{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:44:41Z","timestamp":1776771881830,"version":"3.51.2"},"reference-count":53,"publisher":"AIP Publishing","issue":"12","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2010,6,15]]},"abstract":"<jats:p>A thorough investigation of the ac electrical properties of carbon black (CB) mixed into ethylene butylacrylate copolymer has been conducted using ac impedance spectroscopy in the frequency range 10 Hz\u2013100 kHz and over the temperature range of 150 (Tg\u221248\u2002K)\u2013319\u2008(Tg+121\u2002K) K. For this investigation, a series of eight samples were prepared with various filler contents above the percolation threshold. Using the electric modulus formalism it has been found that the Cole\u2013Cole equation of dielectric relaxation expressed in the electric modulus form is capable of quantitatively describing the experimental data from which we extract the relaxation time and a parameter \u03b1 which gauges the broadening of the loss spectrum. The small values of \u03b1 ranging from 0.06 to 0.10 suggest a behavior close to the state of a single relaxation time. Furthermore, the relaxation time as a function of temperature is characterized by an Arrhenius behavior. While the effective activation energy is on the order of 60 meV and is insensitive to CB volume fraction, the Arrhenius prefactor is found to strongly depend on this volume fraction. The observed relaxation mechanism does not result simply from thermally activated dipolar interactions but is a collective cooperative effect of the CB mesostructure.<\/jats:p>","DOI":"10.1063\/1.3452366","type":"journal-article","created":{"date-parts":[[2010,6,25]],"date-time":"2010-06-25T22:12:59Z","timestamp":1277503979000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":69,"title":["Electric modulus-based analysis of the dielectric relaxation in carbon black loaded polymer composites"],"prefix":"10.1063","volume":"107","author":[{"given":"J.","family":"Belattar","sequence":"first","affiliation":[{"name":"Universit\u00e9 Ibn Tofail 1 D\u00e9partement de Physique, Laboratoire des Syst\u00e8mes des T\u00e9l\u00e9communications et d\u2019Ing\u00e9nierie de la D\u00e9cision, Facult\u00e9 des Sciences, , BP 133, 14000 K\u00e9nitra, Morocco"}]},{"given":"M. P. F.","family":"Gra\u00e7a","sequence":"additional","affiliation":[{"name":"Universidade de Aveiro 2 Department of Physics and I3N, , 3810-193 Aveiro, Portugal"}]},{"given":"L. C.","family":"Costa","sequence":"additional","affiliation":[{"name":"Universidade de Aveiro 2 Department of Physics and I3N, , 3810-193 Aveiro, Portugal"}]},{"given":"M. E.","family":"Achour","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Ibn Tofail 1 D\u00e9partement de Physique, Laboratoire des Syst\u00e8mes des T\u00e9l\u00e9communications et d\u2019Ing\u00e9nierie de la D\u00e9cision, Facult\u00e9 des Sciences, , BP 133, 14000 K\u00e9nitra, Morocco"}]},{"given":"C.","family":"Brosseau","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Brest 3 Universit\u00e9 Europ\u00e9enne de Bretagne, , Lab-STICC and D\u00e9partement de Physique, CS 93837, 6 avenue Le Gorgeu, 29238 Brest Cedex 3, France"}]}],"member":"317","published-online":{"date-parts":[[2010,6,25]]},"reference":[{"key":"2023062410202904400_c1a","volume-title":"An elastic and Dielectric Effects in Polymeric Solids","year":"1991"},{"key":"2023062410202904400_c1b","first-page":"171","volume":"13","year":"1972","journal-title":"Phys. Chem. Glasses"},{"key":"2023062410202904400_c1c","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1111\/j.1151-2916.1972.tb13413.x","volume":"55","year":"1972","journal-title":"J. Am. Ceram. Soc."},{"key":"2023062410202904400_c1d","first-page":"122","volume":"14","year":"1973","journal-title":"Phys. Chem. Glasses"},{"key":"2023062410202904400_c1e","first-page":"51","volume":"23","year":"1998","journal-title":"Bull. Mater. Res. Soc."},{"key":"2023062410202904400_c1f","doi-asserted-by":"publisher","first-page":"9396","DOI":"10.1103\/PhysRevB.60.9396","volume":"60","year":"1999","journal-title":"Phys. Rev. B"},{"key":"2023062410202904400_c2","volume-title":"Broadband Dielectric Spectroscopy","year":"2003"},{"key":"2023062410202904400_c3","first-page":"177","volume-title":"Prospects in Filled Polymers Engineering: Mesostructure, Elasticity Network, and Macroscopic Properties","author":"Brosseau","year":"2008"},{"key":"2023062410202904400_c4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0079-6565(93)80004-D","volume":"25","year":"1993","journal-title":"Prog. Nucl. Magn. Reson. Spectrosc."},{"key":"2023062410202904400_c5"},{"key":"2023062410202904400_c6","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1109\/TDEI.2002.1038664","volume":"9","year":"2002","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"2023062410202904400_c7","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1109\/6144.868841","volume":"23","year":"2000","journal-title":"IEEE Trans. Compon. Packag. Technol."},{"key":"2023062410202904400_c8","doi-asserted-by":"publisher","first-page":"094103","DOI":"10.1063\/1.2912985","volume":"103","year":"2008","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c9","doi-asserted-by":"publisher","first-page":"124102","DOI":"10.1063\/1.3149702","volume":"105","year":"2009","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c10","doi-asserted-by":"publisher","first-page":"104107","DOI":"10.1063\/1.3253744","volume":"106","year":"2009","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c11"},{"key":"2023062410202904400_c12a","doi-asserted-by":"publisher","first-page":"3197","DOI":"10.1063\/1.1447307","volume":"91","year":"2002","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c12b","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1063\/1.366725","volume":"83","year":"1998","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c12c","doi-asserted-by":"publisher","first-page":"104325","DOI":"10.1063\/1.1915539","volume":"97","year":"2005","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c13a","doi-asserted-by":"publisher","first-page":"8297","DOI":"10.1063\/1.1371938","volume":"89","year":"2001","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c13b","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1063\/1.364173","volume":"81","year":"1997","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c13c","doi-asserted-by":"publisher","first-page":"1904","DOI":"10.1088\/0022-3727\/31\/15\/020","volume":"31","year":"1998","journal-title":"J. Phys. D"},{"key":"2023062410202904400_c14a","doi-asserted-by":"publisher","first-page":"084111","DOI":"10.1063\/1.2718867","volume":"101","year":"2007","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c14b","doi-asserted-by":"publisher","first-page":"074105","DOI":"10.1063\/1.2988269","volume":"104","year":"2008","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c14c","doi-asserted-by":"publisher","first-page":"074907","DOI":"10.1063\/1.2988900","volume":"104","year":"2008","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c14d","doi-asserted-by":"publisher","first-page":"123518","DOI":"10.1063\/1.3042218","volume":"104","year":"2008","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c15","volume-title":"Random Heterogeneous Materials: Microstructure and Macroscopic Properties","year":"2002"},{"key":"2023062410202904400_c16","volume-title":"Heterogeneous Materials I: Linear Transport and Optical Properties","year":"2003"},{"key":"2023062410202904400_c17","year":"2003"},{"key":"2023062410202904400_c18","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1080\/00150199608223611","volume":"176","year":"1996","journal-title":"Ferroelectrics"},{"key":"2023062410202904400_c19","doi-asserted-by":"publisher","first-page":"054108","DOI":"10.1063\/1.3080244","volume":"105","year":"2009","journal-title":"J. Appl. Phys."},{"key":"2023062410202904400_c20","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.jnoncrysol.2004.07.089","volume":"351","year":"2005","journal-title":"J. Non-Cryst. Solids"},{"key":"2023062410202904400_c21","doi-asserted-by":"publisher","first-page":"2027","DOI":"10.1023\/A:1004398514901","volume":"33","year":"1998","journal-title":"J. Mater. Sci."},{"key":"2023062410202904400_c22a","volume-title":"Introduction to Percolation Theory","year":"1992"},{"key":"2023062410202904400_c22b","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0079-6425(93)90004-5","volume":"37","year":"1993","journal-title":"Prog. Mater. Sci."},{"key":"2023062410202904400_c22c","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1080\/00018739000101501","volume":"39","year":"1990","journal-title":"Adv. Phys."},{"key":"2023062410202904400_c23a","doi-asserted-by":"publisher","first-page":"1975","DOI":"10.1063\/1.117179","volume":"69","year":"1996","journal-title":"Appl. Phys. Lett."},{"key":"2023062410202904400_c23b","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/S0008-6223(00)00242-6","volume":"39","year":"2001","journal-title":"Carbon"},{"key":"2023062410202904400_c23c","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0008-6223(01)00166-X","volume":"40","year":"2002","journal-title":"Carbon"},{"key":"2023062410202904400_c24a","doi-asserted-by":"publisher","first-page":"14880","DOI":"10.1103\/PhysRevB.58.14880","volume":"58","year":"1998","journal-title":"Phys. Rev. B"},{"key":"2023062410202904400_c24b","doi-asserted-by":"publisher","first-page":"13558","DOI":"10.1103\/PhysRevB.58.13558","volume":"58","year":"1998","journal-title":"Phys. Rev. B"},{"key":"2023062410202904400_c25","volume-title":"Dielectric Properties of Heterogeneous Materials, Progress in Electromagnetics Research","author":"Priou","year":"1992"},{"key":"2023062410202904400_c26"},{"key":"2023062410202904400_c27a","doi-asserted-by":"publisher","first-page":"1068","DOI":"10.1088\/0022-3727\/35\/10\/316","volume":"35","year":"2002","journal-title":"J. Phys. D"},{"key":"2023062410202904400_c27b","doi-asserted-by":"publisher","first-page":"4071","DOI":"10.1002\/app.23274","volume":"101","year":"2006","journal-title":"J. Appl. Polym. Sci."},{"key":"2023062410202904400_c28","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.jnoncrysol.2009.11.008","volume":"356","year":"2010","journal-title":"J. Non-Cryst. Solids"},{"key":"2023062410202904400_c29","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1063\/1.1750906","volume":"9","year":"1941","journal-title":"J. Chem. Phys."},{"key":"2023062410202904400_c30","volume-title":"Principles of Dielectrics","year":"1989"},{"key":"2023062410202904400_c31","doi-asserted-by":"publisher","first-page":"373","DOI":"10.3144\/expresspolymlett.2008.44","volume":"2","year":"2008","journal-title":"Express Polym. Lett."},{"key":"2023062410202904400_c32a","volume-title":"Dielectric Relaxation in Solids","year":"1987"},{"key":"2023062410202904400_c32b","volume-title":"Universal Relaxation Law","year":"1996"},{"key":"2023062410202904400_c32c","doi-asserted-by":"publisher","first-page":"R57","DOI":"10.1088\/0022-3727\/32\/14\/201","volume":"32","year":"1999","journal-title":"J. Phys. D"},{"key":"2023062410202904400_c33"}],"container-title":["Journal of Applied Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jap\/article-pdf\/doi\/10.1063\/1.3452366\/13458898\/124111_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jap\/article-pdf\/doi\/10.1063\/1.3452366\/13458898\/124111_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T23:50:50Z","timestamp":1687650650000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jap\/article\/107\/12\/124111\/145909\/Electric-modulus-based-analysis-of-the-dielectric"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,15]]},"references-count":53,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2010,6,15]]}},"URL":"https:\/\/doi.org\/10.1063\/1.3452366","relation":{},"ISSN":["0021-8979","1089-7550"],"issn-type":[{"value":"0021-8979","type":"print"},{"value":"1089-7550","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2010,6,15]]},"published":{"date-parts":[[2010,6,15]]},"article-number":"124111"}}