Scales larger

There are signs that the use of environmentally degradable polymers and plastics is expanding. As the market begias to become aware of the availabihty of these new materials, it is expected that they will move iato niche opportunities. When this occurs, production will iacrease, and costs, the biggest barrier to acceptance, should begia to come down. Some of the polymers ia production at some scale larger than laboratory are shown ia Table 5. 

The obvious application of microfocus Raman spectroscopy is the measurement of individual grains, inclusions, and grain boundary regions in polycrystalline materials. No special surface preparation is needed. Data can be obtained from fresh fracture surfeces, cut and polished surfaces, or natural surfeces. It is also possible to investigate growth zones and phase separated regions if these occur at a scale larger than the 1-2 pm optical focus limitation. 

Processes that occur at a size scale larger than the individual chain have been studied using microscopy, mainly transmission electron microscopy (TEM), but optical microscopy has been useful to examine craze shapes. The knowledge of the crazing process obtained by TEM has been ably summarised by Kramer and will not be repeated here [2,3]. At an interface between two polymers a craze often forms within one of the materials, typically the one with lower crazing stress. 

The properties of the periodic surfaces studied in the previous sections do not depend on the discretization procedure in the hmit of small distance between the lattice points. Also, the symmetry of the lattice does not seem to influence the minimization, at least in the limit of large N and small h. In the computer simulations the quantities which vary on the scale larger than the lattice size should have a well-defined value for large N. However, in reality we work with a lattice of a finite size, usually small, and the lattice spacing is rather large. Therefore we find that typical simulations of the same model may give diffferent quantitative results although quahtatively one obtains the same results. Here we compare in detail two different discretization... 

A normal diffusion process, however, runs at a finite concentration of particles different from zero. In this situation it was found [101] that a fractal character (73) of the resulting structure is restricted to an interval a < R < if), where d is the diffusion length (67). Larger clusters have a constant density on a length scale larger than They are no longer fractal there. These observations have various consequences for crystal growth, and will be discussed in the next section. 

The physical properties (7-10) of our E-V copolymers are sensitive to their microstructures. Both solution (Kerr effect or electrical birefringence) and solid-state (crystallinity, glass-transitions, blend compatibility, etc.) properties depend on the detailed microstructures of E-V copolymers, such as comonomer and stereosequence distribution. I3C NMR analysis (2) of E-V copolymers yields microstructural information up to and including the comonomer triad level. However, properties such as crystallinity depend on E-V microstructure on a scale larger than comonomer triads. 

Macroscopic dispersion, on the other hand, arises from heterogeneities on a scale larger than individual pores and grains. Such heterogeneities include laminae, layers, and formations of contrasting permeability fractures larger than the microscopic ones already considered and karst channels, joints and faults. Dispersion of this sort is sometimes referred to as differential advection. 

These variables are governed by exactly the same model equations (e.g., (4.103)) as the scalar variances (inter-scale transfer at scales larger than the dissipation scale thus conserves scalar correlation), except for the dissipation range (e.g., (4.106)), where... 

Let us return for the moment to Eq. (2.2). In atmospheric problems it is impossible to solve the equations of motion analytically. Under these conditions information about the instantaneous velocity field u is available only from direct measurements or from numerical simulations of the fluid flow. In either case we are confronted with the problem of reconstructing the complete, continuous velocity field from observations at discrete points in space, namely the measuring sites or the grid points of the numerical model. The sampling theorem tells us that from a set of discrete values, only those features of the field with scales larger than the discretization interval can be reproduced in their entirety (Papoulis, 1%5). Therefore, we decompose the wind velocity in the form... 

Note 2 In most cases, blends are homogeneous on scales larger than several times the wavelengths of visible light. 

The motion of a particle in a turbulent fluid depends upon the characteristics of the particle and of the turbulent flow. Small particles show a fluctuating motion resulting from turbulent fluid motion. Generally speaking, a particle responds to turbulent fluctuations with a scale larger than the particle diameter (K9). A particle which is much larger than the scale of turbulence shows relatively little velocity fluctuation. The effect of turbulence is then to modify the flow field around the particle, so that the drag may be affected. 

On scales larger than unification, the requirement A =0 is needed [94] because otherwise Zo would have a mass greater than empirically measured, or there would be an additional massive boson along with the Zo neutral boson. A... 

As already mentioned, major industrial fluoroaromatics are manufactured by fluorodediazoniation (ca. 9000 tons were consumed in 1991).71 Due to the hazards inherent in the unstable diazonium compounds, safety considerations are very important in this technique which, in general, is not performed batchwise on a unit scale larger than 5 m3. In order to circumvent this limitation, continuous processes have been proposed. 

Our reason for stressing the concept of representative volume element is that it seems to provide a valuable dividing boundary between continuum theories and molecular or microscopic theories. For scales larger than the RVE we can use continuum mechanics (classical and large strain elasticity, linear and non-linear viscoelasticity) and derive from experiment useful and reproducible properties of the material as a whole and of the RVE in particular. Below the scale of the RVE we must consider the micromechanics if we can - which may still be analysable by continuum theories but which eventually must be studied by the consideration of the forces and displacements of polymer chains and their interactions. 

---