Eyring Rate Theory Research Articles

On a thermodynamic foundation of Eyring rate theory for plastic deformation of polymer solids

ABSTRACTThe plastic deformation of almost all solid polymers can be represented by a thermally activated rate process involving the motion of cooperative mobile elements over potential barriers, based on the Eyring activated rate theory. The present study shows that the governing equations for the Eyring rate theory can be completely derived based on the principle of microscopic reversibility in the framework of non-equilibrium dynamics.

Viscosity model of deep eutectic solvents from group contribution method

AbstractDeep eutectic solvents (DESs), a novel category of sustainable solvents, are expected to achieve the design of the chemical processes without utilizing or generating harmful chemicals. In this work, based on the mathematical model inspired by the transition state theory, the group contribution method is used to accurately predict the viscosity of DESs. The model is constrained by Eyring rate theory and hard sphere free volume theory. A dataset of 2229 experimental viscosity data points of 183 DESs from literature is used to determine the model parameters and subsequently verify the model. The rules introduced by this model are simple and easy to follow. The results show that the proposed model is capable to predict the viscosity of DESs with very high accuracy, using only temperature and composition as inputs. The average absolute relative deviations (AARDs) of the model are 8.12% and 8.64% over the training and test sets, respectively, and the maximum ARD is 34.63%. Therefore, the as‐proposed model can be considered a highly reliable tool for predicting the viscosity of DESs when experimental data are absent. It will provide useful guidance for the synthesis of DESs with specific viscosity to meet different application requirements and promote their industrial‐scale implementation.

Scaling equation for viscosity of polydimethylsiloxane in ethyl acetate: From dilute to concentrated solutions

Rheology of polymer solutions suffers from lack of universal model of viscosity applicable across wide range of concentrations. Here we build such a model on the basis of measured viscosity of polydimethylosiloxane (PDMS) in ethyl acetate in a wide range of polymer concentrations: from dilute up to highly concentrated solutions. The relationship between viscosity and different polymer parameters in solution such as coil size, correlation length ξ, monomer–solvent and monomer–monomer interaction parameter were established experimentally as a function of concentrations [from 0.001g∕cm3 to 8.000g∕cm3], temperature [in a range 283–303K] and molecular masses [9–139kg∕mol]. Entanglement onset at the crossover from dilute to semi-dilute solution as well as the solvent–monomer contact reduction at the crossover from semi-dilute to concentrated regime are captured by the model. This model is in accordance with the Eyring rate theory for activated processes.

A Drift and Diffusion Model for PID-s in Solar Modules

A quantitative physical model for potential-induced degradation of the shunting type (PID-s) in solar modules is introduced. Based on a drift and diffusion approach for sodium ions and atoms, it gives insight into the kinetics of degradation and the corresponding regeneration. A simple drift/source term is used to describe the time-dependent flux of Na $^+$ -ions toward stacking faults at the surface of the solar cell. The assumed transport mechanism for Na $^+$ ions through the SiN layer uses the modified Stern–Eyring rate theory but our approach can also be adapted to other mechanisms. Several PID-s and regeneration curves of one-cell solar modules at T = 49 °C and T = 90 °C with 1000 V potential difference between module frame and cell were measured and least-square fits of the in situ measured parallel resistance $R_\text{sh}$ to the model were performed giving very good accordance. Based on a few measurements, the model can predict PID-s and regeneration characteristics of solar modules under different conditions.

Dielectric relaxation of ethanol and N-methyl acetamide polar mixture in C 6 H 6 at 9.90 GHz

Debye relaxation times (τ j k ) and dipole moments (μ j k ) of binary (j k) polar mixtures of ethanol (EtOH) and N-methyl acetamide (NMA) dissolved in benzene(i) are studied by studying conductivity of solution at 9.90 GHz for different temperatures, different mole fractions (x j ) of ethanol and different weight fractions (w j k ) of the mixtures, respectively. The variation of τ j k −x j from linear slope of imaginary $(\sigma _{ijk}^{\prime \prime } )$ against real $(\sigma _{ijk}^{\prime })$ part of total conductivity $(\sigma _{ijk}^{\ast })$ curve reveals solute–solute (dimer) or solute–solvent (monomer) molecular associations up to x j = 0.0−0.3 and thereafter, solute–solvent molecular associations. τ j k s from the ratio of slopes of $\sigma _{ijk}^{\prime \prime }-w_{jk} $ and $\sigma _{ijk}^{\prime }-w_{jk} $ curves exhibit solute–solvent molecular association for all x j s which are consistent with the μ j k −x j curves at all temperatures except at 35∘C. This signifies the validity of both the proposed methods in estimating τ and μ. The molecular dynamics of the polar mixture are ascertained from Eyring rate theory. Theoretical dipole moments from bond angles and bond moments (μ theo) are also calculated to predict associational aspects.

Scaling of activation energy for macroscopic flow in poly(ethylene glycol) solutions: Entangled – Non-entangled crossover

We postulate an empirical scaling equation, which accurately describes flow of polymer solutions, complimenting the paradigm of length-scale-dependent viscosity. We investigated poly(ethylene glycol) aqueous solutions and observed an exponential dependence of viscosity on the hydrodynamic radius of a single coil Rh divided by the correlation length ξ. Properties of the system changed abruptly with the onset of chain entanglement at concentration corresponding to ξ = Rh. We propose a single equation valid for all the investigated systems, analyze the physical meaning of parameters appearing therein and discuss the impact of chain entanglement. Viscous flow is treated as an activated process, following the Eyring rate theory. We show that the difference of activation energy for flow between pure solvent and polymer solution, ΔEa, is a function of concentration, whose derivative has a discontinuity at the crossover concentration. For dilute PEG solutions ΔEa takes values of up to several kJ/mol and is proportional to the intrinsic viscosity. We successfully apply the scaling approach to the diffusive motion of a protein (aldolase) in solutions of 25 kg/mol PEO (concentrations of 2–20%), investigated by fluorescence correlation spectroscopy (FCS). A significant difference in the influence of crowding on translational and rotational motion of the protein is revealed.

Quantitative measurement of mitochondrial membrane potential in cultured cells: calcium‐induced de‐ and hyperpolarization of neuronal mitochondria

Mitochondrial membrane potential (ΔΨM) is a central intermediate in oxidative energy metabolism. Although ΔΨM is routinely measured qualitatively or semi-quantitatively using fluorescent probes, its quantitative assay in intact cells has been limited mostly to slow, bulk-scale radioisotope distribution methods. Here we derive and verify a biophysical model of fluorescent potentiometric probe compartmentation and dynamics using a bis-oxonol-type indicator of plasma membrane potential (ΔΨP) and the ΔΨM probe tetramethylrhodamine methyl ester (TMRM) using fluorescence imaging and voltage clamp. Using this model we introduce a purely fluorescence-based quantitative assay to measure absolute values of ΔΨM in millivolts as they vary in time in individual cells in monolayer culture. The ΔΨP-dependent distribution of the probes is modelled by Eyring rate theory. Solutions of the model are used to deconvolute ΔΨP and ΔΨM in time from the probe fluorescence intensities, taking into account their slow, ΔΨP-dependent redistribution and Nernstian behaviour. The calibration accounts for matrix:cell volume ratio, high- and low-affinity binding, activity coefficients, background fluorescence and optical dilution, allowing comparisons of potentials in cells or cell types differing in these properties. In cultured rat cortical neurons, ΔΨM is −139 mV at rest, and is regulated between −108 mV and −158 mV by concerted increases in ATP demand and Ca2+-dependent metabolic activation. Sensitivity analysis showed that the standard error of the mean in the absolute calibrated values of resting ΔΨM including all biological and systematic measurement errors introduced by the calibration parameters is less than 11 mV. Between samples treated in different ways, the typical equivalent error is ∼5 mV.

Time Lapse Measurement of Mitochondrial Membrane Potential in Absolute Millivolts in Single Intact Cells

Assaying mitochondrial membrane potential (ΔΨM ) in absolute millivolts in intact cells had been previously limited mostly to radioisotope distribution methods. Here we introduce a purely fluorescence based ΔΨM assay to calculate time courses of ΔΨM in absolute millivolts in monolayer cell cultures. We built a biophysical model‐based method to calibrate single‐cell fluorescence of a bis‐oxonol‐type plasma membrane potential (ΔΨP ) indicator and the ΔΨM –probe TMRM to potentials. The ΔΨP ‐dependent distribution of the probes is modeled by Eyring rate theory, which we have verified using fluorescence imaging combined with voltage clamp. ΔΨM is determined in millivolts by deconvoluting TMRM fluorescence in time taking in account the slow, ΔΨP ‐dependent redistribution and its Nernstian behavior. The resting ΔΨM is calculated from a complete step‐depolarization of ΔΨM. The calibration accounts for volume ratios, high and low affinity bindings, activity coefficients, background fluorescence and optical dilution. All of the calibration parameters are back‐calculated from fluorescence intensities or measured by confocal microscopic assays (validated by electron microscopy), allowing comparisons of potentials in cells with different properties. We show that ΔΨM in cultured rat cortical neurons is regulated between −120 and −154 mV as a concerted effect of increased ATP turnover and Ca2+‐dependent metabolic activation.

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state (EOS) for square-well chain fluid with variable range (SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids (ILs). A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures. The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation (AAD) of 0.36%. A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring's rate theory of viscosity and the SWCF-VR EOS. The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases. The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT, vapor-liquid equilibrium, caloric properties, surface tension, and viscosity.

Analysis of [formula omitted] charge recombination with the Arrhenius, Eyring and Marcus theories

The Q band of photosynthetic thermoluminescence, measured in the presence of a herbicide that blocks electron transfer from PSII, is associated with recombination of the S 2 Q A - charge pair. The same charge recombination reaction can be monitored with chlorophyll fluorescence. It has been shown that the recombination occurs via three competing routes of which one produces luminescence. In the present study, we measured the thermoluminescence Q band and the decay of chlorophyll fluorescence yield after a single turnover flash at different temperatures from spinach thylakoids. The data were analyzed using the commonly used Arrhenius theory, the Eyring rate theory and the Marcus theory of electron transfer. The fitting error was minimized for both thermoluminescence and fluorescence by adjusting the global, phenomenological constants obtained when the reaction rate theories were applied to the multi-step recombination reaction. For chlorophyll fluorescence, all three theories give decent fits. The peak position of the thermoluminescence Q band is correct by all theories but the form of the Q band is somewhat different in curves predicted by the three theories. The Eyring and Marcus theories give good fits for the decreasing part of the thermoluminescence curve and Marcus theory gives the closest fit for the rising part.

Energy profiles for sodium ion passage through the single-filing gramicidin transmembrane channel

Sodium-23 nuclear magnetic resonance longitudinal and transverse relaxation studies of sodium ion interaction with the Gramicidin A transmembrane channel are reported in the 30d to 75d temperature range to determine the temperature dependence of the off-rate constant for the doubly occupied channel (kwoff) of the binding constant for going from single to double ion occupancy (Kwb), of the binding constant for going from empty to singly occupied channel (Ktb), and of the off-rate constant for the singly occupied channel, (kkoff). With previous information for the temperature dependence of the intrachannel rate constant for an ion going from one ion binding site to the other (kk) for the singly occupied state of this two-fold symmetric channel, the enthalpy (ΔH and the –TΔS energy profiles are plotted for ion passage through the channel. This provides energy profiles for comparison with theoretical calculations. Comparison of TΔS values defined by equilibrium theory (i.e. entropy changes on going from one minimum to another) with the TΔS values defined by Eyring rate theory (i.e. the entropy change between minima and activated state) shows that, even though Eyring rate theory has the very large pre-exponential factor (kT/h), the changes in entropy obtained from the temperature dependence of equilibrium constants are very nearly the same as the changes in entropy obtained from the temperature dependence of the off-rate constants. Thus application of Eyring rate theory to single filling channels, where the channel wall supplies lateral coordinations of the permeant ion and where the rate constants are of the order of 107 ions/sec, appears quite reasonable.

Human ClCa1 modulates anionic conduction of calcium‐dependent chloride currents

Proteins of the CLCA gene family including the human ClCa1 (hClCa1) have been suggested to constitute a new family of chloride channels mediating Ca2+-dependent Cl− currents. The present study examines the relationship between the hClCa1 protein and Ca2+-dependent Cl− currents using heterologous expression of hClCa1 in HEK293 and NCIH522 cell lines and whole cell recordings. By contrast to previous reports claiming the absence of Cl− currents in HEK293 cells, we find that HEK293 and NCIH522 cell lines express constitutive Ca2+-dependent Cl− currents and show that hClCa1 increases the amplitude of Ca2+-dependent Cl− currents in those cells. We further show that hClCa1 does not modify the permeability sequence but increases the Cl− conductance while decreasing the GSCN−/GCl− conductance ratio from ∼2–3 to ∼1. We use an Eyring rate theory (two barriers, one site channel) model and show that the effect of hClCa1 on the anionic channel can be simulated by its action on lowering the first and the second energy barriers. We conclude that hClCa1 does not form Ca2+-dependent Cl− channels per se or enhance the trafficking/insertion of constitutive channels in the HEK293 and NCIH522 expression systems. Rather, hClCa1 elevates the single channel conductance of endogenous Ca2+-dependent Cl− channels by lowering the energy barriers for ion translocation through the pore.

Double relaxation phenomena of associated binary polar liquid mixture in non-polar solvent under high frequency electric field

Double relaxation times τ 2 and τ 1 due to whole molecular rotation and the flexible parts of the binary polar liquid mixture ( jk) 3-bromoaniline and 1-propanol dissolved in non-polar solvent ( i) benzene were estimated in terms of measured real χ ′ i j k , imaginary χ ″ i j k parts of complex high frequency orientational susceptibility χ i j k * and χ 0 ijk which is real at 20, 30, 40 and 47 °C experimental temperatures for 0.0, 0.25, 0.50,0.75 and 1.00 mole fractions x j 's of 1-propanol under 9.1 GHz electric field. The slopes ω( τ 2 + τ 1) and intercepts ω 2 τ 2 τ 1 of the analytical straight line equations used to estimate τ 2 and τ 1 were derived from Bergmann's equation [U. Saha, S.K. Sit, R.C. Basak, S. Acharyya, J. Phys. D: Appl. Phys. 27 (1994) 596] based on two Debye type dispersion model of binary polar mixture. The systems 3-bromoaniline in C 6H 6 and 1-propanol in C 6H 6 show τ 2 and τ 1 only at 47 °C temperature like 3-bromoaniline + 1-propanol in C 6H 6 at 20 and 47 °C temperatures for 0.25 and 0.50 mole fractions x j 's of 1-propanol. The binary polar mixture for x j = 0.75 of 1-propanol is an exception exhibiting double relaxation times at all the experimental temperatures. The relative contributions c 1 and c 2 due to τ 1 and τ 2 for eight non-rigid systems were calculated from Fröhlich's equation as well as graphical plots of χ ′ i j k / χ 0 i j k − w j k and χ ″ i j k / χ 0 i j k − w j k curve at w j k → 0 . c 1 and c 2 are positive for Fröhlich's method whereas most of the c 2's are negative for graphical method. The dipole moments μ 2 and μ 1 for all the systems are calculated from slopes β of χ ′ i j k − w j k curve at w j k → 0 and compared with the measured μ’s due to τ’s from ratio of slopes of χ ″ i j k − w j k and χ ′ i j k − w j k curves at w j k → 0 as well as χ ″ i j k − χ ′ i j k linear curves and reported μ’s due to Higasi's most probable τ. The reported and measured τ’s and μ’s agree with the most probable τ 0 = τ 1 τ 2 and μ 1's of the eight system like τ 2's and μ 2's of the rest twelve systems. This indicates that double relaxation phenomena yield average τ and μ for binary polar mixture under GHz electric field. The associational behavior of the polar molecules are inferred from the theoretical dipole moments μ theo's in terms of bond angles and bond moments of the substituent polar groups to exhibit solute–solute or solute–solvent molecular association arising out of inductive, mesomeric and electromeric effects of polar groups in them. The associative natures are ascertained from convex or concave shape of τ jk or μ jk – x j curves and μ jk – T curves respectively under different state of molecular environment. The thermodynamic energy parameters are calculated from Eyring's rate theory to know the molecular dynamics of the systems in order to establish the fact that the binary polar mixture obeys the Debye–Smyth relaxation mechanism.

Thermodynamics of Activation Gating in Olfactory-Type Cyclic Nucleotide-Gated (CNGA2) Channels

Olfactory-type cyclic nucleotide-gated (CNG) ion channels open by the binding of cyclic nucleotides to a binding domain in the C-terminus. Employing the Eyring rate theory, we performed a thermodynamic analysis of the activation gating in homotetrameric CNGA2 channels. Lowering the temperature shifted the concentration-response relationship to lower concentrations, resulting in a decrease of both the enthalpy ΔH and entropy ΔS upon channel opening, suggesting that the order of an open CNGA2 channel plus its environment is higher than that of the closed channel. Activation time courses induced by cGMP concentration jumps were used to study thermodynamics of the transition state. The activation enthalpies ΔH‡ were positive at all cGMP concentrations. In contrast, the activation entropy ΔS‡ was positive at low cGMP concentrations and became then negative at increasing cGMP concentrations. The enthalpic and entropic parts of the activation energies approximately balance each other at all cGMP concentrations, leaving the free enthalpy of activation in the range between 19 and 21kcal/mol. We conclude that channel activation proceeds through different pathways at different cGMP concentrations. Compared to the unliganded channel, low cGMP concentrations generate a transitional state of lower order whereas high cGMP concentrations generate a transitional state of higher order.

Different Mechanisms of Free Fatty Acid Flip-Flop and Dissociation Revealed by Temperature and Molecular Species Dependence of Transport across Lipid Vesicles

The mechanism of free fatty acid (FFA) transport across membranes is a subject of intense investigation. We have demonstrated recently that flip-flop is the rate-limiting step for transport of oleic acid across phospholipid vesicles (Cupp, D., Kampf, J. P., and Kleinfeld, A. M. (2004) Biochemistry 43, 4473-4481). To better understand the nature of the flip-flop barrier, we measured the temperature dependence of a series of saturated and monounsaturated FFA. We determined the rate constants for flip-flop and dissociation for small (SUV), large (LUV), and giant (GUV) unilamellar vesicles composed of egg phosphatidylcholine. For all FFA and vesicle types, dissociation was faster than flip-flop, and for all FFA, flip-flop and dissociation were faster in SUV than in LUV or GUV. Rate constants for both flip-flop and dissociation decreased exponentially with increasing FFA size. However, only the flip-flop rate constants increased significantly with temperature; the barrier to flip-flop was virtually entirely due to an enthalpic activation free energy. The barrier to dissociation was primarily entropic. Analysis in terms of a simple free volume (V(f)) model revealed V(f) values for flip-flop that ranged between approximately 12 and 15 Angstroms(3), with larger values for SUV than for LUV or GUV. V(f) values increased with temperature, and this temperature dependence generated the enthalpic barrier to flip-flop. The barrier for dissociation and its size dependence primarily reflect the aqueous solubility of FFA. These are the first results to distinguish the energetics of flipflop and dissociation. This should lead to a better understanding of the mechanisms governing FFA transport across biological membranes.

Are rate constants constant?

Are rate constants constant?

Dielectric relaxation studies of dilute solutions of amides

The dielectric constants and dielectric losses of formamide, acetamide, N-methyl acetamide, acetanilide and N, N-dimethyl acetamide in dilute solutions of 1,4-dioxan/benzene have been measured at 308 K using 9.37 GHz, dielectric relaxation set up. The relaxation time for the over all rotation τ (1) and that for the group rotation τ (2) of (the molecules were determined using Higasi's method. The activation energies for the processes of dielectric relaxation and viscous flow were determined by using Eyring's rate theory. From relaxation time behaviour of amides in non-polar solvent, solute–solvent and solute–solute type of molecular association is proposed.

Ca2+ ions block and permeate serotonin 5-HT3 receptor channels in rat hippocampal interneurons.

The serotonin 5-HT(3) receptor native to rat hippocampal CA1 stratum radiatum interneurons is blocked by Ca(2+) ions in a dose- and voltage-dependent manner, which is reflected by a region of negative slope conductance in the I-V curve. The steep dependence on the extracellular Ca(2+) concentration suggests that the channel contains more than one binding site for Ca(2+). A three barrier-two site model, based on Eyring rate theory, was used to describe the I-V curves. When extra- and intracellular K(+) and Cs(+) were substituted with Na(+), the I-V curves were accurately fit by the model, unlike the I-V curves recorded under standard ionic conditions. This suggests that the K(+) and Cs(+) permeabilities are small compared with that of Na(+). The distribution of the energy barriers and binding sites for Ca(2+) and Na(+) showed that the binding sites are located at approximately the 13' and the -4' position in the ion channel. The model predicts that at large hyperpolarized membrane potentials (more negative than -120 mV), the fractional Ca(2+) current amounts to approximately 1% of the total ion current. However, at physiologically relevant membrane potentials, the fractional Ca(2+) current is smaller (<0.1%) and the relative Ca(2+) permeability (P(Ca)/P(Na)) is estimated to be 0.10 at -60 mV.

Effective diffusion coefficients of K + and Cl − ions in ion channel models

We have used molecular dynamics simulations, corresponding to a total simulation time of 11 ns, to investigate the effective short-time local diffusion coefficient of potassium and chloride ions in a series of model ion channels. These models, which include channels formed by the fungal peptide alamethicin, by a synthetic leucine–serine peptide, and by the pore-lining M2 helix bundle of the nicotinic acetylcholine receptor, have a range of different secondary structures, diameters and hydrophobicities. We find that the diffusion coefficients of both ions are appreciably reduced in the narrower channels, the extent of the reduction being similar for both the anionic and cationic species. This suggests that a difference in mobility cannot be the source of the ion selectivity exhibited by some of the channels (for example, the leucine–serine peptide). We find no evidence for a reduction in mobility of either ion in the nAChR model. These results are broadly in line with a previous similar study of Na + ions, and may be useful in Poisson–Nernst–Planck, Eyring rate theory or Brownian dynamics calculations of channel conductance.

Spermine and Arcaine Block and Permeate N-Methyl- d-Aspartate Receptor Channels

Polyamines such as spermine are thought to be endogenous regulators of NMDA ( N-methyl- d-aspartate)-type glutamate receptors. Polyamine block of NMDA receptors was studied in excised outside-out patches from rat hippocampal neurons and Xenopus oocytes expressing recombinant receptors. Extracellular spermine and arcaine reduced NMDA single-channel conductance in a voltage-dependent manner, with partial relief of block evident at large inside negative membrane potentials. Reducing extracellular Na + concentration increased the apparent affinities for spermine and arcaine, indicating strong interaction between spermine and permeant ions. Internal spermine also blocked NMDA channels in a voltage-dependent manner, with relief of block evident at large inside positive potentials. The Woodhull model of channel block by an impermeant ion adequately described the actions of external spermine from −60 to +60 mV, but failed for more negative potentials. Eyring rate theory for a permeable blocker with two barriers and one binding site adequately described the voltage-dependent block and relief from block by both external and internal spermine over the range of −120 to +60 mV. These findings indicate that polyamines block and permeate neuronal NMDA receptor channels from the extracellular and intracellular sides, although sensitivity to internal spermine is probably too low to be physiologically relevant.