Fluorescence correlation spectroscopy in thin films at reflecting substrates as a means to study nanoscale structure and dynamics at soft-matter interfaces

Structure and dynamics at soft-matter interfaces play an important role in nature and technical applications. Optical single-molecule investigations are noninvasive and capable to reveal heterogeneities at the nanoscale. In this work we develop an autocorrelation function (ACF) approach to retrieve tracer diffusion parameters obtained from fluorescence correlation spectroscopy (FCS) experiments in thin liquid films at reflecting substrates. This approach then is used to investigate structure and dynamics in 100-nm-thick 8CB liquid crystal films on silicon wafers with five different oxide thicknesses. We find a different extension of the structural reorientation of 8CB at the solid-liquid interface for thin and for thick oxide. For the thin oxides, the perylenediimide tracer diffusion dynamics in general agrees with the hydrodynamic modeling using no-slip boundary conditions with only a small deviation close to the substrate, while a considerably stronger decrease of the interfacial tracer diffusion is found for the thick oxides.

Figure 1

(a),(b) Chemical structures. (c) Model (not to scale) of sample structure with 8CB film thickness $L, {\mathrm{SiO}}_2$ layer thickness $d$; with refractive indices changing from $n_{\parallel }$ at the substrate (region i) to $n_{\perp }$ at the interface with air (region iii) and an intermediate region (ii) with mean refractive index $n_{\mathrm{m}}$. Orientation of 8CB dimers highlighted as blue cigars. (d) Scheme illustrating the use of the interference pattern in $I\left(z\right)$ for probing the samples, no fluorescence signal from PDI tracers (red balls) in dark regions. (e),(f) Diffusion coefficients according to hydrodynamics: (e) $D_{xy}\left(z\right)$ and (f) $D_z\left(z\right)$, calculated from (C1) and (C2), respectively, for mean diffusion (solid), as well as diffusion along (dash) and perpendicular (dot) to the LC director.

Figure 2

(a) Scaled model (see Fig. 1) visualizing the vertical LC film structure used in (c) and (d). (b) FCS curves obtained with ${\lambda }_{ex}=465$ nm for PDI in 110-nm-thick 8CB films on glass ($\circ$) and on silicon wafers with native ($\blacksquare$) and with 100-nm-thick thermal oxide ($▴$). (c),(d) Calculated fluorescence intensities $I\left(z\right)$ in 8CB films as a function of distance $z$ to the substrate, using Essential Macleod™  for native (blue, solid), 10-nm (purple, dash), 25-nm (pink, dot), 70-nm (yellow, dash-dot), and 100-nm (red, dot-dash-dot) oxide with (c) ${\lambda }_{ex}=465$ nm and (d) ${\lambda }_{ex}=515$ nm.

Figure 3

Illustration of obtained diffusion coefficients $D_{xy}\left(z\right)$ (red) and $D_z\left(z\right)$ (blue) in $\mu {\mathrm{m}}^2/\mathrm{s}$ from each experiment for (left) ${\lambda }_{ex}=465$ nm and (right) ${\lambda }_{ex}=515$ nm, and $d$ decreasing from top to bottom. For errors in $D\left(z\right)$ see Table 1. Note the change in scale for thin and thick oxides. Approximations of $I\left(z\right)$ are depicted within each 8CB film in grey scale as illustrated in Fig. 1.

Figure 4

Results for 8CB films on 10-nm ${\mathrm{SiO}}_2$. (a) $I\left(z\right)$ calculated for ${\lambda }_{ex}=465$ nm (blue) with $\zeta =15$ nm (solid), $\zeta =25$ nm (dash), and $\zeta =35$ nm (dot), as well as for ${\lambda }_{ex}=514$ nm (green) with $\zeta =15$ nm (dash-dot), $\zeta =25$ nm (dot-dash-dot), and $\zeta =35$ nm (dash-dot-dash). (b) Experimental FCS curves for ${\lambda }_{ex}=465$ nm (light solid) and ${\lambda }_{ex}=515$ nm (black solid) with fits for ${\lambda }_{ex}=515$ nm and $L=110$ nm, and $\zeta =15$ nm (red, dash), $\zeta =25$ nm (blue, dot), and $\zeta =35$ nm (yellow, dot-dash-dot). (c) Fitting errors for ${\lambda }_{ex}=465$ nm ($⧫$) and ${\lambda }_{ex}=515$ nm ($◊$). (d),(e) Diffusion coefficients $D_{xy}$ ($⧫$) and $D_z$ ($\square$) obtained from fits. (c)–(e) Values obtained for $L=100$ nm, $L=110$ nm, and $L=120$ nm displayed with 1-nm spacing. Error bars denote standard deviations using multiple data sets.

Figure 5

Results for 8CB films on 70-nm ${\mathrm{SiO}}_2$. (a) $I\left(z\right)$ calculated for ${\lambda }_{ex}=465$ nm (blue) with $\zeta =15$ nm (solid), $\zeta =25$ nm (dash), and $\zeta =35$ nm (dot), as well as for ${\lambda }_{ex}=514$ nm (green) with $\zeta =15$ nm (dash-dot), $\zeta =25$ nm (dot-dash-dot), and $\zeta =35$ nm (dash-dot-dash). (b) Experimental FCS curves (solids) with fits for ${\lambda }_{ex}=515$ nm. (c) Fitting errors for ${\lambda }_{ex}=465$ nm ($⧫$) and ${\lambda }_{ex}=515$ nm ($◊$). (d),(e) Diffusion coefficients $D_{xy}$ ($⧫$) and $D_z$ ($\square$) obtained from fits. (c)–(e) Values obtained for $L=100$ nm, $L=110$ nm, and $L=120$ nm displayed with 1-nm spacing. Error bars denote standard deviations using multiple data sets.

Figure 6

Results for 8CB films on 25-nm ${\mathrm{SiO}}_2$. (a) $I\left(z\right)$ calculated for ${\lambda }_{ex}=465$ nm (blue) with $\zeta =15$ nm (solid), $\zeta =25$ nm (dash), and $\zeta =35$ nm (dot), as well as for ${\lambda }_{ex}=514$ nm (green) with $\zeta =15$ nm (dash-dot), $\zeta =25$ nm (dot-dash-dot), and $\zeta =35$ nm (dash-dot-dash). (b) experimental FCS curves (solids) with fits for ${\lambda }_{ex}=515$ nm. (c) Fitting errors for ${\lambda }_{ex}=465$ nm ($⧫$) and ${\lambda }_{ex}=515$ nm ($◊$). (d),(e) Diffusion coefficients $D_{xy}$ ($⧫$) and $D_z$ ($\square$) obtained from fits. (c)–(e) Values obtained for $L=100$ nm, $L=110$ nm, and $L=120$ nm displayed with 1-nm spacing. Error bars denote standard deviations using multiple data sets.

Figure 7

Results for 8CB films on native ${\mathrm{SiO}}_2$. (a) $I\left(z\right)$ calculated for ${\lambda }_{ex}=465$ nm (blue) with $\zeta =15$ nm (solid), $\zeta =25$ nm (dash), and $\zeta =35$ nm (dot), as well as for ${\lambda }_{ex}=514$ nm (green) with $\zeta =15$ nm (dash-dot), $\zeta =25$ nm (dot-dash-dot), and $\zeta =35$ nm (dash-dot-dash). (b) Experimental FCS curves (solids) with fits for ${\lambda }_{ex}=515$ nm. (c) Fitting errors for ${\lambda }_{ex}=465$ nm ($⧫$) and ${\lambda }_{ex}=515$ nm ($◊$). (d),(e) Diffusion coefficients $D_{xy}$ ($⧫$) and $D_z$ ($\square$) obtained from fits. (c)–(e) Values obtained for $L=100$ nm, $L=110$ nm, and $L=120$ nm shown with 1-nm spacing. Error bars give standard deviations using multiple data sets.

Figure 8

Results for 8CB films on 100 nm ${\mathrm{SiO}}_2$. (a) $I\left(z\right)$ calculated for ${\lambda }_{ex}=465$ nm (blue) with $\zeta =15$ nm (solid), $\zeta =25$ nm (dash), and $\zeta =35$ nm (dot), as well as for ${\lambda }_{ex}=514$ nm (green) with $\zeta =15$ nm (dash-dot), $\zeta =25$ nm (dot-dash-dot), and $\zeta =$ 35 nm (dash-dot-dash). (b) Experimental FCS curves (solids) with fits for ${\lambda }_{ex}=515$ nm. (c) Fitting errors for ${\lambda }_{ex}=465$ nm ($⧫$) and ${\lambda }_{ex}=515$ nm ($◊$). (d),(e) Diffusion coefficients $D_{xy}$ ($⧫$) and $D_z$ ($\square$) obtained from fits, note the smaller scale. (c)–(e) Values obtained for $L=100$ nm, $L=110$ nm, and $L=120$ nm displayed with 1-nm spacing. Error bars denote standard deviations using multiple data sets.