Quench depth

Thus, the initial selection of average distance between the smectic pearls is determined by e (and consequently quench depth, proportional to e). 

Many simulations of n chains, each with N beads, such that nN < 15 000 and the volume fraction of the polymer, 0 < 0.5, have been performed at different quench depths. The key observations are summarized below. 

Fig. 8 Quantized lamellar thickening. Rg is the radius of gyration of the lamella [22] Lamellar Thickness and Quench Depth... 

Therefore, we expect the scattered intensity /(q, t), proportional to ( /q(t)) to be exponential in time, 7(q, t) exp(2fiqr), with the rate Oq = q AT — q with both lower and upper cutoffs in q. If these arguments are valid, flq/ should rise sharply with q, reach a maximum, and then decrease at higher q values. These predictions are fully consistent with the experimental [10] and simulation [57] observations on /(q, t) and Oq. If the mechanism is simply a spinodal decomposition into two liquid phases, then D. /q should show a monotonic linear decrease from a finite positive value at q 0 with a slope independent of quench depth, which is not experimentally observed during... 

In their paper, Inoue et al. [36] proposed a new approach about phase separation mechanism under successive increases in quench depth. Figure 3.3 shows schematic... 

Figure 3.4 Time dependence of the concentration fluctuation during demixing with successive increases in the quench depth (quench rate = 0.6K/s). (Reproduced from [36])...

The quantity %s is the thermodynamic interaction parameter "/ between the constituent polymers at the stability limit and AT = (T — Ts) is the quench depth. 

Most of the observations reported so far suggest, that there are certain ranges of time, quench depth and wave numbers q where unmixing progresses to a good approximation in the linear branch, i.e. non-linearity is very weak. The conditions for validity of the linear theory can be specified more precisely as follows ... 

Thermal fluctuations can contribute dominantly to the scattering intensity right after the isothermal phase separation starts [70,76], Therefore, conditions 1) and 3) must be fulfilled to ensure that the effect of thermal noise is negligible. The dynamics of phase separation can be adequately described by the mean-field model if condition 2) is satisfied. Condition 2) is a direct consequence of the Landau Ginzburg criterion [75]. Thus, one may establish prerequisites for Eqs. (27) and (33) are the conditions 1) and 3), while Eq. (34) requires conditions 2) and 3). For example, Eq. (27) and as a consequence Eq. (33) cannot be confirmed experimentally not even for small values of q if the quench depth e is too small [70]. Moreover, owing to the effect of thermal fluctuations, Eq. (33) fails at q as qc even if the Landau Ginzburg criterion is fulfilled [70,77]. Thus, in the former case condition 2) is violated whereas in the latter example conditions 1) and 3) are not satisfied. 

A completely different result comes out if one pursues the experimental course of Fig. lib. The variation of the apparent diffusion coefficient as a function of quench depth AT = T — Ts, where Ts is the spinodal point, is shown in Fig. 13. Initially, the apparent diflusity increases with increasing quench depth AT which is in accord with the mean-field theory since (% — Xs)/Xs AT. However, when the quench depth is raised further the apparent diffusion coefficient starts to decrease and finally, apparently levels off. 

Fig. 13. Apparent diffusity as a function of quench depth for the system as in Fig. 12 and the procedure as indicated in Fig. lib. Annealing temperature below LCST 190 C...

It is obvious that the difference (p — p) is closely related to the quench depth or the thermodynamic driving force while the rate of the process is determined by the viscosity. According to these factors structure evolution is ruled by both externally imposed conditions and intrinsic properties of the system. 

The "quench depth e must be sufficiently small, but, e > - is necessary for validity of the mean-field approximation. ... 

Figure 11-14. Snapshots of a collapsing iV=128 chain in MD simulations with quenching depth, of (a) 1.00 and (b) 0.1. The time interval between snapshots is 10 tmd and the sequence is A to H. The surrounding solvent molecules are omitted for clarity. The figure is taken from Chang and Yethiraj [106] with permission...

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