Dielectric constant of the polarizable dipolar hard sphere fluid studied by Monte Carlo simulation and theories

Valisko,; Boda, Dezső

doi:10.5488/cmp.8.2.357

Cited by 17 publications

(13 citation statements)

References 52 publications

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“…Assuming chaotic orientation under zero field, their reorientation and saturation under the applied field can be described by the introduction of an additional term into the CM equation (see Equation (13))

\frac{ε_{normaleff} - ε_{m}}{ε_{normaleff} + 2 ε_{m}} = \frac{n}{3 ε_{0}} (α + \frac{μ_{d}^{2}}{k_{B} T} g_{K})

Here, the Kirkwood g ‐factor (

g_{K}

in Equation (83)) accounts for the correlations between the dipoles at the Langevin level, and its correct value can be computed using molecular dynamics simulations. [ 150 ] Then, by using

α_{normaleff} = α + μ_{d}^{2} g_{K} / false(k_{B} T false)

instead of α in Sections 3– 5, our theoretical model for the nanocomposite permittivity can be extended to include any permanent dipoles of the inclusions. Here, however, extra care should be taken for inclusion rotations which might affect the mechanical properties of the nanocomposite, as discussed in ref.…”

Section: Discussionmentioning

confidence: 99%

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Allahyarov

2020

Advcd Theory and Sims

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A new analytical model is proposed for the nanocomposite permittivity eff in mean-field approach using integrated coefficients for the inclusion clustering and matrix reaction effects. Predictions for eff are in a satisfactory agreement with the Lichtenecker and Bruggeman mixing rules, depending on whether the reaction field is ignored or incorporated into the theory. The observed differences between the Maxwell-Garnett, Lichtenecker, and Bruggeman results are interpreted in terms of the fraction of the stored dipolar energy they take into account. A novel analytical expression for the average dipolar field ⟨ ⃗ E ⟩ in the film shows a U-shaped dependence on the filler packing fraction , with an absolute maximum at m = 1/e. New analytical expressions derived for the average dipolar energy u m and dipole-dipole interaction energy u m in the nanocomposite depend on the cluster orientation parameter , and take into account the film boundary effects. It is found that the enhancement of eff at higher is associated with an increase in the inclusion dipole moment p in the oriented clusters resulting from dipole-dipole correlations, which inflate the energy u p stored inside the inclusions.

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\frac{ε_{normaleff} - ε_{m}}{ε_{normaleff} + 2 ε_{m}} = \frac{n}{3 ε_{0}} (α + \frac{μ_{d}^{2}}{k_{B} T} g_{K})

Here, the Kirkwood g ‐factor (

g_{K}

in Equation (83)) accounts for the correlations between the dipoles at the Langevin level, and its correct value can be computed using molecular dynamics simulations. [ 150 ] Then, by using

α_{normaleff} = α + μ_{d}^{2} g_{K} / false(k_{B} T false)

Section: Discussionmentioning

confidence: 99%

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Allahyarov

2020

Advcd Theory and Sims

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“…(142), and the broken curves give the CM [6,7], Onsager [9], and MSA [12] results. The points are simulation results [8].…”

Section: Clausius-mossotti Results Formentioning

confidence: 99%

“…Sometimes this problem is called the polarization catastrophe. The CM result for is plotted and compared with some simulation results [8] in figure 1. There is no singularity in the simulation results.…”

Section: Clausius-mossotti Results Formentioning

confidence: 99%

Some simple results for the properties of polar fluids

Henderson¹

2011

Condens. Matter Phys.

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The author's lecture notes concerning the correlation functions and the thermodynamics of a simple polar fluid are summarized. The emphasis is on the dipolar hard sphere fluid and the mean spherical approximation and on the relation of these results to the Clausius-Mossotti and Onsager formulae for the dielectric constant. Previous excerpts from these lecture notes, Condens. Matter Phys., 2009, 12, 127; ibid., 2010, 13, 13002, have contained results that were not widely known. It is hoped that this third, and likely final, excerpt will prove equally helpful by gathering several results together and making these more widely available and recording a few new results.

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“…According to the Clausius‐Mosotti (C‐M) equation of dielectric polarization

P_{m} = \frac{ɛ - 1}{ɛ + 2} \times \frac{M}{ρ} = \frac{N_{A}}{3 ɛ_{0}} \times (α_{e} + α_{a} + α_{d})

where

P_{m}

is the polarization,

M

is the relative molecular weight,

ρ

is the density of the material, and

N_{A}

is the Avogadro's constant.…”

Section: Theoretical Analysismentioning

confidence: 99%

“…In the process of SBR's thermo-oxidative aging, a e barely changes from the external electric field which is much weaker than the electric field of the nucleus, so this part of the polarizability hardly changes in the THz field; a a is mainly caused by the deformation and twist of the atoms on the molecular-chain skeleton structure; a d is dependent on the fixed dipole moment and the polarity element. According to the Clausius-Mosotti (C-M) equation of dielectric polarization 36,37…”

Section: T Heor Eti Ca L Ana Lys I Smentioning

confidence: 99%

Evolution of terahertz dielectric permittivity of rubber during thermo‐oxidative aging

Chang

Zhang

Cui

2017

Micro & Optical Tech Letters

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Polymer materials such as rubber and plastics are prone to aging induced degradation, especially thermo-oxidative aging. In this paper, terahertz time-domain spectroscopy was employed to investigate the aging process of styrene butadiene rubber by spectrally following the evolution of its dielectric permittivity in the terahertz frequency region during prolonged high-temperature, accelerated, continuous thermo-oxidative aging. The real and imaginary parts of the dielectric constant in the 0.1-0.8 THz frequency band were obtained and analyzed, and shown to be consistent with present theoretical understanding. The study revealed a close relationship between the evolution of the rubber's dielectric permittivity and the material's physical response to the terahertz electromagnetic radiation during thermo-oxidative aging, manifesting a strong correlation between quantitative changes of the dielectric permittivity and the degree of aging, which can be understood qualitatively in terms of dynamical structural changes at the molecular level. K E Y W O R D Sterahertz, rubber, thermo-oxidative aging, dielectric permittivity | I NT RODU CTI ONThe polymer material styrene butadiene rubber (SBR), also known as polystyrene-butadiene copolymer, is currently the most popular man-made commercial rubber, accounting for more than 40% of sales, among all synthetic rubber materials, including butadiene rubber, styrene-butadiene rubber, isoprene rubber, and many others. 1 SBR resembles closely natural rubber, possessing many advantageous properties, such as wear-resistance and heat-resistance, higher curing rate compared with natural rubber, and good compatibility with natural rubbers and various synthetic rubbers. 2 As such it is widely used in aerospace, electronics, and automotive industries, as well as in consumer products such as appliances, apparel, and sporting goods, among many others. [3][4][5] Rubber is apt to suffer from aging due to high temperature, illumination, oxidation, hydrolysis, biodegradation, salt spray, and other environmental factors, 6,7 which degrades its quality and characteristic over time, and shortens its useful lifetime. Although aging of rubber is a natural phenomenon which is ultimately unavoidable, the prevention and retardation of aging, and proactive life prediction of rubber have been active research topics for many years. [8][9][10][11][12][13][14][15][16] Owing to its plastic nature, there are inherently flaws in the molecular structure of rubber, making it easily susceptible to aging due to invasion of external oxygen atoms. SBR's macromolecular chain has a type of unsaturated double bond structure, which readily reacts with oxygen atoms under common ambient conditions. The whole process has three phases, including chain initiation, chain propagation, and chain termination, with the stable product of degradation and crosslink formed at last. Currently, among the detection technologies for prediction of rubber aging, online spectral inspection approaches are the most popular, including i...

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Dielectric constant of the polarizable dipolar hard sphere fluid studied by Monte Carlo simulation and theories

Cited by 17 publications

References 52 publications

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Some simple results for the properties of polar fluids

Evolution of terahertz dielectric permittivity of rubber during thermo‐oxidative aging

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