765
NOTES
May, 1959 TABLE I CRYSTALLIZATION RATECONSTANT II OF THE RAPID PRIMARY CRYSTALLIZATION PERIOD Sample 1 ,
Sample 2 ,
My 110,000
tf" 98,000
(unfractionated) K (l/min)4 T , OC. AT
119 120 112 123
10 9 7 6
9.11 x 10-6 1.82 x 10-5 5.71 X 7.71 X 10-lo
Sample 3, M , 53,000 (fraction)
T
AT
K
113 115 117 119 121
16 14 12
2.48 X 9.10 X 2.44 X 1.70 x 1.77 X
io
8
T 117 118 119 120 122
T
10low4 lob4 10-5
111 113 114 115
(fraction) AT K
13 12 11 10 8
4.39 X 1.68 X 1 W 4 3.03 X 2.80 X lo-' 2.42 X IO-@
Sample 4, d h 2,100 (fraction) AT K
12 10 9 8
0
- vm/vo
= Ce-K't
2
3
4
6
5
[ Fig. 2.-Log
2.80 x 3 70 X 1.50 X 3.67 X
Quina and Flory,' log X should vary linearly with the term (Tm/AT)21/T, where T , is the melting temperature of the polymer. From the slope of such a plot shown in Fig. 2, the interfacial surface energy can be calculated. With the exception of the data for the highest molecular weight sample, the slopes of all curves seem to be independent of molecular weight. It is not obvious that the data of the highest molecular weight sample should have a different slope in Fig. 2, but the uncertainties involved in calculating the coilstant I< and the fact that a small error in the melting point determination would cause a radical change in the slopes and the positions of the lines in Fig. 2, could easily have caused such an anomaly. The interfacial surface energy calculated from the three parallel lines in Fig. 2 is in the order of 4 ergs per This value, though not too far from what Mandelkern, Quinn and Flory have found for other polymers, is small in comparison to the value found by Burnett and McDevit8 from the direct microscopic observation of Nylon spherulite growth. The slow secondary volume contraction of the present low pressure polyethylene samples is slightly different from that of high pressure polyethylene observed by Kovacs. Kovacs found that the volume change varied linearly with the logarithm of time whereas the slopes of the curves in Fig. 1 change continuously with the logarithm of time. The tail portions of the present curves actually can be fitted by a simple relaxation equation of the type V/VO
I
K
Ap'.
VS.
1
8
9
10
I1
12
( 1/AT)2(T m 2 / T ) .
large temperature coefficient is not likely to be alone responsible for the slow volume contraction. It is interesting to note that the long term crystallization behavior observed by Russell and discussed by Dunning9 on vulcanized rubber also fitted an equation similar to equation 2. TABLE I1 THERATECONSTANT K' (IN ~/R.IIN.) FOR THE TAIL PORTIONS OF THE SLOW SECONDARY VOLUMECONTRACTION Sample 1 Temp., "C.
Jfv 98,000
(unfractionated)
1.35 x 1.06 x 1.34 x 1.39 x
120 115 105 95
10-4 10-4 10-4 10-4
Sample 3 Temp., OC.
120 115 105 95
div 53,000 (fraction)
1.30 x 1.27 x 1.55 x 1.30 x
10-4 10-4 10-4 10-4
Sample 2 M v 110,000 (fraction)
1.02 x 1.15 x 1.24 x 0.64 x
10-4 10-4 10-4 10-4
Sample 4 A!!" 2 100 (fracbion)
... 0.70 1.52 0.99
x x x
10-4 10-4 10-4
Although the tail portions of the present crystallization curves can be fitted by equation 2, the entire crystallization process shown in Fig. 1 is obviously not a simple composite of the processes described by equations 1 and 2. It is conceivable that the secondary nucleation and the subsequent growth of crystallites during the developnlent of spherulites set up stresses in the polymer. The slow volume contraction, resulting from the decay of such stresses is likely to be more complicated than can be described by a single, simple relaxation equation. (9) W. J. Dunning, Trans. Faradaz, SOC.,60, 1115 (1954).
(2)
where v m is the equilibrium specific volume, K' is the rate constant and C is another constant. The data of the high temperature runs followed equation 2 at about 6,000 minutes (3.5 days) after the start of crystallization. For lower temperature runs equation 2 begins to fit the data as early as 2,000 minutes after the start of crystallization. The calculated values of the constant I
