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Home  / GENERAL CHEMISTRY Textbook / Chapter 11. Physical and chemical properties of substances / Theory of electrical conductivity

Theory of electrical conductivity

The  electrical current is a flow of electrons moving in conductors in one direction from anode (the negatively charged electrode) to cathode, charged positively.  Electron, bonding atoms into molecules in the presence of closely situated (0.5 - 2 Å) energy minimums are able to move from one minimum to another with the high rate of speed (> 105 m/sec). 

Single-electron dynamic pond is typical for metals. The electrical current theory, presented in this article, assumes  the valent electron transfer from one bond to another. The study of the process kinetics of the electron transfer from one bond to another showed, that one electron moves from one bond to another much faster than the electron pare and that the transfer speed of electrons in the compounds with correlated bond (typical for the organic conductors) is significantly higher than in the compounds with the simple covalent bonds, typical for isolators. It is most important, that  the conductance of the substances, in which atoms in the solid phase are connected with the single-electron dynamic bonds, have conductance 1020 higher, than the solid substances, in which atoms are connected with two-electron statistical bonds. Also, the increase of dynamic bonds in the system takes place during the polyeten, treated with halogen. As a result , the increase of the dynamic bonds quantity in  polyeten its conductance raises by 8 orders - see the Table)

    Table

The preferable electron movement in the one direction from anode to cathode is determined by the degree of the filling in of the upper electron layers of the solid matter, which is taking place during the electron transition from anode into this solid matter until the outer electron sphere is saturated. Furthermore, one should assume the bonding type change and respectively expect the effect of the bonding type change on the scold matter conductance during the electron spheres of atom saturation (simpler speaking, it is a result of electron connecting to the atoms, bonded to the solid matters with different ore identical chemical bonds). It is supposed to expect in the semi-quantitative approximation, that the that conductance of the saturated with electrons atoms will increase with the increase of the affinity of atoms to electrons It is also expected, that the conductance decreases with the increase of enthalpy of the bond, broken during the electron attachment to one of the two atoms connected with this bond. Accordingly to the chemical bond theory, the enthalpy input in the bond energy of I2 molecule equals approximately a half of the bond energy, i.e. 0.72 eV. Iodine atom affinity to electron equals 3.06 eV. Respectively, the heat of reaction of the electron attachment to I2 molecule accompanied with the breakage of the co-valent bond in I2 molecule can be estimated by the value 2.34 of I2 (3.06 - 0.720= 2.34). Accordingly to the experimental data, the iodine molecule affinity the electron equals 2.55 eV. The analogous calculations for chlorine and bromine molecules gives the estimated values for these molecules affinity of 2.40 and 2.36eV, while the direct experimental determination gives the values of 2.38 and 2.55 eV respectively. For the additional verification of the affinity energy for the two-atom molecules, we estimated and compared with the experimental data the electron affinity to electron of Na2 and K2 using the identical methods. The comparison of the calculated and experimental data showed, that the calculated and experimental (in parenthesis) values of the electron affinity for those molecules is lower, than the ones for halogens molecules and are equal 0.2 (0.43) and 0.23 (0.5) respectively.

For example, in the scheme discussed above, the dynamic bond between two left iodine atoms in the   I - I ... I-  molecules breaks, when the outer atomic layer of the left iodine atom is filled in completely. This bond enthalpy is apprised accordingly to the bond theory by the value of the order of 0.4 - 0.7 eV. The electron affinity of iodine atom is 3.06 eV. I.e., the affinity of fairly conducting metals to electron varies in the range of 0.5 - 1.3 eV. The reaction of electron isomerization goes with the zero heat effect. All this assumes the insignificant energy expenditures for the creation of the electrical current in the substance, consisting of I3 molecules.

 Contrary to the examples, discussed earlier, the calculation of the electron affinity energy for the bonds   C-C and C-H  gave the negative energies of these electrons affinities, which are equal respectively  -1.85 and  -2.0 eV.

The dependence between hydrocarbons and halogens expected on the basis of the offered mechanisms is observed between halogens and hydrocarbons. The conductance of substances increases with the increase of electron affinity for the atoms connected with covalent two-electron bonds, and the conductance of substances drops with the bonding energy between atoms increase.

In the resuming conclusion, one can say, that (while the bond type between atoms in the solid substance is identical) the higher conductance should be expected if the electron affinity to the two-atom molecule is higher.

The comparison of conductance between metals and halogens shows that in this case, the substances with the higher affinity to electron (halogens) have lower electrical conductivity.

 The higher conductance of metals, where atoms connected with the single electron bonds, compare to halogens, consistent with the higher rate of the reversed single electron isomerization. It allows assuming, that the differences in the number of the bonding electrons increase the electrical conductivity more, than its drop due to the molecule affinity to electron decrease.

The appraisal of the stability of two-electron bonding effect on the electrical conductivity of the solids (which atoms are connected with two-electron co-valent bonds) allows to understand why the graphite electrical conductivity is sharply exceeds the one of diamond.  Both substances consist of the identical atoms; i.e. both atoms of graphite and diamond have the same electron affinity. All bonds and valent angles in diamond are the same as in paraffin and are equal to 1.54 Å and 1090 respectively.  Unlike diamond, the bonds in graphite have the different length (Figure 11_4_1).

Fig.11_4_1

The length of the weak bonds between the layers in graphite equals 3.4 Å and between the atoms in the same layer is 1.42 Å.  This distance has the intermediate value between the single covalent bond  C-C length (1.5.4 Å) and the length of the double bond C=C (1.33 Å). The bond length between graphite layers is close the Van der Vaals bond length in the inert gases. The length of these bonds in the case of neon is 3.18 Å and 3.82 Å respectively. L. Pauling (L. Pauling The Nature of the Chemical Bond P.235 1959) guessed, that the carbon atoms in the graphite layers are connected with the single and double bonds (Fig.14_4_2), 

         Fig.11_4_2

and between the layers with Van der Waals bonds.

The length of the central bond in butadiene equaled 1.46 Å  is the independent confirmation of this explanation.

The structure of graphite, suggested by Paling, assumed, that  unlike diamond, in which carbon atoms connected with identical bonds, graphite has carbon atoms connected with the other atoms by different bonds (singular, double and Van der Waals').

Accordingly to the chemical bonding theory in this case the bonds became dynamic.

The experimental data, obtained while studying the graphite electric conductivity provide another confirmation of that the graphite structure formula, suggested by L. Pauling, is correct. It was established during the electric conductivity of diamond and graphite, that electric conductivity of graphite, consisting from the same atoms as diamond, is about ten orders higher then the conductivity of diamond. Besides, it was established, that graphite, while conducting the electrical current, shows the amazing anisotropy: the specific conductivity along the layers ranges from 4x10-5 to  7x10-5  ohm.cm, and perpendicular to the layers ranges from 1x10-1  to 5x10-1  ohm.cm (K.Saito, ''Chemistry and the Periodic Table'', Moscow, Mir,1982, p. 104). These data were in the clear contradiction with the theory, suggesting, that substances, carrying electrical current,  contain free electrons, because there could not be in this case any anisotropy.

Accordingly to the electrical current theory described in this work, the process of the establishment of the electrical current in graphite has to begin from the electron connection  to the double bond. The further electron movement (its transition to another carbon atom in the equivalent energy state) can go into two directions accordingly to the graphite structure. In the graphite case, electron could move along the conjugated bonds (in the ring plane) and perpendicular to the ring plane (transfer from one ring into the parallel to it another ring). The distance between these rings is 3.4 Å  . The existence of these two routes explained  the amazing anisotropy, observed during electric conductivity studying of graphite,  and its absence  in diamond. The data, presented in literature, allows to appraise, even semiquantatively,  the expected ratio of electric conductivities along the routes possible  thanks to  t6he theory. The first route assumes the electron movement along the carbon chain, in which the carbon atoms are connected with the conjugated bonds.  In the previous article, we   said, that determined experimentally electric conductivity of polyethine (polyacetelene  -(CH)x)-CH=CH-CH=CH-CH=) equals  10-5 -10-8  ohm.cm., what is closed to the value of  4x10-5  to 7x10-5  ohm.cm, shown above.

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Theory of electrical conductivity
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