2) W. H. Stookmayer and M. Fixrnan, Ann. N . Y . Acad. Sci., 61, 334 (1953). (3) B. H. Zimm and R. W. Kilb, J. Polymer Sci., 87, 19 (1959).
The problem of determining the relative amount of crosslinking and degradation has also been treated by Charle~by.~His method involves following the amount of gel produced during the process. It has perhaps not been sufficiently forcibly pointed out in previous studies that the quantitative calculations are rather sensitive to the assumed initial molecular weight distribution. Consequently, in the application of the calculations, it is necessary to determine if the experimental polymer actually has the assumed distribution. If this is not the case, the results must be viewed with some scepticism. In this paper we shall make the assumptions: (1) the scissions are directly proportional to the crosslinks throughout the process and their distribution is “random”; (2) the crosslinks are tetrafunctional, i.e., four branches radiate out from the crosslinked site; (3) the initial molecular weight distribution is assumed to be the “most probable” distribution (see below), On the basis of these assumptions, we may combine the results of Zimm and Kilb with the distribution function given by Stockmayer5 to cal(4) A. Charlesby, Proc. Roy. Soc. (London), A224, 120 (1954). (5) W. H. Stookrnayer, J. Chem. Phys., 11, 45 (1943); 12, 125 (1944).
CROSSLINKING AND DEGRADATION ON INTRINSIC VISCOSITYOF
Nov., 1959
culate the change in intrinsic viscosity during the process. The Distribution Function I n order to avoid needless repetition of details, it will be assumed that the reader is familiar with the papers of Stockmayefl and the approximations introduced by Thurmond and Zimm.6 The discussion will be given in terms of an irradiation process. Other processes will be analogous. The initial molecular weight distribution is assumed to have a ratio of weight to number average degree of polymerization of two. Stockmayer’s distribution function deals with a random polymerization of difunctional monomers and multi-functional branch units, driven to extent of reaction p . We may use his results by viewing our crosslinks as randomly distributed tetrafunctional branch units. The scissions will be viewed as changing the extent of reaction p . Using his notation, we define N = no. of tetrafunctional crosslink units L = no. of difunctional units M = no. of polymer molecules
..
-
+ PR
(1) (2) (3)
where Lo and M Oare the original number of difunctional units and polymer molecules present before irradiation. We also define functional groups on branch units all functional groups = 4N/(4N 2L) = aR/Lo (4) P = fraction of groups reacted = 2(N L M ) / ( 4 N 2L) = (Lo Mo PR)/Lo (5) yoo = original no. av. degree of polymern. = LdMo (6) ywo = original wt. av. D.P. = 2yno (7) yni = instantaneous no. av. D.P. of the polymer after dose R if all the crosslinks were broken but scissions p =
.-
+
+
+ -
-
-
After dose R , the number, weight and z-average D.P. (xn, 2 , and x,) of the irradiated polymer are xn = L / M (10) (11) xw = 2(1 P)P/(l P 2PP) xz 3(1 P ) P ( ~ ~ ) / ( lP ~ P P ) * (12)
-
-
- - -
Using the approximations introduced by Thurmond and Zimm,e the weight fraction Wmk of polymer consisting of m crosslinks and k difunctional units is (6) C. D. Thurtnond and B. H. Zitnrn, J. PoZurne7 Sei., 8 , 477 (1952).
POLYMER
1839
YfX8
2m(2m
+ 1)(2m + 2 ) Wm-l.k
where y‘
= p y w i = 2aR/(Mo 2 = 2k/ywi
4- PR)
(15) (16)
The quantity =
w k
(Ywi/2)
wrnk
m
(17)
has been tabulated’ for y’ < 1. The instantaneous number and weight average number of crosslinks per molecule (mn and m,) are given by
-
ma = r’A4 7’) mw = - ~ ‘ / ( l 7’)
(18) (19)
We comment that the number average number of crosslinks per original linear molecule is mayno/xn; per instantaneous linear molecule it is m n y n i / x n . We may also rewrite the respective D.P. averages xn
Let us assume the following for an irradiation process of dose R : (1) a R difunctional units are crosslinked, yielding a R / 2 tetrafunctional units; consequently, aR difunctional units are simultaneously removed; (2) pR scissions are introduced; (3) a and are constant throughout the process. N = aR/2 L = Lo aR A4 = Mo aR/2
=
Wmk
A
--
xw
-~‘/4) - YO 3ywi/2(1 - Y’)* gni/(1
Ywi/(1
(20) (21) (22)
Stockmayer has shown that the critical extent of reaction, pa, at which gelation occurs is given by Pc =
1/(1
+ 2P)
(23)
which implies that a t initial gelation y’ = 1. From equation 15, one finds that the dose R* a t initial gelation is given by (2a
- P)R*
No
(24)
This implies that gelation can occur only if 2a>p. Since a R / 2 is the number of crosslinks, and pR is the number of scissions, equation 24 shows that gelation is possible whenever there are less than four degradations per crosslink. Case I. Gelation Is Possible (2a> p) If 2a > p, then gelation occurs a t R” as determined from equation 24. The quantity R* is an important and readily determinable experimental parameter, and therefore it is desirable to restate the above molecular averages in terms of R and R*, rather than R and 7‘. This may be accomplished by use of equation 24. The results are
-
-
Y‘ = R / R * [ l (1 R/R*)p/2a] (25) R/R* = ~ ’ ( 1 8 / 2 a ) / ( l - y’PJ2a) (26) U w o l y w i = ~ n o / ~ n=i 1 R/R*(2a/P - 1 ) (27)
2s
+
ywO/xw= 1 - R/R* - - R/R*)P/2a]/ 2(1 - @ / 2 ~ ~ ) ~R(/ 1R * ) s m, = R / R * ( l - R / R * ) ( l - ,E/2a) mn = R / R * [ 4 - R / R * - ( 2 P / a ) ( l - R/R*)]
=
(29)
~ Y w o [ ~(1
(30) (31) (32)
Equation 29 shows that the inverse of the weight average D.P., zw,varies directly as the dose R; xw becomes infinite a t gelation. Equation 28 shows that the inverse of the number average D.P., x n ) also varies directly as the dose R; but xn may (7) R. W. Kilb, J. Polymer Sei., in press (1959).
R. W. KILB
1840
Vol. 63
[ d o = .(ywo/2)af(0, a ) (34) The ratio of [q] after dose R, to the initial intrinsic viscosity is therefore [vI/[vIo = ( Y w i / u w o ) a f(r’,a)/f(O, a ) =
(1
- Pr’/2aPf(7‘,
a)/f(O, a ) (35)
Values of f(y’,a)/f(O,a) are given in Table I for various values of y’ and for a = 0.5, 0.68 and 0.75. Other values may be obtained by graphical interpolation. TABLE I u/y’ ‘60
.2
6
4 R/R!
.E
1.0
.2
4 .6 RI R I ,
.8
1.0
.2
.6
.4
R/R
.8
1.0
1.
Fig. 1.-The ratio of [q] after dose R to the initial [?lo versus R/R*, where R* is the dose needed for gelation. The plots are given for several values of the ratio of the number of scissions to crosslinks, 2,9/a. The parameter a is the exponent in the intrinsic viscosity-molecular weight relationship for the linear polymer.
0.5 .68 .75
0.2
Values of f(y‘,u)/f(O,a) 0.4 0.8 0.8 0.9
0.95
1.06 1.13 1.22 1.36 1.48 1 . 5 8 1.10 1.23 1.41 1.74 2.09 2.43 1.11 1.27 1 . 5 1 1.95 2.46 3.00
f(0,u)
1.29 1.48 1.56
By use of equations 26 and 35, one may construct plots of [ q ] / [ q ] o us. R/R* for various values of a and 2p/a. Typical plots are given in Fig. 1. Examination of Fig. 1 confirms Shultz’s’ finding that the intrinsic viscosity may in some cases decrease almost up to the gel point. This occurs when there are about three scissions per crosslink (2p/a > 3). We also note from Fig. 1 that the better solvents (a > 0.65) give a greater absolute change in [VI/ [ q l O . On the other hand, although one can determine intrinsic viscosities quite accurately, the value of R* is difficult to determine experimentally to better than 5%. Consequently because of the steep slopes of the curves for the case of good solvents, the error R* causes a greater uncertainty in finding the value of 2p/a in good solvents than in the 9 solvent (a = 0.5). Thus in general, it is advisable to work with 0 solvents. We also comment that the theory is really developed only for 0 solvents, and its application to other solvents is an extrapolation. * R/R’ Comparison with experimental data is given beFig. 2.-The ratio of [ q ] after dose R to the initial [qlO low. versus RJR’, where R‘ is the dose needed to reduce [ q ] to One can also determine how much greater R* one-tenth of [ql0. The curves are independent of 2p/a, and have a slight dependence on the exponent a in the in- is than the dose Ro*required to produce gel if there trinsic viscosity-molecular weight relationship for the linear were no degradation. This is given by polymer. R* = (1 - p/2a)R* (36) either increase (if 2p < a) or decrease (if 2p > a) Thus if one finds that an unexpectedly large during the process. is required for gelation, it indicates that there From equation 32 we see that a t gelation there is dose are nearly four scissions per crosslink. one cross-link for every three molecules present. The quantity which Shultz, et aZ.,l refer to as “the Case 11. No Gelation Occurs (2a < p) number of crosslinked units per instantaneous priIf no gelation occurs, there does not exist a mary weight average molecule” is given by mwywi/ definite point such as R*, and so one cannot conxw, which is unity at gelation. plots like Fig. 1. But i t was hoped that To find the intrinsic viscosity after dose R, we struct note that the distribution function (equations similar figures could be constructed by plotting [ q ] / [ q ]us. ~ , R/R’, where R’ is that value of dose 13 and 14) has the same mathematical form as for which [ q ] / [ q ] o is one-tenth. This would be that treated previously by Kilb.7 The only dif- convenient for of experimental data. ference is that y,i appears instead of ywo, and y’ Surprisingly, itinterpretation was found that the curves were is defined differently. Consequently, the [v] after virtually independent of 2 p / a in the range of R/R‘ dose R is from 0.005 to 1. Consequently viscosity data 171 = .(vwi/2Pf(rf, a ) (33) alone is not sufficient to vield 2B/a. Plots are Here f(y’,a) is a function dependent on the given in Fig. 2 for a = 0.5 i n d 0.75. The experiamount of branching in the polymer, a is the ex- mental values of Shultz, et u Z . , ~ for irradiated polyponent in the intrinsic viscosity-molecular weight methyl methacrylate I (which has a = 0.73) relationship for the polydisperse linear polymer, follow the expected curve. Casting about for other methods, we note from and K is the corresponding coefficient
.
c
Nov., 1959
CROSSLINKING AND DEGRADATION ON INTRINSIC VISCOSITY OF
A
POLYMER
1841
equations 8, 15 and 20, that the ratio yno/Xn of number average D.P. before and after dose R is ~ n o l x n=
1
=
+ (0 - a/2) RIM0 + knR
1
(37)
Similarly for the weight average D.P. y w o l ~ w=
=
1 1
+ (0 - 2a)R/Mo + k,R
(38)
Consequently by determining the slopes kn and k , of these straight-line plots, one finds that the ratio of scissions to crosslinks is given by
Another method, suggested by A. A. Miller, involves the use of a radical scavenger which is capable of completely suppressing crosslinking (so a! = 0) and yet presumably not affecting degradation (so /3 is unchanged). We also assume that the scavenger need be present in only small concentration (less than 59.1). One then needs three intrinsic viscosities: (1) the [q]O of the original polymer; (2) the [q]* of the polymer irradiated in presence of the scavenger; and (3) the [ q ]of the polymer irradiated to the same dose R in the absence of the scavenger. For the ratio [ q ] * / [ q ]we ~ have (since y' = 0) [TI */[TI0 =
.I
.2
.6 .8 1.0 R/R+ Fig. 3.-The ratio of [7]after dose R to the initial [7]0 versus R/R+, where R f is the dose needed to reduce the weight average molecular weight to one-tenth of the initial value. The exponent a = 1 / ~(a 8 solvent). 0
A
a = 0.75
(Z/wl/Ywa)a
+
= [1/(1 Pn/4rO)l~ (40) This may be solved for ~ / M o . Equation 35 shows the [ q ] / [ q ] *is [71/[71* f ( y f , a)/f(oJ a) (41) Use of Table I and the appropriate a value then yields y'. The quantity 2 4 M 0 may be obtained from equation 15 and the found value of p/Mo
2a/Mo = ~ ' ( 1 f PR/Jfo)/R
(42)
A third method involves the use of light scattering techniques. One finds the dose R f needed to reduce the weight average D.P., x,, to some fraction of the initial ywo(e.g., xw = 0 . 1 1 ~ ~ ~Then ). one plots [q]/ [ q ]versus ~ R/R+. The plots are constructed in the following manner. One chooses xw/ywo; then from equations 9, 15 and 21 one finds Y ~ x ,= " 1
+ R(P - 2or)Mo
R/R Fig. 4.-The
ratio
'.
versus R / R + for a good solvent ( a = 0.75).
[7]/[710
(43)
If one take xw/ywo = 0.1 a t R f , this yields fiI0 Rt(P - 2 a ) / 9 (44) Substituting in equation 15 gives R/R+ = yf(P/2a - 1)/9(1 - r'P/2a)
-I
:.M
135,500
Mn
m,L 2-YP
(45)
The desired plots are obtained by choosing appropriate values of y' and 2p/oc, and using Table I with equations 35 and 45. The results are given in Fig. 3 and 4 for a = 0.5 and 0.75. Once again it is found that solvents give better sensitivity for determining 2 P / a than better solvents. The data of Shultz, et aLll on irradiated PMMA I are also plotted in Fig. 4. This follows the curve for no crosslinking quite well, and confirms their result that there is very little crosslinking on irradiation of PMMA. Actually, they have a = 0.73, which would have the effect of raising all curves in Fig. 4 by a small amount, thus giving even better agreement.
Y.W. I IV'.
Fig. 5.-The experimental distribution for the silicone polymer. The curves for a polymer with no branching ( y = 0); a small amount of branching (y = 0.4, weight average number of branches mw = 0.67); and large amount of branching ( y = 0.8,mw = 4).
Other methods (e.g., plots of [qI/[qlo etc.) might also be employed.
US.
zw/ywo,
1842
R. W. KILB I
I
1
I
I
I
2Eh:O 2.2
0
IS
SILICONE IN
e
SOLVENT
t
Fig. 6.-The experimental [ v ] / [ ~ ] oversus R/R* for irradiated silicone polymer in a e solvent, and in toluene. The data of Schulta, et aE.,' of polystyrene in benzene are also plotted.
Vol. 63
[?.?I = 2 x 10-~MO*6* The fractionation data are given in Table 11. The light scattering M,of the original sample was 142,500, which agrees quite well with M , = 135,500 calculated from the fractionation data. The osmotic M , was 63,500 which is also in good agreement with the calculated value of 62,800. This yields M w / M . = 2.2 which is reasonably close to the expected value of two for a linear random distribution. The found molecular weight distribution is compared to the expected random linear distribution (y = 0) in Fig. 5. The agreement is reasonable, especially in view of the experimental accuracy. Distribution curves for branched polymers ( y = 0.8 and 0.4) of the same M , are also given; the experimental distribution does not resemble these, and so one concludes that there is little or no branching in the original sample. Samples (2 9.) of the polymer were irradiated in aluminum dishes of two inch diameter. Oxygen was removed from the samples by pumping under vacuum for 24 hr. The irradiations were done under N2 with a 800 kv. (peak energy) source of electrons a t a rate of 100 MR./hr. The intrinsic viscosities of the irradiated samdes were found in toluene, and in a mixture of diethylphthalate (21.5 % ' by weight) and toluene, which is a 8 solvent for dimethylsilicones.10 TABLE I1 FRACTIONATION DATAOF ORIGINAL SAMPLE
I---
MmIMn MwoIMw
OOl
I
\
I
.5
I
1.0
Wt. pf material, mg.
mug.
Mol. wt.
1 2 3 4 5 6 7 8 9 10 11
65.4 130.7 120.1 160.2 235.4 313.5 418.2 431.5 514.1 300.7 109.7
4.2 9.0 14.5 20.9 26.7 34.3 43.0 54.0 67.6 81.5 96.3
6,000 16,000 29,000 46,000 62,000 85,000 115,000 150,000 200,000 250,000 315,000
The results are given in Table 111.
\ I
Fraction
I
1.5
MR, Fig. 7.-The ratios of initial light scattering and osmotic average molecular weights of the silicone polymer to the corresponding values for the irradiated samples. The dashed lines give the expected values of M,,/M, for various values of ratios of scissions to crosslinks (2@/a)using the value of R* = 1.5 MR. obtained from the M,,/M, data.
Each of the three above methods could also be used to determine 2P/a if gelation were possible. Experimental A sample of dimethylsilicone oil (120,000 c.P.s.) was ob-
tained from Dr. A. C. Martellock of the General Electric Silicone Products Dept., Waterford, N.Y. This sample had been decatalyzed and also devolatilized by heating a t 200" in a vacuum oven for 24 hours. T o determine the molecular weight distribution, a 2.95-g. sample was fractionated in a one meter thermal gradient column of the Baker and Williams* type; 2.8 g. was recovered. The intrinsic viscosities of the fractions were determined in toluene solution, and the molecular weights were found from the equation [v] = 4.37 X 10-aM0.7g where the [v] is in ml./g. This relationship has been determined recently in this Laboratory from data in the range M = 85,000 to 2,000,000. It differs rather considerably from Barry's9 equation ( 8 ) C. A. Baker and R. J. P. Williams, J . Chem. Soc., 2352 (1956).
TABLEI11 VISCOSITY AND MOLECULAR DATAON IRRADIATED SAMPLES [VI in Dose MR.'
toluene, [ q ] in 9 k i n 0 kin ml./g. toluene solvent solvent
0
50.0 52.5 59.0 64.5 73.5 91.8 112.5
.3 .6 .9 1.2 1.4 1.6
0.33 .36 .39 .44 .37 .55 .76
28.1 29.3 30.1 32.4 34.0 37.3 39.5
0.70 .66 .70 .68
M, X 10-8
10 -8
142.5 63.5 370
.80 780 .82 .90
M. X
77.6-85.5 75.3 70-95
The viscosity was represented by %P/C
= Ill1
+ kIlll2c
I n the irradiated samples there was a slight tendency fork to rise with increasing dose, especially near the gel point. I n the unirradiated fractionated samples, k remained essentially constant at 0.33 3= 0.02 in the mol. wt. range of 50,000 to 300,000. Some difficulty was presented by filtration. Solutions of samplea irradiated to dose 1.2 MR. and less could easily be filtered through fine fritted glass filters. A fraction of the 1.4 MR. sample would not filter through a fine filter, but would easily go through a coarse filter. I n the 1.6 MR. dose sample, a fraction would not go through even a coarse filter. In the viscosity work, therefore, the solutions of dose 1.4 MR. and less were filtered through a coarse filter before viscosity determination, but the solutions of dose 1.6 MR was not filtered. (In the toluene solution, the 1.6 MR sample (9) A. J. Barry, J . A p p l . Phye., 17, 1020 (1946). (10) F. P. Prioe and J. P. Bianohi, J . Polymer Sci.. 16, 355 (1955).
INCLUSION COMPLEXES OF METWLNAPHTHALENEB
Nov., 1950
was found to give a [q]/ [ 7 7 ] 0 value of 2.25 if unfiltered, while the filterable portion gave [q]/[q]o = 2.04.) On close inspection of the ca1culation.s' involved in the evaluation of [q]/[q]ofrom the distribution functions, i t is found that for the 1.6 MR. sample more than one-third of the value of [q]/[q]ois contributed by that portion of the sample which has mol. wt. greater than 6,000,000. The sensitivity to filtration is, therefore understandable. Another problem was in fixing the gel point R*. If one plots the light scattering Mwo/Mwversus dose, one h d s R* = 1.5 MR. (see equation 29). On the other hand, if one allows the 1.6 MR. sample to swell in toluene for several hours and then shakes the flask vigorously, one finds no entrapment of air bubbles, thus indicating no gel." A sample of dose 1.7 MR. does entrap minute. air bubbles by this 1.65 MR. Since this value gives test. This indicates E* better over-all consistency in the viscosity analysis, i t was adopted in the following calculations for purposes of illustrations. Plots of [q]/[q]o versus R/R* for measurements in the e solvent are given in Fig. 6. Comparison of these with 0.5-1.0. For the measurements in theory yields 2B/a toluene, if we take a 0.75, one obtains 2p/a 1.0-1.5. On the other hand, if Barry's value of a = 0.68 is assumed, one finds 2P/a = 0-1.0. This lack of precision is disappointing; furthermore, studies by A. A. Miller12 of this system by chemical techniques indicates that 2p/a 0.1. The difficulty is the 1ack.of sensitivity of [q] to small amounts of degradation. Thus it appears that although the theory gives the correct qualitative features, the method is only useful in a quantitative manner when 2B/a > 1. It is also desirable to use 8 solvents to improve precision. As an alternative method, the osmotic and light scattering molecular weights of several of the irradiated samples were determined. These are given in Table 111. These data are plotted in Fig. 7. Using R* = 1.5 as determined by equa-
-
--
-
-
(11) W. J. Barnes, H. A. Dewhurst, L. St. Pierre and R. W. Kilb, J . Polymer Sci., 36, 525 (1959). (12) A. A. Miller, private communication.
1843
tion 29, lines were constructed from equation 28 for various values of CY. Although the precision of the osmotic pressure data is rather poor, it is clear that 20/a > 1/2, in rough agreement with Miller's value. In Fig. 6, there are also plotted the data of Shdtz, et aZ.,1 on irradiated polystyrene. At R/R* < 0.6, [q]/[q]ofollows the curve for 2D/a 2 fairly well. At larger values of R/R*, [ T ] / [ ~ falls ] O much below the ex ected values. Some ossible experimental causes are: (1) i t r a t i o n difficulties, nonrandom initial molecular weight distribution, (3) incorrect value of the ex onent a, and (4) the crosslinking is not purely tetrafunctionafand so the theory developed here is not applicable. In any case, the apparent difference in the behavior silicones and polystyrene is unexpected and would be an interesting topic for further study.
-
6)
Conclusion The qualitative features of the change in intrinsic viscosity of a polymer with irradiation are predicted satisfactorily by the above model. Quantitatively, it is found that [ ~ l ] / [ q ]iso not very sensitive to 2p/a (the ratio of number of degradations to crosslinks) unless 1 < 2p/a < 10. Consequently viscosity studies by themselves are practically useful only in this range of 2/3/a. Outside this range, other techniques-such as light scattering, osmotic pressure or chemical scavenging of radicals -must be employed to find the ratio of scission to crosslinking. Acknowledgment.-The author is grateful to Mr. W. J. Barnes and Miss W. E. Bals for the light scattering and osmotic pressure measurements, and to Mr. J. S. Balwit for the irradiations. He also wishes to acknowledge the interesting discussions of the problem with Dr. A, A. Miller.
INCLUSION COMPLEXES OF METHYLNAPHTHALENES BY JACKMILGROM Contributionfrom the Research and Development Department, Standard Oil Company (Indiana), Whiting, Indiana Received March $6. I960
A chance observation of an unaccountably high melting point prom ted investigation of the system 2-methylnaphthalenen-heptane. T o confirm complex formation, this system waa studiecf by regular and differential thermal analyses, vaporpressure measurement, solids separation and X-ray analysis. Data have been represented by the usual linear phase diagram and a special logarithmicoone. Six different complexes of 2-methylnaphthalene and n-heptane were found a t temperatures between 25 and -92 . Depending upon temperature, eight moles of &methylnaphthalene combine with one, three or eight moles of n-heptane to form three pairs of complexes. The members of each pair have different crystal modifications. Transitions do not proceed readily; some complexes must be cooled below 0" before they transform and one is metastable. These results suggest a mechanism for complex formation. At room temperature a void ap arently exists in the %methylnaphthalene crystal lattice, which can accommodate guest molecules of a definite shape. dmplexes form with both straight- and branched-chain hydrocarbons, althou h molecules as long as n-hexadecane fail to react. Complex formation is not limited to 2-methylnaphthalene. 1-Methyfnaphthalene and perhaps other polycyclic compounds also adduct paraffis. Below room temperature, a new realm of inclusion complexes probably exists.
Introduction During an attempted purification of l-methylnaphthalene in our laboratories, a 30 mole yo solution of 1-methylnaphthalene in n-pentane solidified unexpectedly a t - 70". If an ideal solution had been formed, it would have solidified below - 130°, the freezing point of n-pentane. Solutions of 2-methylnaphthalene and paraffins behaved similarly. These results suggested that both methylnaphthalenes form complexes with alkanes and led to further investigation. Knowledge of solid-liquid equilibria of methylnaphthalene in binary systems is sparse. 2Methylnaphthalene was observed to form a simple
eutectic mixture with triphenylmethane1 and a solid solution with naphthol.* Complexes were formed between methylnaphthalene and acetone, phenol or hydrogen sulfide.8 A recent calorimetric study4 has revealed that both 1- and 2-methylnaphthalene undergo polymorphic transitions sluggishly, exhibiting supercooling and superheating. The system 2-methylnaphthalene-heptane has (1) V. M. Kravchenko. Ulorain. Khim. Zhur., IS, 36 (1952): C. A . , 48, 3776f (1954). (2) G . Nazario, Rev. inst. Adolfo Lute., 8, 137 (1948): C. A . , 44, 421f (1950). (3) E. Terres and A . Doerges, Brennslofl-Chem., 37, 385 (1956). (4) J. P. McCullough. H. L. Finke, J. F. Messerly, 8. S. Todd, T. C. Kincheloe and G. Waddington, THISJOURNAL, 61, 1105 (1957).
