Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models
To describe non-Debye relaxation phenomena observed in dielectric materials, the Cole–Cole (CC) relaxation model in the frequency domain and the Kohlrausch–Williams–Watts (KWW) relaxation model in the time domain were introduced in the physics of dielectrics. In this paper, we propose a new relaxati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/6/1281 |
| _version_ | 1797592520734015488 |
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| author | Lingjie Duan Junsheng Duan Ming Li |
| author_facet | Lingjie Duan Junsheng Duan Ming Li |
| author_sort | Lingjie Duan |
| collection | DOAJ |
| description | To describe non-Debye relaxation phenomena observed in dielectric materials, the Cole–Cole (CC) relaxation model in the frequency domain and the Kohlrausch–Williams–Watts (KWW) relaxation model in the time domain were introduced in the physics of dielectrics. In this paper, we propose a new relaxation model with two parameters besides a relaxation time by expressing the relaxation function in the time domain in terms of the Mittag–Leffler functions. The proposed model represents a group of non-Debye relaxation phenomena and shows a transition between the CC and the KWW models. The relaxation properties described by the new model are analyzed, including the response function, the normalized complex dielectric permittivity, dielectric storage and loss factors as well as the relaxation frequency and time spectral functions. The presented relaxation function has a concise form and is expected to be applied to more complex relaxation phenomena. |
| first_indexed | 2024-03-11T01:53:15Z |
| format | Article |
| id | doaj.art-998df12b2c8d476496085f2fdab81a32 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T01:53:15Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-998df12b2c8d476496085f2fdab81a322023-11-18T12:52:01ZengMDPI AGSymmetry2073-89942023-06-01156128110.3390/sym15061281Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation ModelsLingjie Duan0Junsheng Duan1Ming Li2School of Materials Science and Engineering, Shanghai Institute of Technology, Shanghai 201418, ChinaSchool of Sciences, Shanghai Institute of Technology, Shanghai 201418, ChinaOcean College, Zhejiang University, Hangzhou 310012, ChinaTo describe non-Debye relaxation phenomena observed in dielectric materials, the Cole–Cole (CC) relaxation model in the frequency domain and the Kohlrausch–Williams–Watts (KWW) relaxation model in the time domain were introduced in the physics of dielectrics. In this paper, we propose a new relaxation model with two parameters besides a relaxation time by expressing the relaxation function in the time domain in terms of the Mittag–Leffler functions. The proposed model represents a group of non-Debye relaxation phenomena and shows a transition between the CC and the KWW models. The relaxation properties described by the new model are analyzed, including the response function, the normalized complex dielectric permittivity, dielectric storage and loss factors as well as the relaxation frequency and time spectral functions. The presented relaxation function has a concise form and is expected to be applied to more complex relaxation phenomena.https://www.mdpi.com/2073-8994/15/6/1281dielectric materialnon-Debye relaxationrelaxation functionCole–Cole relaxationdielectric permittivityMittag–Leffler function |
| spellingShingle | Lingjie Duan Junsheng Duan Ming Li Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models Symmetry dielectric material non-Debye relaxation relaxation function Cole–Cole relaxation dielectric permittivity Mittag–Leffler function |
| title | Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models |
| title_full | Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models |
| title_fullStr | Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models |
| title_full_unstemmed | Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models |
| title_short | Relaxation Functions Interpolating the Cole–Cole and Kohlrausch–Williams–Watts Dielectric Relaxation Models |
| title_sort | relaxation functions interpolating the cole cole and kohlrausch williams watts dielectric relaxation models |
| topic | dielectric material non-Debye relaxation relaxation function Cole–Cole relaxation dielectric permittivity Mittag–Leffler function |
| url | https://www.mdpi.com/2073-8994/15/6/1281 |
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