Secondary transitions in amorphous polymers. 5. Linear form of the Tait equation applied to isotactic poly(methyl methacrylate)

Abstract

is obviously not obeyed in regions containing pressure-induced transitions, other polynomial and multisegment correlations are examined, with the standard error taken as the main criterion of model performance. An automatic computer technique has been developed to systematically test multisegment correlations of y = f(P) data to locate intersection pressures, P, along individual isotherms. A three-segment correlation gives the best results on four high-temperature isotherms (138.2,160.7,174.5, and 190.2 °C), indicating the existence of secondary relaxations in the pressure range 1-2000 bars. These results are strengthened by good correlations of the determined transition points in a T-P plot, both among themselves and in comparison with prior results. Unambiguous interpretation of two lower isotherms (90.4 and 116.3 °C) is more difficult because of experimental uncertainties and the existence of the glass transition in the high-pressure region. Secondary relaxations above Tg include two liquid-liquid transitions, the intermolecular (Tu) and the intramolecular (T¡¡), and a low-pressure glass transition, Tg(LP). Evidence for Ts elevated above Tg at high pressure is also found. Pressure coefficients for these transitions are given.

Several effects of melt viscosity on the nature ofC p ?T data aboveT g for acrylate, methacrylate, and hydrocarbon polymers

“…If the goal is an approximation suitable for engineering calculations, that fact should be stated. For scientific studies we prefer statistical methods which require no a priori assumptions about the nature of the data but rather one(s) which guide the investigator to the true nature of the data, as in [11] and [13].…”

“…A residuals program developed by statisticians for any type of data [9,10]; and applied by us to polymer data generally [11] and specifically to V-T [11,121; V-P [13,14]; Cp-T[15I;/(-P [16]; ~-P…”

“…A so-called "break" program developed by Solc of MMI [13] which automatically searches a set of Y = F (X) data consisting of N data points to find that combination of n linear segments which minimizes the standard deviation for all N points. The slope and intercept of each of the n lines and also values of X and Y for the n-1 intersections are printed out.…”

Comments on Paper by Nemoto et al. Concerning Self Diffusion Coefficient, Ds, and Zero Shear Viscosity, η0 of Polystyrene in Dibutylphthalate

“…1 Tabulated data have been examined by regression analysis with residuals, 9 · 10 by point to point first derivatives 9 ; and by the Sole automatic intersection method which determines the number of linear segments and their coordinates in a given body of data which will minimize the standard deviation. 12 In the present instance, the number of data point -9 for three lines 1050 with FA-40 and FA-50 is borderline for use of computerized intersection method discussed in ref 12.…”

“…21, No. 12,1989 Lacking detailed studies, it is difficult to predict the relative effectiveness of the two diluents in lowering Tu since they differ both in molecular weight and presumably in solubility parameters. data are available in graphical form only.…”