Theoretical analysis of the Rose-Fowler-Vaisberg model

Results of numerical calculations based on the Rose-Fowler-Vaisberg model of radiation-induced conductivity in a case polymer upon long (10⁴ s) irradiation at doses of 5 × 10⁵–10⁷ Gy are reported. Two irradiation modes were considered: (1) preliminary irradiation and irradiation repeated at variable times after the end of the first irradiation and (2) probing the virgin and irradiated polymer with a standard pulse of ionizing radiation. It was shown that the properties of radiation-induced conductivity, such as its overshoot kinetics, a considerable difference between current transients for the initial and the repeated irradiation, extremely long annealing times of dose effects, and the absence of a steady state, are naturally explained in terms of this model (with allowance for the generation of radiation-induced traps as regards the last property). The Rose-Fowler-Vaisberg theory should be considered at present a well-approved semiempirical model of radiation-induced conductivity in polymers.     

Dose effects in radiation-induced conductivity of polypyromellitimide

Dose effects in radiation-induced conductivity of polypyromellitimide were numerically simulated in terms of the Rose-Fowler-Vaisberg model with allowance for bipolar carrier transport and the generation of radiation traps during irradiation. The reasons for the lack of a noticeable dose effect in this polymer upon pulse irradiation in light of its presence in the case of continuous irradiation are discussed.     

Geminate Pairs and Their Role in Radiation-Induced Conductivity of Poly(methyl methacrylate)

Non-steady-state radiation-induced conductivity of poly(methyl methacrylate) was studied at room and elevated temperatures. It was shown that the conductivity is due to electric polarization of geminate pairs. The evolution of geminate pairs was rationalized in terms of the Rose–Fowler–Weisberg generalized model. The conclusions by the model were compared with the results of previous studies on the kinetics of formation and decay of geminate pairs upon pulse radiolysis or flash photolysis of doped poly(methyl methacrylate).     

Numerical simulation of annealing of dose effects in radiation-induced conductivity of polymers

Numerical simulation of dose effects in radiation-induced conductivity in polymers and of roomtemperature annealing of these effects was performed in the formalism of the generalized Rose-Fowler-Vaisberg model, which allows for bipolar electron transport of charge carriers and for generation of radiationinduced traps. It was shown that neither the distinct dose effect nor its long annealing time can be explained unless the radiation-chemical aspect of irradiation is taken into account. It was found that satisfactory fit of theoretical prediction to published data for a number of polymers (PS, PET, LDPE, polyvinylcarbazole) can be achieved in the case of the reasonable choice of the parameter for the injection of radiation-induced traps (free radicals), although certain difficulties are met. This coincidence is attainable if the other parameters of the model are fixed and their values have been determined in independent experiments.     

A Monte Carlo simulation of radiation-induced conductivity of disordered solids

The Monte Carlo method was used to perform a theoretical study of the kinetics of radiation-induced conductivity under pulsed irradiation of a disordered solid with traps having different energy distributions. The kinetics of radiation-induced conductivity in a weak electric field was satisfactorily described by the Rose-Fowler-Vaisberg model. In a strong field, radiation-induced conductivity became a nonlinear field strength function because of distortions of the energy spectrum of trap centers.     

Electron-beam charging of polytetrafluoroethylene

The charging of polytetrafluoroethylene films by irradiation with fast electrons having an energy insufficient for the complete penetration through the entire thickness of the polymer was theoretically analyzed. The calculation results take into account the distribution of both the dose rate and the bulk electron thermalization rate over the film thickness in the approximation of prescribed radiation-induced conductivity of polytetrafluoroethylene. The influence of the parameters of radiation-induced conductivity on the charging behavior and on the time dependence of the transient current detected with the use of the split Faraday cup was examined. It was found that the observed transient current inversion is adequately explained with allowance for the specifics of radiation-induced conductivity in polytetrafluoroethylene.     

Radiation-Induced Conductivity of Polymer Composites Filled by Finely Divided Oxides

The radiation-induced conductivity of polymer composites based on polyisoprene rubber filled with finely divided oxides of various chemical natures was studied in the continuous irradiation mode. It was shown that the radiation conductivity is closely related to the molecular mobility of the rubber. It was found that a change in the character of thermal motion of fragments of rubber macromolecules, which is caused by interaction with the filler, could considerably enhance the radiation-induced conductivity of a polymer composite.     

The role of stable free radicals in the radiation-induced conductivity of low-density polyethylene

The radiation-induced conductivity (RIC) of low-density polyethylene (LDPE) under continuous irradiation with fast electrons (50 keV) was experimentally studied. The dose dependence of the concentration of stable paramagnetic centers was determined. The kinetics of RIC in LDPE was calculated on the basis of the Rose-Fowler-Vaisberg (RFV) model taking into account the buildup of radiation-induced traps. Good correlation between the experimental results and calculated data was found.     

Temporary changes in electrical properties of polymer dielectrics due to ionizing radiation

Measurements of conductivity, permittivity, and dissipation factor on polystyrene, low-density polyethylene, poly(ethylene terephthalate), and polytetrafluoroethylene under irradiation with x-rays at exposure rates from 0.004 to 400 r/sec. are presented. The radiation-induced anomalous conductivity as well as the induced dielectric loss are interpreted by Maxwell-Wagner polarization due to radiation imbalance in surface layers of the specimen. The nature of radiation-induced steady-state conductivity is also discussed.     

Radiation-Induced Electron Transport Processes in Polymeric Dielectrics (A Review)

Recent results that have been obtained in studying the radiation-induced conductivity of low-polar polymeric dielectrics are surveyed. Major attention is given to the analysis of the kinetic behavior of radiation-induced current under different irradiation conditions. The effects of molecular mobility, morphology, and radiation-chemical processes on the transport of radiation-generated charges are considered. The relaxation model and its application to describing the kinetics of excess-charge transport in polymers are discussed.     

Universal technique for studying electron transport in polymers

A universal technique was developed for studying electron transport in polymers, which consists in the combination of the time-of-flight technique in the surface and bulk carrier generation modes with measurement of transient radiation-induced conductivity. Central to the technique in question is the time-of-flight method with homogeneous irradiation. The procedure was implemented on the basis of an ELA-50 electron beam device with variable electron energy (3–50 keV). The practicability of the universal technique was demonstrated using the model polymers polyvinylcarbazole and molecularly doped polycarbonate as examples.     

On the Involvement of Geminate Pairs in Radiation-Induced Conductivity of Polystyrene

Basic parameters of the generalized Rose–Fowler–Weisberg theory were experimentally determined for polystyrene. The obtained data were used to comprehensively analyze the evolution of geminate pairs in this polymer. It was shown that the generation of the prompt component of radiation-induced conductivity occurs by the trapping mechanism with two charge carrier states involved, the quasi-free and trapped. This generation under equilibrium transport conditions (diffusivity and mobility of carriers are constant) reportedly ensured by the geminate recombination itself was not observed in a real experiment. With allowance for dispersive transport of holes (the major carriers), the lifetime of geminate pairs were found to be as long as a few hundred of milliseconds at 300 K. The published data on the formation and decay kinetics in doped polystyrene upon its pulse radiolysis or photolysis were thoroughly analyzed. It was shown that, at ultrashort times before localization of generated carriers, the contribution of electrons to the observed conductivity prevails, although the basic contribution is made by holes in later times.     

Theoretical analysis of the Rose-Fowler-Vaisberg model: Dipolar conductivity

Results of numerical calculations on the kinetics of radiation-induced conductivity (current transients) in a case polymer in terms of the Rose-Fowler-Vaisberg model assuming dipolar carrier transport (irradiation times of 10⁴–10⁶ s) are reported. Unlike the case of unipolar transport, the pattern of current transients noticeably changes at times after passing a maximum in current. A steady-state value is still attained; however, its increase relative to the case of unipolar conductivity is disproportionately high with respect to a relatively small value of the parameter χ, which characterizes the relative contribution of minority carriers to the current. Allowance for the formation of radiation traps during irradiation somewhat mitigates this effect; however, the discrepancy between the conclusions of the theory for the two types of conduction strongly increases for the estimates of polymer recovery time after preliminary irradiation.     

Generation and transport of charge carriers in polyvinylcarbazole

The processes of generation and transport of excess charge carriers in polyvinylcarbazole at room temperature and at 353 K were experimentally studied. The polymer was charged with pulses of electrons at energies of 7 and 50 keV, which differed in both linear energy transfer and track structure. A universal method of investigation based on the combination of the time-of-flight technique in the both (surface and bulk) modes with the measurement of radiation-induced conductivity was used. The radiation-chemical yield of free charges was measured using two independent procedures. It was shown that the radiation chemical yield of free charges at 293 K was somewhat smaller for 7-keV than for 50-keV electrons; in the latter case, G = 1.1 in an electric field of 2 × 10⁷ V/m. The parameters of the generalized physical model were determined for polyvinylcarbazole.     

Theoretical description of the prompt component of pulsed radiation-induced conductivity in polymers in terms of the ion pair mechanism of radiolysis

The properties of the prompt component of radiation-induced conductivity in polymers was theoretically analyzed on the basis of numerical solution of the modified Smoluchowski equation. The time dependences for the concentration of trapped electrons and the geminate-pair current after δ-pulse irradiation were calculated. In addition, calculation for a pulse of a finite duration was performed. The field dependence of the prompt conductivity was determined: deviations from the Ohmís law begin at field strengths on the order of 10⁷ V/m, the character of this dependence strongly varying with a decrease in the electron thermalization length.     

Amorphization of nanocrystalline monoclinic ZrO(2) by swift heavy ion irradiation

Bulk ZrO(2) polymorphs generally have an extremely high amorphization tolerance upon low energy ion and swift heavy ion irradiation in which ballistic interaction and ionization radiation dominate the ion-solid interaction, respectively. However, under very high-energy irradiation by 1.33 GeV U-238, nanocrystalline (40-50 nm) monoclinic ZrO(2) can be amorphized. A computational simulation based on a thermal spike model reveals that the strong ionizing radiation from swift heavy ions with a very high electronic energy loss of 52.2 keV nm(-1) can induce transient zones with temperatures well above the ZrO(2) melting point. The extreme electronic energy loss, coupled with the high energy state of the nanostructured materials and a high thermal confinement due to the less effective heat transport within the transient hot zone, may eventually be responsible for the ionizing radiation-induced amorphization without transforming to the tetragonal polymorph. The amorphization of nanocrystalline zirconia was also confirmed by 1.69 GeV Au ion irradiation with the electronic energy loss of 40 keV nm(-1). These results suggest that highly radiation tolerant materials in bulk forms, such as ZrO(2), may be radiation sensitive with the reduced length scale down to the nano-metered regime upon irradiation above a threshold value of electronic energy loss.     

Changes of the near-surface chemical composition of the 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide room temperature ionic liquid under the influence of irradiation

Radiation induced degradation effects are studied for a model ionic liquid (IL)--[EMIm]Tf(2)N--in order to distinguish in which way the results of X-ray based material analysis methods can be falsified by the radiation supplied by typical X-ray sources itself. Photoelectron spectroscopy is commonly used for determining the electronic structure of ionic liquids. Degradation effects, which often occur e.g. in organic materials during X-ray or electron irradiation, are potentially critical for the interpretation of data obtained from ionic liquids. The changes of the chemical composition as well as the radiation-induced desorption of 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIm]Tf(2)N) fragments are analysed by X-ray photoelectron spectroscopy (XPS) as well as quadrupole mass spectroscopy (QMS) upon exposure to monochromated or non-monochromated AlKα X-rays from typical laboratory sources. During the irradiation of [EMIm]Tf(2)N, an increasing carbon concentration is observed in both cases and especially the [Tf(2)N](-) ion is strongly altered. This observation is supported by the results from the QMS analysis which revealed a variety of different IL fragments that are desorbed during X-ray irradiation. It is shown that the decomposition rate is directly linked to the photon flux on the sample and hence has to be considered when planning an XPS experiment. However, for typical experiments on this particular IL the measurements suggest that the changes are on a larger time scale as typically required for spectra acquisition, in particular if monochromated X-ray sources are used.     

聚乙烯/炭黑复合材料导电体系的结构形态

将导电填料（例如炭黑）加入绝缘的聚合物基体即得到导电复合材料,两组混全物的电阻率随导电填料体积分数的变化而改变,电阻率与导电填料体积分数的关系称为渗流曲线,可分为三个主要区域：低导电填料含量区域,复合材料的电阻率很大,聚合物的电阻率占主导;渗流区域,导电填料含量少量的增加会引起复合材料电阻率很大的提高;高导电填料区域,复合材料电阻率很大的提高;高导电填料区域,复合材料电阻率主要由导电填料的电阻率决定,对于导电复合材料已有大量的实验和理论工作来解释导电复合材料已有大量的实验和理论工作来解释导电填料含量和复合材料各组分的形貌对电性能的影响,其中有效介质普适方程（GEM方程）已经对大量的渗流曲线进行了精确的拟合。聚乙烯／炭黑复合材料中由于炭黑的大量分布很难观测其微观形貌,本文对不同辐照交联程度和不同环境温度下聚乙烯／炭黑复合材料的渗流曲线进行分析,试图找出GEM方程各参数与复合材料各组分形貌的关系,为导电复合材料的设计和制备提供理论基础。     

A percolation model for carbon nanotube-polymer composites using the Mandelbrot-Given curve

A model is introduced for the conductivity of carbon-nanotube polymer composites based upon percolation theory and fractals. These types of polymer composites have been developed in the recent years, and experimental data on their percolation threshold is available. We constructed a fractal space with the aim of the generalized Mandelbrot-Given curve and used the experimental critical exponent of conductivity to calculate the parameters of such a curve. Finally, the moments of the current distribution function are estimated, and the effect of the critical exponent on this function is investigated.     

Light-Controllable Ionic Conductivity in a Polymeric Ionic Liquid

Polymeric ionic liquids (PILs) have attracted considerable attention as electrolytes with high stability and mechanical durability. Light-responsive materials are enabling for a variety of future technologies owing to their remote and noninvasive manipulation, spatiotemporal control, and low environmental impact. To address this potential, responsive PIL materials based on diarylethene units were designed to undergo light-mediated conductivity changes. Key to this modulation is tuning of the cationic character of the imidazolium bridging unit upon photoswitching. Irradiation of these materials with UV light triggers a circa 70 % drop in conductivity in the solid state that can be recovered upon subsequent irradiation with visible light. This light-responsive ionic conductivity enables spatiotemporal and reversible patterning of PIL films using light. This modulation of ionic conductivity allows for the development of light-controlled electrical circuits and wearable photodetectors.