Isochoric relaxation time

FIGURE 11.17 Isochoric relaxation times r of the primary dielectric relaxation (open symbols) at the indicated specific hole free volumes, Vf, along with the relaxation times for ambient pressure (filled symbols) for PMPhS. The hues through the data are a visual aid. (From Dlubek et al. [2007b].)... 

Figure 24. Upper panel Dielectric relaxation time for BMMPC experimental data for 0.1 MPa, other isobars (200 and 600 MPa), and the isochore at V = 0.9032 ml/g were calculated. Dotted line indicates the average of logjo(is) = —6.1 for the different curves. Lower panel Shekel function, with low- and high-71 linear fits, done over the range —4.68 < log10(x[i]) < 3.85 and —8.55 < log10(x[j]) < —6.4, respectively. Vertical dotted lines indicate the dynamic crossover.

Figure 43. Isobaric dielectric relaxation times for salol, PC, BMMPC, PDE, KDE, and PCB62 versus Ta/T, where t(T7 ) — 10 s. Isochors were calculated at the volume at which r= 10 s at atmospheric pressure V = 0.7907 (salol), 0.7558 (PC), 0.9067 (BMMPC), 0.7297 (PDE), 0.7748 (KDE), and 0.6131 (PCB62) ml/g. [Adapted from R. Casalini and C. M. Roland, Phys.Rev. B 71, 014210 (2005).]...

The initial state of the simulations consisted of RDX perfect crystals using simulation cells containing 8 molecules (one unit cell, 168 atoms) and 3D periodic conditions. After relaxing the atomic positions at each density with low temperature MD, we studied the time evolution of the system at the desired temperature with isothermal isochoric (NVT ensemble) MD simulations (using a Berendsen thermostat the relaxation time-scale associated with the coupling between the thermostat and the atomistic system was 200 femtoseconds). 

Real locus of the system in pressure-composition space during an isochoric step from the /f-1th to the kth point on the recorded isotherm (Eqns 7.10, 7.11). The excursion of the pressure in the hydrogenator to pfys,o) occurs when the valve S (Fig. 7.4) is opened instantaneously. The system then approaches equilibrium according to the kinetics of the sample and the thermal relaxation time of the sample/cell sub-system. The pressure excursion is lessened if S is opened slowly, so that absorption commences while Psys is still rising. The slope of the isochore is constant only if the compressibility is constant. 

In Figure 11.17 we show Arrhenius plots of the isobaric [t (7)]/> (F = 0.1 MPa) and isochoric [t (7)] v/ (vy = 20 to 30 mm /g) dielectric relaxation times of PMPhS, where the free volume Vf was obtained from the S-S equation of state. The slopes at the intersection of the isochoric and isobaric curves yield the respective activation enthalpies for ambient pressure. 

Fig. 2.16. Temperature dependences of the dielectric relaxation times for PVAc at atmospheric pressure ( ) and at a constant volume equal to 0.847 mlg (A), 0.849 ml ( ), and 0.852 ml g (V). The slopes at the intersection of the iso-baric and isochoric lines yield values for the respective activation energies at constant pressure and constant volume a = 238 and 448kJmol (r = 2.5 s) and = 166 and 293 kJ mol (r = 0.003 s). The ratio of the isochoric and isobaric activation energies is a measure of the relative contribution of thermal energy and volume that is, this ratio would be unity if the molecular motion were thermally activated, and zero if it were strictly dominated by density. For PVAc, the ratio is 0.6, indicating that both contributions are significant. From Roland and Casalini by permission [132].

---