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Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
\n\nThis achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
\n\nWe are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
\n\nThank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
\n\n\n\n\n'}],latestNews:[{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"}]},book:{item:{type:"book",id:"2994",leadTitle:null,fullTitle:"Bioactive Food Peptides in Health and Disease",title:"Bioactive Food Peptides in Health and Disease",subtitle:null,reviewType:"peer-reviewed",abstract:'"Bioactive Food Peptides in Health and Disease" highlights recent developments on bioactive food peptides for the promotion of human health and the prevention/management of chronic diseases. 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From last few decades, polymer semiconductor-based electronic devices have attracted an enormous deal of interest due to their great achievements both in laboratory and as well as in commercial products [1–10]. Lightweight, flexibility, low-cost, wide-area application, deposition on various substrates, tunability, and many other advantages make these materials an excellent choice for many electronic applications such as light-emitting diode, solar cell, thin-film transistor, laser diode, etc. [11–20]. Another remarkable area of interest for conducting and semiconducting polymer is their application towards highly responsive and low-cost temperature, pressure, humidity, chemical, biochemical, and other types of sensors [21–30]. Despite all of these successes, the complete picture of charge-transport mechanism, which is highly crucial for further achievements, is still not clear [31–40]. Due to such ambiguity, different charge transport models are reported to validate the experimental results performed on various polymer devices [41–54]. Among these charge transport models, space charge–limited current model is counted as highly recited and unanimously accepted charge transport model for disorder organic/polymer semiconductor. In this chapter, we discuss the brief overview of space charge–limited current model with recent development especially for polymer semiconductors.
\nThis chapter starts with the brief discussion of space charge–limited current model and its applications to polymer, especially for conducting and semiconducting polymer. Firstly, the concise overview of historical evaluation and charge transport mechanism of polymer will be discussed. Later on the Child’s Law, Mott-Gurney space charge–limited current model, and trapped space charge–limited current model with single-trap, exponential, and Gaussian distribution of traps and then effects of shallow and deep traps on space charge–limited current are reviewed. Mobility measurement from space charge–limited current and its comparison with other mobility measuring methods such as time-of-flight and different carrier extraction by linearly increasing voltage characteristics are evaluated in the next section. Finally, the application of Poole-Frenkel on space charge–limited equation with other modifications is reviewed before conclusion.
\n(a) Chemical structure of polyacetylene. (b) Comparison of improved conductivity of doped polyacetylene with other conventional materials.
Before 1977, it was generally considered that polymers are electrically insulator. Most of these insulating polymers such as polyethylene, polystyrene, and polypropylene have almost negligible free charge carriers for electrical conductivity. But at the same time, three well-known scientists Heeger, MacDiarmid, and Shirakawa reported a series of great works on the doping of polymer and demonstrated that the proper doping of conjugate polymer improves its conductivity just like as usual semiconductor or metal and they referred it as semiconducting/conducting polymer [3]. They reported first time in the history that the conductivity (10−5 S/m) of insulating polyacetylene (molecular structure shown in Figure 1a) thin film can be increased by doping it with iodine up to a metallic polyacetylene (105 S/m) just like as Cu metal as shown in Figure 1b. No doubt, it was a great turning point in the discipline of polymer engineering and caused to initiate a new field as “Organic Electronics” or “Polymer Electronics”. On the basis of their land-mark achievements, Heeger, MacDiarmid, and Shirakawa were awarded Nobel Prize for chemistry in 2000 [2–4].
\n(a) Sigma (Single bond) hybridization for ethylene, (b) pi (Single bond) hybridization for ethylene and (c) both sigma and pi bond hybridization which give de-localization of pi-electron.
Broadly speaking, conjugate polymers cover the extensive portion of conducting polymers. Conjugate polymers are defined as such polymer which has a combination of alternating double bonds (π bonds) and single bonds (σ bonds) as their backbone structure. As compare to the σ bond, the π bonds are usually unstable in nature and easily ionized or removed. This special combination of single and double bond for conjugate polymer offers a unique arrangement for the de-localization of charge carriers from one end to the other end of polymer chain as extended p-orbital system [19, 55]. This p-orbital overlapping supported with contiguous single bonds allows a de-localization of π-electrons (double-bond electrons are called π-electron offers Px, Py, and Pz hybridization for carbon atoms) throughout the double and single-bond combination just as an ethylene as shown in Figure 2. Such de-localization of free carriers is the main reason for the charge transport within the molecular chain (intra-molecule) of a conducting polymer [56]. Just for the discussion of σ bond and π bond a simple ethylene (IUPAC name ethene H2C = CH2) molecular structure is shown here in Figure 2. Each carbon makes sp2-sp2 hybridization for π bond and the σ bond is formed between carbon and hydrogen atom. The overall hybridization of σ and π bond is shown in Figure 2c for ethylene.
\n(a) Metal work function and (b) metal-polymer interface. Energy to inject electron from metal to vacuum is much higher than the required energy to inject electron from metal to polymer/insulator.
Conducting polymers offer a large number of topological defects as disorder. These defects, such as breaking of bonds in molecular chain, torsion, addition of both internal and external impurity, are produced during the synthesis of polymerization and cause to provide electrical traps for conductivity between molecular chains. Such disorder in conducting polymer presents localization of free carriers inside a molecular chain. Therefore, intermolecular chain transport requires hopping of free carries from one molecular chain to the other molecular chain. So overall, we can say that charge transport in polymer is the combination of both intermolecular and intramolecular charge transport process. Due to the hopping conductivity for intermolecular charge transport, the overall mobility of free carriers for most of polymer is very small as compared to the conventional inorganic semiconductors at normal operating conditions. From charge-transport point of view, there is no fundamental inconsistency between insulating, semiconducting, and conducting polymer except the difference between energy bandgaps, which is larger for insulating polymer semiconductor as compared to semiconducting polymer.
\nFor electronic devices, metal-polymer interface plays a vital role to define the electrical response for conducing polymer. Figure 3 demonstrates the differences between typical metal-vacuum and metal-polymer interface energy band diagrams for further discussion. Apparently both energy band diagrams look same, but actually different charge injection mechanism is observed in both cases. The Fermi-energy level (Ef) of metal is coincide with Ef of vacuum and as well as with polymer. But the barrier height between Ef of metal and vacuum energy level for metal-vacuum interface is very high as compared to the barrier height between Ef of metal and polymer interface. The barrier height difference between metal Ef and vacuum level is defined as metal work function [56]. On the basis of these facts, Mott and Gurneys proposed metal-insulator barrier height reduction theory and justified the low metal-insulator barrier height as compared to the metal work function, which causes space charge–limited current in insulating materials [57]. It is unanimously accepted that Mott and Gurney’s proposed space charge–limited current is also valid for most of insulating, semiconducting, and even conducting polymers [31].
\nThe limitation of current by a polymer can be classified as either (i) injection-limited or (ii) bulk-limited current flow. For injection-limited, the limitation of current through polymer is imposed by non-ohmic metal-polymer interfaces, while for bulk-limited, the limitation is imposed by the bulk properties of polymer. If conducting polymer is sandwiched between two electrodes and anyone electrode offers low barrier height (∼ohmic response) to the polymer-metal interface then the injected carriers from electrode forms a space charge region consisting of a large number of injected carriers and equilibrium free carriers inside polymer. As the mobility of carriers is very small, therefore, before traversing of injected carriers from one to the other electrode, more and more charges are injected. When an external electric field is applied, further charges are injected from low-barrier electrode to the polymer, and an equilibrium stage is reached when injected carriers are comparable or even higher than the free carriers concentration; at this stage, the flow of current is referred as space charge–limited current [57, 58].
\nSpace charge–limited current is a hot topic of research due to their great application for conducting/semiconducting polymers. The origin of space charge theory was founded by C.D. Child and I. Langmuir from 1911 to 1913, when they reported the derivation of space charge–limited current in a parallel-plane vacuum diode as [59, 60]
\nwhere J is space charge–limited current for vacuum diode, ε0 is the dielectric constant for free space, e is the coulomb charge of electron, me is the mass of electron, Va is the applied (anode) voltage, and d is vacuum spacing between two electrodes. The above equation is reported in the literature with different names such as three-halves power law, Langmuir-Child law. From the equation, it is clear that the space charge current is directly proportional to the three-halves power of the applied voltage and inversely proportional to the square of the displacement between electrodes.
\nApparently, Child-Langmuir space charge equation did not find any application for insulator or semiconducting materials due to the presence of vacuum and hence no scattering between electrodes. Therefore, Mott-Gurney proposed another space charge–limited current equation for polymer diode, which is similar to the Child-Langmuir equation with the following assumptions [57].\n
Active layer is trap-free for charge injection
Diffusion of carrier is negligible in active layer
Electric field at the injecting electrode is zero.
Generally, the assumptions 2 and 3 are still valid for most of organic/polymer semiconducting materials. But for assumption 1, space charge–limited current is further modified with new version as trapped space charge–limited current model and will be discussed in the later section.
\nWhen a voltage is applied to an active layer, sandwich between two electrodes as diode, then an electric field (E) is established inside the active layer. Such electric field forces the charges to move with velocity (v) toward another electrode, and therefore, the mobility (μ) of free carrier is defined as\n
Similarly, the current density (J) passing through a semiconductor with conductivity (σ) under the influence of applied electric field E can be defined as
\nwhere σ is direct function of both mobility and carrier density of electron n(x) and hole p(x) and can be define as\n
If we assume single-carrier devices, then Eq. (4) is simplified as\n
By incorporating Eq. (5), Eq. (3) becomes as\n
The injected carriers forms space charge with the distribution of electric field inside insulator and can be defined mathematically by Poisson equation as\n
By solving all above equation for one-dimension path with boundary conditions V (0) = V and V (L) = 0, the pure space charge–limited current without any traps will be obtained as\n
It is important to note that logarithmic graph (log(J) – log (V)) of above Eq. (8) yield a straight line with slope 2, which shows trap-free space charge–limited current behavior of polymer between electrodes as sown in Figure 4.
\nSpace charge–limited current behavior for polymer semiconductor with only ohmic and trap-free space charge–limited current regions.
Figure 4 shows the ideal current-voltage characteristics of conducting polymer diode, where there are only two regions, one is ohmic region and other is space charge region and both regions can be differentiated with the order of slope. The transition of both ohmic and space charge regions is taken place at specific voltage termed as threshold voltage VT. At low voltage, polymer diode offers ohmic behavior (J α V) with slope at order 1, while at higher voltage, polymer exhibits space charge–limited current (J α V2) with slope of an order 2. In other words, there is direct transition is observed from ohmic to space charge–limited region, which is not true in the presence of traps distribution inside polymer.
\nGenerally, an intermediate region is also observed between ohmic to space charge–limited region and this region is termed as trapped space charge region as shown in Figure 5. The charge transport inside polymer within this region is controlled by the trapping and de-trapping of carriers at both energetic and positional distribution. Traps are nothing just as impurity and/or structural defects which provide localized states between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy bandgap of polymer. These localized states trap the free carriers and avoid them to take any role for charge transport process and degraded the electrical properties of polymer and hence device [61]. When applied voltage is higher than the average energy associated with traps density, then polymer behaves trap-free space charge–limited current as shown in Figure 5.
\nTypical space charge–limited current behavior for polymer semiconductor. Four charge-transport regions are clearly visible (i) ohmic region (J α μ V), (ii) trap-SCLC region (J α μ Vn) region, (iii) VTFL region (J α μ Ntd2), and (iv) SCLC region (J α μ V2) [
The trapped space charge–limited current depends on the distribution of traps state at the energy bandgap of the given polymer. Generally three distributions of electronic traps are reported for conducting polymers. These distributions are as follows:\n
Single energy level trap density.
Exponential distribution of trap density.
Gaussian distribution of trap density.
For single energy level trap density (ET, also called transport energy), the current for trapped space charge–limited current can be little modified as [62]
\nwhere θ is defined as trap factor and can be correlated with free and trapped carrier density as [63–67]
\nwhere nf and nt are defined as free carrier and trapped carrier density, respectively. The trapped carrier density nt can be defined with single energy level ET as
\nwhere NT, Ef, k, and T can be defined as trap density, Fermi energy level, Boltzmann constant, and ambient temperature, respectively.
\nExponential distribution of traps (g(E)) with characteristics width of trap energy distribution (Ec) between HOMO and LUMO energy bandgap of polymer can be identified as
\nEc is correlated with characteristic temperature (Tc) as Ec = k Tc. Now, the trapped space charge–limited current for a polymer having exponential distribution of traps can be described as [68–70]
\nwhere l = Tc / T and T is the absolute temperature.
\nBassler proposed Gaussian density of states for polymer material, which are broadened by both energetic and positional disorder [41]. Therefore, many researchers apply Gaussian density of traps (DT (E)) for trapped space charge–limited current as [71].
\nwhere σT is the width of Gaussian distribution traps and Ec – ET is the trap energy. Similarly Steiger and his workers proved that the Gaussian trapped space charge–limited current follow the same exponential distribution of traps Eq. (13), where
If
When light falls on conjugate polymer, huge number of electron and holes are uniformly generated throughout the polymer as free carriers and these carriers move to their respective electrodes as photocurrent under the influence of internal electric field generated by the difference of electrode work-function. If G is the generation rate, L is the length, and q is the electric charge of free carriers, then the photocurrent (Jph) can be defined as [17, 34, 73]\n
By incorporating the effective thickness of polymer (L) for photocurrent, Eq. (17) can be modified as
\nwhere μh and τh are the mobility and charge carrier life time. Blom et al. observed that the photo-generated current in this region (L) follows space charge–limited current and he derived the fundamental space charge–limited photocurrent equation as [33]
\nIncident light power (ILP) dependence of the photocurrent (Jph) versus the effective voltage (V0 - V) measured at T = 210 K. The solid (thick) lines represent the Jph using μh = 1.2 × 10-7 cm2/V s, ϵr 2.6, and G α ILP, where ILP was varied from 80 to 6 mW/cm2. The arrow indicates the voltage (Vsat) at which Jph shows the transition to the saturation regime [
where
Figure 6 clearly shows that the space charge–limited photocurrent as calculated by Eq. (19) is in contrast with the square-root region for the given voltage range of the experimental results.
\nTraps not only decrease the mobility for space charge–limited current but also initiate the thermal and electrical degradation for polymer electronic devices. Traps are generally classified as (i) shallow traps, and (ii) deep traps for both electron and hole. If traps are very close to the conduction band (LUMO) within energy bandgap, then traps are classified as shallow traps for electrons. Similarly if traps are in the vicinity of valence band (HOMO) within energy bandgap, then traps are identified as shallow traps for holes as shown in Figure 8. On the other hand, deep traps of electron and holes are exist far away (mid of the energy bandgap) from conduction (LUMO) and valence (HOMO) band, respectively, as shown in Figure 7.
\nSymbolic representation of shallow and deep traps for polymer semiconductor.
Model simulations of shallow (Ec – Et = 0.1 eV) and deep (Ec – Et = 0.5 eV) trap configurations represented by blue solid lines and red dashed lines. (a) Current density voltage characteristics for a shallow trap and a deep trap are plotted by blue dots and red triangles. Fittings provide the exponent of the voltage. (b) Fermi level representations at 6 V along the thickness, for a shallow trap (blue solid line) and a deep level (red dashed line) [
Conventional space charge and trap space charge–limited current model cannot differentiate between shallow and deep traps for both electron and hole. If space charge–limited current is modeled in frequency domain with single traps, then the dynamic picture of the traps can be obtained. By varying the single-trap energy for frequency-domain analysis of space charge–limited current model, it is possible to differential between shallow and deep traps for both electron and polymer with the condition that polymer is sandwiched between properly selected electrodes [74].
\nThe velocity per unit electric field is defined as the mobility for polymer. Mobility is one of the most important parameter, which comprehensively defined the charge transport mechanism of polymer. The efficiency of many polymer electronic devices depends on mobility; therefore, it is very crucial to determine the exact value of mobility [43, 75]. For polymer, mobility can be measured with different methods; some of them are listed as follows:\n
Time-of-flight method [44].
Carrier extraction by linearly increasing voltage (CELIV) method [44] and photo-CELIV method [76, 77].
Each of this method has some advantages and disadvantages, but these methods are the most commonly used method to determine the mobility of polymer.
\nThe TOF is the most widely used technique for the measurement of mobility. In these techniques, short pulse of light or laser is stroke over the end surface of polymer sample, which result in the generation of photo carriers from the end surface of sample.\n
These photo carriers are immediately swept away from the end surface toward the other end surface through the influence of external DC volts applied at electrodes and give rise to the transient photocurrent as shown in Figure 9. The time (T) taken by the photo carriers from one end to the other end surface is calculated from oscilloscope. If E is the applied electric field, L is the thickness of organic layer then the mobility can be calculated as [78].
\nSchematic setup for typical TOF system for mobility measurements. Here the laser pulse can be illuminated through ITO electrode as well as a semitransparent metal electrode of polymer sample [
The schematic Photo CELIV measurement setup is shown. The measuring process consists of two steps. In first step a laser is shine at transparent electrode of sample which generates excess photo carriers. These carriers are extracted by linearly increasing voltage. The peak-extraction time helps to calculate the mobility.
The charge extraction by increasing the linear voltage is another technique commonly uses to measure the mobility of polymer sandwiched between electrodes. The measuring process consists of two steps. In first step, a laser is shine at transparent electrode of sample which generates excess photo carriers. These carriers are extracted by linearly increasing voltage. The peak-extraction time helps to calculate the mobility of the polymer sample as shown in Figure 10. The detail information about these methods can be found in Ref. [79–81].
\nDark-injection space charge–limited current (DI-SCL) is another commonly used technique for the measurement of mobility for many amorphous, disorder organic/polymer materials [82–85]. To determine the mobility of hole with DI-SCL method, the polymer sample is sandwiched between electrodes and electrodes are managed in such a way that the cathode behaves as blocking electrode and a strong voltage pulse is derived at ohmic anode. The application of voltage pulse will result a transient hole current observed at oscilloscope as shown in Figure 11. Therefore, the hole density μh can be calculated as
\nwhere τ is the arrival time for early sheet of holes carriers to reach the respective cathode. The τ is correlated with space charge free carrier transit time (τSCL) as τ = 0.787 τSCL [86, 87].
\n(a) A sequence of DI signals of Au (treated with UVO)/2TNATA/Au under different applied voltages. The applied voltage varied in steps of 2 V starting from 6 V. (b) An ideal DI-SCLC transient [
For both CELIEV and photo-CELIV mobility measurement method, it is not so simple to differential between electron and hole mobility, specially for bipolar charge-transport polymer. Similarly, the TOF method has two series drawbacks (1) the density of photo-generated carrier is not adequate (very low) to measure the mobility as compare to the usual carrier density at normal operation of many electronic devices, and another drawback is that (ii) TOF method should requires the thickness of polymer above the absorption length of polymer (>1 μm) [78]. In the same way, dark-injection space charge–limited current is required the proper selection of electrode for reliable measurements.
\nRecently, a comprehensive study was performed by Qiu group to compare and evaluate the performance of different mobility measurement methods reported for polymeric materials. They consider various factors such as applied electric field, injection barrier, and energetic disorder, which are crucial for the performance of polymer electronic devices and finally they concluded that the result of both space charge and TOF mobility measurement methods are very close to each other [88]. Therefore, with proper selection of electrodes, space charge–limited mobility measurement is acceptably reliable for most of the cases.
\nAs we discussed earlier, when the current density passing through the polymer with length (L) under the influence of applied voltage (V) shows directly proportional response with the square of voltage (J α V2) and inversely proportional to cube of L (J α L−3) then the polymer sample is modeled with trap-free space charge–limited current. In order to incorporate the variety of the trap distribution, the space charge–limited current model is modified as trapped space charge–limited current model. Traps are both energetically and positional distributed throughout the energy bandgap and capture the free carriers and offer some energy barrier to release them. Both space charge–limited current and trap space charge–limited currents model assume that barrier height of traps are remain constant for entire operating electric field range of the device, which is not true for some of the reported experimental results. In fact, higher electric field lowers the barrier height of traps which cause to increase the emission rate from traps and hence the current density as expected from trap space charge–limited current model as shown in Figure 12a. The lowering of trap barrier height or emission rate from traps at high electric field is identified as Poole-Frenkel effect [89], as shown in schematic energy band diagram (Figure 12b). There is some similarity between Poole-Frenkel and Schottky models [90, 91] for the lowering of traps barrier height. Schottky model represent barrier height reduction at metal-polymer interface, while Poole-Frenkel model shows the lowering of trap barrier height inside the polymer thin film. The overall current density (J) passing through the polymer due to Poole-Frenkel emission can be written as
\nwhere
Murgatroyd was the first who addressed the lowering of trap barrier height by incorporating Poole-Frenkel equation into space charge–limited current equation and drive an approximate equation as [92].\n
(a)\tLowering of energy barrier height of traps at higher electric fields, (b) Pool-Frenkel Effect
Murgatroyd equation is simple and very handy, but it is an approximate equation. Later on, Barbe determined analytically, the effect of trap barrier height reduction on space charge–limited current model and derived an equation as [93, 94]\n
Barbs equation is used to determine the current density (J) as a function of electric field define at position x. It is reported that both these Murgatroyd and Barbe modifications are also applicable with electrical response for many polymers devices [95–99]. As both insulating and semiconducting polymers share the same charge transport mechanism, therefore, above equations are reasonably valid for both types of polymers.
\nThe fundamental work of Frenkel, Murgatroyd, and Barbe is to modify the space charge–limited current to accommodate the lowering of trap barrier height for only in one-dimension trap distribution. For the three-dimension trap distribution, these models not work very well. In this domain, Hartke modification is reasonably accepted for the accommodation of three-dimensional lowering of the trap barrier height for space charge–limited current model [100].
\nSimilarly, Geurst modified the space charge–limited current model in such a way that the thickness of the semiconductor thin film is insignificant with respect to the electrode separation as 2D model [101–104]. While, Chandra derived Mott-Gurney space charge–limited current equation in two dimensions with exponentially distributed traps and other variety of polymer Schottky diodes [105–107].
\nDespite great recent achievements for conjugate polymer-based electronic devices, the clear picture of charge transport mechanism is still not available. Polymers have unique charge transport mechanism as a combination of delocalization and localization of charge carriers with intramolecular and intermolecular charge interaction, respectively. But it is unanimously believed that Mott-Gurney space charge–limited model is appreciably accepted for most of the polymers. As polymers are full of traps, therefore, Mott-Gurney space charge–limited model is also modified as trapped space charge–limited model according to the requirements of polymers. The nature of traps distribution inside polymer is varied and depends on many factors such as nature of materials itself, polymerization process, nature of dopants, and solvent. Generally, three types of traps distributions are reported in the literature for polymers named as single trap, exponential, and Gaussian distribution of traps. Therefore, trapped space charge–limited current model is further modified to accommodate all these distribution of traps. Just like as distribution of traps the nature of traps, such as shallow and deep traps, is also important to define the electrical response of polymer. The most crucial parameter affected by the distribution and as well as nature of traps is mobility, and space charge–limited current model with little variation is also used to measure the charge mobility of polymer. Different other methods such as time-of-flight method and charge extraction by linearly increasing voltage (CELIV) with or without light (photo—CELIV) sources are available to measure the charge mobility. By comparing these measuring methods for polymer, it is reported that the simple space charge–limited model is an acceptable choice for mobility measurements. Similarly, it is also observed the trap barrier height is significantly reduced at higher electric field and temperature due to Poole-Frenkel effect. Therefore, Murgatroyd and Barbe incorporated Poole-Frenkel effect and solved Mott-Gurney space charge–limited equation numerically and analytically, respectively. It is reported that both these modifications are experimentally verified with electrical response of many polymers devices.
\nThe authors are thankful to Umm Al Qura University and GIK Institute of Engineering Sciences and Technology for its support to this work and the facility used. Authors are also thankful to our PhD and Master students for their cooperation, valuable information, and thoughtful suggestions. Special thanks are due for An-Zhong Lin, M.A. Turaeva, and Kh. Akhmedov for their technical support and helpful discussions.
\nLoose connective tissue disorders include lipedema, Dercum’s disease (DD), familial multiple lipomatosis (FML) and multiple symmetric lipomatosis (MSL). All these disorders share many similarities with lipedema including painful lipomas, obesity, fibrosis, a risk of developing lymphedema and difficulty in losing the abnormal fat through diet and exercise. There are clinical characteristics specific for lipedema, including the onset of the disease, fat location and associated health issues (\nTable 1\n) [1, 2].
\nCharacteristic | \nLipedema | \nDD | \nMSL | \nFML | \nMSL | \n
---|---|---|---|---|---|
Abnormal fat location | \nLegs, arms, abdomen | \nGlobal | \nUpper; can be global | \nArms, thighs, trunk, abdomen | \nUpper; can be global | \n
Diet-resistant fat | \nYes | \nYes | \nYes | \nYes | \nYes | \n
Lipomas | \nYes | \nCommon | \nCommon in men | \nCommon | \nCommon in men | \n
Time fat change | \nPuberty; 3rd decade | \nChild-adult | \nAdult; child rare | \nChild-adult | \nAdult; child rare | \n
Painful fat | \nYes | \nYes | \nNot usually | \nLipoma | \nNot usually | \n
Sex predominance | \nFemale | \nFemale | \nMale | \nMale = female | \nMale | \n
Lymphatic dysfunction | \nYes | \nYes | \nYes | \nYes | \nYes | \n
Prevalence | \nPossibly common | \nPossibly common | \nRare | \nRare | \nRare | \n
Associated conditions | \nLymphedema | \nAutoimmune; diabetes | \nNeuropathy | \nMoles; neuropathy | \nNeuropathy | \n
Inheritance pattern | \nAutosomal dominant; incomplete penetrance | \nAutosomal dominant; sex-specific influence | \nAutosomal dominant or recessive | \nAutosomal dominant | \nAutosomal dominant or recessive | \n
Lipedema is often misdiagnosed as lifestyle-induced obesity that affects ~10% of women of European descent as well as other populations [3, 4]. Although both disorders are considered inflammatory diseases due to the presence of increased macrophages and hypertrophic adipocytes, there are significant differences between the two disorders. Among these is the location of the fat, primarily abdominal or spread widely over the body in obesity compared to the symmetric distribution in the lower extremities in lipedema, the texture of the skin (thin and soft in lipedema and thicker in obesity), easy bruising and pain upon the introduction of pressure in lipedema [5, 6].
\nThe focus of this review will be on the disease of lipedema, different stages and types, diagnosis and treatment, pathogenesis and current research in the field.
\nLipedema also referred to as lipedema, is a painful loose connective tissue disorder first described in 1940 by Allen and Hines [7]. Lipedema is characterized by symmetric enlargement of the buttocks, hips and legs due to deposition of loose connective tissue that includes fascia, adipocytes, immune cells and other structures; arms are also affected in 80% of patients [3, 4]. Feet are typically spared, but ankle cuffs are often noted in advanced stages of lipedema where the risk of lymphedema is also high [8, 9]. Patients with lipedema experience mobility issues, psychosocial distress, anxiety, eating disorders, sleep apnea and depression [1, 10].
\nLipedema is considered a hormone-related disorder affecting almost exclusively women during puberty, childbirth or menopause. Case reports of men with lipedema have been described in literature. Men with lipedema have elevated estrogen level and low to absent testosterone levels resulting in cirrhosis, gynecomastia and hypogonadism [11, 12, 13]. While the exact etiopathogenesis of this disease is unknown [10, 14], many studies have demonstrated that inflammatory cells, hypertrophic adipocytes, abnormal blood vessels and lymphatic dysfunction are associated with tissue damage and development of a fibrotic disease [14, 15, 16, 17].
\nLipedema consists of three stages characterized by the texture of skin and tissue formation. Stage 1 involves smooth skin over pearl-sized nodules in a hypertrophic fat layer; Stage 2 has skin indentations over a hypertrophic fat structure of pearl-to-apple-size masses; and Stage 3 includes pearl-sized nodules and much larger fat masses causing lobules of skin and fat to form mainly on the hips, thighs, and around the knees. Lymphedema, causing fluid accumulation in the limbs, may develop during any stage of lipedema and is referred to as lipo-lymphedema [1, 3, 10, 18, 19].
\nHealthcare providers often misdiagnose women with lipedema as they do not take into account the disproportionate size of the legs compared to trunk especially in Stage 1 and 2 along with the inability to lose fat from areas affected by lipedema. It is possible to confuse women with Stage 3 lipedema as having lifestyle-induced obesity due to fat involving more areas of the body.
\nIn addition to stages of lipedema, lipedema is also characterized by types determined by the area of the body that is affected. There are five types of lipedema; types I, II, and III are the most common. In Type I, fat is deposited in the areas of the buttocks and hips resembling saddle bags. In Type II, fat extends to the knees from the buttocks area with the formation of folds of fat around the inside of the knee. In Type III, fat spreads all over the lower body from the hips to the ankles. In Type IV, upper arms are affected causing difficulty in lifting the arm and stress on the shoulder. In Type V, fat is restricted to the lower legs. It is worth noting that patients with lipedema can clinically present with a mixture of types [3, 10].
\nPain, tenderness, bruising easily, symmetrical swelling of the legs, heaviness of affected limbs, burning sensations in the skin and fat, soft skin, negative stemmer’s sign and hypermobile joints are among the common symptoms observed in lipedema patients [2, 3, 6, 13]. Hypermobility in women with has been reported to contribute to joint damage and increase the risk of cardiovascular disease as seen in Ehlers Danlos Syndrome-Hypermobility Type (EDS-HT) with Beighton score higher than 5 [2, 3, 20, 21]. Thus, hypermobility causes structural changes in lipedema tissue resulting in increased fibrosis, dysfunction of blood vessels and accumulation of interstitial fluid.
\nWomen with lipedema also experience emotional symptoms due to unexplained weight gain including embarrassment, anxiety and depression that impact their overall quality of life [22, 23]. Symptoms may progress in advanced stages of lipedema that might be associated with increased cardiovascular and renal diseases. A study conducted by Herbst el al. in 2015 provides a detailed list of symptoms experienced by lipedema patients [3].
\nDiagnosis of lipedema involves a comprehensive physical exam based on the criteria listed by Wold and colleagues in 1951, [4] medical and surgical history, list of medications that might affect weight or fluid retention and family history. A physical examination includes assessment of the enlarged lower extremities carefully noting the texture of the affected areas such as velvety soft skin that can be found in hypermobility, nodular fat, pain when applying pressure, tenderness upon palpation and accumulation of fluid such as pitting or non-pitting edema which may indicate lymphedema [18, 24]. Bruising caused by increased capillary fragility [6], spider veins and telangiectasia showing on the surface of the skin due to venous insufficiency are also observed in lipedema patients [4, 10].
\nAlthough, there is no cure for lipedema, treatments like liposuction (tumescent and water jet) [25], complete decongestive therapy that includes manual lymphatic drainage [26, 27], compression garments, a healthy diet, physical activity, medications and supplements (statins, selenium, diosmin, amphetamines and butcher’s broom) have been shown to reduce pain, improve lymphatic function, decrease leakage from blood vessels, lessen inflammation and fibrosis and maintain a healthy gut [24, 28, 29, 30, 31, 32, 33, 34].
\nLiposuction is by far the most effective treatment to decrease the fibrotic lipedema fat and thereby maintain mobility which is essential for the welfare of women living with lipedema [35, 36, 37]. Water jet-assisted liposuction has been proven to be as effective as tumescent liposuction. Damage to the lymph vessels has not been show as evidenced in a histological study conducted by Stutz et al. on lipoaspirates collected from lipedema patients [32]. Nevertheless, special care should be taken with lipo-lymphedema patients, where accumulated lymph and or fibrotic tissue should be removed first. Furthermore, follow-up and compression therapy are advised for successful and effective treatment.
\nDeep tissue massage has also been demonstrated to improve the quality of subcutaneous adipose tissue by decreasing pain, fibrosis and fat tissue in women with lipedema [29, 38].
\nAdditionally, a healthy non-inflammatory diet is highly recommended, even though it will not reduce the lipedema tissue, but it might slow the progression of the disease by reducing inflammation and pain, lessen the swelling and ultimately improve quality of life. No one plan works for everyone but a ketogenic diet with low processed carbohydrate and mild physical exercises like walking, swimming, Pilates, yoga and other home excise programs are suggested by lipedema specialists. These activates will help the function of lymphatic pump and maintain a normal metabolism.
\nFinally, it is very important to detect and treat lipedema at early stages thus preventing the complications that might occur due to the progression of disease. These complications comprise eating disorders, sleep apnea, diabetes mellitus, arthritis, hypertension, cellulitis, cardiac and renal disease.
\nThere are distinctive criteria for lipedema which are absent in lymphedema including a negative Stemmer’s sign, minimal pitting edema, thin skin, easy bruising, tenderness and pain [14, 39, 40]. Although lymphatic microaneurysms might develop in the later stages of lipedema leading to secondary lymphedema, imaging techniques like high-resolution cutaneous ultrasonography and magnetic resonance imaging showed no defects in the lymphatic system in early stages [24, 41, 42, 43]. Other methods have also been successfully used to differentiate lipedema from lymphedema which includes tissue dielectric constant and dual-energy X-ray absorptiometry techniques [44, 45, 46, 47, 48].
\nDysfunction of lymphatic vessels results in accumulation of interstitial fluid (edema) in adipose tissues triggering inflammation by the recruitment of macrophages resulting in fibrosis and difficulty with weight loss. As a consequence, adipose tissue loses its elasticity suggesting that lipedema might be a connective tissue disorder [15, 49]. Studies have also indicated that edema might induce growth of lipedema fat as well as hypoxia resulting in adipocyte cell death [50].
\nFurther, morphologic changes in lymphatic vessels and accumulation of interstitial fluid are present in some women with lipedema, with no change in transport of lymphatic fluid, which suggests these individuals might have a higher risk of progressing to lipo-lymphedema especially in advanced stages of lipedema [15, 51]. Accurate diagnosis of lipedema in association with lymphedema is essential for treating and following up of lipedema patients.
\nHormones, genetic factors, leaky blood vessels, dysfunctional lymphatics system, inflammation, hypertrophic adipocytes and interstitial thickening are among the factors that contribute to the pathogenesis of lipedema [10, 12, 15].
\nHormones play an essential role in the etiology of the lipedema, but how they affect the metabolism and function of adipocytes function is still unknown. Studies have shown that hormones, like estrogen and progesterone, have a direct effect on lipogenesis, insulin levels and adipose tissue distribution in the body. Dysregulation of hormonal levels lead to fat dysregulation, impairment of the lipogenesis-lipolysis mechanism, hypertension, insulin resistance and hyperinsulinemia [13, 52, 53]. Hormones might also have an impact on the nervous system which might explain the pain experienced by lipedema patients. Szél et al. hypothesized that alteration in estrogen (or estrogen receptors) maybe involved in the pathogenesis of lipedema by suggesting a link between accumulation of adipose tissue, imbalanced estrogen levels and inflammation of the peripheral and sympathetic nerves of the disease [13].
\nLipedema fat tissue is characterized by hypertrophic adipocytes, inflammatory immune cells, dilation of subdermal blood and lymphatic vessels. We and others have shown a high number of infiltrating macrophages in lipedema adipose tissue detected by the CD68 marker and observed as around blood vessels or as crown-like structures surrounding necrotic adipocytes. In addition to macrophages, mast cells and T-lymphocytes were detected in hyper-vascular areas mainly around blood vessels in lipedema fat tissue which might contribute to capillary permeability and accumulation of interstitial fluid [15, 16, 54].
\nAn article published in 2004 by Taylor et al. showed that accumulation of mast cells in lipedema tissue contributed to increased interstitial fluid, deterioration of adipocytes and potentially elastic fiber fragmentation due to the release of elastase [55], confirming that lipedema is a connective tissue disorder. Adding to that, direct cell-cell interaction between hypertrophic adipocyte and macrophages as well as secreted paracrine factors such as vascular endothelial growth factor (VEGF), a marker of angiogenesis, previously reported in the blood of women with lipedema [56] might be associated with increase in the number of blood vessels, dilation of capillaries, hypoxia, inflammation and tissue fibrosis found in lipedema patients [15, 18, 57].
\nAdipose tissue-derived stem cells are widely studied for their immunomodulatory, anti-inflammatory, anti-fibrotic, anti-apoptotic and pro-angiogenic effects [58, 59, 60], but how ASCs contribute to the development of lipedema has not been investigated yet. Due to their high therapeutic potential, ASCs are now considered an indispensable tool in regenerative medicine [61, 62, 63, 64]. Studies have shown the successful treatment with ASCs for many disease including graft-versus-host disease [65], wound healing [66], cardiovascular [67], inflammatory bowel disease [68], diabetes mellitus [69] and several injuries including kidney and spinal cord [70], bone and craniofacial reconstruction [71, 72], liver cirrhosis [73], multiple sclerosis [74]. In addition to their self-renewal ability, ASCs have the ability to differentiate into multiple lineages, including adipocytes, osteoblasts, chondrocytes, and endothelial cells [75, 76]. Thus, ASCs might play a role in lipedema adiposity by inducing the expansion and differentiation of progenitor adipose-derived stem/progenitor cells (pre-adipocytes) into mature adipocytes (hyperplasia). Suga el at. have shown an increase in proliferation of adipose-derived stem/progenitor cell proliferation using Ki67 and CD34 markers suggesting an increase in adipogenesis, hypoxia, and adipocyte necrosis, at least in one case [16].
\nAdding to that, inflammatory cytokines secreted by hypertrophic adipocytes and factors in the interstitial fluid could stimulate ASC differentiation into mature adipocytes. Alternatively, ASCs produce a plethora of pro- and anti-inflammatory cytokines that might contribute to angiogenesis and inflammation resulting in leaky and fragile blood vessels [77, 78]. Priglinger et al. have characterized lipedema ASCs isolated from liposuction samples and showed an increasing number of endothelial/pericytic cells using CD146 marker in lipedema patients compared to healthy individuals proposing that this increase might be a marker of repair of leaky blood and lymphatic vessels in lipedema tissues [54].
\nAlthough, ASCs might induce adipogenesis in lipedema an in-depth characterization of ASCs is required to confirm this theory. Otherwise, if ASCs prove to have anti-inflammatory, anti-fibrotic or pro-angiogenic effects, then they might be used to lessen tissue damage caused by leaky vessels; hence autologous treatment might be a promising tool for lipedema patients.
\nLipedema is a painful fat disease that should be differentiated from obesity and lymphedema. It is the responsibility of the healthcare provider to determine the accurate diagnosis of the disease for successful treatment and management. Liposuction, hands-on therapy, exercise, and a healthy eating plan are recommended for lipedema patients. Although the etiology of lipedema is complicated, hypertrophic adipocytes, inflammatory cytokines, and macrophages, hypoxia, leaky vessels and accumulation of interstitial fluid contribute to the pathogenesis of the disease and may also help guide treatment.
\nThis work was funded by a grant from the Lipedema Foundation.
\nThe authors declare no conflict of interest.
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