According to the classical Einstein formulation [1
], Brownian displacements are expected to diminish with increasing particle size. In the case of particles suspended in water, that size is unclear because effective size depends on hydration, and the extent of hydration has remained a subject of some debate.
Recent findings from this laboratory have shown that the extent of hydration may be much greater than earlier presumed. Extremely large interfacial zones have been demonstrated next to both flat surfaces [3
], and spherical surfaces [8
]. These interfacial zones are physically distinct from bulk water, and exclude solutes [4
]. They cling avidly to the respective nucleating surfaces, diminishing in size only modestly with shear [9
]. One can expect, therefore, that these zones will augment the effective size of the microsphere over and above the nominally specified size. As these zones can grow up to as much as several hundred micrometers in certain circumstances [4
], the potential for seriously augmenting nominal microsphere size is substantial.
We found evidence for hydration effects by exploiting the effect of light. Incident light has a powerful effect on the size of the interfacial exclusion zone. In the presence of light, the exclusion zone grows substantially, easily by a factor of several times for a five-minute exposure to relatively weak light [5
]. Apparently, incident light provides the energy required for expanding this low-entropy zone. The light-dependent increase of exclusion-zone size should increase the effective particle diameter, which in turn should diminish Brownian displacements, and this expectation was confirmed.
We found that Brownian excursions diminished in an intensity-dependent fashion (). Higher intensities caused greater diminutions of displacements. The diminution was greatest at the top of the chamber, closest to the incident light, and least at the bottom, where absorption and scattering along the pathway of incident light should result in lower intensity. We also found a wavelength dependence (), although it is difficult to determine whether the result is due to differential absorption/scattering or to a direct effect of wavelength on the size of the exclusion zone.
None of these effects occurred as a consequence of temperature increase, which was consistently less than 1 °C after five minutes of light exposure (see Methods).
Regarding the effect of wavelength, previous work [5
] had demonstrated larger exclusion zones with exposure to longer wavelengths, but the wave-length-dependence found here was opposite of that. This discrepancy might arise from the differences of water absorption and scattering at different wave-lengths. It is not easy to estimate the true intensity or intensity distribution incident on any given microsphere, and hence it is not easy to interpret the underlying wavelength dependence. More work will be needed to sort this out.
Another expectation is that as particles move about randomly, their center-to-center separation should always be greater than two times their effective radii. If the effective radius increases as a result of light-induced hydration, then their closest approach should likewise increase. This was confirmed. shows that the minimum separation increased substantially in the presence of light.
The effect of light disappeared gradually with time (). Full disappearance required approximately three minutes. This time frame is similar to frame required for the building or diminishing exclusion zones [5
], and is thus in concordance with expectation.
A further expectation is that other factors that influence exclusion zone size will impact Brownian excursions. One of the most obvious of those is salt. We found earlier that the addition of salt diminishes exclusion zone size [3
]. Although we did not test the effect of salt on Brownian displacements, others have done so, and the expectation of a salt-induced increase of Brownian excursions was confirmed [10
The results confirm the anticipated effect of light on effective particle size. From the Langevin equation, increased particle size should diminish Brownian excursions, and that is what was found consistently in all experiments. On the other hand, judging quantitatively the extent of hydration or hydration increase that was responsible for these effects is less easy because of several uncertainties. implies that the light-induced change is possibly on the micrometer scale. This implies that even in the absence of added light but with ambient radiation present, hydration is almost certainly more than the few molecular layers presumed. If the size depends on incident radiant energy, then baseline hydration will depend on the level of illumination used to make the observations, as well any other incident radiation to which the sample is exposed. Even pre-exposure could make a difference.
A semi-quantitative estimate of exclusion-zone size comes from recent work [11
], which has shown that exclusion zones around spheres of various size extend consistently to about a fourth of the sphere diameter. Extrapolating down to a sphere of 1 µm would give an effective hydrated size on the order of 1.5 µm. According to the Langevin formulation, the displacement of a particle of that size over a period of four seconds would be 1.51 µm. For a particle of 1 µm, the displacement would be 1.85 µm. We measured approximately 1.4 µm for the control (no light) experiments; hence, the hydrated size, according to the formulation, should be slightly larger than 1.5 µm — certainly greater than the 1 µm nominal size.
Additional factors make more precise determination of hydration-layer thickness difficult. One of those issues is that the layer itself may have a poorly defined or asymmetrical extent. Another is that the incident light induces multiple effects: not only does it expand the exclusion zone but it also separates charges, adding protons to the region beyond the exclusion zone [5
]. These protons could affect the viscosity term in the Langevin equation, although that effect should not be very large as even far more substantial light intensities produce little noticeable change of viscosity. Nevertheless, because of these uncertainties it seems hazardous to attempt a quantitative determination of exclusion-zone size from these measurements, beyond suggesting that it is at least sub-micrometer and possibly of micrometer scale, either of which would substantially increase effective particle size beyond the nominal 1 µm value. Further experiments will help refine these estimates.
Finally, the results imply the need for caution when interpreting Brownian motion data in general. Because the measured displacements are highly sensitive to incident light, any inferences drawn from such measurements need to take this factor into account.