Molecular equilibrium system, macroscopic

As this system nears equilibrium, the rate of the forward reaction decreases and the rate of the reverse reaction increases. At equilibrium, the macroscopic properties of this system are constant. Changes at the molecular level take place at equal rates. 

Dynamic equilibrium is a condition in which the forward process and its reverse are occurring simultaneously at equal rates. Processes occur at the molecular level the macroscopic system appears unchanged. In a static equilibrium, no process is occurring at any level. 

The formation of this equilibrium colloidal system may take place if the value of d lies within the region where the particle size, d, is significantly larger than molecular dimensions, b d b, for instance in the region where d z (5 - 10)6. Then the necessary condition of spontaneous formation of lyophilic colloidal system, and, consequently, the condition under which this system may be in equilibrium with macroscopic phase, can be expressed by the Rehbinder - Shchukin criterion [3,4] ... 

Thermodynamics consists of a collection of mathematical equations (and also some inequalities) which inter-relate the equilibrium properties of macroscopic systems. Every quantity which occurs in a thermodynamic equation is independently measurable. What does such an equation tell one about one s system Or, in other words, what can we learn from thermodynamic equations about the microscopic or molecular explanation of macroscopic changes Nothing whatever. What is a thermodynamic theory (The phrase is used in the titles of many papers published in reputable chemical journals.) There is no such thing. What then is the use of thermodynamic equations to the chemist They are indeed useful, but only by virtue of their use for the calculation of some desired quantity which has not been measured, or which is difficult to measure, from others which have been measured, or which are easier to measure. 

The equations of motion of a molecular system formally represent a coupled set of nonlinear differential equations. (The nonlinearity comes from the complicated distance-dependence of the pair-potentials.) It is a property of nonlinear differential equations that they are extremely sensitive to small differences in their initial conditions. In nature, these small differences are most generally created by the perturbations of the surroundings while in the computer simulations they are produced by the finite accuracy of the numerical computation. The sensitivity is manifested in the fast increase of these initial differences nearby trajectories separate exponentially until the system boundaries force them to turn back. This mechanism quickly mixes the trajectories and after a short initial period the behavior of the system forgets its past. This obviously happens for equilibrium systems when their macroscopic properties relax to fixed average values. It also occurs for NESS systems because after short transients their distribution function also becomes stationary. ... 

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 ... 

It is often possible to obtain similar or identical results from statistical mechanics and from thermodynamics, and the assumption that a system will be in a state of maximal probability in equilibrium is equivalent to the law of entropy. The major difference between the two approaches is that thermodynamics starts with macroscopic laws of great generality and its results are independent of any particular molecular model of the system, while statistical methods always depend on some such model. 

Figure 19 summarizes the effect of confinement on the macroscopic swelling of the studied block copolymer systems. The systems differ in the molecular weight and composition of the studied block copolymers, in the solvent quality, and in the experimental conditions (which control the solvent atmosphere see Sect. 3). At a constant vapor pressure, the equilibrium 0pOi for each polymer becomes smaller... 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

---