Microscopic molecular

In equilibrium statistical mechanics, one is concerned with the thennodynamic and other macroscopic properties of matter. The aim is to derive these properties from the laws of molecular dynamics and thus create a link between microscopic molecular motion and thennodynamic behaviour. A typical macroscopic system is composed of a large number A of molecules occupying a volume V which is large compared to that occupied by a molecule ... 

Segal D, Nitzan A, Ratner MA, Davis WB (2000) Activated conduction in microscopic molecular junctions. J Phys Chem B 104 2790-2793... 

We look at the simple gas laws to explore the behaviour of systems with no interactions, to understand the way macroscopic variables relate to microscopic, molecular properties. Finally, we introduce the statistical nature underlying much of the physical chemistry in this book when we look at the Maxwell-Boltzmann relationship. 

Reaction dynamics is the part of chemical kinetics which is concerned with the microscopic-molecular dynamic behavior of reacting systems. Molecular reaction dynamics is coming of age and much more refined state-to-state information is becoming available on the fundamental reactions. The contribution of molecular beam experiments and laser techniques to chemical dynamics has become very useful in the study of isolated molecules and their mutual interactions not only in gas surface systems, but also in solute-solution systems. 

Kinetic theory of molecular assembly atomic microscope, molecular assemblies. 

Conventional dimensional analysis uses single length and time scales to obtain dimensionless groups. In the first section, a new kind of dimensional analysis is developed which employs two kinds of such scales, the microscopic (molecular) scale and the macroscopic scale. This provides some physical significance to the exponent of the Reynolds number in the expression of the Sherwood number, as well as some bounds of this exponent for both laminar and turbulent motion. 

What is the physical nature of the Gibbs free energy, and what is free about it We can consider this question first from the viewpoint of fundamental thermodynamic definitions, with no microscopic molecular connotations. For a reversible change of state carried out under conditions of constant T and P, we can write... 

With this bold stroke, Boltzmann escaped the futile attempt to describe microscopic molecular phenomena in terms of then-known Newtonian mechanical laws. Instead, he injected an essential probabilistic element that reduces the description of the microscopic domain to a statistical distribution of microstates, i.e., alternative microscopic ways of partitioning the total macroscopic energy U and volume V among the unknown degrees of freedom of the molecular domain, all such partitionings having equal a priori probability in the absence of definite information to the contrary. 

Recently, several authors have studied solvation dynamics of aqueous solutions using molecular dynamics (MD) computer simulations [36, 57, 58, 112], The simulations offer a detailed molecular approach to interpreting the experimental results, as they focus particularly on the microscopic, molecular aspects of the solvation process. 

Interest in thermotropic liquid crystals has focussed mainly on macroscopic properties studies relating these properties to the microscopic molecular order are new. Lyotropic liquid crystals, e.g. lipid-water systems, however, are better known from a microscopic point of view. We detail the descriptions of chain flexibility that were obtained from recent DMR experiments on deuterated soap molecules. Models were developed, and most chain deformations appear to result from intramolecular isomeric rotations that are compatible with intermodular steric hindrance. The characteristic times of chain motions can be estimated from earlier proton resonance experiments. There is a possibility of collective motions in the bilayer. The biological relevance of these findings is considered briefly. Recent similar DMR studies of thermotropic liquid crystals also suggest some molecular flexibility. 

We should note that a two-humped absorption are pertinent to aqueous media. In terms of a microscopic molecular model, such a behavior could, partially, be explained by a finite depth of a potential well. Indeed, dipoles with rather small energies constitute a subensemble of particles localized in the well, so their maximum deflection (3 is determined by the angular width of the well, while dipoles with sufficiently large energies overcome the potential barrier. These dipoles perform a complete rotation such particles occupy the whole sphere, so that (3 = 7i. This reasoning leads us to a conclusion that generally two types of motion could characterize a given potential well, so that... 

This approach is based on some wide-ranging preconditions. In order to bridge the gap between microscopic molecular nature of a particle surface and macroscopic properties, a multi-scale approach covering several orders of magnitude of space and time is needed. On the most basic level quantum mechanics prevail. However, it is often possible by using the Hellman-Feynman theorem [3] to transfer the intrinsic quantum mechanical nature of surfaces to the physics... 

The transformation from reactants to products can be described at either a phenomenological level, as in classical chemical kinetics, or at a detailed molecular level, as in molecular reaction dynamics.1 The former description is based on experimental observation and, combined with chemical intuition, rate laws are proposed to enable a calculation of the rate of the reaction. It does not provide direct insight into the process at a microscopic molecular level. The aim of molecular reaction dynamics is to provide such insight as well as to deduce rate laws and calculate rate constants from basic molecular properties and dynamics. Dynamics is in this context the description of atomic motion under the influence of a force or, equivalently, a potential. 

To complete the theory we need to specify /, given the friction constant 7. There is, however, nothing in the theory that allows us to determine this function from microscopic molecular data. However, we may get around the problem if we believe, with good reason, that the end point of the evolution of particle motions will lead to a state of thermal equilibrium at temperature T, no matter the original perturbation of... 

At the microscopic (molecular) level, the process of supplying heat, q (q > 0) can be associated with an increase in the thermal motions of the constituent atoms / molecules making up the system and giving rise to an increase in internal energy of that system. Addition of heat to a system generally leads to a rise in the temperature, AT. 

We have already dealt with stationary phase processes and have noted that they can be treated with some success by either macroscopic (bulk transport) or microscopic (molecular-statistical) models. For the mobile phase, the molecular-statistical model has little competition from bulk transport theory. This is because of the difficulty in formulating mass transport in complex pore space with erratic flow. (One treatment based on bulk transport has been developed but not yet worked out in detail for realistic models of packed beds [11,12].) Recent progress in this area has been summarized by Weber and Carr [13]. 

A mechanistic model is a sequence of elementary processes, each of them describing the intrinsic course of the chemical transformation at microscopic molecular level. Thus, a reaction mechanism may be formally described as a set of s irreversible elementary processes involving c constituents Ct, C2,...,Cc (including reactants, short-lived intermediates, products, and inert compounds), for instance... 

Theqpodynamic considerations by themselves are not sufficient to allow calculation of the rates of chemical or physical processes. Rates depend on both driving force and resistance. Although driving forces are thermodynamic variables, resistances are not. Neither can thermodynamics, a macroscopic-property formulation, reveal the microscopic (molecular) mechanisms of physical or chemical processes. On the other hand, knowledge of the microscopic behavior... 

McMorrow D, Thantu N, Melinger JS, Kim SK, Eotshaw WT. Probing the microscopic molecular environment in liquids intermolecular dynamics of CS2 in alkane solvents. J Phys Chem 1996 100 10389-10399. 

The small number of variables needed for thermodynamic state description is certainly surprising from a microscopic molecular dynamic viewpoint. For the complete molecular-level description of an arbitrary state (phase-space configuration) of the order of 1023 particles, we should expect to require an enormously complex nonequilibrium function independent variables (i.e., positions rt and velocities r,-), time evolution until equilibrium is achieved, we find that a vastly simpler description is possible for the resulting equilibrium state state properties R, R2.i.e., for a pure substance,... 

Equation [1] relates a (macroscopic) bulk, empirical property, Y, with some set, X, of (microscopic) molecular structural parameters (descriptors). The equation as shown is linear in that each term involves a first power for its descriptor. Fligher order descriptors may also be used. The coefficients, Uj, are obtained with the aid of statistical methods, particularly, regression... 

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