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Evolution of radius and light scattering properties of single drying microdroplets of colloidal suspension
Journal of Quantitative Spectroscopy & Radiative Transfer 202 (2017) 168–175
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Evolution of radius and light scattering properties of single drying microdroplets of colloidal suspension a ´ J. Archer a,∗, M. Kolwas a, D. Jakubczyk a, G. Derkachov a, M. Wozniak , K. Kolwas a Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, Warsaw PL-02668, Poland
a r t i c l e
i n f o
Article history: Received 14 June 2017 Revised 4 August 2017 Accepted 4 August 2017 Available online 5 August 2017 Keywords: Elastic light scattering Microdroplet evaporation Electrodynamic levitation Sodium dodecyl sulfate Silica nanospheres Aggregation
a b s t r a c t We report on observation of well-pronounced characteristic features of elastic light scattering of evaporating solution and suspension microdroplet of the anionic surfactant sodium dodecyl sulfate (SDS) and colloidal silica (SiO2 ) nanospheres in diethylene glycol (DEG) during SDS surface layer and structure formation (crystallization). For pure DEG/SDS solution droplet evaporation process, characteristic evaporation transitions manifested in the evolution of the droplet radius, a(t) for all the SDS concentrations (C = 20 mM, 40 mM and 100 mM) studied as well as well-pronounced intensity signals characterizing SDS soft gel-solid transitions for initial SDS concentrations, C > 40 mM. In the case of microdroplets composed of DEG/SDS with controlled addition of colloidal silica, the intensity fluctuations were enhanced and had profiles dependent on the initial composition of the suspension. Exemplary wet droplets at the initial evaporation stages and final dry aggregates of SDS and SDS/SiO2 were deposited on a substrate and observed with Scanning Electron Microscopy (SEM). Features of the deposited structures correlate well with the elastic scattered light measurements characterizing the drying processes. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Evaporation of microdroplets containing dispersed particles or dissolved materials exhibit pronounced complex optical and thermodynamic properties [1–6] as well as distinct mechanical instabilities [7] than that of the evaporation of pure liquid microdroplets. Such colloidal suspension of microdroplets represent important morphological type of scattering objects with numerous applications in research and industry [8,9]. The temporal behavior of scattered light on drying colloidal suspension or solution microdroplets depends on both the bulk and surface properties of the droplet. The interaction of the light with the droplet surface at the air-liquid/solid interface manifest in a complex way. However, since the light interacts directly with the surface layer of the evaporating droplet, an inverse inference of the droplets’ surface properties, dry microobject morphology as well as phase transitions at the droplet surface during the evaporation/drying processes can be obtained from the total distribution and evolution of the scattered light intensities. Sodium dodecyl sulfate (SDS) is perhaps the most widely studied anionic surfactant used in both industrial products and for fundamental scientific research. For example, it has been used to sim-
∗
Corresponding author. E-mail address: [email protected] (J. Archer).
http://dx.doi.org/10.1016/j.jqsrt.2017.08.004 0022-4073/© 2017 Elsevier Ltd. All rights reserved.
ulate the behavior of surfactants observed in the atmosphere in the form of aerosol droplets [10] and is observed to posses several crystalline phases under variable temperature conditions [11]. Doganci et al. [12] studied the effects of SDS concentration on the evaporation rate of droplets placed on TEFLON-FEP substrate. In their classic work, they observed that the addition of SDS did not alter the drop evaporation rate within the first 20 min of the evaporation process. They additionally concluded that the main difference was found to be the change of the mode of the drop evaporation on the substrate including contact angle, and area variations when they varied the SDS concentrations in the droplet. However, the presence of substrate via such method can sometimes mar the final morphology of the dried products from the evaporation process. Static and dynamic light scattering methods including quasielastic light scattering [13], small-angle neutron scattering [14,15], infrared spectroscopic technique [11] and many others mentioned in [11] have been used to characterize other specific physical properties of SDS. However, elastically scattered light diagnostics characterizing gradual crystallization of SDS and structure evolutions from single levitating microdroplet composed of SDS with/without other submicron inclusions have not been studied. Here, we present a systematic study of elastically scattered light intensities characterizing the formation of crystallized SDS microstructures and SDS/SiO2 composite micro objects from single evaporating microdroplet of solution and suspension respec-
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Fig. 1. Scheme showing the optical arrangement of the electrodynamic quadrupole trap (A). LP: linear polarizers, PS: polarization sheet plate, L: Lenses, CCD 1 and CCD 2 are cameras used for the in-focus imaging and Mie scattering imaging respectively. Right : Images of out-of-focus interference patterns (a, b) and in focus glare spots (c, d) observed during the microdroplet evaporation process.
tively. In particular, we examine the changes in the integrated Mie scattering vs time evolution and measure the droplet radius on the basis of Mie scattering theory [16] and by electrical weighting of the droplet position [17]. It is important to note here that, the combination of these two complementary methods of droplet size measurement technique (i.e. optical (interferometric) and weighting) enabled very accurate determination of the entire droplet/aggregate radius evolution. Weighting becomes particularly indispensable, when the elastic scattering pattern loses its regular structure, and the determination of droplet size using the interferometric method becomes compromised [10,18] or impossible. Additionally, a parallel experimental setup [19] was used to deposit exemplary initial wet aggregates (patterns) and final dry structures on a substrate and analyzed further with Scanning Electron Microscopy (SEM) to complement the observed elastic scattered light measurements. 2. Experimental section 2.1. Experimental materials and sample preparation The sample materials used for the experiment includes: monodispersed colloidal silica nanospheres (SiO2 ; 125 nm radius, refractive index = 1.465, C-SIO-0.25, Corpuscular Inc.) diethylene glycol (DEG : refractive index = 1.446, 99.0% GC area, BioUltra, Fluka, Sigma-Aldrich) and sodium dodecyl sulfate (SDS: refractive index = 1.461, ACS Reagent, ≥ 99:0% , Sigma-Aldrich). For the DEG/SDS solution droplet experiments, different molar concentrations of SDS at 20 mM, 40 mM, and 100 mM were prepared by mixing weighted SDS with DEG in an insulin syringe, followed by ultrasonication to obtain uniform mixing. In the case of the DEG/SiO2 /H2 O/SDS suspension droplet experiment, an initial approximate mixing ratio of DEG : H2 O : SiO2 = 1 : 3 : 56 by volume was prepared and successive percentages by mass of SDS was added to the mixture and sonicated to obtain uniform mixing. The prepared liquid solution and suspension mixtures were carefully transferred into the droplet on-demand injector under controlled dust free environment to prevent contamination of the samples during the liquid transfer process. 2.2. Experimental setup and procedure A schematic of the electrodynamic quadrupole trap showing the optical arrangement of the major peripherals is presented in Fig. 1A. Detailed description is given elsewhere in [3,4,20]. The trap
system and its component are placed in a climatic chamber with eight side ports for optical access to the trap center. The trap and its auxiliary components are thermally regulated by a circulating liquid from an external gas-liquid heat thermostatic bath. Usually, the temperature in the climatic chamber (trap environment) is maintained at 22 ± 0.15 °C. Additionally, dry nitrogen is provided to the chamber through a gas-liquid heat exchanger to provide dry atmospheric conditions in the trap with relative humidity of not more than 5 ± 3.5% during all the experimental procedures. A droplet suspended at the center of the trap is simultaneously illuminated by a horizontally (H) polarized diode laser (658 nm; 10 mW) and vertically (V) polarized argon ion laser (458 nm; 12 mW) with respect to the scattering plane. The light scattered by the droplet is monitored and recorded by a CCD camera (CCD 2) placed at the right angle of the scattering plane at a scattering angular range of φ = 90 ± 16° (azimuth) and θ = 0 ± 5° (elevation). The scattered light passes through a polarization sheet (PS) that maps the horizontal polarization of the scattered light to the scattering plane in the lower half of the camera and vertical to the plane in the upper half of the camera (see Fig. 1(a)). Fig. 1(a)–(d) show respectively the out-of-focus angularly resolved Mie scattering interference patterns and in-focus images captured from the evaporation of microdroplet composed of DEG/SiO2 /H2 O colloidal suspension. In Fig. 1(a), characteristic, almost equidistant regular Mie interference patterns on both the vertical (upper half) and horizontal (lower half) polarization channels can be seen at the beginning of the evaporation process. The patterns can be ascribed to the interference between the reflected laser light from the surface and the refracted laser light from the inner surface of the droplet. The reflected and refracted lights manifest in the in-focus image as the two horizontally displaced glare spots (Fig. 1(c)) appearing at the droplet equator [21] and is observed with the CCD 1. In our case, the in-focused image provided by CCD 1 is used to balance the weight of the droplet levitating at the center of the trap. From the image, we calculate the position of the center of light distribution (similar to center of mass) and use one of the coordinates as feedback to a PID-type loop software controller that provides a DC loop voltage to stabilize the droplet position at the center of the trap. The stabilizing DC loop voltage is recorded in synchronous with the Mie interference patterns for the entire droplet/aggregate evolution allowing comparable droplet mass-to-charge ( m q ) ratio evolution and subsequently the droplet radius evolution via the weighting signal (droplet mass, m(t) evolution) [17].
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As the evaporation process proceeds, the SiO2 inclusions emerge to the surface of the droplet and the regular interference patterns become depolarized and speckled at the liquid-solid (wet aggregate) transition (see Fig. 1(b)) [3,22]. Additionally, since the size of the droplet decreases through continuous loss of liquid, the distance between the glare spots (Fig. 1(c)) also decreases and eventually come together at the point of liquid-solid (wet aggregate) transition and become speckled (Fig. 1(d)). However, such transition does not influence the droplet weighting signal since the notion of center of brightness of the image is used for the stabilization process. The interference pattern observed in the scattered light is analyzed using Mie theory [16,23], from which the temporal evolution of the droplet radius a(t) is obtained [24,25]. The initial droplet radius a0 (t0 ) corresponding to the time (t0 ) when we start the droplet stabilization process to record the experimental data is obtained from the exact fitting of the spatial scattered light distribution (phase functions) recorded in the first movie frame with the Mie theory. The time lapse between the emergence of the droplet from the nozzle of the droplet on-demand injector and the start of the measurement procedure, mostly required to prestabilize the droplet in the trap varies but is below 1 s. The relative expected radius change within this time lapse is below 0.5% for the fastest droplet evaporation that we studied. For solution droplet evaporation, the corresponding initial concentration (C0 ) increase is below 1.5% at most. Hence C0 , corresponding to a0 , is assumed equal to the prepared initial solution/suspension concentration. However, another possible source of error that can influence the initial concentration of the droplet is the evaporation of solute directly from the nozzle of the droplet on-demand injector prior to injection. This error is hard to estimate, but can be minimized by expelling a few droplets just before the proper measurement. Additionally, the intensity distribution Ivv(θ , φ , t) and Ihh(θ , φ , t) from the vertical (upper half) and horizontal (lower half) polarization channels is integrated over the scattering angles φ and θ to obtain their temporal dependence Ivv(t) and Ihh(t) respectively [3,22]. 3. Results and discussions 3.1. Radius and scattered light intensities from crystallization of SDS The concentrations of SDS solution studied were higher than the critical micelle concentration (CMC, 8.2 mM) [26]. Above the CMC, SDS form insoluble monolayers [18,27], crystalline phases [28] and also aggregate to form metastable microgel state or complex structures of nanocrystals [29]. Here, we examine the elastically scattered light characterizing the transient and final stages of SDS crystallized structure formation from the evaporation of DEG/SDS solution microdroplet. Fig. 2 (a)–(d) show respectively, the temporal evolution of the droplet radius, a(t) (green open circles) and integrated Mie scattered light intensities of DEG/SDS solution at an initial SDS concentration of (a) 20 mM, (b) 40 mM and (c & d) 100 mM. From the observed radius, a(t) evolution and the intensity profiles, the droplet can be considered as optically homogeneous at the initial stages of the evaporation process with isotropic shrinking and with scattered light intensities showing series of regularly spaced structural Mie resonances. The continuous loss of liquid results in decrease of the droplet volume and increasing concentration of SDS preferentially at the droplet surface. At a defined time, tcrit corresponding to critical concentration (crystallization concentration) Ccryst , of SDS (Dash line A, t ∼ 281 s in Fig. 2(a)), the SDS crystallites start to accumulate and populate the droplet surface. During such transition (liquid - wet SDS crystallized (solid) structure), the regularly spaced structural Mie resonances change its temporal characteristics into irregular (depolar-
ized) intensity fluctuations suggesting nonuniformity and crystallization of SDS at the droplet surface (see insert in Fig. 2(a)). The initial evaporation process characterized by the series of the regularly spaced structural resonances before the transition stage is considered as a quasi-steady diffusion-controlled evaporation process and the evaporation rate can be written in the form [18] :
a2 = a20 − β (t − t0 )
(1)
2Di j Pa (Ta ) ρl RTa
is constant under these conditions [30]. Di j is
where β =
the diffusion coefficient for the evaporation species i in surrounding gas j and is mainly temperature dependent [30], Pa is the vapor pressure at the surface of the droplet at surface temperature Ta . R and ρl are respectively the universal gas constant and density of the liquid, a0 is the initial droplet radius at time t0 . The first stage evaporation process is followed by a slow evaporation rate before stabilization when the final form of the SDS crystallized structure is formed. The slow intermediate transition between the initial evaporation stage and the formation of the final SDS crystallized structure is attributed to the formation of soft SDS gel-like phase or gel-like shell made up of porous network of SDS crystals [29,31] at the droplet surface. The three pronounced evaporation/drying stages leading to the formation of the final form of the dry SDS crystallized structure is well seen in the evolution of the droplet radius, a(t) (green open circles in Fig. 2 (a)–(d)). The stages primarily consists of : (i) evaporation of DEG/SDS solution controlled by diffusion. The Mie structural resonances associated with this stage has regularly spaced angularly resolved resonance patterns (a(t) evolution till the point marked A in Fig. 2(a) with similar evolutions in Fig. 2(b)–(d)), (ii) slow evaporation of DEG/SDS gel-like phase (evaporation of DEG/SDS solution through porous network of SDS crystallized surface, A - B radius evolution in Fig. 2(a) and subsequent Figures). The nature of the scattered light fluctuations is controlled by the concentration of SDS (compare Fig. 2(a) and (c) for both Ivv(t) and Ihh(t) polarization signals), and (iii) the SDS gel - solid drying stage leading to the final morphology of the SDS crystallized structure resulting in the stabilization of the droplet radius evolution. Modulation of the amplitude of the scattered light intensity fluctuations depend on the initial droplet size (see Fig. 3). 3.2. Diagnostics of radius and integrated Mie scattered light intensity evolutions At lower SDS concentrations (C = 20 mM , 40 mM), the nature of the observed scattered light intensities (Fig. 2(a) and (b) exhibited nearly stabilized irregular intensity fluctuations after the first stage evaporation process. However, at higher SDS concentration (C = 100 mM), we observed scattered light signals showing transient SDS crystallized surface layer formation and composite structure transformations due to possible transitions of SDS crystallized surface shell creation and deformation at the air-solution interface. It has been suggested that, at the air-solution interface, SDS can form varieties of structures, from broad band-like or lace-like aggregates to multiconnected threads [32]. We believe that, at higher concentrations, the intensity fluctuations observed in the elastically scattered light as well the characteristic temporal modulations in the amplitude of the intensity signals show possible crystallized SDS surface structural transformations dependent on the initial droplet size. In Fig. 2(c), we observed such transformations from t ≈ 184 s to t ≈ 423 s corresponding to the minimum boundaries of the temporal evolution of the amplitude of the fluctuating scattered light signals. After t ≈ 423 s, one can also observe another possible structure onset with scattered light characteristics similar to the
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Fig. 2. Evolution of radius and integrated Mie scattered light intensities for DEG/SDS solution droplet evaporation obtained for different droplets of initial radiuses a0 (t0 ) [μm] and SDS concentrations, C [ mM ]. Ivv(t) and Ihh(t) represent the temporal evolution of vertically and horizontally integrated Mie scattered light intensities from vertical and horizontal polarized incident light respectively. Ivh(t) and Ihv(t) are the cross polarized signals. Green empty circles : Temporal evolution of the droplet radius a(t) [μm]. Insert : fine regular structural Mie resonances to irregular intensity fluctuations characterizing liquid- wet SDS crystallized (solid) surface transition stage.
Fig. 3. (a) Averaged IVV (t) intensity signal obtained from Fig. 2(c) (blue line). Green line with open circles - droplet radius, a(t) evolution with a0 = 9.76 μm. (b) Averaged IVV (t) intensity signal obtained from Fig. 2(d) (blue line). Green line with open circles - droplet radius, a(t) evolution with a0 = 15.40 μm). For bigger droplet, higher number of intensity signal modulations (6) can be seen characterizing possible surface properties of the SDS crystallized microstructure evolutions (structure transformations) during the drying process. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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earlier patterns but at rather lower amplitude. For the bigger initial droplet size (a0 = 15.40 μm , Fig. 2(d)), successive modulations of the amplitude of the fluctuating intensity signals can be observed from t ≈ 673 s–1040 s; 1057 s–1318 s; 1319 s–1508 s; 1511 s–1680 s and 1680 s–1807 s as well as from - 1807 s–1833 s characterizing potentially as well, SDS crystallized product structural transformations during the drying process. Fig. 3(a) and (b) show averaged Ivv(t) signals obtained from Fig. 2(c) and (d) respectively. Characteristic modulations of the amplitude of the intensity fluctuating signals can be observed during the drying process. It is worth noting that, in Fig. 3(b), the amplitude of the first three modulations in the fluctuating intensity signals decreases as the radius evolution during the second stage (ii) evaporation process. After t = 1508 s corresponding to the fourth minima in the intensity signal, the evolution of the droplet radius appear to be stabilized showing the final stages of the drying process. Subsequently, another onset of characteristic intensity fluctuations with decreasing amplitudes similar to the earlier ones begin and after t = 1833 s, the signal seem to be stabilized showing potentially, the final morphology of the SDS crystallized structure evolution. Using a parallel experimental setup and procedure [19], we deposited exemplary wet droplets at the initial evaporation stage (Fig. 6(c)) and (the final dry SDS crystallized structure (Fig. 6(d)) at an initial SDS concentration of 100 mM and analyzed the product with SEM. We observed that the final form of the SDS crystallized microproduct was irregular and had deformed surface symmetry and can be viewed as structure evolution from a more regular object (initially spherical droplet symmetry). As can be seen in Fig. 6(c), the wet DEG/SDS droplet deposited during the initial stages of the evaporation process generally show uniform pattern after drying on the substrate. 3.3. Evolution of mean concentration of SDS Eq. (1) states that, the evolution of the radius squared or the droplet surface area varies linearly with time [33]. However, in the presence of the soluble SDS in the droplet, the surface area deviates from linearity in time. The effect of SDS component in the droplet during the quasi-steady diffusion limited process can be modeled by incorporating a second-order term in Eq. (1) [34] or by expressing the vapor pressure at the droplet surface in terms of the Köhler equation [35–37]. The vapor pressure at the surface of the droplet Pa (Ta ) based on the Köhler equation can be expressed in terms of the volume equivalent dry radius, a3dry = 3mdry /4π ρdry as:
Pa (Ta ) = Psat (Ta ) exp
a3dry M i 2 σl − 3 RT∞ ρa a a − a3dry
(2)
where a is the radius of the droplet at time t. ρa is the density of the droplet, mdry is mass of dry microobject. σl is the surface tension of the liquid. Pa and Psat are the vapor pressure and saturated vapor pressure near the droplet surface at temperature Ta respectively. T∞ and Mi are the temperature far from the droplet surface and the molecular weight of species i respectively. For micronsized droplets, the surface tension effect can be assumed negligible [25] and Eq. (1) together with Eq. (2) can be simplified as:
2 Di j da a =− P (T ) exp dt ρl RTa sat a
−
a3dry a3 − a3dry
(3)
We note here that adry is not necessarily equal to the physical dry radius of the aggregates or the SDS crystallized structure, as such a structure at the point of the drying stages when its mass is measured may contain residual amount of DEG liquid and may have an effective mean density different from that of the initial droplet composition or may not be spherical as observed in
Fig. 6(d). However, since the mass of the SDS solute in the droplet is constant and known a priori, adry provides a measure of the mean concentration of SDS (or inclusions). Fig. 4(a) and (b) show the radii in Fig. 2(a)–(c) and Fig. 2(d) converted to radius squared and the evolution of the mean concentration of SDS at the droplet surface. It can be noticed that, the final mean concentration of SDS is independent of the initial droplet composition. A final mean concentration of 0.55 ± 0.05% can be observed for all the SDS concentrations studied for small droplet (ca. 9 μm) and bigger droplet (ca. 15.4 μm) respectively. The critical concentration of SDS (crystallization concentrations) at which SDS starts to crystallize at the droplet surface can be obtained from the initial droplet radius a0 , the initial concentration of the solution C0 and the critical radius acryst (tcrit ). This can be expressed as [38] :
Ccryst = C 0
a 3 0 acryst
(4)
3.4. Scattered light intensities during crystallization of SDS in suspension microdroplet In our previous study [4], we showed that the temporal evolution of the total integrated scattered light intensities from evaporating microdroplet of colloidal solution composed of DEG/SiO2 /H2 O/SDS, follows three transitory signal patterns. Here, we demonstrate that, the appearance of the intermediate intense scattered light signal due to the addition of SDS to the DEG/SiO2 /H2 O colloidal suspension is dependent on the initial composition of the droplet driven primarily by the concentration of the SDS. Fig. 5(a)–(d) present the temporal evolution of the scattered light intensities obtained for the evaporation of microdroplet composed of 1 : 4 : 19 mixture of DEG : SiO2 : H2 O colloidal suspension by volume respectively with 0%, 0.5%, 1%, and 1.72% fractions of SDS by mass added to the DEG/SiO2 /H2 O colloidal suspension. Features of the deposited structures correlate well with the observed elastic scattered light measurements characterizing their drying processes. At the initial stages, the temporal evolution of the signals exhibited series of sharp-peaked regularly spaced resonances similarly to the SDS solution droplet evaporation stages (compare Fig. 2(a)– (d)) and in agreement with earlier results reported in [4,22] before the transient critical periods. However, controlled addition of SDS to the DEG/SiO2 /H2 O mixture led to the observation of characteristic scattered light features during the SDS surface layer crystal formation on the drying micro object surface. In Figure, 5a, with 0% of SDS added to the DEG/SiO2 /H2 O mixture, we observed a rapid increase in the intensity signals after the initial quasi-steady diffusion limited evaporation process and quick rise and stabilization of the ensuing fluctuating intensity signals . The sharp rise in intensity at t = 321 s and the subsequent stabilization can be understood in terms of the surface and morphology evolution of the SiO2 aggregate symmetry in the droplet during the SiO2 nanosphere aggregation process. A microdroplet injected into the trap maintains its spherical shape due to surface tension and hence the air-liquid interface of the droplet can be considered as a smooth surface. Our SEM studies (Fig. 6(a) and (b)) from sample deposits of the suspension (DEG/SiO2 /H2 O) droplet /aggregate at the initial isotropic evaporation stage and the final dry-aggregate stage indicates a possible rapid transition between scattering on a smooth evaporating droplet surface(air-liquid interface) and on a more corrugated SiO2 nanosphere aggregate surface (air-solid interface). Fig. 6(a) shows the well-known coffee ring effect [39] driven by the capillary flow of the suspended SiO2 nanospheres in the droplet after the deposition on the substrate. The final aggregate observed
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Fig. 4. Evolution of radius squared and mean dried SDS concentration from the evaporation of DEG/SDS solution microdroplet extracted from Fig. 2. (a) : Green line (20 mM), red line (40 mM) and dark grey line (100 mM) respectively for radius squared and concentration evolutions for initial small droplet radius in Fig. 2 (a)–(c). (b) : Evolution of radius squared and mean concentration extracted from Fig. 2(d) (bigger droplet). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Temporal evolution of elastically scattered laser light intensities for the evaporation of DEG/SiO2 /H2 O with (a) 0% SDS, (b) 0.50% SDS (c) 1.0% SDS (d) 1.72% SDS.
showed regular spherical symmetry of highly ordered aggregated SiO2 nanospheres. With systematic addition of SDS to the initial DEG/SiO2 /H2 O colloidal suspension, we observed the influence of SDS surface layer crystallization at the droplet surface manifested in the evolution of the elastic scattered light signals during the drying periods. In Fig. 5(b), with 0.5% of SDS, we observed first, a decrease then a steady increase in the Ivv, Ivh, and Ihh intensity signals from t = 152 s before stabilization after t = 256 s which we attribute to surface layer transitions occurring at the droplet surface. Fig. 5(c) and (d) show the scattering profiles for 1% and 1.72% of SDS added to the DEG/SiO2 /H2 O mixture. The appearance and the duration of the characteristic scattered light intensity features
during the transient SDS crystal layer formation stages is seen to be dependent on the concentration of SDS added to the mixture. In Fig. 5(c), the transitions during the SDS surface layer formation appeared between t = 198 s and 328 s and occurred at 676 s to 1146 s for the 1.72% of SDS. The well-pronounced scattered light intensities observed during the transient SDS/SiO2 composite aggregate evolution seems to suggest possible surface structure and symmetry deformations as the aggregate transforms from loose packing of the SiO2 nanospheres to more compact and regular structure. Fig. 6(e) and (f) show respectively SEM microgragph of a pattern generated by drying of a microdroplet deposited during the initial evaporation stage and SDS/SiO2 aggregate structure deposited
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Fig. 6. SEM images of dried aggregates obtained from the evaporation of 1 : 3 by volume of diethylene glycol and colloidal SiO2 suspension with 0% SDS (a, b), SDS only (c, d) and 1.24% of SDS added to DEG/SiO2 /H2 O mixture (e, f).
at the final drying stage. In Fig. 6(e) we observed that the final SDS/SiO2 microobject formed had an SDS crystal shell filled with the aggregated SiO2 nanospheres. 4. Conclusion The study reported in this paper show well-pronounced elastic light scattering properties of evolving microobject formed by an evaporating microdroplet of DEG/SDS solution and DEG/SiO2 /H2 O colloidal suspension. Intermediate fluctuating higher signals in the scattered light intensities were observed and attributed to the transient surface formation of SDS crystallite on the droplet surface during the evaporation process. For the DEG/SDS solution droplet evaporation, the transient SDS crystal structure formation were also manifested in the temporal evolution of the droplet radius. For the suspension droplet evaporation process, the initial composition of the droplet and in particular the amount of SDS added to the DEG/SiO2 /H2 O mixture defined the well-pronounced changes in the elastically scattered light. Additionally, the SEM images observed for the intermediate wet-structures and final dry structures show features that correlate well with the elastic scattered light measurements characterizing the drying and the structure transformation processes. Acknowledgment The authors acknowledge financial support from the National Science Center, Poland, grants number 2014/13/D/ST3/01882 and 2014/13/B/ST3/04414. References [1] Mishchenko M, Liu L, Cairns B, Mackowski D. Optics of water cloud droplets mixed with black-carbon aerosols. Opt Lett 2014;39:2607–10. [2] Derkachov G, Kolwas K, Jakubczyk D, Zientara M, Kolwas M. Drying of a microdroplet of water suspension of nanoparticles: from surface aggregates to microcrystal. J Phys Chem C 2009;112:16919–23. [3] Kolwas M, Kolwas K, Derkachov G, Jakubczyk D. Surface diagnostics of evaporating droplets of nanosphere suspension: fano interference and surface pressure. Phys Chem Chem Phys 2015;17:6881–8. doi:10.1039/c5cp0 0 013k. ´ M, Jakubczyk D, Kolwas K. Optical [4] Archer J, Kolwas M, Derkachov G, Wozniak diagnostics of surfaces of single evaporating liquid microdroplet of solutions and suspensions. Proc SPIE 2016;9884:988427–1–11. doi:10.1117/12.2225786.
[5] Liu L, Mishchenko MI. Optics of water microdroplets with soot inclusions: exact versus approximate results. J Quant Spectrosc RadiatTransf 2016;178:255– 62. http://dx.doi.org/10.1016/j.jqsrt.2015.12.025. [6] Mishchenko MI, Liu L, Mackowski DW. Morphology-dependent resonances of spherical droplets with numerous microscopic inclusions. Opt Lett 2014;39:1701–4. [7] Tsapis N, Dufresne ER, Sinha SS, Riera CS, Hutchinson JW, Mahadevan L, et al. Onset of buckling in drying droplets of colloidal suspensions. Phys Rev Lett 2005;94:018302. doi:10.1103/PhysRevLett.94.018302. [8] Babick F. Characterisation of colloidal suspensions. Springer International Publishing; 2016. [9] Fung J, Perry RW, Dimiduk TG, Manoharan VN. Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms. J Quant Spectrosc RadiatTransf 2012;113(18):2482–9. http://dx.doi.org/10.1016/j. jqsrt.2012.06.007. [10] Davies JF, Haddrell AE, Miles REH, Bull CR, Reid JP. Bulk, surface, and gas-phase limited water transport in aerosol. J Phys Chemistry A 2012;116(45):10987–98. doi:10.1021/jp3086667. [11] Sperline RP. Infrared spectroscopic study of the crystalline phases of sodium dodecyl sulfate. Langmuir 1997;13(14):3715–26. doi:10.1021/la9702087. [12] Doganci MD, Sesli BU, Erbil HY. Diffusion-controlled evaporation of sodium dodecyl sulfate solution drops placed on a hydrophobic substrate. J Colloid Interface Sci 2011;362(2):524–31. http://dx.doi.org/10.1016/j.jcis.2011.06.060. [13] Corti M, Degiorgio V. Quasi-elastic light scattering study of intermicellar interactions in aqueous sodium dodecyl sulfate solutions. J Phys Chem 1981;85(6):711–17. doi:10.1021/j150606a021. [14] Bergstrom M, Skov Pedersen J. Structure of pure SDS and DTAB micelles in brine determined by small-angle neutron scattering (sans). Phys Chem Chem Phys 1999;1:4437–46. doi:10.1039/A903469B. [15] Hammouda B. Temperature effect on the nanostructure of SDS micelles in water. J Res Natl Inst Stand Technol 2013;118:151–67. doi:10.6028/jres.118.008. [16] Bohren CF, Huffman DR. Absorption and scattering by a sphere. Wiley-VCH Verlag GmbH; 2007. [17] Jakubczyk D, Derkachov G, Kolwas M, Kolwas K. Combining weighting and scatterometry: application to a levitated droplet of suspension. J Quant Spectrosc Radiat Transf 2013;126:99–104. doi:10.1016/j.jqsrt.2012.11.010. [18] Taflin DC, Zhang SH, Allen T, James Davis E. Measurement of droplet interfacial phenomena by light-scattering techniques. AIChE J 1988;34(8):1310–20. doi:10. 1002/aic.690340809. ´ [19] Wozniak M, Derkachov G, Kolwas K, Archer J, Wojciechowski T, Jakubczyk D. Formation of highly ordered spherical aggregates from drying microdroplets of colloidal suspension. Langmuir 2015;31:7860–8. doi:10.1021/acs.langmuir. 5b01621. ´ [20] Derkachov G, Jakubczyk T, Jakubczyk D, Archer J, Wozniak M. Fast data preprocessing with graphics processing units for inverse problem solving in light-scattering measurements. J Quant Spectrosc RadiatTransf 2017;195:189–95. [21] van de Hulst HC, Wang RT. Glare points. Appl Opt 1991;30(33):4755–63. doi:10.1364/AO.30.004755. [22] Kolwas M, Jakubczyk D, Derkachov G, Kolwas K. Interaction of optical whispering gallery modes with the surface layer of evaporating droplet of suspension. J Quant Spectrosc RadiatTransf 2013;131:138–45. doi:10.1016/j.jqsrt.2013.03.009. [23] Mie G. Beitaege zur optik trueber medien, speziell kolloidaler metalloesungen. Annalen Der Physik 1908;330:377–445. doi:10.10 02/andp.1908330 0302.
J. Archer et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 202 (2017) 168–175 [24] Glover AR, Skippon SM, Boyle R. Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems. Appl Opt 1995;34:8409–21. doi:10.1364/Ao.34.008409. [25] Jakubczyk D, Kolwas M, Derkachov G, Kolwas K, Zientara M. Evaporation of micro-droplets: the “radius-square-law” revisited. Acta Phys Polonica A 2012;122:709–16. [26] Cifuentes A, Bernal JL, Diez-Masa JC. Determination of critical micelle concentration values using capillary electrophoresis instrumentation. Anal Chem 1997;69(20):4271–4. doi:10.1021/ac970696n. [27] Davis E, Bridges M. The rayleigh limit of charge revisited: light scattering from exploding droplets. J Aerosol Sci 1994;25(6):1179–99. http://dx.doi.org/10.1016/ 0021- 8502(94)90208- 9. [28] Kékicheff P. Phase diagram of sodium dodecyl sulfate-water system. 2. complementary isoplethal and isothermal phase studies. J Colloid Interface Sci 1989;131:133–52. [29] Buajarern J, Mitchem L, Reid JP. Manipulation and characterization of aqueous sodium dodecyl sulfate/sodium chloride aerosol particles. J Phys Chem A 2007;111:13038–45. doi:10.1021/jp0764034. [30] Erbil HY, Dogan M. Determination of diffusion coefficient-vapor pressure product of some liquids from hanging drop evaporation. Langmuir 20 0 0;16(24):9267–73. doi:10.1021/la0 0 0721b. [31] Moreau F, Colinet P, Dorbolo S. Leidenfrost explosions. Phys Fluids 2013;25(9):091111. doi:10.1063/1.4820127.
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Evolution of radius and light scattering properties of single drying microdroplets of colloidal suspension a ´ J. Archer a,∗, M. Kolwas a, D. Jakubczyk a, G. Derkachov a, M. Wozniak , K. Kolwas a Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, Warsaw PL-02668, Poland
a r t i c l e
i n f o
Article history: Received 14 June 2017 Revised 4 August 2017 Accepted 4 August 2017 Available online 5 August 2017 Keywords: Elastic light scattering Microdroplet evaporation Electrodynamic levitation Sodium dodecyl sulfate Silica nanospheres Aggregation
a b s t r a c t We report on observation of well-pronounced characteristic features of elastic light scattering of evaporating solution and suspension microdroplet of the anionic surfactant sodium dodecyl sulfate (SDS) and colloidal silica (SiO2 ) nanospheres in diethylene glycol (DEG) during SDS surface layer and structure formation (crystallization). For pure DEG/SDS solution droplet evaporation process, characteristic evaporation transitions manifested in the evolution of the droplet radius, a(t) for all the SDS concentrations (C = 20 mM, 40 mM and 100 mM) studied as well as well-pronounced intensity signals characterizing SDS soft gel-solid transitions for initial SDS concentrations, C > 40 mM. In the case of microdroplets composed of DEG/SDS with controlled addition of colloidal silica, the intensity fluctuations were enhanced and had profiles dependent on the initial composition of the suspension. Exemplary wet droplets at the initial evaporation stages and final dry aggregates of SDS and SDS/SiO2 were deposited on a substrate and observed with Scanning Electron Microscopy (SEM). Features of the deposited structures correlate well with the elastic scattered light measurements characterizing the drying processes. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Evaporation of microdroplets containing dispersed particles or dissolved materials exhibit pronounced complex optical and thermodynamic properties [1–6] as well as distinct mechanical instabilities [7] than that of the evaporation of pure liquid microdroplets. Such colloidal suspension of microdroplets represent important morphological type of scattering objects with numerous applications in research and industry [8,9]. The temporal behavior of scattered light on drying colloidal suspension or solution microdroplets depends on both the bulk and surface properties of the droplet. The interaction of the light with the droplet surface at the air-liquid/solid interface manifest in a complex way. However, since the light interacts directly with the surface layer of the evaporating droplet, an inverse inference of the droplets’ surface properties, dry microobject morphology as well as phase transitions at the droplet surface during the evaporation/drying processes can be obtained from the total distribution and evolution of the scattered light intensities. Sodium dodecyl sulfate (SDS) is perhaps the most widely studied anionic surfactant used in both industrial products and for fundamental scientific research. For example, it has been used to sim-
∗
Corresponding author. E-mail address: [email protected] (J. Archer).
http://dx.doi.org/10.1016/j.jqsrt.2017.08.004 0022-4073/© 2017 Elsevier Ltd. All rights reserved.
ulate the behavior of surfactants observed in the atmosphere in the form of aerosol droplets [10] and is observed to posses several crystalline phases under variable temperature conditions [11]. Doganci et al. [12] studied the effects of SDS concentration on the evaporation rate of droplets placed on TEFLON-FEP substrate. In their classic work, they observed that the addition of SDS did not alter the drop evaporation rate within the first 20 min of the evaporation process. They additionally concluded that the main difference was found to be the change of the mode of the drop evaporation on the substrate including contact angle, and area variations when they varied the SDS concentrations in the droplet. However, the presence of substrate via such method can sometimes mar the final morphology of the dried products from the evaporation process. Static and dynamic light scattering methods including quasielastic light scattering [13], small-angle neutron scattering [14,15], infrared spectroscopic technique [11] and many others mentioned in [11] have been used to characterize other specific physical properties of SDS. However, elastically scattered light diagnostics characterizing gradual crystallization of SDS and structure evolutions from single levitating microdroplet composed of SDS with/without other submicron inclusions have not been studied. Here, we present a systematic study of elastically scattered light intensities characterizing the formation of crystallized SDS microstructures and SDS/SiO2 composite micro objects from single evaporating microdroplet of solution and suspension respec-
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Fig. 1. Scheme showing the optical arrangement of the electrodynamic quadrupole trap (A). LP: linear polarizers, PS: polarization sheet plate, L: Lenses, CCD 1 and CCD 2 are cameras used for the in-focus imaging and Mie scattering imaging respectively. Right : Images of out-of-focus interference patterns (a, b) and in focus glare spots (c, d) observed during the microdroplet evaporation process.
tively. In particular, we examine the changes in the integrated Mie scattering vs time evolution and measure the droplet radius on the basis of Mie scattering theory [16] and by electrical weighting of the droplet position [17]. It is important to note here that, the combination of these two complementary methods of droplet size measurement technique (i.e. optical (interferometric) and weighting) enabled very accurate determination of the entire droplet/aggregate radius evolution. Weighting becomes particularly indispensable, when the elastic scattering pattern loses its regular structure, and the determination of droplet size using the interferometric method becomes compromised [10,18] or impossible. Additionally, a parallel experimental setup [19] was used to deposit exemplary initial wet aggregates (patterns) and final dry structures on a substrate and analyzed further with Scanning Electron Microscopy (SEM) to complement the observed elastic scattered light measurements. 2. Experimental section 2.1. Experimental materials and sample preparation The sample materials used for the experiment includes: monodispersed colloidal silica nanospheres (SiO2 ; 125 nm radius, refractive index = 1.465, C-SIO-0.25, Corpuscular Inc.) diethylene glycol (DEG : refractive index = 1.446, 99.0% GC area, BioUltra, Fluka, Sigma-Aldrich) and sodium dodecyl sulfate (SDS: refractive index = 1.461, ACS Reagent, ≥ 99:0% , Sigma-Aldrich). For the DEG/SDS solution droplet experiments, different molar concentrations of SDS at 20 mM, 40 mM, and 100 mM were prepared by mixing weighted SDS with DEG in an insulin syringe, followed by ultrasonication to obtain uniform mixing. In the case of the DEG/SiO2 /H2 O/SDS suspension droplet experiment, an initial approximate mixing ratio of DEG : H2 O : SiO2 = 1 : 3 : 56 by volume was prepared and successive percentages by mass of SDS was added to the mixture and sonicated to obtain uniform mixing. The prepared liquid solution and suspension mixtures were carefully transferred into the droplet on-demand injector under controlled dust free environment to prevent contamination of the samples during the liquid transfer process. 2.2. Experimental setup and procedure A schematic of the electrodynamic quadrupole trap showing the optical arrangement of the major peripherals is presented in Fig. 1A. Detailed description is given elsewhere in [3,4,20]. The trap
system and its component are placed in a climatic chamber with eight side ports for optical access to the trap center. The trap and its auxiliary components are thermally regulated by a circulating liquid from an external gas-liquid heat thermostatic bath. Usually, the temperature in the climatic chamber (trap environment) is maintained at 22 ± 0.15 °C. Additionally, dry nitrogen is provided to the chamber through a gas-liquid heat exchanger to provide dry atmospheric conditions in the trap with relative humidity of not more than 5 ± 3.5% during all the experimental procedures. A droplet suspended at the center of the trap is simultaneously illuminated by a horizontally (H) polarized diode laser (658 nm; 10 mW) and vertically (V) polarized argon ion laser (458 nm; 12 mW) with respect to the scattering plane. The light scattered by the droplet is monitored and recorded by a CCD camera (CCD 2) placed at the right angle of the scattering plane at a scattering angular range of φ = 90 ± 16° (azimuth) and θ = 0 ± 5° (elevation). The scattered light passes through a polarization sheet (PS) that maps the horizontal polarization of the scattered light to the scattering plane in the lower half of the camera and vertical to the plane in the upper half of the camera (see Fig. 1(a)). Fig. 1(a)–(d) show respectively the out-of-focus angularly resolved Mie scattering interference patterns and in-focus images captured from the evaporation of microdroplet composed of DEG/SiO2 /H2 O colloidal suspension. In Fig. 1(a), characteristic, almost equidistant regular Mie interference patterns on both the vertical (upper half) and horizontal (lower half) polarization channels can be seen at the beginning of the evaporation process. The patterns can be ascribed to the interference between the reflected laser light from the surface and the refracted laser light from the inner surface of the droplet. The reflected and refracted lights manifest in the in-focus image as the two horizontally displaced glare spots (Fig. 1(c)) appearing at the droplet equator [21] and is observed with the CCD 1. In our case, the in-focused image provided by CCD 1 is used to balance the weight of the droplet levitating at the center of the trap. From the image, we calculate the position of the center of light distribution (similar to center of mass) and use one of the coordinates as feedback to a PID-type loop software controller that provides a DC loop voltage to stabilize the droplet position at the center of the trap. The stabilizing DC loop voltage is recorded in synchronous with the Mie interference patterns for the entire droplet/aggregate evolution allowing comparable droplet mass-to-charge ( m q ) ratio evolution and subsequently the droplet radius evolution via the weighting signal (droplet mass, m(t) evolution) [17].
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As the evaporation process proceeds, the SiO2 inclusions emerge to the surface of the droplet and the regular interference patterns become depolarized and speckled at the liquid-solid (wet aggregate) transition (see Fig. 1(b)) [3,22]. Additionally, since the size of the droplet decreases through continuous loss of liquid, the distance between the glare spots (Fig. 1(c)) also decreases and eventually come together at the point of liquid-solid (wet aggregate) transition and become speckled (Fig. 1(d)). However, such transition does not influence the droplet weighting signal since the notion of center of brightness of the image is used for the stabilization process. The interference pattern observed in the scattered light is analyzed using Mie theory [16,23], from which the temporal evolution of the droplet radius a(t) is obtained [24,25]. The initial droplet radius a0 (t0 ) corresponding to the time (t0 ) when we start the droplet stabilization process to record the experimental data is obtained from the exact fitting of the spatial scattered light distribution (phase functions) recorded in the first movie frame with the Mie theory. The time lapse between the emergence of the droplet from the nozzle of the droplet on-demand injector and the start of the measurement procedure, mostly required to prestabilize the droplet in the trap varies but is below 1 s. The relative expected radius change within this time lapse is below 0.5% for the fastest droplet evaporation that we studied. For solution droplet evaporation, the corresponding initial concentration (C0 ) increase is below 1.5% at most. Hence C0 , corresponding to a0 , is assumed equal to the prepared initial solution/suspension concentration. However, another possible source of error that can influence the initial concentration of the droplet is the evaporation of solute directly from the nozzle of the droplet on-demand injector prior to injection. This error is hard to estimate, but can be minimized by expelling a few droplets just before the proper measurement. Additionally, the intensity distribution Ivv(θ , φ , t) and Ihh(θ , φ , t) from the vertical (upper half) and horizontal (lower half) polarization channels is integrated over the scattering angles φ and θ to obtain their temporal dependence Ivv(t) and Ihh(t) respectively [3,22]. 3. Results and discussions 3.1. Radius and scattered light intensities from crystallization of SDS The concentrations of SDS solution studied were higher than the critical micelle concentration (CMC, 8.2 mM) [26]. Above the CMC, SDS form insoluble monolayers [18,27], crystalline phases [28] and also aggregate to form metastable microgel state or complex structures of nanocrystals [29]. Here, we examine the elastically scattered light characterizing the transient and final stages of SDS crystallized structure formation from the evaporation of DEG/SDS solution microdroplet. Fig. 2 (a)–(d) show respectively, the temporal evolution of the droplet radius, a(t) (green open circles) and integrated Mie scattered light intensities of DEG/SDS solution at an initial SDS concentration of (a) 20 mM, (b) 40 mM and (c & d) 100 mM. From the observed radius, a(t) evolution and the intensity profiles, the droplet can be considered as optically homogeneous at the initial stages of the evaporation process with isotropic shrinking and with scattered light intensities showing series of regularly spaced structural Mie resonances. The continuous loss of liquid results in decrease of the droplet volume and increasing concentration of SDS preferentially at the droplet surface. At a defined time, tcrit corresponding to critical concentration (crystallization concentration) Ccryst , of SDS (Dash line A, t ∼ 281 s in Fig. 2(a)), the SDS crystallites start to accumulate and populate the droplet surface. During such transition (liquid - wet SDS crystallized (solid) structure), the regularly spaced structural Mie resonances change its temporal characteristics into irregular (depolar-
ized) intensity fluctuations suggesting nonuniformity and crystallization of SDS at the droplet surface (see insert in Fig. 2(a)). The initial evaporation process characterized by the series of the regularly spaced structural resonances before the transition stage is considered as a quasi-steady diffusion-controlled evaporation process and the evaporation rate can be written in the form [18] :
a2 = a20 − β (t − t0 )
(1)
2Di j Pa (Ta ) ρl RTa
is constant under these conditions [30]. Di j is
where β =
the diffusion coefficient for the evaporation species i in surrounding gas j and is mainly temperature dependent [30], Pa is the vapor pressure at the surface of the droplet at surface temperature Ta . R and ρl are respectively the universal gas constant and density of the liquid, a0 is the initial droplet radius at time t0 . The first stage evaporation process is followed by a slow evaporation rate before stabilization when the final form of the SDS crystallized structure is formed. The slow intermediate transition between the initial evaporation stage and the formation of the final SDS crystallized structure is attributed to the formation of soft SDS gel-like phase or gel-like shell made up of porous network of SDS crystals [29,31] at the droplet surface. The three pronounced evaporation/drying stages leading to the formation of the final form of the dry SDS crystallized structure is well seen in the evolution of the droplet radius, a(t) (green open circles in Fig. 2 (a)–(d)). The stages primarily consists of : (i) evaporation of DEG/SDS solution controlled by diffusion. The Mie structural resonances associated with this stage has regularly spaced angularly resolved resonance patterns (a(t) evolution till the point marked A in Fig. 2(a) with similar evolutions in Fig. 2(b)–(d)), (ii) slow evaporation of DEG/SDS gel-like phase (evaporation of DEG/SDS solution through porous network of SDS crystallized surface, A - B radius evolution in Fig. 2(a) and subsequent Figures). The nature of the scattered light fluctuations is controlled by the concentration of SDS (compare Fig. 2(a) and (c) for both Ivv(t) and Ihh(t) polarization signals), and (iii) the SDS gel - solid drying stage leading to the final morphology of the SDS crystallized structure resulting in the stabilization of the droplet radius evolution. Modulation of the amplitude of the scattered light intensity fluctuations depend on the initial droplet size (see Fig. 3). 3.2. Diagnostics of radius and integrated Mie scattered light intensity evolutions At lower SDS concentrations (C = 20 mM , 40 mM), the nature of the observed scattered light intensities (Fig. 2(a) and (b) exhibited nearly stabilized irregular intensity fluctuations after the first stage evaporation process. However, at higher SDS concentration (C = 100 mM), we observed scattered light signals showing transient SDS crystallized surface layer formation and composite structure transformations due to possible transitions of SDS crystallized surface shell creation and deformation at the air-solution interface. It has been suggested that, at the air-solution interface, SDS can form varieties of structures, from broad band-like or lace-like aggregates to multiconnected threads [32]. We believe that, at higher concentrations, the intensity fluctuations observed in the elastically scattered light as well the characteristic temporal modulations in the amplitude of the intensity signals show possible crystallized SDS surface structural transformations dependent on the initial droplet size. In Fig. 2(c), we observed such transformations from t ≈ 184 s to t ≈ 423 s corresponding to the minimum boundaries of the temporal evolution of the amplitude of the fluctuating scattered light signals. After t ≈ 423 s, one can also observe another possible structure onset with scattered light characteristics similar to the
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Fig. 2. Evolution of radius and integrated Mie scattered light intensities for DEG/SDS solution droplet evaporation obtained for different droplets of initial radiuses a0 (t0 ) [μm] and SDS concentrations, C [ mM ]. Ivv(t) and Ihh(t) represent the temporal evolution of vertically and horizontally integrated Mie scattered light intensities from vertical and horizontal polarized incident light respectively. Ivh(t) and Ihv(t) are the cross polarized signals. Green empty circles : Temporal evolution of the droplet radius a(t) [μm]. Insert : fine regular structural Mie resonances to irregular intensity fluctuations characterizing liquid- wet SDS crystallized (solid) surface transition stage.
Fig. 3. (a) Averaged IVV (t) intensity signal obtained from Fig. 2(c) (blue line). Green line with open circles - droplet radius, a(t) evolution with a0 = 9.76 μm. (b) Averaged IVV (t) intensity signal obtained from Fig. 2(d) (blue line). Green line with open circles - droplet radius, a(t) evolution with a0 = 15.40 μm). For bigger droplet, higher number of intensity signal modulations (6) can be seen characterizing possible surface properties of the SDS crystallized microstructure evolutions (structure transformations) during the drying process. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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earlier patterns but at rather lower amplitude. For the bigger initial droplet size (a0 = 15.40 μm , Fig. 2(d)), successive modulations of the amplitude of the fluctuating intensity signals can be observed from t ≈ 673 s–1040 s; 1057 s–1318 s; 1319 s–1508 s; 1511 s–1680 s and 1680 s–1807 s as well as from - 1807 s–1833 s characterizing potentially as well, SDS crystallized product structural transformations during the drying process. Fig. 3(a) and (b) show averaged Ivv(t) signals obtained from Fig. 2(c) and (d) respectively. Characteristic modulations of the amplitude of the intensity fluctuating signals can be observed during the drying process. It is worth noting that, in Fig. 3(b), the amplitude of the first three modulations in the fluctuating intensity signals decreases as the radius evolution during the second stage (ii) evaporation process. After t = 1508 s corresponding to the fourth minima in the intensity signal, the evolution of the droplet radius appear to be stabilized showing the final stages of the drying process. Subsequently, another onset of characteristic intensity fluctuations with decreasing amplitudes similar to the earlier ones begin and after t = 1833 s, the signal seem to be stabilized showing potentially, the final morphology of the SDS crystallized structure evolution. Using a parallel experimental setup and procedure [19], we deposited exemplary wet droplets at the initial evaporation stage (Fig. 6(c)) and (the final dry SDS crystallized structure (Fig. 6(d)) at an initial SDS concentration of 100 mM and analyzed the product with SEM. We observed that the final form of the SDS crystallized microproduct was irregular and had deformed surface symmetry and can be viewed as structure evolution from a more regular object (initially spherical droplet symmetry). As can be seen in Fig. 6(c), the wet DEG/SDS droplet deposited during the initial stages of the evaporation process generally show uniform pattern after drying on the substrate. 3.3. Evolution of mean concentration of SDS Eq. (1) states that, the evolution of the radius squared or the droplet surface area varies linearly with time [33]. However, in the presence of the soluble SDS in the droplet, the surface area deviates from linearity in time. The effect of SDS component in the droplet during the quasi-steady diffusion limited process can be modeled by incorporating a second-order term in Eq. (1) [34] or by expressing the vapor pressure at the droplet surface in terms of the Köhler equation [35–37]. The vapor pressure at the surface of the droplet Pa (Ta ) based on the Köhler equation can be expressed in terms of the volume equivalent dry radius, a3dry = 3mdry /4π ρdry as:
Pa (Ta ) = Psat (Ta ) exp
a3dry M i 2 σl − 3 RT∞ ρa a a − a3dry
(2)
where a is the radius of the droplet at time t. ρa is the density of the droplet, mdry is mass of dry microobject. σl is the surface tension of the liquid. Pa and Psat are the vapor pressure and saturated vapor pressure near the droplet surface at temperature Ta respectively. T∞ and Mi are the temperature far from the droplet surface and the molecular weight of species i respectively. For micronsized droplets, the surface tension effect can be assumed negligible [25] and Eq. (1) together with Eq. (2) can be simplified as:
2 Di j da a =− P (T ) exp dt ρl RTa sat a
−
a3dry a3 − a3dry
(3)
We note here that adry is not necessarily equal to the physical dry radius of the aggregates or the SDS crystallized structure, as such a structure at the point of the drying stages when its mass is measured may contain residual amount of DEG liquid and may have an effective mean density different from that of the initial droplet composition or may not be spherical as observed in
Fig. 6(d). However, since the mass of the SDS solute in the droplet is constant and known a priori, adry provides a measure of the mean concentration of SDS (or inclusions). Fig. 4(a) and (b) show the radii in Fig. 2(a)–(c) and Fig. 2(d) converted to radius squared and the evolution of the mean concentration of SDS at the droplet surface. It can be noticed that, the final mean concentration of SDS is independent of the initial droplet composition. A final mean concentration of 0.55 ± 0.05% can be observed for all the SDS concentrations studied for small droplet (ca. 9 μm) and bigger droplet (ca. 15.4 μm) respectively. The critical concentration of SDS (crystallization concentrations) at which SDS starts to crystallize at the droplet surface can be obtained from the initial droplet radius a0 , the initial concentration of the solution C0 and the critical radius acryst (tcrit ). This can be expressed as [38] :
Ccryst = C 0
a 3 0 acryst
(4)
3.4. Scattered light intensities during crystallization of SDS in suspension microdroplet In our previous study [4], we showed that the temporal evolution of the total integrated scattered light intensities from evaporating microdroplet of colloidal solution composed of DEG/SiO2 /H2 O/SDS, follows three transitory signal patterns. Here, we demonstrate that, the appearance of the intermediate intense scattered light signal due to the addition of SDS to the DEG/SiO2 /H2 O colloidal suspension is dependent on the initial composition of the droplet driven primarily by the concentration of the SDS. Fig. 5(a)–(d) present the temporal evolution of the scattered light intensities obtained for the evaporation of microdroplet composed of 1 : 4 : 19 mixture of DEG : SiO2 : H2 O colloidal suspension by volume respectively with 0%, 0.5%, 1%, and 1.72% fractions of SDS by mass added to the DEG/SiO2 /H2 O colloidal suspension. Features of the deposited structures correlate well with the observed elastic scattered light measurements characterizing their drying processes. At the initial stages, the temporal evolution of the signals exhibited series of sharp-peaked regularly spaced resonances similarly to the SDS solution droplet evaporation stages (compare Fig. 2(a)– (d)) and in agreement with earlier results reported in [4,22] before the transient critical periods. However, controlled addition of SDS to the DEG/SiO2 /H2 O mixture led to the observation of characteristic scattered light features during the SDS surface layer crystal formation on the drying micro object surface. In Figure, 5a, with 0% of SDS added to the DEG/SiO2 /H2 O mixture, we observed a rapid increase in the intensity signals after the initial quasi-steady diffusion limited evaporation process and quick rise and stabilization of the ensuing fluctuating intensity signals . The sharp rise in intensity at t = 321 s and the subsequent stabilization can be understood in terms of the surface and morphology evolution of the SiO2 aggregate symmetry in the droplet during the SiO2 nanosphere aggregation process. A microdroplet injected into the trap maintains its spherical shape due to surface tension and hence the air-liquid interface of the droplet can be considered as a smooth surface. Our SEM studies (Fig. 6(a) and (b)) from sample deposits of the suspension (DEG/SiO2 /H2 O) droplet /aggregate at the initial isotropic evaporation stage and the final dry-aggregate stage indicates a possible rapid transition between scattering on a smooth evaporating droplet surface(air-liquid interface) and on a more corrugated SiO2 nanosphere aggregate surface (air-solid interface). Fig. 6(a) shows the well-known coffee ring effect [39] driven by the capillary flow of the suspended SiO2 nanospheres in the droplet after the deposition on the substrate. The final aggregate observed
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Fig. 4. Evolution of radius squared and mean dried SDS concentration from the evaporation of DEG/SDS solution microdroplet extracted from Fig. 2. (a) : Green line (20 mM), red line (40 mM) and dark grey line (100 mM) respectively for radius squared and concentration evolutions for initial small droplet radius in Fig. 2 (a)–(c). (b) : Evolution of radius squared and mean concentration extracted from Fig. 2(d) (bigger droplet). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Temporal evolution of elastically scattered laser light intensities for the evaporation of DEG/SiO2 /H2 O with (a) 0% SDS, (b) 0.50% SDS (c) 1.0% SDS (d) 1.72% SDS.
showed regular spherical symmetry of highly ordered aggregated SiO2 nanospheres. With systematic addition of SDS to the initial DEG/SiO2 /H2 O colloidal suspension, we observed the influence of SDS surface layer crystallization at the droplet surface manifested in the evolution of the elastic scattered light signals during the drying periods. In Fig. 5(b), with 0.5% of SDS, we observed first, a decrease then a steady increase in the Ivv, Ivh, and Ihh intensity signals from t = 152 s before stabilization after t = 256 s which we attribute to surface layer transitions occurring at the droplet surface. Fig. 5(c) and (d) show the scattering profiles for 1% and 1.72% of SDS added to the DEG/SiO2 /H2 O mixture. The appearance and the duration of the characteristic scattered light intensity features
during the transient SDS crystal layer formation stages is seen to be dependent on the concentration of SDS added to the mixture. In Fig. 5(c), the transitions during the SDS surface layer formation appeared between t = 198 s and 328 s and occurred at 676 s to 1146 s for the 1.72% of SDS. The well-pronounced scattered light intensities observed during the transient SDS/SiO2 composite aggregate evolution seems to suggest possible surface structure and symmetry deformations as the aggregate transforms from loose packing of the SiO2 nanospheres to more compact and regular structure. Fig. 6(e) and (f) show respectively SEM microgragph of a pattern generated by drying of a microdroplet deposited during the initial evaporation stage and SDS/SiO2 aggregate structure deposited
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Fig. 6. SEM images of dried aggregates obtained from the evaporation of 1 : 3 by volume of diethylene glycol and colloidal SiO2 suspension with 0% SDS (a, b), SDS only (c, d) and 1.24% of SDS added to DEG/SiO2 /H2 O mixture (e, f).
at the final drying stage. In Fig. 6(e) we observed that the final SDS/SiO2 microobject formed had an SDS crystal shell filled with the aggregated SiO2 nanospheres. 4. Conclusion The study reported in this paper show well-pronounced elastic light scattering properties of evolving microobject formed by an evaporating microdroplet of DEG/SDS solution and DEG/SiO2 /H2 O colloidal suspension. Intermediate fluctuating higher signals in the scattered light intensities were observed and attributed to the transient surface formation of SDS crystallite on the droplet surface during the evaporation process. For the DEG/SDS solution droplet evaporation, the transient SDS crystal structure formation were also manifested in the temporal evolution of the droplet radius. For the suspension droplet evaporation process, the initial composition of the droplet and in particular the amount of SDS added to the DEG/SiO2 /H2 O mixture defined the well-pronounced changes in the elastically scattered light. Additionally, the SEM images observed for the intermediate wet-structures and final dry structures show features that correlate well with the elastic scattered light measurements characterizing the drying and the structure transformation processes. Acknowledgment The authors acknowledge financial support from the National Science Center, Poland, grants number 2014/13/D/ST3/01882 and 2014/13/B/ST3/04414. References [1] Mishchenko M, Liu L, Cairns B, Mackowski D. Optics of water cloud droplets mixed with black-carbon aerosols. Opt Lett 2014;39:2607–10. [2] Derkachov G, Kolwas K, Jakubczyk D, Zientara M, Kolwas M. Drying of a microdroplet of water suspension of nanoparticles: from surface aggregates to microcrystal. J Phys Chem C 2009;112:16919–23. [3] Kolwas M, Kolwas K, Derkachov G, Jakubczyk D. Surface diagnostics of evaporating droplets of nanosphere suspension: fano interference and surface pressure. Phys Chem Chem Phys 2015;17:6881–8. doi:10.1039/c5cp0 0 013k. ´ M, Jakubczyk D, Kolwas K. Optical [4] Archer J, Kolwas M, Derkachov G, Wozniak diagnostics of surfaces of single evaporating liquid microdroplet of solutions and suspensions. Proc SPIE 2016;9884:988427–1–11. doi:10.1117/12.2225786.
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