Static/dynamic properties, qualitative

In this review, we concentrate on the static problems involving polymer systems, as the dynamic (e.g., the transport) properties have been less extensively studied. Nevertheless, since an understanding of static properties is usually simpler to obtain than that of the dynamic properties for a given system, a discussion of only the former properties introduces a number of the techniques and concepts that are useful in the treatment of the latter properties. Within the category of static problems, the following qualitatively different cases can be classified ... 

Eventually, matching of molecular dynamics with continuous hydrodynamic description may be necessary to take a precise account of microscopic properties of interfaces. Our aim is, however, more modest to gain qualitative understanding. We shall restrict therefore to the simplest but most universal kind of interactions - van der Waals forces, and follow their influence on static and dynamic properties of interfaces and contact lines. We shall review two kinds of models of interfacial regions, assuming either discontinuous or diffuse interphase boundary. The description will remain continuous, even when we go down to molecular-scale distances. 

In this chapter, the binary mixture of GB particles of different aspect ratios has been studied by molecular dynamics simulation. The composition dependence of different static and dynamic properties has been studied. The radial distribution function has been found to show some interesting features. Simulated pressure and overall diffusion coefficient exhibit nonideal composition dependence. However, simulated viscosity does not show any clear nonideality. The mole fraction dependence of selfdiffusion coefficients qualitatively signals some kind of structural transition in the 50 50 mixture. The rotational correlation study shows the non-Debye behavior in its rank dependence. The product of translational diffusion coefficient and rotational correlation time (first rank) has been found to remain constant across the mixture composition and lie above the stick prediction. 

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

The development of various techniques has led to important advances. The possibility to measure intermolecular and intercolloidal forces directly represents a qualitative change from the indirect way such forces had been inferred in the past from aggregation kinetics or from bulk properties such as the compressibility (deduced from small angle scattering) or phase behavior. Both static (i.e., equilibrium) and dynamic (e.g., viscous) forces can now be directly measured, providing information not only on the fundamental interactions in liquids but also on the structure... 

For the middle line R(y) with fixed slope equal to b and horizontal axis intercept equal to a in Figure 4 (A-2), there are maximally three steady states yi, j/2 and 2/3. Stability information of the three steady states and a qualitative analysis of the dynamic behavior of the system can be obtained from the static diagram. The steady-state temperatures 2/1, 2/2 and 2/3 correspond to points where the heat generation and heat removal are equal. That is the defining property of a steady state. 

An attempt is made to generalize the results with the aid of perturbation molecular orbital (PMO) theory (7). This serves as a most useful qualitative framework within which many of the quantitative results may be understood. Hopefully, as experience with PMO theory increases, its application will serve not only to rationalize results obtained from both theoretical and experimental techniques, but also to increase its predictive powers for related systems. This kind of application of PMO theory is in line with the growing tendency to use qualitative orbital arguments to understand both static and dynamic molecular properties, in addition to (and to some extent, instead oO the more conventional resonance theory. 

Sedimentation experiments on semi-dilute solutions are appropriate and many experiments have been performed on neutral polymers like polystyrene and poly(a-methylsty-rene) in good solvents It has been found that the effective exponent Xj increases from 0.59 up to 0.8 as the concentration rises from 0.1 to 10%. Good solvents used in these experiments (benzene, bromobenzene and toluene) are far from athermal conditions (x — 0.45). Two monomers, belonging to a subchain of size and separated by n monomers, experience excluded volume effects when n > n, where iic oc (1 - 2x). As the concentration decreases, the number of monomer per subchain g, increases and excluded volume effects become more and more important. The effective exponent Xs, which is a combination of effective dynamic and static exponents tends monoti-cally to the asymptotic value 0.5 (g > He). Inversely, if the concentration increases, g decreases when g < He, the subchain exhibits purely Gaussian behaviour, and v = 0.5 which leads to oc and Sd °o This cross-over between excluded volume and Gaussian behaviour qualitatively explains the increase of Xj, if p increases. Detaib on the dependence of x, on the concentration can be found in Ref. 110. Whatever the exact value of the exponent, these experiments show that the frictional properties of semi-dilute solutions depend only on the concentration they are independent of the molecular weight of the polymer used 1. 

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