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Gray TH, Yong EH. Effective diffusion in one-dimensional rough potential-energy landscapes. Phys Rev E 2020; 102:022138. [PMID: 32942433 DOI: 10.1103/physreve.102.022138] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.
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Affiliation(s)
- Thomas H Gray
- Department of Chemical Engineering and Biotechnology, West Cambridge Site, Philippa Fawcett Drive, University of Cambridge, CB3 0AS, Cambridge, United Kingdom
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - Ee Hou Yong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
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Bleyl I, Erdelen C, Schmidt HW, Haarer D. One-dimensional hopping transport in a columnar discotic liquid-crystalline glass. ACTA ACUST UNITED AC 2009. [DOI: 10.1080/13642819908206420] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Ingo Bleyl
- a Lehrstuhl Experimentalphysik IV , Universitat Bayreuth , D-95440 , Bayreuth , Germany
| | - Christian Erdelen
- b Lehrstuhl Makromolekulare Chemie I and Bayreuther Institut für Makromolekülforschung , Universität Bayreuth , D-95440 , Bayreuth , Germany
| | - Hans-Werner Schmidt
- b Lehrstuhl Makromolekulare Chemie I and Bayreuther Institut für Makromolekülforschung , Universität Bayreuth , D-95440 , Bayreuth , Germany
| | - Dietrich Haarer
- a Lehrstuhl Experimentalphysik IV , Universitat Bayreuth , D-95440 , Bayreuth , Germany
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Hoofman RJOM, Gelinck GH, Siebbeles LDA, de Haas MP, Warman JM, Bloor D. Influence of Backbone Conformation on the Photoconductivity of Polydiacetylene Chains. Macromolecules 2000. [DOI: 10.1021/ma000485b] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Romano J. O. M. Hoofman
- Radiation Chemistry Department, IRI, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - Gerwin H. Gelinck
- Radiation Chemistry Department, IRI, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - Laurens D. A. Siebbeles
- Radiation Chemistry Department, IRI, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - Matthijs P. de Haas
- Radiation Chemistry Department, IRI, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - John M. Warman
- Radiation Chemistry Department, IRI, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - David Bloor
- Department of Physics, University of Durham, Durham, DH1 3LE, United Kingdom
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van de Craats AM, Siebbeles LDA, Bleyl I, Haarer D, Berlin YA, Zharikov AA, Warman JM. Mechanism of Charge Transport along Columnar Stacks of a Triphenylene Dimer. J Phys Chem B 1998. [DOI: 10.1021/jp9828989] [Citation(s) in RCA: 70] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Anick M. van de Craats
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
| | - Laurens D. A. Siebbeles
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
| | - Ingo Bleyl
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
| | - Dietrich Haarer
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
| | - Yuri A. Berlin
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
| | - Anatoly A. Zharikov
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
| | - John M. Warman
- IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands, Lehrstuhl Experimentalphysik IV and Bayreuther Institut für Makromolekülforschung (BIMF), Universität Bayreuth, D-95440 Bayreuth, Germany, and Technische Universität München, Physik Department T-38, D-85748 München, Germany
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