Kerr-effect measurements on poly(vinylidine fluoride), poly(methyl methacrylate) and their blends

Hartig, Ch.; Kleppinger, Ralf; Jungnickel, B.‐J.

doi:10.1016/0032-3861(95)96823-q

Cited by 8 publications

(6 citation statements)

References 13 publications

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“…Typical material constants for PMMA were estimated and are given in Table 2 and are obtained from Refs. [9,[48][49][50][51][52][53]. Note that the mechanical response is similar to the Mindlin's model of linear elastic solids with microstructure [54].…”

Section: Continuum Flexoelectricitymentioning

confidence: 61%

“…Indeed, if one used Eqs. (45) and (49) for estimating the angles of the shear and the dilatational Mach line pairs, respectively, one can retrieve both of the measured angles by simply inputting the measured normalized rupture speed and by assuming the micro length ratios to be equal to of h p /ℓ p = 1.09 and h s /ℓ s = 1.0, respectively. Indeed, this seems to be a very good prediction given the fact that the widely accepted electromechanical properties for PMMA from the open literature, listed in Table 2, predict h p /ℓ p = 1.11 and h s /ℓ s = 1.00.…”

Section: Explaining An Experimental Paradoxmentioning

confidence: 99%

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Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation

Giannakopoulos

Rosakis

2020

Journal of Applied Mechanics

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Motivated by recent, unexpected, experimental observations of “intersonic” rupture growth in which both shear and dilatational Mach fronts were observed at the tips of dynamic frictional ruptures propagating at rupture speeds below the dilatational wave speed of the surrounding solid, and we formulate the general dynamic flexoelectric problem and we investigate its plane strain/plane polarization specialization. The coupling of the mechanical problem is analogous to a problem of Toupin–Mindlin gradient elasticity, where two micromechanical characteristic lengths and two microinertial lengths emerge as a combination of the mechanical, dielectric, and flexoelectric constants. The solution of the rupture growth problem allows us to provide an explanation of the experimental results. This becomes possible since flexoelectricity predicts a new aspect that was not observed in the classical analysis: subsonic super shear and supersonic crack tip (or rupture) motions are not related exclusively with the problem being elliptic or hyperbolic, respectively. This is due to the influence of the microinertial lengths, which, in addition to the ratios of the rupture to the wave speeds, also affect the slopes of the Mach cones. Moreover, we are able to explain the experimental paradox of the observation of double Mach cone pairs at the tips of supershear, but subsonic, frictional, ruptures in poly-methyl-methacrtylate (PMMA) by demonstrating that both dilatational and shear Mach cones could appear in flexoelectric solids at rupture speeds below the material dilatation wave speed, something that is impossible from the classical elasticity analysis and is due to the dispersive nature of the present problem. Our analysis is of relevance to the dynamic deformation and fracture of both synthetic and naturally occurring flexoelectric materials and systems, with implications to both engineering and earthquake source mechanics.

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Section: Continuum Flexoelectricitymentioning

confidence: 61%

Section: Explaining An Experimental Paradoxmentioning

confidence: 99%

Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation

Giannakopoulos

Rosakis

2020

Journal of Applied Mechanics

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“…The B value of PMMA film is reported to be 1.5 × 10 -15 mV -2 . 39 In the present experiments, light excitation was at around 300 nm, and the applied field strength was 1MV cm -1 ,that is, 1 × 10 8 Vm -1 ; therefore, ∆n is estimated to be 4.6 × 10 -6 . The magnitude of the field-induced change in refractive index is considered to be the same order of magnitude as ∆n.…”

Section: Steady-state Measurements Of E-a and E-e Spectramentioning

confidence: 81%

“…The refractive index of the matrix (PMMA) may change in the presence of an electric field, that is, the so-called DC Kerr effect is expected. 39 It may be pointed out that the field-induced change in emission quantum yield results from the change in radiative decay rate constant, as a result of the field-induced change in refractive index of PMMA. Note that the radiative decay rate constant depends on the refractive index of the matrix.…”

Section: Steady-state Measurements Of E-a and E-e Spectramentioning

confidence: 99%

External Electric Field Effects on Absorption, Fluorescence and Phosphorescence Spectra of 4-(Dimethylamino)benzonitrile in a Polymer Film

et al. 2004

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Electric-field-induced changes in the absorption, fluorescence, and phosphorescence spectra of 4-(dimethylamino)benzonitrile (DMABN) doped in a polymer film were measured, and the electric dipole moment and molecular polarizability in the locally excited (LE) and charge transfer (CT) singlet states as well as in the phosphorescent triplet state were evaluated. Time-resolved fluorescence measurements both in the absence and in the presence of electric fields were also carried out. A field-induced change in the quantum yield of the LE and CT fluorescence as well as of the phosphorescence is found and the charge transfer from the LE to the CT state is shown to be accelerated by an electric field, resulting in the field-induced decrease in the population ratio of the LE relative to the CT state. The dipole moment of the phosphorescent triplet state is found to be smaller than that of the LE state, with a value similar to that of the ground state.

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“…From dynamical Kerr effect measurements of pure PMMA it is well known that, at room temperature, well below the glass transition, a β-relaxation occurs at ν β around 5 to 10 Hz. 20 The δ relaxation in side chain polymers substituted with rod like chromophores, which also would contribute to a reorientation due to the polarizability anisotropy, however, occurs at ambient with extremely slow rates ν β ≈ 10 -8 Hz. 21 From that it is clear that at room temperature no significant contributions from orientational polarization to the electrooptical response are expected if electric modulation frequencies from 200 Hz to 10 kHz or above are applied.…”

Section: Resultsmentioning

confidence: 99%

Electrooptically tunable photonic crystal

Schmidt

Eich

Huebner

et al. 2005

Linear and Nonlinear Optics of Organic Materials V

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We report on electrooptical modulation with a sub 1Volt sensititivity in a photonic crystal slab waveguide resonator which contains a nanostructured nonlinear optical polymer. The electrooptical susceptibility in the core was induced by high-electric-field poling. A square lattice of holes carrying a linear defect was transferred into the slab, creating a photonic crystal slab based resonator. Applying an external electric modulation voltage to electrodes placed underneath and on top of the assembly leads to a modulation of the transmission at a fixed wavelength. This modulation effect is based on the electronic displacement polarization in a noncentrosymmetric medium (Pockels-effect) and is therefore inherently by more than three orders of magnitude faster than any other reported electrooptic modulation effect in nanophotonics. INTRODUCTIONOptically transparent dielectrics which are periodically structured in one two or three dimensions generally are called photonic crystals 1, 2 . The structuring typically results in frequency gaps which inhibit propagation of waves at such frequencies. However, discontinuities or defects implanted on purpose into the otherwise regular lattice lead to localized states which provide the option for micron sized waveguide 3, 4 and optical resonators of high quality factors 5-8 . For reasons of simpler manufacturing processes we concentrate on optical slab waveguides into which vertical holes are drilled. Such photonic crystal slabs typically exhibit gaps for transverse electric (TE-like) polarization. The concept proposed here utilizes the ultrafast response times of the Pockels effect which is a second order nonlinear optical effect based on electronic displacement polarization. This effect can only be observed in noncentrosymmetric media such as single crystalline GaAs, poled LiNbO 3 and in poled organic polymers which carry nonlinear optically active groups. GaAs has a very high refractive index (n=3.4), can be nanostructured well and is widely used as photonic crystal base material. However, it suffers from its small electrooptic susceptibility of only 1.2 pm/V. LiNbO 3 with its moderate refractive index (n=2.2) at NIR wavelengths and its high r 33 =31 pm/V is an interesting candidate also because of its excellent waveguiding properties but up today no feasible technique to structure this material on submicron scales and at the required aspect ratios was reported. Covalently functionalized organic nonlinear optical polymers 9 poled at high field strengths have been shown to exhibit very high electrooptical susceptibilities from several pm/V to well above 100 pm/V. 10, 11 These materials can be structured on submicron scales to form photonic crystal slabs. The relatively low refractive index therefore is an advantage in ultra high bandwidth applications, for instance, in long structures. Whenever direction independent stop gaps are not needed, such as in ultrarefractive dispersive photonic crystals and in one dimensional resonators the low refractive index contrast does...

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Kerr-effect measurements on poly(vinylidine fluoride), poly(methyl methacrylate) and their blends

Cited by 8 publications

References 13 publications

Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation

Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation

External Electric Field Effects on Absorption, Fluorescence and Phosphorescence Spectra of 4-(Dimethylamino)benzonitrile in a Polymer Film

Electrooptically tunable photonic crystal

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