{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:16:33Z","timestamp":1789517793618,"version":"build-2803163510"},"reference-count":50,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T00:00:00Z","timestamp":1759276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Funds"},{"name":"Silesian University of Technology","award":["FESL.10.25-IZ.01-07E7\/23"],"award-info":[{"award-number":["FESL.10.25-IZ.01-07E7\/23"]}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Materials"],"abstract":"<jats:p>Poly(3,4-ethylenedioxythiophene): polystyrene sulfonate (PEDOT:PSS) is a conductive water-processable polymer with many important applications in organic electronics. The electrical conductivity of PEDOT:PSS layers is very diverse and can be changed by changing the processing and post-deposition conditions, e.g., by using different solvent additives, doping or modifying the physical conditions of the layer deposition. Despite many years of intensive research on the relationship between the microstructure and properties of these layers, there are still gaps in our knowledge, especially with respect to the detailed understanding of the charge carrier transport mechanism in organic semiconductor thin films. In this work, we investigate the effect of acid doping of PEDOT:PSS thin films on the intra-chain and inter-chain conductivity by developing a model that treats PEDOT:PSS as a nanocomposite material. This model is based on the effective medium theory and uses the percolation theory equation for the electrical conductivity of a mixture of two materials. Here its implementation assumes that the role of the highly conductive material is attributed to the intra-chain conductivity of PEDOT and its quantitative contribution is determined based on the optical Drude\u2013Lorentz model. While the weaker inter-chain conductivity is assumed to originate from the weakly conductive material and is determined based on electrical measurements using the van der Pauw method and coherent nanostructure-dependent analysis. Our studies show that doping with methanesulfonic acid significantly affects both types of conductivity. The intra-chain conductivity of PEDOT increases from 260 to almost 400 Scm\u22121. Meanwhile, the inter-chain conductivity increases by almost three orders of magnitude, reaching a critical state, i.e., exceeding the percolation threshold. The observed changes in electrical conductivity due to acid doping are attributed to the flattening of the PEDOT\/PSS gel nanoparticles. In the model developed here, this flattening is accounted for by the inclusion shape factor.<\/jats:p>","DOI":"10.3390\/ma18194569","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T09:37:21Z","timestamp":1759311441000},"page":"4569","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Studies of Intra-Chain and Inter-Chain Charge Carrier Conduction in Acid Doped Poly(3,4-ethylenedioxythiophene) Polystyrene Sulfonate Thin Films"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0249-1016","authenticated-orcid":false,"given":"Ayman A. A.","family":"Ismail","sequence":"first","affiliation":[{"name":"Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie-Sk\u0142odowskiej 34, 41-819 Zabrze, Poland"},{"name":"Joint Doctoral School, Silesian University of Technology, Akademicka 2a, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6721-2011","authenticated-orcid":false,"given":"Henryk","family":"Bednarski","sequence":"additional","affiliation":[{"name":"Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie-Sk\u0142odowskiej 34, 41-819 Zabrze, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7934-7861","authenticated-orcid":false,"given":"Andrzej","family":"Marcinkowski","sequence":"additional","affiliation":[{"name":"Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie-Sk\u0142odowskiej 34, 41-819 Zabrze, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5659","DOI":"10.1039\/D0RA07800J","article-title":"Conducting polymers: A comprehensive review on recent advances in synthesis, properties and applications","volume":"11","author":"Namsheer","year":"2021","journal-title":"RSC Adv."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11611","DOI":"10.1039\/C4RA15947K","article-title":"Storing energy in plastics: A review on conducting polymers & their role in electrochemical energy storage","volume":"5","author":"Abdelhamid","year":"2015","journal-title":"RSC Adv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4609","DOI":"10.1021\/acsapm.2c00519","article-title":"Conductive polymers for flexible and stretchable organic optoelectronic applications","volume":"4","author":"Wu","year":"2022","journal-title":"ACS Appl. Polym. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1002\/adfm.201002290","article-title":"Highly conductive PEDOT: PSS electrode with optimized solvent and thermal post-treatment for ITO-free organic solar cells","volume":"21","author":"Kim","year":"2011","journal-title":"Adv. Funct. Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"14138","DOI":"10.1073\/pnas.1509958112","article-title":"Ultrahigh electrical conductivity in solution-sheared polymeric transparent films","volume":"112","author":"Worfolk","year":"2015","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"18561","DOI":"10.1039\/D3TA03213B","article-title":"PEDOT:PSS materials for optoelectronics, thermoelectrics, and flexible and stretchable electronics","volume":"11","author":"Fan","year":"2023","journal-title":"J. Mater. Chem. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1002\/adma.201304611","article-title":"Highly conductive PEDOT:PSS nanofibrils induced by solution-processed crystallization","volume":"26","author":"Kim","year":"2014","journal-title":"Adv Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10035","DOI":"10.1039\/C6NR00818F","article-title":"High-performance planar green light-emitting diodes based on a PEDOT:PSS\/CH3NH3PbBr3\/ZnO sandwich structure","volume":"8","author":"Shi","year":"2016","journal-title":"Nanoscale"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1038\/nmat3012","article-title":"Optimization of the thermoelectric figure of merit in the conducting polymer poly(3,4-ethylenedioxythiophene)","volume":"10","author":"Bubnova","year":"2011","journal-title":"Nat. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1039\/C6NR06156G","article-title":"Laser-patterned functionalized CVD-graphene as highly transparent conductive electrodes for polymer solar cells","volume":"9","author":"Villari","year":"2017","journal-title":"Nanoscale"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17570","DOI":"10.1021\/acsami.9b00934","article-title":"Conducting and stretchable PEDOT:PSS electrodes: Role of additives on self-assembly, morphology, and transport","volume":"11","author":"Dauzon","year":"2019","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3982","DOI":"10.1039\/C9TC06311K","article-title":"The key mechanism of conductivity in PEDOT:PSS thin films exposed by anomalous conduction behaviour upon solvent-doping and sulfuric acid post-treatment","volume":"8","author":"Hosseini","year":"2020","journal-title":"J. Mater. Chem. C"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7118","DOI":"10.1039\/D1MA00290B","article-title":"Mechanisms for doped PEDOT:PSS electrical conductivity improvement","volume":"2","author":"Shahrim","year":"2021","journal-title":"Mater. Adv."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"072101","DOI":"10.1088\/0953-8984\/21\/7\/072101","article-title":"Correlation of morphology and charge transport in poly(3,4-ethylenedioxythiophene)\u2013polystyrenesulfonic acid (PEDOT\u2013PSS) films","volume":"21","author":"Sangeeth","year":"2009","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3859","DOI":"10.1021\/ma300120g","article-title":"PEDOT nanocrystal in highly conductive PEDOT:PSS polymer films","volume":"45","author":"Takano","year":"2012","journal-title":"Macromolecules"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1500017","DOI":"10.1002\/aelm.201500017","article-title":"Effective approaches to improve the electrical conductivity of PEDOT:PSS: A review","volume":"1","author":"Shi","year":"2015","journal-title":"Adv. Electron. Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0379-6779(01)00576-8","article-title":"Enhancement of electrical conductivity of poly(3,4-ethylenedioxythiophene)\/poly(4-styrenesulfonate) by a change of solvents","volume":"126","author":"Kim","year":"2002","journal-title":"Synth. Met."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"10575","DOI":"10.1039\/D4CS00541D","article-title":"PEDOT-based stretchable optoelectronic materials and devices for bioelectronic interfaces","volume":"53","author":"Li","year":"2024","journal-title":"Chem. Soc. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2000641","DOI":"10.1002\/admi.202000641","article-title":"Role of the Processing Solvent on the Electrical Conductivity of PEDOT:PSS","volume":"7","author":"Dong","year":"2020","journal-title":"Adv. Mater. Interfaces"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"116628","DOI":"10.1016\/j.synthmet.2020.116628","article-title":"Morphological modulation to improve thermoelectric performances of PEDOT:PSS films by DMSO vapor post-treatment","volume":"271","author":"Xu","year":"2021","journal-title":"Synth. Met."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1800085","DOI":"10.1002\/adsu.201800085","article-title":"Enhancement of conductivity and thermoelectric property of PEDOT:PSS via acid doping and single post-treatment for flexible power generator","volume":"2","author":"Wang","year":"2018","journal-title":"Adv. Sustain. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2400151","DOI":"10.1002\/apxr.202400151","article-title":"High Conductivity in PEDOT:PSS Thin-Films by Secondary Doping with Superacid Vapor: Mechanisms and Application to Thermoelectrics","volume":"4","author":"Park","year":"2025","journal-title":"Adv. Phys. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"14089","DOI":"10.1021\/acsami.5b03309","article-title":"Conductivity enhancement of PEDOT:PSS films via phosphoric acid treatment for flexible all-plastic solar cells","volume":"7","author":"Meng","year":"2015","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2300979","DOI":"10.1002\/smtd.202300979","article-title":"Enhancing the conductivity of PEDOT:PSS films by the confinement of ice crystals","volume":"8","author":"Chen","year":"2024","journal-title":"Small Methods"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4350","DOI":"10.1039\/C8TC06302H","article-title":"On the anomalous optical conductivity dispersion of electrically conducting polymers: Ultra-wide spectral range ellipsometry combined with a Drude\u2013Lorentz model","volume":"7","author":"Chen","year":"2019","journal-title":"J. Mater. Chem. C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4699","DOI":"10.1039\/D4MA00078A","article-title":"Beyond acid treatment of PEDOT:PSS: Decoding mechanisms of electrical conductivity enhancement","volume":"5","author":"Yousefian","year":"2024","journal-title":"Mater. Adv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"9577","DOI":"10.1021\/acsaem.4c02092","article-title":"Acid doping of PEDOT:PSS strengthens interfacial compatibility toward efficient and stable perovskite solar cells","volume":"7","author":"Deng","year":"2024","journal-title":"ACS Appl. Energy Mater."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1800075","DOI":"10.1002\/adma.201800075","article-title":"All-solution-processed metal-oxide-free flexible organic solar cells with over 10% efficiency","volume":"30","author":"Song","year":"2018","journal-title":"Adv. Mater."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.1002\/polb.10659","article-title":"Conductivity, morphology, interfacial chemistry, and stability of poly(3,4-ethylene dioxythiophene)\u2013poly(styrene sulfonate): A photoelectron spectroscopy study","volume":"41","author":"Crispin","year":"2003","journal-title":"J. Polym. Sci. B Polym. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"100616","DOI":"10.1016\/j.pmatsci.2019.100616","article-title":"Progress in understanding structure and transport properties of PEDOT-based materials: A critical review","volume":"108","author":"Gueye","year":"2020","journal-title":"Prog. Mater. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10368","DOI":"10.1021\/jacs.2c02139","article-title":"Efficient electronic tunneling governs transport in conducting polymer-insulator blends","volume":"144","author":"Keene","year":"2022","journal-title":"J. Am. Chem. Soc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0034-4885\/64\/1\/201","article-title":"Electronic transport properties of conducting polymers and carbon nanotubes","volume":"64","author":"Kaiser","year":"2001","journal-title":"Rep. Prog. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"12964","DOI":"10.1103\/PhysRevB.57.12964","article-title":"Theory of the field-effect mobility in amorphous organic transistors","volume":"57","author":"Vissenberg","year":"1998","journal-title":"Phys. Rev. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0379-6779(97)04167-2","article-title":"Transport properties of poly(3,4-ethylenedioxythiophene)\/poly(styrenesulfonate)","volume":"94","author":"Aleshin","year":"1998","journal-title":"Synth. Met."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"085208","DOI":"10.1103\/PhysRevB.76.085208","article-title":"Anisotropic hopping conduction in spin-coated PEDOT:PSS thin films","volume":"76","author":"Nardes","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"101990","DOI":"10.1016\/j.progpolymsci.2025.101990","article-title":"PEDOT:PSS-based Electronic Materials: Preparation, Performance Tuning, Processing, Applications, and Future Prospect","volume":"166","author":"Chen","year":"2025","journal-title":"Prog. Polym. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3368","DOI":"10.1103\/PhysRevB.12.3368","article-title":"Generalized effective-medium approach to the conductivity of an inhomogeneous material","volume":"12","author":"Stroud","year":"1975","journal-title":"Phys. Rev. B"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Bednarski, H., Ismail, A.A.A., Godzierz, M., Marcinkowski, A., Khan, M.R., Jarz\u0105bek, B., Hajduk, B., and Kumari, P. (2024). Nanostructure-dependent electrical conductivity model within the framework of the generalized effective medium theory applied to poly(3-hexyl)thiophene thin films. Polymers, 16.","DOI":"10.3390\/polym16223227"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1002\/polb.23089","article-title":"Why does the electrical conductivity in PEDOT:PSS decrease with PSS content? A study combining thermoelectric measurements with impedance spectroscopy","volume":"50","author":"Moos","year":"2012","journal-title":"J. Polym. Sci. B Polym. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.12693\/APhysPolA.130.1242","article-title":"The influence of PEDOT to PSS ratio on the optical properties of PEDOT:PSS thin solid films\u2014Insight from spectroscopic ellipsometry","volume":"130","author":"Bednarski","year":"2016","journal-title":"Acta Phys. Pol. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.pquantelec.2014.10.001","article-title":"Hyperbolic metamaterials and their applications","volume":"40","author":"Ferrari","year":"2015","journal-title":"Prog. Quantum Electron."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"069501","DOI":"10.1117\/1.JNP.6.069501","article-title":"Bruggeman formalism versus \u201cBruggeman formalism\u201d: Particulate composite materials comprising oriented ellipsoidal particles","volume":"6","author":"Mackay","year":"2012","journal-title":"J. Nanophotonics"},{"key":"ref_43","first-page":"7","article-title":"Multiscale phenomena in Bruggeman composites","volume":"86","author":"Skomski","year":"2005","journal-title":"MRS Online Proc. Libr."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1088\/0022-3719\/21\/8\/025","article-title":"Measurement and analysis of a model dual-conductivity medium using a generalised effective-medium theory","volume":"21","author":"McLachlan","year":"1988","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_45","first-page":"784","article-title":"The depolarization factors for ellipsoids and some of their properties","volume":"15","author":"Yunos","year":"2019","journal-title":"Malays. J. Fundam. Appl. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.jcis.2020.09.070","article-title":"PEDOT:PSS nano-particles in aqueous media: A comparative experimental and molecular dynamics study of particle size, morphology and z-potential","volume":"584","author":"Jain","year":"2021","journal-title":"J. Colloid Interface Sci."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Griffiths, D.J. (2023). Introduction to Electrodynamics, Cambridge University. [5th ed.].","DOI":"10.1017\/9781009397735"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"5196","DOI":"10.1103\/PhysRevB.50.5196","article-title":"Hopping in disordered conducting polymers","volume":"50","author":"Zuppiroli","year":"1994","journal-title":"Phys. Rev. B"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1002\/adfm.200700796","article-title":"A morphological model for the solvent-enhanced conductivity of PEDOT:PSS thin films","volume":"18","author":"Nardes","year":"2008","journal-title":"Adv. Func, Mater."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1002\/adma.200602575","article-title":"Microscopic understanding of the anisotropic conductivity of PEDOT:PSS thin films","volume":"19","author":"Nardes","year":"2007","journal-title":"Adv. Mater."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/18\/19\/4569\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T04:14:25Z","timestamp":1759464865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/18\/19\/4569"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,1]]},"references-count":50,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["ma18194569"],"URL":"https:\/\/doi.org\/10.3390\/ma18194569","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,1]]}}}