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Earlier work on particles in aqueous solution indicated that particle hydration could be expanded by incident light. To assess the effects of expanded hydration we measured Brownian displacements of microspheres exposed to light of varying intensities and wavelengths. Displacements were consistently diminished in an intensity-dependent and wavelength-dependent fashion, and center-to-center distances between microspheres were shifted to higher values. We conclude that suspended microspheres are surrounded by hydration zones substantial enough to impact Brownian displacements.
Since Robert Brown first reported the seemingly random movements of pollen and other particles suspended in water, the phenomenon of Brownian motion has attracted the interest of physicists. Following Einstein’s pioneering work , physicists have come to understand the phenomenon in terms of thermal energy, i.e., as an expression of the heat associated with temperature. The resulting formulation expresses mean square deviations as a function of temperature, medium viscosity, particle size and time.
According to the Langevin formulation , Brownian displacements in two dimensions can be expressed as follows:
where r2 is the square of the displacement in the x–y plane, µ the viscosity of the solvent, a the radius of the particle, T the temperature of the sample, R the gas constant, N the number of molecules in one mole, and τ the time of interaction. The expression shows an inverse relationship between displacement and particle size.
Recently, an issue related to particle size has emerged. Studies have shown that hydrophilic surfaces contain interfacial water zones that are more extensive than thought; in some instances they can extend many micrometers from the respective surfaces [3, 4]. Since this water clings to the nucleating surface, it has the capacity to increase effective particle size and thereby impact Brownian dynamics. In other words, suspended particles may be effectively larger than presumed.
Further, we found recently that this interfacial water zone is expanded by light . We therefore sought to test the impact of adding incident light at varying intensities and wavelengths. The hypothesis under test was that expanding the interfacial zone, termed the “exclusion zone,” would increase effective particle size and thereby diminish Brownian excursions. The results showed that that was indeed the case, and some rough inferences could be drawn as to the size of the exclusion zone.
The experimental objective was to measure the distance microspheres travel under various intensities and wavelengths of light. One drop of concentrated 1 µm carboxylate-modified polystyrene microspheres (2.65% solids-latex, Polysciences Inc.) was added to 40 ml of distilled, deionized water (NANOpure Diamond). From that suspension a sample of 100 microliters was obtained and placed in an open chamber. The chamber was cylindrical in shape and measured 2 cm across and 0.5 cm deep. It was placed on the stage of an inverted compound microscope (Zeiss Axiovert-35) for visualization. Data were captured by a video camera (CFW-1310C) at 7.5 frames per second.
Brownian dynamics were measured by making a video of the sample for four seconds. The displacement of a microsphere over successive frames was summed up to obtain the total distance the microsphere traveled during the four-second interval. The sample was left uncovered except when taking measurements, during which time it was covered by a thin, transparent slide. This precaution was taken to prevent evaporation and evaporation-induced thermal gradients. Unless otherwise indicated, all measurements were taken near the top of the sample so as to minimize issues of light scattering and absorption. A 20× objective lens was used to view the sample and measurements were made near the center of the field. Given the depth of field of the objective-condenser combination, the error in particle tracking was estimated to be approximately 8.3 nm .
ImageJ was the software used to record videos of the microsphere movement. The recording speed was set to 7.5 frames per second, and data were recorded for 30 frames. The data for the control experiment were obtained after letting the sample sit undisturbed for a period of five minutes in the absence of room or microscope illumination.
The sample was then exposed for five minutes to radiation from one of six different light sources with wavelengths ranging from 310 to 880 nanometers. The light sources used were 12 V LEDs, 8 mm in diameter. Each light source was connected to a power supply, which supplied 11.5 volts. The current was set at a default value of 175 mA. We confirmed that the 175 mA current produced approximately the same intensity for each wavelength. For viewing the microspheres, the microscope light was set at the lowest possible intensity for viewing so as to minimize any effect on the experiments.
Light attracts microspheres . Therefore, the light source was positioned directly above the sample to minimize microsphere drift to one side or the other. After five minutes of exposure, the light source was removed. Microsphere displacements were immediately recorded over a period of four seconds in order to assess how far each microsphere had traveled during that period.
Despite precautions, the field of microspheres inevitably drifted to some extent. To estimate the error arising from this field drift we examined the initial and final coordinates in five fields for both the control and light experiments. For the light experiment, the experiment under the 455 nm light source with a current of 175 mA was examined. Some thirty microspheres were tracked in each of the five fields. Calculating the difference between the final and initial coordinates and taking the mean over all fields gave the mean displacement of the ensemble due to drift. For the control experiment the displacement due to drift was 9.1 ± 0.5% of the Brownian displacement. Under light, the mean displacement caused by drift was 11.4 ± 0.5% of the Brownian displacement. Hence, drift-induced errors are present, but are relatively modest.
A second experiment was carried out by varying the light intensity. To achieve this, the current was varied from 50 mA to 250 mA. We tested this effect using the 455 nm wavelength light source. Once again the sample was exposed to the light for five minutes, and the measurements were taken for four seconds immediately after removing the light source. We did not test currents higher than 250 mA because of the possibility of excessive heat generation.
A final experiment was carried out to test how quickly the effect of incident light energy dissipates. The light source with a wavelength of 455 nm was used once again. The sample was exposed to the light for five minutes. The light source was then removed, and recordings were made at 10, 30, 90, 120, and 180 seconds after removing the light source. Again, measurements of microsphere displacement were made over a period of four seconds.
For all of the experiments, the temperature was measured before and after exposing the sample to the light source, using a temperature probe (Omega HH501DK). Before exposing the chamber to the light source, the bath was at room temperature, approximately 22 °C. After the five minute exposure, the bath temperature had increased by 0.85 ± 0.11 °C.
The experiments were repeated for the bottom of the sample. Because the incident light from the top gets absorbed and scattered by microspheres, the intensity at the bottom was difficult to assess; hence, these data were not analyzed in as much detail as the data obtained from near the sample’s top.
Finally, the separation between microspheres was examined. This was done for the control case and the case in which a light source had been incident for five minutes. The 455 nm light source was used with a current of 200 mA. Measurements were taken every fifth frame at a frame rate of 7.5 fps, starting with the first frame of the recorded period of four seconds. A total of 415 microsphere pairs were examined for the control experiment and 409 pairs in the light experiment. We included data only from pairs of microspheres that were ten micrometers or less apart and discarded instances where the microspheres appeared to be stuck and moving together. From the remaining pairs, we calculated the center-to-center distance between microspheres.
Figure 1 shows the effect of incident light intensity on microsphere displacement. Driving currents ranged from 0 mA to 250 mA. As the intensity increased, the microsphere displacements decreased. The relationship was approximately linear between driving currents of 0 and 250 mA.
Figure 2 shows how the wavelength of incident light affected Brownian displacements. Shorter wavelengths had the most profound effects, with the greatest effect coming from the 310 nm light source.
Figure 3 shows how quickly the effect of incident radiation dissipates over time. The effect diminishes most quickly during the first 30 seconds and then decreases at a slower rate, disappearing completely about 180 seconds after removing the light source. After that time the microspheres resume traveling the same distances they did in the control experiment. Hence the effect of light is cumulative, albeit transient.
The results of the microsphere-separation experiments, processed using one-micron bins, are presented in Figures 4a and b. The effect of light was to diminish the population of smaller separations. This implies that the incident light somehow increased the mean separation between microspheres.
There is also some hint of preferred separations in Figure 4b, which may imply a light-induced ordering of microspheres into colloid crystals, but additional experiments are needed to confirm or deny this possibility.
Figures 4a and 4b show some data points lying at separations of 1 µm, implying that microspheres were touching. This result might arise from an artifact of superposition of microspheres in different horizontal planes but appearing to be in one. The microscope’s depth of focus was measured to be 2.43 µm, substantially larger than microsphere diameter. The separation calculation itself may also have contributed to error, as distances up to 1.49 µm were placed in the 1 µm bin. Nevertheless, the data do show a light-induced shift away from the smaller separations toward the larger separations.
The results above were obtained from near the top of the sample, where the effects of incident light, coming directly from above, were thought to be most direct and most free from the effect of scattering and absorption. Results obtained from the bottom of the sample generally showed similar patterns as those at the top, albeit smaller. For example, microsphere displacement under the 455 nm light source was 92.7 ± 2.0% of the displacement in the control experiment, compared to approximately 70% of control near the top. In these wavelength studies, comparison with controls consistently showed significant difference, with p-values <0.0026 for all six of the wavelengths. Given the smaller magnitude of the effect, we did not study the effects at the bottom in as much detail.
According to the classical Einstein formulation , 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, 4], and spherical surfaces . These interfacial zones are physically distinct from bulk water, and exclude solutes . They cling avidly to the respective nucleating surfaces, diminishing in size only modestly with shear . 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 , 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 . 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 (Figure 1). 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 (Figure 2), 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  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. Figure 4 shows that the minimum separation increased substantially in the presence of light.
The effect of light disappeared gradually with time (Figure 3). Full disappearance required approximately three minutes. This time frame is similar to frame required for the building or diminishing exclusion zones , 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 . 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 .
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. Figure 4 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 , 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 . 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.
Anish Bhalerao recently received his bachelor’s degree in astrophysics from the University of Washington. Some of his research interests include studying particle behavior, random motion, and theoretical physics.
Gerald Pollack is professor of Bioengineering at the University of Washington. He received an honorary doctorate Ural State University and was named an Honorary Professor of the Russian Academy of Sciences. His books have won multiple awards. He was selected to receive his university’s highest distinction: the Annual Faculty Lecturer Award. Pollack is Editor-in-Chief of the journal WATER, and has recently received an NIH Transformative R01 Award.