Crystallization Kinetics of Partially Crystalline Emulsion Droplets in a

May 3, 2016 - will retain their shapes after their formation or if coalescence between droplets .... The scale bars are 100 μm. Figure 2. ... ln(1. )...
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Crystallization Kinetics of Partially Crystalline Emulsion Droplets in a Microfluidic Device Tamás A. Prileszky and Eric M. Furst* Department of Chemical and Biomolecular Engineering, Center for Molecular and Engineering Thermodynamics, Allan P. Colburn Laboratory, University of Delaware, 150 Academy Street, Newark, Delaware 19716, United States ABSTRACT: We measure the crystallization kinetics of petrolatum-hexadecane emulsion droplets as they are produced in a microfluidic device. After droplets form, they are cooled, causing an interior network of wax crystallites to grow. Polarized light microscopy is used to quantify the droplet crystallinity as a function of residence time in the device. Two wavelengths and two polarization orientations are used to decouple the wavelength dependence of the optical retardation, the crystallite orientation, and the crystallite number density. The droplet crystallinity follows the Avrami kinetic model with parameter values in agreement with the theoretically expected values. These results provide a means to engineer the crystallization kinetics, stability, and arrested coalescence of partially crystalline emulsion droplets.

1. INTRODUCTION Endoskeletal droplets are oil-in-water emulsions that can be molded into nonspherical shapes.1 An internal network of wax crystallites forms a structural scaffold in the droplets. The network has a sufficient yield stress to resist the surface tension forces that normally collapse emulsion droplets into spheres. The balance between surface tension and internal elasticity can be upset by increasing temperature to weaken the internal network or decreasing surfactant concentration to strengthen the surface tension. Droplets respond to a dominant surface tension force by changing shape, with unconfined droplets ultimately collapsing to spheres;2 in coalescing droplets, shape change progresses until the new interfacial curvature produces a Laplace pressure balanced by the network’s yield stress.3 The yield stress that governs droplet stability arises from the crystallinity of the internal network, where more crystalline droplets have larger yield stresses. In this study, we use a microfluidic system to generate a continuous stream of partially crystalline endoskeletal droplets. As the initially fluid droplets flow through the device, they cool and crystallize. If a sufficiently strong crystalline network forms, then droplets produced in the device retain nonspherical shapes when they are collected. This process is outlined in Figure 1, which shows the stages of droplet formation as well as droplets under polarized light. Because the droplet stability is dependent on the crystallization kinetics, a technique for monitoring crystallinity as a function of droplet residence time in the device is necessary. In this work, crystallinity is determined by analyzing the transmission of polarized light through droplets at various locations, where the channel position is related to the residence time by the flow velocity. This in situ method for determining © XXXX American Chemical Society

crystallinity is vital to predicting whether endoskeletal droplets will retain their shapes after their formation or if coalescence between droplets will occur completely, partially, or not at all.3 Microfluidic devices have been used effectively to study the crystallization conditions and nucleation kinetics of small molecules and proteins.4−7 The present study extends the use of microfluidics by focusing on the development of a network of crystallites that imparts droplets with characteristic mechanical properties of soft solids, crucially including a yield stress. In this work, we describe the emulsion materials, microfluidic device, and image-processing methods that provide a quantitative measure of the crystallization kinetics. We pay careful attention to decoupling the principal optical parameters, in particular, the polarization orientation and wavelength dependence of the polarized light transmittance. The Results and Discussion presents an analysis of the crystallization kinetics of three endoskeletal droplet compositions that vary in the content of crystallizable material. We conclude by summarizing the results and commenting on the promise of optical crystallinity characterization in microfluidic devices.

2. EXPERIMENTAL METHODS 2.1. Emulsion Materials. Emulsions are prepared in a microfluidic device as an oil phase dispersed in an aqueous phase. The aqueous phase is composed of ultrapure water (resistivity >18.2 MΩ cm) and 10 mM sodium dodecyl sulfate (SDS, OmniPur, 99%), which is greater than the critical micelle concentration of ∼8 mM.8 The oil phase is a mixture of petrolatum (Vaseline, Unilever) and hexadecane (Fisher Received: February 2, 2016 Revised: May 2, 2016

A

DOI: 10.1021/acs.langmuir.6b00420 Langmuir XXXX, XXX, XXX−XXX

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Langmuir

Figure 1. Process of endoskeletal droplet formation in a microfluidic device. From left to right: droplet generation in the T-junction, with heating preserving Newtonian rheology in the dispersed phase; droplet molding in the crystallization channel, with droplets adopting the shape of the channel as crystallization proceeds; comparison of crystalline droplets under crossed and parallel polarizers, with crystallites appearing to be bright under crossed polarizers but dark under parallel polarizers; and ejection of nonspherical, crystalline droplets into the reservoir. Contrast is enhanced in crossed polarizer images. The scale bars are 100 μm. Scientific, 99%) prepared by heating the components to 80 °C, melting the petrolatum, and then mixing the two components in a vial. While still liquid, the mixture is drawn into a glass syringe. Samples of 60, 70, and 80% petrolatum by mass are prepared for the crystallization experiments. 2.2. Microfluidic Fabrication. Soft lithography is used to fabricate the microfluidic devices. Negative photoresist SU-8 (MicroChem) is used as a material for device masters. A layer of uniform SU-8 thickness is deposited onto a silicon wafer in a spin coater, and the wafer is then removed from the spin coater and placed on a hot plate to evaporate the photoresist solvent. The wafer with the hardened SU8 film is then patterned using a printed mylar transparency mask. The mask is adhered to a glass panel using a few droplets of water, and the glass plate is contact-aligned on top of the wafer to minimize spacing between the mask and wafer. Once aligned, the wafer is exposed to UV light, baked again on a hot plate, and transferred to a bath of SU-8 developer (Microchem), which dissolves unexposed regions of the SU8 film. Once the soft lithography step is completed, SU-8 patterns in the shape of the desired features are retained in relief on the silicon wafer. Microfluidic devices are fabricated from poly(dimethylsiloxane) (PDMS, Dow Corning Sylgard 184). PDMS is made by mixing prepolymer with curing agent in a 10:1 ratio. Once mixed, the PDMS is degassed, poured over the silicon master, and allowed to cure for 10 min at 150 °C. Non-cross-linked PDMS oligomers are removed from the PDMS slab by placing the PDMS in a chloroform bath for 4 h where the solvent is refreshed after 2 h. This process is repeated in an acetone bath, after which the PDMS is placed in a 65 °C oven for 8 h to remove residual solvent. Individual devices are cut from the dried PDMS, and ports are punched using a blunted hypodermic needle. The ported devices are bound to glass slides by placing a clean glass slide and a PDMS device, feature side up on a glass slide, in a plasma cleaner and exposing to air plasma for 30 s. The devices are bound to a glass slide by placing the PDMS feature side down and applying light pressure. Stainless steel ports are then inserted into the PDMS ports punched previously. 2.3. Droplet Production. A schematic of the experiment is presented in Figure 2. Programmable syringe pumps are used to pump both continuous aqueous and dispersed oil phases to the device. The dispersed phase is maintained above the 38−60 °C melting temperature range of petrolatum9 leading up to and during droplet production, after which droplets are quenched to promote crystallization. Prior to the device, the oil phase is heated to 65 °C using a circulating water bath at 80 °C, thus reducing the viscosity by melting the crystalline component. The dispersed phase feed tube is run adjacent to the circulating water bath tube to prevent crystallization before reaching the device. The microfluidic device itself has a metalloceramic heater fixed below the T-junction that heats the geometry to 60 °C, preventing crystallization during droplet formation. Formed droplets are quenched to the ambient temperature of 23 °C as they flow down the channel, allowing them to crystallize. Droplets ejected from the device after a sufficient yield stress has developed maintain the shape of the channel.

Figure 2. Schematic of experimental setup. The continuous phase is injected through the port on the left, and the dispersed phase, through the port on top. The two inlets converge at a T-junction, where droplets form. The T-junction is followed by a long crystallization channel where the internal network is allowed to form. Throughout the crystallization channel, the intensity of polarized light transmitted through droplets is measured. Droplets are imaged using a high-speed camera (Phantom v5.1, Vision Research) attached to an inverted microscope (Axiovert 200, Zeiss). The camera is capable of capturing video at 1000 frames per second at 1024 pixel × 1024 pixel resolution and higher frame rates for lower resolutions. The crystallinity of the droplets is measured by the transmission of polarized light, as described in detail in the next section. A polarizer is placed between the condenser and the sample, and the analyzer is placed immediately after the objective in the light path. Both the polarizer and analyzer are mounted on goniometers. The sample orientation is changed by rotating both polarizer and analyzer by 45°. Two bandpass filters dictate the wavelength of transmitted light: a red filter at 700 ± 20 nm and a yellow filter at 585 ± 20 nm (Chroma Technology Corp., Bellows Falls, VT). The polarized light setup is represented in Figure 2. The halogen reflector and condenser of the microscope produce light that is slightly polarized in the absence of polarizing filters. To account for this, the polarizer and analyzer starting angles were calibrated such that the 0 and 45° orientations produced the same intensity of light under parallel and crossed configurations with a clear light path. In addition, the lamp intensity was adjusted in order to produce identical transmitted light intensity under red and yellow filters. These adjustments allow experimental data under different orientation and filter settings to be compared directly, which is necessary to extract the degree of crystallinity information. 2.4. Polarized Light Analysis. The degree of crystallinity of droplets is determined from the transmission of polarized light.10,11 First, the background intensity in each image frame is subtracted by calculating a distance-weighted mean intensity across a portion of the data set according to B

DOI: 10.1021/acs.langmuir.6b00420 Langmuir XXXX, XXX, XXX−XXX

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Langmuir n

x̅ =

n

∑i (xi·∑ j (xi − xj)−2 ) n

∑ j (xi − xj)−2

(1)

where xi is the intensity of a pixel at frame i in a series of images of length n. The inverse distance weighting diminishes the contribution of intensity values far from the mode, which makes it a suitable calculation for the background intensity because the droplets, with intense bright or dark regions, occupy only a fraction of the total frame in a fraction of the total number of frames. After subtracting the background intensity from each image, we identify individual droplets by local increases or decreases in image intensity. In droplets of low crystallinity under crossed polarizers or all droplets under parallel polarizers, the droplet interior is bounded by minima produced by the dark interface, shown in Figure 3a. In contrast, droplets of high crystallinity under crossed polarizers exhibit profiles characterized by rapid increases in intensity from the baseline value shown in Figure 3b. In either case, intensities are measured in the same image region throughout the analysis to mitigate variations in pixel response and optical properties, and only the central regions of droplets are accepted. Under each experimental condition, we observe an average of more than 200 droplets, yielding a good sampling of the stochastic crystallization process. The distribution of measured intensities is narrow in each trial, as demonstrated in Figure 3c,d, where the histograms of both crossed and parallel polarizers are given for a single experimental condition. The transmitted intensity is related to the crystallite optical retardation, orientation, and number of crystallites in the light path; as a result, experimental procedures must be designed to decouple these three contributions through the analytical methods described by Ziabicki10 and summarized here. We start by defining a depolarization ratio, J, which is the fraction of total incident light that is transmitted through the sample and both polarizers after being reoriented by the birefringent material, J=

2I⊥ I + I⊥

(2)

In eq 2, I∥ and I⊥ represent the intensity of light transmitted through the birefringent material under parallel and crossed polarizers, respectively. The depolarization ratio, J = 1 − e−DES, is governed by three variables: D(λ) ≡ sin 2

π Δn(λ)d λ

= ⟨sin 2 Λd⟩, which is the

average optical retardation of a single birefringent plate; E ≡ ⟨n⟩, the average number of birefringent plates in the light path; and S ≡ ⟨sin2 2β⟩, the average orientation characteristic of the crystallites. In the previous equations, λ is the wavelength of transmitted light, Δn is the birefringence of the material, d is the optical retardation of a single birefringent plate, n is the number of plates in the light path at a single point, and β is the sample optical axis relative to the polarizer. The distinct parametric dependencies of D, E, and S allow these three variables to be decoupled. D is the only property that depends on the wavelength of light, and S is the only property that depends on the sample optical axis orientation. As such, S can be calculated independently by measuring the depolarization ratio through identical samples rotated by 45° relative to the incident polarization,

S=

Figure 3. (a) Intensity profile of a droplet-containing image under parallel polarizers is plotted after subtracting the background intensity. The same is plotted in (b), but for a droplet under crossed polarizers. In both images, the white lines indicate the channel boundaries and midline, determined using an edge-detection algorithm. The black signals below the images are the intensity profiles used to detect droplets of arbitrary intensity. Histograms for droplet intensities under parallel and crossed polarizers for a single experimental condition are provided in (c) and (d), respectively.

ln(1 − J45 °) ln(1 − J45 °) + ln(1 − J0 °)

⎡ 3η − 14ξη2 + 21ξ 2η1 6 η 2η − 5ξη1 4 D(λ1) = ξ⎢1 − 1 Δ2 + 2 Δ − 3 Δ ⎢⎣ D(λ 2) 3 45 945

(3)

Measurements of the depolarization ratio at two wavelengths allow the ratio of optical retardations to be determined,

D(λ1)ES D(λ1) = D(λ 2)ES D(λ 2)

+

(4)

2η4 − 15ξη3 + 42ξ 2η2 − 50ξ 3η1 14 175

⎤ Δ8 + ...⎥ ⎥⎦

In Equation 5, ξ is the ratio of optical coefficients Λ =

Ziabicki10 developed the following polynomial expansion used to describe the ratio of optical retardations at different wavelengths:

(5) π Δn λ

at two

different wavelengths, Δ is a reduced plate thickness, Δ2 ≡ Λ21⟨d2⟩, and C

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Langmuir ηk is (1 − ξk). It is useful to introduce a new variable, Z, which results directly from the depolarization ratios at two different wavelengths. Z=

⎡ ln(1 − J0 ° , λ ) ⎤ 3 ⎢ 1 ⎥ 1−ξ 1 − ξ ⎢⎣ ln(1 − J0 ° , λ ) ⎥⎦ 2

converted directly to the more useful variable combination DES through the relationship J = 1 − e−DES, with the result for 80% petrolatum shown in Figure 4. Several features of Figure 4 are

(6)

Z can also be expressed in terms of reduced thickness:

Z = Δ2 − −

2 − 3ξ 4 3 − 11ξ + 10ξ 2 6 Δ + Δ 15 315

2 − 13ξ + 29ξ 2 − 21ξ 3 8 Δ + ... 4725

(7)

Equation 7 allows D and E to be expressed explicitly in terms of Z and ξ,

⎡ 1+ξ 29 − 97ξ + 76ξ 2 2 D(λ1) = Z ⎢1 − Z− Z 5 1575 ⎣ +

⎤ 4 + 87ξ + 3ξ 2 − 60ξ 3 3 Z + ...⎥ 4725 ⎦

Figure 4. DES values as a function of channel residence time for droplets containing 80% petrolatum by weight. Solid lines are stretched exponential fits to each data set.

(8)

where

⎛ 1 ⎞ ln⎜ 1 − J ⎟ ⎡ ln(1 − J0 ° , λ ) ⎤ ⎝ 0 ° ,λ1 ⎠ ⎢ DE(λ1) 1 ⎥ E = 1+ = ⎢⎣ D(λ1) 2Z ln(1 − J45 ° , λ ) ⎥⎦

important in the following analyses: first, the 0 and 45° data overlap closely, implying that the angle of the sample optical axis does not affect the intensity of transmitted light. As a result, the average orientation of crystallites is random in this sample. The differences between transmittance at red and yellow wavelengths imply a nonlinear relationship between DES and the degree of crystallinity; however, the small magnitude of DES values validates the assumptions of a thin sample with few plates in the light path stipulated by the analysis in the previous section, making the calculation of the degree of crystallinity possible. However, the small values of DES make error propagations difficult: while the coefficients of variation of the intensity measurements are below 10% in all cases, the predicted confidence intervals around the data points are large in comparison to the data point magnitudes. We have excluded the propagated uncertainty in Figure 4 for this reason. Although Figure 4 implies that the crystallite orientation is random for 80% petrolatum droplets, it is important to calculate the actual value of S for all data sets. Figure 5 shows

1

⎡ 92 − 29ξ − 13ξ 2 1+ξ Z+ Z × ⎢1 + 5 1575 ⎣ 2

−

⎤ 35 + 1410ξ + 1620ξ 2 + 345ξ 3 3 Z + ...⎥ 23 625 ⎦

(9)

Assuming the birefringent plates are monodisperse and thin, the average thickness of a single plate is

⟨d 2⟩ =

⟨d⟩ ≅

+

Z⎡ 2 − 3ξ Z ⎢1 + 30 Λ1 ⎣

136 − 368ξ + 24ξ 2 2 Z 12 600

⎤ ⎥ ⎥ + 5076ξ 2 − 2133ξ 3 3 Z + ... ⎥ + ⎦ 378 000 1012 − 3954ξ

(10)

Finally, the degree of crystallinity is calculated by the relationship

x≡

E⟨d⟩ = B

⎛ 1 ⎞⎡ ln⎜ 1 − J ⎟⎢1 + ⎝ 0 ° ,λ1 ⎠⎣

ln(1 − J0 ° , λ )

⎤

ln(1 − J45 ° , λ ) ⎥ ⎦ 1

1

2Λ1BZ1/2

⎡ ⎤ 8 + 3ξ 1040 − 220ξ − 332ξ 2 2 Z+ Z + ...⎥ × ⎢1 + 30 12 600 ⎣ ⎦

(11)

where B is the sample thickness. Equations 3 and 11 reveal that the crystallite orientation and degree of crystallinity can be extracted from experiments that measure the depolarization ratio of a birefringent material at two different wavelengths and angles. This enables the crystallinity of partially crystalline emulsions to be measured optically in an active device, providing valuable information regarding structure formation of the soft crystalline network in situ.

Figure 5. Orientation characteristic as a function of residence time for all petrolatum compositions. Increasing petrolatum diminishes the emergence of a preferred crystallite orientation, but all data sets converge to a random orientation at long time. Lines are from stretched exponential fits applied to Figure 4.

3. RESULTS AND DISCUSSION Depolarization ratios are calculated from intensity values of droplet images according to eq 2. The depolarization ratios are D

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Langmuir DES values from each experiment at 60, 70, and 80% petrolatum. S = 0.5 indicates randomly oriented crystallites; for values greater than 0.5, crystallites orient in the flow direction, and for values smaller than 0.5, the orientation is perpendicular to the flow direction. At 60% petrolatum, the value of the orientation characteristic decreases from ∼0.75 to 0.5 with increasing residence time, indicating that crystallites initially orient in the direction of the internal flow of the droplets. As the number and size of crystallites increase, crystallites begin to cross large gradients in flow velocity and impinge on one another, leading to tumbling and the loss of a preferred orientation. In addition, the crystallite network percolates the droplet, breaking down the orienting flow. At larger petrolatum fractions, the condition of many and larger crystallites is reached significantly sooner, preventing any measurable orientation in the structure from emerging. The ultimate isotropic crystallite orientation in all compositions means that the difference between DES values at different compositions at long time is due to the fractional volume of a droplet occupied by crystalline material. As a result, it is of interest to investigate the rate at which a droplet approaches its maximum crystallinity, which is accomplished by normalizing the degree of crystallinity for all data sets such that the kinetics being compared are those regarding the time required to reach the final state at each composition rather than an absolute crystallinity. The resulting crystallinity curves are shown in Figure 6. As the petrolatum fraction is increased, the required time to reach

Table 1. Avrami Equation Fit Values petrolatum fraction (%)

n

k (sn)

60 70 80

2.1 ± 0.2 2.2 ± 0.5 2.4 ± 0.6

3.4 ± 0.5 5.9 ± 2.6 10.0 ± 6.3

exponent is often related to the shape of crystallites, where rod, disk, and spherical particles have Avrami exponents of 1, 2, and 3, respectively, and homogeneous crystallite nucleation adds 1 to the Avrami exponent in each case.14 The results in Table 1 are consistent with these heuristics, assuming nucleation is homogeneous, which is the anticipated nucleation mechanism in microfluidics with large quench rates and depths.15 The Avrami exponent is larger than values for similar materials found in the literature: Ismail et al. report n values near unity.16 The apparatus used by Ismail studies the crystallization upon deposition to a substrate, leading to heterogeneous nucleation and an expected Avrami exponent of 1 were nucleation homogeneous; a larger Avrami exponent would be expected and would be more consistent with the results presented here. The change in the kinetic rate constant with increasing petrolatum fraction is more pronounced than the change in the exponent. This result is also anticipated; fast crystallization processes are diffusion-limited as growing crystallites rapidly deplete local supplies of crystallizable material. Correspondingly, bulk phases of higher petrolatum concentration will have greater material fluxes to the crystalline phase, leading to faster crystallization rates.

4. CONCLUSIONS Our study demonstrates the promise of optical crystallinity characterization in microfluidic devices. The optical technique for measuring crystallinity demonstrates the ability to determine the kinetics and properties of crystallizations in continuous-flow systems with overall crystallization times of fractions of a second, provided there is sufficient spatial resolution to correlate position with residence time. The results of the analysis provide information regarding the emergence and evolution of crystalline structures under the conditions of use rather than in an ideal state, enabling improved testing and design of crystallization processes. The techniques of polarized light transmission proposed by Ziabicki for static systems apply especially well to the microfluidic systems owing to the small sample thickness set by the thin channel dimensions.10,11 Many techniques exist for measuring the kinetics of crystallite formation, each with distinct benefits and drawbacks. As microfluidic science grows as a platform for both the study and generation of unique materials, a technique useful for measuring crystallinity in situ at small length scales is beneficial. Moreover, the dynamic nature of microfluidic systems could result in complex crystallization processesflow patterns cause preferred orientation, temperature gradients cause slow crystallization, and confinement leads to crystallite aggregation. As a result, an optical technique for measuring crystallinity should have a wide number of applications. The results of this analysis suggest several future investigations. Most apparent is the application of the crystallization kinetics measurement technique to different systems, either flowing or stationary. Similar systems of microfluidic production of crystallizing fat droplets can benefit from a quantitative measure of droplet crystallinity on a device,17 as can many crystallization studies in microfluidic

Figure 6. Normalized degree of crystallinity for all compositions as a function of residence time. Petrolatum composition decreases from left to right.

maximum crystallinity is reduced. In order to extract quantitative kinetics information, each curve is fit using the Avrami kinetic model, n

(12) x = 1 − e−kt where k is a kinetic rate constant and n is an equivalent rate order.12−14 Figure 6 shows the degree of crystallinity calculated using eq 11 with Avrami fits from eq 12. The decrease in the time required for crystallization is clear from Figure 6; higher petrolatum fractions have larger rate constants, and to a lesser degree, Avrami exponents, meaning the conversion from liquid to crystal is faster with higher concentrations of crystallizable material. The values of the rate constant k and Avrami exponent n are provided in Table 1. A small change in the Avrami exponent is anticipated: neither the morphology nor the nucleation of crystallites changes with the changing composition of the crystallizable material. The Avrami E

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Langmuir systems.18,19 The result of degrading orientation is interesting, hinting at the ability to design a microfluidic system capable of producing polycrystalline structures from crystallites arranged with specific orientation without the addition of an external field. By tuning the orientation of crystallites within the droplets, structural, optical, and other forms of anisotropy can emerge, leading to particles with numerous forms of asymmetry.

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(19) Stan, C. A.; Schneider, G. F.; Shevkoplyas, S. S.; Hashimoto, M.; Ibanescu, M.; Wiley, B. J.; Whitesides, G. M. A microfluidic apparatus for the study of ice nucleation in supercooled water drops. Lab Chip 2009, 9, 2293.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the National Science Foundation for funding (grant number CBET-1336132).

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REFERENCES

(1) Caggioni, M.; Bayles, A. V.; Lenis, J.; Furst, E. M.; Spicer, P. T. Interfacial stability and shape change of anisotropic endoskeleton droplets. Soft Matter 2014, 10, 7647−7652. (2) Caggioni, M.; Lenis, J.; Bayles, A. V.; Furst, E. M.; Spicer, P. T. Temperature-Induced Collapse, and Arrested Collapse, of Anisotropic Endoskeleton Droplets. Langmuir 2015, 31, 8558−8565. (3) Pawar, A. B.; Caggioni, M.; Hartel, R. W.; Spicer, P. T. Arrested coalescence of viscoelastic droplets with internal microstructure. Faraday Discuss. 2012, 158, 341−350. (4) Laval, P.; Salmon, J.-B.; Joanicot, M. A microfluidic device for investigating crystal nucleation kinetics. J. Cryst. Growth 2007, 303, 622−628. (5) Laval, P.; Crombez, A.; Salmon, J. B. Microfluidic Droplet Method for Nucleation Kinetics Measurements. Langmuir 2009, 25, 1836−1841. (6) Ildefonso, M.; Candoni, N.; Veesler, S. Using microfluidics for fast, accurate measurement of lysozyme nucleation kinetics. Cryst. Growth Des. 2011, 11, 1527−1530. (7) Teychené, S.; Biscans, B. Crystal nucleation in a droplet based microfluidic crystallizer. Chem. Eng. Sci. 2012, 77, 242−248. (8) Mukerjee, P.; Mysels, K. Critical micelle concentrations of aqueous surfactant systems. J. Pharm. Sci. 1972, 61, 222. (9) Guthrie, V. B. Petroleum Products Handbook; Knovel, 2005. (10) Ziabicki, A. Transmission of light through a statistical system of birefringent plates. J. Opt. A: Pure Appl. Opt. 2005, 7, 774−782. (11) Ziabicki, A., Misztal-Faraj, B. Interpretation of light depolarization data in terms of polymer crystallinity. Mater. Sci. 2006,24. (12) Avrami, M. Kinetics of Phase Change. I General Theory. J. Chem. Phys. 1939, 7, 1103. (13) Avrami, M. Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei. J. Chem. Phys. 1940, 8, 212. (14) Avrami, M. Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III. J. Chem. Phys. 1941, 9, 177. (15) Mullin, J. W. Crystallization, 4th ed.; Butterworth-Heinemann, 2001; p 594. (16) Ismail, L.; Westacott, R. E.; Ni, X. On the effect of wax content on paraffin wax deposition in a batch oscillatory baffled tube apparatus. Chem. Eng. J. 2008, 137, 205−213. (17) Kim, J.; Vanapalli, S. A. Microfluidic Production of Spherical and Nonspherical Fat Particles by Thermal Quenching of Crystallizable Oils. Langmuir 2013, 29, 12307−12316. (18) Yu, Y.; Wang, X.; Oberthür, D.; Meyer, A.; Perbandt, M.; Duan, L.; Kang, Q. Design and application of a microfluidic device for protein crystallization using an evaporation-based crystallization technique. J. Appl. Crystallogr. 2012, 45, 53−60. F

DOI: 10.1021/acs.langmuir.6b00420 Langmuir XXXX, XXX, XXX−XXX