DALILIN DA YA SA ƘARAMAR ƘWAYA KE ƊAUKAR CAJIN

Girgiza gari, zuba yashi, niƙa kofi: ƙwayoyin suna bugun juna kuma suna rabuwa da cajin wutar lantarki. Wannan tasiri, da ake kira cajin gogayya (tribocharging), yana taka rawa a fashewar duwatsu masu aman wuta, guguwar ƙura da walƙiya, da kuma a masana’antu, daga electrophotography da fesa shafi (spray coating) zuwa ƙera magunguna. Duk da haka, marubutan sun rubuta, tsarin aikinsa “har yanzu yana da wuyar ganewa”.

Yashi iri ɗaya, caji masu saɓani

Abubuwa biyu da aka lura da su ne suka mai da shi abin mamaki. Na farko, ƙwayoyin abu iri ɗaya suna sa wa juna caji, kuma girmansu ne ke yanke alƙiblar: abin da aka fi yarda da shi shi ne ƙananan ƙwayoyi suna zama korau (negative), manya kuma tabbatacce (positive). Na biyu, wannan alƙiblar caji (polarity) tana juyawa daga wani abu zuwa wani.

Bayanan da suka gabata sun yi tuntuɓe a kan ɗaya ko ɗayan. An ba da shawarar electron masu ƙarfin makamashi da suka maƙale a saman ƙwaya, amma ma’aunai sun gano sun yi ƙaranci da ba za su iya ɗaukar cajin ba. Sannan aka ba da shawarar musayar ions daga shimfiɗun hydroxide (OH⁻) da suka manne a saman (adsorbed), amma ba za ta iya bayyana dalilin da ya sa ƙwayoyi masu sinadarai iri ɗaya ke rarrabuwa bisa girma kawai ba. Tun 2018, a cewar takardar, tambayar tana nan a buɗe gaba ɗaya.

Zafin bugun

Donggeun Kang, Yong-Hyun Kim da abokan aikinsu a KAIST a Koriya ta Kudu, tare da Suranaree University of Technology a Thailand, sun fara daga sakamako mafi sauƙi na gogayya: zafi. Idan ƙwayoyi biyu suka yi karo, sun ɗauka cewa bugun yana ajiye adadin zafi ɗaya a saman ƙwayoyin biyu. Abin da ya bambanta shi ne inda wannan zafin ke zuwa. A ƙaramar ƙwaya, saman mai lanƙwasa yana tattara shi, kuma akwai ƙarancin abu da zai shanye shi. Ƙaramar ƙwayar ce ke ƙarewa da zafi mafi yawa.

Bambancin yanayin zafi tsakanin abubuwa biyu da ke taɓa juna yana haifar da ƙarfin lantarki (voltage): tasirin Seebeck (Seebeck effect), ƙa’idar da thermocouple ke aiki da ita. A nan, ΔV = −SΔT, inda S shi ne ma’aunin Seebeck (Seebeck coefficient) na abin. Wannan ƙarfin lantarki yana tura caji daga wannan ƙwaya zuwa waccan. Alamar S (sign) ce ke yanke alƙiblar: masu ɗaukar caji tabbatacce suna kwarara zuwa ƙwayar da ta fi zafi idan S tabbatacce ne; electron ne ke yin haka idan korau ne.

Zanen ƙaramar ƙwaya ja da babbar ƙwaya shuɗi da ke karɓar zafi daidai a wurin da suka taɓa juna, ƙaramar tana ƙara zafi, da kuma bayanan ƙarfin lantarki guda biyu da ke nuna caji tabbatacce ko korau suna ƙetarewa gwargwadon alamar S.

Zafi daidai, ɗumi ba daidai ba: bambancin zafi ΔT yana haifar da ƙarfin lantarki ΔV = −SΔT, kuma alamar ma’aunin Seebeck S ce ke ƙayyade ta wace hanya cajin ke kwarara. — Figure 1, Kang et al. (2026), arXiv:2610.36757.

’Yan kashi cikin dubu na digiri

Ƙungiyar ta warware lissafin zafi (heat equation) a cikin ƙwayoyi masu siffar ƙwallo yayin karo da ke ɗaukar kashi ɗaya cikin dubu goma na daƙiƙa, ga abubuwa goma sha biyu, daga nylon da siliki zuwa quartz da PVC.

Tsakanin ƙwayoyi biyu masu radius iri ɗaya (micrometre 100), abin da aka yi su da shi kaɗai ne ke canza sakamakon: wurin taɓawar yana ɗumama da kusan digiri 0.6 ga nylon idan aka kwatanta da kusan 0.17 ga quartz, kuma ƙarfin lantarkin suna da alamomi masu saɓani. Jerin abubuwan da aka yi hasashensa ta wannan hanya ya yi daidai da 83% na wani jerin triboelectric (triboelectric series) da aka wallafa, jerin da ke tsara abubuwa bisa cajin da suke ɗauka.
Tsakanin ƙwayoyin quartz biyu, ƙwaya mai radius na micrometre 100 idan aka kwatanta da wadda ta fi girma, bambancin yana ƙaruwa tare da bambancin girman: kashi 4.4 cikin dubu na digiri idan aka kwatanta da ƙwaya mai radius na micrometre 200, 10.5 idan aka kwatanta da mai radius na micrometre 800.

Karo dubu goma

Bugu ɗaya ba shi ne dukkan labarin ba: gari na gaske yana karo akai-akai. A cikin karo da yawa, kowace ƙwaya tana ɗumama gwargwadon ƙarfin ɗaukar zafinta (heat capacity), wanda ke ƙaruwa da kubin (cube) radius ɗinta. Daga nan, ƙarfin lantarkin da ke tsakanin ƙaramar ƙwaya da babba yana bin bambancin juzu’in kubin (inverse cubes) radius ɗinsu, R_s⁻³ − R_l⁻³.

Sannan marubutan sun kwaikwayi (simulated) cakuɗa ta ƙananan ƙwayoyi 600 (radius daga micrometre 50 zuwa 150) da manya 400 (micrometre 100 zuwa 400) a cikin karo 10,000. Ga quartz, wanda ma’aunin Seebeck ɗinsa korau ne, ƙananan ƙwayoyi suna ƙarewa korau, manya kuma tabbatacce: tsarin da aka saba gani. Ga nylon, wanda ma’aunin sa tabbatacce ne, tsarin yana juyawa. Halayen biyu sun yi daidai da abin da gwaje-gwaje suka ba da rahoto ga waɗannan abubuwa.

Hagu, ƙarfin lantarki tsakanin ƙananan ƙwayoyi da manya yana hawa tare da rabon girmansu, tabbatacce ga quartz kuma korau ga nylon; dama, histogram na caji da ke nuna ƙananan ƙwayoyi da manya a ɓangarori masu saɓani na sifili, a juye tsakanin quartz da nylon.

Ƙarfin lantarki tsakanin kowace ƙwaya biyu yana ƙaruwa tare da rabon girma, da alamomi masu saɓani ga quartz (ja) da nylon (shuɗi); ƙananan ƙwayoyi da manya suna ƙarewa da caji masu saɓani, kuma alƙiblar caji tana juyawa tsakanin abubuwan biyu. — Figure 4, Kang et al. (2026), arXiv:2610.36757.

Abin da samfurin ya ɗauka a matsayin gaskiya

Wannan takarda ce ta ka’ida (theory), ba tare da sabon gwaji ba. Tana ɗaukar cewa zafin kowane bugu yana rabuwa daidai tsakanin ƙwayoyin biyu; marubutan sun lura cewa ƙwayoyi masu bambancin tauri ko sassauci (elasticity) za su iya raba shi ba daidai ba, tambayar da ke a buɗe. Ƙwayoyin ƙwallaye ne cikakku (ideal spheres), kuma an ƙayyade wasu ma’aunai (parameters) da hannu, kamar rabon makamashin karon da ke juyawa zuwa zafi.

A cikin samfurinsu, siffa (geometry) ce ke yanke wace ƙwaya za ta fi zafi, abin da aka yi ƙwayar da shi kuma ne ke yanke ta wace hanya cajin zai tafi. Marubutan suna ganin a ciki “dabara ta gama-gari don sarrafa musayar caji da taɓawa ke haifarwa”.