To investigate diffusion processes in agarose gel, nanoparticles with sizes in the range between 1 and 140 nm have been tested by means of fluorescence correlation spectroscopy. Understanding the diffusion properties in agarose gels is interesting, because such gels are good models for microbial biofilms and cells cytoplasm. The fluorescence correlation spectroscopy technique is very useful for such investigations due to its high sensitivity and selectivity, its excellent spatial resolution compared to the pore size of the gel, and its ability to probe a wide range of sizes of diffusing nanoparticles. The largest hydrodynamic radius (R(c)) of trapped particles that displayed local mobility was estimated to be 70 nm for a 1.5% agarose gel. The results showed that diffusion of particles in agarose gel is anomalous, with a diverging fractal dimension of diffusion when the large particles become entrapped in the pores of the gel. The latter situation occurs when the reduced size (R(A)/R(c)) of the diffusing particle, A, is >0.4. Variations of the fractal exponent of diffusion (d(w)) with the reduced particle size were in agreement with three-dimensional Monte Carlo simulations in porous media. Nonetheless, a systematic offset of d(w) was observed in real systems and was attributed to weak nonelastic interactions between the diffusing particles and polymer fibers, which was not considered in the Monte Carlo simulations.

Fluorescence correlation spectroscopy (FCS) was used to determine diffusion coefficients (D) of the Suwannee River fulvic and humic acids (SRFA and SRHA) and to measure the effects of pH, ionic strength, Ca, and humic substance (HS) concentration on the value of D. For these HS, average diffusion coefficients were in the range of (2−3) × 10-10 m2 s-1 (corresponding to hydrodynamic diameters of approximately 1.5−2.1 nm). Small, but significant, decreases in the diffusion coefficients were observed with decreasing pH, most likely indicating that a small degree of aggregation (formation of dimers and trimers) was occurring. The effect of ionic strength (up to 100 mM) was either small or insignificant, but, where a change occurred, there was a tendency toward a reduction in the diffusion coefficient with increasing salt concentration. No effect of HS concentration (1−50 mg L-1) or hydration time (1−14 days) was observed. There were no observable effects of Ca in comparison to Na, at an ionic strength of 5 mM. For all conditions studied, SRFA had a higher diffusion coefficient than SRHA which is in agreement with literature data on their respective molar masses. Since this is the first application of FCS to HS, the technique was systematically tested for artifacts, in particular photo bleaching and the effect of fluorescence excitation wavelength. Despite a small amount of photobleaching due to the intense laser excitation, FCS was found to be suitable for use with fulvic or humic acids.

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