Molecular relaxation time

In the last chapter we saw that the molecular relaxation time is the yardstick against which times are measured. The experimental relaxation time plays a similar role. This is easily seen by an examination of Fig. 3.8b. For... 

As described in the section on nonlinear absorption, the transmission of a pulse which is short compared to the various molecular relaxation times is determined by its energy content. A measurement of the energy transmission ratio will then give the peak intensity of the pulse when its pulse shape is known 44>. In fact, the temporal and spatial pulse shape is of relatively little importance. Fig. 11 gives the energy transmission as a function of the peak intensity I [W/cm2] for the saturable dye Kodak 9860 with the pulse halfwidth as a parameter. It is seen that this method is useful in the intensity region between 10 and 1010 MW/cm2 for pulses with halfwidths greater than 5 to 10 psec. Since one can easily manipulate the cross-section and hence the intensity of a laser beam with a telescope, this method is almost universally applicable. 

This form for reduced compliance is suggested by the dilute solution molecular theories, according to which JeR is governed by the dispersity of molecular relaxation times [from Eq. (4.12)] ... 

With the exception of 550 K, each trajectory was at least 45 times longer than the largest molecular relaxation time at a given temperature. The system at 550 K would have required upwards of 70 ns by these criteria, which is beyond the practical limits imposed by our computational resources. Therefore we stopped the simulations at this temperature after 20 ns, which was sufficient to... 

Perhaps the most important distinction between classical solids and classical liquids is that the latter quickly shape themselves to the container in which they reside, while the former maintain their shape indefinitely. Many complex fluids are intermediate between solid and liquid in that while they maintain their shape for a time, they eventually flowr They are solids at short times and liquids at long times hence, they are viscoelastic. The characteristic time required for them to change from solid to liquid varies from fractions of a second to days, or even years, depending on the fluid. Examples of complex fluids with long structural or molecular relaxation times include glass-forming liquids, polymer melts and solutions, and micellar solutions. 

Significant shifts in S are not expected to occur in small-molecule nematics unless the shear rate is extraordinarily high. For polymeric nematics, however, molecular relaxation times T are typically 0.001-10 sec, or even higher, and therefore molecular elastic effects are produced at shear rates y r = 0.1-1000 sec L Thus, the order parameter S is significantly distorted away from that of equilibrium when the Deborah number De (discussed in Section 3.6.2.1.1) is of order unity or greater, where... 

The degree of molecular mobility (assessed as the average molecular relaxation time r) of amorphous systems in the region near Tg follows a non-Arrhenius temperature dependence. This so-called fragility (dr/dr at Tg) of amorphous materials is a defining characteristic. ... 

To fully understand the performance of amorphous materials, it is necessary to be able to measure the molecular mobility of the samples on interest. This is because at temperatures as far as 50 K below the glass transition temperature, pharmaceutical glasses exhibit significant molecular mobility that can contribute to both chemical and physical instability.The main techniques that have been developed for monitoring molecular motions in amorphous materials are nuclear magnetic resonance (NMR) and calorimetric techniques (e.g., DSC and isothermal microcalorimetry). Average molecular relaxation times and relaxation time distribution functions obtained from these... 

Fig. 8 The temperature dependence of average molecular relaxation times for amorphous pharmaceutical materials. (From Ref.. )...

We must point out two related limitations of the LE theory. First, it applies to small-molecule LCs and to LCPs in the limit of vanishing strain rate. This is because the LE theory uses a vector n to represent the orientation state of the fluid, tacitly assuming that the molecular orientation distribution stays at its equilibrium state. This is reasonable when the molecular relaxation time is much shorter than the characteristic time of the flow. Second, the theory does not allow orientational defects, which would be singularities in the n field. In reality, LCs and LCPs tend to have a high density of defects. ° Near the defect core, large spatial gradients distort the molecular orientation distribution, thus invalidating the LE theory. 

The narrow transformation range commonly referred to as the glass transition is the temperature interval where the characteristic molecular relaxation time becomes of the order of 100 s (the laboratory time scale). The viscosities of several glass-forming liquids are shown in Fig. 3 as a... 

The effect of overall molecular weight or the number of blocks on rheological properties for the samples from the second fractionation can be illustrated as a plot of reduced viscosity vs. a function proportional to the principal molecular relaxation time (Figure 2). This function includes the variables of zero shear viscosity, shear rate, y, and absolute temperature, T, in addition to molecular weight, and allows the data to be expressed as a single master curve (10). All but one of the fractions from the copolymer containing 50% polystyrene fall on this... 

If the Deborah number is large (large molecular relaxation time or small diffusion time), the diffusion process is described by Fickian kinetics and is denoted by an elastic diffusion process. The polymeric structure in this process is essentially unaffected and coefficients of mutual and self-diffusion become identical. Elastic diffusion is observed at low solvent concentrations below the glass transition temperature. ... 

Paying attention to pure acetone, Brodka and Zerda have calculated rotational relaxation times and translational diffusion coefficients by molecular dynamics simulations. In particular, the calculated rotational times of flie dipole moment can be compared with a molecular relaxation time Xm obtained from the experimentally determined Xb by using the following expression, which considers a local field factor ... 

A closer look at this concentration dependence of the first positive maximum N, as well as the shear rate at which this occurs, was conducted by Baek et al [46]. Both were seen to be monotonically increasing functions up to concentrations of 40%. They demonstrated qualitative agreement with the predictions of Doi theory with the Hinch-Leal closure and the Maier-Saupe potential. They also note that the ratio of shear rate at which becomes negative to the shear rate of the first positive maximum remains constant at about 3.5. (Our data from 1978 and 1980 yielded an average ratio of 3.2 with a standard deviation of 0.9 for nine PBG solutions and an average ratio of 2.2 with a standard deviation of 0.3 for three PCBZL solutions.) They determined that the rapid increase in (dy/dt) with concentration cannot be attributed to a decrease in molecular relaxation time with... 

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