Small Polaron Hopping DC Conductivity in 3D and 1D Disordered Materials


Georgios P. Triberis
National and Kapodistrian University of Athens, Physics Department, Solid State Section, Athens, Greece

Series: Materials Science and Technologies
BISAC: TEC021000

Introducing the Generalized Molecular Crystal Model, as a more realistic model for the study of the small polaron transport in disordered materials, in the book the “microscopic” kinetics of small polaron transport is fully described. The percolation theory bridges smoothly the gap between the “microscopic” mechanisms responsible for the small polaron site-to-site transport, and the calculation of the “macroscopic” dc electrical conductivity, ignoring and taking into account correlations. Analytical expressions for the dc electrical conductivity are produced, in 3D and 1D disordered materials, under the influence of an electric field and the temperature. The interplay of these two stimuli is discussed, for the high and low-temperature small polaron hopping regime, and a wide range of electric field values. The effect of energy dependent densities of states is also presented.

Taking into account the directionality imposed by the electric field on the transport path of the small polaron, an extensive study is presented concerning the effect of the magnitude of the density of states and the extent of the electronic wave function upon the calculated dc conductivity of 1D disordered materials. The validity and the significance of the theoretical expressions produced, are systematically tested, interpreting experimental data reported, concerning the behavior of the dc electrical conductivity of various 3D and 1D disordered materials. The results are extensively discussed, revealing, among others, the importance of correlations. Comparison is also made with other theories.

The book aims to be used by the Condensed Matter Physics theoreticians and the experimentalists, as a road map to find their way traveling across the complex paths of small polaron transport in 3D or 1D disordered materials, studying their dc electrical conductivity. Parts of it could also be used in a postgraduate course on transport and percolation theory. (Imprint: Nova)



Table of Contents



Chapter 1. The Small Polaron

Chapter 2. The Generalized Molecular Crystal Model

Chapter 3. Thermodynamics and Thermoelectricity

Chapter 4. The “Microscopic” DC Conductivity

Chapter 5. Percolation Theory

Chapter 6. The DC Conductivity in 3D Disordered Materials

Chapter 7. The DC Conductivity in 1D Disordered Materials



Author Contact Information



[1] Anderson, Phil W. 1958. “Absence of Diffusion in Certain Random Lattices.” Phys. Rev. 109:1492-1505.
[2] Schnakenberg, J. 1968. “Polaronic Impurity Hopping Conduction.” J. Phys. Stat. Sol. 28:623-633.
[3] Cohen, Marvel H., et al. 1969. “Simple Band Model for Amorphous Semiconducting alloys.” Phys. Rev. Lett. 22:1065-1068.
[4] Holstein, Theodore D. 1959. “Studies of Polaron Motion. Part I. The Molecular Crystal Model.” Annals of Physics 8:325-342.
[5] Holstein, Theodore D. 1959. “Studies of Polaron Motion. Part II. The “Small” Polaron.” Annals of Physics 8:343-389.
[6] Emin, David. 1975. “Phonon-assisted Transition Rates I. Opticalphonon-assistedHopping in Ssolids.” Advances in Physics 24:305-348.
[7] Emin, David. 1976. Physics Of StructurallyDisordered Solids. edited by Mitra S. S.,487-8. New York: Plenum.
[8] Triberis, Georgios P. 1980. “Thermoelectric Power due to Small Polaron HoppingMotion in Disordered Systems.” PhD diss. Universityof St. Andrews.
[9] Triberis, Georgios P., and Friedman, Lionel R. 1981. “A Percolation Treatment of the Conductivity for the High-temperature Small Polaron Hopping Regime in Disordered Systems.” J. Phys. C: Solid State Phys. 14:4631-4639.
[10] Landau, Lev D. 1933. “ ¨Uber die Bewegung der Elektronen in Kristalgitter.” Phys. Z. Sowjetunion 3:644-645.
[11] Pekar, Solomon I. 1954. Untersuchungen uber die Elektrontheorie der Kristalle. Berlin: Akademie Verlag.
[12] Fro¨hlich, Herbert, Pelzer H., and Zienau, Singurd. 1950. “Properties of Slow Electrons in Polar Materials.”Phil. Mag 41:221-242.
[13] Yamashita, Jiro, and Kurosawa, Tatumi. 1960. “On Electronic Current in NiO.” J. Phys. Chem. Solids 5:34-43.
[14] Lang, I. G., and Firsov,Yu A. 1963. “Kinetic Theory of Semoconductors with Low Mobility.” Sov. Phys. JETP 16:1301-1312.
[15] Friedman, Lionel R., and Holtein, Theodore T. 1963. “Studies of Polaron motion: Part III: The Hall Mobility of the Small Polaron. Ann. Phys. 21:494-549.
[16] Bo¨ttger Harald, and Bryksin, Valrij V. 1976. “Hopping Conductivity in Ordered and Disordered Solids (II) and (II).” Phys. Stat. Sol.(b) 78:9-56 and 415-451.
[17] Bo¨ttger Harald, and Bryksin, Valrij V. 1985. Hopping Conduction in Solids. Berlin: Akademie Verlag.
[18] Emin, David. 2013. Polarons. Cambridge:Cambridge Univ. Press.
[19] Miller, Allen H., and Aabrahams Elihu. 1960. “Impurity Conduction at Low Concentrations.” Phys. Rev. 120:745-755.
[20] Mott, NevillF. 1968.“Conduction in Glasses containing Transition Metal Ions.” J. Non-Cryst. Sol. 1:1-17.
[21] Austin, I. G., and Mott, NevillF. 1969. “Polarons in Crystalline and Non-Crystalline Materials.” Advances in Physics 18:41-102.
[22] Mott, Nevill F., and Davies E. A. 1979. Electronic Processes in Non-Crystalline Materials. Oxford:Oxford Univ. Press.
[23] Onsager, Lars. 1931. “Reciprocal Relations in Irreversible Processes.I. “Phys. Rev. 38:405-426.
[24] De Groot, Sybren, R. 1951. thermodynamics of irreversible proccesses. Ansterdam: North Holland.
[25] Haug, Albert. 1972. Theoretical Solid State Physics. Vol 2. New York: Pergamon.
[26] Mori, Hirotoshi. 1956. “A Quantum-statistical Theory of Transport Processes.” J. Phys. Soc. Japan 11:1029-1044.
[27] Kubo, Ryoko et al. 1957. “Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance.” J. Phys. Soc. Japan 12: 1203-1211.
[28] Abramowitzn, Milton, and Stegun Irene. 1972.Handbook of Mathematical Functions. Washington:NationalBureau of Standards.
[29] Emin, David. 1975. “Thermoelectric Power Due to Electronic Hopping Motion.” Phys. Rev. Lett. 35:882-885.
[30] Anderson, Phil W. 1972. “The Size of Localized States Near the Mobility Edge.” Proc. Nat. Acad. Sci. USA 69:1097-1099.
[31] Broadbent, S. R., and Hammersley, J. M. 1957. “Percolation Processes. I. Crystals and Mazes”. Proc. Camb. Phil. Soc. 53:629-641.
[32] Frish, H. L., and Hammersley, J M. 1963. “ Percolation Processes and Related Topics.” J. Soc. Ind. Appl. Math. 11:894-918.
[33] Shante, Vinod. K. S., and Kirkpatrick, Scott. 1971. “An Introduction to Percolation Theory.” Adv.Phys. 20:325-357.
[34] Essam, John W. 1972. “Percolation and Cluster Size.” In Phase Transitions and Critical Phenomena, Vol.2 . Editedby Domb and Green, 73-89. London-New York:Academic Press.
[35] Zallen Richard. 1983. The Physics of Amorphous Solids. New York: John Wiley and Sons.
[36] Pollak, Michael. 1978. “Percolation and Hopping Transport.” In The Metal Non-metal Transition in Disordered Systems, edited by Lionel R. Friedman, and David P. Tunstall, 95-148. St. Andrews:Scottish Universities Summer School in Physics.
[37] Domb Cyril., and Sykes, M. F. 1961.” Cluster Size in Random Mixtures and Percolation Processes.” Phys. Rev. 122:77-78.
[38] Ziman, Jim M. 1968. “The Localization of Electrons in Ordered and Disordered Systems I. Percolation of Classical Particles.” J. Phys. 1:15321535.
[39] Zallen Richard, and Scher, Harvey. 1970. “Percolation on a Continuum and the Localization-Delocalization Transition in Amorphous Semiconductors” Phys. Rev. B 4:4711
[40] Ambegaokar, Vinay, et al. 1971.”Hopping Conductivity in Disordered Systems.” Phys. Rev. B 4:2612-2620.
[41] Pollak, Michael. 1972. “A Percolation Treatment of dc HoppingConduction.” J. of Non-Crystall. Solids 11:1-24.
[42] Apsley, Norman, and Hughes, Howard P. 1974. “Temperature and Field-Dependence of Hopping Conduction in Disordered Systems.” Phil. Magazine 30:963-972.
[43] Apsley, Norman, and Hughes, Howard P. 1975. “Temperature and Field-dependence of Hopping Conduction in Disordered Systems, II.” Phil. Mag. 31:1327-1339.
[44] Shante V K et al. 1973. “Hopping Conductivity in “One-Dimensional” Disordered Compounds.” Phys. Rev. B 8:4885.
[45] Shklovskii, Boris I., and Efros, Alexander L. 1975. “Percolation Theory and Conductivity of Strongly Inhomogeneous Media.” Sov. Phys. Usp. 18: 845-862.
[46] Triberis, GeorgiosP. 1985. “Percolation-Theoretic Considerations for the Thermoelectric Power and the Conductivity Due to Small Polaron Motion in Disordered Systems.” J. of Non-Crystall. Solids 74:1-10.
[47] Triberis, Georgios P., and Friedman, Lionel R. 1985. “The Effect of Correlations on the Conductivity of the Small Polaron Hopping Regime in Disordered Systems.” J. Phys. C: Solid State Phys. 18:2281-2286.
[48] Triberis, Georgios P. 1986. “Small Polaron Hopping and Transport Properties of As-Te Based Glasses.” J. of Non-Crystall. Solids 87:86-92.
[49] Triberis, Georgios P. 1988. “A Conductivity Study on V2O5 Layers Deposited from Gels.” J. of Non-Crystall. Solids 104:135-138.
[50] Triberis, Georgios P. 1990. “On the importance of Correlations in the Study of the Conductivity Due to Small Polaron Hopping Motion in Amorphous Materials.” Physica Stat. Sol. B 158: K149-K153 .
[51] Triberis, Georgios P. 1992. “The Effect of Energy-dependent Densities of States and the Importance of Correllations on the Conductivity of the Small Polaron Hopping Regime in Disordered Systems.” Phil. Mag. 65: 631-637.
[52] Mohan, R., and Rao K. J. 1983. “Small Polaron Hopping and High temperature D.C. Conductivity of Chalcogenide Glasses” Mat. Res Bull. 18:195-201.
[53] Selvaraj, U., and Rao K. J. 1988. “Transport Properties of Phosphomolybdate and Phosphotungstate Glasses.” Phil. Mag. B 58:03-2016.
[54] Seager C. M. et al. 1973. “Electrical Transport and Structural Properties of Bulk As-Te-I, As-Te-Ge, and As-Te Chalcogenide Glasses.” Phys. Rev. B 8:4746-1760.
[55] Brahma, P. et al. 1990. “ Transport properties of semiconducting glassceramics in the system BaO − Fe2O3 − B2O − XO3 (X=Sb,As)” J. Phys. D.: Appl. Phys. 23:706-710.
[56] Brahma et al.1991. “DC Conductivityof Dol-Gel Derived Glasses in The System Fe2O3−SiO2.Eur. J. Solid State Inorg. Chem. 28:1139-1150.
[57] Ghosh, A., and Chakravorty, D. J. 1991. “Transport properties of semiconducting CuO-Sb2O3-P2O5 Glasses” J. Phys.: Cond. Matter 3:33353342.
[58] Ru¨scher, C. E. et al. 1988. “The Effect of High Polaron concentration on the Polaron Transport in NbO 2.5-x: Optical and Electrical Properties.” J. Phys. C: Solid State Phys. 21:3737-3749.
[59] Ru¨scher, C. E. et al. 1988. “The Effect of the Nb-W distribution on Polaronic Transport in ternary Nb-W Oxides: electrical and optical properties.” J. Phys. C: Solid State Phys. 21:4465-4480.
[60] Bullot, J. et al. 1984. “Thin Layers Deposited from V2O5 Gels: I. A Conductivity Study” J. Non-Cryst.Solids 68:123-134.
[61] Linsey, G. S. et al. 1970. “Electronic Conduction in Vanadium Phosphate Glasses” J. Non-Cryst. Solids 4: 208:219.
[62] Murawski, L. et al. 1990. “Small Polaron Transport in Amorphous V2O5 Films” J. Non-Cryst. Solids 124:71-75 .
[63] Greaves, G. N. 1973. “Small Polaron Conduction in V2O5 − P2O5 glasses” J. Non-Cryst. Solids 11:427-446.
[64] Triberis, Georgios P., et al. 1991. “The Effect of the Density of States in the Conductivity of the Small Polaron Hopping Regime in Disordered Systems.” J. Phys:Condens. Matter 3:337-346.
[65] Shklovskii, Boris I. 1973. “Hopping Conduction in Semiconductors subjected to a Strong Electric-Field.” Sov. Phys.-Semic. 6:1964-1967.
[66] Pollak, Michael., and Riess, Ilan. 1976. “A Percolation Treatment of High-Field Hopping Transport.” J. Phys. C: Solid State Phys. 9:23392352.
[67] Bo¨ttger, Harald, and Bryksin, Valrij, V. 1980. “Investigation of Non-Ohmic Hopping Conduction by Methods of Percolation Theory.” Phil.Mag. 42:297-310.
[68] Meaudre, M. et al. 1981. “High Field Variable Range Hopping of Holelike Polarons in RF sputtered SiO2 Films.” J. of Non-Crystall. Solids 58:145-150.
[69] Meaudre, M., and Meaudre R. 1984. “Electrical Transport in RF-sputtered SiO2 films. A review.” J. of Non-Crystall. Solids 68:281-299.
[70] Triberis, Georgios P. 1987. “The Field dependence of the Conductivity for the High-temperature Small Polaron Hopping Regime in Disordered Systems.” J. Phys. C: Solid State Phys. 20:23707-3718.
[71] Triberis, Georgios P. 1988. “The Field dependence of the Conductivity for the Low-temperature Small Polaron Hopping Regime in Disordered Systems.” J. Phys. C: Solid State Phys. 21:L821-L825.
[72] Sun, Y., and Kiang C. 2005. “DNA-based Artificial Nanostructures: Fabrication, Properties, and Applications.” In Handbook of Nanostructured Biomaterials and Their Applications in Nanotechnology, 1-33 Nalwa, American Scientific Publishers.
[73] Komineas, S., et al.2002. “Effects of Intrinsic Base-pair Fluctuations on Charge Transport in DNA.” Phys. Rev. E 65:061905-4.
[74] Zhang, M., and Tarn T. 2003. “DNA Electrical Properties and Potential Nano-applications.” Proc. IEEE Conf. Nanotechnology 512-515.
[75] Tran, P., et al. 2000. “Charge Transport Along the lambda-DNA Double Helix.” Phys. Rev. Lett. 85:1564-1567.
[76] Yoo, K. H., et al. 2001. “Electrical Conduction through Poly(dA)Poly(dT) and Poly(dG)-Poly(dC) DNA Molecules.” Phys. Rev. Lett. 87:198102-4.
[77] Otsuka, Y., et al. 2002. “Influence of Humidity on the Electrical Conductivity of Synthesized DNA Film on Nanogap Electrode.” Jpn J. Appl. Phys. 41:891-894.
[78] Hipps, K. W. 2001. “Molecular Electronics: Its All about Contacts.” Science 294:536-537.
[79] Zhang, Y., et al. 2002. “Insulating Behavior of lambda-DNA Double Helix.” Phys. Rev. Lett. 89:198102-198105.
[80] Friedman, A. E. 1990. “Molecular Light-Switch for DNA: Ru(bpy)2(dppz)2+.” J. Am. Chem. Soc. 112:4960-4962.
[81] Murphy, C. J., et al. 1993. “Lomg-Range Photoinduced Electron Transfer Through DNA Helix.” Science 262:1025-1029.
[82] Murphy, C. J. 1994.“Fast Photoinduced Electron Transfer Through DNA Inetrcalation.” Science 91:5315-5319.
[83] Keley, S., et al. 1991. “Photoinduced Electron Transfer in Ethidium-Modified DNA Duplexes: Dependence on Distance and Base Stacking.” J. Am. Chem. Soc. 119:9861-9870.
[84] Brun, A. M., and Harriman A. 1992. “Dynamics of Electron Transfer between Intercalated Polycyclic Molecules: Effect of Interspersed Bases.” J. Am. Chem. Soc. 114:3656-3660.
[85] Brun, A. M., and Harriman A. 1994. “Energy-and Electron-Transfer Processes Involving Palladium Porphyrins Bound to DNA.” J. Am. Chem. Soc. 116:10383-10393.
[86] Lewis, F. D., et al. 1997. “Distance-Dependent Electron Transfer.” Science 277:673-676.
[87] Fink, H. W., and Schonenberger C. 1999. “Electrical Conduction through DNA Molecule.” Nature 398:407-410.
[88] Kasunov, A. Y., et al. 2001. “Proximity Induced Superconductivity in DNA.” Science 291:280-282.
[89] Cai, L., and Tabata H. 2001. “Probing Electrical Properties of Oriented DNA by Conducting Atomic Force Microscopy.” Nanotechnology 12:211-216.
[90] Kutnjak, Z., et al. 2003. “Electrical Conduction in Native Deoxyribonucleic Acid: Hole Hopping Transfer Mechanism? Phys. Rev. Lett. 90:098101-4.
[91] Inomata, A., et al. 2006 “Electrical Conductivity of DNA Double-Stranded Chains by “One-by-One” Cutting Method Using Etomic Force Microscopy.” J. Phys. Soc. Japan 75:074803-4.
[92] Gomez-Navaro, C., et al. 2002. “Contactless Experiments on Individual DNA Molecules show no Evidence for molecular Wire Behavior.” Proc. Natl. Acad. Sci. U.S.A. 99:8484-8487.
[93] Braun, E., et al. 1998.”DNA-templated Assembly and Electrode Attachment of a Conducting Silver Wire.” Nature 391:775-778.
[94] Storm, A. J., et al. 2001. “Insulating Behavior for DNA Molecules Between Nanoelectrodes at the 100 nm length scale.” Appl. Phys. Lett. 79:3881-3883.
[95] Legrand, O., et al. 2006. “Single Molecule Study of DNA Conductivity in Aqueous Environment.” Phys. Rev. E 73:031925-6.
[96] Beratan, D. N., et al. 1997. “DNA: Insulator wire?.” Chem. Biol. 4:3-8.
[97] Kelly, S. O., and Barton J. K. 1999. “Electron Transfer Between Bases in Double Helical DNA.” Science 283:375-381.
[98] Porath, D.,et al. 2000. “Direct Measurement of Electrical Transport Through DNA Molecules.” Nature (London) 403:635-638.
[99] Boon, E. M., and Barton J. K. 2002. “Charge Transport in DNA.” Opin. Struct. Biol. 12:320-329.
[100] Berlin, Y. A., et al. 2002. “Elementary Steps for Charge Transport in DNA: Thermal Activation vs Tunneling.” Chem. Phys. 275:61-74.
[101] Roche, S. 2003. “Sequence Dependent DNA-Mediated Conduction.” Phys. Rev. Lett. 91:108101-4.
[102] Carpena, P., et al. 2003. “Metal-Insulator Transition in Chains with Correlated Disorder.” Nature (London) 421:764.
[103] Maniadis, P., et al. 2005. “Ac Conductivity in a DNA Charge Transport Model.” Phys. Rev. E 72:021912-4.
[104] Kalosakas, G., et al. 2005. “Breather-Induced Anomalous Charge Diffusion.” Phys. Rev. E 71:061901-7.
[105] Schmidt, B. B., et al. 2008. “Nonequilibrium Polaron Hopping Transport through DNA.” Phys. Rev. B 77:165337-8.
[106] Jortner, J. et al. 1998. “Charge Transfer and Transport in DNA.” Proc. Natl. Acad. Sci.(U.S.A.) 95:12759-12765.
[107] Ratner, M. 1999. “Photochemistry Electronic Motion in DNA.” Nature (London) 397:480-481and references cited therein.
[108] Cuniberti, G., et al. 2002. “Backbone-Induced Semiconducting Behavior in Short DNA Strands.” Phys. Rev. B 65: 241314.
[109] Ma, S., et al. 2007. “Hopping Conductivity of DNA sequences with Off-Diagonal Correlations.” Physica B 391:98-102.
[110] Henderson, P. T., et al. 1999.“Long-DistanceCharge Transport in Duplex DNA: The Phonon Assisted Polaron-like Hopping Mechanism.” Proc. Natl. Acad. Sci. (U.S.A.) 96:8353-8358.
[111] Conwell, E. M., and Rakhmanova S. V. 2000. “Polarons in DNA.” Proc. Natl. Acad. Sci. (U.S.A.) 97:4556-4560.
[112] Conwell, E. M. Charge Transport in DNA in Solution. Proc. Natl. Acad. 2005; 102: 8795-8799
[113] Conwell EM, and Bloch S. M. 2006. “Base Sequence Effects on Transport in DNA.” J. Phys. Chem. B 110:5801-5806.
[114] Giese, B., et al. 2001. “Direct Observation of Hole Transfer Through DNA by Hopping Between Adenine Bases and by Tunneling.” Nature (London) 412:318-320.
[115] Grozema, F. C., et al. 2000. “Mechanism of Charge Migration Through DNA: Molecular Wire Bahavior, Single-Step Tunneling or Hopping?.” J. Am. Chem. Soc.122:10903-10909.
[116] Kurnikov, I. V., et al. 2002. “Hole Size and Energetics in Double Helical DNA: Competition between Quantum Delocalization and Solvation Localization.” J. Phys. Chem. B 106:7-10.
[117] Basko, D. M., and Conwell E. M. 2002. “Effect of Solvation on Hole Motion in DNA.” Phys. Rev. Lett.88:098102-4.
[118] Osuka, A., et al. 1996. “A Sequential Electron-Transfer Relay in Diporphyrin-Prphyrin-Pyromellitimide Triads Analogous to That in the Photosynthetic Reaction Center.” Angew Chem. Int. Ed. Engl. 35:92-95.
[119] Hayashi, T., et al. 1996. “Photoinduced Electron Transfer between Multifunctional Porphyrin and Ubiquinone Analogues Linked by Several Hydrogen-Bonding Interactions.” Angew Chem. Int. Ed. Engl. 35:19641966.
[120] Zwang, W., et al. v. “Polarons with a Twist.” Phys. Rev. B 66:060303-4.
[121] Yu, Z. G., and Song X. 2001. “Variable Range Hopping and Electrical Conductivity along the DNA Double Helix.” Phys. Rev. Lett. 86:60186021.
[122] Alexander, S. S., et al. 2003. “Small Polarons in Dry DNA.” Phys. Rev. Lett. 91:108105-4.
[123] Adessi, Ch., and Anantram M. P. 2003. “Influence of Counter-Ion-Induced Disorder in DNA Conduction.” Appl. Phys. Lett. 82:2353-2355.
[124] Schuster, G. B. 2000. “Long-Range Charge Transfer in DNA: Transient Structural Distortions Control the Distance Dependence.” Acc. Chem. Res. 33:253-260.
[125] Seidel, C. AM., et al. 1996. “Nucleobase-Specific Quenching of Fluorescent Dyes. 1. NucleobaseOne-Electron Redox Potentials and their Correlations with Static and Dynamic Quenching Efficiencies.” J. Phys. Chem. 100:5541-5553.
[126] Steenken, S. C., and Jovanovic S. C. 1997. “How Easily Oxidizable is DNA? One-Electron Reduction Potentials of Adenosine and Guanosine Radicals in Aqueous Solution.” J. Am. Chem. Soc. 119:617-618.
[127] Carell, Thomas., et al. 2003. “Electrontransfer through DNA and Metal-containing DNA.” J. Org. Biomol. Chem. 1:2221-2228.
[128] Takada, Tadao., et al. 2004.“Direct Observation of Hole Transfer through Double-Helical DNA over 100 ˚ A.” Natl. Acad. Sci. (USA) 101:1400214006.
[129] Giese, B. 2006. “Electron Transfer Through DNA and Peptides.” Bioorg. and Medic. Chem. 14:6139-6143.
[130] Triberis, Georgios P., et al. 2005. “Small Polaron Hopping Transport Along DNA Molecules.” J. Phys: Condensed Matter 17:2681-2690.
[131] Triberis, Georgios P., and Dimakogianni Margarita. 2009. “Correlated Small Polaron Hopping transport in 1D Disordered Systems at High temperatures:a possible charge Transport Mechanism in DNA.” J. Phys: Condensed Matter 21:035114-23.
[132] Triberis, Georgios P. 1993. “A Small Polaron Hopping Motion in Disordered Systems: A Percolation Treatment of the DC Comductivity.” Semicinductors 27:471-475.
[133] Lee, Patric A. 1984. “Variable-Range Hopping in Finite OneDimensional Wires.”Phys. Rev. Lett. 53:2042-45.
[134] Serota, R. A., et al. 1986. “New aspects of Variable-Range Hopping in finite One-dimensional Wires.” Phys. Rev. B 33:8441-46.
[135] Reedijk, J. A. 1999. “Dopant-Induced Crossover from 1D to 3D Charge Transport in Conjugated Polymers.” Phys. Rev. Lett. 83:3904-07
[136] Heddi, B., et al. 2007.“The DNA Structure Responds differently to Physiological Concentrations of K(+) or Na(+).” J. Mol. Biol. 368:1403-11.
[137] Young, Matthew. A., et al. 1997. “Intrusion of Counterions into the Spine of Hydration in the Minor Groove of B-DNA:? Fractional Occupancy of Electronegative Pockets.” J. Am. Chem. Soc. 119:59-69.
[138] McFail-Isom, Lori, et al. 1999. “DNA Structure: Cations in Charge?” Curr. Opin. Struct. Biol. 9:298-304.
[139] Nebel, C. E., et al. 1992. “High-electric-Field Transport in a-Si:H. I. Transient PhotoConductivity.” Phys. Rev. B 46:6789-6902.
[140] Gleve, B., et al. 1995. “High-Field Hopping Transport in Band Tails of Disordered Semiconductors.” Phys. Rev. B 51:16705-13
[141] Godet, C., and Kumar S. 2003. “Field-enhanced Electrical Transport Mechanisms in Amorphous carbonFilms.” Phil. Mag. 83:3351-65.
[142] Campbell, I. H., et al. 1999. “Consistent time-of-flight Mobility Measurements and Polymer Light-emitting Diode CurrentVoltage Characteristics.” Appl. Phys. Lett. 74:2809-11.
[143] Mozer, Attila. J., et al. 2005. “Charge carrier Mobility in regioregular poly(3-hexylthiophene)probed by Transient Conductivity Techniques: A comparative study.” Phys. Rev. B 71:035214-9.
[144] Novikov, S. V., et al.1998. “Essential Role of Correlations in Governing Charge Transport in Disordered Organic Materials.” Phys. Rev. Lett. 81: 4472-5.
[145] Yu, Z. G., et al. 2000. ‘Molecular Geometry Fluctuation Model for the Mobility of conjugated Polymers.” textitPhys. Rev. Lett. 84:721-24.
[146] Yu, Z. G., et al. 2001. “Molecular Geometry Fluctuations and Field-dependentMobility in conjugated Polymers.” Phys. Rev. B 63:085202-6.
[147] Burroughs, J. H., et al. 1990.“Light-emitting Diodes based on conjugated Polymers.” Nature London 347:539-41.
[148] Sheats, J. R., et al. 1996. “Organic Electroluminescent Devices” Science 273:884-8.
[149] Yurke, B., et al. 2000. “A DNA-fuelled Molecular Machine made of DNA.” Nature 406:605-8.
[150] Sherman, William B., and Seeman Nadrian C. 2004. “A Precisely Controlled DNA Biped Walking Device.” Nano Letters 4:1203-7.
[151] Pennadam, Sivanand S., et al. 2004. “Protein-Polymer Nano-Machines. Towards Synthetic Control of Biological Processes.” J. Nanobiotech. 2:17.
[152] Seelig, G., et al. 2006. “Enzyme-free Nucleic Acid Logic Circuits.” Science 314:1585-8.
[153] Bath, Jonathan, and Turberfield Andrew J. 2007. “DNA Nanomachines.” Nature Nanotech. 2:275-84.
[154] Fogler, M. M., and Kelley R. S. 2005. “Non-Ohmic Variable-Range Hopping Transport in One-Dimensional Conductors.” Phys. Rev. Lett. 95:166604-4
[155] McInnes, J. A., et al. 1990. “Numerical Calculations of non-Ohmic Hopping Conductivity in One-dimensional systems.” J. Phys. Condens. Matter 2:7861-5.
[156] Ma, Songshan ., et al. 2007. “Hopping Transport and Electrical Conductivity in One-dimensional Systems with off-diagonal Disorder.” Physica B 398:55-9.
[157] Cumings, John., and Zettl A. 2004. “Localization and Nonlinear Resistance in telescopically Extended Nanotubes.” Phys. Rev. Lett. 93:0868014.
[158] Aleshin, A. N., et al. 2004. “Hopping Conduction in Polydiacetylene Single Crystals.” Phys. Rev. B 69:214203-6.
[159] Tang, Z. K., et al. 2000. “Electrical Transport Properties of monodispersed single-wall Carbon Nanotubes formed in Channels of zeolite Crystal.” Physica B 279:200-3.
[160] Triberis Georgios P., and Dimakogianni Margarita. 2009. “Field and Temperature Dependence of the Small Polaron Hopping Electrical Conductivity in 1D Disordered Systems”. J..Phys. Cond. Matter 21:38540615.
[161] Bryksin, Valrij V., et al. 1998. “Motion of Localized Carriers in a Strong Electric Field. J. Phys. Cond. matter 10:7907-21
[162] Bo¨ttger Harald, and Bryksin, ValrijV. 1980. “Investigation of non-Ohmic Hopping Conduction by methods of Percolation theory.” Phil. Mag. 42:297310.
[163] Van Lien, Nguyen, and Shklovskii B. I. 1981. “Hopping Conduction in Strong Electric Fields and Directed Percolation.” Solid State Commun. 38:99-102.
[164] Kurkijarvi, J. 1973. “Hopping Conductivity in One Dimension.” Phys. Rev. B 8:922-4.
[165] Raikh, M. E. and Ruzin I. M. 1989. “ Fluctuations of the Hopping Conductance of One-dimensional Systems.” Sov. Phys. JETP 68:642-7.
[166] Triberis, Georgios P., and Dimakogianni Margarita. 2009. “DNA in the Material World: Electrical Properties and Nano-applications.” Rec. Pat. Nanotechnol. 3:135-153.
[167] Dimakogianni, Margarita, and Triberis, Georgios P. 2010. “The Effect of Correlations on the non-Ohmic Behavior of the Small Polaron Hopping Conductivity in 1D and 3D Disordered Systems.” J. Phys.: Condens. Matter 22:355305-14.
[168] Hill, R. M. 1971. “Hopping Conduction in Amorphous Solids.” Phil. Mag. 24:1307-1325.
[169] Dimakogianni, Margarita, et al. 2013. “Density of States and extent of Wave Function: two Crucial Factors for Small Polaron Hopping Conductivity in 1D.” Phil. Mag. 93:2729-2748.
[170] Hawke, L.G.D. et al. 2010. “Electronic Parameters for Charge Transfer along DNA.” Eur. Phys. J. E 32:291-305.
[171] Hawke, L.G.D. et al. 2011. Erratum to: Electronic parameters for Charge Transfer along DNA textitEur. Phys. J. E 34:118.
[172] Bourbie, D., et al. 2007.“Temperature-and Field-dependent Conductivity in Disordered Materials.” Phys. Rev. B 75:184204(6).
[173] Bourbie, D. 2011. “Field-induced Crossover from Phonon to Field Assisted Hopping Conductivity in Organic Materials.” Appl. Phys. Lett. 98:012104-7.
[174] Hawke, L.G.D. et al. 2009. “Empirical LCAO Parameters for Molecular Orbitals in Planar Organic Molecules.” Mol. Phys. 107:1755-1771.
[175] Hawke, L.G.D. et al. 2009. “The * Molecular Structure of flavin of FADH? Enzymatic Cofactor using the LCAO Method.” Mater. Sci. Eng. B 165:266-9.
[176] Rakhmanova, S. V., and Conwell E.M. 1999. “Polaron Dissociation in Conducting Polymers by High Electric Fields.” Appl. Phys. Lett. 75:1518-20.
[177] Liu, Xiaojing, et al. 2006. “Effect of the Electric Field mode on the Dynamic Process of a polaron.” Phys. Rev. B 74:172301-6.
[178] Qiu, Yu, and Zhu Li-Ping. 2009. “Field Effect on Polaron Dynamics and Charge Transport in Conducting Polymers.” J. Chem. Phys. 131:134903(6).
[179] D. Bourbie, N. Ikrelef and P. Nedellec, Phys. Stat. Sol. (c) 1 (2004) p.79.
[180] Wang, Jiaxiong.2008.“Electrical Conductivity of Double Stranded DNA measured with ac Impedance Spectroscopy.” Phys. Rev. B 78:245304-14.
[181] Pavlenko, Natalie. 2000. “Some Peculiarities of Proton Transport in Quasi-one-Dimensional hydrogen-bonded Chains.” J. Chem. Phys. 112:8637-8644.
[182] Pavlenko, Natalie. 2003.“ProtonWires in an Electric Field: the Impact of the Grotthuss Mechanism on Charge Translocation.”J. Phys.: Condensed Matter 15:291-307.
[183] Rak, Janusz. et al. 2006. “Effect of Proton Transfer on the Electronic Coupling in DNA .” Chemical Physics 325:567-74.

The book aims to be used by the the Condensed Matter Physics theoreticians and the experimentalists, as a road map to find their way traveling across the complex paths of small polaron transport in 3D or 1D disordered materials, studying their dc electrical conductivity. Parts of it could also be used in a postgraduate course on transport and percolation theory.

Additional information