Interfacial Partitioning Enhances Microextractionby Multicomponent Nanodroplets

The sensitive and reliable in-droplet chemical analysis benefits from the enhanced partition of an analyte into the droplets. This work, we will show that chemical reactions in surface nanodroplets can shift the partition of analytes from a highly diluted solution to the droplets. Seven types of organic acids with partition coefficients (LgP) ranging from -0.7 to 1.87 are used as model analytes dissolved in an oil solution that are extracted from the flow into aqueous nanodroplets immobilized on a substrate. The timescale of integrated extraction and reaction in droplets was represented by the decoloration time of the droplets. Our results show that the effective distribution coefficient of the analyte can be decreased by 3 to 11 times of the distribution coefficient of the analyte in the bulk liquids. The principle behind the significantly shifted partition is proposed to be enhanced the transfer of the analyte across the droplet surface. The chemical reaction in the droplets enhances the partition of the analyte from a highly diluted solution. Our results show that the interfacial behavior of the analyte may be advantageous as it may improve extraction and partition. Such enhanced extraction may be leveraged for sensitive chemical detection using reactive droplets.


Introduction
Sample pretreatment plays a vital role in chemical identification and quantification with reliability and sensitivity. [1][2][3] Many analytic techniques require the analytes to be separated from interfering substances in the sample or be transferred to a suitable medium for meaningful and high-quality measurements. Standard bulk protocols for separation of the analyte from a complex samples consume a large amount of toxic solvents and therefore are regarded as one of the most polluting steps in chemical analysis. It is estimated that the solvent waste from liquid chromatography alone is about 34 million liters in a year. 4 Integrating separation and detection of the analyst in small droplets is a way to minimizing solvent use, automating and streamlining sample pretreatment and detection, and developing greener and cleaner analytic protocols. Transferring the analyst to small droplets can be fast and efficient across the interface of two immiscible phases due to the large surface area to volume ratio of the droplets. Moreover, the droplets may provide a discrete local environment where indicative reactions with the extracted analyte may take place to produce detectable signatures for in-droplet analysis. However, a fundamental question to be addressed for in-droplet chemical analysis is how the chemical reaction in droplets impacts the dynamics and the equilibrium of the analyst partition from the surrounding medium.
Liquid-liquid microextraction is based on the solubility difference to extract the compunds from the surrounding phase into microdroplets. 5 The concentration of the compound in microdroplet is related to the droplet size, solubility of the compound and the extraction time. 6,7 Assuming the droplet is water and the compound is dissolved in oil at the concentration of C o , C w(t) is the concentration of the compound in the water droplet at time t.
Here V w is the volume of the droplet and A is the interface area where the partition of the compound takes place. β is a coefficient that describes the interfacial transfer of the com-pound from the surrounding solution into the droplet. At thermodynamic equilibrium, the enrichment efficiency is limited by the partition coefficient p ( Co C w(f ) ), defined as the ratio of the analyte solubility in the extractant liquid and the aqueous solution. Eq. 1 suggests that for a given concentration of the surrounding solution C o , the concentration of the solute in extractant droplets increases faster for smaller droplets.
As separation and extraction of the analyte is coupled with chemical reaction, the rate of the entire process is determined by the slowest rate-limiting step. The dimensionless number Damköhler number (Da) relates the timescale of chemical reaction to that of the mass transport in a system. 8 However, the reaction rate in droplets is a complicated topic that has not been fully addressed in the literature, even for some basic and well-known chemical reactions.
Many chemical reactions are reported to be usually much faster in smaller droplet than in the bulk, 9,10 such as acid-base reaction, 9 dehydration, 11 organometallic reactions, 12 and among others. The reaction rate in microdroplets may be accelerated to a factor of one million, 13,14 while other reactions that requires catalysts in the bulk may take place spontaneously in micro-sized droplets without a catalyst. 15 Accelerated chemical reactions in droplets are also confirmed under various configurations, 11,[16][17][18] including spray droplets, 16,19 colliding droplet, 14,20 or levitated droplets, 11,21 and among others. 22,23 To date, the mechanism that leads to the accelerated chemical reaction in microdroplets remains elusive. 13 The hypothesis is that the molecules are more energetic at the droplet surface, 24 analogous to the enhanced rate of reaction and product collection at the liquidliquid or liquid-gas interfaces. 13 Perhaps the interface region of the droplets may also have a faster refresh rate than in bulk liquid. 25 Apart from the chemical reaction rate in the droplets, chemical species at the interface may also have a profound influence on the thermodynamic equilibrium of the partition of the compound in the droplets, 25 especially for those amphiphilic molecules with a strong affinity to the interface. 26,27 Recently surface nanodroplets have emerged to be a well-controlled platform for integrated droplet extraction and chemical analysis. These nanodroplets are ultrasmall droplets on substrates submerged in an immersible liquid surrounding. 28 Here nanoscale refers to the maximal height of droplets that are tens to several hundreds of nanometers, although the base diameter of the droplets ranges from several hundred nanometers to tens of micrometers. 29 Several characteristics of surface nanodroplets are advantageous for integrated extraction and analysis. With such small dimensions surface nanodroplets remain stationary for long time under a flow, complementary to extracting microdroplets that flow in microfluidic devices. The concentration of the analyte in the surrounding that surface nanodroplets are exposed to can be easily mediated by the flow condition of the analyte solution. Furthermore, the concentration of the reactive components in surface nanodroplets can be tuned during a bottom-up nanodroplet production by the solvent exchange method. 30,31 In our latest work, 7 surface nanodroplets of an aqueous solution were applied to separate and quantify mixtures of organic acids from oil solutions. The originally blue droplets lost color due to the reaction between the extracted acid and the halochromic compound in the droplets. Interestingly, the timescale of the reaction as reflected by decoloration time was found to be specific to the acid type as well as the combination of acids in a mixture of the same pH level. Although the acid specificity of droplet decoloration time may be possibly related to the interfacial properties of individual acids, it remains unclear how interfacial phenomena are intertwined with microextraction and the reaction of the analyte in the droplets.
In this work, we try to address the role of interfacial partitioning in integrated extraction and chemical reaction in colorimetric detection by multicomponent nanodroplets. Our model compounds are organic acids that are extracted into surface nanodroplets and react with a pH indicator dissolved in the droplets. The timescale of the colorimetric reaction in the nanodroplets will be examined as the droplets are exposed to diluted and concentrated solutions of seven types of acids with a wide range of partition and solubility properties.
Significant shifting in acid partitioning is revealed at low concentrations of acids in the surrounding solution. A unified theoretic model is proposed to rationalize the rate of integrated extraction and reaction in droplets and the enhanced partition of the acids. This work may contribute to better understanding of extraction efficiency of reacting droplets, in particular, on the coupling between interfacial transfer and chemical reaction with highly diluted analytes. The insights from this work may be valuable for downscaling the processes of separation in sensitive detection by using nanodroplets.
Some relevant properties of these organic acids (dissociation constant (pKa) and partition coefficient(LgP) along with their chemical structures are listed in Table 1. When LgP >0, the acid is unfavorable to the water, while LgP <0 is favorable to the water.
1-Octanol (95 %, Fisher scientific, Canada) was used as the solvent for droplet formation and for the analyte solution. Ethanol (90 %, Fisher scientific, Canada) was used as a co-solvent in our ternary liquid system (1-octanol, water and ethanol). The halochromic compound (pH indicator) was Bromocresol green (BG), which changes color from blue to yellow at a pH of 5.4 to 3.8. Water was obtained from the Milli-Q water purification unit (Millipore Corporation, Boston, MA, USA). Silicon wafer (University Wafer, USA) coated by APTES (3-aminopropyl triethoxysilane) was cut to 1.3 cm × 1.5 cm as the substrate in our fluid chamber. The procedure for preparing APTES coating was followed identically to the reported work. 32 A frame of silicon rubber was used as a spacer to control the channel height of the fluid chamber to 300 µm. A transparent glass slide was cleaned by piranha solution (30% H 2 O 2 and 70% H 2 SO 4 )(caution: piranha solution is highly caustic!) and then used to seal the fluid chamber as cover.

Formation of functional surface nanodroplets
Following the process illustrated in Figure 1a, aqueous droplets containing BG are formed on a substrate in a microfluid chamber by solvent exchange. The protocol is the same as our previous report. 7 Colored surface nanodroplets were preformed in a microchamber by the solvent exchange, 7,29 as sketched in Figure 1

Extraction of acid from the flow and colorimetric reaction in droplets
Once colored droplets were formed, acid extraction was from solution C , which had been In the laminar flow regime, the temporal concentration of the analyte in the displacing flow is well-described by Tayler-Aris dispersion. 35 The real-time concentration of the analyte as represented by the fluorescence intensity can be fitted with an error function.
Here, C o (t) is the real-time compound concentration in the external solution in contact with the surface nanodroplets at time t (in second). C ini is the organic acid concentration in solution, and is also the concentration when C o (t) reaches the maximum. τ is a characteristic timescale determined by the flow condition. From the fitting shown in Figure 2 (d) and SI-1a and b, τ was determined to be around 12.87 seconds.
The temporal concentration of the model analytes of organic acids in our following experiments is expected to follow the same error functions for the dye concentration in the displacing flow. The acid concentration will increase initially from 0 to C ini in the oil solution and afterward remained constant at C ini . The acid concentration C o (t) in the displacing flow will be determined by Eq.2 with the same τ based on the dye concentration.

Partition-dominated droplet decoloration at high concentration of acids
The organic acids used in our experiments can be defined as two groups, the alkyl acid group and the aromatic acid group. The molecule structure, partition coefficient (LgP in octanol and water) and the dissociation constant (pKa) of those acids in water are shown in Table   1.
We first compared the decoloration time of the droplets at a given concentration of acids. A representative case in Figure 3a shows the color of droplets in contact with the flow of acid solution at C o of 50 mM. The droplets were 25 µm in radius. All the droplets changed from blue to colorless within 100 s. Figure 3b shows the plot of the droplet decoloration time as a function of the droplet size. The droplet decoloration is systematically slightly faster  Compared to others acids, it takes the longest time for the droplets to decolor at 50 mM.
The slowest decoloration may be due to the highest partition coefficient of heptanoic acid (least soluble in water) among all acids.
Here, C o (t) is represented in Eq.2. The extracted acid dissociates, producing protons that lead to the colorimetric reaction. The concentration of acid that is sufficient for droplet decoloration is defined as critical acid concentration C * w , calculated by pKa of a given acid and the pH value of the pH indicator. 7 When pH value is 3.8, the proton concentration is  Table 2.
LgP and pKa of a given acid were found from the data available in the literature, as listed in Table 1. C o is known as our experimental condition, Eq.3 can be integrated to obtain the decoloration time t decoloration for C w (t) to increase from 0 to C * w . The interfacial transfer coefficient β is a fitting parameter.
The solid lines in Figure 3b

Enhanced partition at low concentration of acids
Interesting phenomena of enhanced extraction are discovered at low concentrations of acids.
As shown in Table 1 Table 2 is much later than the moment when the acid concentration reaches equilibrium in the surrounding.

Interfacial partition enhanced by nanodroplet reaction
To rationalize the extraction in droplets at low concentration of acids, we propose interfacial partition enhanced by nanodroplet reaction as below. The droplet decoloration process is decoupled into several steps as depicted in Figure 5. (1)  HA w The influence from 1/t 2 and 1/t 3 is not evident at the high concentration of the solute in the surrounding phase, because the time is short for the acid concentration of the solute in the droplets to reach a level for decoloration. However, 1/t 1 , 1/t 2 and 1/t 3 can not attribute to the rate-limiting step for decoloration at a low concentration of acid, because the decoloration is also much slower than the partition, as shown in Table 2. Once acid are extracted in water droplets, the dissociation and the protonization of the indicator can be completed on a timescale of less than 1 ms.
The proposed interfacial enrichment of acids may explain both the long duration of decoloration and the high sensitivity of droplet decoloration to the acid at low concentrations.
We noticed that the long duration of decoloration occurs for acids with a positive partition coefficient which is more concentrated in the surrounding octanol than in water droplets.
There is a boundary layer with a concentration gradient of acids that is lower in water droplets, and higher in the oil phase in the external solution, as sketched in Figure 5b.
The concentration inside the droplet is regulated by the acid dissociation and reaction between protons and the indicator. The colorimetric reaction consumes the extracted acid, driving a net influx of the acid into the droplet. Such influx is slow, because the transfer through the interface of the droplets remains quasi-equilibrium. Therefore, step 1 is the rate-limiting step.
The above partition shifting of acids to the droplets could happen, as the liquid-liquid interface is permeable and dynamic. In the absence of chemical reactions (step 2 and 3) in droplets, the amount of molecules into the droplet is same as that of molecules out of the droplets at the equilibrium of partition. However, for reacting droplets, the fast chemical reaction through step 2 and then 3 cleans up the captured molecules quickly from the interface, so the droplets surface is adsorbed and reset to accommodate more acid molecules from the outside solution. The droplet decoloration can take place even if the concentration of acid in bulk is below the level predicted by pure partition, based on the solubilities in two phases.
Although not required, the interfacial activity of the acids may also contribute to the enhanced microextraction of the droplets. Several acids are like surfactants, accumulating at the droplet interface. Those amphiphilic acid molecules may preferentially stay at the interface, due to the interfacial adsorption. The transfer through the oil-water interface of the droplets remains at adsorption-desorption equilibrium.

Theoretical decoloration rate coupling interfacial partition and chemical reaction in droplets
At low concentration of acids, the reaction rate may not be simply neglected for acids. As discussed above, the chemical reaction may drive the extraction of the acid to the droplets.
C w (t) is expressed as: The first term on the right determines acid transfer (partition and interfacial transfer). The second term determines reaction in the droplets (acid dissociation and pH indicator protonation).
A reaction rate r of (r=r 1 × r 2 ) accounts for the effects from acid dissociation and chemical reaction in the droplets. Here, r 1 represents the acid dissociation rate and r 2 represents the reaction rates of acid and the indicator in droplet. Both r 1 and r 2 defined in Eq.5 and 6 are given by the acid dissociation and by the reactant in the droplets, respectively. Eq. 7 can be integrated to obtain the decoloration time t decoloration , that is, the time for C w (t) to increase from 0 to C * w . The fitting parameters are the apparent partition coefficient p * , the reaction rate r and mass transfer coefficient β. The shift of distribution coefficient from p to p * accounts for more acids extracted into the droplet to the level of C * w .
Rate-limiting step in droplet decoloration at low acid concentration At the low acid concentration of 5 mM in Figure 4(b-d), the decolor time from the two longchain alkyl acids (n-butyric acid and valeric acid) can be described by Eq. 7, as shown in Figure 6c. Here, the value of the fitting parameter apparent partition p * is much lower than the intrinsic coefficient of the acid in octanol and water in the absence of chemical reactions.
The other fitting parameter r is 0 from these two alkyl acids. Similar to surfactant, the hydrophilic part (carboxylic acid group) of these acids can penetrate the oil-water interface and stay in the water phase, while the hydrophobic component remains in the oil phase.
The rates of acid dissociation (step 2) and colorimetric reaction (step 3) in the droplets are fast compared to interfacial transfer. So the second term on the left side of Eq. 7 can be neglected (r=0).
As for acetic acid, its solubility in water is much higher than in the surrounding. Compared to water-less soluble valeric acid and butyric acid, aromatic acids have the less surface activities. Droplet decoloration from acetic acid and aromatic acid show good agreement with the prediction from Eq. 7. Different from r=0 for valeric acid and butyric acid, a positive value of r was obtained in Eq. 7, as shown in Figure 6d. Park et al. demonstrated that the dissociation of acetic acid is a very fast process, completed in few picoseconds. 36 However, the effect from the reaction rate r on the decoloration time can be revealed in decoloration rate, possibly due to the fast partition process of acetic acid and aromatic acids in droplets.
We also found that r decreases with C o , as shown in Table 3 and 4, suggesting less influence from chemical reaction in droplets and more solubility-dominated partition at higher C o .
The partition shifting happens to the droplets at low concentrations specific of acids. The apparent distribution p * obtained at all concentrations, is shown in Figure 6 a and b. The revers of p * represents the concentration in droplets over that in the surrounding. As the acid concentration decreases, the partition shifting (p/p * ) becomes more significant. Up to 11 times larger p * was found for butyric acid at C o = 1 mM in Figure 6. p and p * become the same at high concentrations of acids, for example, at 2.5 M for heptanoic, and 100 mM for benzoic acid and PHBA, 50 mM for other acids.   Acid specificity of mass transfer coefficient β The mass transfer coefficient (β) shown in Figure 6c mainly reflects the rate of the acid crossing the interface. We found that β is independent of the concentration in the oil phase (C o ) for a given acid. But for different acids, expect heptanoic acid, β increases with the distribution coefficient p. As shown in Figure 6c, possibly acids with a lower distribution coefficient (p) established as lower the acid concentration gradient between the droplet and the surrounding for a slow transfer of the acid. The interfacial activity of the acid also influences the transfer coefficient β. At the same p, the coefficient β of aromatic acids with lower interfacial activity is lower than that of alkyl acids. On the other hand, the long hydrophobic chain in the heptanoic acid molecule makes it much more likely to stay on the oil phase than in water droplets. Hence, transferring heptanoic acid into water droplets becomes energetically unfavorable, leading to a very low β.

Effects of reactant concentration in droplets on reaction rates
In the above, the concentration of the BG in the droplets was the same in all of the experiments (0.02 g/ml in solution A). Considering the crucial role of chemical reactions in the droplets for acid detection, another important parameter to influence the detection sensitiv-ity is the concentration of BG in the droplets. We varied the pH indicator concentrations by changing the concentration of BG in solution A. After the formation of the droplets by solvent exchange, a higher concentration of BG showed a darker color (lower color intensity), as shown in Figure 7a. We used benzoic acid as the model analyte to measure the LoD under different BG concentrations in solution A. The results in Figure 7b demonstrates that a higher concentration of BG had a higher LoD. Figure 7. The initial color intensity along droplet diameter and the images (a) and the limit of detection (LoD) (b) for benzoic acid of the droplets that formed by solution A containing BG at the concentration of 0.02g/ml, 0.002 g/ml and 0.0004 g/ml. Scale bar: 25 µm. Here, distance 0 means the edge of the droplets.
Higher sensitivity (lower LoD) in a lower concentration of BG in the droplets is attributed to a shorter time to reach the critical concentration. The decoloration of the droplets is determined by the ratio of the concentration of HR and R − ( [HR] [R − ] ), as shown in the Eq.6. As the [R − ] increased when the BG concentration increased in the droplets, the amount of the HA for droplets to accomplish the decoloration is also increased.
More HA molecules need a longer time to reach the critical concentration. When the concentration of the HA increases, the reaction rate (r 2 ) also increases. However, compared to the reaction rate, the acid dissociation rate (r 1 ) is faster. 36 Considered the organic acids used in this work are weak acid and thus the acid dissociation is partial, more acid molecules accumulated in the droplet. Those redundant HA molecules slow down the mass transfer rate due to the decreases of the driven force (C o -C w ).

Conclusions
This work experimentally and theoretically investigates the rate and efficiency of integrated extraction and detection of analytes in surface nanodroplets. Seven acids were used as the model analysts, and the extraction of the acid was coupled with a colorimetric reaction in surface nanodroplets. We found a significant shift in the partition of the acids into the reacting droplets at a low concentration of acid in the external solution. The interfacial partitioning of the acids was proposed to be the rate-limiting step in integrated extraction and detection, and meanwhile contribute to the highly sensitive detection from the shifted partition of the acids. The proposed theoretical model for the extraction process that takes the partition shift into consideration is in good agreement with experimental results. This work provides a comprehensive analysis for the enhance of extraction and sensitive colorimetric etection in nanodroplets.