Crystallization Behavior and Nucleation Kinetics of Organic Melt

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Crystallization Behavior and Nucleation Kinetics of Organic Melt Droplets in a Microfluidic Device Burkard Spiegel, Alexander Käfer, and Matthias Kind Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01697 • Publication Date (Web): 25 Apr 2018 Downloaded from http://pubs.acs.org on April 25, 2018

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Crystal Growth & Design

Crystallization Behavior and Nucleation Kinetics of Organic Melt Droplets in a Microfluidic Device Burkard Spiegel, Alexander Käfer, Matthias Kind* Institute of Thermal Process Engineering, Karlsruhe Institute of Technology (KIT)

The powerful technique of microfluidics is applied for the first time to investigate the crystallization behavior and nucleation kinetics of monodisperse organic melt droplets in the range of a few nanoliters. Multiple characteristic timescales in the fraction of (un)crystallized droplets are found. We interpret these findings regarding mechanisms discussed in microfluidics or oil-in-water emulsions and with the help of inverse Laplace transformation. Heterogeneous active centers, for example various catalytic impurities, cause fast nucleation in multiple droplet populations with different rates. The nucleation of the remaining droplets in the later stage of the experiment is dominated by only one, slower nucleation rate. The related mechanism is most likely surfactant-driven heterogeneous nucleation at the surface or in the droplet volume. Homogeneous nucleation is excluded at this droplet size and the supercooling values examined. Hexadecane (C16) and ethylene glycol distearate (EGDS) are used as exemplary organic melt substances. Our results prove that the application of microfluidics to organic melt droplets enables an optical examination of monodisperse droplets without droplet interactions to study nucleation. This provides new opportunities to investigate fundamental parameters in the field of emulsion crystallization.

MatthiasKind Kaiserstraße 12 76131 Karlsruhe Germany Phone: +49 721 608 42390 Fax: +49 721 608 43490 E-Mail [email protected] Web address: www.tvt.kit.edu

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Crystallization Behavior and Nucleation Kinetics of Organic Melt Droplets in a Microfluidic Device Burkard Spiegel, Alexander Käfer, Matthias Kind* Institute of Thermal Process Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany, [email protected]

The powerful technique of microfluidics is applied for the first time to investigate the crystallization behavior and nucleation kinetics of monodisperse organic melt droplets in the range of a few nanoliters. Multiple characteristic timescales in the fraction of (un)crystallized droplets are found. We interpret these findings regarding mechanisms discussed in microfluidics or oil-in-water emulsions and with the help of inverse Laplace transformation. Heterogeneous active centers, for example various catalytic impurities, cause fast nucleation in multiple droplet populations with different rates. The nucleation of the remaining droplets in the later stage of the experiment is dominated by only one, slower nucleation rate. The related mechanism is most likely surfactant-driven heterogeneous nucleation at the surface or in the droplet volume. Homogeneous nucleation is excluded at this droplet size and the supercooling values examined. Hexadecane (C16) and ethylene glycol distearate (EGDS) are used as exemplary organic melt substances. Our results prove that the application of microfluidics to organic melt droplets enables an optical examination of monodisperse droplets without droplet interactions to study nucleation. This provides new opportunities to investigate fundamental parameters in the field of emulsion crystallization.


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INTRODUCTION Crystallization of oil-in-water (O/W) emulsions is a core process for separation, purification or control of product properties in several industrial fields, such as pharmaceuticals, food, cosmetics, heat storage or specialty compounds.1 The development and employment of these processes still rely on a high level of expertise due to the complex mechanisms involving crystallization.2 Crystallization in emulsion droplets is dominated by nucleation rather than by growth, because of the small droplet volume.3 In addition to classical parameters from bulk crystallization, additional factors, such as surfactant (structure), additives, level of impurities, mean droplet size and droplet interactions, influence nucleation in emulsions. A detailed overview is provided by several reviews.4–6 Numerous studies were carried out and several methods were developed in the field of crystallization of O/W emulsions to identify key parameters and understand their underlying mechanisms, especially in the field of food science.7– 13

In addition to these kinds of studies, emulsified droplets are used as an established technique

for the determination of nucleation kinetic parameters, for example, the surface energy. The main advantages are the large numbers of independent nucleation sites and small volumes that may enable the examination of homogeneous nucleation by eliminating the effect of heterogeneous active centers (for example catalytic impurities). Beginning with the work of Vonnegut14, homogeneous nucleation has been investigated in a variety of materials, including n-alkanes and liquid metals.15–17 However, nucleation in emulsions is not necessarily as straightforwardly homogeneous as other studies emphasize. Povey and coworkers 9,18,19 proved a collision mechanism (i.e. interdroplet nucleation) as one key factor in the crystallization of emulsions in several studies. Herhold et al.20 found an impurity-mediated mechanism for their µm emulsions.


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These different explanations reflect the complexity and challenges in the interpretation of nucleation measurements. All the studies mentioned above observed a polydisperse ensemble of droplets. However, polydispersity can be a large source of error,21 though several studies accounted for this problem.17,20,22 In addition, the change of an integral quantity (e.g. released heat, ultrasound velocity, x-ray intensity) was measured to characterize nucleation. Nucleation may vary from droplet to droplet due to its stochastic nature. This becomes a challenge for interpretation if more than one nucleation mechanism is present.1,20 Techniques that observe the crystallization in single or isolated droplets directly would give valuable insight into emulsion droplet crystallization as stated by Coupland5 in 2001. Weidinger et al.23 determined nucleation kinetics of single alkane droplets by an electrodynamic balance at an air interface. These results cannot be transferred straight to emulsions, as a solid monolayer is formed particularly at the alkane/air interface.24 Some studies looked visually at crystallization in single emulsified droplets25 or highly diluted emulsions.26,27 However, none of these determined the nucleation kinetics to quantify crystallization. In the work presented here, we utilize microfluidics as an optical technique with single, isolated droplets for this purpose. Microfluidic studies, either in small capillaries or microfluidic chips, have been used lately to study and explain nucleation of a variety of substances from solution.28– 32

The obvious advantages are a large set of monodisperse, isolated droplets in the size range of

several 100 µm, which can be observed directly by a microscope. The droplets act as miniature crystallization vessels which produce crystals in contact with a residual liquor to cover the stochastic nature of crystallization. In contrast to this, the entire droplet solidifies after nucleation in the case of emulsified organic melts. To the best of our knowledge, there has been no study of


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nucleation kinetics of organic melt droplets by microfluidics so far. We use this beneficial technique to determine the nucleation rates of organic melt droplets of a few nl (~250 µm) and discuss them regarding nucleation mechanisms known from microfluidic experiments and emulsions, for example, heterogeneous active centers and homogeneous or inter-droplet heterogeneous nucleation. In addition, data analysis by inverse Laplace transformation (ILT) and multiple runs on the same set of droplets are conducted to identify the dominant mechanisms of organic melt droplets. To this end, we investigated two exemplary organic melts by microfluidics: the alkane hexadecane (C16) and the diglyceride ethylene glycol distearate (EGDS). C16 is a common model substance for food emulsions.8 It crystallizes over a transient rotor phase into a stable triclinic structure in the bulk state.33 A metastable rotator phase of C16 has been found in confined spaces.34–36 EGDS is used as a cosmetic ingredient for its pearlescent effect. No data about its crystalline structure were available. EXPERIMENTAL SECTION Materials Two types of organic melts, EGDS with a mass purity of 98 % (Wako Chemicals, Germany) and C16 (> 99 % pure, Sigma-Aldrich, Germany), were used as the droplet phase. The melting point of EGDS and C16 was determined by differential scanning calorimetry (Phoenix DSC 204, Netzsch, Germany) with a value of 60.5 °C and 18.0 °C, respectively, and an error of 0.1 K. A solution of deionized water (Milli-Q, Merck Millipore, USA) with 2 wt% of surfactant Polysorbate 20 (Tween 20, Carl Roth, Germany) was used as a continuous phase to mimic common emulsion compositions. The surfactant concentration was more than 100 times above the critical micelle concentration of Tween 20. All substances were used without any further


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purification. Additional experiments with filtered substances (syringe filter pore size 0.2 µm) were performed, because impurities can have a pronounced effect on nucleation.37 No significant difference was found. Polycarbonate (Makrolon®, Bayer, Germany) was used as microfluidic chip material. A solution of 20 wt% Tin(II) chloride dihydrate (> 98 %, Carl Roth, Germany) in ethanol (> 99.9 %, Merck, Germany) was used for the hydrophilic surface modification of the channel walls.38 Experimental Setup Figure 1 shows the experimental microfluidic setup used to perform nucleation experiments. The setup consists of a charge-coupled device camera (pco.edge 5.5, PCO AG, Germany) coupled to a stereo microscope (SZ61, Olympus), a temperature controlled container for the two syringe pumps (CETONI, Germany) thermostatted by a heating fan (LE Mini Sensor, Leister Technologies, Germany) and a temperature control unit. In the temperature control unit, the microfluidic chip can be supercooled using a Peltier element (QUICK-OHM, Küpper, Germany). An enclosure was installed and flushed with dry air during the C16 experiments (T < Tambient) to avoid condensation on the top of the supercooled microfluidic chip, especially in the summer time.


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Figure 1. Experimental microfluidic setup: (1) Charge-coupled device camera, (2) microscope, (3) polarizer, (4) thermostatted box with two syringe pumps, (5) temperature control unit with microfluidic chip and (6) enclosure. A sketch and photograph of the microfluidic chip is depicted in Figure 2. The chip was made of a polycarbonate slab (thickness 2 mm) by CNC milling at a revolution speed of 30,000 rpm and sealed with a polycarbonate cover foil (250 µm) by thermal bonding. Subsequently, a surface modification was carried out to create a strongly hydrophilic channel surface. Consequently, a stable generation of organic melt droplets was possible and interaction between the dispersed phase and the channel walls could be excluded.39 Droplet generation was realized in the first part of the microfluidic chip via a T-junction (marked by the dotted line in Figure 2a). The oil phase was injected through inlet 1, whereas the continuous phase was injected via inlet 2. The second part consists of a serpentine channel acting as storage area (dashed line in Figure 2a) to observe as many droplets as possible in the field of view of the microscope during each crystallization experiment. The channels had a rectangular cross section with smaller dimensions of 200 x 100 µm for the first part (droplet generation) compared to 200 x 200 µm for the second part of the microfluidic chip to investigate almost spherical droplets rather than elongated plugs. A more detailed description of the experimental setup and of the microfluidic chip can be found in our previous published work.40


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Figure 2. (a) Sketch and (b) photograph of the microfluidic chip with inlets for continuous (1) and dispersed (2) phase, channel to insert a thermocouple (3) and outlet (4). Experimental Procedure The microfluidic chip, capillaries and syringes were kept above the melting temperature at 20 °C to avoid clogging for experiments with C16. Monodisperse droplets with a volume of around 7.1 nl and a volume deviation of less than 5 % were generated, as explained previously, at a flow rate of 200 µl/h for the continuous and 40 µl/h for the dispersed phase. In the case of EGDS, the experimental temperature was 70 °C, the droplet volume was 9.4 nl and the flow rates were 300 and 60 µl/h, respectively. Once a sufficient droplet number was generated, the flow was stopped, and the microfluidic chip was cooled down at quiescent conditions. The predefined, isothermal temperature and, thus, a constant supercooling ∆Tset was achieved after less than 60 s. The actual crystallization temperature and supercooling ∆Tcryst (hereinafter just ∆T) in the microchannel is slightly different (about 0.2 -0.5 K). It was calculated with the help of temperatures measured beneath (Tset) and above the microchannel and relevant material parameters (dimensions and thermal conductivity) assuming steady state heat transfer. Images of the storage part of the chip were taken every second for a maximum duration of 5000 s during supercooling. Exemplarily, in


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Figure 3a a section of the microfluidic chip is shown at different times for a constant supercooling of 7.0 K. The number of crystallized C16 droplets increases with time. Polarized light was used for the better detection of the crystallized droplets, which appear as bright white circles. The individual induction time of each droplet and the number of crystallized droplets, Ncryst(t), as a function of time were determined by an image processing program. Together with the total number of droplets at time zero, N0, the fraction of crystallized droplets, Pcryst(t), can be calculated to quantify nucleation:

. 1

On average about 400 droplets were observed in each C16 experiment. This value was around 260 for EGDS. These numbers are a statistically significant amount to study nucleation phenomena, according to recent works41,42 on uncertainty associated with nucleation rates estimated in small volumes.


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Figure 3. (a) Section of the microfluidic chip at different times (in min) for a C16 experiment with a constant supercooling of 7.0 K. The white circles display crystallized droplets, intensified by polarized light for better detection. (b) Time lapse series showing the crystallizing of an EGDS droplet. In our case, the induction time is defined as the time between the achievement of supercooling and the first detectable occurrence of crystallization in the droplet. The induction time is equivalent to the nucleation time if the time required for a critical nucleus to grow to a detectable size is much smaller than the nucleation time. This assumption is true for our experiments, as demonstrated for EGDS in a time lapse series in Figure 3b. The whole droplet crystallizes in a few seconds. This time period is negligibly small compared to the induction times measured. Similar argumentation has been used before for µm emulsions in literature.1,20 RESULTS AND DISCUSSION Crystallization Experiments Figure 4 shows the experimentally determined fraction of crystallized droplets, Pcryst(t), as a function of time for C16 at five different constant supercooling values, ∆Tset, of 7.0, 7.5, 8.0, 8.5 and 9.0 K. Several experiments were performed for each temperature. Only one experiment per supercooling is depicted and only data points are shown where crystallization of at least one droplet occurred for reasons of clarity. A figure of all runs is available in the Supporting Information (see Figure S1a).


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Figure 4. Experimentally determined fraction of crystallized droplets, Pcryst(t), for C16 at five different constant supercooling values ∆Tset of 7.0 (blue diamonds), 7.5 (green circles), 8.0 (yellow squares), 8.5 (red triangles) and 9.0 K (black stars) as a function of time. About 3 % of the droplets were crystallized after 5000 s at the smallest supercooling of 7.0 K (blue diamonds) investigated. Below this value, the nucleation rate is too low to observe any crystallization during our experiments (data not shown). This is a typical characteristic of small volumes or droplets due to the stochastic nature of nucleation. In contrast to bulk samples a temperature (far) below the equilibrium is necessary to cause nucleation. The crystallized fraction of C16 droplets increases as expected with increasing supercooling. This value is about 70 % at the end for a supercooling of 8.5 K (red triangles). All droplets crystallized in just a few minutes at a supercooling of 9.0 K (black stars) and higher. Looking at the temporal evolution of the crystallized fraction, the nucleation times span several orders of magnitude: Firstly, a rapid increase to a certain threshold value within the first 400 s; afterwards, the change of Pcryst(t) slows down significantly. For example, at a ∆Tset = 8.0 K (yellow squares) around 20 % of the droplets crystallize inside 400 s, but 70 % still remain liquid after 5000 s. It is noteworthy that this trend is similar for all experiments, though the threshold value increases with supercooling.


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A second, different organic melt, EGDS, was investigated to check and validate these findings. Analogous to C16, the temporal evolution of Pcryst(t) for selected EGDS experiments is depicted in Figure 5. A figure of all runs can be found in the Supporting Information (see Figure S1b).

Figure 5. Experimentally determined fraction of crystallized droplets, Pcryst(t), for EGDS at five different constant supercooling values ∆Tset of 3.5 (blue diamonds), 4.5 (green circles), 5.5 (yellow squares), 6.0 (red triangles) and 6.5 K (black stars) as a function of time. A similar behavior and trend is visible for EGDS. Overall, the supercooling in the experiments is lower compared to C16. The critical supercooling for the occurrence of no crystallization is below 3.5 K and almost instantaneous crystallization of all droplets appears around 6.5 K. The main reason is probably the dependence of nucleation on substance-specific properties. Another reason may be the different degree of purity of the C16 and EGDS used or the different absolute experimental temperatures. Determination of Nucleation Rates


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Nucleation rates J can be obtained from the measured fraction of crystallized droplets, Pcryst(t), by curve fitting to an appropriate model that is capable to describe the stochastic process of nucleation at isothermal conditions. In the simplest case, the nucleation rate is time independent and constant in all droplets (e.g. purely homogeneous nucleation or just one well-defined type of heterogeneous nucleation). The fraction of liquid droplets P(t) and also Pcryst(t) is a simple exponential with the constant nucleation frequency k: 1 exp ∙ . 2 k is related to the nucleation rate J by the nucleation volume Vnuc. Vnuc varies depending on the type and site of nucleation, e.g. the droplet volume for homogeneous nucleation or the catalytic surface in the case of active heterogeneous centers.

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Figure 6. Experimental C16 data from Figure 4, now plotted as ln(1-Pcryst). The dashed line is a best approximation of the experimental data at ∆Tset = 8.5 K (red triangles) to a simple model with one constant nucleation frequency. A poor agreement is evident.


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Eq. 2 is not suitable to describe our data appropriately. This is demonstrated in Figure 6 by the dashed line, a best approximation of the experimental data at ∆Tset = 8.5 K (red triangles) according to eq. 2. Figure 6 shows the C16 data from Figure 4, now plotted as the logarithm of liquid, not crystallized droplets. Consequently, the gradient of the data equals the nucleation frequencies. Both the rapid increase in the beginning and the slow change of P(t) at the end cannot be equally well represented by a model with one constant nucleation frequency. A modification of eq. 2, which was used by several authors41,43 to describe nucleation experiments in small ml volumes, includes a time offset (e.g. growth time until detection) in the exponential term. This modification shifts the origin of the fit from the zero point, but has no effect on the gradient. More complex models with decreasing nucleation frequencies/rates are necessary to describe our data. Several authors1,9,12,20 investigated nucleation of organic melts in emulsions of a few µm and smaller. They proposed models with either inter-droplet heterogeneous nucleation or the expulsion and transport of active centers from already crystallized droplets. These models are inapplicable to our results, as isolated, quiescent droplets are used. For microfluidics no comparable work and no specific nucleation models regarding organic melts exist. Therefore, we consider models summarized by Sear in his review44 for a P(t) with decreasing nucleation rate and discuss them regarding our experimental data in the following section. 1) Models for a P(t) with decreasing nucleation rate A time dependence of the nucleation rates can be a result of two generally different physical mechanisms. In the first case (case A), the droplets are not identical. There exist two or more types of droplets with a time independent, but different nucleation rate in each droplet population, for example, droplets with different types of active nucleation sites (various catalytic impurities) or a mixture of droplets with heterogeneous and homogeneous nucleation15. The


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temporal evolution of P(t) is a superimposition of the nucleation of each population i and is described by an multi-exponential function: 1 ∑ ∙ ! "# $ . 4 ξi represents the droplet fraction and ki the nucleation frequency of population i. With evolving time, different nucleation frequencies dominate the current evolution of P(t). In the second physical explanation (case B) for a decreasing nucleation rate, there is only one identical nucleation rate in all droplets, but it is not constant and decreases with time. One explanation could be molecular rearrangement of molecules (proteins45) or an alteration of a heterogeneous catalytic surface. It was also suggested for microgel-induced nucleation.46 The evolution of P(t) is described by an exponential of a power law, also called Weibull function: 1 exp [/()*+ , ]. 5 τmed is a timescale parameter related to the median nucleation time and β is an exponent. For β = 1, eq. 5 reduces to the simple exponential model. Decreasing nucleation relates to β < 1. The time-dependent nucleation frequency is given by

,$ /01 2345 /

. 6

One way to identify the dominant physical mechanism is the use of experiments similar to Laval et al. 47. They carried out multiple crystallization runs on the same set of droplets. In the case of multiple droplet populations, the same droplets should always crystallize in multiple runs. For case B, the crystallization of droplets should be randomly distributed. The assumption of multiple, more specifically, two populations is common for microfluidic studies investigating the


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nucleation from solution in nl volumes (e.g. inorganic salts47 or proteins31 in aqueous solution or organic molecules in organic solvents29). Moreover, we have no physical sound explanation for case B regarding the organic melts used. The molecular rearrangement of C16 and EGDS is rapid compared to large protein molecules45. The surface may alter by formation of the rotator phase48, but it acts as a precursor and should promote nucleation23, not inhibit it. Thus, we hypothesize that two or more droplet populations are present in our experiment (case A) and that case B is not the dominant mechanism. The results are presented the next section. 2) Review of the hypothesis of multiple droplet populations 4 crystallization runs on the same set of 228 droplets (C16) were performed using the procedure described in the experimental section with the temperature profile displayed in Figure 7a. During each cycle, the temperature was lowered from 25 °C to 10.5 °C (∆Tset = 7.5 K) and kept constant for 5000 s. All droplets that crystallized during this time were analyzed in each run for reviewing the hypothesis. Afterwards, in contrast to Laval et al47, nucleation in the remaining liquid droplets was triggered by lowering the temperature to about 6.5 °C for 2 min before melting the crystallized droplets at 25°C for 10 min. Thus, misleading results by a possible memory effect of the droplets that crystallized after 5000 s are avoided. We also varied the temperature and the duration of the melting process. There is no significant influence on the following conclusions. Figure 7b shows the evolution of Pcryst(t) and a section of the chip after the isothermal crystallization period of the first (square) and last cycle (triangle). On average 49 ± 3 droplets (21,5 ± 1,2 %) crystallized. During the heating and cooling of the chip, droplets moved up to a distance of about one channel height. Therefore, a direct visible comparison between each cycle and also the two images shown in Figure 7b is not possible. A manual tracking was necessary to determine the crystallization behavior of each individual droplet. Moreover, coalescence took


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place between some of the droplets by movement and melting of the droplets during heating (larger liquid and crystallized droplets in the image marked by the triangle). This fact is considered in the data analysis. Still, coalescence limited the number of cycles (to 4 runs). Interestingly, coalesced droplets practically always crystallize if one of the involved droplets has crystallized during the previous isothermal period. This did not occur, if two liquid droplets merged.


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Figure 7. (a) Temperature profile of the 4 crystallization runs on the same set of 228 C16 droplets. (b) Fraction of crystallized droplets over time for each run with an image of a microchannel section after the first (square) and the last run (triangle). (c) Experimentally determined relative frequency that a droplet crystallizes nc times in 4 runs (bars) and corresponding probability pc (squares) assuming random nucleation for an average nucleation probability of p = 21.5 %. A significant discrepancy is present. In Figure 7c the experimentally determined relative frequency that a droplet crystallizes in total nc times during the 4 cycles is plotted together with the corresponding probability pc assuming randomly distributed nucleation events. The expected probability pc for an experiment with 4 cycles is given from combinatorics by the binominal distribution 7 8 9

:!

C15 is approximately 0.95·Tm.51 This corresponds to a ΔT of 14.6 K, which is far below the temperatures examined in this work. On these grounds, homogeneous nucleation is excluded, particularly for C16 (no literature is available for EGDS).Thus, the mechanism for


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slow nucleation is most likely another sort of heterogeneous nucleation in the volume or surfactant-driven nucleation at the droplet interface as the interface can play a decisive role in droplet nucleation11. If the hydrophobic moiety of the surfactant or an additive at the interface has a similar molecular structure compared to the oil, it can increase the nucleation rate.8,10 The surfactant used in this study, Tween 20, has fewer C-atoms (12) than C16 or the fatty acid (stearic acid) in EGDS and we expect no accelerating effect in the droplets. This was demonstrated for C16 emulsions with Tween 20.8 Microfluidic experiments with various surfactants should help to clarify the origin of the slow nucleation mechanism and the role of surfactant on the nucleation of organic melt droplets. Work on this topic is currently in progress.52 CONCLUSIONS In this paper, nucleation of organic melts (C16 and EGDS) was studied for the first time via microfluidics. The experimental setup allows the investigation of isolated, monodisperse droplets. In contrast to studies based on the emulsion technique, interaction between droplets can be excluded and crystallization of droplets is visible. We demonstrated the benefit of this technique for the determination of crystallization behavior and nucleation kinetics. Heterogeneous active centers (for example various catalytic impurities) cause nucleation in multiple droplet populations with fast nucleation frequencies. The remaining droplets nucleate by only one, slower nucleation frequency. The related mechanism is most likely surfactant-driven heterogeneous nucleation at the surface or in the droplet volume. This work is the basis for the investigation of fundamental parameters in crystallization of emulsions at well-defined conditions in the future, for example, the effect of different surfactants or added heterogeneous active centers on nucleation. However, a transfer of results from larger microfluidic droplets to


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emulsions with sizes of a few µm and smaller needs to be treated with caution, considering the tremendous effect of droplet size on dominant nucleation mechanisms. NOTATION Symbols A

[m-3·s-1]

kinetic parameter

B

[K3]

thermodynamic parameter

g(s)

[-]

distribution of nucleation frequencies

∆Hf

[J·mol-1]

enthalpy of fusion

J

[m-3·s-1]

nucleation rate

k

[s-1]

nucleation frequency

kB

[J·K-1]

Boltzmann constant

l0

[m]

length of one molecule

nc

[-]

crystallization frequency of the same droplet on multiple runs

p

[-]

probability for droplet nucleation

P

[-]

fraction of uncrystallized droplets

Pcryst

[-]

fraction of crystallized droplets

m

[-]

average number of active centers per droplet

N0

[-]

total number of droplets at time zero

Ncryst

[-]

number of crystallized droplets

∆T

[K]

supercooling

T

[K]

temperature

Tm

[K]

melting point

V

[m3]

droplet volume

Vnuc

[m3]

nucleation volume

α

[-]

regularization parameter

β

[-]

exponent parameter


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γsl

[N·m-1]

interfacial tension between crystal and liquid

ξ

[-]

fraction of “fast crystallizing” droplets

ν0

[m3·mol-1]

molecular volume

τ

[s]

induction time

τmed

[s]

timescale parameter

Abbreviations C16

hexadecane

EGDS ethylene glycol distearate ILT

inverse Laplace transformation

O/W

oil-in-water

RSD

relative standard deviation

ACKNOWLEDGMENTS The authors thank the AIF-Forschungsvereinigung (Forschungs-Gesellschaft VerfahrensTechnik e.V, Project no. 18462 N) for the financial support of this work. We also wish to thank Andreas Roth for his active support in microfluidic chip production.

ASSOCIATED CONTENT Supporting Information. Figure S1: Temporal evolution of Pcryst for all experimental runs (C16 and EGDS); Figure S2: Effect of regularization parameter α on the peak maxima and intensity of the nucleation frequency distribution g(s) calculated by ILT; Figure S3: Comparison of the experimental data from Figure S1, now plotted as ln(1-Pcryst), with the fits using ILT method. Table S1: Nucleation frequencies determined by ILT and estimated fraction of “fast


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crystallizing” droplets ξ. This material is available free of charge via the Internet at http://pubs.acs.org.

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For Table of Contents Use only, Crystallization Behavior and Nucleation Kinetics of Organic Melt Droplets in a Microfluidic Device Burkard Spiegel, Alexander Käfer, Matthias Kind* Institute of Thermal Process Engineering, Karlsruhe Institute of Technology (KIT)

Microfluidics is applied to investigate crystallization behavior and nucleation kinetics of monodisperse organic melt droplets. Heterogeneous active centers cause fast nucleation in multiple, temperature-dependent fractions of droplets and only one, slow nucleation is found in the remaining ones. Application of microfluidics enables an optical examination of droplets without interactions and provides new opportunities to investigate fundamental parameters in emulsion crystallization.


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Crystallization Behavior and Nucleation Kinetics of Organic Melt

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