Affinity, thermodynamic forces

Equation (12.33) is a measure of the distance of a nonequilibrium chemical reaction from equilibrium. At equilibrium, the affinity vanishes. Equation (12.34) shows a nonlinear relation between the reaction velocity Jr (flow) and the affinity (thermodynamic force). If the chemical system is close to equilibrium, that is, A/ RT) 1, then the contents of the square parentheses of Eq. (12.34) are approximated asAKRT), and we have the following linear flow-force relation between the reaction velocity and the affinity... 

The roots of both chemical thermodynamics and contemporary kinetics both lie in the eighteenth-century ideas of chemical "affinity" and "force," transformed into nineteenth-century conceptions of "work" and "energy." Berthollet identified the fundamental difficulty for eighteenth-century theories of affinity in a critique that applied equally to early-nineteenth-century theories of electrochemical dualism. In "Recherches sur les lois de l affinite" (1799), Berthollet wrote,... 

Different Irreversible Processes with Their Affinity or Thermodynamic Force and Their Current J. ... 

In nonequilibrium steady states, the mean currents crossing the system depend on the nonequilibrium constraints given by the affinities or thermodynamic forces which vanish at equihbrium. Accordingly, the mean currents can be expanded in powers of the affinities around the equilibrium state. Many nonequilibrium processes are in the linear regime studied since Onsager classical work [7]. However, chemical reactions are known to involve the nonlinear regime. This is also the case for nanosystems such as the molecular motors as recently shown [66]. In the nonlinear regime, the mean currents depend on powers of the affinities so that it is necessary to consider the full Taylor expansion of the currents on the affinities ... 

There exist a large number of phenomenological laws for example, Fick s law relates to the flow of a substance and its concentration gradient, and the mass action law explores the reaction rate and chemical concentrations or affinities. When two or more of these phenomena occur simultaneously in a system, they may couple and induce new effects, such as facilitated and active transport in biological systems. In active transport, a substrate can flow against the direction imposed by its thermodynamic force. Without the coupling, such uphill transport would be in violation of the second law of thermodynamics. Therefore, dissipation due to either diffusion or chemical reaction can be negative only if these two processes couple and produce a positive total entropy production. 

Mass flow, heat flow, and chemical reaction rate are some examples of the flows J,. The thermodynamic forces A of the chemical potential gradient, temperature gradients, and the chemical affinity cause the flows. The affinity A is... 

In chemical kinetics, the reaction rates are proportional to concentrations or to some power of the concentrations. Phenomenological equations, however, require that the reaction velocities are proportional to the thermodynamic force or affinity. Affinity, in turn, is proportional to the logarithms of concentrations. Consider a monomolecular... 

With the respective affinities as the thermodynamic forces, Eq. (8.268) becomes... 

Nonisothermal reaction-diffusion systems represent open, nonequilibrium systems with thermodynamic forces of temperature gradient, chemical potential gradient, and affinity. The dissipation function or the rate of entropy production can be used to identify the conjugate forces and flows to establish linear phenomenological equations. For a multicomponent fluid system under mechanical equilibrium with n species and A r number of chemical reactions, the dissipation function 1 is... 

The thermodynamic force (affinity) X is a pivotal concept in thermo dynamics of nonequilibrium processes because of its relationship to the concept of driving force of a particular irreversible process. Evidently, thermodynamic forces arise in spatially inhomogeneous systems with, for example, temperature, concentration, or pressure inhomogeneity. In spatially uniform homogeneous systems, such forces arise either in the presence of chemically reactive components that have not reached thermodynamic equiHbrium via respective chemical transformations or at the thermodynamic possibility of some phase transformations. 

Obviously, quantities hot and hi are always symbate to the respective chemical potentials and P . It is important that the difference between the logarithms of rushes fij and hj be proportional to the current thermo dynamic affinity A j of the reaction between reaction groups i and j—in other words, to the thermodynamic force Xy related to flux... 

In addition, as shown in Section 1.3, the fluxes of the concentration of chemical components are determined generally by the differences in the thermodynamic rushes of corresponding reaction groups rather than by true thermodynamic forces (chemical affinities of the reactions). Consider the simplest pathway of cocurrent transformations, which includes two parallel channels of independent reversible transformation of initial reactant R into products Pi and P2 ... 

We must emphasize that in this example, again, Ai2 / A21. However, it is also easy to demonstrate that Li2 = L2i on approaching the equilibrium of the stepwise transformations when the true Onsager coefficients Ly relate to true thermodynamic forces (the affinities of the stepwise processes). 

Thus, in the course of any catalytic transformation, the active com ponent exists necessarily in a thermodynamically nonequilibrium state (stationary or other) that is governed by thermodynamic forces that exist in the nonequilibrium system—that is, by current affinities of aU of the involved elementary chemical transformations. 

The structure of the expression for totai is that of a bilinear form it consists of a sum of products of two factors. One of these factors in each term is a flow quantity (heat flux q, mass diffusion flux jc, momentum flux expressed by the viscous stress tensor o, and chemical reaction rate rr)- The other factor in each term is related to a gradient of an intensive state variable (gradients of temperature, chemical potential and velocity) and may contain the external force gc or a difference of thermodynamic state variables, viz. the chemical affinity A. These quantities which multiply the fluxes in the expression for the entropy production are called thermodynamic forces or affinities. 

Another important relationship between the kinetic coefficients is the so-called principle of symmetry , as formulated by P. Curie and introduced to nonlinear thermodynamics by Kondepudi and Prigogine [37]. As applied to thermodynamics, this postulates that a scalar quantity could not evoke a vector effect. For example, a scalar thermodynamic force - chemical affinity (driving the process of chemical reaction) that has very high isotropy symmetry - could not cause heat flow, which has a particular direction and is therefore anisotropic. Taking into account the reciprocal relationships, this can be formulated as... 

Ligand affinity and efficacy both emanate from the thermodynamic forces that promote association of the ligand with the receptor, thus they are related. However, they can also be dissociable properties that vary independently with changes in chemical structure. In fact, it is the fact that the affinity of a series of alkyltrimethylammonium compounds for... 

X ( corresponding generalised thermodynamic force (gradient or chemical affinity) the Gibbs adsorption of component y defined by = 5f" / 6f e cross chemical potential e = 0 equilibrium condition of the system... 

The expression for shows, that the entropy flux for open systems consists of two parts the thermal flux associated with the heat transfer, and the flux due to diffusion. The second expression consists of four terms associated with, respectively, the heat transfer, diffusion, viscosity, and chemical reactions. The expression for the dissipative function a has quadratic form. It represents the sum of products of two factors a flux (specifically, the heat flux /, diffusion flux momentum flux n, and the rate of a chemical reaction and a thermodynamic force, proportional to gradient of some intensive variable of state (temperature, chemical potential, or velocity). The second factor can also include external force F]t and chemical affinity Aj. 

The affinity is the thermodynamic force and vanishes at equilibrium. The fluctuation theory states that the ratio of the probability of a forward rotation of the shaft to the probability of a backward rotation determines the affinity of the process (Andrieux and Gaspard, 2006). 

A = A - A is the over-all affinity of the reaction, cf. (4.24). Quite a similar transformation is performed in the case of a diffusion 2-port such that by comparison of (7.39) or (7.41) with the definition of generalized thermodynamic forces and fluxes in (3.79) we eventually may write... 

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