Combining quantitative photothermal microscopy and light scattering microscopy as well as accurate MIE scattering calculations on single gold nanoparticles, we reveal that the mechanism of photothermal single-molecule/particle detection is quantitatively explained by a nanolensing effect. The lensing action is the result of the long-range character of the refractive index profile. It splits the focal detection volume into two regions. Our results lay the foundation for future developments and quantitative applications of single-molecule absorption microscopy.
We derive the markovian description for the nonequilibrium brownian motion of a heated nanoparticle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nanoparticles and provide a practical rational basis for emerging photothermal tracer and nanoparticle trapping and tracking techniques.
The action of a nanoscopic spherically symmetric refractive index profile on a focused Gaussian beam may easily be envisaged as the action of a phase-modifying element, i.e. a lens: Rays traversing the inhomogeneous refractive index field n(r) collect an additional phase along their trajectory which advances or retards their phase with respect to the unperturbed ray. This lens-like action has long been understood as being the mechanism behind the signal of thin sample photothermal absorption measurements [Appl. Opt. 34, 41-50 (1995)], [Jpn. J. Appl. Phys. 45, 7141-7151 (2006)], where a cylindrical symmetry and a different lengthscale is present. In photothermal single (nano-)particle microscopy, however, a complicated, though prediction-wise limited, electrodynamic scattering treatment was established [Phys. Rev. B 73, 045424 (2006)] during the emergence of this new technique. Our recent study [ACS Nano, DOI: 10.1021/nn300181h] extended this approach into a full ab-initio model and showed for the first time that the mechanism behind the signal, despite its nanoscopic origin, is also the lens-like action of the induced refractive index profile only hidden in the complicated guise of the theoretical generalized Mie-like framework. The diffraction model proposed here yields succinct analytical expressions for the axial photothermal signal shape and magnitude and its angular distribution, all showing the clear lens-signature. It is further demonstrated, that the Gouy-phase of a Gaussian beam does not contribute to the relative photothermal signal in forward direction, a fact which is not easily evident from the more rigorous EM treatment. The presented model may thus be used to estimate the signal shape and magnitude in photothermal single particle microscopy.
Temperature dependent measurements of the rotational diffusion of single dye molecules in the polymer poly(methyl acrylate) (PMA) are presented and compared to shear viscosity data and numerical simulations of the rotational diffusion process. It is found that single molecule rotational diffusion very accurately follows the Debye-Stokes-Einstein predictions for the shear viscosity without any additional parameter. We employ a simple model of dynamic changes of the rotational speed of a single molecule. This dynamic heterogeneity model is based on a Gaussian distribution of activation energies in a VFTH (Vogel-Fulcher-Tammann-Hesse) type temperature dependence of the polymer viscosity. The simulations explain all experimental details concerning the stretched exponential single molecule relaxation dynamics and the related distributions. They also reveal that the observed distributions are related to the intrinsic physical properties of the polymer but do not in general reflect the instantaneous spread of local viscous properties.
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