Bulk concentration fluctuations

For a polymer pair that would undergo phase separation at high relative molecular masses, such as an isotopic polymer mixture like polystyrene/ deuterated polystyrene, this criterion means that one would have to approach closer to the critical point than about 0.05 °C for these fluctuation effects to be important. Even for much more strongly immiscible pairs, that undergo phase separation at much lower relative molecular masses, the non-classical region will be within only a few degrees of the critical point (Schwahn et al. 1987, Bates et al. 1990). This is in sharp contrast to the situation for small-molecule liquids, for which fluctuations must always be taken into account in order to predict the phase behaviour. Mean-field theories - neglecting bulk concentration fluctuations - often can be expected to work quite well for polymers. 

With the boundary condition that the concentration fluctuation disappears at the bulk solution, i.e.,... 

Since the nonequilibrium concentration fluctuation arises from the dissolution of substrate metal, as shown in Fig. 43, the value of is independent of the metallic ion concentration in the bulk solution. 

With the more conductive liquids, the ion concentration becomes so great that ion concentration fluctuations on a statistical basis are likely to be small. However, charging can take place by three other mechanisms (1) mechanical disruption of any double layer of ions that may exist at the surface in times that are short compared with the relaxation time, with a predominance of the surface ions going to the portion of fluid coming from the surface (2) unequal ion mobility with the larger ions unable to return to the bulk of liquid as readily as the smaller and more mobile ones and (3) contaminating materials, such as dust or surfactants at the interfaces serving as ion carriers into one portion or the other of the ruptured liquid. 

NUCLEATION. Nucleation creates a new phase that is organizationally more related to the crystal lattice than to the monomeric species that undergoes crystallization. This process permits solutions that are of high relative supersaturation to crystallize and thereby reach equilibrium between liquid and sohd phases . Nucleation occurs when the local concentration of components that will comprise the solid phase exceeds a threshold level as a result of short-range concentration fluctuations in the bulk solution. In this respect, the kinetics of nucle-... 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

Although the above work was serendipitous, the study of concentration fluctuations in bulk polymers should be a fruitful area of research. Intentional polymer mixtures could be prepared which would allow the mutual diffusion of polymers in polymers to be obtained. Although the molecular weights might need to be kept low, the measurement of polymer motions in the bulk state would be very valuable. 

Paints, adhesives and lubricants are typically multicomponent polymer systems. The behavior of phase-separated blends in the bulk after quenching into the unstable region of the phase diagram is variable. In the bulk, the concentration fluctuations... 

Treatments of this problem are greatly simplified by uncoupling the long-term diffusion due to Edc from the rapid diffusional fluctuations due to Eac- We do that by recognizing that Edc sets up mean surface concentrations that look like bulk values to the ac perturbation because of the difference in time scale. In Section 10.3, we defined the faradaic impedance in terms of bulk concentrations thus the current response in ac voltammetry as a function of is readily obtained by substituting the surface concentrations imposed by directly into these impedance relations. Since this strategy is simple and intuitive, we will pursue it. More rigorous treatments are available in the literature for the interested reader (2, 3, 5). The results are the same by either approach. 

Let us now consider the effect of the scattering of the bulk of the film due to density and concentration fluctuations of dissolved components. 

Figure 5.6. Schematic plots of the polymer segment concentration as a function of the distance in bulk polymer solutions. In (a) the concentration of chains is low enough that on average different polymer chains do not overlap. The segment concentration has large spatial fluctuations this is a dilute solution. In (b) chains start to overlap, but there are still strong composition fluctuations imposed by the connectivity of the chains characterised by a correlation length This is the so-called semi-dilute concentration regime. In (c) the solution is concentrated and there are no concentration fluctuations on length scales larger than the monomer size.

Light scattering techniques are useful tools to investigate both interfacial properties such as surface tension and viscoelasticity (4) and bulk properties such as droplet size and interaction forces between these droplets (5,6). It must be pointed out that in each case, light is probing thermal fluctuations in the medium but the fluctuations are of a very different nature surface roughness in the first case, and droplet concentration fluctuations in the case of bulk scattering. 

---