Variable	Definition
~	Tilde: a complex parameter
^	Hat: a complex amplitude
$A_{\mathrm{eff}}$	Effective area of the resonator	$A_{\mathrm{eff}}=\frac{n\mathsf{\pi }}{{32Z}_{\mathrm{q}}{d}_{26}^2{f}_0^{ 2}}\frac{G_{\max }}{Q}$	(A1)
$C_0$	Resonator’s electrical capacitance (parallel capacitance)	$C_0=\frac{{\mathsf{\epsilon }}_{\mathrm{q}}{\mathsf{\epsilon }}_0{A}_{\mathrm{electrode}}}{d_{\mathrm{q}}}$	(A2)
$C_1$	Motional capacitance	$C_1 = \frac{8{\mathsf{\varphi }}^2}{{n\mathsf{\pi }A}_{\mathrm{eff}}{Z}_{\mathrm{q}}}\frac{1}{{2\mathsf{\pi }nf}_0} \mathrm{with} \mathsf{\varphi } = \frac{A_{\mathrm{eff}}{d}_{26}}{d_{\mathrm{q}}}$ $C_1 = \frac{{8k}_{\mathrm{t},\mathrm{eff}}^2}{{\left(n\mathsf{\pi }\right)}^2}{C}_0{ \mathrm{with} k}_{\mathrm{t},\mathrm{eff}}^2 \approx 0.8\%$	(A3)
D	Dissipation factor	$D=\frac{1}{Q}=\frac{2\mathsf{\Gamma }}{f_{\mathrm{res}}}$	(A4)
$\tilde{G}$	Shear modulus	$\begin{array}{c}\tilde{G}=G^{\prime }+i{G}^{″}=1/\tilde{J}={\left(J^{\prime }-i{J}^{″}\right)}^{-1} = i\mathsf{\omega }\tilde{\mathsf{\eta }}\\ \tilde{G}=\left|G\right|{\left(\cos \left({\mathsf{\delta }}_{\mathrm{L}}\right)+\mathrm{i}\sin \left({\mathsf{\delta }}_{\mathrm{L}}\right)\right)}_{}\end{array}$ ${\tan (\mathsf{\delta }}_{\mathrm{L}}) = G^{″}/G^{\prime } = J^{″}/J^{\prime }$	(A5)
$G_{\mathrm{q}}$	Shear modulus of AT-cut quartz	$G_{\mathrm{q}}$ ≈ 29 × 109 Pa
$\tilde{J}$	Shear compliance	$\tilde{J}=1/\tilde{G}=\left(J^{\prime }-{\mathrm{i}J}^{″}\right)$	(A6)
$L_1$	Motional inductance	$L_1=\frac{1}{4{\mathsf{\varphi }}^2}{A}_{\mathrm{eff}}\frac{m_{\mathrm{q}}}{2} \mathsf{\varphi }=\frac{A_{\mathrm{eff}}{e}_{26}}{d_{\mathrm{q}}}$	(A7)
Q	Quality factor	$Q=\frac{f_{\mathrm{res}}}{2\mathsf{\Gamma }}$	(A8)
R 1	Motional resistance, the inverse of Gmax (Equation (13))
$\tilde{Z}$	Shear-wave impedance	$\tilde{Z}=\mathsf{\rho }\tilde{c}=\sqrt{\mathsf{\rho }\tilde{G}}=\sqrt{\mathrm{i}\mathsf{\omega }\mathsf{\rho }\tilde{\mathsf{\eta }}}=\frac{\mathrm{i}\tilde{\mathsf{\eta }}\tilde{k}}{\mathsf{\omega }}$	(A9)
${\tilde{Z}}_{\mathrm{L}}$	Load impedance	${\tilde{Z}}_{\mathrm{L}}=\frac{-{\widehat{\sigma }}_S}{{\widehat{v}}_S}$	(A10)
$Z_q$	Shear-wave impedance of AT-cut quartz	$Z_q$ = 8.8 × 106 kg m−2 s−1
${\tilde{c}}_{\mathrm{f}}{, c}_{\mathrm{q}}, {\tilde{c}}_{\mathrm{bulk}}$	Speed of shear sound	$\tilde{c}=\sqrt{\tilde{G}/\mathsf{\rho }}$
$d_{26}$	Piezoelectric strain coefficient of AT-cut quartz	$d_{26}$ = 3.1 × 10−12 m/V
$e_{26}$	Piezoelectric stress coefficient of AT-cut quartz	$e_{26}= d_{26}{G}_{\mathrm{q}}$ = 9.65 × 10−2 C/m2
$d_f, d_q$	Thickness of film and resonator
${\tilde{k}}_f{, k}_{\mathrm{q}}, {\tilde{k}}_{\mathrm{bulk}}$	Wave vector in the film, the resonator plate, and the bulk	${\tilde{k}}_{\mathrm{bulk}}=\frac{\mathsf{\omega }}{{\tilde{c}}_{\mathrm{bulk}}}=\sqrt{\frac{{\mathsf{\omega }\mathsf{\rho }}_{\mathrm{bulk}}}{{\mathrm{i}\mathsf{\eta }}_{\mathrm{bulk}}}}=\sqrt{-2\mathrm{i}}\frac{1}{\mathsf{\delta }}=\left(1-\mathrm{i}\right)\sqrt{\frac{{\mathsf{\omega }\mathsf{\rho }}_{\mathrm{bulk}}}{{2\mathsf{\eta }}_{\mathrm{bulk}}}}$	(A11)
$k_{\mathrm{t}}$	Electromechanical coupling coefficient	$k_{\mathrm{t},\mathrm{ideal}}^2=\frac{{ e}_{26}}{{\mathsf{\epsilon }}_{\mathrm{q}}{\mathsf{\epsilon }}_0{G}_{\mathrm{q}}}$ $k_{\mathrm{t},\mathrm{eff}}^2=\frac{C_1}{C_0}\frac{{\left(n\mathsf{\pi }\right)}^2}{8}$	(A12)
$f_{\mathrm{cen}}$	A frequency in the center of the QCM’s frequency range (Section 4.7)
$f_{\mathrm{ref}}$	Resonance frequency in reference state
$f_{\mathrm{res}}$	Resonance frequency	$f_{\mathrm{res}}{=nf}_0$
$f_0$	Fundamental frequency	$f_0=\frac{Z_{\mathrm{q}}}{{2m}_{\mathrm{q}}}$
$m_{\mathrm{f}} {, m}_{\mathrm{q}}$	Mass per unit area of the film and the resonator plate	$m_{\mathrm{q}}{=\mathsf{\rho }}_{\mathrm{q}}{d}_{\mathrm{q}}=\frac{Z_{\mathrm{q}}\mathsf{\lambda }}{2}=\frac{1}{2}\frac{Z_{\mathrm{q}}{c}_{\mathrm{q}}}{f_0}=\frac{Z_{\mathrm{q}}}{{2f}_0}$	(A13)
$m_{\mathrm{R}}$	Effective mass of a resonator	${\mathrm{parallel} \mathrm{plate}: m}_{\mathrm{R}}=\frac{A_{\mathrm{eff}}{m}_{\mathrm{q}}}{2}$	(A14)
n	Overtone order
$n_{\mathrm{P}}$	Number of particles in contact with the resonator
$n_{\mathrm{r}}$	Refractive index
$u, \widehat{u}$ ${ u}_{\mathrm{S}}, {\widehat{u}}_{\mathrm{S}}$	Displacement, amplitude of displacement (^) subscript S: at the surface	$\widehat{u}=\frac{\widehat{v}}{\mathrm{i}\mathsf{\omega }} {\widehat{v}}_{\mathrm{S}}=\frac{d_{\mathrm{q}}}{2e_{26}{A}_{\mathrm{eff}}}\widehat{I}$	(A15)
$v, \widehat{v}$, $v_{\mathrm{S}}, {\widehat{v}}_{\mathrm{S}}$	Velocity, amplitude of velocity (^)	$\widehat{v}=\mathrm{i}\mathsf{\omega }\widehat{u}$	(A16)
${\mathsf{\beta }}^{\prime }, {\mathsf{\beta }}^{″}$ ${\mathsf{\gamma }}^{\prime }, {\mathsf{\gamma }}^{″}$	Power law exponents, Section 4.7	${J_f}^{\prime }\left(f\right) \approx {{ J}_f}^{\prime }\left(f_{\mathrm{cen}}\right){\left(\frac{f}{f_{\mathrm{cen}}}\right)}^{{\mathsf{\beta }}^{\prime }}$ ${G_f}^{\prime }\left(f\right) \approx {{ G}_f}^{\prime }\left(f_{\mathrm{cen}}\right){\left(\frac{f}{f_{\mathrm{cen}}}\right)}^{{\mathsf{\gamma }}^{\prime }}$ ${J_f}^{″}\left(f\right) \approx {{ J}_f}^{″}\left(f_{cen}\right){\left(\frac{f}{f_{\mathrm{cen}}}\right)}^{{\mathsf{\beta }}^{″}}$ ${G_f}^{″}\left(f\right) \approx {{ G}_f}^{″}\left(f_{\mathrm{cen}}\right){\left(\frac{f}{f_{\mathrm{cen}}}\right)}^{{\mathsf{\gamma }}^{″}}$	(A17)
$\tilde{\mathsf{\eta }}$	Viscosity	$\tilde{\mathsf{\eta }}=\frac{\tilde{G}}{\mathrm{i}\mathsf{\omega }}={\mathsf{\eta }}^{\prime }-\mathrm{i}{\mathsf{\eta }}^{″}$	(A18)
Γ	Imaginary part of resonance frequency, half-band half width
$\Delta R+\mathrm{i}\Delta X$	Load impedance in electrical units (in older publications)	$\Delta R+\mathrm{i}\Delta X=\frac{A_{\mathrm{eff}}}{4{\mathsf{\varphi }}^2}{\tilde{Z}}_{\mathrm{L}}=-\mathrm{i}\frac{\pi }{16}\frac{Z_{\mathrm{q}}^3}{A_{\mathrm{eff}}{e}_{26}^2{\epsilon }_{\mathrm{q}}^2{f}_0^3}(\Delta f+\mathrm{i}\Delta \mathsf{\Gamma })$	(A19)
${\mathsf{\epsilon }}_{\mathrm{q}}$	Dielectric constant of AT-cut quartz	${\mathsf{\epsilon }}_{\mathrm{q}}$ = 4.54
${\mathsf{\kappa }}_{\mathrm{R}}$	Effective spring constant	${\mathsf{\kappa }}_{\mathrm{R}}=\frac{A_{\mathrm{eff}}{G}_{\mathrm{q}}}{d_{\mathrm{q}}}\frac{{\left(n\mathsf{\pi }\right)}^2}{2}=\frac{{\left(n\mathsf{\pi }\right)}^2}{2}{\mathsf{\kappa }}_{\mathrm{q},\mathrm{stat}}$	(A20)
${\mathsf{\rho }}_{\mathrm{q}}$	Density of α-quartz	${\mathsf{\rho }}_{\mathrm{q}}$ = 2.65 × 103 kg/m3
$\mathsf{\sigma }, \widehat{\sigma }$, ${\mathsf{\sigma }}_{\mathrm{S}}, {\widehat{\sigma }}_{\mathrm{S}}$	Tangential stress, amplitude thereof
${\mathsf{\xi }}_{\mathrm{R}}$	Effective drag coefficient