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Hole transport in mixtures of 1,1‐bis(di‐4‐tolylaminophenyl) cyclohexane and bisphenol‐A‐polycarbonate
Journal of Applied Physics
Abstract
Hole mobilities have been measured in mixtures of 1,1‐bis(di‐4‐tolylaminophenyl) cyclohexane and bisphenol‐A‐polycarbonate. The temperature and electric field dependencies can be described as exp‐(T 0 /T)2 and exp(βE1/2), respectively. At high temperatures, T≫316 K, the mobilities decrease with increasing electric field. The results are described within the framework of the disorder transport formalism introduced by Bässler and co‐workers. The negative field dependence of the mobility is attributed to off‐diagonal disorder and based on the assumption that fluctuations of the wavefunction overlap parameter increase with increasing temperature.
... [9] However, for some molecularly doped polymers, many reports show more complex behaviors. [10][11][12][13][14][15][16][17] Borsenberger et al. found that the mobility follows a linear relationship with the electric field in a triphenylamine-doped bisphenol-A-polycarbonate system, [18] and Stolka et al. observed that in films of solid solution of N,N'-diphenyl-N,N'-bis(3-methylphenyl)-[1, 1'-biphenyl]-4,4'-diamine in bisphenol-A-polycarbonate, the electric field dependence of the mobility is ln µ ∝ E. [19] Obviously, these two relationships cannot be explained by the Poole-Frenkel effect, and the investigation of the physics beneath these different relationships is still missing so far. The Poole-Frenkel effect reveals the main physical picture of the carrier hopping process, i.e., an electric field lowers the energy barrier by β PF √ E, and it can be applied to explain many experimental results about the electric field dependency of mobility; [11] however, it considers only the influence of the electric field on the Coulomb potential of a single trap while ignoring the effect of the adjacent traps. ...
... In the present case, the mobility of the carriers is proportional to the tunneling probability, i.e., µ ∝ T (E). Combining this insight with the relationship between tunneling probability and electric field, it can be concluded that when α increases from 0.7 nm to 3 nm, the electric field dependence of mobility changes from µ ∝ E to ln µ ∝ E. Many investigations about the organic small-molecule materials, polymers, and molecularly doped polymers have shown that the carrier mobility satisfies an empirical expression [3][4][5][6][7]11,14,20] ...
... ing in ln µ ∝ √ E. [11,[13][14][15][16][17]21,22] However, two other µ-E relationships, µ ∝ E and µ ∝ exp(E/E 0 ), were also observed and cannot be explained by the Poole-Frenkel effect. [18,19] The Poole-Frenkel effect only accounts for the influence of the electric field on a single trap, while no accommodation is made for the effect of adjacent traps, which will affect the hopping process of the carriers. ...
In some organic materials, varying the finite distance between adjacent carrier traps modifies the Coulomb potential around each trap, resulting in a more complex field-dependence of mobility, differing from (but not incompatible with) the usually considered relationship of ln μ ∝ √E, a relationship which has been successfully explained by the Poole—Frenkel effect. To investigate the influence of the adjacency of traps, a model system is proposed, which consists of two traps separated by distance α. Our numerical calculation shows that with increasing α, the dependence of mobility on the electric field changes from linear to exponential. Moreover, beyond a certain large α, i.e., as the distance to the nearest trap approaches infinity, the proposed model is essentially the same as the Poole—Frenkel effect. The proposed model accounts for the effect of the energy barrier shape, especially the effect of the location of the potential-energy maximum, a phenomenon which is not accommodated in the Poole—Frenkel model. Because the model assumes the Coulomb interaction between the adjacent traps, it applies to those charged traps which may exist in organic materials for various reasons.
... Such a situation reduces the number of carriers that can reach the electrode. 43,46,47 The Gaussian disorder model (GDM) was used to analyze this result. 48 This model expresses the nature of the charge transfer in disordered solids by considering that the energy and distance of hopping sites have the statistical distribution. ...
The aggregation states and physical properties of polymers in thin films deviate from those found in the bulk. Although an effect of the thickness on the carrier mobility for thin films of poly(3-hexylthiophene) (P3HT) has been widely studied, there is a lack of discussion in terms of crystallographic distortion. Here, we demonstrate how the out-of-plane hole mobility in P3HT, which is a typical semiconducting polymer, changes with decreasing film thickness. Time-of-flight measurements with an analysis using the Gaussian disorder model revealed that the zero-field out-of-plane hole mobility decreased with decreasing thickness because of an increase in the energetical and spatial distribution of hopping sites. Grazing incidence wide-angle x-ray diffraction measurements revealed that such distributions of charge carriers were induced by the crystallographic distortion of P3HT in the thin films.
... Others observe similar behavior in P3OT, 13 PHPS, 12 and doped polymers. 30,31 Shen et al. 32 observe a negative field dependence in P3HT above 120°C, close to the melting point. Finally, some CELIV reports 33 observe negative field dependence for P3HT over all fields. ...
While transport in conjugated polymers has many similarities to that in crystalline inorganic materials, several key differences reveal the unique relationship between the morphology of polymer films and the charge mobility. We develop a model that directly incorporates the molecular properties of the polymer film and correctly predicts these unique transport features. At low degree of polymerization, the increase of the mobility with the polymer chain length reveals trapping at chain ends, and saturation of the mobility at high degree of polymerization results from conformational traps within the chains. Similarly, the inverse field dependence of the mobility reveals that transport on single polymer chains is characterized by the ability of the charge to navigate around kinks and loops in the chain. These insights emphasize the connection between the polymer conformations and the transport and thereby offer a route to designing improved device morphologies through molecular design and materials processing.
... This is quite different from the previous observation that the conductance of most organic materials increases with increasing temperature. 6 In the present study, all the devices were fabricated and measured in the way described in Ref. 9. A Photo-Research SpectraScan 750 photocolorimeter was used to measure the brightness and EL spectra. Since such measurements were taken at the same current density, the current efficiency can be acquired. ...
The electron conductance of N,N′-bis-(1-naphthl)-diphenyl-1,1′-biphenyl-4,4′-diamine was found to increase with decreasing temperature experimentally. This phenomenon is quite abnormal since for most organic materials the conductance increases with increasing temperature. A probable explanation was given according to a previous work about soliton diffusion in polyacetylene within the framework of SSH model.
Organic photoconductor (OPC) is the term given to the light‐sensitive element in an electrophotographic printer. The OPC is an organic electronic device consisting of multilayer thin coatings of insulating organic materials (organic semiconductors) on a conductive substrate. The organic layers electrically conduct positive charge injected into their highest occupied molecular orbital (HOMO) and/or negative charge injected into their lowest unoccupied molecular orbital (LUMO). The electrophotographic printing process exploits the charge transport characteristic of organic semiconductors to form an electrical charge pattern on the OPC surface that is subsequently “developed” to form the printed image. In this chapter, the history of the development of electrophotographic printing is described, as well as how the development of OPCs enabled the commercialization of today's “laser printers.” The chemistry and physics of the materials comprising the OPC are described focusing on the mechanisms of charge generation, and hole and electron charge transport, and how these characteristics influence the electrophotographic performance. At the end of this chapter, we discussed about how OPC technology has evolved into more advanced printing technologies and how current organic semiconductor research has been directed to the development of new organic electronic devices/organic light‐emitting diodes (OLEDs), organic transistors, and organic photovoltaics.
After carefully theoretical research, as for the concepts of P- and N- type semiconductors, it is found that there are contradictions between inorganic and polymer semiconductors. Then through the basic concepts of hole and electron, it can be derived that all the polymer semiconductors should have ambipolar transporting characteristics, which has been proved by the subsequently experimental data through the impedance spectroscopy from the common materials. Such general ambipolar transporting properties of polymers are firstly systematically investigated in diode structure, which is closer to their intrinsic properties. The hole can be seen as “electron group of hole”, and it is difficult to be quenched than one electron, which can then help to get the common reported data that the number of hole transporting polymers are more popular than that of electron transport. Moreover, the experimental mobility curves mostly show the negative slope, which seems to be opposite to the basic fact that the electric field will accelerate the directional movement of carrier. The concept of carrier segment is then proposed for such negative slope, which is one conjugation projection system. In one carrier segment, the carrier can move freely as in one molecule, which can be accelerated by external electric field. From one carrier segment to another carrier segment, the kinetic energy of carrier could be relaxed by the vibration of carrier segment dipole. If the energy loss from vibration relaxation of carrier segment is larger than the energy increment from the external electric field, the carrier mobility curve will show the whole negative characteristic. Which effect can have the main influence is determined by the molecular structure of polymers. At last, the vibration model of the polymers has been investigated through the IR spectroscopy and the calculation methods. It is showed that the vibration models of P3HT have some special characteristics, which are corresponding to the fact that its slopes of hole and electron mobility curves are contrary to each other.
Charge transport properties of a P3HT:DIPBI bulk heterojunction solar cell are modelled by kinetic Monte Carlo simulations based on a morphology obtained from coarse-grained molecular dynamics. Different methods for calculating the hopping integrals entering the charge transfer rates are compared and calibrated for hole transport in amorphous P3HT. The influence of intermolecular and intramolecular charge transfer on the total charge carrier mobility and hence the power conversion efficiency is investigated in detail. An analysis of the most probable pathways with low resistance for hole transport is performed, establishing a connection between charge mobility and morphology.
Considering the basic concepts of P‐type and N‐type originated from inorganic semiconductors, it has been deduced in this report that the non‐doped polymer semiconductors should be ambipolar materials. Thus, the carrier dynamics of hole‐only and electron‐only devices of poly(N‐vinylcarbazole) (PVK) are researched through impedance spectroscopy. The results show that the hole and electron transports both possess high dispersion with parameter of 0.1–0.2 and 0.1, respectively. In addition, the hole and electron mobilities under different electric field are basically in the same order of magnitude, which shows that PVK is one intrinsically ambipolar polymer semiconductor although it is traditionally thought to “P‐type.” Finally, the abnormal negative slope phenomenon of transferring curve is analyzed, which is ascribed to the energy relaxation through vibration in polymer segment.
Charge transport has been studied in indolo[2,3-a]carbazole, IC, a pentacyclic polyheteroaromatic system that can be easily synthesised using a one-step methodology. The characterisation of thin film Organic Field Effect Transistors (OFETs) and by Time Of Flight (TOF) has been used to determine the mobility in the interfacial region of the transistor and in the bulk of an organic layer, respectively. The mobility dependence on low electric fields has been studied in devices that work under different conditions, showing dissimilar trends for OFETs and TOF measurements. Interestingly, the later revealed a balanced ambipolar transport with negative electric field dependence of hole and electron mobilities.
In traditional viewpoint, poly-3,4-ethylenedioxythiophene: polystyrenesulfonate (PEDOT:PSS) in solid state photoelectronic device is considered to be conducting or hole transporting polymer. So at the beginning, this work researched the conducting mechanism of PEDOT:PSS, which leads to that the PEDOT:PSS should not be good conductor. Then one simple model is used to theoretically analyse the carrier dynamics, and its results show that PEDOT:PSS should be ambipolar polymer in theory. Based on the theory, the hole- and electron-only diodes fabricated by PEDOT:PSS are investigated through the impedance spectroscopy method, and such experimental data fully proved the theoretical results. Besides the ambipolar characteristic, mobility verse E1/2 curves show the abnormal negative slopes, that hole and electron mobilities decrease with the increment of biased electric field, which is not in accordance with the common standpoint that the charge carrier should be accelerated by electric field. Thus such experimental data in further propel us to propose the concepts of HOMO trap and LUMO trap, which exists in the energy space of frontier orbital and decelerates the movement of charge carrier.
Low charge carrier mobility is one key factor limiting the performance and applicability of devices based on organic semiconductors. Theoretical studies on the mobility using kinetic Monte Carlo or Master equation are mainly based on a Gaussian energetic disorder and regular cubic lattices. The dependence of the mobility on the electric field, temperature and charge carrier density is well studied for the Gaussian disorder model. In this work, we investigate the influence of spatially correlated site energies and spatial disorder in the lattice sites on the mobility using kinetic Monte Carlo simulations. Our analysis is based on both a regular cubic and a non-cubic Voronoi lattice. The latter is used to include spatial disorder in order to study its influence on the mobility for amorphous organic materials. Our results show, that the charge carrier mobility is strongly influenced by correlations in the site energies. Strong correlations even invert the field dependence of the mobility as observed experimentally in semi-crystalline polymers such as P3HT. Evaluation of local currents between localized states reveals the formation of current filaments with rising correlation. Furthermore, the influence of the electric field and the energy landscape on the transport energy is studied by evaluation of active sites. A strong correlation between the transport energy, filaments in the local currents and the charge carrier mobility is observed. Our studies on the spatial disorder model do not indicate an inversion of the field dependence as observed by other researchers. The negative field-dependence in semi-crystalline materials may be explained by a higher correlation in the site energies as shown in the strongly correlated energetic landscape.
This review traces the history and development of organic photoconductors (OPCs), the multilayer thin film photosensitive element in electrophotographic printers, from Chester Carlson's 1938 demonstration of xerography to the present. A brief discussion of the history of electrophotography is followed by a review of OPC basics and the development of specific charge generating materials (CGMs) and charge transporting materials (CTMs). Next is a discussion of OPC commercialization and the last section demonstrates the cycle of OPC research and development by the number of OPC presentations at international conferences. (C) 2016 Society for Imaging Science and Technology.
Polarizabilities and dipole moments of hole transport molecules with different mobilities were measured. The zero-field mobilities of the molecularly-doped polymers increase with increasing polarizabilities and decrease with increasing dipole moments of the dopants. Concerning molecules with similar dipole moments, mobilities correlate well with polarizabilities. Also concerning molecules whose polarizabilities are almost equal, the correlation between mobilities and dipole moments is clear. The 3-D plot of the mobility as a function of the polarizability and the dipole moment is nearly coplanar. Within a framework of the small polaron formalism, polarizabilities are good indices to evaluate the degree of electron cloud extension that affects transfer integral J. On the other hand, the magnitude of the polaron binding energy Ep is macroscopically influenced mostly by the intramolecular structural relaxation. However, we propose that the Ep has a distribution caused by intermolecular interactions, which is not considered in the small polaron formalism. Such distributions, which have recently been discussed within a framework of the disorder formalism, are due to the random internal field caused by the local charge-dipole interaction. These analyses support the experimental data that the logarithm of mobility is described as a linear combination of the polarizability and the dipole moment.
Two methods for studying charge carrier transport in disordered polymer materials are compared, the time-of-flight technique and transient radiation-induced conductivity. Reasons for which the experimental data obtained using these two techniques disagree with one another for the same material are discussed. In the former mode, carriers are generated in the vicinity of one of the electrodes, whereas the latter method provides the uniform generation of charges of both signs in the bulk. Different spatial patterns of charge generation inevitably lead to differences in the carrier transport. Arguments for the preferable use of time-of-flight measurements for determining the carrier mobility are set forth.
Electrophotography, as the name suggests, is a process in which an image can be reproduced by means of electricity and light. Literature detailing examples of electrophotographic processes date back to the early 1920s. Initial attempts to develop photo-electrical imaging processes were centred on the use of electrosensitive papers which could be activated by photocurrents (Von Bronk, 1922). Commercially, the most significant invention in the field of electrophotography was the discovery of the process most commonly known as xerography. Xerography, derived from the Greek, means ‘dry writing’ and was developed out of the original inventions by Chester Carlson (Carlson, 1938).
The charge-carrier mobility of the blend films consisting of organic small molecule and quantum dots (QDs), Alq3 and CdSeS, are studied by time-of-flight (TOF) technique. The dependence of charge-carrier mobility in the blend films on electric filed and QD concentration is measured. The results show that the positional disorders in the blend films are increased with the increase of QD concentration. Moreover, the charge transport mechanisms between Alq3 and QDs and the number of electron hoppings between QDs will lead to the change of the charge-carrier mobility.
The Materials and Manufacturing Directorate of the Air Force Research Laboratory (AFRL) began studies of deoxyribonuclaic acid (DNA) as a polymer material in 2001 due to the availability of multi-gram quantities of 98% pure DNA extracted from Japanese salmon waste products. The research studies that followed explored the electrical, optical and electrooptical characteristics of thin films of DNA combined with the surfactant hexacytltrimethylammonium chloride making the resulting DNA-CTMA complex soluble in most polar solvents and insoluble in water. The films were produced mainly by spin coating although other techniques were also used. The focus was to measure the fundamental properties, such as volume electrical resistivity, dielectric constant, refractive index and thermal conductivity, and to explore various applications using test device configurations such as an optical modulator, OFET, OLED and energy storage capacitor fabricated using DNA-CTMA. The initial high molecular weight of 2,000 to >8,000 kDa was reduced by high power ultrasonic treatment, which provided molecular weight materials from 1,000 down to similar to 200 kDa. These lower molecular weight materials revealed changes in some properties of the DNA-CTMA material. This paper brings together the results of these studies to show the potential of DNA as a polymer material.
This paper is a retrospective on the career and research accomplishments of the late Dr. Paul M. Borsenberger. A Senior Research Associate in the Eastman Kodak Company, Paul was internationally renowned for his accomplishments in electrophotographic photoreceptor technology and research on charge generation and transport in amorphous systems. With his passing on July 17, 1998, we lost a colleague and a friend. In this paper we summarize his major research accomplishments and provide guidance for those wishing to review his scientific output of over 140 research publications.
The correlated disorder model (CDM) has been proposed as a theory of charge transport in molecularly doped polymers (MDPs). Recently a test of the CDM was proposed: it was predicted that the dipolar disorder energy can be obtained from the slope of the log of the mobility versus square root of the electric field (the Poole-Frenkel or PF slope). We find that the dipolar disorder energy obtained from the experimental PF slopes are almost always larger than the theoretical predictions, especially for MDPs made from dopants with low dipole moments. In addition, the theory relates the dipolar disorder energy to the temperature T0 at which the electric field dependence of the mobility vanishes. We find that the observed T0 does appear to increase as the dipolar disorder increases but is in quantitative agreement (within 25 K) with the theoretical predictions for only a limited set of the measurements. We conclude that it appears that the CDM needs further development to be consistent with charge transport in organic materials.
The concept of hopping within a Gaussian density of localized states introduced earlier to rationalize charge transport in random organic photoconductors is developed further to account for temporal features of time of flight (TOF) signals. At moderate degree of energetic disorder (σ/kT~3.5…4.5) there is a transport regime intermediate between dispersive and quasi-Gaussian type whose signatures are (i) universal TOF signals that can appear weakly dispersive despite yielding a well defined carrier mobility and (ii) an asymmetric propagator of the carrier packet yielding a time dependent diffusivity.
Photoinduced electron‐transfer processes between fullerenes (C60) and three triphenylamines (TPA's) including bis(tolylaminophenyl)cyclohexane in the absence and presence of hexylviologen dication (HV2+) and 1‐benzyl‐1,4‐dihydronicotinamide (BNAH) have been studied by the transient absorption method in the visible and near‐IR regions. Electron‐transfer takes place initially from TPA's to the triplet states of fullerenes (3C60*), giving the radical anions of fullerenes (C60−) and the radical cations of TPA's (TPA+). The rate constants and efficiencies of electron transfer are quite high, because of the high electron‐donor abilities of TPA's as their low oxidation potentials indicate. On addition of HV2+ to the C60 and TPA systems, the electron‐mediating process from C60− to HV2+ occurs, yielding the viologen radical cation (HV+). In the further addition of BNAH, which acts as a sacrificial donor, steady‐state concentration of HV+ was accumulated during continuous photoirradiation and persisted for a long time.
Basic models proposed to describe charge carrier transport in polymers are reviewed as applied to the results obtained by time-of-flight and radiation-induced conductivity techniques. It was shown that discrepancy between data obtained in these measurements should be attributed to different modes of generation of charge carriers: the surface generation in the former case and the bulk generation in the latter case. The most likely reason for the observed discrepancy is the effect exerted by the surface layer of a polymer on the shape of transient current curves (appearance of plateau), which is especially strong in the time-of-flight technique. A theoretical explanation of this phenomenon is proposed. Calculations showed the possibility of appearance of a plateau in the transient current curve upon pulse generation and electrode injection of charge carriers used in the time-of-flight method.
Hole mobilities have been measured in vapor deposited films of 1,1‐bis(di‐4‐tolylaminophenyl)cyclohexane (TAPC) and TAPC‐doped bisphenol‐A‐polycarbonate (BPPC). Over an extended range of temperatures, the mobilities decrease with increasing field at low fields. At high fields, a log μ∝E1/2 relationship is observed with a slope that approaches zero at high temperatures. The results are described within the framework of the disorder transport formalism. By comparison of the experimental results with Monte Carlo simulations, we show that the observed behavior is a signature of the simultaneous presence of diagonal and off‐diagonal disorder. Agreement between simulation results and experiment is excellent. Generalizing these results provides a framework for determining the magnitude of the relevant diagonal and off‐diagonal disorder parameters from an analysis of mobility measurements.
The charge transport properties of conjugated polymer semiconductors are governed by strong electron phonon coupling, leading to polaron formation as well as the presence of structural and electronic disorder. However, the relative contribution which polaronic relaxation and disorder broadening make to the temperature activation of the mobility of these materials is not well understood. Here we present a combined study of the temperature and concentration dependences of the field-effect mobility and the optically induced electron-transfer transitions of a series of poly(3-hexylthiohene) field-effect transistors of different molecular weight. We apply a vibronic coupling model to extract the reorganization energy and the strength of electronic coupling from the optical spectra. We observe a transition from a localized to a delocalized transport regime as a function of molecular weight and crystalline quality. Polaron activation is comparable to disorder-induced activation in the low-mobility regime [∼10−3 cm2∕(V s)] and needs to be taken into account when interpreting the field-effect mobility, while disorder becomes the dominant mechanism to limit charge transport in the high-mobility regime with mobilities >10−2–10−1 cm2∕(V s).
Before the invention of the transistor in the 1940s, semiconductors were used as detectors in radios in a device called a “cat’s whisker”. At that time their operation was completely mysterious. Only after the introduction of semiconductor band theory did it become clear that the “cat’s whisker” is a primitive example of a metal-semiconductor Schottky diode. Today organic materials are being investigated for their electronic properties. Such materials are especially attractive for lightweight, flexible, and low-cost solar cells and light emitting devices, as well as transistors and electrophotographic photoreceptors. Yet, even after 40 years of work and a large database, the physics and chemistry that determines the electronic properties of organic materials are not well understood. Practicing organic electronics is like attempting to do silicon device design without semiconductor band theory. It is the purpose of this paper to briefly summarize what is known about the electronic properties of organic materials from charge transport data. It will be shown that our understanding of the charge transport mechanism and the electronic properties of organic materials is at a rudimentary phase which is a limiting factor in applying these materials to practical devices, very similar to the “cat’s whisker” phase of inorganic semiconductor research.
Using a dipole trap model we propose an explanation of the experimentally observed drastic decrease of the carrier drift mobility with the increase of average distance between transport sites. We demonstrate that in general case mobility activation energy depends on this distance. In addition we demonstrate that observation of the decreasing dependence of activation energy on average intersite distance must be a very rare event, in full agreement with experimental data. We show that the absolute value of the mobility, calculated using our approach, is in good agreement with the experimental one. We demonstrate that it is natural to expect the approximate independence of the activation enery on the average intersite distance for dopants with high dipole moments. Such correlation was really observed in experiments.
It is well known that charge carrier mobilities μ in molecularly doped polymers, determined by transient photoconductivity experiments, depend on the temperature T, the mean distance p between dopant molecules and the electric field E. Recently introduced deconvolution procedures have made possible the systematic analysis of the dependence of μ on T, p and E. Two theories which have been proposed to account for the data are the polaron theory and the disorder theory of Bässler and co-workers. The current status of these and other theories in explaining the data is reviewed.
Hole mobilities have been measured in vapor-deposited layers of N,N′,N″,N‴-tetrakis(4-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TTB) and N,N′-diphenyl-N,N′-bis(3-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TPD). The results are described within the framework of a formalism based on disorder, due to Bässler and co-workers. The formalism is based on the assumption that charge transport occurs by hopping through a manifold of localized states with superimposed energetic and positional disorder. The key parameters of the formalism are σ, the energy width of the distribution of hopping site energies, and Σ, the degree of positional disorder. For TTB, σ = 0.078 eV and Σ = 1.7. The values for TPD are 0.077 eV and 1.6. The width of the hopping site energies can be described by a model based on dipolar disorder. The degree of positional disorder is in agreement with results observed for a wide range of vapor-deposited molecular glasses and is attributed to packing constraints. The results show that transport in both compounds can be described by simple disorder-controlled hopping without invoking polaronic contributions.
Charge transport in a novel molecular glass of tri(o-terphenyl-4-yl)amine has been studied. A negative electric-field dependence of hole drift mobility was found for the molecular glass. It is shown that a small diagonal disorder in terms of the disorder formalism is responsible for this phenomenon.
Photocurrent transients are determined in polycarbonate doped with 17 wt% of p-p-EFTP (see structure below) as a function of the electric field strength and the temperature. The hole mobilities are obtained both by a graphical method and by computational analysis based on an analytical expression for the transient photocurrent which has been recently proposed by Scott et al. The comparison of the results obtained with the two methods shows that, although the absolute values of the mobilities differ by a factor of 1.5, the field and temperature dependencies of the hole mobility are similar. The system studied shows an anomalous field dependence of the mobility which at low fields increases with increasing field to a maximum above which it decreases with increasing field. Such a behaviour is analysed in the framework of two different theoretical models: one based on the Marcus theory of electron-transfer processes and Bässler's model which takes into account the fluctuations in hopping sites due to the simultancous presence of diagonal and off-diagonal disorder. While the first model does not provide a satisfactory description of the experimental data, the latter cannot explain qualitatively the observed field dependence over a wide range of applied fields. The predicted saturation of the drift velocity of the holes at high fields does not agree with the observed temperature dependence of the mobility high fields. This disagreement with the conventional models is probably due to the large dimensions of the molecules allowing a change in the free energy for nearest-neighbour hops which is large compared to the polaron binding energy or the width of the distribution of the density of states.
We report a time-of-flight transient photocurrent study of the hole mobility, measured as a function of electric field and temperature, within (i) poly(9,9-dioctylfluorene), (ii) poly(9,9-dioctylfluorene-co-bis-N,N-(4-butylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine) (PFB), and (iii) three copolymers that contain differing proportions of the moieties 9,9-dioctylfluorene, N-(4-butylphenyl)diphenylamine, and bis-N,N-(4-butylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine. The results are analyzed using the Gaussian disorder model as proposed by H. Bässler Phys. Status Solidi B 175 15 (1993)], the correlated disorder model as proposed by S. V. Novikov et al. Phys. Rev. Lett. 81 4472 (1998)], and finally, the polaronic correlated disorder model of R. E. Parris et al. Phys. Rev. Lett. 87 126601 (2001)]. We deduce values for the corresponding energetic and spatial disorder parameters, intersite hopping distance, wave-function decay constant, and polaronic activation energy, and consider how variations in chemical structure impact thereon.
The field and temperature dependencies of the hole mobility of 1,1‐bis(di‐4‐tolylaminophenyl)cyclohexane (TAPC) doped polystyrene have been measured and compared to results obtained for the TAPC doped polycarbonate and pure TAPC. The results are described by the disorder formalism, due to Bässler and co‐workers. The mobility of TAPC doped polystyrene is approximately 100‐fold greater than that observed for TAPC doped polycarbonate. This effect is interpreted in terms of (1) the elimination of random dipolar fields due to static dipole moments of the polycarbonate that affect the energetic disorder, and (2) improved electronic intermolecular coupling with a concomitant reduction of positional disorder.
The effects of doped fluorescent dye 4-(dicyanomethylene)-2-i-propyl-6-(1, 1, 7, 7-tetramethyljulolidyl-9-enyl)-4H-pyran (DCJTI) on the charge carrier injection, transport and electroluminescence (EL) performance in polyfluorene (PFO)-based polymer light-emitting diodes (PLEDs) were investigated by steady-state current-voltage (I−V) characteristics and transient EL measurements. A red EL from DCJTI was observed and the EL performance depended strongly on the DCJTI concentration. The analysis of the steady-state I−V characteristics at different DCJTI concentrations found that three regions was shown in the I−V characteristics, and each region was controlled by different processes depending on the applied electric field. The effect of the dopant concentration on the potential-barrier height of the interface is estimated using the Fowler–Nordheim model. The dopant concentration dependence of the current-voltage relationship indicated clearly the carrier trapping by the DCJTI molecules. The mobility in DCJTI: PFO changed significantly with the DCJTI concentration, and showed a nontrivial dependence on the doping level. The behavior may be understood in terms of the formation of an additional energy disorder due to potential fluctuation caused by the Coulomb interaction of the randomly distributed doping molecules.
Hole mobilities have been measured in vapor deposited films of 1,1‐bis(di‐4‐tolylaminophenyl)cyclohexane over an extended range of fields and temperatures. At 295 K, the mobility is approximately 10−2 cm2/V s, the highest value for a disordered molecular solid reported thus far. Monte Carlo simulations of random walk in a geometrically and energetically disordered medium demonstrate that the time dependence of the photocurrent and the field and temperature dependencies of the mobility can be described quantitatively in terms of the inherent disorder and its effect on charge transport. No polaronic or trapping phenomena need to be invoked to reproduce even subtle features of the experimental results.
Hole transport in the glassy state of arylaldehyde and arylketone hydrazones, 4-diphenyl-aminobenzaldehyde diphenylhydrazone (DPH) and 4-diphenylaminoacetophenone diphenylhydrazone (M-DPH), has been studied. The values of the hole drift mobility in the glassy state of DPH and M-DPH are over one order of magnitude greater than those of 50 wt% molecularly dispersed systems in polycarbonate. The hole drift mobility of DPH is ca. twice as high as that of M-DPH. Temperature and electric-field dependencies of the hole drift mobilities in the glassy state are discussed.
It is shown that the relative widths of photoconductive current transients, obtained in molecularly doped polymers, are independent of the electric field and sample thickness, even when the current before the transit time is nearly time independent. Such a result has been termed universality in the Scher-Montroll theory of dispersive transport. The implications of these results for the field and temperature dependence of the mobility are considered.
A new class of electron acceptors, unsymmetrically substituted diphenoquinones with methyl and bulky alkyl substituents, has been developed for electron-transport compounds, which possess high dispersibility in a wide range of polymers owing to their unsymmetrical and bulky substitutions. 3,5-Dimethyl-3',5'-di-tert-butyl-4,4'-diphenoquinone (MBDQ), a representative member of these acceptors, dispersed molecularly in polycarbonate exhibited electron mobilities over 10(-6) cm2/V s at a conventional concentration of 40 wt %, which are the highest for electron transport in molecularly doped polymers. The photoinduced discharge measurements demonstrated that electrons can be injected from titanylphthalocyanine into the MBDQ-doped polycarbonate, indicating a possible application to xerography.
We present a development of the dipole-trap model for the description of the field and temperature dependences of the non-dispersive charge-carrier transport in disordered organic matrices. Very good agreement between our numerical results and the phenomenological Gill-Pfister equation is obtained. Our consideration reveals the physical meaning of the parameters of this equation.
The transient current response of molecularly doped polymers have been numerically modelled under space-charge-limited (SCL) conditions for the situation in which a step potential is applied to an ideal injecting contact. Under trap-free conditions, the transient SCL current pulse shape is found to be sensitive not only to the underlying field dependence of the injected carrier mobilities and diffusivities, but also to the magnitude of the applied step potential. A progressive reduction in the ratio of the peak current density jp to the final steady-state magnitude jss is obtained by increasing either the field strength of the mobility or the relative amount of diffusion. It is demonstrated, however, that for times preceding the location tp of the current peak, the rate of current increase displays a gradual transition from a super-linear to linear time dependence upon the introduction of diffusion. The diminishing observability of jp/jss is accompanied by a shift in the position of tp relative to the space-charge-free carrier transit time t0. The classical fixed-mobility value tp/t0 = 0.786 is modestly reduced as the field strength of the mobility or amount of carrier diffusion is enhanced. The numerical predictions are compared with experimental SCL current transients obtained from hydrazone doped polyester samples fitted with gold contacts.
We shell discuss the transport of charge carriers (electron and holes) in disordered polymeric dielectric matrices and electroluminescence phenomena in transport layers of various structures, and also the injection of charges into transport layers through a boundary bearing a solid layer of a different type. The temperature, field, and concentration dependences of the mobility of the carriers will be considered, as well as the effect of the structure of the polymer matrix and of the transport centres on the mobility. The most reliable, theoretical models of charge transport in these media will be examined. The bibliography includes 150 references.
Regioregular poly(3-hexylthiophene) (RR-P3HT) is a widely used donor material for bulk heterojunction polymer solar cells. While much is known about the structure and properties of RR-P3HT films, important questions regarding hole mobilities in this material remain unresolved. Measurements of the out-of-plane hole mobilities, μ, of RR-P3HT films have been restricted to films in the thickness regime on the order of micrometers, beyond that generally used in solar cells, where the film thicknesses are typically 100 to 200 nm. Studies of in-plane carrier mobilities have been conducted in thinner films, in the thickness range 100-200 nm. However, the in-plane and out-of-plane hole mobilities in RR-P3HT can be significantly different. We show here that the out-of-plane hole mobilities in neat RR-P3HT films increase by an order of magnitude, from 10(-4) cm(2)/V·s, for a 80 nm thick film, to a value of 10(-3) cm(2)/V·s for films thicker than 700 nm. Through a combination of morphological characterization and simulations, we show that the thickness dependent mobilities are not only associated with the differences between the average morphologies of thick films and thin films, but specifically associated with changes in the local morphology of films as a function of distance from the interfaces.
The measurements of hole mobility in microcrystalline chlorophyll a (Chl a) as a function of temperature and field have been carried out. The results are described in terms of disorder formalism of charge transport put forward by Bssler and co-workers. Noteworthy feature of the study is the negative field dependence of the mobility at room temperature. This is explained on the basis of the presence of large positional disorder parameter, Σ, compared to the energetic disorder, σ, in microcrystalline Chl a. Their respective values are ≈4 and 77 meV. The intercalation of a water molecule that holds the two Chl a molecules together to form microcrystalline Chl a is a possible responsible for the increased hopping site distances that leads to larger Σ and, thus, to the negative field dependence of the mobility.
The temperature and electric-field dependence of charge carrier mobility has been studied by a conventional time-of-flight technique in chemically purified, low dark conductivity samples of regioregular poly3-hexylthiophene. Subsequently, the mobility of doping-induced charge carriers has been determined using the technique of charge carrier extraction by linearly increasing voltage in the same samples exposed to air. The charge carrier mobility determined by both experimental techniques correspond well to each other at tempera-tures above 130 K, indicating that these experimental techniques are mutually consistent. The study clearly shows that the typical log E 1/2 , 0 Poole–Frenkel-like electric-field dependence of the charge carrier mobility diminishes at temperatures around 250– 270 K, and becomes negative at higher temperatures. Such negative electric-field dependence of mobility observed by both experimental techniques is attributed to posi-tional disorder in a random-organic dielectric and analyzed in the framework of the disorder formalism. Finally, the overall agreement indicates that the mode of charge generation has negligible effect on the temperature-and electric-field dependence of mobility except at the lowest temperatures 110 K, where transit time dispersion of the photogenerated charge carriers probed by the ToF technique is more pronounced.
The electric‐field dependence of the drift mobility of holes in a polymer matrix doped with various different molecules was studied by means of time‐of‐flight (TOF) photoconductivity measurements. It was first found that the degree of the positive field dependence of the drift mobility increases with decreasing magnitude of the drift mobility at zero field. The tail of the Gaussian TOF current signal becomes broad in molecularly doped polymers having a large disorder of hopping site energies. It was pointed out that the field dependence of the mobility and the energy barrier for charge transport are largely related to energetic disorder of hopping sites.
The dependences of electron mobility on the electric field F, temperature T, and hopping site distance R have been characterized in 3,5‐dimethyl‐3’,5’‐di‐tert‐butyl‐4,4’‐diphenoquinone dispersed molecularly in a polycarbonate according to Schein’s analytical technique. The electron mobility can be described in the form a 0 R2 exp(-2R/R 0 ) exp(-E 0 /kT) × exp[β(1/kT-1/kT 0 )F1/2], where a 0 , R 0 , β, and T 0 are constants. Moreover, it is found that the zero‐field activation energy E 0 is independent of R. The invariable E 0 and the exponential dependence of the Arrhenius prefactor on R strongly suggest that the electron transport therein is due to nonadiabatic small‐polaron hopping. Based on the small‐polaron theory, the transport properties are qualitatively discussed in terms of molecular properties.
In this letter, carrier-transport properties of a homologous series of oligofluorenes with C9 diaryl substitution have been examined. These substituted oligofluorenes possess stable amorphous states, ambipolar carrier-transport properties, and processability to thin films for a range of oligomer lengths, rendering feasible investigating dependence of carrier transport on oligomer length in disordered systems. It is found that carrier mobilities of these oligofluorenes show a clear decreasing trend with the oligomer length. Such findings are in contrast with previous observations for crystalline oligomers and impose certain implications in carrier transport of conjugated polymers and oligomers.
The temperature and electric field dependence of the hole mobility in regioregular poly(3-hexylthiophene) (P3HT) is studied by time-of-flight (TOF) technique. It is observed that above ∼250 K the slope of the electric field dependence of mobility becomes negative. Such phenomenon has been reported previously for a variety of amorphous charge transport materials, but not clearly observed in conjugated semiconducting polymers. The temperature and electric field dependence of mobility is analyzed both in the framework of Gill’s phenomenological data analysis and disorder formalism. The occurrence of negative field dependence in the measured regioregular P3HT samples is attributed to the small energetic (σ=70 meV), but large spatial disorder (Σ=3.4).
Orientador: José Arruda de Oliveira Freire Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Curso de Pós-Graduaçao em Física. Defesa: Curitiba, 2007 Inclui bibliografia
In this paper, we present measurements of the charge-carrier transport in the conjugated polymer poly(paraphenylenevinylene) (PPV) and its substituted derivative poly(1,4-phenylene-1,2-diphen- oxyphenyl vinylene) (DPOP-PPV) by using the time-of-flight technique. A method for evaluating the experiments, based on Fourier transform techniques, is presented to calculate the density of localized states from the measured photocurrent within a multiple trapping model. The transport properties of DPOP-PPV can be described by a conventional hopping mechanism, where nearly every monomer acts as a trap. At room temperature, the effective mobility for holes in DPOP-PPV is in the range of 10-4 cm2/V s, whereas for PPV, a value of less than 10-8 cm2/V s can be estimated.
The hole mobilities in the molecularly doped polymer, pyrazoline: polycarbonate, have been characterized as a function of the electric field, temperature, and pyrazoline concentration. At sufficiently low concentrations (10%) and high temperatures (T⪢ 375K), the mobility decreases as the electric field increases, contrary to intuition but consistent with known empirical relations.
Electronic transport in the polycarbonate polymer Lexan molecularly doped with triphenylamine (TPA) has been studied by time-of-flight techniques as a function of temperature, applied field, and TPA concentration. Only hole transport could be observed. The experimental data provide evidence that the transport of holes occurs by a hopping process which connects sites associated with the TPA molecule. The results are analyzed in terms of the theory of stochastic non-Gaussian transport by Scher and Montroll. This theory provides a consistent description of all experimental results if field-induced barrier lowering and temperature-dependent dispersion are formally introduced in the final expression for the transit time.
One of the most puzzling aspects of the hole mobility in molecularly doped polymers, its electric field dependence, is studied. New data over the widest electric field range yet reported have been obtained and are compared with various functions proposed in the literature. Comprehensive linear and nonlinear statistical analysis reveals that only the function exp(E)1/2 is consistent with the data. The theoretical implications of this result are discussed.
Extensive characterization of the hole mobilities mu in dispersions of p-diethylamino- benzaldehyde-diphenyl hydrazone (DEH) in polycarbonate has been carried out. We report the effect of varying the electric field E, temperature T, and spacing between DEH molecules rho on mu. These data are analyzed by a procedure that allows proper separation of the functional dependencies of the mobility on E, T, and rho. It is found that lnmu is proportional to En(T-1-T-10), where n=0.5 and T0 is a fitted parameter which decreases with increasing rho, behavior opposite to the dependence of the glass transition temperature on rho. These experimental results are not yet understood theoretically. Our procedure for separating the rho and T dependence is applied to data taken on DEH-polycarbonate and to data taken from the literature on another molecularly doped polymer system, N,N'-diphenyl-N,N'-bis (3-methylphenyl)-(1,1'-biphenyl)-4,4'-diamine (TPD) in polycarbonate. For DEH-polycarbonate, the activation energy is found to be independent of rho. In contrast, for TPD-polycarbonate the activation energy is strongly dependent on rho. Our data suggest that small-polaron hopping is occurring in molecularly doped polymers; this different dependence of the activation energy on rho is consistent with different small-polaron hopping regimes, adiabatic and nonadiabatic, in these two systems.
The application of rate theory to the kinetics of localized electronic transport yields a temperature and field dependent drift mobility relationship. The formalism is consistent with recent experimental results on the transport properties of amorphous semiconductors. In addition, it is suggested that a field dependent mobility yields a simple electronic mechanism for the explanation of the electrical instabilities (switching effects) observed in semiconductors.ZusammenfassungAus der Anwendung der Geschwindigkeitstheorie auf die Kinetik des lokalen Elektronentransports ergibt sich ein temperatur und feldabhängiges Verhältnis der Driftbeweglichkeit Der Formalismus steht mit neuen Messergebnissen hinsichtlich der Transporteigenschaften amorpher Halbleiter in Einklang. Zudem wird vorgeschlagen, eine feldabhängige Beweglichkeit ergebe einen einfachen Mechanismus zur Deutung der an Halbleitern festgestellten elektrischen Labilitäten (Schalteffekte).
New hole drift mobility measurements for the molecularly doped polymer DEH (p-diethylaminobenzaldehyde-diphenyl hydrazone) in polycarbonate and literature data for TPD (N,N′-diphenyl-N,N′-bis (3-methylphenyl)-[1,1′-biphenyl]-4,4′-diamine) in polycarbonate are analyzed by a new procedure which separates the functional dependence of the mobility on temperature and molecular spacing ϱ. Our analysis indicates that the dependence of the mobility on ϱ arises from different sources. In DEH: polycarbonate it is due to an overlap integral, as normally expected. In TPD: polycarbonate it is due entirely to the dependence of the activation energy on p, a significant clue to the underlying microscopic hole hopping mechanism. These data are consistent with the small polaron hopping theory in two regimes, non-adiabatic hopping in DEH:polycarbonate and adiabatic hopping in TPD: polycarbonate.
This paper re-examines literature data on the charge-carrier mobility in tri-phenyl methane/polycarbonate, triphenyl amine/lexan and PVK: TNF composite systems. In all cases the dependence of μ on both temperature T and electric field E, as well as its absolute magnitude, can be interpreted consistently in terms of hopping across a Gaussian density-of-states distribution of width σ. The exponential dependence of μ on T and E predicted by computer simulation and analytic theory for transport in the long-time limit are recovered. The essential parameters that control μ are μ0= lim μ(T) which is the mobility of the hypothetical crystalline counterpart structure, and σ. The latter quantity increases with increasing polarity of the constituent molecules and is responsible for the variation of μ upon chemical substitution reported for the triphenyl methane polycarbonate system.
By use of Monte Carlo simulation techniques it has been shown that inclusion of random variations of the wavefunction overlap parameter (‘off-diagonal’ disorder) generates Poole-Frenkel behavior of the charge-carrier mobility (μ) in random organic solids within an experimentally relevant range. The results are in quantitative agreement with experimental data, notably the work of Peled and Schein (Chem. Phys. Lett., 153 (1988) 422) reporting on a temperature-induced change of sign of the field dependence of μ.
Time-of-flight measurement show that the hole hopping mobility in polyvinycarbazole layers is independent of thickness between 3 and 80 μm. Long-tailed transit current profiles with “knees” are observed at all thicknesses and down to −80°C, but scale only superficially with transit time. The discrete mobility is reconciled with the transit pulse dispersion by reference to Marshall's computer model of trap-controlled transport.
A new method has been developed to study non-equilibrium transport and energy relaxation phenomena in disordered organic and inorganic semiconductors. Given a distribution of localized states, the mean-square displacement and average energy of the excitation may be evaluated as functions of initial energy and time.The theory has a wide range of possible applications, for example to exciton and carrier transport in disordered organic and inorganic semiconductors. In disordered organic semiconductors, the density of excited states is usually well described by a Gaussian model. Current and energy relaxation and temperature-dependent mobilities have been studied for this Gaussian model using Monte-Carlo simulations. The theoretical results are found to be in excellent agreement with those of the simulations.
The Monte Carlo technique has been employed to simulate hopping transport through a Gaussian energy distribution of hopping sites located on a cubic lattice having a nearest-neighbour distance of 10 cm. Dispersive transport is observed at temperatures where the width of the Gaussian [sgrave] > kT and for electric fields where eE x 10/[sgrave] < 1. The dispersive regime is observed over a considerable range in the average number of jumps and in this range both ⟨x⟩ and ⟨x ⟩ can be described by a mobility and a diffusion constant which are proportional to t and where α is a function of electric field and [sgrave]/kT.
Recent computer simulations have shown that the temperature dependence of the charge-carrier mobility in an amorphous organic hopping system, where the profile of the energy distribution of the hopping sites is a Gaussian, should follow μ(T)=μ0exp[-(T0/T)2]. T0 is proportional to the Gaussian width σ. Experimental data obtained for the hole mobility in a variety of organic glasses confirm this relationship and yield σ values on the order 0.1 eV and μ0 values on the order 10-2 cm2/V s. Changes of the μ(T) dependence observed near the glass transition temperature are attributed to an increase of σ above Tg as a result of dynamic disorder superimposed on the static fluctuations of site energies. The model predicts a field dependence of μ of the form μ(E)=μ(E=0)exp(E/E0) which is observed. Agreement between simulation results and experiment is excellent. It demonstrates that the field dependence of μ is an inherent consequence of hopping transport in a system subject to a Gaussian type of diagonal disorder. No charged trap states have to be invoked.
Measurements of the mobility, whose temperature dependence suggests a band-hopping transition is occurring near 100 K, are reported for electrons in the {c}^{\ensuremath{'}} and b directions of naphthalene and the {c}^{\ensuremath{'}} direction of deuterated naphthalene. A review of the status of the theoretical understanding of this transition indicates that while progress is being made toward understanding the hopping mechanism of transport, significant aspects of these data remain unexplained.
The hole mobility mu has been measured in dispersions of N-isopropyl carbazole in polycarbonate for relative concentrations c between 100% (PVK) and 2%. At sufficiently high temperature (T) and field (F), transport is essentially coherent. For c less than 40%, mu varies directly as c**n where n congruent 4, i. e. transport is non-percolative. For c greater than 10%, mu varies directly as R**2exp( minus 2 alpha R), where R is the average carbazole spacing and alpha approximately equals 0. 62 multiplied by 10**8cm** minus **1, almost independent of T and F. For c less than 5% and high T and F, mu becomes substantially greater than predicted by the above relation. At constant T, log mu is proportional to F** one-half rather than to F. At constant F, an approximate fit to a relation mu varies directly as exp left bracket minus (T//0/T)**2 right bracket is obtained, but systematic deviations suggest an apparently field-dependent activation energy of about 0. 35 ev at F equals 0. These observations are interpreted in terms of field-enhanced polaron tunnelling, leading, in first approximation, to a Poole-Frenkel-like behaviour of mu .
A complete list of mobilities in molecular organic crystals is preseneted. This updates the 1977 list and includes many new developments in the field.
A simple model of hopping transport in a molecularly doped polymer is described based on a small electric-field perturbation of diffusional (random walk) electron self-exchange reactions in the solid state. A master expression is derived which quantitatively accounts for the electrical field, temperature and concentration dependence of the hole mobility in the N,N′-diphenyl-N,N′-bis(3-methylphenyl)-[1,1′-biphenyl]-4,4′-diamine/polycarbonate system in terms of fundamental electron exchange parameters employed in modern (semi-classical) electron-transfer theory. Charge mobility which is simply related to electron hopping between neighbouring oxidized/reduced sites is assumed and shown to be normally thermally activated. The electric-field dependence of mobility is derived by modifying the zero-field Arrhenius rate expression for charge diffusion in a manner analogous to the derivation of the overpotential (electric field) dependence of charge transfer at an electrified interface. The intersite distance dependence of the mobility arises from the pre-exponential factor A′. Predictions of the model are an exponential field dependence of mobility at high fields, field-independent mobility at low fields, normal Arrhenius behaviour, decreasing activation enthalpy with increasing field, and an exponential decrease in mobility with increasing intersite distance. The free energy of activation for the elementary electron exchange reaction for this system at zero field is 0·3 eV while the inner (small molecule) and outer-sphere (medium) contributions to the overall free energy of activation are estimated, respectively, to be 0·19 and 0·13eV at 80wt%.
In order to investigate further the mechanism of the phenyl ring motion put forth by Schaefer et al. (Schaefer, J.; Stejskal, E. 0.; Perchak, D.; Skolnick, J.; Yaris, R. Macromolecules 1985,18,368), Brownian dynamics computer simulations on two-dimensional lattices of interacting benzene rings have been performed. Two versions of this model were studied. One was a "rigid" lattice, which only allowed rotational motions of the rings, and the other was a "flexible" lattice, where vibrational motion of the rings was also allowed in the lattice plane. Consistent with the conjecture of Schaefer et al., for the simple models studied, flexibility in the lattice provided the mechanism that allowed rings to flip.
The amplitudes of ring- and main-chain motions of a variety of polystyrenes have been established from the 13C NMR magic-angle spinning sideband patterns of dipolar and chemical shift tensors. The frequencies of the same motions have been determined by T 1(C) and T 1ρ(C) experiments. The most prevalent motion in these polymers is restricted phenyl rotation with a sizable average jump angle. Both the amplitude and frequency of this motion vary from one substituted polystyrene to another and from site to site within the same polystyrene. A small fraction of sites within some of the polystyrenes permits high-frequency (megahertz) ring flips in combination with main-chain rotational reorientation, also at high frequency. The concentration of these sites does not depend upon intrachain conformational or configurational defects but rather is determined by interchain glassy-state packing. Low-frequency (kilohertz) main-chain motion is insensitive to ring substitution for some of the polystyrenes, suggesting the presence of a cooperative motion in which the rings only translate as the main chain rotates.
Hole transport has been investigated in films of solid solutions of N,N′-diphenyl-N,N′-bis(3-methylphenyl)-[1,1′-biphenyl]-4, 4′-diamine in bisphenol A polycarbonate. Charge carrier mobilities in excess of 10-3 cm2/(V s) have been observed at room temperature at electric fields lower than 104 V/cm. The values of hole mobility were between 10-10 and 10-3 cm2/(V s) as the molecular concentration was varied from 9 to 100 wt%. At high concentrations of the transport molecule and at fields less than 105 V/cm, the mobility is essentially independent of electric field. Field dependence was observed at lower concentrations and higher fields.
Hole and electron drift mobilities have been measured in thin films of charge‐transfer complexes of 2,4,7‐trinitro‐9‐ fluorenone (TNF) with poly‐n‐vinylcarbazole (PVK). The film compositions ranged from pure PVK to mixtures of TNF : PVK in a 1.1 : 1 molar ratio with respect to the monomer unit. Measurements have also been made on amorphous films of pure TNF. The drift mobilities are extremely low (≪ 10-6 cm2/V sec) and are strongly field and temperature dependent. The field dependence is due to the measured activation energies decreasing as the square root of the applied field from zero‐field values of about 0.7 eV for both carriers. The field dependence of the mobilities is similar to that observed for conductivity modified by the Poole‐Frenkel mechanism; however, several objections make this model unacceptable for this case. At this time, no satisfactory explanation of the observed field dependence can be given. As the TNF concentration is increased, the hole mobility decreases rapidly, while the electron mobility increases. The results suggest that charge carriers are highly localized with transport taking place by a thermally assisted intermolecular hopping process as for the case of small ppolaron motion. Hole transport is apparently due to hopping via uncomplexed carbazole states, while electron transport is due to hopping between TNF sites which may be complexed or uncomplexed. Estimates of the charge‐carrier localization obtained from the exponential dependence of mobility on the site separation give characteristic distances of 1.1 × 10-8 cm for holes and 1.8 × 10-8 cm for electrons.
Hole drift mobilities have been measured in films of solid solutions of trans‐1,2‐bis (9H‐carbazole‐9‐yl) cyclobutane (DCZB) in various polymer binders. The hole drift mobilities differ by more than two orders of magnitude depending on the polymer binder used. In poly (methacrylates) films the hole drift mobility is large and the temperature dependence is small when the glass transition temperature of pure polymer is about 50 °C. The difference in rotational mobility of DCZB molecules is considered as the origin of this binder and temperature dependence on the hole mobility.
Hole‐drift‐mobility measurements are presented for a molecularly doped polymer, p‐diethylaminobenzaldehyde‐diphenyl hydrazone in polycarbonate, over the widest temperature (213–373 K) and electric‐field range (3.3–111 V/μm) yet reported. Use of these data and graphical techniques which we introduce allow us to unambiguously determine for the first time the functional form of the electric field and temperature dependence of the mobility. Consistent with results obtained by others, the observed field dependence cannot be accounted for by any known hopping model. The observed temperature dependence suggests that the activation energy may be temperature dependent.
In this paper we examine the following problem: Given a band of localized states randomly distributed in space and obeying a distribution function for energies, how does an excitation diffuse as a function of time and initial energy\? This question is encountered in luminescence, photoconductivity, and transport work in organic and inorganic semiconductors and in novel quantum-well structures. We also allow random processes which do not conserve excitation number (radiative and nonradiative recombination). We present analytic solutions and exact Monte Carlo simulations and discuss the validity of approximation procedures focusing in this paper on Gaussian energy distributions appropriate to organic materials.