Apparent activation volume

Thus, the apparent activation energy is changing much more rapidly near Tg than the apparent activation volume. The use of pressure greatly expands the level of information that can be gained with regard to the dynamics of the glass transition. 

T is the absolute temperature. These plots are shown in Figure 4 for both ASA polymers. Both rate quantities give approximately the same value, ca. 3500A3, for the apparent activation volume yv for both polymers. 

A similar graph can be plotted for the maximum lateral strain rate d/dt (—ei) (see Figure 5) this gives an apparent activation volume of ca. 3000 A3 for the shear processes in both ASA polymers. 

In principle, the effect of rubber content upon y can be determined from the differences in apparent activation volume yv obtained from Figure 4, since the true activation volume should be the same for both materials. In practice, the scatter in the results reduces the reliability of the estimate in the present work. 

Kinetics of Yielding. Tensile yield stresses were measured at several Instron rates for block polymer B. These results and those of Bauwens-Crowet et ah (9) for BPA polycarbonate were analyzed in the framework of the Rhee-Eyring stress bias activation theory for comparison purposes. Yield stress of the block polymer is roughly half that of the homopolymer at a given temperature. The apparent activation volume for the block polymer is double that of the homopolymer at each temperature. Activation energies at zero stress are essentially the same (60 kcal/mole for the block polymer vs. 70 kcal/mole for BPA polycarbonate above —50°C). 

The modulus and yield kinetic parameters of the block polymer B can be related to those of the homopolymer in terms of a microcomposite model in which the silicone domains are assumed capable of bearing no shear load. Following Nielsen (10) we successfully applied the Halpin-Tsai equations to calculate the ratio of moduli for the two materials. This ratio of 2 is the same as the ratio of the apparent activation volumes. Our interpretation is that the silicone microdomains introduce shear stress concentrations on the micro scale that cause the polycarbonate block continuum to yield at a macroscopic stress that is half as large as that for the homopolymer. The fact that the activation energies are the same however indicates that aside from this geometric effect the rubber domains have little influence on the yield mechanism. 

Given the remarkably large quantum yield for emission. 4 -1 = 0.55 + 0.03, this gives k300/ 1 = 1.34 0.03, from which an apparent activation volume for the nonradiative deactivation path can be calculated to be — 2.4 0.5cni3mol. In acetonitrile, a AF value of —0.2cm3 mol 1 was determined [45]. 

Let us first consider the situation where initial excitation is followed by relaxation to a bound LEES, which is then responsible for the ligand substitution chemistry. In accord with the above discussion, the quantum yield <1>S for ligand substitution from that state would be fl>lscfcst, where intersystem crossing from the state(s) initially formed, ks is the rate constant for ligand substitution from the LEES, and r = kd1 (kd being the sum of the rate constants for the decay of the LEES). The apparent activation volume for the photoreaction quantum yields is therefore defined as... 

The two most common parameters measured in photochemistry are the quantum yield (Pi for a specific process, and the lifetime t of the excited state. The quantum yield is operationally defined as the moles of product formed (or starting species reacted) per einstein of light absorbed by the system at a particular wavelength of irradiation (Am). In this context, the pressure effect on the quantum yield gives an "apparent activation volume , i.e. AV = -RT[d(ln )/dP]j. from a plot of In O vs. P. 

This gives = 1.34 + 0.03, from which an apparent activation volume for... 

Theoretical predictions are, however, difficult because the activation volumes of reaction steps and the compressibilities of SCFs change with pressure. A further complication is that, by changing pressure, one simultaneously changes the density-dependent physictd parameters of the supercritical fluid. Effects of mass transfer are also always present to some extent. Therefore, only apparent activation volumes have been measured for enzymatic reactions in SCFs. The reaction mechanisms of enzymatically catalyzed reactions are often not known. 

Kamat et al. found that the initial transesterification rate with Candida cylin-dracea lipase decreased markedly upon increasing the pressure from 80 to 120 bar [5]. They ran the reaction in fluoroform at 50 °C and calculated the apparent activation volume of the reaction from initial reaction rates at different pressures. The apparent activation volume showed a maximum near the critical point of fluoroform. As the pressure increased from 60 to 180 bar the apparent activation volume approached zero and the reaction rate decreased to one tenth. 

The apparent activation volume appeared to be dependent on the temperature, increasing with deformation temperature and becoming constant beyond 90.3 °C. This coincides with the onset of rubbery plateau temperature as discussed previously. 

Figures 6 show the Eyring plots derived from the same dataset at various strain levels at a given temperature. An interesting feature exhibited by these plots is the transformation of the parallel slopes (i.e. constant apparent activation volume) at 85.3 °C to nonparallel (i.e. variable activation volume) at 92.9 °C, and becoming more significant thereafter, up to 115.6 °C studied in this work.

A related quantity is the pressure sensitivity of the relaxation times, defined through the apparent activation volume, AV5f... 

Figure 11 (Left) Temperature dependence of the relaxation times for the different processes in PEMA (/I4=2.0 x lO g moE ). At higher tEmperatures, the process due to the ion motion (squares) and the (ap)-relaxation (circles) are shown, while at lower temperatures, the a- (up triangles) and p- (down triangles) processes are shown. The lines are fits to the VFT equation forthe slow, (ap)-, and a-processes, and to the Arrhenius equation forthe p-process. (Right) Apparent activation volume, Al/, as a function of temperature forthe a- (filled squares), the (ap)- (open up triangles), the p-(filled circles), and the ion mobility (filled down triangles) processes of PEMA. The horizontal line gives the repeat unit volume (14,=102 cm moE ). Erom Mpoukouvalas, K. Floudas, G. Williams, G. Macromolecules 2009, 42, 4690. ...

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