Joint Experimental and Theoretical Study on Deposition Morphologies in Polymer Sessile Droplets.

Although past experimental and theoretical research has made substantial progress in understanding evaporation behaviors in various suspensions, the fundamental mechanism for polymer sessile droplets is still lacking. One critical effect is the molecular weight on the evaporation behaviors. Here, systematic experiments are carried out to investigate the evaporation behavior of polymer droplets under the effects of polymer concentration, evaporation rate, and especially molecular weight. We obtain polymer films with various morphologies with molecular weights ranging from 2 orders of magnitude to 4 orders of magnitude and polymer concentration across 4 orders of magnitude. We further develop a theoretical model based on the Onsager principle to explain the evaporation mechanism from a dynamic perspective. Analysis indicates that increasing molecular weight or polymer concentration enhances the contact angle hysteresis and slows down the evaporation, resulting in the transition from multiring to coffee ring and eventually to uniform films. The findings offer a guideline for achieving the desired deposition patterns via droplet processing techniques.

Accelerating the stimuli-responsive bending of a gel using mechanical constraints.

Gel bends in response to external stimuli, which has important technical applications ranging from artificial muscle to drug delivery. Here, we predict a simple and effective method to accelerate the bending of gel using mechanical constraints. We propose an exact theory of the bending dynamics of gel, which gives analytical solutions for the time evolution of the gel curvature and the relaxation time with which the system approaches to its final equilibrium state. The theory shows that the relaxation time of a slender gel confined between two parallel and rigid plates is smaller than it of a free gel with no constraints, indicating that gel bends faster when swollen in the direction parallel to the two confined plates by adding more mechanical constraints. The advantages of this new method is no need to change the microstructure and components of gel itself as previous methods. This finding brings valuable approach in designing soft robotics and healthcare devices, and is subject to experimental test.

The Process-Directed Self-Assembly of Block Copolymer Particles.

The kinetic paths of structural evolution and formation of block copolymer (BCP) particles are explored using dynamic self-consistent field theory (DSCFT). It is shown that the process-directed self-assembly of BCP immersed in a poor solvent leads to the formation of striped ellipsoids, onion-like particles and double-spiral lamellar particles. The theory predicts a reversible path of shape transition between onion-like particles and striped ellipsoidal ones by regulating the temperature (related to the Flory-Huggins parameter between the two components of BCP, χAB ) and the selectivity of solvent toward one of the two BCP components. Furthermore, a kinetic path of shape transition from onion-like particles to double-spiral lamellar particles, and then back to onion-like particles is demonstrated. By investigating the inner-structural evolution of a BCP particle, it is identified that changing the intermediate bi-continuous structure into a layered one is crucial for the formation of striped ellipsoidal particles. Another interesting finding is that the formation of onion-like particles is characterized by a two-stage microphase separation. The first is induced by the solvent preference, and the second is controlled by the thermodynamics. The findings lead to an effective way of tailoring nanostructure of BCP particles for various industrial applications.

Evaporation Dynamics of Sessile Droplets: The Intricate Coupling of Capillary, Evaporation, and Marangoni Flow.

A single-component droplet placed on a completely wetting substrate shows a pseudostable apparent contact angle (θapp) during evaporation. We propose a simple theory to explain the phenomenon accounting for the liquid evaporation and the internal flow induced by the capillary and Marangoni effects. The theory predicts that when evaporation starts, the contact angle approaches to θapp in a short time τs, remains constant for most of the time of evaporation, and finally increases rapidly when the droplet size becomes very small. This explains the behavior observed for alkane droplets. Analytical expressions are given for the apparent contact angle θapp and the relaxation time τs, which predict how they change when the evaporation rate, droplet size, and other experimental parameters such as thermal conductivity of the substrate are changed.

The contact angle of an evaporating droplet of a binary solution on a super wetting surface.

We study the dynamics of the contact angle of a droplet of a binary solution evaporating on a super wetting surface. Recent experiments have shown that although the equilibrium contact angle of such a droplet is zero, the contact angle can show complex time dependence before reaching the equilibrium value. We analyse such phenomena by extending our previous theory for the dynamics of an evaporating single component droplet to a double component droplet. We show that the time dependence of the contact angle can be quite complex. Typically, it first decreases slightly, and then increases and finally decreases again. Under certain conditions, we find that the contact angle remains constant over a certain period of time during evaporation. We study how the plateau or peak contact angle depends on the initial composition and the humidity. This theory explains the experimental results reported previously.

Formation of Deposition Patterns Induced by the Evaporation of the Restricted Liquid.

Evaporation-induced self-assembly of colloids or suspensions has received increasing attention. Given its critical applications in many fields of science and industry, we report deposition patterns constructed by the evaporation of the restricted aqueous suspension with polystyrene particles at different substrate temperatures and geometric container dimensions. With the temperature increases, the deposition patterns transition from honeycomb to multiring to island, which is attributed to the competition between the particle deposition rate UP and the contact line velocity UCL, and the dimension of the geometric container has an effect on the characteristics of patterns. In this paper, the formation of an ordered multiring pattern is mainly focused on as a result of UP keeping up with UCL such that the entire contact line can be pinned, that is, the periodic stick-slip motion of the contact line and the particle sedimentation. Moreover, based on the Onsager principle, we develop a theoretical model to reveal the physical mechanisms behind the multiring phenomena. The position and spacing of rings are measured, which shows that the theoretical prediction agrees well with experiments. We also find that the ring spacing decays exponentially from center to edge experimentally and theoretically. This may not only help us to understand the formation of the deposition patterns but also assist future design and control in practical applications.

Drying Droplets with Soluble Surfactants.

We propose a theory for the drying of liquid droplets of surfactant solutions. We show that the added surfactant hinders droplet receding and facilitates droplet spreading, causing a complex behavior of the contact line of an evaporating droplet: the contact line first recedes, then advances, and finally recedes again. We also show that the surfactant can change the deposition pattern from mountain-like to volcano-like and then to coffee-ring-like. Specially, when the contact line motion undergoes a clear receding-advancing transition, a two-ring pattern is formed. The mechanism of the two-ring formation is different from the stick-slip mechanism proposed previously and may be tested experimentally.

Vapor-induced motion of two pure liquid droplets.

The movement of evaporating liquid droplets on a surface can be triggered by the Marangoni effect arising from heterogeneities in the surface tension or a gradient in the surface energy of the substrate. Here, we show that, on a high energy surface that remains uniform, the motion of two pure liquid droplets can be induced by a gradient in the liquid vapor resulting from evaporation. The droplets always attract each other, moving from the high evaporation side to the low evaporation side, to reduce energy dissipation. By varying the volume of the droplets or the distance between droplets, the motion of the droplets can be effectively controlled.

Multi-ring Deposition Pattern of Drying Droplets.

We propose a theory for the multi-ring pattern of the deposits that are formed when droplets of the suspension are dried on a substrate. Assuming a standard model for the stick-slip motion of the contact line, we show that as droplets evaporate many concentric rings of deposits are formed but are taken over by a solid-circle pattern in the final stage of drying. An analytical expression is given to indicate when the ring pattern changes to a solid-circle pattern during the evaporation process. The results are in qualitative agreement with existing experiments, and the other predictions on how the evaporation rate, droplet radius, and receding contact angle affect the pattern are all subject to an experimental test.

Translocation of a vesicle through a narrow hole across a membrane.

We study the translocation process of a vesicle through a hole in a solid membrane separating two chambers by using the Onsager principle. By considering the stretching energy of the vesicle and the driving force due to pressure difference, we derive a free energy that shows clearly a decrease in the energy barrier as the pressure difference between two sides of the membrane increases. The difference between the reaction path obtained from the string method and the actual kinetic paths obtained from the Onsager principle is discussed when the friction parameter changes. The translocation time decreases as the pressure difference increases or the initial size of the vesicle decreases.

Vapor-Induced Motion of Liquid Droplets on an Inert Substrate.

Evaporating droplets are known to show complex motion that has conventionally been explained by the Marangoni effect (flow induced by the gradient of surface tension). Here, we show that the droplet motion can be induced even in the absence of the Marangoni effect due to the gradient of the evaporation rate. We derive an equation for the velocity of a droplet subject to the nonuniform evaporation rate and nonuniform surface tension placed on an inert substrate, where the wettability is uniform and unchanged. The equation explains the previously observed attraction-repulsion-chasing behaviors of evaporating droplets.

Deposition Patterns of Two Neighboring Droplets: Onsager Variational Principle Studies.

When two droplets containing nonvolatile components are sitting close to each other, asymmetrical ring-like deposition patterns are formed on the substrate. We propose a simple theory based on the Onsager variational principle to predict the deposition patterns of two neighboring droplets. The contact line motion and the interference effect of two droplets are considered simultaneously. We demonstrate that the gradients of evaporation rate along two droplets is the main reason for forming asymmetrical deposition patterns. By tracing the relative motion between the contact line and the solute particles, we found that the velocities of solute particles have no cylindrical symmetry anymore because of the asymmetrical evaporation rate, giving the underlying mechanism of forming asymmetrical patterns. Moreover, controlling the evaporation rate combined with varying the contact line friction, fan-like and eclipse-like deposition patterns are obtained. The theoretical results of pinned contact line cases are qualitatively consistent with the pervious experimental results.

Ring to Mountain Transition in Deposition Pattern of Drying Droplets.

When a droplet containing a nonvolatile component is dried on a substrate, it leaves a ringlike deposit on the substrate. We propose a theory that predicts the deposit distribution based on a model of fluid flow and the contact line motion of the droplet. It is shown that the deposition pattern changes continuously from a coffee ring to volcanolike and to mountainlike depending on the mobility of the contact line and the evaporation rate. An analytical expression is given for the peak position of the distribution of the deposit left on the substrate.

Coherent states formulation of polymer field theory.

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.

A Unified Model for Non-Fickian Diffusion and Anomalous Swelling of Glassy Polymer Gels.

A sheet of glassy polymers placed in a solvent shows swelling behaviors quite different from that of soft polymers (rubbers and gels). (1) Non-Fickian diffusion (called case II diffusion): As solvent permeates into the sample, a sharp front is created between the swollen part and the glassy part, and it moves toward the center at constant speed. (2) Nonmonotonous swelling: The thickness of the sample first increases and then decreases toward the equilibrium value. Here we propose a theory to explain such anomalous behavior by extending the previous theory for swelling of soft gels. We regard the material as a continuum mixture of a glassy polymer network and solvent. We assume that the polymer network is a viscoelastic gel of glassy polymers, and its relaxation time depends strongly on solvent concentration. We show that this theory explains the above two characteristics of glassy polymers in a simple and unified framework. The theory predicts how the permeation speed of the solvent and the characteristic times of the swelling process depend on material parameters and experimental conditions, which can be checked experimentally.

Fabrication of heterocellular spheroids with controllable core-shell structure using inertial focusing effect for scaffold-free 3D cell culture models.

Three-dimensional (3D) cell culture models capable of emulating the biological functions of natural tissues are pivotal in tissue engineering and regenerative medicine. Despite progress, the fabrication of in vitro heterocellular models that mimic the intricate structures of natural tissues remains a significant challenge. In this study, we introduce a novel, scaffold-free approach leveraging the inertial focusing effect in rotating hanging droplets for the reliable production of heterocellular spheroids with controllable core-shell structures. Our method offers precise control over the core-shell spheroid's size and geometry by adjusting the cell suspension density and droplet morphology. We successfully applied this technique to create hair follicle organoids, integrating dermal papilla cells within the core and epidermal cells in the shell, thereby achieving markedly enhanced hair inducibility compared to mixed-structure models. Furthermore, we have developed melanoma tumor spheroids that accurately mimic the dynamic interactions between tumor and stromal cells, showing increased invasion capabilities and altered expressions of cellular adhesion molecules and proteolytic enzymes. These findings underscore the critical role of cellular spatial organization in replicating tissue functionality in vitro. Our method represents a significant advancement towards generating heterocellular spheroids with well-defined architectures, offering broad implications for biological research and applications in tissue engineering.

Zebra-Patterned Stretchable Helical Yarn for Triboelectric Self-Powered Multifunctional Sensing.

Smart textiles capable of both energy harvesting and multifunctional sensing are highly desirable for next-generation portable electronics. However, there are still challenges that need to be conquered, such as the innovation of an energy-harvesting model and the optimization of interface bonding between fibers and active materials. Herein, inspired by the spiral structure of natural vines, a highly stretchable triboelectric helical yarn (TEHY) was manufactured by twisting the carbon nanotube/polyurethane nanofiber (CNT/PU NF) Janus membrane. The TEHY had a zebra-stripe-like design that was composed of black interval conductive CNTs and white insulative PU NFs. Due to the different electron affinity, the zebra-patterned TEHY realized a self-frictional triboelectric effect because the numerous microscopic CNT/PU triboelectric interfaces generated an alternating current in the external conductive circuit without extra external friction layers. The helical geometry combined with the elastic PU matrix endowed TEHY with superelastic stretchability and outstanding output stability after 1000 cycles of the stretch-release test. By virtue of the robust mechanical and electrical stability, the TEHY can not only be used as a high-entropy mechanical energy harvester but also serve as a self-powered sensor to monitor the stretching or deforming stimuli and human physiological activities in real time. These merits manifested the versatile applications of TEHY in smart fabrics, wearable power supplies, and human-machine interactions.

Bioinspired Superhydrophobic Fibrous Materials.

Natural fibers with robust water repellency play an important role in adapting organisms to various environments, which has inspired the development of artificial superhydrophobic fibrous materials with applications in self-cleaning, antifogging, water harvesting, heat exchanging, catalytic reactions, and microrobots. However, these highly textured surfaces (micro/nanotextured) suffer from frequent liquid penetration in high humidity and abrasion-induced destruction of the local environment. Herein, bioinspired superhydrophobic fibrous materials are reviewed from the perspective of the dimension scale of fibers. First, the fibrous dimension characteristics of several representative natural superhydrophobic fibrous systems are summarized, along with the mechanisms involved. Then, artificial superhydrophobic fibers are summarized, along with their various applications. Nanometer-scale fibers enable superhydrophobicity by minimizing the liquid-solid contact area. Micrometer-scale fibers are advantageous for enhancing the mechanical stability of superhydrophobicity. Micrometer-scale conical fibrous structures endow a Laplace force with a particular magnitude for self-removing condensed tiny dewdrops in highly humid air and stably trapping large air pockets underwater. Furthermore, several representative surface modification strategies for constructing superhydrophobic fibers are presented. In addition, several conventional applications of superhydrophobic systems are presented. It is anticipated that the review will inspire the design and fabrication of superhydrophobic fibrous systems.

Enhanced Electro-actuation in Dielectric Elastomers: The Nonlinear Effect of Free Ions.

Plasticized poly(vinyl chloride) (PVC) is a jelly-like soft dielectric material that attracted substantial interest recently as a new type of electro-active polymers. Under electric fields of several hundred volt/mm, PVC gels undergo large deformations. These gels can be used as artificial muscles and other soft robotic devices, with striking deformation behavior that is quite different from conventional dielectric elastomers. Here, we present a simple model for the electro-activity of PVC gels and show a nonlinear effect of free ions on its dielectric behaviors. It is found that their particular deformation behavior is due to an electro-wetting effect and to a change in their interfacial tension. In addition, we derive analytical expressions for the surface tension as well as for the apparent dielectric constant of the gel. The theory indicates that the size of the mobile free ions has a crucial role in determining the electro-induced deformation, opening up the way to novel and innovative designs of electro-active gel actuators.

Epitaxial growth of bilayer Bi(110) on two-dimensional ferromagnetic Fe3GeTe2.

Heterostructures of two-dimensional (2D) layered materials with selective compositions play an important role in creating novel functionalities. Effective interface coupling between 2D ferromagnet and electronic materials would enable the generation of exotic physical phenomena caused by intrinsic symmetry breaking and proximity effect at interfaces. Here, epitaxial growth of bilayer Bi(110) on 2D ferromagnetic Fe3GeTe2(FGT) with large magnetic anisotropy has been reported. Bilayer Bi(110) islands are found to extend along fixed lattice directions of FGT. The six preferred orientations could be divided into two groups of three-fold symmetry axes with the difference approximately to 26°. Moreover, dI/dVmeasurements confirm the existence of interface coupling between bilayer Bi(110) and FGT. A variation of the energy gap at the edges of bilayer Bi(110) is also observed which is modulated by the interface coupling strengths associated with its buckled atomic structure. This system provides a good platform for further study of the exotic electronic properties of epitaxial Bi(110) on 2D ferromagnetic substrate and promotes potential applications in the field of spin devices.