One-dimensional Hopping Model Research Articles

Effect of heparin calcium different concentrations on some physical properties and structure in polyacrylamide matrix

Films of polyacrylamide (PAAm) doped with different concentrations of heparin calcium, from 0.0 to 8 wt%, have been prepared by casting method. Studies were carried out utilizing X-ray, FT-IR, UV/VIS, DSC and DC electrical conduction to characterize the structural, optical and thermal properties of the films. Results revealed that the structural and chemical characterizations of PAAm films are affected by the addition of heparin calcium content. XRD spectra revealed that the amorphous phases increase with increase in filling levels of heparin (FLs). FT-IR analysis revealed that incorporation of heparin calcium leads to a small modification in the spectra of films. The optical absorption spectra in the UV/VIS region revealed structural variation increases with increase in concentration, which is reflected in the form of decrease in the energy band gap E g . Significant changes of DSC curves of the films suggest that strong interaction established between heparin calcium and PAAm molecules. The DC electric conduction data were interpreted on the basis of an intrachain one-dimensional interpolaron hopping model of Kuivalainen.

The role of intrinsic muscle properties for stable hopping—stability is achieved by the force–velocity relation

A reductionist approach was presented to investigate which level of detail of the physiological muscle is required for stable locomotion. Periodic movements of a simplified one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements) were analyzed. Force–length and force–velocity relations of the muscle were varied in three levels of approximation (constant, linear and Hill-shaped nonlinear) resulting in nine different hopping models of different complexity. Stability of these models was evaluated by return map analysis and the performance by the maximum hopping height. The simplest model (constant force–length and constant force–velocity relations) outperformed all others in the maximum hopping height but was unstable. Stable hopping was achieved with linear and Hill-shaped nonlinear characteristic of the force–velocity relation. The characteristics of the force–length relation marginally influenced hopping stability. The results of this approach indicate that the intrinsic properties of the contractile element are responsible for stabilization of periodic movements. This connotes that (a) complex movements like legged locomotion could benefit from stabilizing effects of muscle properties, and (b) technical systems could benefit from the emerging stability when implementing biological characteristics into artificial muscles.

Structure, DC and AC conductivity of oxazine thin films prepared by thermal evaporation technique

Thin films of oxazine (OXZ) were prepared using thermal evaporation technique under high vacuum. The thermogravimetric analysis (TGA/DSC) was investigated. Thin films of nano-crystalline OXZ were identified by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD). Temperature dependence of the DC electrical conductivity was investigated in the temperature range 300–425 K. Measurements revealed that the DC behavior of the films can be described by Mott's one-dimensional variable range hopping (VRH) model in the entire temperature range. The AC conductivity of the sample is found to be proportional to ω s . The temperature dependence of the AC conductivity and the frequency exponent, s is reasonably well interpreted in terms of the correlated barrier-hopping CBH model. Frequency dependence of the capacitance in the frequency range 42 Hz–5 MHz indicates that the capacitance is strongly frequency dependent. The capacitance was determined to decrease with increasing frequency at low frequency and less rapidly at higher frequencies. This is quantitatively interpreted using an equivalent circuit model.

Duality Symmetries in Driven One-Dimensional Hopping Models

We consider some duality relations for models of non-interacting particles hopping on disordered one-dimensional chains. In particular, we discuss symmetries of bulk-driven barrier and trap models, and relations between boundary-driven and equilibrium models with related energy landscapes. We discuss the relationships between these duality relations and similar results for interacting many-body systems.

Duality symmetries and effective dynamics in disordered hopping models

We identify a duality transformation in one-dimensional hopping models that relatespropagators in general disordered potentials linked by an up–down inversion of the energylandscape. This significantly generalizes previous results on a duality between trapand barrier models. We use the resulting insights into the symmetries of thesemodels to develop a real-space renormalization scheme that can be implementedcomputationally and allows rather accurate prediction of propagation in these models.We also discuss the relation of this renormalization scheme to earlier analyticaltreatments.

Some studies on calcium phosphate embedded in polyvinyl alcohol matrix before and after γ-irradiation

Abstract The Ca–P ratio in polymer matrix was adjusted to 1.67 as in hydroxyapatite. The complexed polyvinyl alcohol (PVA) materials exhibit the characteristic absorption bands of phosphate at 601 and 962 cm –1 indicating the presence of (HPO 4 ) −1 anions in the structure. The X-ray diffraction (XRD) revealed that the reaction between Ca and P ions in the PVA medium has a great effect on polymeric matrix crystallization. After irradiation, XRD results for sample c showed more sharp peaks indicating that irradiation can break the principal chemical bonds and favoring additional crystallization processes and therefore the crystallinity increases. An improvement in the thermal stability of PVA doped with calcium phosphate could be seen with the increase of calcium phosphate intercalated with PVA. The surfaces of films were analyzed by scanning electron microscope (SEM) before and after γ-irradiation. The formation of hydroxyapatite is confirmed by energy dispersive X-ray spectroscopy (EDX analysis). The electric conduction data were interpreted on the basis of an intrachain one-dimensional interpolaron hopping model of Kuivalainen.

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity V N and effective diffusion coefficient D N of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient D eff of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient D eff from the moments of the particle's coordinate.

Effect of molybdenum trioxide (MoO3) on the electrical conductivity of polyaniline

In situ polymerization of aniline was carried out in the presence of molybdenum trioxide to synthesize polyaniline/molybdenum trioxide composites (PANI/MoO3) by chemical oxidation method. The composites have been synthesized with various compositions (10, 20, 30, 40 and 50 wt%) of MoO3 in PANI. The surface morphology of these composites was studied with scanning electron micrograph (SEM). The PANI/MoO3 composites were also characterized by X-ray diffractometry (XRD) and infrared spectroscopy (FTIR). The ac conductivity behaviour has been investigated in the frequency range 102–106 Hz. The dc conductivity has been studied in the temperature range from 40 °C to 200 °C and supports the one-dimensional variable range hopping (1D-VRH) model proposed by Mott. The presence of MoO3 in the matrix has a greater influence on the observed conductivity values than that of PANI. The results obtained for these composites are of scientific and technological interest.

Field-dependent ion transport in disordered solid electrolytes

We have carried out experimental and theoretical studies of the electric field-dependent ion transport in disordered materials and in disordered potential landscapes, respectively. In our experiments, we work in an electric field range up to 100 kV cm(-1), which is characterised by a weak nonlinear response of the mobile ions. We detect remarkable differences between different ion-conducting glasses regarding the temperature dependence of the nonlinear response. Theoretically, we study one-dimensional hopping models and continuous disordered potential models, respectively. When comparing theoretical and experimental data, we find both analogies and discrepancies.

Synthesis, characterization and conductivity measurements of polyaniline and polyaniline/fly‐ash composites

AbstractPolyaniline (PANI) and polyaniline/fly ash (PANI/FA) composites with various concentrations of fly ash (20%, 40% and 50%) were synthesized by the process of in‐situ polymerization. The samples were characterized by powder X‐ray diffraction, thermogravimetric analysis, infrared spectroscopy, and scanning electron microscopy. Moreover, the dc conductivity of the samples was measured as a function of temperature in the range 80–290 K and it was found that the addition of FA decreases the conductivity. The temperature dependence of the dc conductivity for PANI and FA/PANI composites has been explained on the basis of the quasi one‐dimensional variable hopping model. A very good agreement was found between the experimental data and the theory. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of dopant mixture on structural, optical and electron spin resonance properties of polyvinyl alcohol

Pure polyvinyl alcohol (PVA) and PVA/( x)AgNO 3(15− x)MnCl 2 films, where x = 0.0 % , 1%, 5%, 7.5%, 10%, 14% and 15%, were prepared by casting technique. The prepared films were studied by differential thermal analysis, X-ray diffraction (XRD), spectral (UV–Vis–IR spectroscopy), DC conductivity and electron spin resonance (ESR). Thermal stability of the prepared films was decreased for doped films. XRD and spectral studies revealed that the structural and chemical characterizations of PVA are strongly affected by mixed fillers. The electric conduction data were interpreted on the basis of an intrachain one-dimensional interpolaron hopping model. The calculated values of the charge carriers hopping distance were in the range 2–6 nm. ESR spectra revealed that (i) aggregated forms of Mn 2+ ions were formed at higher concentration and isolated forms at lower concentration and (ii) silver clusters were formed at x = 15 wt % . The filling level dependence of ESR parameters was discussed.

Conjugated Chromophore Arrays with Unusually Large Hole Polaron Delocalization Lengths

We report variable temperature X-band EPR spectroscopic data for the cation radical states of meso-to-meso ethyne-bridged (porphinato)zinc(II) (PZnn) oligomers. These [PZn2-PZn7]+ species span an average 18-75 A length scale and display peak-to-peak EPR line widths (DeltaBp-p) that diminish with conjugation length. Analysis of these EPR data show that PZnn+ structures possess the largest hole polaron delocalization lengths yet measured; experiments carried out over a 4-298 K temperature domain demonstrate remarkably that the charge delocalization length remains invariant with temperature. These cation radical EPR data are well described by a stochastic, near barrierless, one-dimensional charge hopping model developed by Norris for N equivalent sites on a polymer chain, where the theoretical EPR line width is given by DeltaBp-p(N-mer) = (1/N1/2)DeltaBp-p(monomer); PZnn+ oligomers are the first such systems to verify a Norris-type hole delocalization mechanism over a substantial ( approximately 75 A) length scale. Given the time scale of the EPR measurement, these data show that either (i) Franck-Condon effects are incapable of driving charge localization in [PZn2-PZn7]+, resulting in cation radical wave functions which are globally delocalized over a spatial domain that is large with respect to established benchmarks for hole-doped conjugated materials, or (ii) polaron hopping rates in these oligomers exceed 107 s-1, even at 4 K. Finally, this study demonstrates that polymeric building blocks having low magnitude inner sphere reorganization energies enable the development of electronic materials having long polaron delocalization lengths.

Conductivity measurements of PEDOT nanowires on nanoelectrodes

We have prepared very thin, conducting polymer nanowires of poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS) with diameters under 5 nm on a thermally grown SiO 2/Si substrate by a molecular combing method. We have measured the conductivity of the nanowires using nanoelectrodes. Ohmic behavior of the PEDOT nanowires was obtained when applied voltages were smaller than 100 mV. The conductance of the nanowires decreased with decreasing temperature and the temperature dependence of the conductance was explained by the quasi one-dimensional variable range hopping (VRH) model. After all the nanowires placed on the gap of the nanoelectrodes were cut, the current was drastically decreased, down to the background level. We have thus provided direct evidence that the PEDOT nanowires were responsible for conduction between the nanoelectrodes.

From discrete hopping to continuum modeling on vicinal surfaces with applications to Si(001) electromigration

Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the diffusion of adatoms on terraces with boundary conditions at sharp steps, as first studied by Burton, Cabrera, and Frank (BCF). Recent electromigration experiments on vicinal Si surfaces suggest the need for more general boundary conditions in a BCF approach. We study a discrete one-dimensional hopping model that takes into account asymmetry in the hopping rates in the region around a step and the finite probability of incorporation into the solid at the step site. By expanding the continuous concentration field in a Taylor series evaluated at discrete sites near the step, we relate the kinetic coefficients and permeability rate in general sharp step models to the physically suggestive parameters of the hopping models. In particular we find that both the kinetic coefficients and permeability rate can be negative when diffusion is faster near the step than on terraces. These ideas are used to provide an understanding of recent electromigration experiment on Si(001) surfaces where step bunching is induced by an electric field directed at various angles to the steps.

Effect of equal amounts of Mn and Co dopant addition on the structural, electrical and magnetic properties of PVDF films

Pure and doped poly(vinylidene fluoride) (PVDF) films were prepared by casting. Films with various concentrations of equal amounts of two fillers (MnCl 2 and CoCl 2) were prepared. The microstructure and physical properties of these films were studied by X-ray diffraction (XRD), infrared (IR), optical absorption, direct current (DC) electric conduction, DC magnetic susceptibility and electron spin resonance (ESR). The XRD scans evidenced a semicrystalline structure containing α- and/or β-PVDF phases. IR spectra confirmed these findings and revealed some structural defects such as mono-fluorinated alkenes and head-to-head segments. The optical absorption spectra suggested the presence of: (a) an optical gap ( E g) which depends on filler concentration ( W) and (b) tetrahedral Co 2+ coordination for all the filling levels (FLs). The electric conduction data were interpreted on the basis of an intrachain one-dimensional interpolaron hopping model and the calculated charge hopping distance was in the range of 3.0–4.4 nm. The temperature dependence of the DC magnetic susceptibility exhibited Curie–Wiess behaviour with positive values of the paramagnetic Curie temperature ( θ P) for W⩽6 wt% and negative θ P for W>6. The ESR analysis revealed the existence of: (a) both isolated and aggregated Mn 2+ and/or Co 2+ ions within the PVDF matrix and (b) octahedral Co 2+ and/or divalent state of Mn 2+, which confirmed the optical absorption implications. The present films could be used for optical and magnetic sensors.

Synthesis and electrical properties of freestanding film of azobenzene side-chain polyaniline

We report on the electrical properties of a conducting polyaniline (PANI) derivative film containing azobenzene side chain. The freestanding thin film of HCl-doped PANI derivative was synthesized through an N-alkyl-substituted reaction. We found that the side of the film irradiated by a weak ultraviolet light during the preparation is a poor conductor at room temperature and shows abnormal V–I characteristics. Its resistance decreases sharply with increasing temperature. However, the other side of the film without irradiation is highly conductive. The room-temperature conductivity is about 1.2 S/cm, which is much higher than that of other N-alkyl-substituted polyanilines (10−2–10−7 S/cm). The temperature dependence of resistance follows one-dimensional variable-range hopping model.

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps**The project supported by National Natural Science Foundation of China (10075007), Hebei Provincial Natural Science Foundation (102001), and the Doctoral Fund of Hebei Province (00547001D)

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps between arbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probability distribution as a function of the time and position for any initial distribution with all the transients included. Next, the transient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecular motor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kinetic behaviors of a molecular motor under external load F.

Physical characterization of polyaniline-Na +-montmorillonite nanocomposite intercalated by emulsion polymerization

We report the results of temperature dependence of dc conductivity ( σ dc( T)), X-ray photoelectron spectroscopy (XPS), electron paramagnetic resonance (EPR), and X-ray diffraction (XRD) experiments for dodecylbenzenesulfonic acid (DBSA) doped polyaniline (PAN)-Na +-montmorillonite (MMT) nanocomposite. The PAN-Na +-MMT nanocomposite was synthesized by intercalating the emulsion of aniline monomer with zylene and DBSA in the layer of Na +-MMT with distilled water and then initiating the polymerization of aniline inside the layer of Na +-MMT. From the results of X-ray diffraction experiments, we observe the insertion of PAN-DBSA between the interlayer of the Na +-MMT, whose separation consequently becomes larger (1.52 nm) than in a polymer-free clay (0.96 nm). The σ dc of the systems is ∼10 −1 S/cm at room temperature, and its temperature dependence follows a quasi one-dimensional variable range hopping (VRH) model. The slope of σ dc is ∼7.0×10 3 K. From the result of XPS experiment, we obtain the doping level of the system quantitatively. We measure temperature dependence of EPR linewidths. Base on those results, we discuss the effect of the layer of montmorillonite on PAN-DBSA samples.

A Simplified “Ratchet” Model of Molecular Motors

A limiting case of one of the ratchet models of Ajdari, Prost, et al. is analyzed. An explicit solution is obtained for the probability distribution as a function of the time for any initial distribution with all the transients included. In the long-time limit the drift velocity and diffusion coefficient are obtained in terms of the microscopic transition rates that are the parameters in the model. In spite of its extreme simplicity, with realistic values of its kinetic parameters the model yields values of the drift velocity and effective force that are of the right magnitude for a molecular motor. The model proves to be a simple special case of Derrida's periodic one-dimensional hopping model, for which he found a solution in the long-time limit.

Electronic energy transfer in the charge-transfer crystal of 2,3-dimethylnaphthalene-tetracyanobenzene

Optical, spectroscopic and kinetic studies of mixed-stack charge-transfer crystals of 2,3-dimethylnaphthalene with tetracyanobenzene (DMN-TCNB), undoped and doped with anthracene (concentrations 10 −5 − 2 × 10 −3 M/M), were performed between 5 and 300 K. The kinetic analysis of fluorescence and delayed fluorescence confirmed that excitons are self-trapped at low temperatures and they become mobile at higher temperatures. The obtained activation energies of mobility of singlet and triplet excitons are (380 ± 50) and (165 ± 30) cm −1, respectively. Triplet exciton motion (50–80 K range) is well described by the one-dimensional hopping model. Above 80 K, the intersystem crossing transition, T 1 → S 1, with the activation energy of (1450 ± 100) cm −1, becomes an efficient deactivation channel for triplet excitons. The experiments point to a possibility of structural disorder in DMN-TCNB crystals.