On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 1409–1418, doi:10.3762/bjnano.11.125

• viscoelastic harmonic functions as a function of frequency in the range of frequencies involved in the experiment. For example, for the Generalized Maxwell model, which this paper focuses on, the storage shear modulus, G′, which accounts for the elastic behavior of the material under harmonic excitation, is

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 2230–2244, doi:10.3762/bjnano.8.223

• imaging method. Keywords: atomic force microscopy; harmonic functions; tapping-mode AFM; viscoelasticity; Introduction Several current applications demand physical understanding of soft dissipative materials at the nanoscale [1][2][3][4][5]. This type of materials, such as polymers, biological cells and

Computing the T-matrix of a scattering object with multiple plane wave illuminations

• Martin Fruhnert,
• Ivan Fernandez-Corbaton,
• Vassilios Yannopapas and
• Carsten Rockstuhl

Beilstein J. Nanotechnol. 2017, 8, 614–626, doi:10.3762/bjnano.8.66

• for theoretical considerations, but experimentally a strict distinction is not possible. In the following we largely skip the space and frequency dependency of the fields for simplicity but these dependencies are always assumed. Then, the fields are expanded into vector spherical harmonic functions

• ′ to n. For a sphere, T11 would contain the first Mie coefficient a1 on the diagonal, T22 the second and so on. Please note that the vector spherical harmonic functions and in their presented form are normalized to the unit sphere. Therefore, also the T-matrix is normalized. In many cases it is

• coefficients of the incident, scattered and internal fields are related, but without the expensive surface integrations needed for the extended boundary condition method. Another established strategy to compute the T-matrix of an arbitrary object is to excite it with pure vector spherical harmonic functions to