Studies were made of the physical properties of the commercially available polyimide Upilex-SGA, which is prepared from biphenyl dianhydride and p-phenylene diamine. Annealing the Upilex-SGA for 2 hr Linder N2 at 400°C gave a film that expanded continuously when heated at a fixed rate, in contrast to the as-received film. The linear expansion showed a change of slope at 84°C and also at 295°C, the later being Tg. The thermal coefficient of linear expansion at all temperatures was very smap, even above 295°C it is 27.8 x 10−6. Its stress-strain curve did not exhibit a yield point, even though its ultimate elongation is ~23%. Similar behavior is shown by the PMDA-ODA polyimide, except its ultimate elongation is ~70’%,. The unusual stress- strain curves exhibited by these polyimides is undoubtedly caused by their liquid-crystalline morphology. The stress-relaxation modulus was measured at 0.5% extension and 12 temperatures from 30 to 330°C. Derived isochrones showed that the 1-s tensile modulus at 20°C is 9.0 GPa, but at 330°C it is 2.0 GPa. Creep curves were also measured at a stress of 30 MPa and at 10 temperatures from 30 to 340°C. Master curves prepared from the relaxation and creep data are discussed briefly and evidence is given which, show that the superposition method is not truly valid for this polyimide, which actually is not surprising.

AbstractA novel method has been developed and tested to determine accurately the linear coefficient of thermal expansion α of flexible films without subjecting a specimen to a tensile load continuously during the measurement of expansion data. Other methods have invariably required the application of a tensile load which commonly leads to creep during the experimental time. The new method involves mounting an Invar jig in the lower grip in a Dynastat. The closed‐loop servo control in the Dynastat enables the length of a specimen to be determined at a series of decreasing or increasing temperatures without subjecting the specimen to a tensile load, except momentarily on occasion while length data are being determined. Otherwise, a specimen is subjected to a small bending force. To demonstrate that the method gives valid results, α for an aluminum foil was determined and found to agree exactly with literature data. Expansion coefficients and values of the glass transition temperature (Tg) were determined on FEP and PFA Teflon films and also on a commercially available polyimide film, Upilex‐SGA.

In 1910 Weyl [9] inaugurated the modern theory of singular self-adjoint differential operators, considering, in particular, second-order differential operators with real coefficients. Since then, his results have been generalized by various authors to the case of arbitrary even order self-adjoint differential equations with real coefficients. Also, in 1954 Coddington [2] treated the case of an arbitrary n-th order self-adjoint differential equation with complex coefficients, He obtained the Parseval equality and spectral expansion associated with the singular case directly, through the consideration of such a problem as a limiting case of corresponding self-adjoint two-point boundary-value problems on compact subintervals of the reals. Using the same general concept, Coddington and Levinson [3] derived a Green’s function, which in turn enabled them to obtain the spectral matrix for a singular problem involving a linear homogeneous n-th order differential operator, and then proceeded to derive the Parseval equality and spectral expansions. Recently Brauer [I] treated similar problems which involve a definitely self-adjoint vector differential operator, of the sort that has been treated by Reid [6] and others. He obtained the Green’s matrix and spectral matrix through the use of the spectral theorem and the theory of direct integrals. The main purpose of the present paper is to employ the general method