Dynamic crossover

For PS/d-cyclohexane, the only system where comparable static and dynamic data from the crossover regime are available, the static and dynamic crossover points Q (x) = l/c/x) do not coincide... 

The dynamic crossover occurs at fcross 40 ns. From r (tcross))= 50 a crossover length A is deduced. This length scale may be identified with the... 

The problem of the dynamic crossover from the asymptotic critical to the mean field regime has been treated by Jacob et al. [94] and by Kostko et al. [95], Kostko et al. derived a decomposition of D = Db + AD into a background contribution Db and an enhancement AD of the form... 

Figure 45. (left) The quantity displayed AB285 is a measure of the spectral width which is reduced by the change of the amplitude of the fast dynamics with temperature different EPR probes (as indicated) were chosen to probe the dynamic crossover Tc values reported are 297 2 K (o-terphenyl, OTP) and 221 2K (polybutadiene, PB). (right) Typical EPR spectrum indicated are two parameters characterizing the line width. (From Ref. 369.)... 

Concerning the slow dynamics below the crossover temperature Tc, the predictive power of the theory seems to be rather limited. In particular, the emergence of intrinsic slow secondary processes, which seems to be associated with the dynamic crossover in the experimental spectra, is not contained even in the extended versions of the theory consequently, the slow dynamics spectrum is not reproduced correctly. In this respect, the extended theory introducing the hopping mechanism for describing the susceptibility minimum below Tc is misleading. On the other hand, the most prominent prediction of MCT below Tc is the anomaly of the nonergodicity parameter, which, as discussed, is found by different model-independent approaches. However, within the framework of MCT, this anomaly is closely connected with the appearance of a so-called knee feature in the spectral shape of the fast dynamics spectrum below Tc. This feature, however, has not been identified experimentally in molecular liquids, and only indications for its existence are observed in colloidal systems [19]. In molecular systems, merely a more or less smooth crossover to a white noise spectrum has been reported in some cases [183,231,401]. Thus, it may be possible that the knee phenomenon is also smeared out. 

In the present work, we have reviewed results on molecular glass formers, but it is not clear to what extent the observed relaxation features are also found in more complex systems, such as polymers and inorganic network glasses. Susceptibility spectra covering, say, more than 10 decades in frequency are still rare for the case of more complex systems. For example, how does the manifestation of the dynamic crossover change when going from a molecular liquid to a polymer ... 

Liu L, Mon CY, Chen SH. The fragile-to strong dynamic crossover transition in confined water nuclear magnetic reso- 57. nance results. J. Chem. Phys. 2006 124 161102. 

Chen SH, Liu L, Fratini E, Baglioni P, Faraone A, Mamontov E. Observation of fragile-to-strong dynamic crossover in protein hy- 95. dration water. Proc. Nat. Acad. Sci. U.S.A. 2006 103 9012-9016. 

Faraone A, Mamontov E. Experimental evidence of fragile-to- 96. strong dynamic crossover in DNA hydration water. J. Chem. 

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.

Table 1 Values of fitted parameters for EOS (eq. (3)) and time-scales for the dynamic crossover from the Arrhenius domain in tested glass forming liquids.

Novikov, V. N., and Sokolov, A. P. (2003) Universality of the dynamic crossover in glass-forming liquids A magic relaxation time, Phys. Rev. A 67, 031507. 

Drozd-Rzoska, A., Rzoska, S. J., and Pawlus, S., Tamarit, J. LI. (2006) Dynamics crossover and dynamic scaling description in vitrification of orientationally disordered crystal, Phys. Rev. B 73, 224205. 

II. Kumar, P., Buldyrev, S. V., and Stanley, H. E. (2007) Water liquid-liquid dynamic crossover and liquid-liquid critical point in the TIP5P model of water, in S. J. Rzoska and V. Mazur (eds.) Soft Matter under Exogenic Impacts , NATO Sci. Series II, vol. 242 (Springer, Berlin)... 

Lagi M, Chu X, Kim C, MaUamace F, Baghoni P, Chen S-H The low-temperature dynamic crossover phenomenon in protein hydration water simulations vs. experiments. J. Phys. Chem. B 2008,112 1571-1575. 

Figure 9. The bare dynamic correlation length Figure 10., d, and 5 for solution PS (Eq.l2) vs. X. The symbols are spelled ontin the (M 5700)inCH-d. The sohd and dashed arrows insets. show the static and dynamic crossovers.

Casalini, R., and Roland, C. M., Scaling of the supercooled dynamics and its relation to the pressure dependence of the dynamic crossover and the fragility of glass formers, Phys. Rev. B, 71, 014210 (2005). 

It helps if we eategorize the anomalies discussed above into three different types (1) thermodynamie anomalies (for example, in density, Cp, Kt and Up), (2) dynamic anomalies (relaxation time or diffusion, dynamic crossover), and (3) stmctural anomalies (in translational and orientational order). 

P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Phase behavior of metastable water. Nature, 360 (1992), 324—328 L. Xu, P. Kumar, S. V. Buldyrev, et ah. Relation between the Widom line and the dynamic crossover in systems with a liquid-liquid phase transition. Proc. Natl. Acad. Sci. USA, 102 (2005), 16558-16562. 

The interpretation of the dynamic crossover could have implications for nanofluidics and perhaps even for natural confined water systems, for example, biological macromolecules. 

Using MD simulations [82,83], we studied three models, each of which has a LL critical point. Two (the TIP5P and the ST2) treat water as a multiple-site rigid body that interacts via electrostatic site-site interactions complemented by a Lennard-Jones potential. The third is the spherically symmetric two-scale Jagla potential with attractive and repulsive ramps. In all three models the loci of maxima of the relevant response functions, Ki and Cp, which coincide close to the critical point and give rise to the Widom line, were evaluated. The hypothesis that, for all three potentials, a dynamic crossover occurs when the Widom line is crossed, was carefully explored. 

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