Macroscopic aggregate

Modern thermodynamics has grown from the phenomenological study of matter with a view to establish its general properties without reference to composition. The results are qualitative in nature and represent relationships between apparently unrelated properties of all types of system in macroscopic aggregation. 

The statistical analysis required for real systems is no different in conception from the treatment of the hypothetical two-state system. The elementary particles from which the properties of macroscopic aggregates may be derived by mechanical simulation, could be chemical atoms or molecules, or they may be electrons and atomic nuclei. Depending on the nature of the particles their behaviour could best be described in terms of either classical or quantum mechanics. The statistical mechanics of classical and quantum systems may have many features in common, but equally pronounced differences exist. The two schemes are therefore discussed separately here, starting with the simpler classical sytems. 

The rate of migration of low molecular weight residual molecules from plastics into foods and interactions of the plastics with food components or other filled products depends on the molecular structure and the macroscopic (aggregate) nature of the plastic material. In order to perform useful estimations of mass transfers, for example from plastics to food, a basic knowledge of the structure of the plastic and food components and their influences on this phenomenon is necessary. 

The LVFS has been successfully deployed on 11 cruises in the Atlantic and Pacific Oceans. Analyses of the samples have made known the distributions of over 20 elements and have documented the importance of particulate organic matter as a complexing and ion-exchange agent. Furthermore, the results have demonstrated that macroscopic aggregates (fecal matter)... 

A further quantity calculated by Asakura and Oosawa (1954) is Ae mtical volume concentration 3 of the colloidal particles at which macroscopic aggregation takes place. They showed that for relatively small changes in the depth of the potential energy well into which the particles flocculate (e.g. an increase in well depth of ca 30%), the state of the particles changes from essentially total dispersion to complete aggregation. 

A phase is a macroscopic aggregate of molecules, usually with well defined boundaries. To be able to describe the phase thermodynamically, one assumes that all molecules are inside the boundaries. As the phase volume approaches in at least one direction micrometre-dimensions, the surface properties affect the phase, now called a microphase. Microphases were first observed in the form of colloids. More recently, nanophases are being studied that have at least one dimension in the nanometre range. 

The detailed chemical structure of many small molecules is dominated by intramolecular interactions, and the shape is independent of the state of macroscopic aggregation (gas, liquid, or solid). On the other hand, the shape of a macromolecule is often a fimction of its environment. One of the earliest evidences of this fact was the large difference in the intrinsic viscosity, [tj], of macromolecules in different solvents. The measurement of solution viscosity has played a central role in the development of polymer science. The theory of hydrodynamics was well developed by the end of the 19th century, and Einstein derived the equation for the viscosity of a dilute solution of rigid spheres with volume fraction 9 ... 

S. M. Kuznicki, T. W. Langner, J. S. Curran, and V. A. Bell, Macroscopic aggregates of microcrystalline zeoUtes for static water softening applications. Pat. Appl Publ 20020077245, 2002. 

Alldredge A.L. 1979. The chemical comp>osition of macroscopic aggregates in two neritic seas. 

Only the association of echogenic pyramids with posterior acoustic shadow is visible on abdominal X-ray. Macroscopic aggregates of calcification seem to be necessary for this (Glazer et al. 1982). 

As already mentioned the possibility of delocalization of electrons within a macroscopic aggregate is a characteristic of the crystalline solid state. The outer electrons of metals, in particular, behave as a confined electron gas. This is readily recognized by considering an arrangement of 4 Na atoms. Such an ensemble represents a markedly electron-deficient state (one valence electron per Na) the energetically relevant mesomeric structures are ... 

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