Mesoscopics

A similar approach, in spirit, has been proposed [212] for the study of two-component classical systems, for example poly electrolytes, which consist of mesoscopic, highly-charged, poly ions, and microscopic. 

Greet R D and Warren P B 1997 Dissipative particle dynamics bridging the gap between atomistic and mesoscopic simulation J. Chem. Phys. 107 4423-35... 

Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

The hierarchy of models is complemented by a variety of methods and tecluiiques. Mesoscopic models tliat incorporate some fluid-like packing (e.g., spring-bead models for polymer solutions) are investigated by Monte Carlo... 

Coarse-grained models have a longstanding history in polymer science. Long-chain molecules share many common mesoscopic characteristics which are independent of the atomistic stmcture of the chemical repeat units [4, 5 and 6]. The self-similar stmcture [7, 8, 9 and 10] on large length scales is only characterized by a single length scale, the chain extension R. 

Another important class of materials which can be successfiilly described by mesoscopic and contimiiim models are amphiphilic systems. Amphiphilic molecules consist of two distinct entities that like different enviromnents. Lipid molecules, for instance, comprise a polar head that likes an aqueous enviromnent and one or two hydrocarbon tails that are strongly hydrophobic. Since the two entities are chemically joined together they cannot separate into macroscopically large phases. If these amphiphiles are added to a binary mixture (say, water and oil) they greatly promote the dispersion of one component into the other. At low amphiphile... 

Thongh this entry has focnsed on eqnilibrinm properties, mesoscopic and continnum models in chemical physics can also describe non-eqnilibrinm phenomena, and we shall mention some techniqnes briefly. 

Mesoscopic models can often be treated by molecnlar dynamics simnlations. This method generates a realistic... 

Kopelman R, Tan Wand Birnbaum D 1994 Subwavelength spectroscopy, exciton supertips and mesoscopic light-matter interactions J. Lumin. 58 380-7... 

Poon W C K and Haw M D 1997 Mesoscopic structure formation in colloidal aggregation and gelation Adv. Colloid Interface Sc/. 73 71-126... 

Datta S 1997 Electronic Transport in Mesoscopic Systems (Cambridge Cambridge University Press)... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

Van Vlimmeren, B.A.C., Fraaije, J.G.E.M. Calculation of noise distribution in mesoscopic dynamics models for phase-separation of multicomponent complex fluids. Comput. Phys. Comm. 99 (1996) 21-28. 

Maurits, N.M., Fraaije, J.G.E.M. Mesoscopic dynamics of copolymer melts from density dynamics to external potential dynamics using nonlocal kinetic coupling. J. Chem. Phys. 107 (1997) 5879-5889. 

Groot R D and P B Warren 1997. Dissipative Particle Dynamics Bridging the Gap Between Atomist and Mesoscopic Simulation. Journal of Chemical Physics 107 4423-4435. 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

Nanocones of carbon are found[3] in some areas on the substrate together with tubes and other mesoscopic structures. In Fig. 7 two carbon cones are displayed. For both cones we measure opening angles of 19.0 0.5°. The cones are 240 A and 130 A long. Strikingly, all the observed cones (as many as 10 in a (800 A) area) have nearly identical cone angles -19°. 

Carbon nanotubes (CNTs) as well as fullerenes are splendid gift brought to the Earth from the red giant carbon stars in the long-distant universe through the spectroscopy. Moreover, those belong to new carbon allotropes of the mesoscopic scale with well-defined structures. In particular, CNTs are considered to be the materials appropriate to realise intriguing characteristics related to the mesoscopic system based on their size and physicochemical properties. 

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