najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-1-122-129najo-74Research ArticleCHEMISTRY AND MATERIAL SCIENCEХИМИЯ И МАТЕРИАЛОВЕДЕНИЕDetermining Young’s and shear moduli of a rod-shaped object in an AFM bending testОпределение модулей Юнга и сдвига стержнеобразного объекта в АСМ-испытании на изгибhttps://orcid.org/0000-0002-3450-0420АнкудиновА. В.AnkudinovA. A.

Александр Витальевич Анкудинов

Санкт Петербург, 194021

Alexander V. Ankudinov

Polytekhnicheskaya, 26, St. Petersburg, 194021

alexander.ankudinov@mail.ioffe.ruhttps://orcid.org/0000-0001-6038-223XДунаевскийM. С.DunaevskiyM. S.

Михаил Сергеевич Дунаевский

Санкт Петербург, 194021

Mikhail S. Dunaevskiy

Polytekhnicheskaya, 26, St. Petersburg, 194021

mike.dunaeffsky@mail.ioffe.ruhttps://orcid.org/0000-0002-3938-3024КрасилинА. А.KrasilinA. A.

Андрей Алексеевич Красилин

Санкт Петербург, 194021

Andrei A. Krasilin

Polytekhnicheskaya, 26, St. Petersburg, 194021

ikrasilin@mail.ioffe.ruhttps://orcid.org/0000-0002-5171-4690ХалисовМ. M.KhalisovM. M.

Максим Миндгалеевич Халисов

Санкт Петербург, 194021; Санкт Петербург, 199034

Maksim M. Khalisov – Ioffe Institute; Pavlov Institute of Physiology, Russian Academy of Sciences.

Polytekhnicheskaya, 26, St. Petersburg, 194021; Makarova emb., 6, St. Petersburg, 199034

khalisovmm@infran.ruhttps://orcid.org/0000-0003-2674-9653ХраповаЕ. К.KhrapovaE. K.

Екатерина Константиновна Храпова

Санкт Петербург, 194021

Ekaterina K. Khrapova

Polytekhnicheskaya, 26, St. Petersburg, 194021

arganella@yandex.ruФедеральное государственное бюджетное учреждение науки Физико-технический институт им. А.Ф. Иоффе Российской академии наукIoffe InstituteФедеральное государственное бюджетное учреждение науки Физико-технический институт им. А.Ф. Иоффе Российской академии наукIoffe Institute.Федеральное государственное бюджетное учреждение науки Физико-технический институт им. А.Ф. Иоффе Российской академии наук; Федеральное государственное бюджетное учреждение науки Институт физиологии им. И.П. Павлова Российской академии наукIoffe Institute; Pavlov Institute of Physiology, Russian Academy of Sciences202431052025151122129Copyright © Ankudinov A.A., Dunaevskiy M.S., Krasilin A.A., Khalisov M.M., Khrapova E.K., 20252025Анкудинов А.В., Дунаевский M.С., Красилин А.А., Халисов М.M., Храпова Е.К.Ankudinov A.A., Dunaevskiy M.S., Krasilin A.A., Khalisov M.M., Khrapova E.K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/74

The technique of AFM bending test of a suspended nanoobject has been improved. An analytical method has been created for calculating Young’s and shear moduli of object’s material based on data of such tests. In Timoshenko approximation, we consider problems of bending a beam one or both ends of which lie on elastic Winkler foundations. The obtained solutions are used to eliminate uncertainties in the calculation of elastic moduli that arise when the conditions of fixing an object (console or bridge) on the edges of a recess in the substrate are unknown.

Усовершенствована методика АСМ–испытаний подвешенного нанообъекта на изгиб. Создан аналитический способ расчета модулей Юнга и сдвига материала объекта по данным таких испытаний. В приближении Тимошенко рассмотрены задачи об изгибе балки, один или оба конца которой лежат на упругих основаниях Винклера. Полученные решения использованы для устранения неопределенностей в расчете упругих модулей, возникающих, когда неизвестны условия закрепления объекта (консоли или мостика) на краях углубления в подложке.

атомно-силовая микроскопияизгибупругие модулиупругое основание Винклераatomic force microscopybendingnanoscrollelastic modulielastic Winkler foundationThis work was supported by the Russian Science Foundation, project no. 19-1300151ReferencesBinnig G., Quate C.F., Gerber Ch. Atomic Force Microscope. Phys. Rev. Lett., 1986, 56(9), P. 930–933.Binnig G., Quate C.F., Gerber Ch. Atomic Force Microscope. Phys. Rev. Lett., 1986, 56(9), P. 930–933.Bhushan B. Nanotribology and Nanomechanics. An Introduction. Springer-Verlag, Berlin–Heidelberg, 2005, 928 p.Bhushan B. Nanotribology and Nanomechanics. An Introduction. Springer-Verlag, Berlin–Heidelberg, 2005, 928 p.Salvetat J.-P., Kulik A. J., Bonard J.-M., Briggs G., Andrew D., Sto¨ckli T., Me´te´nier K., Bonnamy S., Be´guin F., Burnham N. A., Forro´ L. Elastic Modulus of Ordered and Disordered Multiwalled Carbon Nanotubes. Adv. Mater., 1986, 11(2), P. 161–165.Salvetat J.-P., Kulik A. J., Bonard J.-M., Briggs G., Andrew D., Sto¨ckli T., Me´te´nier K., Bonnamy S., Be´guin F., Burnham N. A., Forro´ L. Elastic Modulus of Ordered and Disordered Multiwalled Carbon Nanotubes. Adv. Mater., 1986, 11(2), P. 161–165.Cuenot S., Demoustier-Champagne S., Nysten B. Elastic Modulus of Polypyrrole Nanotubes. Phys. Rev. Lett., 1999, 85(8), P. 1690–1693.Cuenot S., Demoustier-Champagne S., Nysten B. Elastic Modulus of Polypyrrole Nanotubes. Phys. Rev. Lett., 1999, 85(8), P. 1690–1693.Kis A. Mechanical properties of mesoscopic objects. // PhD Thesis. Lausanne, 2003, 166 p.Kis A. Mechanical properties of mesoscopic objects. // PhD Thesis. Lausanne, 2003, 166 p.Gangadean D., McIlroy D.N., Faulkner B.E., Aston D.E. Winkler boundary conditions for three-point bending tests on 1D nanomaterials. Nanotechnology, 2010, 21(22), P. 225704.Gangadean D., McIlroy D.N., Faulkner B.E., Aston D.E. Winkler boundary conditions for three-point bending tests on 1D nanomaterials. Nanotechnology, 2010, 21(22), P. 225704.Landau L.D., Lifshitz E.M. Theory of Elasticity. Pergamon Press, Oxford, 1970. 177 p.Landau L.D., Lifshitz E.M. Theory of Elasticity. Pergamon Press, Oxford, 1970. 177 p.Ankudinov A.V., Khalisov M.M. Contact Stiffness Measurements with an Atomic Force Microscope. Tech. Phys., 2020, 65(11), P. 1866–1872.Ankudinov A.V., Khalisov M.M. Contact Stiffness Measurements with an Atomic Force Microscope. Tech. Phys., 2020, 65(11), P. 1866–1872.Mai W., Wang Zh.L. Quantifying the elastic deformation behavior of bridged nanobelts. Appl. Phys. Lett., 2006, 89(7), P. 073112.Mai W., Wang Zh.L. Quantifying the elastic deformation behavior of bridged nanobelts. Appl. Phys. Lett., 2006, 89(7), P. 073112.Chen Yu., Dorgan B.L., McIlroy D.N., Eric Aston D. On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires. J. Appl. Phys., 2006, 100(10), P. 104301.Chen Yu., Dorgan B.L., McIlroy D.N., Eric Aston D. On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires. J. Appl. Phys., 2006, 100(10), P. 104301.Kluge D., Abraham F., Schmidt S., Schmidt H.-W., Fery A. Nanomechanical Properties of Supramolecular Self-Assembled Whiskers Determined by AFM Force Mapping. Langmuir, 2010, 26(5), P. 3020–3023.Kluge D., Abraham F., Schmidt S., Schmidt H.-W., Fery A. Nanomechanical Properties of Supramolecular Self-Assembled Whiskers Determined by AFM Force Mapping. Langmuir, 2010, 26(5), P. 3020–3023.Ankudinov A.V. A New Algorithm for Measuring the Young’s Modulus of Suspended Nanoobjects by the Bending-Based Test Method of Atomic Force Microscopy. Semiconductors, 2010, 53(14), P. 1891–1899.Ankudinov A.V. A New Algorithm for Measuring the Young’s Modulus of Suspended Nanoobjects by the Bending-Based Test Method of Atomic Force Microscopy. Semiconductors, 2010, 53(14), P. 1891–1899.Khalisov M.M., Lebedev V.A., Poluboyarinov A.S., Garshev A.V., Khrapova E.K., Krasilin A.A., Ankudinov A.V. Young’s modulus of phyllosilicate nanoscrolls measured by the AFM and by the in-situ TEM indentation. Nanosyst.: Phys. Chem. Math., 2021, 12(1), P. 118–127.Khalisov M.M., Lebedev V.A., Poluboyarinov A.S., Garshev A.V., Khrapova E.K., Krasilin A.A., Ankudinov A.V. Young’s modulus of phyllosilicate nanoscrolls measured by the AFM and by the in-situ TEM indentation. Nanosyst.: Phys. Chem. Math., 2021, 12(1), P. 118–127.Krasilin A.A., Khalisov M.M., Khrapova E.K., Kunkel T.S., Kozlov D.A., Anuchin N.M., Enyashin A.N., Ankudinov A.V. Surface Tension and Shear Strain Contributions to the Mechanical Behavior of Individual Mg-Ni-Phyllosilicate Nanoscrolls. Part. Part. Syst. Charact., 2021, 38(12), P. 2100153.Krasilin A.A., Khalisov M.M., Khrapova E.K., Kunkel T.S., Kozlov D.A., Anuchin N.M., Enyashin A.N., Ankudinov A.V. Surface Tension and Shear Strain Contributions to the Mechanical Behavior of Individual Mg-Ni-Phyllosilicate Nanoscrolls. Part. Part. Syst. Charact., 2021, 38(12), P. 2100153.Ankudinov A., Dunaevskiy M., Khalisov M., Khrapova E., Krasilin A. Atomic force microscopy bending tests of a suspended rod-shaped object: Accounting for object fixing conditions. Phys. Rev. E., 2021, 107(2), P. 025005.Ankudinov A., Dunaevskiy M., Khalisov M., Khrapova E., Krasilin A. Atomic force microscopy bending tests of a suspended rod-shaped object: Accounting for object fixing conditions. Phys. Rev. E., 2021, 107(2), P. 025005.Winkler E. Die Lehre von der Elastizita¨t und Festigkeit. Dominicus, Prague, 1867, 388 p.Winkler E. Die Lehre von der Elastizita¨t und Festigkeit. Dominicus, Prague, 1867, 388 p.Lekhnitskii S.G. Theory of Elasticity of an Anisotropic Body. Holden-Day, San Francisco, 1963, 404 p.Lekhnitskii S.G. Theory of Elasticity of an Anisotropic Body. Holden-Day, San Francisco, 1963, 404 p.Ting T.C.T., Chen T. Poisson’s ratio for anisotropic elastic materials can have no bounds. Q. J. Mech. Appl. Math., 2005, 58(1), P. 73–82.Ting T.C.T., Chen T. Poisson’s ratio for anisotropic elastic materials can have no bounds. Q. J. Mech. Appl. Math., 2005, 58(1), P. 73–82.Timoshenko S.P. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. London Edinburgh Dublin Philos. Mag. J. Sci., 1921, 41(245), P. 744–746.Timoshenko S.P. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. London Edinburgh Dublin Philos. Mag. J. Sci., 1921, 41(245), P. 744–746.Cowper G.R. The Shear Coefficient in Timoshenko’s Beam Theory. J. Appl. Mech., 1966, 33(2), P. 335–340.Cowper G.R. The Shear Coefficient in Timoshenko’s Beam Theory. J. Appl. Mech., 1966, 33(2), P. 335–340.Ankudinov A.V., Khalisov M.M. Bending test of nanoscale consoles in atomic force microscope. Tech. Phys. Lett., 2022, 48(2), P. 21–24.Ankudinov A.V., Khalisov M.M. Bending test of nanoscale consoles in atomic force microscope. Tech. Phys. Lett., 2022, 48(2), P. 21–24.Khrapova E.K., Ugolkov V.L., Straumal E.A., Lermontov S.A., Lebedev V.A., Kozlov D.A., Kunkel T.S., Nomine´ A., Bruyere S., Ghanbaja J., Belmonte T., Krasilin A.A. Thermal behavior of Mg-Ni-phyllosilicate nanoscrolls and performance of the resulting composites in hexene-1 and acetone hydrogenation. ChemNanoMat, 2021, 7(3), P. 207–207.Khrapova E.K., Ugolkov V.L., Straumal E.A., Lermontov S.A., Lebedev V.A., Kozlov D.A., Kunkel T.S., Nomine´ A., Bruyere S., Ghanbaja J., Belmonte T., Krasilin A.A. Thermal behavior of Mg-Ni-phyllosilicate nanoscrolls and performance of the resulting composites in hexene-1 and acetone hydrogenation. ChemNanoMat, 2021, 7(3), P. 207–207.Hutter J.L., Bechhoefer J. Calibration of atomic-force microscope tips. Rev. Sci. Instrum., 1993, 64(7), P. 1868–1873.Hutter J.L., Bechhoefer J. Calibration of atomic-force microscope tips. Rev. Sci. Instrum., 1993, 64(7), P. 1868–1873.Necˇas D., Klapetek P. Gwyddion: an open-source software for SPM data analysis. Open Phys., 2012, 10(1), P. 181–188.Necˇas D., Klapetek P. Gwyddion: an open-source software for SPM data analysis. Open Phys., 2012, 10(1), P. 181–188.

The authors declare that there are no conflicts of interest present.