Terms Of Irreversible Thermodynamics Research Articles

Current-Induced Concentration Polarization of Nanoporous Media: Role of Electroosmosis.

Current-induced concentration polarization of nanoporous media is explored theoretically by using approach of local thermodynamic equilibrium within nanopore cross-sections. The problem is solved in quadratures in terms of irreversible thermodynamics. The phenomenological coefficients are further specified by using capillary space-charge model for straight slit-like and cylindrical capillaries. This analysis reveals several novel features of current-induced concentration polarization related to the (electro)osmotic volume transfer. It confirms the previous finding that volume transfer can suppress the limiting-current phenomena but obtains more accurate criteria for this. In particular, it shows that the critical nanopore size and/or electrolyte concentration depend on the nanoporous-medium relative thickness. Under no-limiting-current conditions, the salt concentration at the interface between nanoporous medium and unstirred layer is a nonmonotone function of current density. This gives rise to unconventional current-voltage characteristics. Moreover, under certain conditions, the analysis predicts the existence of ranges of "prohibited" current densities where the problem does not have 1D stationary solution, which could give rise to a kind of "phase separation" with coexisting zones of different local current densities corresponding to the same voltage. Besides the advanced understanding of current-induced concentration polarization of nanoporous media, this analysis provides guidelines for the optimization of sample preconcentration systems in (bio)chemical microanalysis.

The solid-state photo-CIDNP effect

The solid-state photo-CIDNP effect is the occurrence of a non-Boltzmann nuclear spin polarization in rigid samples upon illumination. For solid-state NMR, which can detect this enhanced nuclear polarization as a strong modification of signal intensity, the effect allows for new classes of experiments. Currently, the photo- and spin-chemical machinery of various RCs is studied by photo-CIDNP MAS NMR in detail. Until now, the effect has only been observed at high magnetic fields with 13C and 15N MAS NMR and in natural photosynthetic RC preparations in which blocking of the acceptor leads to cyclic electron transfer. In terms of irreversible thermodynamics, the high-order spin structure of the initial radical pair can be considered as a transient order phenomenon emerging under non-equilibrium conditions and as a first manifestation of order in the photosynthetic process. The solid-state photo-CIDNP effect appears to be an intrinsic property of natural RCs. The conditions of its occurrence seem to be conserved in evolution. The effect may be based on the same fundamental principles as the highly optimized electron transfer. Hence, the effect may allow for guiding artificial photosynthesis.

Stationary cell size distributions and mean protein chain length distributions of Archaea, Bacteria and Eukaryotes described with an increment model in terms of irreversible thermodynamics

In terms of an increment model irreversible thermodynamics allows to formulate general relations of stationary cell size distributions observed in growing colonies. The treatment is based on the following key postulates: i) The growth dynamics covers a broad spectrum of fast and slow processes. ii) Slow processes are considered to install structural patterns that operate in short periods as temporary stationary states of reference in the sense of irreversible thermodynamics. iii) Distortion during growth is balanced out via the many fast processes until an optimized stationary state is achieved. The relation deduced identifies the numerous different stationary patterns as equivalents, predicting that they should fall on one master curve. Stationary cell size distributions of different cell types, like Hyperphilic archaea, E. coli (Prokaryotes) and S. cerevisiae (Eukaryotes), altogether taken from the literature, are in fact consistently described. As demanded by the model they agree together with the same master curve. Considering the "protein factories" as subsystems of cells the mean protein chain length distributions deduced from completely sequenced genomes should be optimized. In fact, the mean course can be described with analogous relations as used above. Moreover, the master curve fits well to the patterns of different species of Archaea, Bacteria and Eukaryotes. General consequences are discussed.

Hole-trapping effect on thermoelectric power of mixed ionic electronic conductor BaTiO3

The effect of hole-trapping on the thermopower of a mixed ionic electronic conductor, e.g., BaTiO3, is analyzed in terms of irreversible thermodynamics by taking trapped holes as a fourth kind of electronic charge carrier in addition to free electrons, free holes and mobile oxide ions. It is found that the effect manifests itself in two ways: thermostatically in the ionic thermopower via the thermodynamic factor and dynamically in the electronic thermopower via the electrical conductivity contribution of the trapped holes. The thermopowers of both 99.995% pure, undoped and 1.8 m/o Al-doped BaTiO3, that were measured against oxygen activity in the range of -18 < log aO2 < or = 0 at elevated temperatures of 800 degrees to 1100 degrees C [H.-I. Yoo and C. R. Song, J. Electroceram., 2001, 6, 61, ref. 6], are reanalyzed by taking into account the hole-trapping for the doped case. It is found that while the reduced heats-of-transport of free electrons and holes are, respectively, close to their thermal energy k(B)T (k(B) being the Boltzmann constant), that of trapped holes is close to their migration energy that is essentially the same as the trapping energy onto the acceptors doped, 1.04 eV.

Probing the metabolism of genetically-engineered mammalian cells by heat flux

With the onset of the commercial production of target proteins by hybridoma and genetically engineered cells, there is a pressing requirement for biosensors to monitor on-line and in real-time their growth in culture. In terms of irreversible thermodynamics, most of the Gibbs energy provided in substrates for this process is dissipated as heat, with only a relatively small quantity being conserved in biomass and the target proteins. Calorimetry would appear, therefore, to be a strong contender for a metabolic probe. A flow microcalorimeter was modified for use with animal cells and tested using CHO 320 cells which produce the heterologous glycoprotein dimer, Interferon-γ. Preliminary results showed that heat flow did not follow the increase in cell-number concentration and it was realised that this technique must be combined with one to assess biomass on-line accurately to reflect metabolic activity. Dielectric spectroscopy was chosen because capacitance measurements of the culture measures the volume fraction of viable cells and not the dead ones. A commercial version, the viable cell monitor, was validated by parallel measurements of the volume of viable cells by flow cytometry. The combined probe showed that heat flux was a function of the specific growth rate which, in turn, was related to the fluxes for glucose and glutamine utilisation and possibly to the accumulation of toxic end products, lactate and ammonia. The calorimetric-respirometric (CR) ratio was highly negative during growth in the fully aerobic conditions, indicating simultaneous anaerobic metabolism during growth. The CR ratio gave a value consistent with solely oxidative processes once there was no growth. This might indicate that ATP demand was greater than could be satisfied by oxidative processes, but this was not the case since the cells were respiring at only ca. 60% of capacity, as judged by uncoupling with FCCP. It appears likely that lactate production was due to the need to produce biosynthetic precursors which were not supplied in the medium. A better medium design would probably decrease this requirement and thereby reduce the accumulation of toxic end products. The heat flux probe was shown to be invaluable in exploring the metabolism of CHO 320 cells grown in batch culture.

Osmosis and reverse osmosis in fine-porous charged diaphragms and membranes

The theory of osmosis and reverse osmosis in fine-porous charged membranes and diaphragms is presented in a deductive way with several well-structured levels of consideration. The analysis starts from the discontinuous version of irreversible thermodynamics where the membrane is considered as an absolutely black box without any information needed about its internal structure. As a trade-off for generality, however, the thermodynamic forces must be small. A number of qualitative conclusions is drawn proceeding from rather evident assumptions about the order of magnitude of various phenomenological coefficients. In the case of electrolyte mixtures those conclusions turn out surprisingly numerous and non-trivial including predictions of reflection coefficients larger than unity and strong negative osmosis. Both those anomalous phenomena are confirmed by experimental findings. The next step is the introduction of a ‘uniformly black’ box, namely a macroscopically homogeneous membrane with otherwise unspecified internal structure. That permits to employ the continuous version of irreversible thermodynamics thus allowing to drop the restriction of small thermodynamic forces. In the case of binary electrolytes general solutions in quadratures are obtained for the problems of apparent osmotic pressure and of reverse osmosis, and a very accurate approximate solution in quadratures is obtained for the problem of osmosis. Some of the theoretical predictions are compared with experimental data on the reverse osmosis of binary electrolytes in track-etched membranes with the pore size of 8 nm. In the case of electrolyte mixtures a semi-quantitative asymptotic analysis is performed in the limiting case of reverse osmosis at sufficiently large Péclet numbers, and in the particular case of one dominant electrolyte in the mixture an exact solution in quadratures is obtained. Those analyses make possible to predict a number of non-trivial regularities that are confronted with experimental data on the pressure-driven transport or ternary electrolyte mixtures across various charged porous membranes. A good qualitative agreement between the theory and experiments is recorded. The next step is the specification of phenomenological coefficients within the scope of a general capillary model. That makes the box grey but not transparent, yet, as the shape of capillary cross-section as well as the nature of surface forces are not specified. General expressions for phenomenological coefficients derived in terms of ion distribution and diffusion coefficients make possible a qualitative analysis of the effect of inhomogeneity of ion distribution inside pores. Finally, the capillary space charge model is introduced making the analysis completely mechanistic. Several approaches are considered to the approximate description of the structure of overlapped diffuse parts of double electric layers in fine pores. Since qualitative effects of microscopic heterogeneity appear to be not dependent on the details of the pore geometry sample numerical calculations are performed for slit-like capillaries where there is a general solution of Poisson-Boltzmann equation in quadratures. A more general model of pores in an electrically conducting gel is introduced in an attempt to quantitatively describe the results of complete characterization of cation-exchange membranes in terms of irreversible thermodynamics.

Changes in pH Value Caused by Pressure-Driven Transport of Strong Electrolytes across Charged Membranes

The pressure-driven transport of small additions of strong acids (bases) to strong electrolytes across charged membranes has been studied theoretically. The basic equations bare been formulated in terms of irreversible thermodynamics. Approximate thermodynamic solutions have been obtained under the assumption that the concentration of H+ ions in the membrane phase is substantially higher than that of OH- ions or vice versa. The phenomenological coefficients in the basic equations have been further specified within the scope of the homogeneous membrane model and the resulting equations have been solved numerically. It has been shown that in the case of negatively charged membranes in the acidic region up to a certain pH value, H+ ions can be considered merely highly mobile cations of a strong electrolyte; the reaction of water dissociation plays no role. Within that region pH changes are independent of the feed pH value and may be very large. At higher feed pH values there occurs a "buffer" region where the permeant pH value is practically independent of the feed pH value. Here the reaction of water dissociation plays a substantial role. At still higher feed pH values there is a rather sharp transition to a "basic" region where the H+ ion rejection is again almost independent of the feed pH value but, in contrast to the acidic region, is rather small. It has been shown that at sufficiently high membrane electrochemical activity and Peclet number, changes in pH value may be described by approximate thermodynamic solutions within the whole range of validity of the small addition approximation.

Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary space-charge model

The problem of transport of binary electrolyte solutions through macroscopically homogeneous membranes under reverse osmosis conditions with arbitrary thermodynamic forces has been solved in quadratures in terms of irreversible thermodynamics. Phenomenological coefficients have been specified for the model of straight cylindrical capillaries with an arbitrary cross-section and surface forces of an arbitrary nature. These general expressions have been further specified for the space-charge model and identical capillaries with a circular cross-section. A new technique to describe the structure of strongly and moderately overlapped double electrical layers has been developed. As a result, analytical expressions for the main characteristics of charged reverse osmosis membranes have been derived at arbitrary fixed charge densities. Limiting rejection, hydrodynamic permeability, filtration potential and the rate of approaching limiting rejection have been calculated as functions of fixed charge density, pore size, binary electrolyte concentration, valency type and the ratio of cation and anion mobilities. A comparison with experiment has been carried out for model membranes having identical straight circular cylindrical pores with radius 40 or 50 Å.

Membranes and meters

We present a mathematical examination of the measurement and representation of membrane transport systems. Confronted with a coupled, multicomponent system, the experimentalist must choose meters which project out and make measurements upon subsystems in a rational manner. With a proper choice of projection operations, a representation of the composite system can be synthesized directly from the results of measurement. Starting from a set of basic axioms governing the measurement process, we apply the tenets of operator theory to the action of meters. We derive the projection operators associated with the representation of transport systems in terms of irreversible thermodynamics. The metric structure of this representation is explored from the viewpoint of measurement and the specification of identity. By means of concrete examples and a computational algorithm, the abstract, mathematical formalism is related to standard laboratory procedures.

Environmental stress cracking and crazing in polymers in terms of irreversible thermodynamics

The processes in environmental stress cracking and crazing in polymers are analysed in terms of the irreversible thermodynamics. The thermodynamic potential of the system composed of the polymer matrix at a flaw tip region and its environmental liquid is constructed as a function of the concentration of the liquid migrated in the matrix and the dilative stress due to stress concentration. A state of the system is represented by a point in the thermodynamic potential diagram. The paths of the state shifts leading to failure in the diagram are governed by the shapes of the thermodynamic potential curves, the liquid concentrations giving the potentials a minimum, the critical concentration and the breakdown concentrations here introduced. Various kinetic data of environmental stress cracking in low density polyethylenes can be understood by the unified picture. The predictions of the theory are also consistent with the reported kinetic nature of crazing.

COUPLING OF ION FLOWS IN CELL SUSPENSION SYSTEMS*

A valid test for cotransport between solutes is a demonstration that the degree of coupling between all coupled solute flows concerned, q defined in terms of Irreversible Thermodynamics, is sufficiently close to unity. The usual method to determine q kinetically by pulses and responses of flows can not simply be applied to rheogenic ion flows, as electrical potential difference changes due to the pulses can hardly be avoided. If, however, the ion flows are all electrically silent, changes in electrical potential difference (PD.) should not interfere with the determination of q. This holds for the furosemide-sensitive fluxes of Na+, K+, and Cl- in Ehrlich cells, each of which could be shown to be unaffected by a change in electrical PD and vice versa. Hence the q values could be determined for any pair of the three ion flows concerned and none differed significantly from unity. These results appear to indicate a furosemide-sensitive, electrically silent ternary symport mechanism for Na+, K+, Cl- with the stoichiometry 1:1:2, which is active but does not utilize ATP. It is assumed to function as a very efficient regulator of cellular volume and may be identical with other previously described binary symport systems.

Individual contributions of overpotentials at iron mixed electrodes

The Nagel formulation of overpotential for a single electrode from an E H (pH, log a i ) equilibrium diagram has been developed in the case of iron as a mixed electrode. A detailed discussion is presented concerning the possibilities of determining the kinetics of corrosion processes in terms of irreversible thermodynamics. The distribution of overpotential for Fe + Fe 2+; 2H + + 2 e − = H 2 and its division into activation, reaction, concentration and diffusion factors is represented graphically as a function of pH at constant a Fe 2+ (= 10 −5M).

Coupling phenomena in the transfer of elements between a gas phase and iron melts

The simultaneous transfer of Si and C from a gas phase containing SiO and CO to liquid Fe-C alloys has been investigated. It was found that, although the silicon content of the melt increased with time as expected, the carbon content initially decreased, in spite of the fact that the carbon potential of the gas phase was above that of the liquid alloy. These phenomena are interpreted in terms of irreversible thermodynamics which shows that the overall transfer reactions are comprised of coupled reactions: SiO(g) + CO(g) →Si + CO2(g) andC + CO2(g) → 2CO(g). It is also shown that the simultaneous transfer of carbon and oxygen from gas mixtures of CO and CO2 to liquid iron occurs via the coupled reactions CO2(g) →O + CO(g) and 2CO(g) →C + CO2. In each case there is a predominant, or driving reaction which promotes the other.

On the Current-Voltage Relationships of Energy-Transducing Membranes: Submitochondrial Particles

A transmembrane electrochemical proton gradient is widely held to constitute the link between electron transport and ATP synthesis in biological membranes (Boyer et al., 1977), but much debate surrounds the issue of the stoicheiometry of H+ movement that either generates (by electron transport) or dissipates (by ATP synthesis) this proton gradient (proton-motive force, l'.p) (Brand, 1977). Our estimates of both l'.p and the phosphorylation potential generated by submitochondrial particles indicate that l'.p is thermodynamically competent to serve as such a link provided that 3 H+ ions are translocated through the mitochondrial adenosine triphosphatase for each molecule of ATP synthesized (Sorgato et al., 1978). Although the thermodynamic competence of !'ip in submitochondrial particles has now been scrutinized in some detail (Azzone et al., 1978; Sorgato et al., 1978) rather less attention has been paid to two other-related matters: (1) the relationship between l'.p and the rate of proton translocation; (2) the relationship between l'.p and the rate of ATP synthesis. It was found (Sorgato et al., 1978) that the oxidation of either succinate or NADH by submitochondrial particles generated virtually the same 1'.p, despite the fact that, after correction for the slower rate of succinate oxidation, the rate of proton translocation was approximately 2-fold slower when succinate was the substrate. Decrease, by titration with malonate, of the rate of succinate oxidation to 18 % of its maximal value is now found to cause only a small decline in l'.p from approx. 140mV to approx. 135mV. [l'.p was determined in a reaction mixture of 10 mM-phosphate/Tris, 5 mM-magnesium acetate, pH 7.3, by using a flow dialysis assay for SCNuptake to estimate /11/f, the sole detectable component of l'.p under these reaction conditions (Sorgato et al., 1978).] These two sets of observations suggest either that the protic resistance of the inner mitochondrial membrane (at least in submitochondrial particles) is variable or that the membrane capacitance is strongly voltage-dependent. Thus as the rate of proton translocation is decreased there is a corresponding decrease in the rate at which protons are able to pass back across the membrane down their electrochemical gradient. This type of behaviour has also been suggested for rat liver mitochondria (Nicholls, 1974) and for chloroplast thylakoids (Schonfeld & Neumann, 1977), although it is noteworthy that with intact mitochondria a decline in l'.p was observed when the rate of succinate oxidation was decreased by only 40% (Nicholls, 1974). Titration of the rate ofNADH oxidation by submitochondrial particles with rotenone indicated that, except at the highest respiratory rates, there was an almost ohmic relationship between l'.p and the rate of proton translocation (Kell et al., 1978). This result appears to contrast markedly with that found when succinate is the substrate. The reasons for this difference remain to be elucidated, but it may be relevant to note that Nicholls ( 1977) has suggested that the second and third segments of the respiratory chain have the ability, for a given rate of electron transfer, to maintain l'.p at a higher value than that produced at the first segment between NADH and ubiquinone. A knowledge of the resistive (and capacitative) characteristics of the membrane is essential both for the relationship between oxidation and phosphorylation to be treated in terms of irreversible thermodynamics, and for the identification of l'.p as the deterdeterminant (or otherwise) of respiratory control (Boyer et al., 1977; Kupriyanov & Pobochin, 1978). The results in the present paper indicate that treatments (Hinkle et al.,

General treatment of junction potentials in solids using irreversible thermodynamics

The authors propose a new general method making it possible to obtain the measurable voltage across a chain of metals and semiconductors in thermodynamic disequilibrium. Use is made of the concept of electrochemical potential of free electrons. The interaction between the metal electrons, the interface states and the semiconductor is described by means of chemical reactions. Studying the kinetics and electrochemical affinities of these chemical reactions, and using Onsager’s theorem, it is shown that the measurable voltage across this structure under thermodynamic disequilibrium lies between two extreme values, ΔV12 + [KT/e ln(p/p0)] and ΔV12 − [KT/e ln(n/n0)], where n, p are the densities of free electrons and holes in the volume of semiconductor at the space charge boundary; n0 and p0 are the equilibrium values. ΔV12 is the Dember voltage. Furthermore, the temporal evolution of the measured voltage across the examined structure are investigated and it is found that it may evolve successively through several pseudosteady states before reaching a real and final steady state. The same method allows an original and rigorous definition of the ohmic metal−semiconductor contact. To confirm these conclusions, some experiments performed on metal−Ge contacts are presented. This approach, which describes the system in terms of irreversible thermodynamics, is particularly simple and efficient. It could be a useful tool for investigating the performance of energy−conversion devices (for example, photo−voltaic devices).

Statistical Mechanics of the Collective Jahn-Teller Phase Transition

An exact treatment of a cooperative Jahn-Teller transition is presented. The results are expressed in terms of the thermodynamic properties of the Ising model. The dynamic behavior of fluctuations is discussed in terms of irreversible thermodynamics. I. INTRODUCI'ION II. FREE ENERGY Models describing cooperative Jahn-Teller transitions have for the most part been treated in the random-phase approximation (RPA). ' 4 In RPA, the static thermal averages are determined in the mean-field approximation, while the dynamic behavior is described by equations of motion linearized about the mean-field values. A somewhat improved approximation, which has been considered by Halperin, is applicable under certain conditions for the case of two nondegenerate electronic levels. ' In the present paper an exact statistical mechanical treatment is given for a model containing all the essential features of the cooperative Jahn-Teller transition. The results are expressed in terms of the statistical mechanical properties of the Ising model. The model describes the interaction of a doubly degenerate electronic level at each lattice site with nondegenerate elastic strain and optic phonons of a given symmetry (at q = 0). Only a linear coupling between the phonons and the electronic system wi)l be considered. The Hamiltonian then takes the form'

Sieving equations and effective glomerular filtration pressure

Sieving equations and effective glomerular filtration pressure. The curvilinear relationship between the sieving coefficients for 125 I-PVP (fractional clearances/GFR) and the radii of hydrodynamically equivalent spheres has been studied in 15 normal mongrel dogs. Starting from the formula used to describe membrane permeability in terms of irreversible thermodynamics (Kedem and Katchalsky), new equations have been developed to account for the glomerular sieving of these molecules. The new equations differ from the older equations based merely on kinetics (Pappenheimer and Renkin, Landis and Pappenheimer) by the values given to the concentration term and the restriction factors used in calculating the contributions of bulk flow and diffusion to solute flow across the membrane. The equations allow the derivation of two parameters characterizing the porosity of an isoporous membrane equivalent to the glomerular sieve: r, the radius of cylindrical pores and A p/Δx, the total area of the pores per unit of path length. From these, effective glomerular filtration pressure (GFP e ) has been calculated applying Poiseuille's law. A mean value of 14.5± 1.4 or 17.8 ± 2.1 mm Hg has been derived, depending on the limits for molecular radii within which the mean pore radius is calculated. Sieving equations assuming a log normal distribution model are less satisfactory for calculating GFP e than those based on the isoporous model, although they provide an excellent alignment of the calculated and the experimental sieving curves over a wide range of molecular sizes.

Thermoelectric Power of Molten Salt ‐ Metal Solutions, I, Bi + BiBr3 Solutions

AbstractThe determination of thermoelectric power of Bi + BiBr3 was made between 10 and 100 mole‐% Bi, and 300 and 550 °C. The initial thermoelectric power (uncorrected for the contribution of the tungsten leads) and the stationary‐state potential respectively ranged from ‐ 132 to 45 μ V/deg and from ‐ 594 to 41 μV /deg. The results are discussed in terms of irreversible thermodynamics. The formulation for the electronic part of thermoelectric powers is shown on the basis of the scattering electron model as well as hopping electron model. In particular the data in metal‐rich region can rather quantitatively be estimated on the basis of the scattering electron model due to Ziman. The ionic contribution to thermoelectric powers may be discussed on the basis of the free volume theory of Cohen and Turnbull and the concept of Macedo and Litovitz for the viscosity of liquids.

Kinetics of steady state phase transitions

AbstractA fundamental investigation of the departure from equilibrium in steady‐state phase transitions has been made in terms of irreversible thermodynamics and absolute rate theory. The present status of the concept of accommodation coefficients was reviewed and hypotheses were advanced for the reconciliation of opposing viewpoints. Formulas for the magnitude of the departure from equilibrium were derived for single‐ and multicomponent systems. The deviation from equilibrium appeared to be small for ordinary rates of phase change, but interpretation of the available data was hampered by lack of a detailed molecular picture of the phase‐change process.