The kinetics of cluster fragmentation and depolymerisation
Open accessAbstract
The equation that describes fragmentation kinetics, such as that which occurs in cluster breakup and polymer chain degradation (depolymerisation), is solved for models where the rate of breakup depends upon the size of the object breaking up. The resulting dynamic scaling behaviour is investigated. Both discrete and continuous models are considered.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Kumar and Ramkrishna [292] technique applied to binary and multiple breakages, aggregation with constant, sum, and product kernels, and simultaneous breakage and aggregation; comparison between analytical and numerical results shows good agreement.
“The technique has been applied to binary and multiple breakages with power-law breakage rates, aggregation with constant, sum, and product kernel, and simultaneous breakage and aggregation. Comparison between analytical [293-295] and numerical results show good agreement.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [293]
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredEQMOM numerical results compare favorably with available analytical ones for PBE considering aggregation, breakage, condensation, and evaporation.
“The EQMOM has been used to solve a PBE considering aggregation, breakage, condensation, and evaporation terms, and the numerical results compare favorably with the available analytical ones [288,293,301,318,322].”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [293]
The Introduction and Conclusions present analytical solutions for fragmentation (breakage), so this paper can serve as an example of an available analytical result. It does not report EQMOM calculations or compare their numerical results with analytical ones, and it does not solve a PBE containing all four listed processes. Page numbers are not available in our copy. (LLM, conf=0.87)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Formation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation
Meakin, P. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.1119 · Cited by 1,647 · see citing works
Scaling of Kinetically Growing Clusters
Kolb, M., Botet, R. S., & Jullien, R. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.1123 · Cited by 1,065 · see citing works
Dynamic Scaling for Aggregation of Clusters
Vicsek, T., & Family, F. (1984) · Physical Review Letters · doi:10.1103/physrevlett.52.1669 · Cited by 583 · see citing works
Theory of Depolymerization of Long Chain Molecules
Montroll, E. W., & Simha, R. (1940) · The Journal of Chemical Physics · doi:10.1063/1.1750807 · Cited by 275 · see citing works
Coagulation equations with gelation
Hendriks, E. M., Ernst, M. H., & Ziff, R. M. (1983) · Journal of Statistical Physics · doi:10.1007/bf01019497 · Cited by 245 · see citing works
Self-citationOn the effect of high energy radiation to polymers I. Cross-linking and degradation
Saito, O. (1958) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.13.198 · Cited by 235 · see citing works
Molecular-weight changes in the degradation of long-chain polymers
Charlesby, A. (1954) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1954.0145 · Cited by 192 · see citing works
Note on the Kinetics of Systems Manifesting Simultaneous Polymerization-Depolymerization Phenomena
Blatz, P. J., & Tobolsky, A. V. (1945) · The Journal of Physical Chemistry · doi:10.1021/j150440a004 · Cited by 169 · see citing works
Kinetics of reversible polymerization
van Dongen, P. G. J., & Ernst, M. H. (1984) · Journal of Statistical Physics · doi:10.1007/bf01011836 · Cited by 133 · see citing works
Equilibrium and kinetic theory of polymerization and the sol-gel transition
Cohen, R. J., & Benedek, G. B. (1982) · The Journal of Physical Chemistry · doi:10.1021/j100216a005 · Cited by 126 · see citing works
Kinetic Studies on the Acid Hydrolysis of Dextran
Basedow, A. M., Ebert, K. H., & Ederer, H. J. (1978) · Macromolecules · doi:10.1021/ma60064a031 · Cited by 120 · see citing works
Degradation of chain molecules. 1. Exact solution of the kinetic equations
Ballauff, M., & Wolf, B. A. (1981) · Macromolecules · doi:10.1021/ma50004a039 · Cited by 100 · see citing works
The degradation of long‐chain molecules by ultrasonic waves. I. Theoretical
Jellinek, H. H. G., & White, G. (1951) · Journal of Polymer Science · doi:10.1002/pol.1951.120060609 · Cited by 97 · see citing works
Large-time behavior of the Smoluchowski equations of coagulation
Leyvraz, F. (1984) · Physical Review A · doi:10.1103/physreva.29.854 · Cited by 64 · see citing works
Degradation of long chain molecules
Mark, H. W., & Simha, R. (1940) · Transactions of the Faraday Society · doi:10.1039/tf9403500611 · Cited by 49 · see citing works
Polymers and Theory of Numbers. I. The Single-Chain Theory of Degradation
Nanda, V. S., & Pathria, R. K. (1959) · The Journal of Chemical Physics · doi:10.1063/1.1729885 · Cited by 21 · see citing works
Theory of a Non-Random Degradation of Linear Chain Molecules
Amemiya, A. (1962) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.17.1245 · Cited by 10 · see citing works
Further Investigation on the Non-Random Degradation on Linear Chain Molecules
Amemiya, A. (1962) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.17.1694 · Cited by 9 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- Charlesby A 1954 Proc. R. Soc. A 224 120
- Mark H and Simha R 1940 Trans. Faraday Soc. 35 611
Cited by
Sorted by citations
On the solution of population balance equations by discretization—I. A fixed pivot technique
Kumar, S., & Ramkrishna, D. (1996) · Chemical Engineering Science · doi:10.1016/0009-2509(96)88489-2 · Cited by 1,109 · see citing works
A Theoretical Model of Erosion and Macromolecular Drug Release from Biodegrading Microspheres
Batycky, R. P., Hanes, J., Langer, R., & Edwards, D. A. (1997) · Journal of Pharmaceutical Sciences · doi:10.1021/js9604117 · Cited by 374 · see citing works
An extended quadrature method of moments for population balance equations
Yuan, C., Laurent, F., & Fox, R. O. (2012) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2012.04.003 · Cited by 225 · see citing works
Analytical solution for a population balance equation with aggregation and fragmentation
J. McCoy, B., & Madras, G. (2003) · Chemical Engineering Science · doi:10.1016/s0009-2509(03)00159-3 · Cited by 92 · see citing works
Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review
Luzi, G., & McHardy, C. (2022) · Energies · doi:10.3390/en15113966 · Cited by 44 · see citing works
Lage, P. L. C. (2011) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2011.05.017 · Cited by 43 · see citing works
- Authors
- Ziff, R. M., & McGrady, E. D.
- Affiliations
- University of Michigan (US)
- ORCID
- Ziff, R M
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1985-10-21
- Volume
- 18
- Issue
- 15
- Pages
- 3027-3037
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2124966449
- Cited by
- 397
- References
- 18
- Citations by year
- 2026: 15 · 2025: 15 · 2024: 15 · 2023: 16 · 2022: 14 · 2021: 12 · 2020: 14 · 2019: 11 · 2018: 8 · 2017: 11 · 2016: 10 · 2015: 15 · 2014: 17 · 2013: 7 · 2012: 8
- FWCI
- 1.27
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Deep Blue (University of Michigan) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Keywords
- fragmentation kinetics, cluster fragmentation, depolymerization, polymer chain degradation, dynamic scaling, discrete models, continuous model
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
