Physico-chemical systems

In physics and chemistry the elementary units composing the basic system are well known. These consist of elementary particles and photons or of composite units like atoms and molecules. The interactions between the units are also known there exist strong, electromagnetic, weak and gravitational interactions between elementary particles. More complex interactions like the interatomic forces responsible for chemical bonds and the van der Waals forces between molecules of a gas can be derived from these elementary interactions. The elementary units, their position and momentum vectors and their interactions constitute the basic microscopic level of a physico-chemical system. 

On the other hand, the gross features of a system consisting of many particles are relatively easily accessible to experiment on the macroscopic level. 

According to experimental conditions the system may be closed or open. A closed system is at most confined by static boundary conditions. It has internal interactions, but no further interaction with the environment. An open system, however, has not only internal interactions between its constituents, but also external interactions with the environment, for instance, with external heat and particle reservoirs by exchange of energy and particles. 

Closed or open systems on the macroscopic level turn out to be characterized by relatively few collective macroscopic observable quantities, also denoted here as grossvariables or macrovariables. Examples are pressure, density entropy, energy- and particle-fluxes, correlation functions and further parameters characterizing the macroscopic state or dynamic space-time structure of fields and particles. 

If the external conditions of an open system are changed by varying certain control parameters the system may undergo a radical change in its macroscopic global state if the control parameters pass certain critical values. Such transitions are denoted as phase transitions [1.10, 11, 13, 14, 17, 24, 48]. 

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L.S. Polak and A.S. Mikhailov, Self-Organization in Non-Equilibrium Physico-Chemical Systems (Nauka, Moscow, 1983). 

Patterning in biological and physico-chemical systems typically involves the spatial variation of ionic concentrations. It should thus not be surprising that interesting electric effects arise in such systems. We show here that the situation in these systems is very rich in important and surprising developmental phenomena as has been realized historically in isolated studies dating from the last century and more generally since the 19 t0 s (8, 28, 53. 5 0. 

If affective disorder could be eliminated by the simple expedient of administering a chemical substance, did this not suggest that the basis of these disorders might take a chemical form And not only that might affect, mood, emotion, and the whole gamut of human conscious experience be translated into chemical terms At a stroke, the elusive "aetherial" Freudian psyche was replaced as the primary object of attention by the polyphasic physico-chemical system called the brain. Psychiatry came of age and took its place among the biological sciences. 

In the study of physico-chemical systems, the intuitive concept of energy always precedes the more refined treatment based on die more subtle idea of entropy. This evolution from energy to entropy is such a characteristic feature of refinement in theory and experiment that die appearance of entropy considerations in a given field signals its coming of age. 

Quantitative Structure-Activity Relationships (QSARs) are the final result of the process that starts with a suitable description of molecular structures and ends with some inference, hypothesis, and prediction on the behavior of molecules in environmental, biological, and physico-chemical systems in analysis. 

The existence of another force driving physico-chemical systems to equilibrium can be further illustrated if we consider systems whose energy is constant. 

The existence of this extra factor explains why, in order to understand equilibrium in physico-chemical systems, we require a more sophisticated analysis than sufficed for mechanical systems. 

Physico-chemical systems are of course much more complex than this, but they can nevertheless be represented in similar terms, the free energy being plotted against an appropriate reaction parameter . Thus a chemical reaction is also characterised by an activation energy associated with the ratecontrolling molecular mechanism involved in the reaction. 

Once the functional relation between the electric quantity and the concentration of a gas constituent is well known for a solid/gas system, numerous development steps remain until a sensor can be put to practical use. The determining factor is the goal of application, for example the gas analysis in the laboratory, industrial gas analysis, its use in medical devices or in motor vehicles. In any case, long-term stable physico-chemical systems have to be established which have to fulfill certain conditions. These concern for example the sample extraction and treatment, the temperature, the stability of total pressure and of material qualities, and the construction in a miniature or mechanically and thermally robust form. With solid electrolytes of the same kind one has come across to completely different sensor designs, depending on the application (Figure 25-1). 

That aspect of the living cell in which it most clearly appears as a physico-chemical system is the one which reveals its functioning as a complex pattern of relatively simple chemical reactions. 

Solving this system makes it possible to express all the concentrations of intermediate species as functions of the physico-chemical system s parameters. 

Principal Research Scientist, Physico-Chemical Systems Battelle Columbus Laboratories 505 King Avenue Columbus, OH 43201... 

Relaxation methods provide a useful tool to probe the dynamical properties of physico-chemical systems. In this framework, the knowledge concerning how fast a gel shrinks or swells is essential for many technological applications. The relaxation time r of small perturbations about a steady state 0s is obtained by linearizing Eq. (8) to give... 

It may be noted that along AB and FF, one gets only one value of Y for a particular value of X. There are three values of Y corresponding to states BC, CD and DF when X lies in the region denoted by <->. These correspond to multiple steady states. In many physico-chemical systems, one of the solutions along CD is not permissible on account of theoretical constraints as in electro-kinetic phenomenon. In such cases, bistability and hysterisis are obtained. The points C and D where the nature of the solution changes is called the bifurcation point. 

For biological systems, the desired experimental studies can be performed. These can be strengthened by investigating physico-chemical system, which can serve as a model. However, this is not possible with socio-political and socio-economic systems where similar types of experiments cannot be designed. In the case of social sciences, one has to depend on the following sequence of activities. 

In Social Dynamics and Finance and even in the case of living systems, steady states can easily be perturbed by random variables or by appearance of new variables. Whereas in physico-chemical systems, the correlation coefficients can be experimentally determined or estimated theoretically this is not possible in the case of other systems. Only some guess can be made from satisfied data. 

These are quite relevant in socio-economic systems. Variation of population in a particular region with time and variation of population density from point to point have their own importance. The first one may be called extensive variable and the second one may be called intensive variable. Spatio-temporal behaviour of population can be studied by the proper choice of variables. Similar phenomena in physico-chemical systems are easy to analyse since the important variables are diffusion coefficients of particular species and those associated with autocatalytic reaction. 

We have seen in Part One that when entropy increase in a system is compensated by entropy export to the surrounding, different types of order or organization can result. Hence, order can emerge out of chaos, provided necessary conditions are satisfied. It should be noted that increase of entropy is associated with the increase of disorder in the system. Such a situation occurs in physico-chemical systems, several examples of which have been cited in previous chapters. 

Globalization due to advances in technology and communication and mutual interaction between nations, ethnic groups, different strata in the society is a part of evolutionary non-equilibrium process. However, bifurcation from one state to another and self-organization as observed in physico-chemical systems discussed in previous chapters do occur in social systems as well. Earlier, decolonization was one such process which brought a change in outlook in the whole world and eliminated barriers between different countries... 

Such a mathematical model of a non-equilibrium physico-chemical system is represented in terms of a system of differential equations (as a rule, essentially nonlinear). These equations are derived from appropriate physical balances of substances, energy, and charge. Following rules are useful in the process of construction of the model ... 

Establishing the bifurcation point and finding out the post-bifurcation trends are the main and most valuable results of the theoretical study of non-equilibrium physico-chemical systems. After that, the investigation of mathematical model is essentially completed. Sometimes, in simplest cases, one can derive an approximate analytical solution for evolution of the system in time, or obtain the numerical solution by computer simulations, and compare these with real experimental dependencies. Though, such solutions could never be rigorous. Because of complexity of real processes and unavoidable simplifications adopted in the model, they would reflect only qualitative trends and, thus, could not be used for quantitative calculations. 

Thermokinetic Models of Dynamics in Physico-Chemical Systems Thermal Self-destruction of Lithium Power Sources with High Energy Density... 

Thermokinetic Models of Dynamics in Physico-Chemical Systems ... 

According to contemporary data on the oxygen formation in physico-chemical systems and upon photosynthesis the pathway of oxygen formation in a chloroplast may be represent-... 

For a long time the rate-determining step for the development of natural sciences has been the possibility to perform numerical calculations. Even when possible, detailed modelling of actual physico-chemical systems was considered useless because of the practical impossibility to perform numerical calculations. The ingenuity of theoreticians was accordingly concentrated more on the search of exactly or approximately solvable models rather than on the search of accurate but unsolvable models. Solvable and unsolvable are however related to the deployed mathematical apparatus - much of what remained unsolvable after centuries of development of calculus and analysis, has become solvable after the advent of electronic computers (even in pime mathematics - think of the four-colour problem). 

The enormous progress of electronic computers has allowed physico-chemical systems to be accurately described (by means of new theoretical disciplines like computational physics and theoretical chemistry) via numerical solution of the basic equations. This hard modelling of physico-chemical systems is characterized by extended numerical computations ab initio methods accurate description of the system specificity but non extensibility of the results from one system to another. 

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