UDK 537.22
The Ion Theory of Electrets
E.T. Kulin
Summary
In solid dielectrics and semiconductors, under the influence of strong electric or magnetic fields, corona discharge, gamma radiation, and other power factors, a system consisting of anisotropically oriented ion-molecular complexes is formed. These complexes absorb the energy from the environment and disintegrate into molecules and electrically charged particles: anions, cathions, and their pairs (quasi-dipoles). As the result of the superposition of electric fields of these particles, a strong long-term electric field of the system is created, which is a characteristic feature of electrets. The theory helps to explain basic features of electrets.
The article consists of 14 pages, a list of 22 references, 2 tables, and 2 pictures.
1. An Electret State of Matter
At the beginning of the 20th century M. Eguchi found out that hardened in strong electric field (electric field) fusion of carnauba resin, rosin, and beeswax got ability to generate an external electric field for a long time (months and years) [1]. Thus by analogy to magnets, the class of the physical objects named electrets has been discovered.
In following years many scientists showed that the electret state of matter can be created in amorphous, crystal, both polar and not polar solid dielectrics, and high-resistance semiconductors[1] as the result of their exposure to a strong electric or magnetic field, ionic and electronic bunches, corona discharge, gamma radiation, and other power factors [2,3].
Along with an electric field, electrets possess a very weak electric current, which increases multifold during heating of electret. This increasing current is named thermo stimulated current (ТSС) and is the second characteristic feature of the electret state of matter.
A long-term electric field, which can be registered in the air, and TSC were also found in human, animal and plant tissues [4 - 8]. This allowed identifying a natural electret state in biological structures [6, 7].
The electric field of living tissues, which is caused by an electret state of protein structures, correlates with a functional state of a human body, animals and plants. Moreover, its intensity is enough to influence the course of biological processes [8, 9].
Currently, a notion of electrical charges freed from traps and electrical dipoles as the field source is used to explain the origin of electrets’ electric field. However, based on this idea it is impossible to explain such electret features as surface charge density dynamics and dipole electret TSC specter during its heating (pic. 2), as well as natural electret state of biological tissues. Taking this into consideration, the significance of an electret theory, which would allow to explain a set of their basic properties and which could be used to solve scientific and practical problems, is evident. There is no such theory in available publications. In this connection, the theory, which allows explaining main properties of the electret state of solid dielectrics and semiconductors, is suggested below.
2. Development of a Molecular Theory of Electrets
One of characteristic displays of the electret state of a matter is a long-term generation of a relatively strong external electric field. The first hypothesis about the mechanism of generation of this field was offered by M.Eguchi [1]. According to him, the source of the field is an electric polarization of dielectrics due to orientation of polar molecules in a strong electric field.
This hypothesis was developed and concretized by E.Adams [10]. In his interpretation, free charges of an opposite sign shift to the connected electric charges of the oriented polarized molecules. As a result, electric fields of these charges mutually compensate each other. However, due to relaxation of electric polarization the compensated state of electric fields of the free and connected charges is broken. As the result, an internal electric field extends outside the matter. Thus, a characteristic property of the electrets--a relatively strong long-term electric field--is exhibited.
Currently, along with the hypothesis of the relaxation electric polarization, the hypothesis of defects in the structure of solid dielectrics is used to explain the generation of an electret field. These defects capture free charges like traps; hold them for a long time and gradually release [11, 12]. Real quasi-constant charges are thus formed and due to a fields superposition they create a macroscopic integrated field that is measured outside of the matter. The described hypotheses allow explaining the generation of electret fields, but do not explain other features of the electret state such as dynamics of a value and a sign of electret field intensity, the duration of its generation, TSC dynamics, etc. In this connection, the urgency of development of the molecular theory of electrets is obvious.
3. The System of IM complexes is the Basis of the Matter Electret State.
3.1. Possible sources of electric field of electrets.
According to the stated above hypotheses, the sources of the electrets’ electric field are the same sources that are characteristic for dielectrics before their transition into the electret state. Such sources are their structural elements: Ions and polar molecules [13]. However, as the electret state is formed in polar as well as in not polar matter, then ions and molecule-associated ions (ion-molecular complexes) are a necessary and sufficient source of the electric field of dielectrics in the electret state.
In dielectrics, ions are continuously formed under the influence of a natural radiation background, fluctuation of thermal energy, and other ionogenic factors and they exist during the Maxwell free charge relaxation time. Within this time ions interact among themselves forming electro neutral atoms or molecules[2] (ion recombination), and interact with molecules forming ion-molecular complexes (further IM complexes).
3.2. Formation and Properties of IM complexes
The Ion-molecular complexes—also named complex or cluster ions—are spontaneously formed in gases and consist of an ion and one to six molecules associated with it [14, 15, 16]. They are characterized by high durability: 80 to 150 kJ/mol energy is required to separate a molecule from an ion [14]. Dimeric IM complexes, defined by the energy of their dissociation, essentially depend on matter from which they were formed (pic. 1). It is necessary to pay attention to a 5-fold difference in dissociation energy values of anion- and cathion-molecular complexes (further for brevity anion and cathion particles). Therefore, dissociation energy of anion particles of oxygen (0-2∙02) is 0.09 eV, and cathion particles (0⁺2∙02) – 0.44 eV.
The electric field of two-dimensional IM complexes is characterized by the electric field of a constant electric dipole along with electric field of an ion. The constant electric dipole electric field is formed due to electronic polarization of a molecule in an ion electric field. In addition, ion electric field energy is distributed between its field and the electric field of an induced dipole.
Structure and properties of IM complexes, their durability in particular, are caused by the molecules and ions interactions in those complexes. These intermolecular interactions are carried out by electromagnetic fields, which can be distinguished in the following types depending on a pondemotor action character and a degree of their correlation between the intensity and distance.
Molecules are mutually attracted due to fields of dispersive and polarizing interaction (further attraction fields – A-fields). The value of their intensity is in inverse proportion to a distance in power of 6 [14].
The fields that cause molecules mutually push away (further pushing away fields – PA-fields), dominate in the zone around a molecule where its width is equal to its linear size. The value of this field intensity decreases in inverse proportion to a distance in power of 12 [14].
Along with A-fields and PA-fields, ions and polar molecules possess an electric field that can attract or push away depending on their source charge sign: the sources with the opposite signs are attracted, and with the same sign are pushed away. The intensity of an ion electric field decreases inversely to a distance in power of 2, and the intensity of a polar molecule electric field -- to a distance in power of 3.
Intermolecular interactions are anisotropic, i.e. their power differs depending on a direction of their action [17]. It means that values of intensity of fields of this interaction vary on three mutually perpendicular lines passing through the centre of a source of the field. It is possible to accept that intensity of a field is high on one of these lines, average - on the second, and low on the third. In addition, the field intensity in each zone decreases in the direction from the molecule center to its periphery. The same is correct about electric fields of the charged molecules, i.e. to fields of ions.
Along with A- and PA-fields, IM complexes have anisotropic field of an electric dipole, which as shown above is formed due to a molecule electric polarization under the influence of the ion field.
Thus, a molecule and an ion each have three pairs of zones with high, average and low intensity of fields of intermolecular interaction. In the A-field, depending on orientation of ions and molecules, anion- and cathion-particles are formed with various degrees of durability, which is presented in table 1. A characteristic feature of interaction inside and between molecules is anisotropic electric field of their constant electric dipole.
The table 1 reflects the IM complexes, which are formed by interaction of ions with not polar molecules. In the processes of interaction between ions and polar molecules, it is necessary to consider not only their A-fields interaction but also interaction of electric fields of an ion and a polar molecule.
3.3. Formation and Properties of IM Complexes in Solid Dielectrics
The indispensable condition of formation of IM complexes is rapprochement of an ion with a molecule on a distance, at which the A-fields prevail. In gases, this happens in an ion and molecule oncoming traffic. In firm matter, as it is noted above, the ion arises when a molecule absorbs a quant of radiating background energy or due to other ionogenic factors. Thus, at the moment of formation the ion at once appears in the sphere of A-fields of 12-14 surrounding molecules[3]. In these conditions, the ion is drawn to that molecule which is closer to it and to which the ion is turned by a side with the high voltage zone of the A-field. However, the molecule can be turned to an ion by a side with any zone of intensity of the A-field. The ion approaches the molecule to the point where A-fields are counterbalanced by PA-fields. As a result, a formed complex gets a rather high durability and secures a stationary position in a solid-state structure. Such 2-D IM complexes are presented in table 1.
When an ion appears near a 2-D IM complex, it is possible that the ion is drawn to and interacts either with an ion of the complex or with a molecule. In the first case, because of an ions’ recombination, an associate is formed, which consists of three electrically neutral molecules. In the second case, a three-dimensional (3-D) IM complex is formed, which consists of three elements: an anion, a molecule and a cathion (an anion-cathion particle) or a cathion, a molecule and an anion (a cathion-anion particle). The kinds and types of durability of these particles are presented in table 2.
3-D IM complexes possess the constant electric dipole moment and the electric field that is peculiar to an electric dipole. These complexes are stronger than 2-D because along with the mutual attraction of their elements due to A-fields, they are drawn together due to the electric field of ions with opposite charges.
The following process occurs during interaction of ions with 3-D IM complexes. An ion shifts along the gradient of a pressure of an electric field of a dipole to one of its ions with the opposite sign and recombines with it. As the result a complex consisting of an ion and three molecules is formed. Such complexes are formed rather seldom. Therefore, they are not considered as possible sources of an electret electric field.
3.4. Disintegration of IM Complexes
Continuous spontaneous formation of IM complexes in dielectrics is combined with their continuous disintegration when complexes absorb radiating background energy and thermal movement energy. During such 2-D IM complexes, disintegrations independent anions and cathions are formed, each of which contains as much electricity as in an elementary electric charge, i.e. 1.6x10-19 Coulomb. During 3-D IM complexes disintegration pairs of independent opposite charged ions are formed, each of which also contains the quantity of electricity equal to its quantity in an elementary electric charge. These pairs of ions are similar to electric dipoles and further will be called quasi-dipoles.
2-D and 3-D complexes and products of their disintegration are sources of electric fields and their superposition creates the integrated electric field of a dielectric. Because of a chaotic (isotropic) placement of the specified sources, intensity of their integrated field is comparable to intensity of the integrated electric field of water solutions of electrolytes that represent a set of electric dipoles of molecules of water and opposite charged ions. At the distance of 2-3 mm from the surface of such solutions the intensity of the electric field is around 1 - 100 V/m [18]. Therefore, it is possible to believe that a dielectric external field, which further will be called its background electric field, has the intensity of the same order.
Thus, IM complexes should be added to structural elements of hard matter alongside with atoms, molecules, and ions. [13] These complexes are spontaneously formed, and absorbing environmental energy, they disintegrate forming ions and their pairs. Because of an isotropic placement of these complexes and products of their disintegration, the integrated electric field is created due to superposition of their electric fields. The intensity of this field has values of 1- 100 V/m at a distance of 2-3 mm from a dielectric surface (a background electric field of dielectric).
3.5. Formation of The Electret State of Matter
The electret state in solid dielectrics and semiconductors is formed when they are affected by a strong electric or magnetic field, corona charge, ion and electron beams, gamma radiation, and other factors, which cause molecules to transition from isotropic into an anisotropic placement (further anisotropogenic factors – AG-factors).
The transition of molecules and ions from an isotropic into anisotropic placement due to AG-factors is testified by anisotropy of some properties of the matter, which has acquired an electret state, namely: electric anisotropy of matter, i.e. electric polarization, which is shown in piezo- and pyro-electric effects, anisotropy of dielectric and magnetic permeability, and anisotropy of a visible light refraction coefficient [2].
According to modern views, a molecule turn is one of formation stages of the electret state of matter [19]. During a turn and a molecule interaction with an ion, an IM complex is formed with its electrical axis parallel to the AG-factor vector. The proof of it is electrical anisotropy in a dielectric, which shifted into the electret state. The quantity of turned molecules is limited, as the aggregate state of matter does not change during such turns. With this consideration, only those molecules turn that absorbed enough energy to overcome intermolecular fields. The same is correct for a power action to turn a molecule.
Molecules and ions being in an anisotropic placement under the influence of the AG-factor interact and form anisotropic IM complexes located stationary in solid dielectrics. As the result, the texture consisting of anisotropic IM complexes is created in a dielectric molecular mass.
Formation of IM complexes under the AG-factor occurs as described above but much more intensively than without the AG-factor. This is caused by the fact that AG-factors, except for a magnetic field, ionize the matter. Thereof the quantity of ions in a volume unit increases and accordingly the quantity of their interaction with molecules increases with formation of anisotropic IM complexes. Simultaneously with the beginning of texture formation, the integrated electric field is created due to superposition of electric fields of anisotropic IM complexes and products of their disintegration. Intensity of this field increases with the quantity of IM complexes. Ions appearing due to ionizing factors shift in this field. This accelerates processes of their interaction with molecules and increases the quantity of formed anisotropic IM complexes.
For the formed texture, the electric polarization, caused by anisotropic IM complexes, and a strong long distant electric field, created by products of their disintegration, is inherent. All elements of the texture interact in the field that allows to consider the texture as a system and to name it an ion-molecular system (IM-system). Durability of anisotropic IM complexes in the IM-system increases due to its electric field. And the products of IM complexes’ disintegration--ions and their pairs--from the moment of their formation settle down in such a manner that one of the lines passing through pairs of ion zones with identical intensity of the A-field is oriented parallel to the vector of intensity of the system electric field.
Formed in the IM-system anions, cathions and their pairs shift slowly, and their properties correspond to properties of constant electric charges. In particular, the intensity of an electric field of anions and cathions decreases in inverse proportion to the power 2 of distance and the intensity of an electric field of anion-cathion pairs decreases in inverse proportion to the power 3 of distance. Considering this, it is possible to call these anions and cathions quasi-constant charges, and their pairs -- quasi-constant dipoles (quasi-dipoles), i.e. it is possible to apply names that were used by G.Sessler in his basics of physics of electrets [11]. Due to the fields superposition of quasi-constant charges and quasi-dipoles, a relatively strong IM system electric field is formed, which is a characteristic feature of the matter electret state.
3.6. IM System as an Electric Field Generator
Generation of electric field in an IM system goes on the following scenario. Anisotropic IM complexes absorb energy and disintegrate into molecules and anisotropic ions: anions, cathions and their pairs. Thus due to superposition of their electrical fields a strong integral field of the system is formed. Having left the IM complex, ions stay in an anisotropic dislocation for a short period equal to a free charge Maxwellian relaxation time, and then switch into an isotropic dislocation due to heat movement. That is why the quantity of anisotropic ions decreases constantly. However, this decrease is being restored by anisotropic ions due to constant disintegration of anisotropic IM complexes. The process of generation of anisotropic ions, which in turn generate an IM system electrical field, lasts until anisotropic IM complexes last.
Isotropic ions and free ions due to external and internal factors shift along an intensity gradient of the IM system electrical field and form its ion current. The power of this current is quite small firstly due to the opposite direction of a concentration gradient and the intensity gradient, and secondly due to high electrical resistance of the system matter.
The IM system electric field voltage value and a sign as well as their dynamics depend upon types and strength of IM complexes, upon the correlation between the number of disintegrated electrically charged particles and the speed of their formation, and upon a location of IM complexes and products of their disintegration. The quantity of IM complexes, their type and strength correlation are conditioned by properties of matter used to make electrets and technology (type of AG factor, time, temperature, etc).
As with the other types of molecular interaction fields, ion electrical fields possess anisotropy [17]. Considering this, out of three lines drawn through an ion at a 90o angle one has higher electric field intensity than the other two. That line we will consider the ion electrical axis.
Ions and their pairs (quasi-dipoles), formed during disintegration of anisotropic IM complexes, line up with their electrical axes alongside lines parallel to the intensity vector of the IM system integral field. Further, those lines will be considered horizontal. As the result, during anion-cathion particles disintegration anion-cathion pairs are formed, i.e. quasi-dipoles with electrical axes lined up alongside horizontal lines. In this case the quasi dipole negative pole is directed to the left (table 2). Such quasi-dipole will be called minus-quasi-dipole. During a similar cathion-anion particles disintegration quasi-dipoles are formed with the positive pole directed to the left (table 2). Such quasi-dipole will be called a plus quasi-dipole.
The value and a sign dynamics of the electrical field and the IM system depend on the system IM complexes disintegration speed. This speed is conditioned by an intensity of external and internal system energy.
During an IM system heating, quantity of quants sufficient for IM complexes disintegration is increasing constantly. As the result the concentration of anions, cathions and quasi-dipoles in the volume unit grows, which results in increasing of electric field intensity and the system electro conductivity. Thus, the ionic current increases multifold. This current is an analogue of TSC, which is observed during a slow heating of electrets.
Note that while the IM system intensity increases instantly, the ionic current increases gradually. This can be explained that ions, shifting alongside the gradient of increased intensity of the system electrical field, move slowly overcoming stabilizing factor of molecular interaction A-fields. As the result, a change in TSC is delayed in comparison with a change in intensity. The time of that delay (t) is in direct proportion to electrical resistance (R) of the system matter and in reverse proportion to its intensity (V). Hence, t=aR/V, where a is a proportional coefficient.
Thus, in solid dialectics under the influence of a strong electric or magnetic field, corona discharge, gamma-radiation and other factors an IM system is formed with characteristic appearance of a matter electret state, which are an external long-term electrical field and TSC. This is evidence that the IM system is physical basis of the electret state in solid dielectrics. A leading role in the system functions belongs to ions. Hence, a theory with an IM system as a basis can be called an ion theory of electrets.
4. The Electret State of Matter in the Ion Theory Aspect
In this sector the solvency of the Ion Theory of Electrets (further -- the Theory) is estimated by its ability to explain a set of the following displays of the electret state of solid dielectrics:
· Formation of hetero- and homo-charged electrets;
· Piezo- and pyro-electric properties of electrets;
· Dynamics of density and of a superficial charge sign of as well as their dependency upon temperature;
· An origin and a quantity of peaks of TSC;
· Long-term generation of the electret field.
Mono-polar electrets are electrets with the same electric charge sign on whole their surface, i.e. monocharged. A dipolar electret has different charge signs on its opposite sides.
According to the offered Theory, the IM-system of a monopolar electret contains an equal quantity of anion- and cathion-particles. As it has been noted above, anion-particles are approximately 5 times less stable than cathion-particles. Thereof anion-particles break up more intensively. As a result, during each instant anions prevail over cathions that causes a prevailing presence of negatively charged electrets.
Negative volume charges are inherent to monopolar electret [11]. However, a positive charge can be present on its surface due to positive ions from an environment being absorbed by electrets. In this case, monopolar electret has the electric structure consisting of electric dipoles located in its peripheral zone in such a way that their negative poles are directed inside, and their positive poles are directed outside.
In case of dipolar electret, if to divide it along planes perpendicular to its electret axis, there will be fragments with the same signs on the opposite sides as in a whole electret. This fact testifies that a physical base of dipolar electret is formed by electric dipoles spread within all its volume [2]. According to the Theory, these dipoles are quasi-dipoles, which are formed at disintegration of trimeric IM complexes in the IM-system of dipolar electret.
Hetero-charged electret is the electret with superficial charge of an opposite sign to the sign of electric voltage on an adjoining electrode during manufacturing of the electret. Homo-charged electret is the electret with superficial charge coinciding with a sign of voltage on an adjoining electrode. Hetero- and homo-charged electrets (further hetero- and homoelectrets) are formed if an AG-factor is used as an electric field.
Hetero- and homoelectrets formation depends on matter and technology of electret manufacturing. Therefore, while manufacturing of dipolar electrets from ceramics, application of an electric field with intensity of 5 kW/cm causes formation of a heteroelectret and application of an electric field with intensity of 15 kW/cm causes formation of a homoelectret [2].
According to the Theory, in the first case while manufacturing the electret, a subsystem[4] had been generated consisting of cathion-anion particles, which disintegrate into plus quasi-dipoles, i.e. dipoles with the positive pole directed to the left. In the second case, a subsystem consisting of anion-cathion particles had been formed with disintegrated minus-quasi-dipoles, i.e. dipoles with their negative pole turned to the left. Hence, in the first case a heteroelectret is formed, and in the second – a homoelectret.
The fact that piezo- and pyroelectric effects are characteristic to electrets is evidence of electric polarization of their matter [20].
According to the Theory, a substantial basis of the IM-system of electrets is the texture with orderly located IM complexes. In other words, the texture of an IM-system of the electret is one of versions of electric polarization of matter with inherent piezo- and pyroelectric effects.
During slow heating, electrets’ density of a superficial charge and its sign change in a complex way, this correlates with the power and the direction of TSC. In particular, it is observed at a dipolar electret of polyethilenteraftalate (fig. 2).
According to the Theory, the IM system of a dipolar electret consists of two types of trimeric complexes with a different degree of durability (See table 2). During heating of the dipolar electret the surface charge density changes and its positive sign turns into negative. The change of the charge sign is an evidence of two subsystems forming this electret: the subsystem with cathion-anion particles, which disintegrate into plus quasi-dipoles, and the subsystem with anion-cathion particles, which disintegrate into minus-quasi-dipoles. The first subsystem has IM complexes with a lesser strength degree that the latter. Considering this, the dynamics of surface charge density is explained as follows.
During slow temperature increase between 20 - 800С disintegration of cathion-anion particles prevails. As the result, the plus quasi-dipoles are formed causing the positive sign of a superficial charge. As temperature is raised further, disintegration of anion-cathion particles increases and begins to prevail. As the result the minus-quasi-dipoles creating the negative superficial charge are formed. Thereof the positive superficial charge density decreases and is being changed by the negative charge, which density eventually reaches a maximum. The subsequent reduction of density of the negative superficial charge to zero is caused by exhaustion of anisotropic IM complexes in the IM-system of electret.
According to the Theory, the power and the direction of ion current in the IM system depends on the voltage value and sign of the system integral field and electro conductivity of its matter. Thereof the electrical conductivity depends on the concentration of ions in matter and increases with temperature. On this basis, TSC dynamics in the electret can be explained as follows.
A slight increase in density of a positive surface charge with the temperature increase between 20 - 80°С is caused by a close ratio of plus- and minus-quasi-dipoles, which define the value of the surface charge and correspondingly the value of electrical field voltage (V). Within mentioned temperature increase this ratio changes slightly, thus is a slight change in voltage. However, the electrical conductivity increases significantly in the same temperature interval due to an increase of the quantity of ions as the result of disintegration of both anisotropic and isotropic IM complexes and the temperature increase. Hence, according to the Ohm law, current increases. (I=Vγ)
TSC changes are delayed in comparison with voltage because the voltage changes instantly where as the ion current is significantly slowed down due to high electrical resistance of the system matter. Based on data from fig.2, the delay in a TSC change in relation to a change of density of surface charge is defined as equal to 3.3 min. The calculation is made given the speed of heating equal to 30/min.
In the temperature interval between 80-115°С surface charge density increase, which corresponds to increase of negative voltage of the IM system electrical field, is caused only by increase of a quantity of minus-quasi-dipoles. That is why a TSC graph repeats a negative voltage graph but with a slight time shift. See fig 1.
Nowadays electrets with observed one to four TSC peaks are obtained [2, 21]. According to the Theory, it is explained by the fact that their IM-systems correspondingly contain one to four subsystems, which differ in kinds and types of durability of IM complexes.
Therefore, an IM system with one TSC peak contains one of three possible subsystems consisting of dimeric IM complexes and an IM system with four TSC peaks contains four subsystems consisting of dimeric and trimeric IM complexes. For example, one subsystem consisting of dimeric complexes and three subsystems consisting of trimeric IM complexes with different durability (see tables 1 and 2).
The period of an electret external electric field existence is called its life span. Duration of this time depends on a material of which electret is made, technologies of its manufacture, storage conditions, and influences of some factors: temperature, level of a radiating background, moisture, etc. Thereof an electret life span fluctuates from several hours while heating to several years and more with absence of the specified influences and appropriate storage conditions.
According to the Theory, an electret life span is conditioned by a quantity of IM complexes in a volume unit of its IM-system and by intensity of their disintegration.
Anions, cathions and their pairs (quasi-dipoles) are formed during an IM complex disintegration and they serve as point sources of electret electric field. Superposition of these fields creates an integrated electric field of the electret. These point sources exist during a short time frame of a free charge Maxwellian relaxation. For many electrets, it lasts from seconds to a few hundred seconds. Hence continuous--during an electret life span—generation of these point sources is necessary for long-term generation of the electret electric field. This is provided by continuous disintegration of IM complexes. In this connection, a question is justified: What quantity of complexes should be contained in an electret IM-system volume unit in order to provide field generation during its lifetime? This question is connected with a question about a quantity of molecules necessary for generation of a corresponding quantity of IM complexes in the IM-system. An answer to this question is of fundamental importance for assessing the consistency of the Theory as a quantity of molecules in an IM complex has a certain limit. Namely, this quantity should be much less than the quantity of molecules in a volume unit, for instance one cubic centimeter. This is conditioned by the fact that a transition into the electret state of matter does not involve a change in its physical state, i.e. amorphous matter stays amorphous.
To determine the number of molecules in IM complexes of the IM-system of a dipole ceramic electret a sample in the form of a cube is taken with an edge of 1.0 cm, which has surface charge density of 10-8 Coulomb/cm2, electrical conductivity of 10-12 Ohm-1 ∙ cm-1, the dielectric permeability of 50, and a lifetime of 2.6 years [2, 22].
Surface charge density of electret reflects the amount of electricity, which is contained in the elementary electric charges in its volume [2]. Accordingly, the estimated number of elementary charges in 1.0 cm3 of the sample under consideration is equal to 0.6×1011 charges.[5]
According to the Theory, ions and ions in pairs are formed at disintegration of IM complexes, and each ion contains a quantity of electricity equal to the quantity of electricity in an elementary charge, i.e. 1.6×10-19 Coulomb. Consequently, the number of the ions formed at IM complexes disintegration corresponds to the number of elementary charges. The lifetime of these ions corresponds to the Maxwellian relaxation time of free charges (τM) and according to calculations is equal to five seconds.[6] According to the Theory, a strong electrical field of the IM system is created by superposition of ion and their pairs electric fields while they are in the anisotropic arrangement. We assume that this time is a tenth of the Maxwellian relaxation time of a free charge. From this, it follows that during the life of the sample under consideration, i.e. within 2.6 years on the average, 6×1010 IM complexes should break up every 0.5 seconds. In 2.6 years 9.6×1018 complexes (6×1010 complexes × 1.6×108 half-second periods) will break up. Considering that there are three molecules in each complex, the total number of molecules in IM complexes in 1.0 cm3 of the IM-system sample is equal to 2.88×1019 molecules/cm3.
There are 1022 molecules in 1.0 cm3 of firm matter [13]. Out of this number of molecules, 2.88×1019 molecules are used to form IM complexes, i.e. about one molecule out of 340 (1022÷2.88×1019).
It is obvious that 0.3% molecules, which have changed their spatial position while matter transition into the electret state, do not change its aggregate state. This is consistent with the fact of an unchanged physical state of matter at its transition into the electret state.
A rather small quantity of molecules necessary for formation of the IM-system of electret allows explaining the existence of the electret state in crystal matter. Crystals are characterized by dislocations, i.e. defects of a crystal lattice in which molecules are isotropic arranged. It can be assumed that the number quantity of molecules in dislocations is sufficient to form the electret state in them.
Thus, we can conclude that the Ion Theory of Electrets can explain the above set of the main manifestations of the electret state of matter in solid dielectrics and semiconductors.
The author is deeply grateful to A.I.Kulak for valuable advices and remarks during the work on the Theory, to N.M.Alehnovich, V.A.Goldade and A.N.Furs for the useful remarks made at the analysis of the Theory. The author is especially grateful to A.E. Kulina-Pate for valuable advices during editing and translation of the article.
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[1] Further, high-resistance semiconductors as well are implied while mentioning solid dielectrics.
[2] Further, processes are considered applied to molecules.
[3] The quantity of molecules in the ion closest surrounding is calculated on a model, in which each molecule is at a double linear distance from its neighbor. At such distance influence on molecules’ A- and PA-fields is equalized and molecules take a stationary position in a solid structure. [13]
[4] A subsystem in the IM system is a combination of IM complexes of the same kind and degree of strength (table 2).
[5] To create the surface charge density equal to 10-8 Coulomb/cm2 in 1.0 cm3 of the electret sample requires approximately 0.6×1011 elementary charges, each of which contains 1.6×10-19 Coulomb, i.e. (10-8÷ (1.6×10-19)).
where
εо – dielectric permittivity of vacuum = 10-13
ε - dielectric permittivity of electret matter = 50
γ – specific conductivity of the substance of the electret = 10-12 Ohm-1 • cm-1
Pictures
Pic. 1 Dynamics of density and a sign of superficial charge (solid line) and dynamics of power and direction of TSC (breaking line) during slow heating of polyethilentereftalat electret.
Electret is made with a starting temperature of 130 /min. [21]
Pic. 2 Diagram of dissociation energy for Van-der-vaals molecules, cluster ions and molecules with a chemical connection. In parenthesis next to the molecule or ion is the value of power: in eV for cluster ions and molecules with a chemical connection; in 10-3 eV for van-der-vaals molecules. [16]
Table 1
Durability Index of anion and cathion particles
(H) zone of high tension of A-field,
(M) zone of medium tension
(L) zone of low tension
Anion particles Cathion particles Durability
1. Anion (H)∙(H)molecule Cathion (H) ∙(H)molecule High
2. Anion (H)∙(M)molecule Cathion (H) ∙(M)molecule Medium
3. Anion (H)∙(L)molecule Cathion (H) ∙(L)molecule Low
Note: along with different durability indexes among anion particles and cathion particles, the latter are approximately 5 times more durable (see pic. 2)
Table 2
Durability Index of anion-cathion and cathion-anion particles
(H) zone of high tension of A-field,
(M) zone of medium tension
(L) zone of low tension
Anion-cathion particles Durability
1. Anion (H) ∙ (H) molecule (H) ∙ (H) Cathion High
2. Anion (H) ∙ (M) molecule (M) ∙ (H) Cathion Medium
3. Anion (H) ∙ (L) molecule (L) ∙ (H) Cathion Low
Anion-cathion particles
1. Cathion (H) ∙ (H) molecule (H) ∙ (H) anion High
2. Cathion (H) ∙ (M) molecule (M) ∙ (H) anion Medium
3. Cathion (H) ∙ (L) molecule (L) ∙ (H) anion Low
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