(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites

When asked to explain the importance of the discovery of conducting polymers, I offer two basic answers: first they did not (could not?) exist, and second, that they offer a unique combination of properties not available from any other known materials. The first expresses an intellectual challenge; the second expresses a promise for utility in a wide variety of applications.

Semiconducting and Metallic Polymers: The Fourth Generation of Polymeric Materials (Nobel Lecture).

This is an overview of some of the important, challenging, and problematic issues in contemporary electron transfer research. After a qualitative discussion of electron transfer, its time and distance scales, energy curves, and basic parabolic energy models are introduced to define the electron transfer process. Application of transition state theory leads to the standard Marcus formulation of electron transfer rate constants. Electron transfer in solution is coupled to solvent polarization effects, and relaxation processes can contribute to and even control electron transfer. The inverted region, in which electron transfer rate constants decrease with increasing exoergicity, is one of the most striking phenomena in electron transfer chemistry. It is predicted by both semiclassical and quantum mechanical models, with the latter appropriate if there are coupled high- or medium-frequency vibrations. The intramolecular reorganizational energy has different contributions from different vibrational modes, whic...

Contemporary Issues in Electron Transfer Research

Polyaniline: a polymer with many interesting intrinsic redox states

Influence of chemical polymerization conditions on the properties of polyaniline

Spectroscopic studies of polyaniline in solution and in spin-cast films

Morphology of conductive, solution-processed blends of polyaniline and poly(methyl methacrylate)

Polyaniline (PANI) films of superior homogeneity can be prepared by using functionalized protonic acids to protonate the polymer and simultaneously induce solubility, in the conducting form, in common organic solvents. The results of measurements of the temperature dependence and magnetic-field dependence of the conductivity of films of PANI complexed with camphor sulfonic acid (CSA) are reported. The intrinsic metallic nature of conducting polyaniline can be observed from the positive temperature coefficient of resistivity in the temperature interval from 180 to 300 K. Signatures of hopping transport are observed below 180 K, indicative of marginal metallic behavior with disorder-induced localization at low temperatures. Resistivity ratios as low as 1:3 (300 to 1.2 K) are found. Analysis of the dependence of the resistivity on temperature and magnetic field indicates that the typical electronic localization length in PANI-CSA films is 100\char21{}150 \AA{}. Thus the PANI-CSA is on the metal-insulator (M-I) boundary. A magnetic field (H) shifts mobility edge and causes the system to crossover from disordered metal to insulator: in zero field, \ensuremath{\rho}(T)\ensuremath{\propto}${\mathit{T}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$ where \ensuremath{\beta}=0.36, consistent with transport in the critical region near the M-I boundary, whereas, in H=8 T, \ensuremath{\rho}(T)=${\mathrm{\ensuremath{\rho}}}_{0}$exp[(${\mathit{T}}_{0}$/T${)}^{1/4}$] indicating variable range hopping between localized states with mean localization length, ${\mathit{L}}_{\mathit{c}}$(H=8 T)\ensuremath{\approxeq}100\char21{}140 \AA{}.

Counterion-induced processibility of polyaniline: Transport at the metal-insulator boundary.

Critical behavior of the electrical conductivity near the disorder-induced metal-insulator (MI) transition has been observed in polyaniline (PANI) doped with camphor sulfonic acid (CSA). The temperature dependence of the resistivity (\ensuremath{\rho}) depends on the degree of disorder present in the PANI-CSA films. In the most metallic samples the resistivity is nearly temperature independent; whereas in the critical region of MI transition, \ensuremath{\rho}(T) is characterized by a power-law temperature dependence, \ensuremath{\rho}(T)\ensuremath{\propto}${\mathit{T}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$. Resistivity ratios \ensuremath{\rho}(1.4 K)/\ensuremath{\rho}(300 K) as low as 1.6 have been observed in the most metallic samples of PANI-CSA. In the metallic regime, the conductivity is characterized by \ensuremath{\sigma}(T)=\ensuremath{\sigma}(0)+${\mathit{mT}}^{1/2}$ at low temperatures; the dependence of m(H) on magnetic field provides information on the role of electron-electron interactions in the transport near the MI transition. The ${\mathit{T}}^{\mathrm{\ensuremath{-}}1}$ dependence found for inelastic-scattering time (${\mathrm{\ensuremath{\tau}}}_{\mathrm{in}}$) is in agreement with that predicted for metallic systems near the MI transition. For the samples initially in the critical regime, a magnetic field of 8--10 T induces the transition to variable-range hopping. The typical localization length in PANI-CSA just on the insulating side of the MI transition is about 80--130 \AA{}. The magnitude of the positive magnetoresistance increases considerably as the system moves from the metallic to the insulating regime. The magnitude and quasilinear temperature dependence of the thermopower near the critical regime of the MI transition is typical of that expected for a metal.

Yong Cao

Papers

Influence of chemical polymerization conditions on the properties of polyaniline

Spectroscopic studies of polyaniline in solution and in spin-cast films

Morphology of conductive, solution-processed blends of polyaniline and poly(methyl methacrylate)

Counterion-induced processibility of polyaniline: Transport at the metal-insulator boundary.

Transport in polyaniline near the critical regime of the metal-insulator transition.