Mesoscopic parameters

The mesoscopic parameters and B, as was shown earlier in Section 3.3.4, can be written as functions of a single argument, which can now be rewritten as... 

The mesoscopic approach gives an amazingly consistent picture of the different relaxation phenomena in very concentrated solutions and melts of linear polymers. It is not surprising the developed theory is a sort of phenomenological (mesoscopic) description, which allows one to get a consistent interpretation of experimental data connected with dynamic behaviour of linear macromolecules in both weakly and strongly entangled polymer systems in terms of a few phenomenological (or better, mesoscopic) parameters it does not require any specific hypotheses. 

Mesoscopic parameters, such as the full-diffusion tensor and potential V, are usually determined phenomenologically or from complementary approaches. For instance, dissipative properties described by the diffusion tensor can be obtained on the basis of hydrodynamic modeling (see below). The internal potential can be evaluated as a potential energy surface scan over the torsional angle 6. For small molecules this operation can be easily conducted at the DFT level, while for big molecules such as proteins, mixed quantum mechanical/molecular mechanics (QM/MM) methodologies can be employed. 

Soto-Figueroa C, Vicente L, Martinez-Magadan JM, Rodriguez-Hidalgo MD. Self-organization process of ordered structures in linear and star poly(styrene)-poly(isoprene) block copolymers Gaussian models and mesoscopic parameters of polymeric systems. J Phys ChemB 2007 11 11756. 

In the structure with all the surfactant molecules located at monolayers, the volume fraction of surfactant should be proportional to the average surface area times the width of the monolayer divided by the volume, i.e., Ps (X Sa/V. The proportionality constant is called the surfactant parameter [34]. This is true for a single surface with no intersections. In our mesoscopic description the volume is measured in units of the volume occupied by the surfactant molecule, and the area is measured in units of the area occupied by the amphiphile. In other words, in our model the area of the monolayer is the dimensionless quantity equal to the number of amphiphiles residing on the monolayer. Hence, it should be identified with the area rescaled by the surfactant parameter of the corresponding structure. 

An alternative or additional step to flame annealing is electrochemical or chemical polishing. The fundamental aspects of electropolishing were reviewed recently [185], and a list of polishing procedures and parameters is available [185,186]. This method has been successfully applied to the preparation of gold, silver, and copper electrodes for STM studies [177,180,188]. It is important to note that different mesoscopic structures may arise according to the specific preparation procedures. For example, electropolishing a mechanically prepared Au(lOO) surface followed by... 

Finally, a key highlight of this investigation is that the systematic estimation of the effective transport parameters for the porous CL and GDL from the mesoscopic modeling can quantitatively predict the fuel cell performance from the macroscopic fuel cell models. 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

The formal homogenization process is accomplished by considering every property depending on both global and meso-length scales in the form / = f(x,y), where x and y are the macroscopic and mesoscopic coordinates respectively. The relation between the length scales is y = e 1x. This shows that quantities vary e-1 faster on the meso level than those the macro one. We then postulate two-scale asymptotic expansions for the unknowns in terms of the perturbation parameter e... 

Contemporary research trends related to the development of mesoscopic materials, which contain nanosized inclusions of guest compounds and phases in a host matrix, are among the most prospective fields for technological applications. The physical characteristics of nanoobjects in such materials can substantially differ from those of their macroscopic analogs. As a result there is a strong need to investigate both the properties of individual nano-objects and their parameter modifications when they interact with their environment. 

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