removed from the network by solubil- 
ity tests. 
Elastic properties. Figure 4 shows 
the change in elastic properties of 
polyethylene after various irradiation 
doses (7). At first there is a drop in 
Young’s modulus until the usual melt- 
ing point is reached (about 115° C). 
Unirradiated polyethylene becomes a 
viscous liquid. Irradiated polyethyl- 
ene is transformed into a transparent 
and elastic material that is amorphous 
in character. The elastic properties 
above this temperature are found 
to follow the theoretical formula 
for amorphous rubber-like elasticity 
that has been deduced from entropy 
considerations 
E = 3pRT/M, 
where FE is Young’s modulus, p is the 
density, R is the gas constant, 7’ is the 
absolute temperature, and M, is the 
average molecular weight between 
crosslinks. Since density of cross- 
linking is directly proportional to 
radiation dose, E is'proportional to the 
degree of irradiation over a wide range 
of doses. The curves of Fig. 5 show 
that the formula fails only for very 
high crosslinking densities where elas- 
ticity corresponds to that of a glass- 
like structure. 
Once crystallinity has been de- 
stroyed by radiation, the density of an 
amorphous structure can be determined 
in terms of both crosslinking density 
and temperature. The results can be 
expressed in terms of an equation very 
reminiscent of a simplified Van der 
Waals equation 
(P + Po)(V — Vo) = RT[1 — B(c)] 
where P and P» are the external and 
internal pressures, V is the volume of 
polyethylene per gram mole of C2H,, 
and Vo is the volume at 0° K. The 
term G(c) is a function of the degree of 
crosslinking c, and approximates to c 
(the proportion of carbons crosslinked). 
This equation of state applies ap- 
proximately to other crosslinked poly- 
mers in the amorphous state. 
Solubility. The solubility charac- 
teristics of many long-chain polymers 
are affected considerably by radiation. 
Ordinary polyethylene is readily 
soluble in many organic materials at 
temperatures above 70° C. A very 
slight amount of crosslinking (corre- 
sponding to less than 0.03 units of 
radiation) does not greatly affect this 
property, since molecules are only 
linked together in small numbers to 
alter the molecular weight distribution. 
A somewhat larger radiation dose 
(about 0.05 units), corresponding to 
about 0.5 crosslink per molecule, links 
a large number of molecules together 
into one large molecule or gel that is in- 
soluble in all usual organic solvents. 
The remainder of the specimen (the 
molecules that have not been linked into 
the structure) can still be removed by 
solvents, but the amount of this soluble 
fraction or sol is limited. Further ir- 
radiation gives a rapidly decreasing 
amount of soluble material. From the 
relationship between the sol fraction 
and the radiation dose, useful informa- 
tion can be derived as to the molecu- 
lar weight distribution in the original 
polymer. 
In solvents, crosslinked polyethylene 
swells to an extent that depends on its 
temperature and degree of crosslinking. 
Considerable swelling can be produced 
in lightly-linked specimens at tem- 
peratures above the usual melting 
point. 
Other paraffinic structures. The 
effect of radiation on other paraffinic 
structures has also been studied (8). 
Paraffin wax and paraffin molecules of 
known molecular weight from heptane 
(C7His) to hexatriacontane (C3.H74) 
in both liquid and solid state have been 
successfully crosslinked into an in- 
fusible gel. The amount of radiation 
required to do this is inversely propor- 
tional to the molecular chain length. 
In all cases the energy absorbed is 
about 25 ev per crosslink. 
Polystyrene 
Insolubility of the product and 
changes in the softening point show 
that polystyrene can be crosslinked by 
ionizing radiation. Radiation doses 
to achieve these effects are far greater 
than for polyethylene despite the much 
larger number of monomer units in the 
average polystyrene molecule. For 
example, a polystyrene molecule con- 
taining an average of about 8,000 
carbon. atoms in the main chain of the 
molecule requires 1 unit of radiation 
per crosslink, whereas a polyethylene 
chain of the same chain length would 
only need about 0.02 units to achieve 
the same amount of crosslinking. The 
difference can be ascribed to the ben- 
zene ring in styrene. Such a ring 
stabilizes many organic compounds 
against the effects of radiation. The 
resonant levels of the benzene structure 
act as a sink and dissipate the added 
energy that otherwise might produce 
crosslinking or degradation. 
It can be shown directly that the 
stabilizing effect is due to the resonat- 
ing benzene ring. Molecules con- 
sisting of either a naphthyl or decalyl 
ring structure to which similar paraf- 
finic side chains are attached, have 
been irradiated. The former, which 
has a resonant structure, requires far 
more radiation to induce gel formation 
than the latter, although there is no 
significant difference in the rate of 
energy absorption by the two types of 
molecule. 
Surface oxidation. As in poly- 
ethylene, surface oxidation occurs 
when polystyrene is irradiated in the 
presence of air. After considerable 
irradiation, a brown powder is formed 
that contains substantial amounts of 
oxygen. Unlike the oxidation product 
on the surface of polyethylene, this 
material is not sticky and can be 
removed readily. Apart from this 
slight oxidation the only obvious 
change to irradiated polystyrene rods 
is a yellow coloration that increases 
rapidly with radiation dose. 
Melting. Figure 6 shows how irra- 
diated polystyrene rods withstand high 
temperature. In spite of the slight- 
ness of crosslinking, the irradiated 
specimens retain their shape and do not 
melt or flow when heated to 250° C. 
At the same temperature, the unir- 
radiated specimen forms a viscous 
liquid. For a radiation dose (0.6 units) 
corresponding to only 0.6 crosslinks 
per molecule (1 crosslink per 6,000 
carbon atoms) there is a marked effect 
in the melting character of the polymer. 
It would be expected that at least 
1 crosslink per chain is needed to 
obtain an infusible network. How- 
ever, the wide variation in chain 
lengths means that most of the longer 
molecules will contain at least one link 
and will form a network that can 
withstand the high temperature while 
retaining the shorter molecules within 
itself. 
Solubility. Results obtained on sol- 
ubility and swelling of crosslinked 
polystyrene are of considerable interest 
in polymer research (9, 10). 
For a small amount of radiation and 
crosslinking, the molecular weight 
distribution is altered with a corre- 
sponding change in the viscosity of the 
product when dissolved. For such 
radiation doses certain molecules be- 
171 
