Explicit Solutions in a Probabilistic Cellular Automaton Model for Self-Assembled Monolayer Degradation

@misc{caldwell2026explicit,
  title = {{Explicit Solutions in a Probabilistic Cellular Automaton Model for Self-Assembled Monolayer Degradation}},
  author = {Wes Caldwell and Ryan Evans and Jacob Majikes and Anthony Kearsley},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14256},
  eprint = {2610.14256},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14256},
}

TY  - UNPB
TI  - Explicit Solutions in a Probabilistic Cellular Automaton Model for Self-Assembled Monolayer Degradation
AU  - Wes Caldwell
AU  - Ryan Evans
AU  - Jacob Majikes
AU  - Anthony Kearsley
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.14256
UR  - https://arxiv.org/abs/2610.14256
AB  - Self-assembled monolayers (SAMs), formed by the adsorption of a monomolecular layer of adsorbate onto a surface, have emerged as leading candidates for plat- forms for electrochemical biosensors. In order to characterize the working age of a SAM-based biosensor, it is necessary to understand the long-term degradation of the monolayer, with particular emphasis on the intermolecular forces present in the self-assembly process. In this work, discrete- and continuous-time proba- bilistic cellular automaton (PCA) models for the degradation of SAMs involving adsorbate-adsorbate interactions are proposed in which adsorbate molecules desorb at a rate dependent only on the number of adsorbed neighbors. Impor- tantly, we make no assumptions on the relationship between degradation rate and adsorbed neighbors. Using techniques from generating function theory and complex analysis, the expected degradation curve is solved for explicitly in one dimension and shown to be a sigmoid curve related to the Gompertz function.
ER  -