come linked together in pairs, threes, 
etc. As radiation dose is increased, a 
point is reached where a network of 
theoretically infinite extent is formed 
that includes a large number of the 
original molecules linked together into 
one gigantic molecule. By definition, 
this is insoluble and is referred to as 
the gel. Molecules not linked into 
this structure are still soluble and form 
the sol fraction. With further radia- 
tion and increased crosslinking, the 
gel fraction increases while the sol 
fraction diminishes. It can be shown 
that if only crosslinking occurs, the 
soluble fraction tends to zero with 
increasing radiation dosage, whereas, 
if some degree of random main chain 
fracture also is produced, the sol frac- 
tion tends to a finite amount charac- 
teristic of the ratio of chain fracture 
to chain crosslinking. For polysty- 
rene, the curves of Fig. 7 indicate that 
little or no main chain fracture occurs 
under radiation. 
Several theoretical studies have been 
made of the variation of gel fraction 
with crosslinking density—the latter 
being accurately proportional to radia- 
tion dose. The relation is found to 
depend on the initial molecular weight 
distribution. Experimental measure- 
ments of the gel fraction in polystyrene 
crosslinked by pile radiation have been 
combined with this theory to obtain 
information on this molecular weight 
distribution. 
Irradiated polystyrene also has been 
used in connection with studies of 
swelling of crosslinked polymers. A 
crosslinked polymer will swell in com- 
pounds that are usually solvents for the 
uncrosslinked molecules. The solvent 
molecules (benzene, toluene) enter the 
network and try to force the molecules 
apart. This tendency is resisted by 
the elastic properties of the crosslinked 
network. With higher degrees of 
radiation (and, hence, of crosslinking) 
the swelling is reduced. 
An approximate theory of this effect 
has been worked out (11). Irradiation 
provides the polymers of varying and 
known degrees of crosslinking that are 
necessary for full experimental analysis. 
Figure 8 shows that the theory is 
remarkably accurate over a wide range 
of degrees of crosslinking, in spite of 
several approximations made in the 
theoretical relationships. For exam- 
ple, the theory does not allow for the 
existence of a soluble fraction nor for 
the difference in crosslinking between 
172 
gel and sol (the gel will tend to contain 
a higher proportion of crosslinked 
polymers). A detailed analysis shows 
that the errors due to these various 
factors tend to cancel each other out 
so that the excellent agreement ob- 
served is to some extent fortuitous. 
By calibrating the swelling of a series 
of polymers crosslinked by irradiation 
it should prove possible to provide 
laboratory standards of crosslinking 
for use in industrial and research 
laboratories dealing with polymer 
behavior. 
Rubber 
Rubber can be considered a natur- 
ally occurring polymer that, for most 
practical purposes, has to be vulcanized 
(crosslinked). This crosslinking can 
be achieved by exposure to ionizing 
radiation alone, without introducing 
sulfur or accelerators and without heat 
treatment (12). The process can take 
place in the absence of oxygen, and 
Fig. 9 shows that the degree of cross- 
linking is proportional to the radiation. 
The efficiency of crosslinking (number 
of monomer units crosslinked per unit 
radiation) is somewhat higher for 
rubber than for polyethylene. Cross- 
linking efficiency can be deduced both 
from swelling experiments and from the 
network’s elasticity. 
Experiments on the gelation of rub- 
ber by radiation have been carried out 
to determine the changes in molecular 
weight produced by crosslinking; these 
may be followed approximately by 
studying the viscosity of the soluble 
fraction. An alternative method is 
based on measurements of gel fraction 
for various radiation doses. Both 
sets of data give similar values for the 
initial average molecular weight of the 
rubber; it should prove possible to use 
these techniques to obtain information 
on molecular weight distribution. The 
results already obtained amply confirm 
the theory of gelation and the assump- 
tion of random crosslinking. 
The technique of using radiation to 
crosslink oriented structures might 
have useful industrial applications. If 
specimens of rubber are stretched and 
irradiated in an oriented form, they 
FIG. 6. 
0, 0.6, 2, and 6 units of radiation. 
Xe x, on} 
Expemmental \ 
N 
points -- an 
linking only 
“EAN 
uniform mole- 
“oy DX Veue size 
Theoretical curve, a 
crosslinking only “\ 
=s 
(initial random 
Aer 
x Theoretical 
curve, cross- 
= 18) 
a 
molecular size 
distribution ) 
Soluble Fraction (per cent) 
Theoretical curve, -- a 
crosslinking + 20% degradation 
(initial random molecular size 
distribution) 
o5 o8' 152 
Crosslinks Per Molecule 
FIG. 7. Solubility decrease of irradiated 
polystyrene 
Effect of heat on irradiated polystyrene. 
All samples were heated at 250° C for 30 minutes 
From left to right, samples received 
Volume Swelling Ratio 
10 5 fa 
Radiation Dose (units) 
FIG. 8. Decrease in swelling in toluene of 
polystyrene crosslinked by radiation 
