We used Langevin dynamics simulations of short associative polymers with two stickers placed symmetrically along their contour to study the effect of the primary sequence of these polymers on their organization inside condensed droplets. We observed that the shape, size and number of sticker clusters inside the condensed droplet change from a single cylindrical fiber to many compact clusters, as one varies the location of stickers along the chain contour. Aging due to conversion of intramoleclular to intermolecular associations was observed in droplets of telechelic polymers, but not for other sequences of associating polymers. The relevance of our results to condensates of intrinsically disordered proteins is discussed.
Associative polymers with sticker-and-spacer architectures undergo phase transitions that combine phase separation and bond percolation. Here, we generalize mean-field models for bond percolation and extract effective sticker interaction strengths from experimental data for specific proteins. We use graph-based Monte Carlo simulations to evaluate effects ignored by mean-field models. These include bond cooperativity defined as changes to strengths of new bonds (physical crosslinks) given the presence of a prior bond. We find that bond cooperativity fundamentally alters phase behavior, especial…
A liquid droplet impacting on a solvophobic surface normally rebounds. The rebound is suppressed by a small amount of dissolved polymer. In this work, using multi-body dissipative particle dynamics simulations, two anti-rebound mechanisms, the slow-retraction and the slow-hopping mechanisms, are identified. Which of them dominates depends on the polymer-surface attraction strength. However, these two mechanisms are not excluding each other but may coexist. During the droplet rebound, the surface-adsorbed polymer acts in two ways: the adsorbed beads mediate solvent-surface interactions, and hig…
A small amount of polymer dissolved in a droplet suppresses droplet rebound when it impinges on a supersolvophobic surface. This work investigates impacting dynamics of a droplet of dilute polymer solution depending on the molecular weight and the concentration of the polymer by using multi-body dissipative particle dynamics simulations. Either the longer polymer or the high polymer concentration suppresses rebound of a droplet although its shear viscosity and the liquid-vapor surface tension are not different from those of a pure solvent droplet. We found a new mechanism of the anti-rebound i…
The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer de…
We study the influence of chain stiffness on droplet flow in a nano-channel, coated with semiflexible hydrophobic polymers by means of non-equilibrium molecular-dynamics simulations. The studied system is then a moving droplet in the slit channel, coexisting with its vapor and subjected to periodic boundary conditions in the flow direction. The polymer chains, grafted by the terminal bead to the confining walls, are described by a coarse-grained model that accounts for chain connectivity, excluded volume interactions and local chain stiffness. The rheological, frictional and dynamical properti…
Dried droplets of polymer solutions of different molecular weights and concentrations leave various types of 'coffee-ring' patterns. These patterns are consequence of contact line motion. We have observed for very low molecular weight the droplet periphery part contains spheroidal structures whereas central part contains continuous layer. For higher molecular weight contact line exhibits 'stick-slip' motion. Whereas for very high molecular weight contact line delays enough to start motion and finally moves uninterruptedly leaving a continuous layer of polymer. We have explained this phenomena …
We report observations of weird but interesting phenomenon from the molecular dynamics simulations, occurrence of second blows in the head-on collisions of two equal-sized spherical nano polymer droplets. In the head-on collisions, we usually expect a single peak of impact forces between two colliding droplets. But, in the simulations, the second peak of the impact forces is actually observed. Its underlying mechanisms at the molecular scale are also proposed.
We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core--shell structures (with the short polymers forming the shel…
Phase separated macromolecules play essential roles in many biological and synthetic systems. Physical characterization of these systems can be challenging because of limited sample volumes, particularly for phase-separated proteins. Here, we demonstrate that a classic method for measuring the surface tension of liquid droplets, based on the analysis of the shape of a sessile droplet, can be effectively scaled down for this application. The connection between droplet shape and surface tension relies on the density difference between the droplet and its surroundings. This can be determined with…
An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or `colloidomers'. The distribution of cluster sizes is consistent with a polymerization process in which the droplets achieve their prescribed valence. Conformational dynamics reveals that the chains are freely-jointed, such that the end-to-end length scales with the number of bonds $N$ as $N^ν$, where $ν\approx3/4$, in agreement with the Flory theory in 2D. The chain diffusion coefficient $D$ ap…
Nature is remarkably adept at using interfaces to build structures, encapsulate reagents, and regulate biological processes. Inspired by Nature, we describe flexible polymer-based ribbons, termed "mesoscale polymers" (MSPs), to modulate interfacial interactions with liquid droplets. This produces unprecedented hybrid assemblies in the forms of flagellum-like structures and MSP-wrapped droplets. Successful preparation of these hybrid structures hinges on interfacial interactions and tailored MSP compositions, such as MSPs with domains possessing distinctly different affinity for fluid-fluid int…
The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation o…
The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time $τ…
Using Molecular Dynamics simulations of a coarse-grained polymer liquid we investigate the transport of droplets on asymmetrically structured (saw-tooth shaped), vibrating substrates. Due to a continuous supply of power by substrate vibrations and the asymmetry of its topography, the droplets are driven in a preferred direction. We study this directed motion as a function of the size of the droplets, the linear dimensions of the substrate corrugation, and the period of vibrations. Two mechanisms of driven transport are identified: (i) one that relies on the droplet's contact lines and (ii), in…
The spreading of polymer droplets is studied using molecular dynamics simulations. To study the dynamics of both the precursor foot and the bulk droplet, large drops of ~200,000 monomers are simulated using a bead-spring model for polymers of chain length 10, 20, and 40 monomers per chain. We compare spreading on flat and atomistic surfaces, chain length effects, and different applications of the Langevin and dissipative particle dynamics thermostats. We find diffusive behavior for the precursor foot and good agreement with the molecular kinetic model of droplet spreading using both flat and a…
Microcapsules allow for the controlled containment, transport, and release of cargoes ranging from pharmaceuticals to fragrances. Given the interest from a variety of industries in microcapsules and other core-shell structures, a multitude of fabrication strategies exist. Here, we report on a method relying on a mixture of temperature-responsive microgel particles, poly(N-isopropylacrylamide) (pNIPAM), and a polymer which undergo fluid-fluid phase separation. At room temperature this mixture separates into colloid-rich (liquid) and colloid-poor (gas) fluids. By heating the sample above a criti…
The dynamic behavior of a partially wetting polymer droplet driven over a nanostructured interface is studied using molecular dynamics simulations. We consider the bead-spring model to represent a polymeric liquid that partially wets a rough surface composed of a periodic array of spherical particles. It is shown that at sufficiently small values of the external force, the droplet remains pinned at the particles' surface, while above the threshold, its motion consists of alternating periods of pinning and rapid displacements between neighboring particles. The latter process involves large peri…
The spreading of one- and two-component polymer nanodroplets is studied using molecular dynamics simulation in a cylindrical geometry. The droplets consist of polymer chains of length 10, 40, and 100 monomers per chain described by the bead-spring model spreading on a flat surface with a surface-coupled Langevin thermostat. Each droplet contains ~350,000 monomers. The dynamics of the individual components of each droplet are analyzed and compared to the dynamics of single component droplets for the spreading rates of the precursor foot and bulk croplet, the time evolution of the contact angle,…
We perform simulations of a system containing simple model proteins and a polymer representing chromatin. We study the interplay between protein-protein and protein-chromatin interactions, and the resulting condensates which arise due to liquid-liquid phase separation, or a via a 'bridging-induced attraction' mechanism. For proteins which interact multivalently, we obtain a phase diagram which includes liquid-like droplets, droplets with absorbed polymer, and coated polymer regimes. Of particular interest is a regime where protein droplets only form due to interaction with the polymer; here, u…
We consider concentration dependence of rheological properties of associative telechelic polymer solutions. Experimental results for model telechelic polymer solutions show rather strong concentration dependence of rheological properties. For solutions with relatively high concentrations, linear viscoelasticity deviates from the single Maxwell behavior. The concentration dependence of characteristic relaxation time and moduli is different in high and low concentration cases. These results suggest that there are two different concentration regimes. We expect that densely connected (well percola…
Using a coarse-grained bead-spring model of flexible polymer chains, the structure of a polymeric nanodroplet adsorbed on a chemically decorated flat wall is investigated by means of Molecular Dynamics simulation. We consider sessile drops on a lyophilic (attractive for the monomers) region of circular shape with radius R_D while the remaining part of the substrate is lyophobic. The variation of the droplet shape, including its contact angle, with R_D is studied, and the density profiles across these droplets also are obtained. In addition, the interaction of droplets adsorbed on two walls for…
The concept of network immunity, i.e., the robustness of the network connectivity after a random deletion of edges or vertices, has been investigated in biological or communication networks. We apply this concept to a self-assembling, physical network of microemulsion droplets connected by telechelic polymers, where more than one polymer can connect a pair of droplets. The gel phase of this system has higher immunity if it is more likely to survive (i.e., maintain a macroscopic, connected component) when some of the polymers are randomly degraded. We consider the distribution $p(σ)$ of the num…
The formation of (bio)molecular condensates via liquid-liquid phase separation in cells has received increasing attention, as these coacervates play important functional and regulatory roles within biological systems. However, the majority of studies focused on the behavior of pure systems in bulk solutions, thus neglecting confinement effects and the interplay between the numerous molecules present in cells. To advance our knowledge, we perform simulations of binary polymer mixtures in droplets, considering both monodisperse and polydisperse molecular weight distributions for the longer polym…
The effect of viscoelasticity on sprays produced from agricultural flat fan nozzles is investigated experimentally using dilute aqueous solutions of polyethylene oxide (PEO). Measurements of the droplet size distribution using laser diffraction reveal that polymer addition to water results in the formation of overall bigger droplets with a broader size distribution. The median droplet size $D_{50}$ is found to increase linearly with the extensional relaxation time of the liquid. The non-dimensional median droplet sizes of different polymer solutions, sprayed at different operating pressures fr…
Effect of distribution of stickers along the backbone on structural properties in associating polymer solutions is studied using self-consistent field lattice model. Only two inhomogeneous morphologies, i.e., microfluctuation homogenous (MFH) and micelle morphologies, are observed. If the system is cooled, the solvent content within the aggregates decreases. When the spacing of stickers along the backbone is increased the temperature-dependent range of aggregation in MFH morphology and half-width of specific heat peak for homogenous solutions-MFH transition increase, and the symmetry of the pe…
The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in the so-called 'blob model', which incorporates the solvent in an implicit way. The next step is the study of a metastable droplet phase formed by imposing a chemical potential different from that at coexistence. The pressure difference across the curved interface, which corresponds to this higher chemical potential, is used to calculate the curvature propertie…
Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data co…
Polymer-Regulated Freezing of Water Droplets Revealed by Synchrotron X-ray Imaging and Raman Spectroscopy
Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）；Korea Polar Research Institute (KOPRI)（韩国极地研究所）；Pohang Accelerator Laboratory, Pohang University of Science and Technology (POSTECH)（浦项科技大学波项加速器实验室）；UNIST Research Center for Soft and Living Matter, Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院软体与生命物质研究中心）
Evaporation of water droplets deposited on metal and polymer substrates was studied. The evaporated droplet demonstrates different behaviors on low-pinning (polymer) and strong-pinning (metallic) surfaces. When deposited on polymer surfaces, the evaporated droplet is featured by stick-slip sliding, whereas on strong-pinning metallic surfaces it does not show such kind of motion and demonstrates the giant contact-angle hysteresis. Stick-slip motion of droplets is described satisfactorily by the Shanahan-Sefiane model relating this kind of motion to surmounting potential barriers caused by the p…
Droplet deposition after impact on superhydrophobic surfaces has been an important area of study in recent years due to its potential application in reduction of pesticides usage. Minute amounts of long chain polymers added to water has been known to arrest the droplet rebound effect on superhydrophobic surfaces. Previous studies have attributed different reasons like extensional viscosity, dominance of elastic stresses or slowing down of contact line in retraction phase due to stretching of polymer chains. The present study attempts to unravel the existence of critical criteria of polymer con…
From biological tissues to layers of paint, macroscopic non-porous materials with the capacity to swell when brought in contact with an appropriate solvent are ubiquitous. Here, we study experimentally and theoretically one of the conceptually simplest of such systems, the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental setup, we observe fast absorption leading to a radially spreading axisymmetric blister. Employing a linear poroelastic framework and thin-layer scalings, we develop a non-linear one-dimensional diffusion equation for the evolution of the b…
In this paper we examine the effective interactions introduced between the droplets of an oil in water microemulsion upon progressive addition of hydrophobically modified water soluble poly(ethylene oxide)-PEO using essentially small angle neutron scattering. To discuss the relative importance of decoration and bridging of the droplets we compare analogous samples with addition of a PEO grafted at both extremities with hydrophobic C12H 25 chains (PEO-2m) or addition of a PEO grafted at one extremity only with a C12H 25 chain (PEO-m). PEO-m or PEO-2m adsorb onto the droplets via their hydrophob…
The present article highlights the role of non-Newtonian (elastic) effects on the droplet impact phenomenology at temperatures considerably higher than the boiling point, especially at or above the Leidenfrost regime. The Leidenfrost point (LFP) was found to decrease with increase in the impact Weber number (based on velocity just before the impact) for fixed polymer (Polyacrylamide, PAAM) concentrations. Water droplets fragmented at very low Weber numbers (~22), whereas the polymer droplets resisted fragmentation at much higher Weber numbers (~155). We also varied the polymer concentration an…
The presence of a very small amount of high molecular weight polymer significantly delays the pinch-off singularity of a drop of water falling from a faucet, and leads to the formation of a long-lived cylindrical filament. In this paper we present experiments, numerical simulations, and theory which examines the pinch-off process in the presence of polymers. The numerical simulations are found to be in excellent agreement with experiment. As a test case, we establish the conditions under which a small bead remains on the filament; we find that this is due to the asymmetry induced by the self-s…
When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a stiffness gradient, droplets in relatively stiff regions of the network tend to dissolve, favoring growth of droplets in softer regions. Here, we show that this elastic ripening can be strong enough to reverse the direction of Ostwald ripening: large droplets can shrink to feed the growth of smaller ones. To numerically model these experiments, we generaliz…
We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behavior of biopoly…
We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and …
