Application of Kramers-Kronig relations to the interpretation of dielectric data

Lovell, R.

doi:10.1088/0022-3719/7/23/024

Cited by 43 publications

(27 citation statements)

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“…We have followed the numerical procedure described in [2]. The code of the computer program used for the calculations is given in [1].…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…To apply simple methods of integrations it is therefore necessary to interpolate between the points, which involves fitting exact parabolae to sets of three consecutive data points (see Eq. 8) [2].…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…An interpolating interval is the region in which a single interpolation equation is used. The following order was kept to perform the numerical integration over one interval (or part of an interval) at a time [2]:…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…In this work, we have investigated a numerical algorithm previously proposed in the literature for calculation of the K-K transform on experimental data [2]. The aim was to assess the validity and the accuracy of the approach in the case of dielectric spectra containing QDC response.…”

Section: Introductionmentioning

confidence: 99%

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Limitations of kramers-kronig transform for calculation of the DC conductance magnitude from dielectric measurements

Chalashkanov

Dodd

Fothergill

2012

2012 Annual Report Conference on Electrical Insulation and Dielectric Phenomena

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Abstract-The Kramers-Kronig (K-K) transform relates the real and imaginary parts of the complex susceptibility as a consequence of the principle of causality. It is a special case of the Hilbert transform and it is often used for estimation of the DC conductance from dielectric measurements. In this work, the practical limitations of a numerical implementation of the Kramers-Kronig transform was investigated in the case of materials that exhibit both DC conductance and quasi-DC (QDC) charge transport processes such as epoxy resins. The characteristic feature of a QDC process is that the real and imaginary parts of susceptibility (permittivity) follow fractional power law dependences with frequency with the low frequency exponent approaching -1. Dipolar relaxation in solids on the other hand has a lower frequency exponent <1. The computational procedure proposed by Jonscher for calculation of the K-K transform involves extrapolation and truncation of the data to low frequencies so that convergence of the integrals is ensured. The validity of the analysis is demonstrated by performing K-K transformation on real experimental data and on theoretical data generated using the Dissado-Hill function. It has been found that the algorithm works well for dielectric relaxation responses but it is apparent that it does not work in the case of a low frequency power law in which the low frequency exponent approaches -1, i.e. in the case of QDC responses. In this case convergence can only be guaranteed by extrapolating the low frequency power law over many decades towards zero frequency.

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“…We have followed the numerical procedure described in [2]. The code of the computer program used for the calculations is given in [1].…”

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Limitations of kramers-kronig transform for calculation of the DC conductance magnitude from dielectric measurements

Chalashkanov

Dodd

Fothergill

2012

2012 Annual Report Conference on Electrical Insulation and Dielectric Phenomena

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“…Therefore, the real and imaginary parts of the permittivity are dependent between them, they are related by the Kramers-Kroning relationships (Lovel, 1974;Wübbenhorst, et al, 2002). …”

Section: Phenomenological Description Of the Dielectric Measurementsmentioning

confidence: 99%

A contribution to the study of the molecular mobility in polymeric materials by Thermal and Dielectric Analysis

Foj¹,

Belén²

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T h e s i s S u p e r v i s o r : P R O F . D r . M a r í a J e s ú s S a n c h i s S á n c h e z t o o b t a i n t h e d e g r e e o f D o c t o r o f P h i l o s o p h y a t t h e U n i v e r s i t a t P o l i t è c n i c a d e V a l è n c i a Prof. Dr. María Jesús Sanchis SánchezThe work presented in this thesis was carried out at the Universitat Politècnica de València and was financially supported by the Spanish Ministry of Economy and Competitiveness (Projects Nos. MAT2008-06725-C03-03 and MAT2012-33483)."Cuando quieres algo, todo el Universo conspira para que ACKNOWLEDGEMENTSTras estos años de trabajo, llega el momento de mostrar mi agradecimiento a todas las personas que me han acompañado y apoyado durante el desarrollo de mi tesis doctoral.En primer lugar, me gustaría expresar mi gratitud a mi directora de tesis María J.Sanchis por su inestimable ayuda durante todos estos años. Muchas gracias por confiar en mí, por darme esta oportunidad y por las incalculables horas invertidas tanto para el desarrollo de esta tesis como al mío propio.También me gustaría agradecer a mis estimadas compañeras Marta Carsí y Pilar Ortiz su ayuda y amistad en este largo recorrido que suponer realizar una tesis doctoral. He aprendido mucho de vosotras tanto científica como personalmente. En este punto, no puedo olvidarme de mi querida Aurora Alonso, que pese a no formar parte de nuestro grupo de investigación, me ha apoyado, aconsejado y dado su amistad durante todos estos años.Quiero mostrar mi agradecimiento a los profesores José M. García y Félix C. García ABSTRACTThe development of new and more complex polymeric materials involves challenging problems to basic sciences. The relationship between structure and molecular dynamics assumes great importance for the future development of novel technologies based on such polymers. Thus, the understanding of how small changes in the chemical structure affect the properties of the material is essential to progress in the technological and scientific area. An in-depth analysis of the molecular mobility leads to establish the structure-properties relationships. On this basis, the main aim of the present work is to study the molecular mobility of two different families of polymeric materials. For this purpose, the experimental techniques mainly used were Differential Scanning Calorimetry (DSC) and Dielectric Relaxation Spectroscopy (DRS) (Chapter 3).The first family of polymers characterized was a series of chemically cross-linked copolymers composed by Vinylpyrrolidone (VP) and Butyl Acrylate (BA) monomers. The study was divided in two parts, which are collected in Chapter 4 and 5.In the first place, Chapter 4 contains the influence of the monomer molar ratio (XVP/YBA) on the copolymer properties. Thus, a Fourier Transform Infrared Spectroscopy (FTIR) analysis verified dipole-dipole interactions between amide groups. The influence of these interactions on several parameters related to the molecular mobility was evidenced by the DSC, DRS and Dynamic Mechanical Analysis (DMA) techni...

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Dielectric properties of propylene carbonate and propylene carbonate solutions

Barthel

Feuerlein

1984

J Solution Chem

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Application of Kramers-Kronig relations to the interpretation of dielectric data

Cited by 43 publications

References 1 publication

Limitations of kramers-kronig transform for calculation of the DC conductance magnitude from dielectric measurements

Limitations of kramers-kronig transform for calculation of the DC conductance magnitude from dielectric measurements

A contribution to the study of the molecular mobility in polymeric materials by Thermal and Dielectric Analysis

Dielectric properties of propylene carbonate and propylene carbonate solutions

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