1-01. 65
COMMVSICATIOS TO THE EDITOR
2276
c - a [ p ( i H ) % coth p ( i H ) l / z - 11 dr
A(iH) =
(5)
where If is Blizard's reduced frequency. The results of eq. 3 were subsequently expressed in terms of the reduced variables corresponding to the Rouse theory G'R; = G'ii?,/cRT G"R; = (G" - wq,)&f,,/~RT W R ~= wsl; = w a 2 Z , 2 ~ o / 6 ~ 2 h T
( 6) (7 ) ( 8)
By identifying the results of the Blizard and Rouse formulations at low and high frequencies, it can be iG",, = A12, and WR; = shown that G'RG H/7?. In Fig. I, G ' R ~and G " R ~are plotted against WR.; The only difference in shape from the familiar curves for a polymer homogeneous in molecular weight is a more gradual curvature where the slopes change. Curves also are drawn to show the relative positions (ie., relative for unreduced scales, G'
+
and G" us. w directly) for homogeneous samples with the same number and weight average molecular weights, respectively, taking the lo-ratios as unity. At high frequencies, the curves all coincide; at low frequencies, their separations on the modulus scale are all in agreement with the formulas given in Table I. These calculations are valid, of course, only for systems in which there is no entanglement coupling. Experiments on dilute solutions of homogeneous and polydisperse polymers are in progress. For concentrated and undiluted systems, it will be necessary to extend the calculations t o take entanglement coupling into account, except when the entire range of molecular weights is below the critical entanglement limit. Acknowledgment.-This work mas supported in part by n grant from the National Science Foundation.
~
~~
~
~~~
COMMIJNICATION TO THE EDITOR POLYMERIZATION OF SOLID ETHYLENE BY IONIZING RADIATIOS: EVIDENCE FOR ION-MOLECULE CONDENSATION
iSir: A recent study from this Laboratory1 disclosed that irradiation of liquid propylene gives dimer olefin derived in part by direct condensation of two propylene molecules, with all their hydrogen atoms retained in the product. This was taken as support for an ion-molecule mechanism that was proposed originally for 1-hexene radiolysis:2 e-
+ CnH:n
+C2nII,n+ +CmH,, However, proof was lacking that propagation could proceed to give the higher polymers C L , , H , ~ ~C,H,, --+CdnHbn+,etc. It now has been found that ethylene irradiated at - 196' gives low molecular weight, mostly branched CnHm+
+
C13 and by the light hydrogen isotopic impurity in the C2D4 (0.83%). Corrections for fragment ions were necessary only for 1-butene; these were applied assuming no isotope effect, a correction leading to some error, but not a serious one. Data are shown in the table. The strong maxima at species with deuterium atoms in multiples of four make it clear that hydrogen exchange between monomer and propagating polymer is negligible. It is also clear that the initiating species must contain two carbon atoms and four hydrogen atoms, and cannot be a vinyl or an ethyl entity. An initiating species with the formula CzH4 could be the molecule ion, C2H4+,or some excited state of the molecule. We believe only the molecule ion could supply the driving force for carbon-carbon bond formation at such a low temperature. The character of this initiating ion contrasts with that of the t-butylmrbonium ion, which ap-
TABLEI ISOTOPIC DISTRIBLTION OF PRODUCTS OF C2D4-C2H4RADIOLYSIS AT - 196": SPECIESDISTRIBUTION I N EACHCARBON NCMBER,MOLEPERCENT. do
dl
dz
C422 3 '7 C o l 5 3 2 Cg 9 1 1 Clo 3 2 0
da
d4
8 3 2 4 2 9 1 2 5 2 14
dr
ds
d7
da
2 5 4 0
6 1 1 2
2
18
6
2
4 4
d9
2 30 28
3 3
0
polymers, >90% monoolefins, of carbon number through CI8. Products from the irradiation of an equimolar mixture of C2D4 and C2H4 mere separated by gas chromatography, and mass spectra of the major C 4 (1-butene), Ce, Cs, and Clo components recorded. Corrections were made in the parent ion region of the mass spectra for contributions by (1) C. D. Wagnei, Tetrahedron, 14, 164 (1961). (2) P. C. Chanr. N. C. Y a w , and C. D. Wagner, J . A m . Chem. Soc., 81, 2060 (1959).
dlo
1 2 2
du
dlz
dia
dlr
dls
dls
d17
d18
dig
dm
3 6 1 1 5 4 25
1 0
1 2
0 2
4 0
0
0
0
