Article pubs.acs.org/ac
Long Working-Distance Optical Trap for in Situ Analysis of ContactInduced Phase Transformations Ryan D. Davis,*,†,‡ Sara Lance,† Joshua A. Gordon,∥ and Margaret A. Tolbert*,†,‡ †
Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, Colorado 80309, United States ‡ Department of Chemistry and Biochemistry, University of Colorado, UCB 216, Boulder, Colorado 80309, United States ∥ National Institute of Standards and Technology (NIST), Communications Technology Lab, Boulder, Colorado 80305, United States S Supporting Information *
ABSTRACT: A novel optical trapping technique is described that combines an upward propagating Gaussian beam and a downward propagating Bessel beam. Using this optical arrangement and an on-demand droplet generator makes it possible to rapidly and reliably trap particles with a wide range of particle diameters (∼1.5−25 μm), in addition to crystalline particles, without the need to adjust the optical configuration. Additionally, a new image analysis technique is described to detect particle phase transitions using a template-based autocorrelation of imaged far-field elastically scattered laser light. The image analysis allows subtle changes in particle characteristics to be quantified. The instrumental capabilities are validated with observations of deliquescence and homogeneous efflorescence of well-studied inorganic salts. Then, a novel collision-based approach to seeded crystal growth is described in which seed crystals are delivered to levitated aqueous droplets via a nitrogen gas flow. To our knowledge, this is the first account of contact-induced phase changes being studied in an optical trap. This instrument offers a novel and simple analytical technique for in situ measurements and observations of phase changes and crystal growth processes relevant to atmospheric science, industrial crystallization, pharmaceuticals, and many other fields.
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range of conditions, providing access to new measurements as well as insight into important fundamental processes. Levitation in an optical trap is an attractive technique for studying phase changes of microparticles.7 Optical levitation utilizes focused laser beams, where the momentum transferred from the photons to the microparticle creates a scattering force in the direction of laser propagation as well as a transverse gradient force toward the region of highest light intensity. These forces, termed radiation pressure, are used to balance other forces acting upon the particle (e.g., gravity) resulting in levitation.12 Optical levitation provides the ability to monitor single particles in situ; removes any ambiguity associated with depositing microdroplets on a substrate; and avoids the requisite droplet charging necessary for single particle levitation in an electrodynamic balance.7,13 While optical traps have been used to study homogeneous phase changes, they have not been used to study heterogeneous phase changes induced by collision with an externally located solid particle. Here, we describe a long working-distance optical trap that can be used to study a diverse range of phase transformations,
ucleation of a crystalline phase from a liquid solution results in substantial changes to the physical and chemical properties of the substance. Controlling nucleation and crystal growth is important in, e.g., industrial and pharmaceutical crystallization, 1,2 while simply predicting the onset of crystallization is important in the environmental sciences. In the environment, crystallization of dissolved inorganic material in groundwater can damage buildings and other structures.3 In the atmosphere, the phase state of atmospheric particles influences their size, optical properties, and chemical reactivity, with important consequences on global climate and air quality.4−7 Nucleation and crystal growth characteristics are highly dependent on the solute supersaturation S,1,6−11 where S is defined as the ratio of ionic activity in the supersaturated solution to the ionic activity of the solution at saturation. Crystallization experiments are often performed on bulk solutions where the range of experimentally accessible S values is limited due to heterogeneous nucleation on the walls of the container or particulate contamination.8−11 Microdroplets can often reach higher levels of S than typically observed in bulk solutions due to the small volume and decreased probability of contamination.8−10 Microdroplets are thus excellent systems to study nucleation and crystal growth characteristics over a wide © 2015 American Chemical Society
Received: March 2, 2015 Accepted: May 11, 2015 Published: May 11, 2015 6186
DOI: 10.1021/acs.analchem.5b00809 Anal. Chem. 2015, 87, 6186−6194
Article
Analytical Chemistry
mounted to an X−Y manual positioner for horizontally guiding droplets into the trapping site. Droplets were generated at a rate of 1 Hz, and the position of the chamber was adjusted until a droplet became trapped. For large sizes (e.g., > 4 μm in diameter), droplets were generated above the trapping site and guided as they fell downward (as demonstrated in Video S1 (ac5b00809_si_002.avi), Supporting Information). For smaller diameters, the orientation of the flow chamber was inverted (but the optical configuration was not changed) and droplets were generated below the trapping site. Droplets were then guided as they were carried upward by a N2 gas flow. Occasionally, 2−3 droplets became trapped simultaneously. In these cases, the droplets were intentionally ejected and the trapping procedure was repeated. (See online Supporting Information for more details on generating droplets.) An upward N2 gas flow was introduced at the bottom of the flow tube through a side-mounted port. A second side port at the top of the flow tube vented the flow with the assistance of a small air pump equipped with a needle valve and mass flow meter. Relative humidity (RH) was controlled by mixing a dry N2 gas flow and a N2 gas flow humidified using a water bubbler. Both the humidified and dry gas flows were controlled using individual mass flow controllers. A total flow rate of ≤25 sccm was typical. Temperature and RH were monitored using capacitance probes (Vaisala HMP60, ±3% RH, ±0.5 °C) placed before and after the levitation chamber. The probe uncertainty was reduced to ca. ±0.5% RH by calibrating with saturated salt solutions (see online Supporting Information for calibration details). The RH at the trapping site was taken as the average of the two probe readouts (±σ). Droplets were generated from a solution of (NH4)2SO4, NaCl, NaBr, Na2SO4, or K2SO4. Once generated, the droplets equilibrated with the ambient RH in the levitation chamber. The initial concentration of the solution was varied to control droplet size. Droplets for the phase transformation experiments were generated from a 5 wt % solution and were ∼10 ± 3 μm in diameter. (NH4)2SO4 seed crystals for seeded crystal growth experiments were generated using a medical nebulizer (Omron NE-U22). A 10 wt % solution of (NH4)2SO4 was nebulized into the dry N2 gas flow. The nebulized droplets were then directed through a diffusion dryer where the RH was 100 droplets were typically generated prior to trapping a single droplet. (For additional discussion, see online Supporting Information.) Droplets with an average diameter of ∼10 ± 3 μm were used to obtain the phase transformation results reported in Homogeneous Phase Changes and Contact-Based Seeded Crystal Growth. Homogeneous Phase Changes. To validate the far-field image analysis and the instrumental setup, the efflorescence RH and deliquescence RH of several inorganic salts were measured for comparison to literature values. The inorganic salts studied were (NH4)2SO4, NaCl, NaBr, Na2SO4, and K2SO4. Using NaBr as an example, a detailed discussion of the analysis procedure follows. Efflorescence. Figure 4a−c shows how the efflorescence RH of NaBr was determined using the far-field image analysis. Examples of far-field and defect images are shown in Figure 4a. Past work has used the total intensity of imaged light (i.e., I or I)̅ to detect phase changes.7,13 A plot of the time dependence of I ̅ is shown along with ID̅ in Figure 4b. Efflorescence is not immediately distinct when considering I ̅ alone. The intensity becomes more random and deviates from the intensity distribution predicted from Mie theory. However, the intensity value does not change appreciably. In contrast to I,̅ the distinction between a liquid and crystalline particle is clear in the plot of ID̅ . Although measuring ID̅ is a clear advantage over the more common method of measuring total intensity of scattered light to detect phase changes of levitated particles,7,13 one aspect of Figure 4b remains ambiguous. As expected, ID̅ increases at the onset of efflorescence from 1.7 in frame 1 to 13.9 in frame 2. However, ID̅ subsequently decreases to 8.9 in frame 3 because the particle was partially removed from the camera field of view as a result of water loss. Without the recorded image, this decrease would be misleading. The normalization step of calculating C removed this ambiguity. Figure 4c shows a plot of C calculated using eq 2. The transition from liquid-to-solid is distinct and C decreases sharply, even though the particle is partially removed from the images. (See Supporting Information, Figure S2 for an additional example.) The efflorescence RH was determined by comparing the timestamp of the RH probe readout to the timestamp associated with the image where C initially decreased. In the example shown, the efflorescence RH was 24 ± 1%. 6191
DOI: 10.1021/acs.analchem.5b00809 Anal. Chem. 2015, 87, 6186−6194
Article
Analytical Chemistry ± 3% RH for (NH4)2SO4, NaCl, NaBr, Na2SO4, and K2SO4, respectively. The deliquescence RH values for (NH4)2SO4, NaCl, NaBr, and Na2SO4 were 81 ± 2, 75 ± 2, 48 ± 3, and 84 ± 2% RH, respectively. Deliquescence of K2SO4 was not observed because the deliquescence RH of K2SO4 (96% RH)27 is beyond the maximum achievable RH in the current setup ( 1). At low S (high RH), droplets contain a large amount of water compared to droplets at the high S (low RH) where homogeneous efflorescence occurs. This high water content results in a large change in equilibrium position due to the loss of water mass during crystal growth. This large change in equilibrium position often results in the particle being removed from the field of view of the imaging optics before the completion of crystal growth. Thus, the analysis for these seeded crystal growth experiments is based on induction time rather than total time of crystal growth. Induction Times. An example for determining tcol, tobs, and tind is shown in Figure 6 for a levitated (NH4)2SO4 droplet that was seeded through a collision with a (NH4)2SO4 seed crystal at 77 ± 1% RH (T = 295 K). The presence of the seed crystal introduced complications in the interpretation of the particle position and far-field image analysis. For example, the levitated droplet began moving downward in the trapping site prior to collision, as seen in the plot of particle position shown in Figure 6b prior to tcol at timestamp 9:30:58.128. This was likely due to a reduction in radiation pressure as the approaching crystal
scattered a portion of the upward oriented trapping beam. However, at timestamp 9:30:58.594, the particle moved upward markedly, signaling significant loss of water. Furthermore, there was an increase in ID̅ immediately upon contact due to the presence of the seed crystal. However, this was followed by a decrease in ID̅ , likely due to diffusion of the seed crystal further into the interior of the droplet. Because of these additional complications, tobs was determined as the time at which both ID̅ and equilibrium position were higher than their precollision values. Figure 6b shows this occurs at timestamp 9:30:58.601. From eq 5, tind for this experiment is 473 ms. This same criteria for determining tind was used for additional experiments at a range of RH values. A plot of tind as a function of RH is shown in Figure 7 for a series of (NH4)2SO4 droplets seeded with size-selected 1.5 μm diameter (NH4)2SO4 crystals. All experiments were performed at room temperature (T = 295 ± 1 K). A general trend is observed in which tind increases with RH, from ∼20 ms at 65% RH to ∼600 ms at 78% RH. Below 62% RH, crystallization occurred faster than the time between frames captured by the CCD cameras (∼5−10 ms) and induction times became indistinguishable. Thus, collisions below 62% RH are not considered in any further analysis. Induction time measurements are specific to a particular experimental detection scheme and therefore are not characteristic quantities of a crystallizing substance. However, the analysis of a series of induction times that were measured at a range of S can be used to determine trends in crystal growth. 6192
DOI: 10.1021/acs.analchem.5b00809 Anal. Chem. 2015, 87, 6186−6194
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Analytical Chemistry
Figure 8. (a) A plot of ln tind vs ln (S − 1). The equations for the bestfit lines are y = −0.7(±0.3)x − 1.6 ± 0.2 and −3.4(±0.6)x + 0.7 ± 0.8 for the experiments above 69% RH and below 69% RH, respectively. (b) A plot of ln Je vs (ln S)−1 focusing on the experimental data below 69% RH. The equation for the best-fit line is y = −10.4(±0.8)x + 28 ± 1.
Figure 7. A plot of tind as a function of relative humidity (RH) for a set of droplets seeded with a 1.5 μm diameter (NH4)2SO4 crystal. The black boxed inset shows a bright-field image typical for an effloresced (NH4)2SO4 crystal below 69% RH, and the blue boxed inset shows an example of a (NH4)2SO4 crystal formed at 77% RH.
homogeneous efflorescence and were roughly spherical. This visible change in typical crystal habit was likely due to the kinetic roughening associated with nucleation-mediated growth.29 Application of Classical Nucleation Theory to tind. The more complex S dependence of nucleation necessitates further analysis to extract meaningful conclusions. Classical nucleation theory (CNT) was thus used to further analyze the data below 69% RH. The 2D nucleation rate J2D, defined as the number of nucleation events on the surface of the crystal per unit time (cm−2s−1), is given as
Physically meaningful values can then be calculated from these trends, as demonstrated in the following analysis. Crystal Growth Mechanisms from tind. Experimental data was compared to theoretical models to distinguish normal crystal growth, spiral growth, and two-dimensional (2D)nucleation mediated growth. The various growth mechanisms can be distinguished from each other based on their different S dependence of crystal growth rate (G).23,24 G and S can be related using the equation G = kGf (S)
(6)
⎛ πhγ 2ν ⎞ J2D = B exp⎜ − 2 2 ⎟ ⎝ k T ln S ⎠
where kG is an S-independent kinetic factor and f(S) is a function that describes the S dependence of the different growth models. S was determined using the measured RH and the thermodynamic model of Clegg et al.19 For normal and spiral crystal growth, f(S) can be expressed as f (S) = (S − 1)n
where B is a kinetic pre-exponential factor, k is the Boltzmann constant, T is temperature, ν is the molecular volume of a structure unit, γ is the interfacial surface energy between the crystal structure and the surrounding aqueous phase, and h is the height of the 2D nucleus (typically ca. the molecular diameter of a structure unit).11 Experimental nucleation rates Je were calculated as Je = (Astind)−1, where As is the surface area of the crystalline (NH4)2SO4 particles. It was assumed here that the surface area of the crystal could be approximated by treating the crystal as a spherical particle. A plot of ln Je versus (ln S)−1 is shown in Figure 8b for the region of data where 2D nucleation was determined to mediate crystal growth. From eq 9, a plot of ln Je as a function of (ln S)−1 would be linear with a slope equal to −(πγ2νh)/(kT)2 if 2D surface nucleation-mediated growth was indeed the acting mechanism. Although a linear trend is observed for these data points, this in itself is not proof of 2D-nucleation mediated growth. As a validation, a value for γ was calculated for comparison to literature values. On the basis of the slope given by the linear regression analysis of the data (−10.4 ± 0.8) and using typical values for ammonium sulfate (h = 5 × 10−10 m, ν = 1.24 × 10−28 m3), γ was calculated here to be 30 ± 2 mJ m−2 at the experimental temperature (T = 295 K). Values reported in the literature for γ range from 7 to 70 mJ m−2 for (NH4)2SO4.1,30−33 The value calculated in the current study (30 ± 2 mJ m−2) is within this range, demonstrating that 2D-nucleation is likely the dominant crystal growth mechanism between 62% and 69% RH (S = 1.5−5.3). Similar calculations using expressions for 3D nucleation did not derive a physically
(7) 23,24
where n = 1 or 2, respectively. G is inversely related to tind and eq 6 can thus be combined with eq 7 to derive the general relationship t ind ∝ kG−1(S − 1)−n
(9)
(8)
Figure 8a shows the experimental results plotted as ln tind versus ln (S − 1). From eq 8, such a plot would have a linear trend with a slope n = −1 for normal crystal growth, −2 for spiral crystal growth, and ≤−3 for 2D-nucleation mediated growth.23,24 Contrary to this prediction, the data set does not present a linear trend when considering all points simultaneously. However, a clear distinction exists within the data when considering the cases above and below 69% RH independently, with both regimes exhibiting linear behavior. A best-fit line to the data yields a slope of −0.7 ± 0.3 for the data above 69% RH and −3.4 ± 0.5 for the data below 69% RH. Within error, these slopes, respectively, correlate with what would be expected for normal crystal growth (−1) and 2Dnucleation mediated growth ( 30); the ability to deliver a size-selected seed crystal to the aqueous droplet at any desired level of supersaturation; and in situ tracking and measurements of the time evolution of crystal growth. The ability to reach high levels of supersaturation prior to seeding can provide insight into nucleation and crystal growth processes over a wider range of solution supersaturations than are accessible in bulk crystallization experiments. The ease of use and ability to trap a wide range of particle diameters and morphologies demonstrates that the dual Gaussian beam-Bessel beam optical configuration may be of practical use for a diverse field of applications. Applications are not limited to the crystallization and deliquescence of inorganic systems as studied here. The techniques can be extended to other atmospheric, biological, and pharmaceutically relevant compounds, including those that form amorphous phases. ASSOCIATED CONTENT
* Supporting Information S
Four videos, seven figures, expanded experimental detail, and additional discussion. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.5b00809.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. Phone: (303)492-3179. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The funding for this work was provided by the CIRES Innovative Research Program. R.D.D. acknowledges a NASA Earth and Space Science Fellowship (NNX13AN69H). S.L. acknowledges support from the NOAA climate and air quality programs. The authors thank Alex Moyer for his early experimental contributions to the project, Dan Murphy and the NOAA Chemical Sciences Division for equipment, and Shuichi Ushijima for assistance with the experiment shown in Figure S3. 6194
DOI: 10.1021/acs.analchem.5b00809 Anal. Chem. 2015, 87, 6186−6194
