How sticky droplets behave when there's a lot of them

I've been writing my dissertation, so updates have been scarce, but I can report some interesting papers I've read along the way.

There is a great paper by Ryotaro Shimizu and Hajime Tanaka that explains a new mechanism for how immiscible droplets within a fluid merge into bigger droplets, and has universal applications from emulsions to cosmetics and foods.  Immiscible means two fluids cannot mix.  The models described here work are applicable for low viscosities.  This work is based on computer simulations, but the authors claim there are experiments to back up their claims.  The paper has been recently published in Nature Communications, so time will tell on what further peer review will reveal. 

Shimizu and Tanaka focus on phase separation, which is a fundamental physical phenomenon of multiple bodies collectively interacting.  Most familiar encounter I can think in everyday life is olive oil droplets merging into a single mass in a cooking pot.  The process is called coarsening, and the oil droplets can be thought of as domains in a continuous medium called water.  The way by which droplets coalesce is dependent on their initial concentration.  The concentration changes the mechanism by which they interact.  

When the concentration is low, droplets merge via a mechanism called Ostwald ripening.  This is as old as the hills (actually since the 1890s), and works by smaller droplets steadily diffusing into large droplets at the expense of the smaller droplets.  

Figure 1.  Small droplets spontaneously dissolve due to their instability.  The material then diffuses into larger droplets, which are more energetically stable.    Source: Wikipedia

Another mechanism is works when there are enough droplets to occupy about 50% of the total volume in a given object.  There, hydrodynamic forces coarsen the droplets into a so-called bicontinuous pattern, as seen in Figure 2.  Bicontinuous refers to two continuous phases.   You can see the black and white patterns continuing beyond the box in the moments of the animation.  The merging is so rapid that normal diffusion is dwarfed by the swift currents that result in the final structure of the animation. 

Figure 2.  Emergence of bicontinuous structure.  Note the rapid emergence of two continuous phases; that is indicative of rapid flow.

The third mechanism accounts for an intermediate droplet concentration, somewhere between 21 and 35% of the volume occupied by the droplets.  This is the most difficult mechanism and has been the subject of various researchers for decades.  That is because neither diffusion nor hydrodyanmcs can be neglected and thus makes it difficult to make approximations.  Hydrodynamic forces stem from thermally-induced Brownian motion, the technical term for the random collisions between particles in a fluid, as seen in Figure 3.    Diffusion occurs during the collision, and thus the hydrodynamics and diffusion are coupled.

Figure 3.  Animation of Brownian motion without coalescence.   The blue path traces the trajectory taken by the yellow particle from  incessant collisions.

However, what Shimizu and Tanaka claim is that the collisions are not random, but are driven by a so-called composition Marangoni force, which is induced by long-range interfacial tension gradients on the droplets.  In other words, the interfacial energy on a droplet varies because of other droplets near it.   This is illustrated from the paper in Figure 4.

Figure 4.  Snapshot of droplets with interfacial energy gradients, with blue color being the minimum, and red as the maximum.  Velocity arrows are drawn on and in the droplets of b to indicate preferred velocities on a given droplet region.  Thus, the droplet in the low left is drawn toward the small droplet next to it due to the largest arrows pointing toward it from the further end of this droplet.

A droplet much smaller than its neighbors draws neighboring droplets toward it and eventually induce them to collide.  In short, a larger droplet tends to eat a smaller droplet by direct collision.   The attraction from droplets stems from the different gradients of surface tension between the droplets.  The merging then lowers the overall energy of the system, since equilibrium just means the system has fallen to its lowest energy state.  

Source:  R. Shimizu, H. Tanaka, A novel coarsening mechanism of droplets in immiscible fluid mixtures, Nature Communications, 6 (2015).

Confined Crystallization of Polyethylene Oxide in Nanolayer Assemblies

We live in an era of increasing reliance on the very small to satisfy humanity’s endless needs and desires for new technologies.  Nanotechnology manifests itself in numerous scientific fields, and polymer chemistry is no exception.  Polymers are generally amorphous, but polymer crystallinity can be observed if the conditions are right.  Semi-crystalline polymer chains (possesses crystalline and amorphous phases) such as polyethylene and nylon are often used as barrier films in food, medicine, and electronics industries.  A barrier is considered highly efficient if small gas molecules are relegated to permeating through only the amorphous regions of the chains (crystalline regions are impenetrable).   Efficiency can be fine-tuned by varying the polymer-film processing conditions to suit the desired amount of crystallinity and chain orientation.  Polymer films can now be made thin enough to effectively confine the crystallization process to 2D; this leads to surprising results. 

Conventionally, confined polymer chains crystallize into lamellae with thicknesses of ~10-20 nm with spherelitic morphology.   However, this convention is skirted at the nanoscale, as isotropic growth is severely hampered to the point of producing lamellar crystal orientation.  This orientation is usually perpendicular to the layer (edge-on), but parallel orientations have been reported several times in the literature; mechanisms for orientation determination remain mysterious for the time being. 

Normally, researchers prepare 2D crystallization of polymers via solution processes such as spin-coating or Langmuir-Blodgett (LB) techniques, but these are limited by the solvent requirement and the small quantity of material fabricated.  LB techniques enable layered nm morphologies due to microphase separation of dissimilar block copolymers within the thin films.  Alas, block copolymers are notoriously difficult to synthesize and align with respect to the direction of the thin films. 

Enter a new technique known as layer-multiplying extrusion.  It uses forced assembly to create alternating layers of two polymers that number up to the 100,000s.  Almost any melt-processable polymer can be formulated into kilometers of nanolayered films with thicknesses of ~10 nm.  With less material comes an explosion of new previously unknown properties (“less is more”). 

The materials used in this study are polyethylene oxide (PEO, also known as polyethylene glycol), which has the following structure:

                                                   HO-CH₂-(CH₂-O-CH₂-)_n-CH₂-OH

The other is ethylene-co-acrylic acid (EAA), a copolymer with much lower crystallinity than PEO:  

Films with 33, 257, and 1025 alternating EAA and PEO layers were extruded, with various thicknesses and composition ratios, including (EAA/PEO vol/vol) 50/50, 70/30, 80/20, and 90/10.  The nominal PEO layer varied from 3.6 µm to 8 nm. 

The films were subjected to oxygen permeability tests with respect to to layer thickness.  The results are shown below:

Fig. 1 The effect of layer thickness on oxygen permeability. (A) Oxygen permeability of films with equal volume fractions of EAA and PEO. The dashed line indicates P_// calculated from Eq. 1. (B) Oxygen permeability of the PEO layers from films of varying composition calculated from Eq. 2. The dashed line indicates PPEO. The open symbol is for a film with PEO layer breakup. The solid lines are drawn to guide the eyes. 

The plots show a significant decrease in O₂ permeability.  Gas permeability for layered assemblies is modeled by the following equation. 

     (1)

where 𝜙_PEO is the volume fraction of PEO and P_PEO and P_EAA are the permeabilities of PEO and EAA, respectively.  Upon plugging determined values of P_PEO and P_EAA from literature into Eq. (1), the result did not agree with the findings reported in the plot above. Eq. (1) predicts increasing permeability with respect to decreasing PEO thickness, but the data show the opposite trend. Eq. (1) was then modified to account for the apparent sensitivity to P_PEO due to the far lesser permeability of PEO; it still did not agree with the plotted data with the exception of thicker PEO layers as indicated by the dashed line.  Clearly, the PEO nanolayers possess some previously unknown crystalline morphology that bestowed them with staggeringly low permeability.  However, differential scanning calorimetry revealed that the PEO and EAA layers (even the very thin ones) share the same melting enthalpy and melting temperature as the control films; this means that the changes in crystalline morphology granting the PEO nanolayers low permeability was not accompanied by changes in crystallinity nor lamellar thickness. 

Upon examination by AFM, the authors found that the thin 20 nm PEO layers exhibited single lamellae that extended beyond the field of the AFM image.  The single lamellae are said to be very large single crystals.  Reducing the PEO layer thickness to 8 nm then induces breakage, thereby increasing the permeability.  Fig. 2 below shows the AFM image of the 20 nm PEO layer, and an accompanying schematic showing a gas diffusion pathway through the layered assembly.

Fig. 2  AFM phase images of partial cross sections of the layered EAA/PEO films. The PEO layer has substantially higher crystallinity than the EAA layers and hence appears bright in the AFM images. (A) A low-resolution image of an EEA/PEO film with 50/50 composition, 33 alternating layers, and nominal PEO layer thickness of 3.6 mm. (B) A higher-resolution image showing the spherulitic morphology of the 3.6-mm-thick PEO layer. (C) A low-resolution image of an EAA/PEO film with 70/30 composition, 1025 alternating layers and nominal PEO layer thickness of 110 nm. (D) A higher-resolution image of the 110-nm-thick PEO layers showing the oriented stacks of PEO lamellae. (E) A high-resolution image of an EAA/PEO film with 90/10 composition, 1025 alternating layers, and nominal PEO layer thickness of 20 nm showing that the PEO layers crystallized as single, extremely large lamellae. (F) A schematic showing the gas diffusion pathway through the layered assembly with 20-nm- thick PEO layers. The arrows identify the EAA layers and PEO layers. 

The lamellar crystalline region is considered impermeable, with the lamellar fold surfaces constituting the permeable amorphous regions.  As seen in Fig. 2, the gas pathways depend on the frequency of defects such as lamellar edges.  The permeability is now expressed by

   (2)

 where α is the aspect ratio of the impermeable platelets (length/width), and 𝜙 is the volume fraction of impermeable platelets; the platelets are orientated perpendicular to the flux.  For the thinnest PEO layers, the aspect ratio was as high as 120, which meant the lamellae extended up to 2 µm for the 20 nm thick layers.   Gradually thickening the PEO layer relaxed the restrictions on 3D growth, which returned the morphology to spherelitic.   The results were further confirmed by small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS). 

This work is a major breakthrough in polymeric applications for nanotechnology because it shows experiment trumping theory, and possibly describes a major advance for gas-barrier films.  Its importance is amply demonstrated by the 51 citations it has generated since its publication in 2009.  Science Magazine accepted the paper because of its reliance on well-established analytical techniques (AFM, differential scanning calorimetry, SAXS, WAXS), and, more importantly, because of its broad significance in the field of nanoscience. 

This significance is underscored by the novel utilization of a relatively new technique–coextrusion–on readily available polymers to engineer nanolayered polymeric formations in sufficient amounts to allow for probing links between the confined crystalline morphology and the properties exhibited.  This opens up new possibilities for packaging methods, i.e., incorporating polymer nanolayers into common polymeric films for less cost, thereby reducing the environmental and energy consequences.