Conjugated Polymers at Nanoscale by Karen K. Gleason Meysam Heydari Gharahcheshmeh

Author:Karen K. Gleason, Meysam Heydari Gharahcheshmeh
Language: eng
Format: epub
Publisher: De Gruyter
Published: 2021-06-25T09:36:05.870000+00:00

4.1

Frequency dependent dielectric behavior

All the fixed and mobile charges in a material respond to the electromagnetic field of light [3, 5]. The response depends on the angular frequency of the light and is described by the complex dielectric function, ε(ω) = ε1(ω) + iε2(ω). The dielectric function can be obtained from transmission or reflection measurements. Absorption peaks in the spectral range for ultraviolet and visible light typically correspond to transitions between electronic states that can be displayed on a DOS diagram. Covalent chemical bonds act as local oscillators at infrared frequencies. The corresponding transitions between vibronic states are typically observed at infrared frequencies using Fourier transform infrared (FTIR) or Raman spectroscopies. Because of the quantum mechanical selection rules governing the allowable optical transitions differ for FTIR and Raman, these two methods are complementary. Higher frequency processes can be accessed through terahertz (THz) spectroscopy. In nonisotropic materials, the optical constants can depend on the direction of measurement. This anisotropy can be observed using variable angle spectroscopic ellipsometry.

The frequency-dependent optoelectronic response of an electron has been modeled as Lorentz oscillator [11]. In a localized covalent bond, there is restorative force which depends on bond strength. Conventional dielectric polymers give rise to multiple optical adsorption peaks, each centered at a different frequency. A given peak appears at the energy which is signature of a particular type of covalent chemical bond, enabling the assignment of peaks in FTIR and Raman spectroscopy. Since bonding orbitals are often not isotropic, varying the angle of incidence of the light can reveal the orientation distribution of the polymer chains.

The Drude model assumes only a single oscillator with no restoring force. The Drude model is widely used for conventional metals and has also been applied for conjugated polymers [3, 5, 7]. When low-frequency light is incident upon a metal, the displacement of mobile charge carriers can maintain a zero value of electric field in the solid. In this case, the incident oscillating electromagnetic wave is reflected. Reflection gives common metals their shiny appearance. Highly conductive poly(acetylene) (PA) has also been reported to have a silvery appearance [12].

At high frequencies, metals become transparent. Transparency occurs when the external field oscillates too rapidly for the free charge carrier gas of the metal to follow. According to the Drude model, the transition between a reflective and transparent response occurs at the plasmon frequency, ωp, as given by [7, 13]

(4.1)

An important consequence of eq. (4.1) is that charge carrier density, nc, determines range of the frequencies yielding transparent behavior, ω > ωp.

More complex models incorporate deviations from the assumption of completely free charge carriers [5]. For example, the Drude–Smith model considers weak carrier confinement, where the mean free path of the charge carrier is comparable to the mesoscale of the confining structure. Indeed, the Drude–Smith model has been applied to a wide range of nanomaterials, where short-range charge carrier dynamics are studied by THz spectroscopy [14]. The Drude–Smith model also provides an accurate description of the frequency dependent dielectric behavior of conjugated polymers with mesoscale crystalline domains [5].

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