data is well
fit by the form of eq 15. For PPO
blended with PS oligomers, the pure-component glass-
transition temperatures differ by >200 K, and the value
reproduces blend transition temperatures to
K.I* Equations 16 and 17 give, respectively, K1
1.60. Thus, although strictly the differ-
ence between pure-component glass-transition tempera-
tures might seem rather large for the single-term expan-
sions necessary for eq 16 and 17, the former is the more
acceptable for compatible blends of PPO and PS (for
1) and, indeed, is fairly accurate.
phenomenological theory for the compositional vari-
ation of glass-transition temperatures in one-phase mix-
tures based on a model of these as regular solutions has
now been shown to account with some success for the
phenomenon in binary mixtures of high polymers and, also,
to give an acceptable description of the variation of
glass-transition temperatures with molecular mass for
homopolymers. Further, as described in the present con-
tribution, these two formal treatments can be combined
to predict glass-transition temperatures in compatible
blends of arbitrary composition and pure-component de-
gree of polymerization from component chain end and
high-polymer glass-transition temperatures and their re-
ciprocal heat-capacity increments, equivalent to the gen-
eration of a %n-dimensional
Acknowledgment. This research was supported by the
National Science Foundation Division of Materials Re-
search under Grant DMR79-151715, Polymers Program.
References and Notes
(I) Gordon, M.; Taylor, J.
1958, 28, 319.
Kelley, F. N.; Bueche, F.
J. Polym. Sci.
1961, 50, 549.
Am. Phys. SOC.
Martin, G. M.; Quinn, F. A.
J. Res. Natl.
1957, 58, 137.
DiMarzio, E. A.
1958, 28, 807.
M.; Beatty, C. L.; Pochan, D. F. Polymer
Kovacs, A. J. Adu. Polym. Sci.
Couchman. P. R.; Karasz, F. E. Macromolecules
Couchman; P. R.’Macro&olecules
Couchman. P. R.
J. ADDL Phvs.
Couchman; P. R.
J. 6ter. SEi.
Kanig, G. Kolloid
Fox, T. G.; Flory, P. J.
J. Polym. Sci.
J. Macromol. Sci., Phys.
1973, 7, 487.
See, for example: Naito, G.; Johnson, G. E.; Allara, D. L.;
Kwei, T. K. Macromolecules
Karasz, F. E.; Fried, J. R. In “Polymer
Paul, D. R., Eds.; Academic Press: New
Vol. 11, Chapter
Kwei, T. K.; Frisch, H. L. Macromolecules
Fried, J. R.; Karasz, F. E.; MacKnight,
Ueberreiter, K.; Otto-Laupenmuhlen, E.
Laboratoire de Spectroscopie Optique, UniuersitB de Sauoie,
Chambery Cedex, France
Laboratoire de SpectromBtrie Physique,+ UniversitB Scientifique et MBdicale de
Grenoble, 38041 Grenoble Cedex, France. Received February 6, 1980
ABSTRACT: A comparison is made between the longitudinal elastic modulus and the shear modulus in
polyacrylamide gels. The former is measured by inelastic light scattering as well as by osmotic deswelling;
the latter is measured by observation of the frequency of standing waves excited in the samples. The ratio