Effect of gamma irradiation on the polymer electrolyte PEO-NH4ClO4

Irradiation affects the structures of materials at different scales, thus changing physical and chemical properties. We study here the effect of gamma irradiation at different doses on the polymer electrolyte PEO-NH₄ClO₄. Optical micrographs show cracks in the irradiated samples and impedance spectroscopy measurements indicate reduced ion-conductivity at room temperature but slight enhancement at higher temperature. At high frequencies, the real part of the admittance shows a power-law variation; the exponent, which is a measure of self-similarity of the structure, is reduced on irradiation. The overall results point to a more disordered structure at higher radiation doses.     

Probing microstructure of polymer electrolyte-salt complex through impedance spectroscopy

In study of polymer-salt complexes usually one is interested in the dc conductivity, which can be extracted from impedance spectroscopy. However, impedance spectroscopy yields a host of additional information, for example, frequency variation of the measured admittance or impedance, nature of the Cole-Cole plot and dielectric function. Proper analysis of this information reveals details of the microstructure and transport processes in the sample. This in turn, will lead to development of better solid electrolytes with tailor-made properties. The polymer electrolyte PEO-NH₄ClO₄ shows an interesting variation in its properties in two different regimes, (1) where salt concentration is below ∼ 19 wt.% and (2) above this concentration. In the present paper we suggest an equivalent circuit incorporating a constant phase element (CPE), which reproduces the complex admittance behavior at different salt fractions. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.     

Ionic conductance behaviour of plasticized polymer electrolytes containing different plasticizers

The effect of different plasticizers on the properties of PEO-NH₄F polymer electrolytes has been studied. Aprotic organic solvents like propylene carbonate (PC), ethylene carbonate (EC), γ-butyrolactone (γ-BL), dimethylacetamide (DMA), dimethylformamide (DMF), diethylcarbonate (DEC) and dimethylcarbonate (DMC) having different values of donor number, dielectric constant, viscosity etc. have been used as plasticizers in the present study. The addition of plasticizer has been found to modify the conductivity of polymer electrolytes by increasing the amorphous content as well as by dissociating the ion aggregates present in polymer electrolytes at higher salt concentrations. The conductivity enhancement with different plasticizers has been found to be closely related to the donor number of the plasticizer used rather than its dielectric constant. The increase in conductivity with the addition of plasticizer has further been found to be dependent upon the level of ion association present in the electrolytes. The variation of conductivity as a function of plasticizer concentration and temperature has also been studied and maximum conductivity of ∼ 10⁻³ S /cm at room temperature has been obtained. X-ray diffraction studies show an increase of amorphous content in polymer electrolytes with the addition of plasticizers.     

The melting phenomenon in random-walk model of DNA

The melting phenomenon in a double-stranded homopolypeptide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the two competing interactions of monomers inside the chains, we obtain a completely denatured state at finite temperature T _c .     

Solid polymer electrolytes in a poly(butadiene-acrylonitrile)–LiBr system

Poly(nitriles) are among the polymer matrices providing high salt solubility and, in some cases, superionic lithium conductivity at ambient temperatures observed in highly concentrated solvent-free polymer electrolytes. However, the properties of these electrolytes in which ionic aggregation prevails remain difficult to reproduce and predict, as current theories do not adequately model their attributes. The development of new concepts for ion transport in highly concentrated solid polymer electrolytes (SPEs) requires a better understanding of the fundamentals of structure formation in a polymer–salt system over a wide concentration range including salt precipitation. In an attempt to approach this goal, a series of fundamental studies was carried out on the systems based on a rubbery random copolymer of butadiene and acrylonitrile (abbreviated as PBAN). In the present work, LiBr with monatomic halide anion was used as a lithium salt. The effect of LiBr concentration (0.05 to 3.35 mol kg^?1) on phase composition, ion–molecular interactions, glass transition temperature, and ionic conductivity was studied by optical microscopy, FTIR, X-ray diffraction, DSC, and impedance measurements. The results were compared with those of PBAN–LiClO₄ and PBAN–LiAsF₆ studied previously. Low salt solubility and separation of a metastable cubic CsCl-type polymorph of LiBr were established. The highest conductivity of ～10^?4 S cm^?1 at >50 °C was observed for heterogeneous samples comprising this phase. While the conductivity of PBAN–LiBr was lower than that of PBAN–LiClO₄ and PBAN–LiAsF₆, this study provides a new insight into the nature of polymer electrolyte systems.     

From random to self-avoiding walks

A brief review will be given of the current situation in the theory of self-avoiding walks (SAWs). The Domb-Joyce model first introduced in 1972 consists of a random walk on a lattice in which eachN step configuration has a weighting factor Π _i=0 ^N?2 Π_j=i+2/N(1?ωδ_ij). Herei andj are the lattice sites occupied by the ith and jth points of the walk. When ω=0 the model reduces to a standard random walk, and when ω=1 it is a self-avoiding walk. The universality hypothesis of critical phenomena will be used to conjecture the behavior of the model as a function ofω for largeN. The implications for the theory of dilute polymer solutions will be indicated.     

Structural and thermal studies of PVA:NH4I

Proton-conducting polymer electrolytes based on poly vinyl alcohol (PVA; 88% hydrolyzed) and ammonium iodide (NH₄I) has been prepared by solution casting method with different molar ratios of polymer and salt using DMSO as solvent. DMSO has been chosen as a solvent due its high dielectric constant and also its plasticizing nature. The ionic conductivity has been found to increase with increasing salt concentration up to 25 mol% beyond which the conductivity decreases and the highest ambient temperature conductivity has been found to be 2.5×10⁻³ S cm⁻¹. The conductivity enhancement with addition of NH₄I has been well correlated with the increase in amorphous nature of the films confirmed from XRD and differential scanning calorimetry (DSC) analyses. The temperature-dependent conductivity follows the Arrhenius relation. The polymer-proton interactions have been analyzed by FTIR spectroscopy.     

AC impedance studies on proton-conducting PAN : NH4SCN polymer electrolytes

Solid polymer electrolytes based on polyacrylonitrile (PAN) doped with ammonium thiocyanate (NH₄SCN) in different molar ratios of polymer and salt have been prepared by solution-casting method using DMF as solvent. The increase in amorphous nature of the polymer electrolytes has been confirmed by XRD analysis. A shift in glass transition temperature (T _g) of the PAN?:?NH₄SCN electrolytes has been observed from the DSC thermograms which indicates the interaction between the polymer and the salt. From the AC impedance spectroscopic analysis, the ionic conductivity has been found to increase with increasing salt concentration up to 30 mol% of NH₄SCN beyond which the conductivity decreases and the highest ambient temperature conductivity has been found to be 5.79?×?10^?3 S cm^?1. The temperature-dependent conductivity of the polymer electrolyte follows an Arrhenius relationship which shows hopping of ions in the polymer matrix. The dielectric loss curves for the sample 70 mol% PAN?:?30 mol% NH₄SCN reveal the low-frequency β-relaxation peak pronounced at high temperature, and it may be caused by side group dipoles. The ionic transference number of polymer electrolyte has been estimated by Wagner’s polarization method, and the results reveal that the conductivity species are predominantly ions.     

Random walks on random lattices with traps

A critical examination is presented of the continuous time random walk (CTRW) approximation and of frequency-dependent effective transition rate methods for calculating the configurational average of the Laplace transform of the probabilityPs, t|₀) that a particle performing a random walk will be at site s timet after it reached the site s₀. Some exact results are derived for the form of P(s, t|s₀) at long times, and these indicate that the effective transition rate methods are the better approximation for systems with symmetric effective hopping rates, while the CTRW approximation is better for systems containing traps, i.e., states that are much easier to enter than to leave. The implications of these results for calculations of transient currents and of the ac conductivity for amorphous semiconductors are discussed.     

A.c. hopping conduction in Mn-Co-Ni-Cu complex oxide semiconductors with spinel structure

The radio-frequency (RF) conductivities of spinel-type Mn-Co-Ni-Cu complex oxide semiconductors were investigated at low temperatures for ceramic samples with various Cu contents. The a.c. conductivities show large frequency dependences, which are ascribed to hopping of localized carriers between Mn ions at oxygen octahedral sites. When the Cu content is increased, the conductivity increases markedly and its frequency dependence is weakened. The hopping is considered to be a random walk process because the hopping sites are randomly distributed at the spinel oxygen octahedral sites. In this situation, the random walk theory in disordered systems developed by Scher and Lax is applicable, and the experimental results agree with this theory very well. The reduced frequency dependence is also successfully explained in this way. The Cu ions in these complex oxides lead to an increase in the localized carrier transition probability, and consequently lead to an increase in conductivity and a reduction in the frequency dependence of the a.c. conductivity.     

Structural,electrical conductivity,and transport analysis of PAN–NH<Subscript>4</Subscript>Cl polymer electrolyte system

Poly (acrylonitrile) (PAN) and ammonium chloride (NH₄Cl)-based proton conducting polymer electrolytes with different compositions have been prepared by solution casting technique. The amorphous nature of the polymer electrolytes has been confirmed by XRD analysis. The FTIR analysis confirms the complex formation of the host polymer (PAN) with the salt (NH₄Cl). DSC measurements show a decrease in T_g with the increase in salt concentration. The conductivity analysis shows that the 25 mol% ammonium chloride doped polymer electrolyte has a maximum ionic conductivity, and it has been found to be 6.4 × 10^?3 Scm^?1, at room temperature. The temperature dependence of conductivity of the polymer electrolyte complexes appears to obey the Arrhenius nature. The activation energy (E_a = 0.23 eV) has been found to be low for 25 mol% salt doped polymer electrolyte. The dielectric behavior has been analyzed using dielectric permittivity (ε*), and the relaxation frequency (τ) has been calculated from the loss tangent spectra (tan δ). Using this maximum ionic conducting polymer electrolyte, the primary proton conducting battery with configuration Zn + ZnSO₄·7H₂O/75 PAN:25 NH₄Cl/PbO₂ + V₂O₅ has been fabricated and their discharge characteristics have been studied.     

Proton-conducting I-Carrageenan-based biopolymer electrolyte for fuel cell application

The essential part of electrochemical devices, such as fuel cells and batteries, is the polymer electrolyte with good mechanical, thermal, and chemical stability. The search for a new proton-conducting membrane with easy processability, non-toxic, and low-cost has been growing rapidly. The bio-based polymer electrolytes are now receiving much attention due to the green environment. Among the commercially available biopolymers, iota-Carrageenan (I-Carrageenan) is one of the biopolymer with good film-forming nature and with good mechanical stability. I-Carrageenan-based biopolymer membranes doped with ammonium bromide (NH₄Br) have been prepared using solution-casting technique, and distilled water is used as a solvent. The prepared I-Carrageenan-based biopolymer membranes have been characterized using FTIR, XRD, and AC impedance techniques. The complexation between the polymer and salt has been revealed by FTIR. The increase in the amorphous nature of the film due to the addition of salt has been confirmed by XRD. From AC impedance technique, the conductivity of pure I-Carrageenan has been found to be 1.46 × 10⁻⁵ S/cm. The addition of different wt% of NH₄Br increases the conductivity and reaches the highest value of 1.08 × 10⁻³ S/cm for 20% NH₄Br, and the conductivity decreases on further addition of NH₄Br due to the formation of ion aggregates.

     

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy’s law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials.     

Influence of extreme fluctuations of impurity relief on the evolution of kink solitons in doped materials

The dynamics of kink solitons is very sensitive to random irregularities of the potential relief. The evolution of kinks after their generation is essentially modified by strong fluctuations of the potential. The stochastic nature of such modification is taken into account by the theory of extreme deviations on a random walk.     

A simple model for diffuse reflection

Diffuse reflection from a matte nonabsorbing inhomogeneous medium such as white paint or paper can be described by a simple model in which light rays enter the volume of medium and then undergo a random walk until they reemerge from the surface. Lambert's law of diffuse reflection is an immediate consequence of the random walk. Another consequence of the volume interaction is that the light emerges from a different point than where it enters. This spreading of the light was measured for BaSO₄ white reflectance paint and for several kinds of paper. The random walk model implies a diffusion equation which makes predictions that are in reasonable agreement with the experiments. The spreading is proportional to an interaction length which, in this model, represents the range of distances that light rays penetrate before beginning their random walk.     

Conductivity and thermal studies of blend polymer electrolytes based on PVAc–PMMA

The polymer electrolytes comprising blend of poly(vinyl acetate) (PVAc) and poly(methylmethacrylate) (PMMA) as a host polymer and LiClO₄ as a dopant are prepared by solution casting technique. The amorphous nature of the polymer–salt complex has been confirmed by XRD analysis. The DSC thermograms show two T_g's for PVAc–PMMA blend. A decrease in T_g with the LiClO₄ content reveals the increase of segmental motion. Conductance spectra results are found to obey the Jonscher's power law and the maximum dc conductivity value is found to be 1.76 × 10^− 3 S cm^− 1 at 303 K for the blend polymer complex with 20 wt.% LiClO₄, which is suitable for the Li rechargeable batteries. The conductivity–temperature plots are found to follow an Arrhenius nature. The dc conductivity is found to increase with increase of salt concentration in the blend polymer complexes.     

Random Walks and Polymers in the Presence of Quenched Disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local transition rules, and on ‘polymer models’, where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points: thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures T _c(i,L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland–Scheraga model of DNA denaturation.Conference Proceedings “Mathematics and Physics”, I.H.E.S., France, November 2005     

Conductivity spectra and ion dynamics of a salt-in-polymer electrolyte

We present, for the first time, broadband conductivity spectra of a salt-in-polymer electrolyte, i.e., of 1 molal NaPF₆ dissolved into a crosslinked PEO-PPO random copolymer. The experimental frequency range spans nearly 12 decades, extending up to the far infrared. The temperature range is from 303 K to 363 K. The conductivity spectra show a remarkably gradual onset of the dispersion, which is reminiscent of ion conducting glasses and crystalline ion conductors, where ions hop via well-defined sites. On the other hand, the DC conductivity of the polymer electrolyte shows a non-Arrhenius temperature dependence, thus resembling dynamically coupled systems such as supercooled melts. Any approach to understanding these seemingly contradictory features must include ion–ion interactions and, hence, go beyond models based on free volume theory. Such an approach is provided by the MIGRATION concept (MIsmatch Generated Relaxation for the Accommodation and Transport of IONs). In this treatment, the non-Arrhenius DC conductivity is described by an equation which yields, e.g., the elementary hopping rate and the shape of the conductivity spectra at higher frequencies. The entire conductivity spectra with the vibrational component suitably removed is a superposition of two components—one due to ionic displacements resulting in translational motion, the other due to localized movements causing a Nearly Constant Loss (NCL) type behaviour.     

Diffusion with restrictions

A nonlinear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additional repulsive and attractive forces leading to a changed local mobility. The stationary and the time dependent behaviour of the system are studied based upon the master equation approach. Different to conventional diffusion it results in a time dependent bump the position of which increases with time described by an anomalous diffusion exponent. The fractal dimension of this random walk is exclusively determined by the space dimension. The applicability of the model to describe glasses is discussed.     

Structural, vibrational, thermal, and conductivity studies on proton-conducting polymer electrolyte based on poly (N-vinylpyrrolidone)

The proton-conducting polymer electrolytes based on poly (N-vinylpyrrolidone) (PVP), doped with ammonium chloride (NH₄Cl) in different molar ratios, have been prepared by solution-casting technique using distilled water as solvent. The increase in amorphous nature of the polymer electrolytes has been confirmed by XRD analysis. The FTIR analysis confirms the complex formation of the polymer with the salt. A shift in glass transition temperature (T _g) of the PVP/NH₄Cl electrolytes has been observed from the DSC thermograms which indicates the interaction between the polymer and the salt. From the AC impedance spectroscopic analysis, the ionic conductivity of 15?mol% NH₄Cl-doped PVP polymer complex has been found to be maximum of the order of 2.51?×?10^?5?Scm^?1 at room temperature. The dependence of T _g and conductivity upon salt concentration has been discussed. The linear variation of the proton conductivity of the polymer electrolytes with increasing temperature suggests the Arrhenius type thermally activated process. The activation energy calculated from the Arrhenius plot for all compositions of PVP doped with NH₄Cl has been found to vary from 0.49 to 0.92?eV. The dielectric loss curves for the sample 85?mol% PVP:15?mol% NH₄Cl reveal the low-frequency ?? relaxation peak pronounced at high temperature, and it may be caused by side group dipoles. The relaxation parameters of the electrolytes have been obtained by the study of Tan?? as a function of frequency.