116 TOSHIRO MASUDA,KEISHI KITAGAWA, TOSHIO INOUE, AND SHIGEHARU ONOGI
TABLE V ENTANGLEMENT MODULUS AND ENTANGLEMENT SPACINGS FROM THE MARVIN-OSER THEORY
L18 L19 L22 L15
581,000 513,000 275,000 215,000 Av
3.86 X 4.35 X 3.48 X 3.48 X 3.79 X
lo6 lo6 lo6 IO6
106
9,300 8,300 10,300 10,300 9,600
179 159 199 199 184
and J”,,,
=
0.417fezr0
(1 8)
Macromolecules
Therefore, from G”max we can determine G,$ using eq 17, and hence Me and Ze using eq 14. The values thus determined for some of the narrow-distribution polystyrenes shown in Figure 2 are listed in Table V. The values in this table differ from those in Table IV by a factor of 1.9. Recently, it has been reported33 that Me calculated by the use of the Hayashi theory30 for several polymer systems is two or three times larger than that obtained by the Marvin-Oser theory.28 Acknowledgments. This study was supported by a grant for scientific research (Kagaku Kenkyuhi) from the Ministry of Education. The authors wish to thank Professor John D. Ferry, University of Wisconsin, for his helpful discussions during his stay at our department in 1968. The gpc measurements by Mrs. K. Koga are also gratefully acknowledged. (33) I
