{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T08:55:15Z","timestamp":1777625715598,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,8,3]],"date-time":"2017-08-03T00:00:00Z","timestamp":1501718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A practical model of quartz crystal microbalance (QCM) is presented, which considers both the Gaussian distribution characteristic of mass sensitivity and the influence of electrodes on the mass sensitivity. The equivalent mass sensitivity of 5 MHz and 10 MHz AT-cut QCMs with different sized electrodes were calculated according to this practical model. The equivalent mass sensitivity of this practical model is different from the Sauerbrey\u2019s mass sensitivity, and the error between them increases sharply as the electrode radius decreases. A series of experiments which plate rigid gold film onto QCMs were carried out and the experimental results proved this practical model is more valid and correct rather than the classical Sauerbrey equation. The practical model based on the equivalent mass sensitivity is convenient and accurate in actual measurements.<\/jats:p>","DOI":"10.3390\/s17081785","type":"journal-article","created":{"date-parts":[[2017,8,3]],"date-time":"2017-08-03T09:47:19Z","timestamp":1501753639000},"page":"1785","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":76,"title":["A Practical Model of Quartz Crystal Microbalance in Actual Applications"],"prefix":"10.3390","volume":"17","author":[{"given":"Xianhe","family":"Huang","sequence":"first","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingsong","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianguo","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9563","DOI":"10.3390\/s150409563","article-title":"A Study of a QCM Sensor Based on TiO2 Nanostructures for the Detection of NO2 and Explosives Vapours in Air","volume":"15","author":"Procek","year":"2015","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.bios.2015.12.071","article-title":"Metal-organic frameworks supported surface-imprinted nanoparticles for the sensitive detection of metolcarb","volume":"79","author":"Qian","year":"2016","journal-title":"Biosens. Bioelectron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.3390\/s110101177","article-title":"Respiratory Monitoring by Porphyrin Modified Quartz Crystal Microbalance Sensors","volume":"11","author":"Selyanchyn","year":"2011","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7580483","DOI":"10.1155\/2016\/7580483","article-title":"Using Quartz Crystal Microbalance for Field Measurement of Liquid Viscosities","volume":"2016","author":"Bai","year":"2016","journal-title":"J. Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"8540","DOI":"10.3390\/s150408540","article-title":"A Label-Free Immunosensor for Ultrasensitive Detection of Ketamine Based on Quartz Crystal Microbalance","volume":"15","author":"Yang","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.snb.2014.07.009","article-title":"Graphene nanostructures with plasma polymerized allylamine biosensor for selective detection of mercury ions","volume":"203","author":"Wang","year":"2014","journal-title":"Sens. Actuators Chem. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.snb.2009.08.029","article-title":"Designing of MIP-based QCM sensor for the determination of Cu(II) ions in solution","volume":"142","author":"Yang","year":"2009","journal-title":"Sens. Actuators Chem. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2807","DOI":"10.1109\/JSEN.2014.2316819","article-title":"Application of Molecularly Imprinted Polymer for Determination of Glucose by Quartz Crystal Nanobalance Technique","volume":"14","author":"Mirmohseni","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.bios.2014.10.055","article-title":"Quartz crystal microbalance detection of protein amplified by nicked circling, rolling circle amplification and biocatalytic precipitation","volume":"65","author":"Zhang","year":"2015","journal-title":"Biosens. Bioelectron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Diltemiz, S.E., Ke\u00e7ili, R., Ers\u00f6z, A., and Say, R. (2017). Molecular Imprinting Technology in Quartz Crystal Microbalance (QCM) Sensors. Sensors, 17.","DOI":"10.3390\/s17030454"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1038\/nprot.2010.65","article-title":"Quartz crystal microbalance with dissipation monitoring of supported lipid bilayers on various substrates","volume":"5","author":"Cho","year":"2010","journal-title":"Nat. Protoc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6946","DOI":"10.3390\/s130606946","article-title":"Detection of Fibrinogen and Coagulation Factor VIII in Plasma by a Quartz Crystal Microbalance Biosensor","volume":"13","author":"Yao","year":"2013","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1016\/j.snb.2015.11.002","article-title":"A piezoelectric immunosensor for the rapid detection of p16 (INK4a) expression in liquid-based cervical cytology specimens","volume":"224","author":"Yang","year":"2016","journal-title":"Sens. Actuators Chem. B"},{"key":"ref_14","first-page":"206","article-title":"Use of quartz vibration for weighing thin films on a microbalance","volume":"155","author":"Sauerbrey","year":"1959","journal-title":"J. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1039\/a702998e","article-title":"Mechanical behaviour of films on the quartz microbalance","volume":"107","author":"Kanazawa","year":"1997","journal-title":"Faraday Discuss."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2272","DOI":"10.1021\/ac00020a015","article-title":"Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading","volume":"63","author":"Martin","year":"1991","journal-title":"Anal. Chem."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Huang, X.H., Bai, Q.S., Zhou, Q., and Hu, J.G. (2017). The Resistance\u2013Amplitude\u2013Frequency Effect of In\u2013Liquid Quartz Crystal Microbalance. Sensors, 17.","DOI":"10.3390\/s17071476"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1021\/ac9908290","article-title":"Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance","volume":"72","author":"Martin","year":"2000","journal-title":"Anal. Chem."},{"key":"ref_19","first-page":"539","article-title":"Effective mass layer of a single drop of liquid located on a quartz crystal microbalance","volume":"29","author":"Bai","year":"2017","journal-title":"Sens. Mater."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1021\/bm020116i","article-title":"Quartz crystal microbalance: A useful tool for studying thin polymer films and complex biomolecular systems at the solution-surface interface","volume":"4","author":"Marx","year":"2003","journal-title":"Biomacromolecules"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1021\/ac9706032","article-title":"Analysis of the Radial Dependence of Mass Sensitivity for Modified-Electrode Quartz Crystal Resonators","volume":"70","author":"Josse","year":"1998","journal-title":"Anal. Chem."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1088\/0957-0233\/1\/7\/002","article-title":"The quartz crystal microbalance; 1 radial\/polar dependence of mass sensitivity both on and off the electrodes","volume":"1","author":"Cumpson","year":"1990","journal-title":"Meas. Sci. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1109\/TUFFC.2013.2788","article-title":"The modified design of ring electrode quartz crystal resonator for uniform mass sensitivity distribution","volume":"60","author":"Gao","year":"2013","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/S0925-4005(00)00550-5","article-title":"The quartz crystal microbalance: Mass sensitivity, viscoelasticity and acoustic amplification","volume":"70","author":"Lucklum","year":"2000","journal-title":"Sens. Actuators Chem. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1021\/ac00009a009","article-title":"Radial mass sensitivity of the quartz crystal microbalance in liquid media","volume":"63","author":"Ward","year":"1991","journal-title":"Anal. Chem."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1063\/1.1145993","article-title":"Local sensitivity of an electrochemical quartz crystal microbalance: Spatial location of the low frequency mode","volume":"66","author":"Oltra","year":"1995","journal-title":"Rev. Sci. Instrum."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1021\/ac00045a014","article-title":"Scanning electrochemical mass sensitivity mapping of the quartz crystal microbalance in liquid media","volume":"64","author":"Hillier","year":"1992","journal-title":"Anal. Chem."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.2116\/analsci.25.1069","article-title":"Laser response of a quartz crystal microbalance: Frequency changes induced by light irradiation in the air phase","volume":"25","author":"Kawaski","year":"2009","journal-title":"Anal. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/8\/1785\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:45:09Z","timestamp":1760208309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/8\/1785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,3]]},"references-count":28,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2017,8]]}},"alternative-id":["s17081785"],"URL":"https:\/\/doi.org\/10.3390\/s17081785","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,3]]}}}