Intermediate dynamic length

Phillies, et a/. (69) present results confirming Streletzky and Phillies s(64) prior interpretation that HPC solutions have a dominant, concentration-independent characteristic dynamic length scale, namely the radius of a polymer chain, which for this species is i 50 nm. In particular (i) There are distinct small-probe and large-probe phenomenologies, with the division between small and large probes being about 50 nm, the same at all polymer concentrations, (ii) For small probes, the relative amplitude of the sharp and broad modes depends markedly on scattering vector q with a crossover near q 70 nm. (iii) The mean relaxation rate of the small-probe broad mode increases markedly near 50 nm. (iv) The probe intermedi-... 

Models of a second type (Sec. IV) restrict themselves to a few very basic ingredients, e.g., the repulsion between oil and water and the orientation of the amphiphiles. They are less versatile than chain models and have to be specified in view of the particular problem one has in mind. On the other hand, they allow an efficient study of structures on intermediate length and time scales, while still establishing a connection with microscopic properties of the materials. Hence, they bridge between the microscopic approaches and the more phenomenological treatments which will be described below. Various microscopic models of this type have been constructed and used to study phase transitions in the bulk of amphiphihc systems, internal phase transitions in monolayers and bilayers, interfacial properties, and dynamical aspects such as the kinetics of phase separation between water and oil in the presence of amphiphiles. 

The bond fluctuation model not only provides a good description of the diffusion of polymer chains as a whole, but also the internal dynamics of chains on length scales in between the coil size and the length of effective bonds. This is seen from an analysis of the normalized intermediate coherent scattering function S(q,t)/S(q,0) of single chains ... 

Precise knowledge of the critical point is not required to determine k by this method because the scaling relation holds over a finite range of p at intermediate frequency. The exponent k has been evaluated for each of the experiments of Scanlan and Winter [122]. Within the limits of experimental error, the experiments indicate that k takes on a universal value. The average value from 30 experiments on the PDMS system with various stoichiometry, chain length, and concentration is k = 0.214 + 0.017. Exponent k has a value of about 0.2 for all the systems which we have studied so far. Colby et al. [38] reported a value of 0.24 for their polyester system. It seems to be insensitive to molecular detail. We expect the dynamic critical exponent k to be related to the other critical exponents. The frequency range of the above observations has to be explored further. 

In the discussion on the dynamics in the bead-spring model, we have observed that the position of the amorphous halo marks the relevant local length scale in the melt structure, and it is also central to the MCT treatment of the dynamics. The structural relaxation time in the super-cooled melt is best defined as the time it takes density correlations of this wave number (i.e., the coherent intermediate scattering function) to decay. In simulations one typically uses the time it takes S(q, t) to decay to a value of 0.3 (or 0.1 for larger (/-values). The temperature dependence of this relaxation time scale, which is shown in Figure 20, provides us with a first assessment of the glass transition... 

Chapter 5 considers the connection between the universal large scale dynamics discussed first and the local specific dynamics discussed in the second step. The dynamics at intermediate length scales bridges the two and we will address the leading mechanism limiting the universal dynamics in flexible polymers. 

The above expressions provide a universal description of the dynamics of a Gaussian chain and are valid for real linear polymer chains on intermediate length scales. The specific (chemical) properties of a polymer enter only in terms of two parameters N =Rl and The friction parameter is gov-... 

Up to date the only published work on the dynamic structure factor of a glass forming system at intermediate length scales is a study on PIB [147]. The NSE measurements explored the Q-range 0.20[Pg.136]

K and 390 K (Tg=205 K). As can be seen in Fig. 4.32a, the dynamics were accessed from the intermediate length scales region to the valley between the first and the second peaks of across Qmax Figure 5.13 shows some of the... 

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