[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81882-en":3,"doc-seo-81882-105":31,"detail-sidebar-cat-0-en-105":85},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},81882,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Graph-Based Kirchhoff Modeling of Non-Ohmic Electron Transport in Self-Assembled Nanonecklace Networks","Gold nanonecklace networks enable single-electron switching, chemical sensing, and biogating through nonlinear current–voltage behavior caused by collective Coulomb-blockade transport, yet the governing mechanisms remain unclear because experiments often reveal only network topology and global I–V response. A graph-based Kirchhoff framework models the network as a conductance graph, returning active nodes, conducting subgraphs, nodal potentials, and edge currents. The approach reproduces I ∝ (V−VT)ζ and attributes threshold behavior to staggered junction activation and voltage-driven percolation, with parameter sweeps isolating activation statistics, density, and topology effects.","arXiv :2607 .03698v1 [ cond-mat .mes-hall ] 4 Jul 2026  \nGraph-Based Kirchhoff Modeling of Non-Ohmic Electron Transport in Self-Assembled Nanonecklace Networks  \nObed Issakah,† Srivathsan Badrinarayanan,‡ Ravi F. Saraf,† and Janghoon  \nOck∗ ,†  \n†Department of Chemical and Biomolecular Engineering, University of Nebraska–Lincoln,  \nLincoln, NE 68588, USA  \n‡Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue,  \nPittsburgh, PA 15213, USA  \nE-mail: [jock2@unl.edu](jock2@unl.edu)  \nAbstract  \nGold nanonecklace networks are promising platforms for single-electron switching, chemical sensing, and biogating devices because of their nonlinear current–voltage (I– V ) characteristics arising from collective Coulomb-blockade transport. However, the mechanisms governing this macroscopic behavior remain poorly understood because experimental measurements are generally limited to the network topology and global I–V response. To address this, we developed a graph-based Kirchhoff framework that represents a self-assembled nanonecklace network as a graph, with nodes corresponding to junctions between necklace segments and edges to the conducting segments themselves. The solver returns the active nodes, conducting subgraph, nodal potentials, and edge currents at each applied bias, while allowing the activation-voltage statistics,  \nnetwork density, and structural topology to be varied independently. The model reproduces the experimentally observed non-Ohmic response, I ∝ (V −VT)ζ , and shows that this behavior emerges from the collective, staggered activation of threshold junctionsand voltage-driven percolation of the conducting subgraph. Independent parameter sweeps reveal that the mean activation voltage shifts the threshold VT while leaving ζ nearly unchanged, increasing network density raises ζ from approximately 1.9 to  \n3.1 and enhances current, and topology controls the response even at fixed density and node characteristics. These trends agree qualitatively with experimental observations and establish the model as a design tool for engineering collective transport in self-assembled nanonecklace devices.  \nKeywords: Nanonetworks, Self-assembly, Percolation threshold, Kirchhoff’s law, Disordered charge transport.  \nIntroduction  \nGold nanonecklace networks are an emerging class of functional nanomaterials. They exhibit a sharp non-Ohmic conduction threshold, with current suppressed below a critical voltage and rising steeply above it. This switch-like behavior at room temperature makes them promising for single-electron switching, chemical sensing, and biogating. These quasione-dimensional chains of closely spaced gold nanoparticles spontaneously form in solution through directed self-assembly. 1 Within each chain, ligand chemistry and ion-mediated interactions set the inter-particle gaps with sub-nanometer precision, 2–4 giving direct control over the local capacitance, charge energy, and plasmonic coupling at each junction; the ionmediated growth that sets this spacing itself proceeds through a sharp transition between distinct kinetic regimes.4 As the necklace solution then deposits onto a substrate and interconnects into two-dimensional networks, single-electron charging and tunneling effects that are normally washed out in bulk conductors begin to dominate. 5,6 This network structure, its density, branching, connectivity, and disorder, is in turn tunable through particle concen-  \ntration, ligand choice, substrate, and assembly time, 4,7 enabling multiscale structural control through fabrication conditions alone.  \nThis structural hierarchy has direct and quantifiable material consequences. Each interparticle gap behaves as a nanoscale dielectric barrier whose capacitance is determined by particle size and ligand spacing. 8 For sub-10 nm particles with alkanethiol ligands, adding a single electron across this barrier costs a charging energy EC = e2 /2C that can exceed kB Tat room temperature. 5 So sing","cbCaipm5qN9KLy8P","https://ap.wps.com/l/cbCaipm5qN9KLy8P","pdf",28555510,5,1,34,"English","en",105,"# Abstract\n# Introduction\n## Non-Ohmic threshold and room-temperature switching\n## Self-assembled structure and nanoscale gap physics\n## Collective transport via percolation and topology","[{\"question\":\"How do mean activation voltage, network density, and topology separately affect the I–V response?\",\"answer\":\"Changing the mean activation voltage shifts the threshold VT while keeping ζ nearly unchanged; increasing network density raises ζ (about 1.9 to 3.1) and enhances current; topology continues to control the response even when density and node characteristics are fixed.\"}]","Graph-Based Kirchhoff Modeling of Non-Ohmic Electron Transport in Self-Assembled Nanonecklace Networks | PDF",1784176840,86,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":80,"head_meta":82,"extra_data":84,"updated_unix":29},"graph-based-kirchhoff-modeling-of-non-ohmic-electron-transport-in-self-assembled-nanonecklace-networks","",{"@graph":37,"@context":79},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/graph-based-kirchhoff-modeling-of-non-ohmic-electron-transport-in-self-assembled-nanonecklace-networks/81882/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-07-29","2026-07-16",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73],{"name":74,"@type":75,"acceptedAnswer":76},"How do mean activation voltage, network density, and topology separately affect the I–V response?","Question",{"text":77,"@type":78},"Changing the mean activation voltage shifts the threshold VT while keeping ζ nearly unchanged; increasing network density raises ζ (about 1.9 to 3.1) and enhances current; topology continues to control the response even when density and node characteristics are fixed.","Answer","https://schema.org",{"og:url":53,"og:type":81,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":83,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":86},[87,91,95,99,103,108,113,116,121,124,128],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":88,"show_sort_weight":89,"slug":90},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":92,"show_sort_weight":93,"slug":94},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Comic",60,"comic",{"id":104,"doc_module":4,"doc_module_name":47,"category_name":105,"show_sort_weight":106,"slug":107},6,"Technology",50,"technology",{"id":109,"doc_module":4,"doc_module_name":47,"category_name":110,"show_sort_weight":111,"slug":112},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":114,"slug":115},30,"research-report",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},9,"Religion & Spirituality",20,"religion-spirituality",{"id":119,"doc_module":4,"doc_module_name":47,"category_name":122,"show_sort_weight":119,"slug":123},"World Cup","world-cup",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":125,"slug":127},10,"Lifestyle","lifestyle",{"id":129,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":20,"slug":131},19,"General","general"]