Liquid-like behavior

The calculations of g(r) and C(t) are performed for a variety of temperatures ranging from the very low temperatures where the atoms oscillate around the ground state minimum to temperatures where the average energy is above the dissociation limit and the cluster fragments. In the course of these calculations the students explore both the distinctions between solid-like and liquid-like behavior. Typical radial distribution functions and velocity autocorrelation functions are plotted in Figure 6 for a van der Waals cluster at two different temperatures. Evaluation of the structure in the radial distribution functions allows for discussion of the transition from solid-like to liquid-like behavior. The velocity autocorrelation function leads to insight into diffusion processes and into atomic motion in different systems as a function of temperature. 

E. Liquid-like Behavior in Doped Ferroelectric Crystals... 

In the previous section we considered in detail the behavior of liquid-glass-forming substances. However, such liquid-like behavior can be also inherent in the dielectric properties of crystalline samples. 

Fig. 11-13. Effect of frequency on dynamic response of an amorphous, lighlly cross-linked polymer (a) elastic behavior at high frequency—stress and strain are in phase, (b) liquid-like behavior at low frequency—stress and strain are 90" out of phase, and (c) general case—stress and strain are out of phase.

Figure 6-5 shows the evolution of the dynamic moduli for a LM pectin/caldum system in the vicinity of the gel point as a function of the aging time. The evolution of the dynamic moduli was similar to that one observed as a function of the calcium concentration. In the initial period of aging the system showed the typical liquid-like behavior. Then both moduli increased with time, G increasing more rapidly than G" and with lower dependence on frequency. After 15 hr of aging, the system was just above the critical gel point, with a viscoelastic exponent A in the range of0.65-0.68. After the gel point, G passed beyond G", first in the lower frequency range where one can observe the initial formation of the elastic plateau. 

In region FG the polymer is completely amorphous and the properties of the polymer-solute solution can be investigated. Care must be taken to ensure that any contribution from surface adsoption is taken into account. Usually for thick polymer films contributions from surface adsorption will be small. For noncrystalline polymers, liquid-like behavior is observed from point C onwards. The location of point C on the temperature axis depends both on the polymer-solute system considered and on experimental conditions, film thickness and flow rate. For most polymers, equilibrium bulk sorption is achieved at temperatures in excess of about Tg + 50°. 

Pharmaceutical materials are rarely described by simple mechanical equivalents such as the Kelvin (solid-like behavior) or the Maxwell (liquid-like behavior) model. 

We can also suppose that the formation of crystals or of amorphous particles is controlled by the content of SCF in the liquid (and vice versa), i.e., a liquid containing small quantities of SCF has a liquid-like behavior and crystals are obtained as the SCF content increases (SCF rich phase), we can observe the formation of amorphous particles. 

The molar Helmholtz free energy of the adsorbed phase is simply the sum of the intrinsic Helmholtz free energy and the solid-fluid potential averaged over the adsorbed phase. Assuming a liquid-like behavior of the adsorbed phase, this free energy is given by... 

Small finite systems exhibit solid- and liquid-like behavior much like that of bulk matter and, on the other hand, exhibit specific, quite interesting properties that distinguish them from the bulk [1-3]. Small is defined here with respect to the... 

This implies liquid-like behavior of a dominating water fraction with a liquid-like single correlation time as predicted by the theory of Bloembergen, Purcell, and Pound (BPP) (22). 

---