Dielectric constant of several polymers and inorganic materials. (Adapted from Ref 3)
\r\n\t
",isbn:"978-1-83969-164-5",printIsbn:"978-1-83969-163-8",pdfIsbn:"978-1-83969-165-2",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"918540a77975243ee748770aea1f4af2",bookSignature:"Dr. Aakash Goyal",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9651.jpg",keywords:"GWAS, Cereals, Breeding, Disease Resistance, Wheat, Rice, Maize, Drought Tolerance, Genetics, Production, Quality, Yield",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 21st 2020",dateEndSecondStepPublish:"December 4th 2020",dateEndThirdStepPublish:"February 2nd 2021",dateEndFourthStepPublish:"April 23rd 2021",dateEndFifthStepPublish:"June 22nd 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Elected fellow member of the International College of Nutrition (FICN) and Society of Applied Biotechnology (FSAB) with research experience at Agriculture and Agri-Food Canada, Bayer Crop Science, ICARDA, InnoTech Alberta, and Palm Gardens Inc.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"97604",title:"Dr.",name:"Aakash",middleName:null,surname:"Goyal",slug:"aakash-goyal",fullName:"Aakash Goyal",profilePictureURL:"https://mts.intechopen.com/storage/users/97604/images/system/97604.jpg",biography:"Aakash Goyal was born in India, and graduated from MDU, Ajmer (Biology) in 1999, then obtained Master’s in Biotechnology in 2002 from GJU, Hissar specialization in Plant biotechnology & molecular breeding, and PhD. in Genetics and Plant Breeding in 2007 from CCSU, Meerut India, specialization in Wheat Breeding. After completion of PhD, he obtained NSREC Visiting Fellowship (in 2008) and thus, joined the wheat and triticale breeding program at Lethbridge Research Center, Agriculture and Agri Food Canada (AAFC), Lethbridge, AB., Canada. In 2012, he achieved a position as a Wheat Breeder for Bayer Crop Science, Saskatoon, Canada. In 2014 he had the honor to obtain Senior Research Scientist position with International Center of Agriculture Research in Dry Areas (ICARDA). In 2017, he moved back to Canada and joined as Native Plant Research Scientist with InnoTech Alberta. In November 2019 he joined as an Agriculture Specialist with Palm Gardens Inc. to help in breeding and cultivation of Cannabis. In this time (2002-2020), he has published nine Books and 50 research papers, reviewed articles, book chapters and book reviews. He is also an elected fellow member of International College of Nutrition (FICN) and Society of Applied Biotechnology (FSAB).",institutionString:"Palm Gardens Inc. Canada",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"3",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"5",title:"Agricultural and Biological Sciences",slug:"agricultural-and-biological-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"259492",firstName:"Sara",lastName:"Gojević-Zrnić",middleName:null,title:"Mrs.",imageUrl:"https://mts.intechopen.com/storage/users/259492/images/7469_n.png",email:"sara.p@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"596",title:"Crop Plant",subtitle:null,isOpenForSubmission:!1,hash:"8f6c77633a473d10f044598b3768e23f",slug:"crop-plant",bookSignature:"Aakash Goyal",coverURL:"https://cdn.intechopen.com/books/images_new/596.jpg",editedByType:"Edited by",editors:[{id:"97604",title:"Dr.",name:"Aakash",surname:"Goyal",slug:"aakash-goyal",fullName:"Aakash Goyal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5137",title:"Grain Legumes",subtitle:null,isOpenForSubmission:!1,hash:"9af17ac91fc66472889985bd48d3fdb3",slug:"grain-legumes",bookSignature:"Aakash Kumar Goyal",coverURL:"https://cdn.intechopen.com/books/images_new/5137.jpg",editedByType:"Edited by",editors:[{id:"97604",title:"Dr.",name:"Aakash",surname:"Goyal",slug:"aakash-goyal",fullName:"Aakash Goyal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3357",title:"Crop Production",subtitle:null,isOpenForSubmission:!1,hash:"6ed9774e3d9e1d7664640db03e659146",slug:"crop-production",bookSignature:"Aakash Goyal and Muhammad Asif",coverURL:"https://cdn.intechopen.com/books/images_new/3357.jpg",editedByType:"Edited by",editors:[{id:"97604",title:"Dr.",name:"Aakash",surname:"Goyal",slug:"aakash-goyal",fullName:"Aakash Goyal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"6418",title:"Hyperspectral Imaging in Agriculture, Food and Environment",subtitle:null,isOpenForSubmission:!1,hash:"9005c36534a5dc065577a011aea13d4d",slug:"hyperspectral-imaging-in-agriculture-food-and-environment",bookSignature:"Alejandro Isabel Luna Maldonado, Humberto Rodríguez Fuentes and Juan Antonio Vidales Contreras",coverURL:"https://cdn.intechopen.com/books/images_new/6418.jpg",editedByType:"Edited by",editors:[{id:"105774",title:"Prof.",name:"Alejandro Isabel",surname:"Luna Maldonado",slug:"alejandro-isabel-luna-maldonado",fullName:"Alejandro Isabel Luna Maldonado"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"39574",title:"Polymer Dielectric Materials",doi:"10.5772/50638",slug:"polymer-dielectric-materials",body:'The definition for dielectric constant relates to the permittivity of the material (symbol use here ε). The permittivity expresses the ability of a material to polarise in response to an applied field. It is the ratio of the permittivity of the dielectric to the permittivity of a vacuum. Physically it means the greater the polarisation developed by a material in an applied field of given strength, the greater the dielectric constant will be. Traditionally dielectric materials are made from inorganic substances eg. mica and silicon dioxide. However polymers are gaining wider use as dielectric materials. This is due to the easier processing, flexibility, able to tailor made for specific uses and better resistance to chemical attack. As early as mid-60’s polymers eg polyvinyl fluoride [1] and aromatic-containing polymers [2] are used as dielectric materials in capacitors. Further improvement in organic film fabrication was established as revealed in US Patent 4153925. Polymers can be fabricated fairly easily into thin film by solution casting and spin coating, immersion in organic substrate, electron or UV radiation and glow discharge methods. This is mainly due to lower thermal properties such as glass transition and melting temperature which contribute to a lower temperature processing windows. Their solubility is controllable without offsetting their intrinsic properties. In the case of inorganic material and ceramic, they have much higher thermal properties hence temperature requirement leads to an extreme end of processing temperatures. On the other hand polymers cannot stand too high a temperature. Their coefficient of thermal expansion is relatively larger than ceramic materials and susceptible to atmospheric and hydrolytic degradation. Table 1 shows the values of dielectric properties of several polymers with comparisons with several inorganic materials.
Inorganic/ceramics materials have higher dielectric constant than polymers. Water has a relatively high dielectric constant. This is quite cumbersome as any traces of moisture trapped or absorb will dramatically alter the desired dielectric properties. Inorganic materials generally have higher dielectric constant compared to polymeric materials. Intrinsically they contains ions and polar groups which contribute to their high dielectric constant. Air having a dielectric constant of 1.02 is taken as reference dielectric.
Materials | Dielectric constant, ε | Materials | Dielectric constant, ε |
TiO2 | 100 | Fluorinated polyimide | 2.5 – 2.9 |
H2O | 78 | Methylsilsesquioxane | 2.6 – 2.8 |
neoprene | 9.8 | Polyarelene ether | 2.8 – 2.9 |
PVDF | 6.0 | Polyethylene | 2.3 – 2.7 |
SiO2 | 3.9 – 4.5 | Polystyrene | 2.5 – 2.9 |
Fluorosilicate glass | 3.2 – 4.0 | Teflon AF | 2.1 |
Polyimide | 2.8 – 3.2 | Air | 1.02 |
Dielectric constant of several polymers and inorganic materials. (Adapted from Ref 3)
Both dielectrics with low and high dielectric constant are essential in electronic industries. Low dielectric constant is required basically as insulators. They are known as passivation materials. Their applications ranged in isolating signal-carrying conductors from each other, fast signal propagation, interlayer dielectric to reduce the resistance-capacitance (RC) time delays, crosstalk and power dissipation in the high density and high speed integration [4]. They are of necessity in very dense multi-layered IC\'s, wherein coupling between very close metal lines need to be suppressed to prevent degradation in device performance. This role involve packaging and encapsulation. In electronic packaging, they separate interlayers and provide isolated pathways for electronic devices connection in multilayer printed circuit boards. As the trends are towards miniaturization in microprocessor fabrication, any decrease in relative permittivity will reduces the deleterious effect of stray and coupling capacitances. Dielectric naterials are also employed to encapsulate the balls which bridged the die and substrate. This encapsulation is specifically called underfill which helps to protect any circuitary failures as well as reducing thermal mismatch between the bridging layers.(Figure 1) In LED encapsulation low dielectric materials is used for insulation at the lead frame housing.
Application of dielectric polymers in IC packaging
As an active components, designing is geared towards high ε value and are used as polarizable media for capacitors, in apparatus used for the propagation or reflection of electromagnetic waves, and for a variety of artifacts, such as rectifiers and semiconductor devices, piezoelectric transducers, dielectric amplifiers, and memory elements. Despite being insulators, hence non-polar, these materials can be made polar by introducing small amount of impurities. In this state, the material is able to store large amount of charges at small applied electrical field. This is the case with polyvinylidene fluoride when introduced with impurities chlorotrifluoroethylene.[5] Indeed several works have been performed on polymers like polyimide with added Al2O3, BaTiO3 and ZrO3 ‘impurities’ [6,7,8] which showed an improved dielectric constant. Once there is large charge storage, it can be readily released on demand. In a rectifier, a capacitor is used to smooth off the pulsating direct current.
Quantitative treatment of a dielectric in an electric field can be summarized using Clausius–Mossotti equation (1).
P is the molar polarisability,
It shows that relative permittivity
Physically, polarisability is induced when there is electric field applied onto the materials. In the absence of electric field, the electrons are distributed evenly around the nuclei. When the electric field is applied the electron cloud is displaced from the nuclei in the direction opposite to the applied field. This result in separation of positive and negative charges and the molecules behave like an electric dipole. There are three mode of polarizations [10]:
Electronic polarization – slight displacement of electrons with respect to the nucleus.
Atomic polarization – distortion of atomic position in a molecule or lattice
Orientational polarization – For polar molecules, there is a tendency for permanent dipole to align by the electric field to give a net polarization in that direction
When a static electric field is applied on to these materials the dipoles become permanently polarized giving a dielectric constant as εstatic. However if the field changes as when alternating electric current is applied, polarization will also oscillate with the changing electric field. All three modes of polarization contributing to the overall dielectric constant will be dependent on the frequency of the oscillating electric field. Obviously the electronic polarization is instantaneous as it is able to follow in phase with the changing electric field compared to atomic polarization which in turn better able to follow the oscillating electric field compared to the orientational polarization. Certain structures and elements display a higher polarisibility than the others. Aromatic rings, sulphur, iodine and bromine are considered as highly polarisable. The present of these groups induced an increase in dielectric constant. The π bond in the aromatic rings is loosely attached compared to the sigma bond. Therefore it is easily polarized. For large size atoms like bromine and iodine, the electron cloud is so large and further apart from the influence of electrostatic attraction of the positive nucleus. It is expected to display a high polarisibility. This is as oppose to fluorine which has small atomic radius and concentrated negative charge. It is able to hold the electron cloud much tightly resulted in a low polarisability. This will induce a lower dielectric constant.
Free volume is also an important factor in determining the dielectric constant. Free volume is defined as the volume which is not occupied by the polymeric material. The free volume associated with one mole of repeat units of the polymer may be estimated by subtracting the occupied molar volume of a repeat unit, Vo, from the total molar volume, M/ρ, where M is the molar mass of the repeat unit. [10] The fractional free volume Vn is given by Equation (3):
The addition of pendant groups, flexible bridging units, and bulky groups which limit chain packing density have been utilised to enhance free volume. [21] The presence of free volume in the form of pores will similarly result in a decrease in dielectric constant as it being occupied by air whose relative permittivity is about one. A higher fractional free volume means that the density of the material will be lower resulting in a lower polarisible group per unit volume. Replacement of hydrogen with fluorine result in lowering of dielectric constant since fluorine occupies higher volume. Thus beside being low polarisability, introduction of fluorine induce a significant decrease of dielectric constant through an increase in free volume.
Polymers can be polar or non-polar. This feature affect significantly the dielectric properties. Examples of polar polymers include PMMA, PVC, PA (Nylon), PC while non-polar polymers include PTFE (and many other fluoropolymers), PE, PP and PS. Under alternating electric field, polar polymers require sometime to aligned the dipoles. At very low frequencies the dipoles have sufficient time to align with the field before it changes direction. At very high frequencies the dipoles do not have time to align before the field changes direction. At intermediate frequencies the dipoles move but have not completed their movement before the field changes direction and they must realign with the changed field. The electronic polarization and to some extent atomic polarization, is instantaneous weather at high or low frequency for both polar and non polar polymers. Therefore, polar polymers at low frequencies (eg 60 Hz) generally have dielectric constants of between 3 and 9 and at high frequencies (eg 100 Hz) generally have dielectric constants of between 3 and 5. For non-polar polymer the dielectric constant is independent of the alternating current frequency because the electron polarization is effectively instantaneous hence they always have dielectric constants of less than 3. The chain geometry determines whether a polymer is polar or non-polar. If the polymer is held in a fix confirmation, the resulting dipole will depend whether their dipole moments reinforce or cancell each other. In the case of extended configuration of PTFE, the high dipole moment of –CF2- units at each alternating carbon backbone cancelled each other since their vector are in opposite directions. Its dielectric constant therefore is low (2.1). On the other hand, PVC has its dipole moment directing parallel to each other resulting in reinforcement of dipole. Its dielectric constant is 4.5. This is illustrated as in Figure 2.
PTFE (a) and PVC (b) with arrow showing the net dipole moment.
The designing of dielectric material so as to achived the desired dielectric properties should take careful consideration of net polarity of the structure. This has been exemplified by the opposite effect in indiscriminately subsitituting fluorine atom into a polyimide chain resulting in an increase in otherwise low dielectric constant material.[11] There is no dipole polarization contribution for non-polar polymers as found in polar polymers. This different mode of mechanism lead to the resonance spectra in the case of electronic polarization which occur at frequency beyond 1012 Hz. At below this frequency, the relaxation spectra prevail relating to the behavior of dipole polarization. This observation can best be summarized as in the following Figure 3:
Dielectric constant and loss dispersion of dielectric materials against frequency (adapted from Wikipedia)
Relative permittivity can be express in complex form as in Equation (4) below:
It consist of the real part which is dielectric constant and the imaginary part which is the dielectric loss. The ratio between the dielectric loss with the dielectric constant is quantified as tan δ ie:
Dielectric loss result from the inability of polarization process in a molecules to follow the rate of change of the oscillating applied electric field. This arise from the relaxation time (τ) in a polymer which is the time taken for the dipoles to return to its original random orientation. It does not occur instatntaneously but the polarization diminished exponentially. If the relaxation time is smaller or comparable to the rate of oscillating electric field, then there would be no or minimum loss. However when the rate of electric field oscillate well faster than the relaxation time, the polarization cannot follow the oscillating frequency resulting in the energy absorption and dissipated as heat. Dipole polarisability is frequency dependent and can be shown as in Equation (5)
where αd is the dipole polarisability and αo is the low frequency (static) polarisability. It normally occur in the microwave region. Figure 3 above shows the variation in real dielectric constant with the imaginary dielectric loss. There is a sudden drop in dipole polarization region (< 1012 Hz) for dielectric constant ε accompanied with the maximum dielectric loss ε”. This maximum represent the complete failure for the dipole to follow the oscillating electric field beyond which the dipole remain freeze with no effective contribution to the dielectric constant. The mechanism for electronic and atomic polarization occur at higher frequency (shorter wavelength eg. infra-red region). This region involved excitation of electrons which is characterized by the quantized energy level hence is known as resonance behaviour. The dielectric constant display a maximum before a symmetrical drop about a certain frequency. These maximum and minimum represent the optimum polarization in phase with the oscillating frequency. The frequency at which the turning point occur is term the natural frequency ωo. At this point the frequency of applied electric field is at resonant with the natural frequency hence there is a maximum absorption. Consequently this lead to maximum dielectric loss ε’.
Temperature affect dielectric properties. As the temperature is increased the intermolecular forces between polymer chains is broken which enhances thermal agitation. The polar group will be more free to orient allowing it to keep up with the changing electric field. At lower temperature, the segmental motion of the chain is practically freezed and this will reduce the dielectric constant. At sufficiently higher temperature, the dielectric constant is again reduced due to strong thermal motion which disturb the orientation of the dipoles. At this latter stage the polarization effectively contribute minimal dielectric constant. Beside the kinetic energy acquired, free space in the polymer matrix is of necessity so as to induce segmental movement. Throughout the measured frequency and temperature, electronic and atomic polarization are spontaneous. The dipole polarization, on the other hand, would significantly be affected during heat treatment by effectively reducing the relaxation time (τ) since the polymer chain τ would reduced as the temperature is increased hence the polymer segment would be better able to follow in phase with the oscillating electric field. Significant chain and segmental motions occur in polymers and they are identified as follows [39]:
α relaxation: Micro-Brownian motion of the whole chain. Formally this motion is designated as glass transition.
β relaxation: Rotation of polar groups about C-C bond eg. CH2Cl and –COOC2H5, conformational flip of cyclic unit.
γ relaxation: libration of phenyl ring and limited C-H segmental chain movement.
The dielectric loss will show maxima at respective relaxation mechanisms as the temperature is increased. The loss in dielectric can be schematically represented as in the following Figure 4
Schematic dielectric loss curve for polymer as temperature is increased.
The γ relaxation occur at lower temperature as it involved small entities of phenyl rings and C-H units whose motion are readily perturbed at low thermal energy. This is followed by β relaxation and finally α relaxation corresponding to the longer scale segmental motion. The broadness for each peaks signify dispersion in relaxation time as the result of different local environment of polarisable groups.
The earliest model of relaxation behavior is originally derived from Debye relaxation model [12] In this model, real and imaginary part of dielectric constant can be represented as in Figure 5
Debye dielectric dispersion curve.
where
This model relates the dielectric properties with the relaxation time. The relationship between ε’and ε’’ can be formulated by eliminating the parameter ωτ to give Equation (6):
This is a form of a semispherical plot which is popularly known as Cole-Cole plot. See Figure 6.
Cole-Cole Plot showing the relationship between dielectric constant and dielectric loss.
The plot shows that at dielectric constant of infinite frequency, ε∞ and static dielectric constant, εs there will be no loss. Maximum loss occur at the midpoint between the two dielectric values. The larger the different between the static and infinite dielectric constant, the higher will be the loss. This model fit very well with polar small molecular liquids. However, polymeric materials are bigger in size, higher viscosity with entanglement between chains. This contribute to visco-elastic properties which requires some modifications to the original model. It can be noted that the above relationship involved only one specific relaxation time. This is contrary in polymeric system whose relaxation time is dependent on mobility of dipoles which behave differently in varying local environments. This result in distribution in relaxtion time. Modification include Cole and Cole semiemperical equation [13] Davidson and Cole [14] Williams and Watt [15] and Navriliak and Nagami [16]. The last modification lead to the new equation (7):
where α and β is in the range 0 and 1. No physical meaning as yet is assignable to these parameters.[17] This modification result in a broader peak and smaller loss value with asymmetrical in features. The behaviour of dielectric constant and loss at variable frequencies and temperatures is exemplified in the following Figure 7 for polyvinylchloride.
Plot of dielectric constant (a) and dielectric loss with the change in frequency and temperature for polyvinylchloride. (From Ref 18)
Figure 7a shows the variation of ε’ and ε” at the region of glass transition (85 0C) of polyvinylchloride. At the onset of glass transition the PVC showed a relatively low dielectric constant of 4.1 to 3.2 within the measured frequency range. With the increased in temperature, chain mobility begin to increase thus reducing the relaxation time. The dipole polarization of the polymer chain is better able to align in phase with the changing frequency and this account for the increase in dielectric constant as the temperature is increased. However this alignment with the applied oscillating field gradually failed as the frequency is increased. The optimum rate of decreased of dielectric constant occur at higher frequency as the temperature is increased. This correspond to the maximum dielectric loss in Fig 7b. Based on Cole-Cole plot, when there is a big difference in static and infinite dielectric constant, as under high thermal treatment, then the dielectric loss will be correspondingly large. It can be noted that at temperature 128 oC, there is a large dielectric loss occurring at higher frequency compared to those of lower temperature. Glass transition of polymer is a vital consideration that need to take into account during use of polymers as this affect the dielectric properties substantially. Substitution of fluorine into polyimide, for example, only affect the electronic polarization since PI is mostly used at temperature lower then its Tg (<260 oC). At this temperature, no effective polar orientation occurr which reduce any possibility of intrusion effect from this mechanism into the dielectric properties. The following Table 2 present the dielectric constant and loss of commercially used polymers.
Material | Dielectric constant (ε’) | Loss tangent (tan δ) | Frequency (Hz) |
ABS (plastic) | 2.0 – 3.5 | 0.005 – 0.0190 | |
Butyl rubber | 2.35 2.35 | 0.001 0.0009 | 1 MHz 3 GHz |
Gutta percha | 2.6 | ||
HDPE | 1.0 – 5.0 | 0.00004 – 0.001 | |
Kapton (Type 100) (Type 200) | 3.9 2.9 | ||
Neoprene rubber | 6.26 4.0 | 0.038 0.34 | 1 MHz 3 GHz |
Nylon | 3.2 - 5 | ||
Polyamide | 2.5 – 2.6 | ||
Polycarbonate | 2.8 – 3.4 | 0.00066 – 0.01 | |
Polypropylene | 2.2 | ||
Polystyrene | 2.5 – 2.6 | 0.0001 0.00033 | 100 MHz 3 GHz |
PVC | 3 | ||
Silicone (RTV) | 3.6 | ||
Teflon (PTFE) | 2.0 – 2.1 | 0.0005 0.00028 | 100 Hz 3 GHz |
Dielectric parameters for some polymers at various frequencies.
Polymers are often cross-linked to improve their properties. The cross linking or curing process can be conveniently monitored based on relaxation time changes with the progress of reaction. This is exemplified during curing of diglycidylether bisphenol A (DGEBA) with diethyltetraamine (DETA)[19]. During the cross-linking process, the chains are covalently bonded to each other which induce chain rigidity.
Affect of crosslink network on rigidity of polymer chains
This rigidity is proportional to cross-link density henceforth affecting the change in relaxation time. This can be illustrated in the following Figure 8:
Effect of degree of reaction on the α and β relaxation time of DGEBA-DETA system
Figure 8 shows that both the α and β relaxation time increase with the increase in amount of cross-linking reaction. With the increase in cross-link density, the polymer chains are mostly bounded to each other much tighter hence inducing a longer time to return to their original equilibrium configuration. The rate of increase in α relaxation is higher as it approaches glassy state compared to β relaxation as the former relates to the segmental chain motion of larger in scale compared to the latter. The dielectric constant ε and loss is illustrated in the following Figure 9. In Figure 9a there is a significant drop in dielectric constant which correspond to the maximum frequency for dielectric loss in Figure 9b. This transition represent the frequency at which the dipole polarization is completely out of phase with the applied oscillating electric field. The maximum frequency ωmax of dielectric loss was extracted and applied into the equation τ = 1/ ωmax to yield the α relaxation time. It can be observed that as the level of curing is increased the maximum dielectric loss shift towards lower frequency while the change in dielectric constant at αstatic with αinfinity become diminished. This behaviour represent the gradual transition from the rubbery state to glassy state of the polymer with the increase of cross-link density.
Polarizability and free volume are two important factors that influence the dielectric properties as formulated in the Clausius–Mossotti equation. These effects can be exemplified by introducing fluorine into a polymer chains.[20] Fluorination of polyimide film was performed through gaseous phase in a vacuum chamber. The impregnated fluorine content was determined using XPS analysis and the dielectric constant is shown as in following Table 3:
Effect of cross-link density on dielectric constant (ε’ above) and dielectric loss (ε” below) for DGEBA-DETA system
Repeat unit of the polyimde (from Ref 20)
Sample | F1s/C1s(%) | Dielectric constant,ε | |
102(Hz) | 106 (Hz) | ||
F0 | 0 | 2.93 | 2.90 |
F2 | 57.8 | 2.64 | 2.60 |
F3 | 67.7 | 2.42 | 2.41 |
F4 | 78.6 | 2.28 | 2.27 |
F5 | 87.4 | 2.37 | 2.26 |
The effect of Fluorine content on the dielectric constant of a polyimide
Similar result was obtained in a series of polyimides synthesised from starting monomers bearing varying percentage of fluorine content. [21] The decreased in dielectric constant as the fluorine content is increased can be explained as due to the low polarizability of fluorine. The electrons of fluorine being very tightly held and close to the nucleus. The polarizability of the fluorinated polyimides is decreased as the number of fluorine atoms is increased, due to the lower electronic polarizability of a C–F bond relative to that of a C–H bond that has been displaced. [22,23] The free volume concomitantly increases due to the relatively large volume of fluorine compared with hydrogen, which reduces the number of polarizable groups per unit volume.
The effect of free volume can be seen when introducing adamantane into a polyimide chain. [24] Adamantane is a bulky group which induce an increase in the free volume. The dielectric constant achieved was 2.7 at 1 KHz. This value is well below the commercial Kapton H film (25.4 μm) with a dielectric constant of approximately 3.5 at 1 kHz and 3.3 at 10 MHz. Besides, hydrophobicity was reduced thus preventing absorption of moisture. Low dielectric loss is important for a good capacitors and insulation. The strategy of introducing bulky substituents is further exemplified in a commercial Avatrel™ dielectric polymer made up of polynorbonene for passivation applications. It has a dielectric constant of 2.55, a loss tangent less than 0.002. These electrical properties held constant up to above 1 GHz. The bulky structures in these polymers are illustrated in the following Figure 10:
Adamantane structure incorporated into polyimide chain (a, from Ref 12) and the generic structure for polynorbonene (b).
Electrical breakdown occurs when the dielectric strength which is the maximum electric field applicable on dielectric material is exceeded. It underwent catastrophic failure leading to short circuit or blown fuse. This occurs when at a given applied voltage the heat generated due to the losses is greater than the heat dissipated and if the voltage is applied long enough period then the dielectric is unable to reach a state of internal thermal equilibrium. The favourable condition for the occurrence of breakdown is large thickness of the dielectric, high temperature of both the dielectric and the surrounding, continous application of high voltage and large dielectric loss (high tan δ). The last factor is the most important to occur at high frequency. The high humidity in air can similarly affect dielectric breakdown through electrolytic process.
Based on the preceding discussions, designing of polymer dielectric materials can be made using several approaches. The following examples review two approaches undertaken of late namely free volume and copolymerization.
Based on Maxwell-Garnet theory, the presence of second phase of lower dielectric constant in a composite will affect a significant decrease in dielectric constant.[25] This concept was applied in generating foam structure with the introduction of air-filled pores. At least two methods were utilised. One is to synthesised block copolymer of different thermal lability [26] and the other is performing solution etching of soluble component in a composite matrix. [27] The former method involved the use of block copolymer composed of high temperature and high Tg polymer and a second component of lower thermal property which can preferentially undergoes thermal decomposition. One of such a triblock polymer is shown below:
Triblock polyimide structure illustrating the thermally labile and stable segments.
This triblock composed of thermally stable polyimide and thermally labile phosphate ester block. This copolymer is subjected to thermal treatment such that the temperature is sufficient to degrade the thermally labile block and leaving the thermally stable block intact. A small size scale of microphase saparation is then generated with spherical pore morphology, monodispersed in size and discontinuous. These nanopores are filled with air (ε = 1.0) which is responsible for the reduction in dielectric constant. Thermally labile oligomers include polymethylstyrene, polypropylene oxide and polymethylmethacrylate. Nanofoam with dielectric constant of 2.3 was achievable with system made-up from PMDA/4BDAF/PPO triblock of void volume 16%. Figure 11 illustrate the relationship between the void content with the dielectric constant for PMDA/3FDA/PPO triblock system.[28]
Relation between the dielectric constant with the void fractional volume in PMDA/3FDA/PPO triblock system.
In solution etching method, porosity were achieved by solution etching of soluble component in a nanocomposites leaving the chemically stable matrix intact. This was attempted using polyamic acid, a polyimide prepolymer, as the matrix while inorganic TEOS was incorporated through sol-gel method. Once the inorganic phase was homogeneously distributed in the polymer matrix, the composite was thermally cured followed by hydrofluoride etching. This will dissolved away the acid labile inorganic phase with the generation of nanosize closed cell pore of uniform density. The steps involved during its fabrication is illustrated as in the following Scheme (4):
Preparation of porous Polyimide using sol-gel method
The level of porosity is dependent on the TEOS content incorporated into the polymer matrix. Table 4 shows the dependence in dielectric constant on fluorine content and level of porosity based on TEOS content added during the materials fabrication
F (Wt %) | 0% TEO | 10% TEOS | % TEOS | |
0 | 2.71 | 2.84 | 3.41 | |
15 | 2.45 | 2.71 | 3.25 | |
17 | 2.61 | 2.69 | 3.18 | |
33 | 2.50 | 2.62 | 2.98 |
Dielectric constant of a series of polyimides at varying TEOS content
The results above display a general trend of decreasing dielectric constant as the TEOS concentration used during sol gel technique were increased. This was ascribed to an increased in void structures which reduced the dielectric property as the result of the presence of air. There was a linear decreased in dielectric constant as the weight percent of fluorine content in the structures were increased. Further the rate of decrease is almost constant between different TEOS content. Of the four synthesized polyimides, BAPP-BPDA showed the highest dielectric constant since this sample contains no fluorine. The SEM picture for the fracture surface morphology is shown in the following Figure 12.
SEM scan of fracture surface of pure (a) PI/SiO2 10% (b) and PI/SiO2 20 % porosity (c)
Simpsons et al [21] concluded that the presence of fluorine increases the free volume, lower electronic polarization and can either increase or decrease the dielectric constant depending on whether the substitution of the atoms are symmetric or asymmetric.
Copolymerisation of two or more polymers together is a strategy to produce a new materials of tailored dielectric properties. In copolymersation, two or more different monomer units were covalently bound thus producing a synergesic effect of respective constituents. Copolymerisation of polyimide with polysiloxane is popularly performed due to the complementary chemical and mechanical properties between the two. The polyimide has superior thermal and mechanical properties but too intractable to normal processing methods. For example the modulus of polyimides are in the range of 109 to 1012 Pa but their Tg are above 260 oC. On the other hand the polysiloxane is flexible and easily processable beside having a stable thermal degradation (> 400 oC). Copolymers of these materials produce an optimized dielectric material of practical application for several electronic packagings. Attempt was made with the following structures. [29]
Series of PI-polysiloxane copolymers
Their dielectric constant are shown in the following Table 5:
Sample | Dielectric constant at 1 kHz 293 oC | n (Si-O repeat unit) |
S1 | 2.90 | 0 |
S2 | 2.57 | 1 |
S3 | 2.43 | 34 |
Effect of silicone content in silicon-polyimide copolymers on dielectric constant.
The table above shows there is a decreasing trend in dielectric constant with the increase in siloxane units. Silicon is comparatively larger than a carbon atom and the Si - O bond is more flexible than the C - C bond. Thus, the bulky silicone units would be less mobile. Its presence affects the bulk movement of the whole polyimide network which reduces the efficiency of the dipole in reacting to polarity change during treatment with an alternating frequency. Furthermore, the molar polarization significantly decreases as the result of an increase in free volume. Several recent studies have demonstrated a similar trend of a decreasing dielectric constant, with an increasing siloxane content into polyimide structures [30,31]
The traditionally used inorganic material as a dielectric possesses several superior qualities such as excellent thermal, dielectric and magnetic properties. However they are brittle and consume high energy for processing. [32] On the other hand polymers are more flexible, strong resistivity and offer a tractable prosessibility. The disadvantages of polymeric materials are that they possesses lower thermal and dielectric properties. Combining the two materials in the form of nanocomposites offer an alternative in fabricating material of synergesic properties which displayed a tremendous improvement in dielectric properties with high flexibility and ease of processing. Their combination could readily geared towards miniaturization of electronic devices fabrication.
Of late several attempts were made towards this strategy. Incorporation of alumina (Al2O3), barium titanate (BaTiO3), titania (TiO2) and zirconia (ZrO2) into PI matrix were attempted.. [33,34] Several methods were employed in preparing these nanocomposites. It has been established that method of preparation affect the dielectric properties of these materials. A nanocomposite of PI/Al2O3 was prepared by mechanical stirring of prepolymer polyamic acid with the inorganic filler followed by thermal curing. [35] The nanocomposite showed an improved dielectric constant compared to a neat polymer material from about 3.0 to 3.4 at 1 MHz. This values increases correspondingly with the amount of filler loading. A further increase in dielectric constant was achieved when mixing was performed using ultrasonication. It has been shown from SEM result that this improvement was due to a better mixing during the latter treatment. Under these processes, the crystal structure of the inorganic fillers remains intact as shown by XRD data. The effect of good miscibility in improving the dielectric constant was proven when using a 3-Aminopropyltrimethoxysilane-treated (APS) ultrasonication. The APS served as an interface layer between the two immiscible organic PI with inorganic filler which reduced any agglomeration between the different phases. This is brought about possibly through the formation of hydrogen bond between the amine moeity of APS with the polar group of polyimide while the inorganic part of the methoxysilane of APS form secondary interaction with the inorganic fillers. Figure 13 reveals the SEM images of PI/ Al2O3 composites doped by the treated Al2O3 powder.
PA0 demonstrated a neat and clean morphology. The Al2O3 particles were homogeneously dispersed into PI matrix in all PA10, PA20 and PA30. The inset images revealed the average size of Al2O3 was around 2µm - 4µm. There was no obvious aggregation observed suggesting the improved compatibility between PI matrix and Al2O3 attributed to the APS coupling agent. The bahaviour of PI-nanocomposites for BaTiO3, TiO2 and ZrO2 displayed similar trend with that of PI-Al2O3 nanocomposites. They can be summarized as in the following Figures 14:
The morphology of PA0, PA10, PA20 and PA30 (a, b, c and d), respectively.
Dielectric constant of PI/inorganic (a) with 30 wt% inorganic content at varying frequency and (b) at 1MHz for several type of inorganic fillers.
All composite systems displayed a decreased in dielectric constant with the increase in frequencies. The dielectric constants increased as the inorganic filler content were increased. This can be attributed to the increase in polarizability group with the incorporation of the inorganic fillers which replace significant part of the PI in the matrix. As the result the polarizable units per unit volume and the space charge polarizability which occurred at the interfaces between PI matrix and inorganic particles were increased. Fig 13(a) shows the dielectric constant of PI/BaTiO3 composite films demonstrating the highest value of dielectric constant followed by PI/TiO2, PI/Al2O3, PI/ZrO2 and neat PI films. Apparently this property is dependent on the dielectric constant of the respective fillers. BaTiO3 was known to display highest value of dielectric constant [36] followed by TiO2, ZrO2 and Al2O3 in their neat form. BaTiO3 possesed perovskite structure which is capable to polarize in the absence of electric field. This feature remains in the composite as the crystal structure remains intact as established in XRD data. The low dielectric constant for PI/ZrO2 was attributed to the poor compatibility between phases resulted in the presence of voids and even led to cracks. The presence of voids naturally induce a low dielectric constant.
Several models were proposed in predicting the dielectric constant of the composites which include Maxwell-Wagner model, Logarithmic Mixing Law and Bruggeman Model. [37] These models allow designing of composite materials based on respective dielectric constant of the polymer, inorganic filler, composition ratio as well as the filler sizes. The slight discrepancy of these models which do not fit to most composite systems are mainly due to inconsistency in treatment for the interphase interaction hence further modification is required. An interphase interaction factor, K, was introduced during fitting into this models.[38] A typical plot of composite dielectric constant with respect to the volume fraction of the fillers is illustrated in the following Figure 15:
The prediction of the effective dielectric constant as a function of filler volume fraction for different K values. (a) The case of εpolymer > εfiller. (b) The case of εpolymer > εfiller (Adapted from Ref 38)
At K = 0, there is no interaction between phases while a high K values showed a strong interaction. This interaction also dependent on the filler sizes. For a given volume fraction filler, a smaller particle size has a larger fraction of interphase volume in the region between the filler and the matrix granting more polarization to operate. Thus they lead to a relative increase in dielectric constant.
A major concern with polymer/ceramic composites is the heterogeneity in phase which lead to formation of cracks and voids. This effect is known as Maxwell-Wagner effect which reduce the dielectric constant. A more serious type of heterogeneity is that the composite comprised of conductive inorganic fillers which could lead to a mistaken interpretation of dipole polarization occurring at very low frequency region.
Polymers offer an alternative to the traditionally inorganic and ceramic material as dielectric amterials. This is due to their highly flexible, tractable processing, good chemical stability and readily tunable properties. The main drawback is they have lower thermal stability which limit their wider applications. Generally their dielectric constant is lower than non-polymeric materials. The mechanism which contribute to the dielectric properties are the interaction of electric field with electronic, atomic and dipole poalarization. These are dependent on polarizabity of constituents structure and the free volume as formulated in Clausius-Mossotti equation. The electronic and to some extent the atomic polarization are instantaneous throughout the measureable range of frequencies. However in dipole polarization there is relaxation time allowing an exponential decay of motion to return to equilibrium state. This different behavior contribute significantly to the values of dielectric constant and dielectric loss. These properties can be utilized to detect for any local or segmental motion during change in frequency and temperature treatment. Dielectric properties can be design by introducing polarizable groups into polymer chains, increasing free volume by inducing porosity as well as copolymerization. Increasing dielectric constant can be effectively made by producing nanocomposites with inorganic fillers possessing high dielectric constant.
The author wish to express a grateful acknowledgement to Universiti Sains Malaysia for financial support through Short Term and Research University (Individual) Grants awarded for the accomplishment of related works quoted in this paper.
Generating functions are a powerful tool for solving problems in number theory, combinatorics, algebra, probability theory, and other fields of mathematics. One of the advantages of generating functions is that an infinite number sequence can be represented in a form of a single expression. Many authors have studied generating functions and their properties and found applications for them (for instance, Comtet [1], Flajolet and Sedgewick [2], Graham et al. [3], Robert [4], Stanley [5], and Wilf [6]).
\nGenerating functions have an important role in the study of polynomials. Vast investigations related to the generating functions for many polynomials can be found in many books and articles (e.g., see [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]).
\nA special place in this area is occupied by research in the field of obtaining new identities for polynomials and special numbers with using their generating functions. Interesting results in the field of obtaining new identities for polynomials can be found in some recent works by Simsek [18, 19, 20], Kim et al. [21, 22], and Ryoo [23, 24, 25].
\nAnother trend in study of polynomials is getting new representation and explicit formulas for those polynomials. For instance, Qi has recently established explicit formulas for the generalized Motzkin numbers in [26] and the central Delannoy numbers in [27]. One can find interesting results in papers of Srivastava [28, 29], Cenkci [30], and Boyadzhiev [31].
\nIn this chapter, we obtain some interesting properties of polynomials defined by generating functions of the form \n
According to Stanley [32], ordinary generating functions are defined as follows:
\n\nDefinition 1. An ordinary generating function of the sequence \n
Kruchinin et al. [33, 34, 35] introduced the mathematical notion of the composita of a given generating function, which can be used for calculating the coefficients of a composition of generating functions.
\n\nDefinition 2. The composita of the generating function \n
where \n
Using the expression of the composita of a given generating function \n
Compositae also can be used for calculating the coefficients of generating functions obtained by addition, multiplication, composition, reciprocation, and compositional inversion of generating functions (for details see [33, 34, 35]).
\nBy the reciprocal generating function we mean the following [6]:
\n\nDefinition 1. A reciprocal generating function \n
By the compositional inverse generating function we mean the following:
\n\nDefinition 2. A compositional inverse \n
Also the compositional inverse can be written as \n
For example, we will use the following formulas:
\nIf we consider the composition \n
If we consider the composition \n
Let us consider a special case of generating functions that can be presented as the product of the powers of generating functions \n
\nTheorem 1. If \n
\nFor the composition of generating functions \n
\n
\nFor the compositional inverse generating function \n
\n
\nWe have the following identities\n
\nand\n
\n\nwhere \n
\nProof. First we get the \n
Hence, the composita of \n
Using Eqs. (6) and (13), we get Eq. (9).
\nAccording to [36], the composita of the compositional inverse generating function \n
where \n
For getting the composita of the compositional inverse generating function \n
Then we get the \n
Hence, the composita of Eq. (15) is
Using Eqs. (14) and (17), we get
For \n
Applying Eq. (7) for the composition \n
Applying Eq. (7) for the composition \n
□
\nAs an application of Theorem 1, we present several examples of its usage for such polynomials as the Bernoulli, Euler, Frobenius-Euler, Sylvester, Laguerre, Abel, Bessel, Stirling, Narumi, Peters, Gegenbauer, and Meixner.
\nThe generalized Bernoulli polynomials are defined by the following generating function [37, 38]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the generalized Bernoulli polynomials:
The generalized Euler polynomials are defined by the following generating function [37]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the generalized Euler polynomials:
The Frobenius-Euler polynomials are defined by the following generating function [39]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Frobenius-Euler polynomials:
The generalized Sylvester polynomials are defined by the following generating function [40]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the generalized Sylvester polynomials:
The generalized Laguerre polynomials are defined by the following generating function [8]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the generalized Laguerre polynomials:
The Abel polynomials are defined by the following generating function [8, 41]:
where \n
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Abel polynomials:
The Bessel polynomials are defined by the following generating function [8]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Bessel polynomials:
The Stirling polynomials are defined by the following generating function [8, 42]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Stirling polynomials:
The Narumi polynomials are defined by the following generating function [8]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Narumi polynomials:
The Peters polynomials are defined by the following generating function [8]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Peters polynomials:
The Gegenbauer polynomials are defined by the following generating function [43]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Gegenbauer polynomials:
and
\nThe Meixner polynomials of the first kind are defined by the following generating function [8, 44]:
where
According to Eq. (13), the composita for the generating function \n
The triangular form of this composita is
Using Eq. (17), the composita for the compositional inverse generating function \n
The triangular form of this composita is
Also we can get the following new identities for the Meixner polynomials of the first kind:
and
\nIn this chapter, we find new explicit formulas and identities for such polynomials as the generalized Bernoulli, generalized Euler, Frobenius-Euler, generalized Sylvester, generalized Laguerre, Abel, Bessel, Stirling, Narumi, Peters, Gegenbauer, and Meixner polynomials that are defined by generating functions of the form \n
A lot of studies have recently showed that polynomials are a solution for practical problems related to modeling, quantum mechanics, and other areas. So a study of obtaining explicit formulas and representations of polynomials will be important and influential. Also the further research can be conducted to find practical means of obtained properties.
\nThis work was partially funded by the Russian Foundation for Basic Research and the government of the Tomsk region of Russian Federation (Grants No. 18-41-703006) and the Ministry of Education and Science of Russian Federation (Government Order No. 2.8172.2017/8.9, TUSUR).
\nThis is a brief overview of the main steps involved in publishing with IntechOpen Compacts, Monographs and Edited Books. Once you submit your proposal you will be appointed a Author Service Manager who will be your single point of contact and lead you through all the described steps below.
",metaTitle:"Publishing Process Steps and Descriptions",metaDescription:"This is a brief overview of the main steps involved in publishing with InTechOpen Compacts, Monographs and Edited Books. Once you submit your proposal you will be appointed a Publishing Process Manager who will be your single point of contact and lead you through all the described steps below.",metaKeywords:null,canonicalURL:"page/publishing-process-steps",contentRaw:'[{"type":"htmlEditorComponent","content":"1. SEND YOUR PROPOSAL
\\n\\nPlease complete the publishing proposal form. The completed form should serve as an overview of your future Compacts, Monograph or Edited Book. Once submitted, your publishing proposal will be sent for evaluation, and a notice of acceptance or rejection will be sent within 10 to 30 working days from the date of submission.
\\n\\n2. SUBMIT YOUR MANUSCRIPT
\\n\\nAfter approval, you will proceed in submitting your full-length manuscript. 50-130 pages for compacts, 130-500 for Monographs & Edited Books.Your full-length manuscript must follow IntechOpen's Author Guidelines and comply with our publishing rules. Once the manuscript is submitted, but before it is forwarded for peer review, it will be screened for plagiarism.
\\n\\n3. PEER REVIEW RESULTS
\\n\\nExternal reviewers will evaluate your manuscript and provide you with their feedback. You may be asked to revise your draft, or parts of your draft, provide additional information and make any other necessary changes according to their comments and suggestions.
\\n\\n4. ACCEPTANCE AND PRICE QUOTE
\\n\\nIf the manuscript is formally accepted after peer review you will receive a formal Notice of Acceptance, and a price quote.
\\n\\nThe Open Access Publishing Fee of your IntechOpen Compacts, Monograph or Edited Book depends on the volume of the publication and includes: project management, editorial and peer review services, technical editing, language copyediting, cover design and book layout, book promotion and ISBN assignment.
\\n\\nWe will send you your price quote and after it has been accepted (by both the author and the publisher), both parties will sign a Statement of Work binding them to adhere to the agreed upon terms.
\\n\\nAt this step you will also be asked to accept the Copyright Agreement.
\\n\\n5. LANGUAGE COPYEDITING, TECHNICAL EDITING AND TYPESET PROOF
\\n\\nYour manuscript will be sent to SPi Global, a leader in content solution services, for language copyediting. You will then receive a typeset proof formatted in XML and available online in HTML and PDF to proofread and check for completeness. The first typeset proof of your manuscript is usually available 10 days after its original submission.
\\n\\nAfter we receive your proof corrections and a final typeset of the manuscript is approved, your manuscript is sent to our in house DTP department for technical formatting and online publication preparation.
\\n\\nAdditionally, you will be asked to provide a profile picture (face or chest-up portrait photograph) and a short summary of the book which is required for the book cover design.
\\n\\n6. INVOICE PAYMENT
\\n\\nThe invoice is generally paid by the author, the author’s institution or funder. The payment can be made by credit card from your Author Panel (one will be assigned to you at the beginning of the project), or via bank transfer as indicated on the invoice. We currently accept the following payment options:
\\n\\nIntechOpen will help you complete your payment safely and securely, keeping your personal, professional and financial information safe.
\\n\\n7. ONLINE PUBLICATION, PRINT AND DELIVERY OF THE BOOK
\\n\\nIntechOpen authors can choose whether to publish their book online only or opt for online and print editions. IntechOpen Compacts, Monographs and Edited Books will be published on www.intechopen.com. If ordered, print copies are delivered by DHL within 12 to 15 working days.
\\n\\nIf you feel that IntechOpen Compacts, Monographs or Edited Books are the right publishing format for your work, please fill out the publishing proposal form. For any specific queries related to the publishing process, or IntechOpen Compacts, Monographs & Edited Books in general, please contact us at book.department@intechopen.com
\\n"}]'},components:[{type:"htmlEditorComponent",content:'1. SEND YOUR PROPOSAL
\n\nPlease complete the publishing proposal form. The completed form should serve as an overview of your future Compacts, Monograph or Edited Book. Once submitted, your publishing proposal will be sent for evaluation, and a notice of acceptance or rejection will be sent within 10 to 30 working days from the date of submission.
\n\n2. SUBMIT YOUR MANUSCRIPT
\n\nAfter approval, you will proceed in submitting your full-length manuscript. 50-130 pages for compacts, 130-500 for Monographs & Edited Books.Your full-length manuscript must follow IntechOpen's Author Guidelines and comply with our publishing rules. Once the manuscript is submitted, but before it is forwarded for peer review, it will be screened for plagiarism.
\n\n3. PEER REVIEW RESULTS
\n\nExternal reviewers will evaluate your manuscript and provide you with their feedback. You may be asked to revise your draft, or parts of your draft, provide additional information and make any other necessary changes according to their comments and suggestions.
\n\n4. ACCEPTANCE AND PRICE QUOTE
\n\nIf the manuscript is formally accepted after peer review you will receive a formal Notice of Acceptance, and a price quote.
\n\nThe Open Access Publishing Fee of your IntechOpen Compacts, Monograph or Edited Book depends on the volume of the publication and includes: project management, editorial and peer review services, technical editing, language copyediting, cover design and book layout, book promotion and ISBN assignment.
\n\nWe will send you your price quote and after it has been accepted (by both the author and the publisher), both parties will sign a Statement of Work binding them to adhere to the agreed upon terms.
\n\nAt this step you will also be asked to accept the Copyright Agreement.
\n\n5. LANGUAGE COPYEDITING, TECHNICAL EDITING AND TYPESET PROOF
\n\nYour manuscript will be sent to SPi Global, a leader in content solution services, for language copyediting. You will then receive a typeset proof formatted in XML and available online in HTML and PDF to proofread and check for completeness. The first typeset proof of your manuscript is usually available 10 days after its original submission.
\n\nAfter we receive your proof corrections and a final typeset of the manuscript is approved, your manuscript is sent to our in house DTP department for technical formatting and online publication preparation.
\n\nAdditionally, you will be asked to provide a profile picture (face or chest-up portrait photograph) and a short summary of the book which is required for the book cover design.
\n\n6. INVOICE PAYMENT
\n\nThe invoice is generally paid by the author, the author’s institution or funder. The payment can be made by credit card from your Author Panel (one will be assigned to you at the beginning of the project), or via bank transfer as indicated on the invoice. We currently accept the following payment options:
\n\nIntechOpen will help you complete your payment safely and securely, keeping your personal, professional and financial information safe.
\n\n7. ONLINE PUBLICATION, PRINT AND DELIVERY OF THE BOOK
\n\nIntechOpen authors can choose whether to publish their book online only or opt for online and print editions. IntechOpen Compacts, Monographs and Edited Books will be published on www.intechopen.com. If ordered, print copies are delivered by DHL within 12 to 15 working days.
\n\nIf you feel that IntechOpen Compacts, Monographs or Edited Books are the right publishing format for your work, please fill out the publishing proposal form. For any specific queries related to the publishing process, or IntechOpen Compacts, Monographs & Edited Books in general, please contact us at book.department@intechopen.com
\n'}]},successStories:{items:[]},authorsAndEditors:{filterParams:{sort:"featured,name"},profiles:[{id:"6700",title:"Dr.",name:"Abbass A.",middleName:null,surname:"Hashim",slug:"abbass-a.-hashim",fullName:"Abbass A. Hashim",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/6700/images/1864_n.jpg",biography:"Currently I am carrying out research in several areas of interest, mainly covering work on chemical and bio-sensors, semiconductor thin film device fabrication and characterisation.\nAt the moment I have very strong interest in radiation environmental pollution and bacteriology treatment. The teams of researchers are working very hard to bring novel results in this field. I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. I have served as the editor for many books, been a member of the editorial board in science journals, have published many papers and hold many patents.",institutionString:null,institution:{name:"Sheffield Hallam University",country:{name:"United Kingdom"}}},{id:"54525",title:"Prof.",name:"Abdul Latif",middleName:null,surname:"Ahmad",slug:"abdul-latif-ahmad",fullName:"Abdul Latif Ahmad",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"20567",title:"Prof.",name:"Ado",middleName:null,surname:"Jorio",slug:"ado-jorio",fullName:"Ado Jorio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidade Federal de Minas Gerais",country:{name:"Brazil"}}},{id:"47940",title:"Dr.",name:"Alberto",middleName:null,surname:"Mantovani",slug:"alberto-mantovani",fullName:"Alberto Mantovani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"12392",title:"Mr.",name:"Alex",middleName:null,surname:"Lazinica",slug:"alex-lazinica",fullName:"Alex Lazinica",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/12392/images/7282_n.png",biography:"Alex Lazinica is the founder and CEO of IntechOpen. After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. Today his focus is on defining the growth and development strategy for the company.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"19816",title:"Prof.",name:"Alexander",middleName:null,surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/19816/images/1607_n.jpg",biography:"Alexander I. Kokorin: born: 1947, Moscow; DSc., PhD; Principal Research Fellow (Research Professor) of Department of Kinetics and Catalysis, N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow.\r\nArea of research interests: physical chemistry of complex-organized molecular and nanosized systems, including polymer-metal complexes; the surface of doped oxide semiconductors. He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). He is the member of many Pharmaceutical Associations and acts as a reviewer of scientific journals and European projects under different research areas such as: drug delivery systems, nanotechnology and pharmaceutical biotechnology. Dr. Sezer is the author of many scientific publications in peer-reviewed journals and poster communications. Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. I received a B.Eng. degree in Computer Engineering with First Class Honors in 2008 from Prince of Songkla University, Songkhla, Thailand, where I received a Ph.D. degree in Electrical Engineering. My research interests are primarily in the area of biomedical signal processing and classification notably EMG (electromyography signal), EOG (electrooculography signal), and EEG (electroencephalography signal), image analysis notably breast cancer analysis and optical coherence tomography, and rehabilitation engineering. I became a student member of IEEE in 2008. During October 2011-March 2012, I had worked at School of Computer Science and Electronic Engineering, University of Essex, Colchester, Essex, United Kingdom. In addition, during a B.Eng. I had been a visiting research student at Faculty of Computer Science, University of Murcia, Murcia, Spain for three months.\n\nI have published over 40 papers during 5 years in refereed journals, books, and conference proceedings in the areas of electro-physiological signals processing and classification, notably EMG and EOG signals, fractal analysis, wavelet analysis, texture analysis, feature extraction and machine learning algorithms, and assistive and rehabilitative devices. I have several computer programming language certificates, i.e. Sun Certified Programmer for the Java 2 Platform 1.4 (SCJP), Microsoft Certified Professional Developer, Web Developer (MCPD), Microsoft Certified Technology Specialist, .NET Framework 2.0 Web (MCTS). I am a Reviewer for several refereed journals and international conferences, such as IEEE Transactions on Biomedical Engineering, IEEE Transactions on Industrial Electronics, Optic Letters, Measurement Science Review, and also a member of the International Advisory Committee for 2012 IEEE Business Engineering and Industrial Applications and 2012 IEEE Symposium on Business, Engineering and Industrial Applications.",institutionString:null,institution:{name:"Joseph Fourier University",country:{name:"France"}}},{id:"55578",title:"Dr.",name:"Antonio",middleName:null,surname:"Jurado-Navas",slug:"antonio-jurado-navas",fullName:"Antonio Jurado-Navas",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/55578/images/4574_n.png",biography:"Antonio Jurado-Navas received the M.S. degree (2002) and the Ph.D. degree (2009) in Telecommunication Engineering, both from the University of Málaga (Spain). He first worked as a consultant at Vodafone-Spain. From 2004 to 2011, he was a Research Assistant with the Communications Engineering Department at the University of Málaga. In 2011, he became an Assistant Professor in the same department. From 2012 to 2015, he was with Ericsson Spain, where he was working on geo-location\ntools for third generation mobile networks. Since 2015, he is a Marie-Curie fellow at the Denmark Technical University. His current research interests include the areas of mobile communication systems and channel modeling in addition to atmospheric optical communications, adaptive optics and statistics",institutionString:null,institution:{name:"University of Malaga",country:{name:"Spain"}}}],filtersByRegion:[{group:"region",caption:"North America",value:1,count:5766},{group:"region",caption:"Middle and South America",value:2,count:5227},{group:"region",caption:"Africa",value:3,count:1717},{group:"region",caption:"Asia",value:4,count:10367},{group:"region",caption:"Australia and Oceania",value:5,count:897},{group:"region",caption:"Europe",value:6,count:15790}],offset:12,limit:12,total:118189},chapterEmbeded:{data:{}},editorApplication:{success:null,errors:{}},ofsBooks:{filterParams:{topicId:"14"},books:[{type:"book",id:"10666",title:"Noble Metals Recent Advanced Studies and Applications",subtitle:null,isOpenForSubmission:!0,hash:"7322b325b1276e2b4185a7db798d588a",slug:null,bookSignature:"Dr. Mousumi Sen",coverURL:"https://cdn.intechopen.com/books/images_new/10666.jpg",editedByType:null,editors:[{id:"310218",title:"Dr.",name:"Mousumi",surname:"Sen",slug:"mousumi-sen",fullName:"Mousumi Sen"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10668",title:"Sustainable Concrete",subtitle:null,isOpenForSubmission:!0,hash:"55856c6a8bc3a5b21dae5a1af09a56b6",slug:null,bookSignature:"Prof. Hosam M. Saleh",coverURL:"https://cdn.intechopen.com/books/images_new/10668.jpg",editedByType:null,editors:[{id:"144691",title:"Prof.",name:"Hosam",surname:"Saleh",slug:"hosam-saleh",fullName:"Hosam Saleh"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10669",title:"Corrosion",subtitle:null,isOpenForSubmission:!0,hash:"4a76d54f8a40fc2e7002a8d13fd617c1",slug:null,bookSignature:"Dr. Fahmina Zafar, Dr. Anujit Ghosal and Dr. Eram Sharmin",coverURL:"https://cdn.intechopen.com/books/images_new/10669.jpg",editedByType:null,editors:[{id:"89672",title:"Dr.",name:"Fahmina",surname:"Zafar",slug:"fahmina-zafar",fullName:"Fahmina Zafar"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10670",title:"Properties and Applications of Alginates",subtitle:null,isOpenForSubmission:!0,hash:"062083e53cc5c808af597de6426cea06",slug:null,bookSignature:"Dr. Irem Deniz, Dr. Esra Imamoglu and Dr. Tugba Keskin Gundogdu",coverURL:"https://cdn.intechopen.com/books/images_new/10670.jpg",editedByType:null,editors:[{id:"204855",title:"Dr.",name:"Irem",surname:"Deniz",slug:"irem-deniz",fullName:"Irem Deniz"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10941",title:"Ferrite",subtitle:null,isOpenForSubmission:!0,hash:"f6a323bfa4565d7c676bc3733b4983b0",slug:null,bookSignature:"Dr. Maaz Khan",coverURL:"https://cdn.intechopen.com/books/images_new/10941.jpg",editedByType:null,editors:[{id:"107765",title:"Dr.",name:"Maaz",surname:"Khan",slug:"maaz-khan",fullName:"Maaz Khan"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],filtersByTopic:[{group:"topic",caption:"Agricultural and Biological Sciences",value:5,count:14},{group:"topic",caption:"Biochemistry, Genetics and Molecular Biology",value:6,count:3},{group:"topic",caption:"Business, Management and Economics",value:7,count:1},{group:"topic",caption:"Chemistry",value:8,count:7},{group:"topic",caption:"Computer and Information Science",value:9,count:6},{group:"topic",caption:"Earth and Planetary Sciences",value:10,count:7},{group:"topic",caption:"Engineering",value:11,count:15},{group:"topic",caption:"Environmental Sciences",value:12,count:2},{group:"topic",caption:"Immunology and Microbiology",value:13,count:3},{group:"topic",caption:"Materials Science",value:14,count:5},{group:"topic",caption:"Mathematics",value:15,count:1},{group:"topic",caption:"Medicine",value:16,count:24},{group:"topic",caption:"Neuroscience",value:18,count:1},{group:"topic",caption:"Pharmacology, Toxicology and Pharmaceutical Science",value:19,count:2},{group:"topic",caption:"Physics",value:20,count:2},{group:"topic",caption:"Psychology",value:21,count:4},{group:"topic",caption:"Social Sciences",value:23,count:2},{group:"topic",caption:"Technology",value:24,count:1},{group:"topic",caption:"Veterinary Medicine and Science",value:25,count:1}],offset:12,limit:12,total:5},popularBooks:{featuredBooks:[{type:"book",id:"9385",title:"Renewable Energy",subtitle:"Technologies and Applications",isOpenForSubmission:!1,hash:"a6b446d19166f17f313008e6c056f3d8",slug:"renewable-energy-technologies-and-applications",bookSignature:"Tolga Taner, Archana Tiwari and Taha Selim Ustun",coverURL:"https://cdn.intechopen.com/books/images_new/9385.jpg",editors:[{id:"197240",title:"Associate Prof.",name:"Tolga",middleName:null,surname:"Taner",slug:"tolga-taner",fullName:"Tolga Taner"}],equalEditorOne:{id:"186791",title:"Dr.",name:"Archana",middleName:null,surname:"Tiwari",slug:"archana-tiwari",fullName:"Archana Tiwari",profilePictureURL:"https://mts.intechopen.com/storage/users/186791/images/system/186791.jpg",biography:"Dr. Archana Tiwari is Associate Professor at Amity University, India. Her research interests include renewable sources of energy from microalgae and further utilizing the residual biomass for the generation of value-added products, bioremediation through microalgae and microbial consortium, antioxidative enzymes and stress, and nutraceuticals from microalgae. She has been working on algal biotechnology for the last two decades. She has published her research in many international journals and has authored many books and chapters with renowned publishing houses. She has also delivered talks as an invited speaker at many national and international conferences. Dr. Tiwari is the recipient of several awards including Researcher of the Year and Distinguished Scientist.",institutionString:"Amity University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Amity University",institutionURL:null,country:{name:"India"}}},equalEditorTwo:{id:"197609",title:"Prof.",name:"Taha Selim",middleName:null,surname:"Ustun",slug:"taha-selim-ustun",fullName:"Taha Selim Ustun",profilePictureURL:"https://mts.intechopen.com/storage/users/197609/images/system/197609.jpeg",biography:"Dr. Taha Selim Ustun received a Ph.D. in Electrical Engineering from Victoria University, Melbourne, Australia. He is a researcher with the Fukushima Renewable Energy Institute, AIST (FREA), where he leads the Smart Grid Cybersecurity Laboratory. Prior to that, he was a faculty member with the School of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA. His current research interests include power systems protection, communication in power networks, distributed generation, microgrids, electric vehicle integration, and cybersecurity in smart grids. He serves on the editorial boards of IEEE Access, IEEE Transactions on Industrial Informatics, Energies, Electronics, Electricity, World Electric Vehicle and Information journals. Dr. Ustun is a member of the IEEE 2004 and 2800, IEC Renewable Energy Management WG 8, and IEC TC 57 WG17. He has been invited to run specialist courses in Africa, India, and China. He has delivered talks for the Qatar Foundation, the World Energy Council, the Waterloo Global Science Initiative, and the European Union Energy Initiative (EUEI). His research has attracted funding from prestigious programs in Japan, Australia, the European Union, and North America.",institutionString:"Fukushima Renewable Energy Institute, AIST (FREA)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"National Institute of Advanced Industrial Science and Technology",institutionURL:null,country:{name:"Japan"}}},equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8985",title:"Natural Resources Management and Biological Sciences",subtitle:null,isOpenForSubmission:!1,hash:"5c2e219a6c021a40b5a20c041dea88c4",slug:"natural-resources-management-and-biological-sciences",bookSignature:"Edward R. Rhodes and Humood Naser",coverURL:"https://cdn.intechopen.com/books/images_new/8985.jpg",editors:[{id:"280886",title:"Prof.",name:"Edward R",middleName:null,surname:"Rhodes",slug:"edward-r-rhodes",fullName:"Edward R Rhodes"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9027",title:"Human Blood Group Systems and Haemoglobinopathies",subtitle:null,isOpenForSubmission:!1,hash:"d00d8e40b11cfb2547d1122866531c7e",slug:"human-blood-group-systems-and-haemoglobinopathies",bookSignature:"Osaro Erhabor and Anjana Munshi",coverURL:"https://cdn.intechopen.com/books/images_new/9027.jpg",editors:[{id:"35140",title:null,name:"Osaro",middleName:null,surname:"Erhabor",slug:"osaro-erhabor",fullName:"Osaro Erhabor"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7841",title:"New Insights Into Metabolic Syndrome",subtitle:null,isOpenForSubmission:!1,hash:"ef5accfac9772b9e2c9eff884f085510",slug:"new-insights-into-metabolic-syndrome",bookSignature:"Akikazu Takada",coverURL:"https://cdn.intechopen.com/books/images_new/7841.jpg",editors:[{id:"248459",title:"Dr.",name:"Akikazu",middleName:null,surname:"Takada",slug:"akikazu-takada",fullName:"Akikazu Takada"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8558",title:"Aerodynamics",subtitle:null,isOpenForSubmission:!1,hash:"db7263fc198dfb539073ba0260a7f1aa",slug:"aerodynamics",bookSignature:"Mofid Gorji-Bandpy and Aly-Mousaad Aly",coverURL:"https://cdn.intechopen.com/books/images_new/8558.jpg",editors:[{id:"35542",title:"Prof.",name:"Mofid",middleName:null,surname:"Gorji-Bandpy",slug:"mofid-gorji-bandpy",fullName:"Mofid Gorji-Bandpy"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9668",title:"Chemistry and Biochemistry of Winemaking, Wine Stabilization and Aging",subtitle:null,isOpenForSubmission:!1,hash:"c5484276a314628acf21ec1bdc3a86b9",slug:"chemistry-and-biochemistry-of-winemaking-wine-stabilization-and-aging",bookSignature:"Fernanda Cosme, Fernando M. Nunes and Luís Filipe-Ribeiro",coverURL:"https://cdn.intechopen.com/books/images_new/9668.jpg",editors:[{id:"186819",title:"Prof.",name:"Fernanda",middleName:null,surname:"Cosme",slug:"fernanda-cosme",fullName:"Fernanda Cosme"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7847",title:"Medical Toxicology",subtitle:null,isOpenForSubmission:!1,hash:"db9b65bea093de17a0855a1b27046247",slug:"medical-toxicology",bookSignature:"Pınar Erkekoglu and Tomohisa Ogawa",coverURL:"https://cdn.intechopen.com/books/images_new/7847.jpg",editors:[{id:"109978",title:"Prof.",name:"Pınar",middleName:null,surname:"Erkekoglu",slug:"pinar-erkekoglu",fullName:"Pınar Erkekoglu"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8620",title:"Mining Techniques",subtitle:"Past, Present and Future",isOpenForSubmission:!1,hash:"b65658f81d14e9e57e49377869d3a575",slug:"mining-techniques-past-present-and-future",bookSignature:"Abhay Soni",coverURL:"https://cdn.intechopen.com/books/images_new/8620.jpg",editors:[{id:"271093",title:"Dr.",name:"Abhay",middleName:null,surname:"Soni",slug:"abhay-soni",fullName:"Abhay Soni"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9660",title:"Inland Waters",subtitle:"Dynamics and Ecology",isOpenForSubmission:!1,hash:"975c26819ceb11a926793bc2adc62bd6",slug:"inland-waters-dynamics-and-ecology",bookSignature:"Adam Devlin, Jiayi Pan and Mohammad Manjur Shah",coverURL:"https://cdn.intechopen.com/books/images_new/9660.jpg",editors:[{id:"280757",title:"Dr.",name:"Adam",middleName:"Thomas",surname:"Devlin",slug:"adam-devlin",fullName:"Adam Devlin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9122",title:"Cosmetic Surgery",subtitle:null,isOpenForSubmission:!1,hash:"207026ca4a4125e17038e770d00ee152",slug:"cosmetic-surgery",bookSignature:"Yueh-Bih Tang",coverURL:"https://cdn.intechopen.com/books/images_new/9122.jpg",editors:[{id:"202122",title:"Prof.",name:"Yueh-Bih",middleName:null,surname:"Tang",slug:"yueh-bih-tang",fullName:"Yueh-Bih Tang"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9043",title:"Parenting",subtitle:"Studies by an Ecocultural and Transactional Perspective",isOpenForSubmission:!1,hash:"6d21066c7438e459e4c6fb13217a5c8c",slug:"parenting-studies-by-an-ecocultural-and-transactional-perspective",bookSignature:"Loredana Benedetto and Massimo Ingrassia",coverURL:"https://cdn.intechopen.com/books/images_new/9043.jpg",editors:[{id:"193200",title:"Prof.",name:"Loredana",middleName:null,surname:"Benedetto",slug:"loredana-benedetto",fullName:"Loredana Benedetto"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9731",title:"Oxidoreductase",subtitle:null,isOpenForSubmission:!1,hash:"852e6f862c85fc3adecdbaf822e64e6e",slug:"oxidoreductase",bookSignature:"Mahmoud Ahmed Mansour",coverURL:"https://cdn.intechopen.com/books/images_new/9731.jpg",editors:[{id:"224662",title:"Prof.",name:"Mahmoud Ahmed",middleName:null,surname:"Mansour",slug:"mahmoud-ahmed-mansour",fullName:"Mahmoud Ahmed Mansour"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],offset:12,limit:12,total:5227},hotBookTopics:{hotBooks:[],offset:0,limit:12,total:null},publish:{},publishingProposal:{success:null,errors:{}},books:{featuredBooks:[{type:"book",id:"9385",title:"Renewable Energy",subtitle:"Technologies and Applications",isOpenForSubmission:!1,hash:"a6b446d19166f17f313008e6c056f3d8",slug:"renewable-energy-technologies-and-applications",bookSignature:"Tolga Taner, Archana Tiwari and Taha Selim Ustun",coverURL:"https://cdn.intechopen.com/books/images_new/9385.jpg",editors:[{id:"197240",title:"Associate Prof.",name:"Tolga",middleName:null,surname:"Taner",slug:"tolga-taner",fullName:"Tolga Taner"}],equalEditorOne:{id:"186791",title:"Dr.",name:"Archana",middleName:null,surname:"Tiwari",slug:"archana-tiwari",fullName:"Archana Tiwari",profilePictureURL:"https://mts.intechopen.com/storage/users/186791/images/system/186791.jpg",biography:"Dr. Archana Tiwari is Associate Professor at Amity University, India. Her research interests include renewable sources of energy from microalgae and further utilizing the residual biomass for the generation of value-added products, bioremediation through microalgae and microbial consortium, antioxidative enzymes and stress, and nutraceuticals from microalgae. She has been working on algal biotechnology for the last two decades. She has published her research in many international journals and has authored many books and chapters with renowned publishing houses. She has also delivered talks as an invited speaker at many national and international conferences. Dr. Tiwari is the recipient of several awards including Researcher of the Year and Distinguished Scientist.",institutionString:"Amity University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Amity University",institutionURL:null,country:{name:"India"}}},equalEditorTwo:{id:"197609",title:"Prof.",name:"Taha Selim",middleName:null,surname:"Ustun",slug:"taha-selim-ustun",fullName:"Taha Selim Ustun",profilePictureURL:"https://mts.intechopen.com/storage/users/197609/images/system/197609.jpeg",biography:"Dr. Taha Selim Ustun received a Ph.D. in Electrical Engineering from Victoria University, Melbourne, Australia. He is a researcher with the Fukushima Renewable Energy Institute, AIST (FREA), where he leads the Smart Grid Cybersecurity Laboratory. Prior to that, he was a faculty member with the School of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA. His current research interests include power systems protection, communication in power networks, distributed generation, microgrids, electric vehicle integration, and cybersecurity in smart grids. He serves on the editorial boards of IEEE Access, IEEE Transactions on Industrial Informatics, Energies, Electronics, Electricity, World Electric Vehicle and Information journals. Dr. Ustun is a member of the IEEE 2004 and 2800, IEC Renewable Energy Management WG 8, and IEC TC 57 WG17. He has been invited to run specialist courses in Africa, India, and China. He has delivered talks for the Qatar Foundation, the World Energy Council, the Waterloo Global Science Initiative, and the European Union Energy Initiative (EUEI). His research has attracted funding from prestigious programs in Japan, Australia, the European Union, and North America.",institutionString:"Fukushima Renewable Energy Institute, AIST (FREA)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"National Institute of Advanced Industrial Science and Technology",institutionURL:null,country:{name:"Japan"}}},equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8985",title:"Natural Resources Management and Biological Sciences",subtitle:null,isOpenForSubmission:!1,hash:"5c2e219a6c021a40b5a20c041dea88c4",slug:"natural-resources-management-and-biological-sciences",bookSignature:"Edward R. Rhodes and Humood Naser",coverURL:"https://cdn.intechopen.com/books/images_new/8985.jpg",editors:[{id:"280886",title:"Prof.",name:"Edward R",middleName:null,surname:"Rhodes",slug:"edward-r-rhodes",fullName:"Edward R Rhodes"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9027",title:"Human Blood Group Systems and Haemoglobinopathies",subtitle:null,isOpenForSubmission:!1,hash:"d00d8e40b11cfb2547d1122866531c7e",slug:"human-blood-group-systems-and-haemoglobinopathies",bookSignature:"Osaro Erhabor and Anjana Munshi",coverURL:"https://cdn.intechopen.com/books/images_new/9027.jpg",editors:[{id:"35140",title:null,name:"Osaro",middleName:null,surname:"Erhabor",slug:"osaro-erhabor",fullName:"Osaro Erhabor"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7841",title:"New Insights Into Metabolic Syndrome",subtitle:null,isOpenForSubmission:!1,hash:"ef5accfac9772b9e2c9eff884f085510",slug:"new-insights-into-metabolic-syndrome",bookSignature:"Akikazu Takada",coverURL:"https://cdn.intechopen.com/books/images_new/7841.jpg",editors:[{id:"248459",title:"Dr.",name:"Akikazu",middleName:null,surname:"Takada",slug:"akikazu-takada",fullName:"Akikazu Takada"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8558",title:"Aerodynamics",subtitle:null,isOpenForSubmission:!1,hash:"db7263fc198dfb539073ba0260a7f1aa",slug:"aerodynamics",bookSignature:"Mofid Gorji-Bandpy and Aly-Mousaad Aly",coverURL:"https://cdn.intechopen.com/books/images_new/8558.jpg",editors:[{id:"35542",title:"Prof.",name:"Mofid",middleName:null,surname:"Gorji-Bandpy",slug:"mofid-gorji-bandpy",fullName:"Mofid Gorji-Bandpy"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9668",title:"Chemistry and Biochemistry of Winemaking, Wine Stabilization and Aging",subtitle:null,isOpenForSubmission:!1,hash:"c5484276a314628acf21ec1bdc3a86b9",slug:"chemistry-and-biochemistry-of-winemaking-wine-stabilization-and-aging",bookSignature:"Fernanda Cosme, Fernando M. Nunes and Luís Filipe-Ribeiro",coverURL:"https://cdn.intechopen.com/books/images_new/9668.jpg",editors:[{id:"186819",title:"Prof.",name:"Fernanda",middleName:null,surname:"Cosme",slug:"fernanda-cosme",fullName:"Fernanda Cosme"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7847",title:"Medical Toxicology",subtitle:null,isOpenForSubmission:!1,hash:"db9b65bea093de17a0855a1b27046247",slug:"medical-toxicology",bookSignature:"Pınar Erkekoglu and Tomohisa Ogawa",coverURL:"https://cdn.intechopen.com/books/images_new/7847.jpg",editors:[{id:"109978",title:"Prof.",name:"Pınar",middleName:null,surname:"Erkekoglu",slug:"pinar-erkekoglu",fullName:"Pınar Erkekoglu"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8620",title:"Mining Techniques",subtitle:"Past, Present and Future",isOpenForSubmission:!1,hash:"b65658f81d14e9e57e49377869d3a575",slug:"mining-techniques-past-present-and-future",bookSignature:"Abhay Soni",coverURL:"https://cdn.intechopen.com/books/images_new/8620.jpg",editors:[{id:"271093",title:"Dr.",name:"Abhay",middleName:null,surname:"Soni",slug:"abhay-soni",fullName:"Abhay Soni"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9660",title:"Inland Waters",subtitle:"Dynamics and Ecology",isOpenForSubmission:!1,hash:"975c26819ceb11a926793bc2adc62bd6",slug:"inland-waters-dynamics-and-ecology",bookSignature:"Adam Devlin, Jiayi Pan and Mohammad Manjur Shah",coverURL:"https://cdn.intechopen.com/books/images_new/9660.jpg",editors:[{id:"280757",title:"Dr.",name:"Adam",middleName:"Thomas",surname:"Devlin",slug:"adam-devlin",fullName:"Adam Devlin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9122",title:"Cosmetic Surgery",subtitle:null,isOpenForSubmission:!1,hash:"207026ca4a4125e17038e770d00ee152",slug:"cosmetic-surgery",bookSignature:"Yueh-Bih Tang",coverURL:"https://cdn.intechopen.com/books/images_new/9122.jpg",editors:[{id:"202122",title:"Prof.",name:"Yueh-Bih",middleName:null,surname:"Tang",slug:"yueh-bih-tang",fullName:"Yueh-Bih Tang"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],latestBooks:[{type:"book",id:"9550",title:"Entrepreneurship",subtitle:"Contemporary Issues",isOpenForSubmission:!1,hash:"9b4ac1ee5b743abf6f88495452b1e5e7",slug:"entrepreneurship-contemporary-issues",bookSignature:"Mladen Turuk",coverURL:"https://cdn.intechopen.com/books/images_new/9550.jpg",editedByType:"Edited by",editors:[{id:"319755",title:"Prof.",name:"Mladen",middleName:null,surname:"Turuk",slug:"mladen-turuk",fullName:"Mladen Turuk"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10065",title:"Wavelet Theory",subtitle:null,isOpenForSubmission:!1,hash:"d8868e332169597ba2182d9b004d60de",slug:"wavelet-theory",bookSignature:"Somayeh Mohammady",coverURL:"https://cdn.intechopen.com/books/images_new/10065.jpg",editedByType:"Edited by",editors:[{id:"109280",title:"Dr.",name:"Somayeh",middleName:null,surname:"Mohammady",slug:"somayeh-mohammady",fullName:"Somayeh Mohammady"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9313",title:"Clay Science and Technology",subtitle:null,isOpenForSubmission:!1,hash:"6fa7e70396ff10620e032bb6cfa6fb72",slug:"clay-science-and-technology",bookSignature:"Gustavo Morari Do Nascimento",coverURL:"https://cdn.intechopen.com/books/images_new/9313.jpg",editedByType:"Edited by",editors:[{id:"7153",title:"Prof.",name:"Gustavo",middleName:null,surname:"Morari Do Nascimento",slug:"gustavo-morari-do-nascimento",fullName:"Gustavo Morari Do Nascimento"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9888",title:"Nuclear Power Plants",subtitle:"The Processes from the Cradle to the Grave",isOpenForSubmission:!1,hash:"c2c8773e586f62155ab8221ebb72a849",slug:"nuclear-power-plants-the-processes-from-the-cradle-to-the-grave",bookSignature:"Nasser Awwad",coverURL:"https://cdn.intechopen.com/books/images_new/9888.jpg",editedByType:"Edited by",editors:[{id:"145209",title:"Prof.",name:"Nasser",middleName:"S",surname:"Awwad",slug:"nasser-awwad",fullName:"Nasser Awwad"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8098",title:"Resources of Water",subtitle:null,isOpenForSubmission:!1,hash:"d251652996624d932ef7b8ed62cf7cfc",slug:"resources-of-water",bookSignature:"Prathna Thanjavur Chandrasekaran, Muhammad Salik Javaid, Aftab Sadiq",coverURL:"https://cdn.intechopen.com/books/images_new/8098.jpg",editedByType:"Edited by",editors:[{id:"167917",title:"Dr.",name:"Prathna",middleName:null,surname:"Thanjavur Chandrasekaran",slug:"prathna-thanjavur-chandrasekaran",fullName:"Prathna Thanjavur Chandrasekaran"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9644",title:"Glaciers and the Polar Environment",subtitle:null,isOpenForSubmission:!1,hash:"e8cfdc161794e3753ced54e6ff30873b",slug:"glaciers-and-the-polar-environment",bookSignature:"Masaki Kanao, Danilo Godone and Niccolò Dematteis",coverURL:"https://cdn.intechopen.com/books/images_new/9644.jpg",editedByType:"Edited by",editors:[{id:"51959",title:"Dr.",name:"Masaki",middleName:null,surname:"Kanao",slug:"masaki-kanao",fullName:"Masaki Kanao"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10432",title:"Casting Processes and Modelling of Metallic Materials",subtitle:null,isOpenForSubmission:!1,hash:"2c5c9df938666bf5d1797727db203a6d",slug:"casting-processes-and-modelling-of-metallic-materials",bookSignature:"Zakaria Abdallah and Nada Aldoumani",coverURL:"https://cdn.intechopen.com/books/images_new/10432.jpg",editedByType:"Edited by",editors:[{id:"201670",title:"Dr.",name:"Zak",middleName:null,surname:"Abdallah",slug:"zak-abdallah",fullName:"Zak Abdallah"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9671",title:"Macrophages",subtitle:null,isOpenForSubmission:!1,hash:"03b00fdc5f24b71d1ecdfd75076bfde6",slug:"macrophages",bookSignature:"Hridayesh Prakash",coverURL:"https://cdn.intechopen.com/books/images_new/9671.jpg",editedByType:"Edited by",editors:[{id:"287184",title:"Dr.",name:"Hridayesh",middleName:null,surname:"Prakash",slug:"hridayesh-prakash",fullName:"Hridayesh Prakash"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8415",title:"Extremophilic Microbes and Metabolites",subtitle:"Diversity, Bioprospecting and Biotechnological Applications",isOpenForSubmission:!1,hash:"93e0321bc93b89ff73730157738f8f97",slug:"extremophilic-microbes-and-metabolites-diversity-bioprospecting-and-biotechnological-applications",bookSignature:"Afef Najjari, Ameur Cherif, Haïtham Sghaier and Hadda Imene Ouzari",coverURL:"https://cdn.intechopen.com/books/images_new/8415.jpg",editedByType:"Edited by",editors:[{id:"196823",title:"Dr.",name:"Afef",middleName:null,surname:"Najjari",slug:"afef-najjari",fullName:"Afef Najjari"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9731",title:"Oxidoreductase",subtitle:null,isOpenForSubmission:!1,hash:"852e6f862c85fc3adecdbaf822e64e6e",slug:"oxidoreductase",bookSignature:"Mahmoud Ahmed Mansour",coverURL:"https://cdn.intechopen.com/books/images_new/9731.jpg",editedByType:"Edited by",editors:[{id:"224662",title:"Prof.",name:"Mahmoud Ahmed",middleName:null,surname:"Mansour",slug:"mahmoud-ahmed-mansour",fullName:"Mahmoud Ahmed Mansour"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},subject:{topic:{id:"329",title:"Microbiology",slug:"agricultural-and-biological-sciences-bromatology-microbiology",parent:{title:"Bromatology",slug:"agricultural-and-biological-sciences-bromatology"},numberOfBooks:1,numberOfAuthorsAndEditors:19,numberOfWosCitations:35,numberOfCrossrefCitations:10,numberOfDimensionsCitations:45,videoUrl:null,fallbackUrl:null,description:null},booksByTopicFilter:{topicSlug:"agricultural-and-biological-sciences-bromatology-microbiology",sort:"-publishedDate",limit:12,offset:0},booksByTopicCollection:[{type:"book",id:"4653",title:"Food Production and Industry",subtitle:null,isOpenForSubmission:!1,hash:"594525624cedb1e236bca2a13e2997cf",slug:"food-production-and-industry",bookSignature:"Ayman Hafiz Amer Eissa",coverURL:"https://cdn.intechopen.com/books/images_new/4653.jpg",editedByType:"Edited by",editors:[{id:"32499",title:"Prof.",name:"Ayman",middleName:"Hafiz",surname:"Amer Eissa",slug:"ayman-amer-eissa",fullName:"Ayman Amer Eissa"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],booksByTopicTotal:1,mostCitedChapters:[{id:"48909",doi:"10.5772/60934",title:"Biotechnological Production of Oligosaccharides — Applications in the Food Industry",slug:"biotechnological-production-of-oligosaccharides-applications-in-the-food-industry",totalDownloads:3208,totalCrossrefCites:6,totalDimensionsCites:24,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Tathiana Souza Martins Meyer, Ângelo Samir Melim Miguel, Daniel\nErnesto Rodríguez Fernández and Gisela Maria Dellamora Ortiz",authors:[{id:"97955",title:"Dr.",name:"Gisela Maria",middleName:null,surname:"Dellamora Ortiz",slug:"gisela-maria-dellamora-ortiz",fullName:"Gisela Maria Dellamora Ortiz"},{id:"162156",title:"Dr.",name:"Ângelo Samir",middleName:null,surname:"Melim Miguel",slug:"angelo-samir-melim-miguel",fullName:"Ângelo Samir Melim Miguel"},{id:"162157",title:"MSc.",name:"Tathiana Souza",middleName:null,surname:"Martins Meyer",slug:"tathiana-souza-martins-meyer",fullName:"Tathiana Souza Martins Meyer"},{id:"174539",title:"Dr.",name:"Daniel Ernesto",middleName:null,surname:"Rodriguez Fernandez",slug:"daniel-ernesto-rodriguez-fernandez",fullName:"Daniel Ernesto Rodriguez Fernandez"}]},{id:"48827",doi:"10.5772/60877",title:"The Role of Yeast and Lactic Acid Bacteria in the Production of Fermented Beverages in South America",slug:"the-role-of-yeast-and-lactic-acid-bacteria-in-the-production-of-fermented-beverages-in-south-america",totalDownloads:3761,totalCrossrefCites:2,totalDimensionsCites:15,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Fábio Faria-Oliveira, Raphael H.S. Diniz, Fernanda Godoy-Santos,\nFernanda B. Piló, Hygor Mezadri, Ieso M. Castro and Rogelio L.\nBrandão",authors:[{id:"95616",title:"Dr.",name:"Fabio",middleName:"Luis Silva",surname:"Faria-Oliveira",slug:"fabio-faria-oliveira",fullName:"Fabio Faria-Oliveira"},{id:"174630",title:"Prof.",name:"Rogélio",middleName:null,surname:"L. Brandão",slug:"rogelio-l.-brandao",fullName:"Rogélio L. Brandão"},{id:"174631",title:"Prof.",name:"Ieso",middleName:null,surname:"M. Castro",slug:"ieso-m.-castro",fullName:"Ieso M. Castro"},{id:"174632",title:"Dr.",name:"Margarete",middleName:null,surname:"Saraiva",slug:"margarete-saraiva",fullName:"Margarete Saraiva"},{id:"174633",title:"Dr.",name:"Fernanda",middleName:null,surname:"Piló",slug:"fernanda-pilo",fullName:"Fernanda Piló"},{id:"174634",title:"Dr.",name:"Raphael",middleName:"Hermano Santos",surname:"Diniz",slug:"raphael-diniz",fullName:"Raphael Diniz"},{id:"174647",title:"MSc.",name:"Hygor",middleName:null,surname:"Mezadri",slug:"hygor-mezadri",fullName:"Hygor Mezadri"},{id:"176135",title:"Dr.",name:"Fernanda",middleName:null,surname:"Godoy-Santos",slug:"fernanda-godoy-santos",fullName:"Fernanda Godoy-Santos"}]},{id:"48938",doi:"10.5772/60848",title:"New Cheese-Like Food Production from Soy Milk — Utility of Soy Milk Curdling Yeast",slug:"new-cheese-like-food-production-from-soy-milk-utility-of-soy-milk-curdling-yeast",totalDownloads:2180,totalCrossrefCites:2,totalDimensionsCites:4,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Makoto Kanauchi, Sakiko Hatanaka and Makoto Shimoyamada",authors:[{id:"85984",title:"Ph.D.",name:"Makoto",middleName:null,surname:"Kanauchi",slug:"makoto-kanauchi",fullName:"Makoto Kanauchi"},{id:"175567",title:"Ms.",name:"Sakiko",middleName:null,surname:"Hatanaka",slug:"sakiko-hatanaka",fullName:"Sakiko Hatanaka"},{id:"175568",title:"Prof.",name:"Makoto",middleName:null,surname:"Shimoyamada",slug:"makoto-shimoyamada",fullName:"Makoto Shimoyamada"}]}],mostDownloadedChaptersLast30Days:[{id:"48827",title:"The Role of Yeast and Lactic Acid Bacteria in the Production of Fermented Beverages in South America",slug:"the-role-of-yeast-and-lactic-acid-bacteria-in-the-production-of-fermented-beverages-in-south-america",totalDownloads:3765,totalCrossrefCites:2,totalDimensionsCites:15,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Fábio Faria-Oliveira, Raphael H.S. Diniz, Fernanda Godoy-Santos,\nFernanda B. Piló, Hygor Mezadri, Ieso M. Castro and Rogelio L.\nBrandão",authors:[{id:"95616",title:"Dr.",name:"Fabio",middleName:"Luis Silva",surname:"Faria-Oliveira",slug:"fabio-faria-oliveira",fullName:"Fabio Faria-Oliveira"},{id:"174630",title:"Prof.",name:"Rogélio",middleName:null,surname:"L. Brandão",slug:"rogelio-l.-brandao",fullName:"Rogélio L. Brandão"},{id:"174631",title:"Prof.",name:"Ieso",middleName:null,surname:"M. Castro",slug:"ieso-m.-castro",fullName:"Ieso M. Castro"},{id:"174632",title:"Dr.",name:"Margarete",middleName:null,surname:"Saraiva",slug:"margarete-saraiva",fullName:"Margarete Saraiva"},{id:"174633",title:"Dr.",name:"Fernanda",middleName:null,surname:"Piló",slug:"fernanda-pilo",fullName:"Fernanda Piló"},{id:"174634",title:"Dr.",name:"Raphael",middleName:"Hermano Santos",surname:"Diniz",slug:"raphael-diniz",fullName:"Raphael Diniz"},{id:"174647",title:"MSc.",name:"Hygor",middleName:null,surname:"Mezadri",slug:"hygor-mezadri",fullName:"Hygor Mezadri"},{id:"176135",title:"Dr.",name:"Fernanda",middleName:null,surname:"Godoy-Santos",slug:"fernanda-godoy-santos",fullName:"Fernanda Godoy-Santos"}]},{id:"48602",title:"Low-Fat Foods",slug:"low-fat-foods",totalDownloads:1768,totalCrossrefCites:0,totalDimensionsCites:1,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Suzana Caetano da Silva Lannes and Alline Aurea do Amaral",authors:[{id:"160554",title:"Dr.",name:"Suzana",middleName:"Caetano Da Silva",surname:"Lannes",slug:"suzana-lannes",fullName:"Suzana Lannes"}]},{id:"48909",title:"Biotechnological Production of Oligosaccharides — Applications in the Food Industry",slug:"biotechnological-production-of-oligosaccharides-applications-in-the-food-industry",totalDownloads:3213,totalCrossrefCites:6,totalDimensionsCites:24,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Tathiana Souza Martins Meyer, Ângelo Samir Melim Miguel, Daniel\nErnesto Rodríguez Fernández and Gisela Maria Dellamora Ortiz",authors:[{id:"97955",title:"Dr.",name:"Gisela Maria",middleName:null,surname:"Dellamora Ortiz",slug:"gisela-maria-dellamora-ortiz",fullName:"Gisela Maria Dellamora Ortiz"},{id:"162156",title:"Dr.",name:"Ângelo Samir",middleName:null,surname:"Melim Miguel",slug:"angelo-samir-melim-miguel",fullName:"Ângelo Samir Melim Miguel"},{id:"162157",title:"MSc.",name:"Tathiana Souza",middleName:null,surname:"Martins Meyer",slug:"tathiana-souza-martins-meyer",fullName:"Tathiana Souza Martins Meyer"},{id:"174539",title:"Dr.",name:"Daniel Ernesto",middleName:null,surname:"Rodriguez Fernandez",slug:"daniel-ernesto-rodriguez-fernandez",fullName:"Daniel Ernesto Rodriguez Fernandez"}]},{id:"48671",title:"Alternative Foods — Marketing Perspectives on the Production and Distribution Systems",slug:"alternative-foods-marketing-perspectives-on-the-production-and-distribution-systems",totalDownloads:1393,totalCrossrefCites:0,totalDimensionsCites:1,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Mehdi Zahaf",authors:[{id:"94609",title:"Dr",name:"Mehdi",middleName:null,surname:"Zahaf",slug:"mehdi-zahaf",fullName:"Mehdi Zahaf"}]},{id:"48938",title:"New Cheese-Like Food Production from Soy Milk — Utility of Soy Milk Curdling Yeast",slug:"new-cheese-like-food-production-from-soy-milk-utility-of-soy-milk-curdling-yeast",totalDownloads:2181,totalCrossrefCites:2,totalDimensionsCites:4,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Makoto Kanauchi, Sakiko Hatanaka and Makoto Shimoyamada",authors:[{id:"85984",title:"Ph.D.",name:"Makoto",middleName:null,surname:"Kanauchi",slug:"makoto-kanauchi",fullName:"Makoto Kanauchi"},{id:"175567",title:"Ms.",name:"Sakiko",middleName:null,surname:"Hatanaka",slug:"sakiko-hatanaka",fullName:"Sakiko Hatanaka"},{id:"175568",title:"Prof.",name:"Makoto",middleName:null,surname:"Shimoyamada",slug:"makoto-shimoyamada",fullName:"Makoto Shimoyamada"}]},{id:"48903",title:"Safety and Quality in the Agricultural Product Chain in Brazil",slug:"safety-and-quality-in-the-agricultural-product-chain-in-brazil",totalDownloads:1215,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"food-production-and-industry",title:"Food Production and Industry",fullTitle:"Food Production and Industry"},signatures:"Elisa Y. Hirooka, Elisabete Y.S. Ono, Cássia R. Takabayashi-\nYamashita, Angélica T. Ishikawa, Douglas F. Barbin, Jaqueline G.\nBordini, Melissa T. Hirozawa, Wagner E. Risso, Ana L.S.M. Felício,\nArtur K. Bagatin, Tatiana Á. Miguel, Thiago M. Souza, Yumi Tabuchi,\nJosemarque L. Rosa, Leonardo F. Maciel, Dani L. D. Silva, Renata P.\nSobottka, André M. Prando, Sandra Garcia, Claudemir Zucareli,\nEmilia K. Kuroda, Elisabete H. Hashimoto, Diva de Souza Andrade,\nMartha Z. Miranda, Maria S. Miranda, Eliete S. Bispo, Adriana L.\nSoares, Massami Shimokomaki, Myrna Sabino, Eiko N. Itano,\nTomoaki Tsutsumi, Satoshi Nagata, Yoshitsugu Sugiura, Ken-Ichi\nHarada and Osamu Kawamura",authors:[{id:"95925",title:"Dr.",name:"Elisa",middleName:null,surname:"Hirooka",slug:"elisa-hirooka",fullName:"Elisa Hirooka"}]}],onlineFirstChaptersFilter:{topicSlug:"agricultural-and-biological-sciences-bromatology-microbiology",limit:3,offset:0},onlineFirstChaptersCollection:[],onlineFirstChaptersTotal:0},preDownload:{success:null,errors:{}},aboutIntechopen:{},privacyPolicy:{},peerReviewing:{},howOpenAccessPublishingWithIntechopenWorks:{},sponsorshipBooks:{sponsorshipBooks:[{type:"book",id:"10176",title:"Microgrids and Local Energy Systems",subtitle:null,isOpenForSubmission:!0,hash:"c32b4a5351a88f263074b0d0ca813a9c",slug:null,bookSignature:"Prof. Nick Jenkins",coverURL:"https://cdn.intechopen.com/books/images_new/10176.jpg",editedByType:null,editors:[{id:"55219",title:"Prof.",name:"Nick",middleName:null,surname:"Jenkins",slug:"nick-jenkins",fullName:"Nick Jenkins"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],offset:8,limit:8,total:1},route:{name:"chapter.detail",path:"/books/dielectric-material/polymer-dielectric-materials",hash:"",query:{},params:{book:"dielectric-material",chapter:"polymer-dielectric-materials"},fullPath:"/books/dielectric-material/polymer-dielectric-materials",meta:{},from:{name:null,path:"/",hash:"",query:{},params:{},fullPath:"/",meta:{}}}},function(){var m;(m=document.currentScript||document.scripts[document.scripts.length-1]).parentNode.removeChild(m)}()