A new kinetic equation for the temperature dependence of the frequency shift factor

Abstract

2 = 5 {[exp(KAi -__ AHA)]-' RT + [ exp ( Kui -__ A: ' ) ] -' }-' VgE i = l AH$, and AH$, are the respective experimental activation energies, KA, and Ku, are the respective natural logarithms of the experimental collision term, R and T have their usual meaning. Macrokinetical interpretation: Each thermal transition (step) is caused by a sum A,+B, ofconsecutive reactions. The slowest reaction determines the rate of the whole transition. The different thermal transitions (steps) are concurrent reactions summarized from i= 1 to m. The fastest step determines which thermal transition occurs. Microkinetical interpretation: Process B, in Eq.(1) is a chain segment motion that occurs with low activation energy. The high activation energy process A, in Eq. (1) occurs in advance and makes the process B, possible perhaps by producing free volume. Temperature Dependence of the Shift Factor (Isomodulus)The logarithmic complex tensile modulus log E* or the storage modulus log E of amorphous polymers plotted against the logarithmic frequency log vat constant temperature (isothermal) results in an S-shaped curve. If the temperature as parameter increases the similar isotherms are shifted along the logarithmic frequency coordinate to higher frequencies. The shift factor %/ vgt of each isotherm is found to be the frequency y of the considered isotherm at a fixed value of the E-modulus normalized by the frequency ugE of the glass transition isotherm. Because the temperature dependence of the shift factor is considered at a constant E-modulus it is called "isomodud,

Glass (Tg) and Stimuli-Responsive (TSR) Transitions in Random Copolymers

“…In order to determine which molecular entities are responsible for the T SR endotherm, ATR FT-IR, Raman, and 13 C NMR measurements were performed as a function of temperature. While spectroscopic results are provided in the Supporting Information, Figure 2A-D To further elucidate the origin of molecular changes responsible for the T SR transitions, thermodynamic computer simulations were performed, in which infinite copolymer chains were constructed by randomly connecting energy minimized monomer units under 3D periodic boundary conditions.…”

“…Solid-state 13 C NMR spectra were acquired using a UNITY INOVA 400 spectrometer equipped with a Chemagnetics 7.5 mm two-channel solids probe. The samples were spun at a rate of 4.0 kHz.…”

“…The samples were spun at a rate of 4.0 kHz. The 1 H 90°pulse duration was 5.5 μs, and the acquisition time was 45 ms. A proton decoupling field strength of 52 kHz was used to remove 13 C-1 H dipolar broadening. The free induction decays (FIDs) were zero-filled to 32 K data points, and Lorentzian and Gaussian apodization was applied prior to Fourier transformation.…”

“…9 These endothermic relaxations occur above the T g , whereas the low-T g nBA provids free volume for spatial rearrangements. Since at T g the kinetic energy of the segmental motions results from the access of free volumes above the T g , [12][13][14] the T SR transitions were related to the compositional changes.…”