Macroscopic parameters

Table 1. Experimental values for the macroscopic parameters of the superconducting phases of KaCeo and RbaCeo.

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

Assuming that our LG is in a local equilibrium, it is reasonable to expect that the one-particle distribution functions should depend only on the macroscopic parameters u x,t) and p x,t) and their derivatives [wolf86c]. While there is no reason to believe that this dependence should be a particularly simple one, it is reasonable to expect that both u and p are slowly varying functions of x and t. Moreover, in the subsonic limit, we can assume that li << 1. 

To close this chapter we emphasize that Hie statistical mechanical definition of macroscopic parameters such as temperature and entropy are well designed to describe isentropic equilibrium systems, but are not immediately applicable to the discussion of transport processes where irreversible entropy increase is an essential feature. A macroscopic system through which heat is flowing does not possess a single tempera-... 

Sharma, A. (1993) Relationship of thin film stability and morphology to macroscopic parameters of wetting in the apolar and polar systems. Langmuir,... 

Almost all problems that require knowledge of free energies are naturally formulated or can be framed in terms of (1.15) or (1.16). Systems 0 and 1 may differ in several ways. For example, they may be characterized by different values of a macroscopic parameter, such as the temperature. Alternatively, they may be defined by two different Hamiltonians, 3%o and 3%, as is the case in studies of free energy changes upon point mutation of one or several amino acids in a protein. Finally, the definitions of 0 and 1 can be naturally extended to describe two different, well-defined macroscopic states of the same system. Then, Q0 is defined as ... 

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

It follows that the surface excess properties are macroscopic parameters only. 

Several recent molecular dynamics simulations (e.g. [10] and references therein) have focussed on the wetting of interfaces (Section 6.1) and, for example, the behaviour of very small droplets at the nanoscale. Such simulations are able to relate the atomistic behaviour directly to relevant macroscopic parameters such as the contact angle and are able to show the dramatic effects at this length scale of addition of surfactant molecules or roughening of the surface. 

We should first emphasize that viscosity is a macroscopic parameter which loses its physical meaning on a molecular scale. Therefore, the term microviscosity should be used with caution, and the term fluidity can be alternatively used to characterize, in a very general way, the effects of viscous drag and cohesion of the probed microenvironment (polymers, micelles, gels, lipid bilayers of vesicles or biological membranes, etc.). 

In other words, viscosity is a macroscopic parameter and any attempt to get absolute values of the viscosity of a medium from measurements using a fluorescent probe is hopeless. 

Investigators have often used pH studies to aid in the identification of active-site residues. However, care must be exercised in this regard since observed pK values may refer to macroscopic parameters rather than microscopic values and pi values of groups can be greatly affected by the immediate environment. Because of these influences, it may be difficult to identify specific moieties responsible for binding and/or catalysis. 

Instabilities and dissipative structures play a basic role in our understanding of chemical kinetics in far from equilibrium situations. Through dissipative structures the characteristics of the system become explicitly dependent on macroscopic parameters (dimensions, boundary conditions) that relate it to its environment. 

The aim of this chapter is to clarify the conditions for which chemical kinetics can be correctly applied to the description of solid state processes. Kinetics describes the evolution in time of a non-equilibrium many-particle system towards equilibrium (or steady state) in terms of macroscopic parameters. Dynamics, on the other hand, describes the local motion of the individual particles of this ensemble. This motion can be uncorrelated (single particle vibration, jump) or it can be correlated (e.g., through non-localized phonons). Local motions, as described by dynamics, are necessary prerequisites for the thermally activated jumps responsible for the movements over macroscopic distances which we ultimately categorize as transport and solid state reaction.. 

Equation (5.1) described the vibrational response of a single particle to an applied forceF(t). In a (crystalline) system of many mobile particles (ensemble), the problem is analogous but the question now is how the whole system responds to an external force or perturbation Let us define the system s state (a) as a particular configuration of its particles and the probability of this state as pa. In a thermodynamic system, transitions from an a to a p configuration occur as thermally activated events. If the transition frequency a- /5 is copa and depends only on a and / (Markovian), the time evolution of the system is given by a master equation which links atomic and macroscopic parameters (dynamics and kinetics)... 

Figure D3.5.1 Basic macroscopic parameters of general thermodynamic systems.

The only relevant macroscopic parameter of the noninteracting model is the end-to-end distance, which is invariant under this transformation ... 

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