Multi-excitation Entropy Research Articles

Entropy and Isokinetic Temperature in Fast Ion Transport.

Ion transport in crystalline solids is an essential process for many electrochemical energy converters such as solid-state batteries and fuel cells. Empirical data have shown that ion transport in crystal lattices obeys the Meyer-Neldel Rule (MNR). For similar, closely related materials, when the material properties are changed by doping or by strain, the measured ionic conductivities showing different activation energies intersect on the Arrhenius plot, at an isokinetic temperature. Therefore, the isokinetic temperature is a critical parameter for improving the ionic conductivity. However, a comprehensive understanding of the fundamental mechanism of MNR in ion transport is lacking. Here the physical significance and applicability of MNR is discussed, that is, of activation entropy-enthalpy compensation, in crystalline fast ionic conductors, and the methods for determining the isokinetic temperature. Lattice vibrations provide the excitation energy for the ions to overcome the activation barrier. The multi-excitation entropy model suggests that isokinetic temperature can be tuned by modulating the excitation phonon frequency. The relationship between isokinetic temperature and isokinetic prefactor can provide information concerning conductivity mechanisms. The need to effectively determine the isokinetic temperature for accelerating the design of new fast ionic conductors with high conductivity is highlighted.

Enthalpy-entropy compensation in the slow Arrhenius process.

The Meyer-Neldel compensation law, observed in a wide variety of chemical reactions and other thermally activated processes, provides a proportionality between the entropic and the enthalpic components of an energy barrier. By analyzing 31 different polymer systems, we show that such an intriguing behavior is encountered also in the slow Arrhenius process, a recently discovered microscopic relaxation mode, responsible for several equilibration mechanisms both in the liquid and the glassy state. We interpret this behavior in terms of the multiexcitation entropy model, indicating that overcoming large energy barriers can require a high number of low-energy local excitations, providing a multiphonon relaxation process.

The Basic Theorem of Temperature-Dependent Processes

The basic theorem of isokinetic relationships is formulated as “if there exists a linear correlation “structure∼properties” at two temperatures, the point of their intersection will be a common point for the same correlation at other temperatures, until the Arrhenius law is violated”. The theorem is valid in various regions of thermally activated processes, in which only one parameter changes. A detailed examination of the consequences of this theorem showed that it is easy to formulate a number of empirical regularities known as the “kinetic compensation effect”, the well-known formula of the Meyer–Neldel rule, or the so-called concept of “multi-excitation entropy”. In a series of similar processes, we examined the effect of different variable parameters of the process on the free energy of activation, and we discuss possible applications.

Charge Carrier Transport in a Polymeric Semiconductor: Poly(3-hexylthiophene-2,5-diyl) (P3HT)

Organic semiconductors are now widely employed in electronic and optoelectronic devices due to their solution processability and compatibility with flexible substrates. 1 The Meyer Neldel (MN) Rule or isokinetic (IK) law means that a set of comparable samples exhibit kinetic behavior independent of activation energy at an IK or MN temperature.2 It is obeyed by the electron or hole mobility, µ, in many organic semiconductors, including pentacene3, fullerene4, N-Alkyl Perylene Diimides,5 etc. The existence of MNR is still not widely known. Further, despite considerable evidence in its favor, the multi-excitation entropy (MEE) model of its origin is still frequently contested. We fabricated organic field effect transistors (FETs) based on regioregular poly(3-hexylthiophene-2,5-diyl) (RR P3HT) of three different values of molecular weight, MW, and studied the dependence of the mobility, µ, upon the gate bias, Vg , and temperature, T. For all values of MW, we found that in the range 200 to 290 K (low T), the µ of the FET carriers exhibits an exponential dependence upon 1/T for different Vg , with an MN temperature about 290K. Between this temperature and 350K (high T), µ increases more rapidly than it did below, and is independent of Vg . We believe that, in the low T regime, the polaronic carriers hop along the polymer backbone chain. We attribute the high temperature behavior to the alpha relaxation of the polymers, that is to the movement of the backbone chains. We believe that in this regime, the polaronic carriers move with the mobile chains. We have also observed the effect of source-drain voltage upon µ.Reference 1. F. Cicoira and C. Santato, Organic Electronics: Emerging Concepts and Technology, Wiley-VCH Verlag GmbH & Co. KGaA, 2013, Germany.2. A. Yelon, et al., Multi-excitation entropy: its role in thermodynamics and kinetics, Rep. Prog. Phys., 69, 1145-1194, 2006.3. E. J. Meijer, et al., The Meyer–Neldel rule in organic thin-film transistors, Appl. Phys. Lett., 76, 3433, 2000.4. J. C. Wang and Y. F. Chen, The Meyer–Neldel rule in fullerenes, Appl. Phys. Lett., 73, 948 1998.5. R. J. Chesterfield, et al., Organic Thin Film Transistors Based on N-Alkyl Perylene Diimides: Charge Transport Kinetics as a Function of Gate Voltage and Temperature, J. Phys. Chem. B, 108, 19281-19292, 2004.

Meyer-Neldel rule in the conductivity of phase separated manganites

Abstract Meyer-Neldel behaviour of the conductivity of phase separated La1−xCaxMnO3 manganite system in the low Ca-doping range has been investigated. Evolution of the isokinetic temperature of the conductivity, modified by Ca-doping, hydrostatic pressure and current bias has been determined. In addition, the evolution of the isokinetic temperature with ageing has also been studied. It is found that the Meyer-Neldel behaviour of the manganite system stems from multi-excitation entropy mechanism. The isokinetic temperatures estimated from pressure and doping effects coincide but differ from those determined using current and ageing controlled conductivity changes. It is concluded that in the presence of a detailed theoretical model of the excitations coupling in manganites, the investigations of the Meyer-Neldel effect may became a powerful tool for characterization and investigation of transport mechanisms in phase separated manganites.

Meyer-Neldel rule in the conductivity of manganite single crystals

The Meyer-Neldel behavior of conductivity of low-doped manganite ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{\mathit{x}}{\mathrm{MnO}}_{3}$ single crystals has been investigated. The evolution of the isokinetic temperature of conductivity, modified by Ca-doping, hydrostatic pressure, and current bias has been determined. In addition, the evolution of isokinetic temperature with ageing has also been studied. The Meyer-Neldel behavior of the manganite system stems from the multiexcitation entropy mechanism. The isokinetic temperature turned out to be a sensitive parameter characterizing changes in the transport properties of mixed valence manganites, which in the presence of a detailed theoretical model of the excitations coupling in manganites could become a powerful tool for the characterization and investigation of transport properties of manganites.

Incorporation of Si during vapor phase epitaxy of III-V compounds: Evidence of an enthalpy-entropy compensation effect

The incorporation of dopants in III-V compound semiconductor epilayers during chemical vapor deposition involves complex homogeneous and surface reaction kinetics and is expected to be an activated process. In particular, silicon is an element of choice for n-type doping of various III-V compound epilayers for which there is a wealth of data involving different growth and doping precursors. Kinetic arguments such as the role of multi-excitation entropy or quasi-equilibration at the growth interface during incorporation predict an enthalpy-entropy compensation effect (EECE), which is observed from compiled data for more than 14 orders of magnitude of the prefactor describing the activated incorporation rate. For this particular observation of the EECE, an explanation involving data pre-selection imposed by restrictive growth conditions may also be invoked.

Lithium Conductivity and Meyer-Neldel Rule in Li3PO4–Li3VO4–Li4GeO4 Lithium Superionic Conductors

The ionic conductivity and activation energy of lithium in the Li3PO4–Li3VO4–Li4GeO4 system was systematically investigated. The sharp decrease in activation energy upon Ge substitution in Li3PO4 and Li3VO4 was attributed to the reduction in the defect formation energy while the variation in activation energy upon increasing Ge content was rationalized in term of the inductive effect. We also found a correlation between the pre-exponential factors and the activation energies in agreement with the well-known Meyer-Neldel rule. The series of compound with and without partial lithium occupancy were shown to fall into two distinct lines. The slope of the line was found to be related to the inverse of the energy scale associated with phonons in the system, which agrees with the multiexcitation entropy theory. The intercept of the line was found to be related to the Gibbs free energy of defect formation. Compiled data of pre-exponential factor and activation energy for commonly studied lithium-ion conductors sh...

High and low activation energy kinetics are different: Implications for hydrogen and protons in condensed matter

ABSTRACTAt high activation energy, kinetic processes require the accumulation of several excitations in order to take place. This accumulation implies an entropy, which we call multi-excitation entropy. This explains the isokinetic rule, which itself explains the existence of isoequilibrium relations. Understanding the implications of these effects helps clarify the microscopic mechanisms in kinetic processes, including hydrogen storage, and transport of protons, and potentially, of other ions, in condensed matter.

Dielectric relaxation properties of carboxylic acid-terminated n-alkyl monolayers tethered to Si(1 1 1): dynamics of dipoles and gauche defects

Molecular-level insights into the organization and dynamics of n-alkyl monolayers covalently bonded to Si(1 1 1) were gained from admittance measurements of dipolar relaxation in rectifying Hg HOOC-C10H25–n Si junctions performed as a function of applied voltage and temperature. A collective behavior of dipole dynamics is inferred from the non-Debye asymmetric relaxation peak shape and strong coupling of the dipole relaxation path with some bending vibrations of the n-alkyl OML (multi-excitation entropy model). A variety of relaxation mechanisms is observed in the frequency range (0.1 Hz–10 MHz) with different dependence of relaxation frequency and dipolar strength on measurement temperature and applied voltage. Their microscopic origin is discussed by comparing the activation energy of relaxation frequency with previous molecular mechanics calculations of saddle point energy barriers for structural defects such as gauche conformations or chain kinks in n-alkanes assemblies. Gauche conformations organized in pairs (kinks) have vanishing relaxation strength below an order–disorder transition temperature TD = 175 K and their probability strongly increases with applied reverse voltage, above TD. The presence of hydrogen bonds between terminal carboxylic acid functionalities is inferred from a comparison with a similar junction bearing a low density of carboxylic acid end groups. This temperature-dependent hydrogen-bond network provides some additional stiffness against external electrostatic stress, as deduced from the rather weak sensitivity of relaxation frequencies to applied bias voltage.

Entropy effects in the collective dynamic behavior of alkyl monolayers tethered to Si(111).

Dynamic properties of n-alkyl monolayers covalently bonded to Si(111) were studied by broadband admittance spectroscopy as a function of the temperature and the applied voltage using rectifying Hg/C12H25/n-type Si junctions. Partial substitution of methyl end groups by polar (carboxylic acid) moieties was used to enhance the chain end relaxation response. Two thermally activated dissipation mechanisms (B1 and B2, with fB1 < fB2) are evidenced for all reverse bias values. The strong decrease of both relaxation frequencies with increasing reverse dc bias reveals increasing motional constraints, attributed to electrostatic pressure applied to the densely-packed nanometer-thick monolayer. Spectral decomposition of the frequency response shows a power-law dependence of their activation energies on |VDC|. A large reverse bias reversibly increases the B2 response attributed to the distribution of gauche defects, in contrast with the constant strength of the acid dipole loss (B1). A trans–gauche isomerization energy of 50 meV is derived from the temperature dependence of the B2 dipolar strength. For both dissipation mechanisms, the observed linear correlation between activation energy and logarithm of pre-exponential factor is consistent with a multi-excitation entropy model, in which the molecular reorientation path is strongly coupled with a large number of low energy excitations (here the n-alkyl bending vibrational mode) collected from the thermal bath. This collective dynamic behavior of alkyl chains tethered to Si is also confirmed by the asymmetric relaxation peak shape related to many-body interactions in complex systems.

Meyer Neldel rule application to silicon supersaturated with transition metals

This paper presents the results for the transverse conductance across a bilayer formed by supersaturating with diverse transition metals a thin layer of a silicon wafer. The layer is formed by ion implantation and annealed by pulsed laser melting. The transverse conductance is exponentially activated, obtaining values ranging from 0.018 to 0.7 eV for the activation energy and pre-exponential factors of 10−2–1012 S depending on the annealing energy density. A semi-logarithmic plot of the pre-exponential factor versus activation energy shows an almost perfect linear behaviour as stated by the Meyer Neldel rule. The Meyer Neldel energy obtained for implantation with different transition metals and also annealed in different conditions is 22 meV, which is within the range of silicon phonons, thus confirming the hypothesis of the multi excitation entropy theory.

Origin of Meyer-Neldel type compensation behavior in organic semiconductors at large carrier concentrations: Disorder versus thermodynamic description

We have extended an effective medium approximation theory [Fishchuk, Kadashchuk, Genoe, Ullah, Sitter, Singh, Sariciftci, and B\assler, Phys. Rev. B 81, 045202 (2010)] to investigate how polaron formation affects the Meyer-Neldel (MN) compensation behavior observed for temperature-dependent charge-carrier transport in disordered organic semiconductors at large carrier concentrations, as realized in organic field-effect transistors (OFETs). We show that the compensation behavior in organic semiconductor thin films can be consistently described for both nonpolaronic and polaronic hopping transport in the framework of the disorder formalism using either Miller-Abrahams or polaron Marcus rates, respectively, provided that the polaron binding energy is small compared to the width of the density of states (DOS) distribution in the system. We argue that alternative models based on thermodynamic reasoning, like the multiexcitation entropy (MEE) model, which assumes charge transport dominated by polarons with multiphonon processes and ignores the energy disorder, are inherently not applicable to describe adequately the charge-carrier transport in disordered organic semiconductors. We have suggested and realized a test experiment based on measurements of the compensation behavior for the temperature-dependent conductivity and mobility in OFET devices to check the applicability of these models. We point out that the MN behavior observed in thin-film OFETs has nothing to do with the genuine MN rule predicted by the MEE approach, but rather it is an apparent effect arising as a consequence of the functional dependence of the partial filling of the DOS in a disordered system with hopping transport. This fact is fully supported by experimental results. The apparent MN energy was found to depend also on the shape of the DOS distribution and polaron binding energy.

Meyer-Neldel Rule in Plasma Polythiophene Thin Films

In polymers, the electronic activation energy depends on the fragmentation, crosslinking, dopants, moisture and in general on the structure-environment interaction. This has a special importance in plasma polymers because fragmentation and crosslinking are usually higher than in other polymers. In this work, DC electrical conductivity of polythiophene thin films prepared by plasma (pPTh) was studied using the Meyer-Neldel (MN) rule to calculate the characteristic MN energy and temperature as a function of moisture and metallic dopants. The experimental data for pPTh synthesized in different conditions indicated that EM = 32 meV and TM = 373 K, suggesting a thermally activated conduction mechanism; however, in polymer-metal matrices with metal concentration higher than the percolation threshold, the conduction mechanism is different causing that the MN rule was only partially fulfilled. The congruence of the experimental data with the multiexcitation entropy model is discussed.

Meyer-Neldel rule and Poole-Frenkel effect in chalcogenide glasses

A theoretical model for dc conductivity under high electric field in chalcogenide glasses is developed. This model, of correlated barrier hopping is used to treat both low field conductivity, which obeys Meyer-Neldel rule (MNR), and high field Poole-Frenkel (PF) effect. Both are incorporated in one model because the origin of electronic emission is the same: a deep well in which a polaron is trapped. We show that the characteristic temperatures associated with MNR and PF should be the same, as has been predicted using a rigorous adiabatic polaron hopping model, and previously demonstrated experimentally for fullerene films. We also predict that the extrapolated conductivity prefactors will be the same in the two cases. Experimental evidence from the literature suggests, but does not demonstrate conclusively, that the two predictions are satisfied for chalcogenide glasses. Finally, we interpret the result in terms of the multi-excitation entropy model for MNR.

Entropy–enthalpy compensation of biomolecular systems in aqueous phase: a dry perspective

We survey thermodynamic measurements on processes involving biological macromolecules in aqueous solution, which illustrate well the ubiquitous phenomenon of entropy-enthalpy compensation. The processes include protein folding/unfolding and ligand binding/unbinding, with compensation temperatures varying by about 50 K around an average near 293 K. We show that incorporating both near-exact entropy-enthalpy compensation (due to solvent relaxation) and multi-excitation entropy (from vibrational quanta) leads to a compensation temperature in water of about 230 K. We illustrate a general procedure for subtracting solvent and environment-related terms to determine the bare Gibbs free energy changes of chemical processes.

The compensation law in dielectric polymer relaxations

The compensation law in polymer relaxations is briefly reviewed along with some transition state theories often used in that context. Some experimental data illustrating the compensation law in some polymers are shown. A modified Kramers equation is proposed to explain the compensation law and it is shown that the compensation temperature corresponds to the limits of two different friction regimes in one given relaxation. The possible relation with multi-excitation entropy theory is also discussed.

Multi-Excitation Entropy, Entropy–Enthalpy Relations, and their Impact on Catalysis

Catalyzed reactions involve large activation enthalpies, requiring a fluctuation in which many excitations, in the form of infrared vibrations or phonons, are needed to surmount the activation barrier. It was previously shown that this results in a multiexcitation entropy (MEE) term in the free energy of activation. For a series of related reactions, this leads to an isokinetic rule. We show here that this almost always implies that the series will also obey an isoequilibrium relation. This provides a necessary and sufficient condition for the Hammett substituent constant equation to be obeyed. Finally, we discuss the importance of MEE in catalysis. This has not generally been recognized.

Electron emission from deep traps in hydrogenated amorphous silicon and silicon-germanium: Meyer-Neldel behavior and ionization entropy

ABSTRACTWe have measured electron drift in amorphous silicon-germanium nip photodiodes using the photocarrier time-of-flight technique. The samples show electron deep-trapping shortly after photogeneration, which is generally attributed to capture by a neutral dangling bond (D0) to form a negatively charged center (D-). An unusual feature is that electron re-emission from the trap is also clearly seen in the transients. Temperature-dependent measurements on the emission yield an activation energy of about 0.8 eV and the remarkably large value of 1015 Hz for the emission prefactor frequency. We also compiled results on electron emission from deep traps in a-Si:H, a-SiGe:H, and a-SiC:H from six previous publications. Collectively, these measurements exhibit "Meyer Neldel" behavior for electron emission over a range of activation energies from 0.2–0.8 eV and a prefactor range extending over nine decades, from 106 to 1015 Hz. The Meyer-Neldel behavior is consistent with the predictions of the multi-excitation entropy model. We extract a ionization entropy of 20kB from the measurements, which is very large compared to crystal silicon. We discuss this result in terms of a bond charge model.

Interpretation and consequences of Meyer–Neldel rule for conductivity of phase change alloys

AbstractMeasurements of conductivity as a function of temperature were performed on a large number of memory cells of a GeSbTe phase change memory alloy, in both the set and reset states. Conductivity obeys the Meyer–Neldel rule in both states, with the same Meyer–Neldel, or isokinetic, temperature, but with conductivity prefactors about six orders of magnitude larger in the set than in the reset state. These observations are interpreted in terms of the multiexcitation entropy model, and conduction mechanisms are suggested. Their effect on the expected behavior of memories is considered.