Optimal Reactivity and Improved Self-Healing Capability of Structurally Dynamic Polymers Grafted on Janus Nanoparticles Governed by Chain Stiffness and Spatial Organization

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Entropic control of nanoparticle self-assembly through confinement

Entropy can be the sole driving force for the construction and regulation of ordered structures of soft matter systems. Specifically, under confinement, the entropic penalty could induce enhanced entropic effects which potentially generate visually ordered structures. Therefore, spatial confinement or a crowding environment offers an important approach to control entropy effects in these systems. Here, we review how spatial confinement-mediated entropic effects accurately and even dynamically control the self-assembly of nanoscale objects into ordered structures, focusing on our efforts towards computer simulations and theoretical analysis. First, we introduce the basic principle of entropic ordering through confinement. We then introduce the applications of this concept to various systems containing nanoparticles, including polymer nanocomposites, biological macromolecular systems and macromolecular colloids. Finally, the future directions and challenges for tailoring nanoparticle organization through spatial confinement-mediated entropic effects are detailed. We expect that this review could stimulate further efforts in the fundamental research on the relationship between confinement and entropy and in the applications of this concept for designer nanomaterials.

Entropy-Driven Self-Healing of Metal Oxides Assisted by Polymer-Inorganic Hybrid Materials

Enabling self-healing of materials is crucially important for saving resources and energy in numerous emerging applications. While strategies for the self-healing of polymers are advanced, mechanisms for semiconducting inorganic materials are scarce due to the lack of suitable healing agents. Here a concept for the self-healing of metal oxides is developed. This concept consists of metal oxide nanoparticle growth inside the bulk of halogenated polymers and their subsequent entropy-driven migration to externally induced defect sites, leading to recovery of the defect. Herein, it is demonstrated that the pool of self-healing materials is expanded to include semiconductors, thereby increasing the reliability and sustainability of functional materials through the use of metal oxides. It is revealed that electrical properties of tin-doped indium oxide can be partially restored upon healing. Such properties are of immediate interest for the further development of transparent flexible electrodes.

Enhanced Heterogeneous Diffusion of Nanoparticles in Semiflexible Networks

The transport of nanoparticles in semiflexible networks, which form diverse principal structural components throughout living systems, is important in biology and biomedical applications. By combining large-scale molecular simulations as well as theoretical analysis, we demonstrate here that nanoparticles in polymer networks with semiflexible strands possess enhanced heterogeneous diffusion characterized by more evident hopping dynamics. Particularly, the hopping energy barrier approximates to linear dependence on confinement parameters in the regime of moderate rigidity, in contrast to the quadratic dependence of both its soft and hard counterparts. This nonmonotonic feature can be attributed to the competition between the conformation entropy and the bending energy regulated by the chain rigidity, captured by developing an analytical model of a hopping energy barrier. Moreover, these theoretical results agree reasonably well with previous experiments. The findings bear significance in unraveling the fundamental physics of substance transport confined in network-topological environments and would provide an explanation for the dynamics diversity of nanoparticles within various networks, biological or synthetic.

Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

A Local-Exchange Model of Folding Chain Surface of Polymer Crystal Based on Worm-Like Chain Model within Single-Chain in Mean-Field Theory

The structure of amorphous layer of folding surface controls the properties of the polymer lamellar crystal, which consists of chains with a loop conformation. The surface tension depends on the length and the distance between two injection points of the loop which involving the reptation motion and lateral exchange motion of the stems. In the present work, a local-exchange motion model based on the worm-like chain model is developed to investigate the effects of lateral motion of stems on the release the surface tension. The optimal distance between two injection points is determined by the balance of chain bending energy and conformational entropy. The numerical results provide evidences to the adjacent re-entry model for various loop lengths. A possible explanation involving density of injection points is proposed to interpret the mechanism.

Entropy at Bio-Nano Interfaces

Entropy, one of the central concepts of thermodynamics, can be a predominant contribution to structural formation and transition. Although it is well-known that diverse forces and energies can significantly contribute to the structures and activities at bio-nano interfaces, the potential entropic contribution remains less well understood. Therefore, this review article seeks to provide a conceptual framework demonstrating that entropy can be exploited to shape the physicochemical properties of bio-nano interfaces and thereby regulate the structures, responses, and functions of biological systems. We introduce the typical types of entropy that matter at bio-nano interfaces. Moreover, some key characteristics featuring entropy at bio-nano interfaces, such as the difference between entropic force and energetic interaction and the associated implications for biomimetic research, are discussed. We expect that this review could stimulate further effort in the fundamental research of entropy in biology and in the biological applications of entropic effects in designer biomaterials.

Bistable adhesion behavior of an anisotropic particle on a sliding polymer brush

Bistable adhesion behavior of an anisotropic particle adsorbed on a sliding polymer brush was found by a single chain in mean field theory (SCMFT) study. Adjacent to the normal adhesion state at which the entropy is depressed, an additional abnormal adhesion state appears. The numerical results demonstrate that the physical mechanism of the bistable adhesion behavior is from the cooperation of the reptation motion of the sliding polymers and the rotating motion of the anisotropic particle. In the abnormal adhesion state, the orientational entropy of the anisotropic particle dominates the adhesion behavior, although the translational entropy is depressed. This bistable adhesion behavior works like a lasso rope in that the abnormal state provides a wide, sensitive, and responsive range, and the normal state furnishes stable adhesion depending on the particle anisotropy.

Optimal ligand-receptor binding for highly efficient capture of vesicles in nanofluidic transportation

Optimizing ligand-receptor binding is essential for exploiting advanced biomedical applications from targeting drug delivery to biosensing. A key challenge is how optimized ligand-receptor binding can be realized during the transport of ligand-modified soft materials through a nanofluidic channel. Here, by combining computer simulations and theoretical analysis, we report that the ligand-receptor binding and resulting capture probability of ligand-functionalized vesicles nonmonotonically depend on their some intrinsic properties, e.g., chain stiffness and vesicle rigidity, during their transport through a nanochannel with imposed Poiseuille flow. Particularly, we find that the systems with semiflexible ligand and receptor chains possess the optimal ligand-receptor binding and capture probability. An analytical model of the blob theory is developed to capture the simulation results quantitatively, leading to a mechanistic interpretation of the optimal vesicle capture based on the conformational-entropy effect. Examination of the detailed dynamics reveals the active rearrangement of ligand-receptor binding during the transport process. Furthermore, the hairy vesicle with moderate rigidity is found to display an enhanced capture probability superior to that of both its soft and hard counterparts, which is rationalized by the faster and more periodic tumbling motion of the semi-rigid vesicle. Our findings highlight that precise control of the intrinsic properties of ligands and receptors as well as the vesicle rigidity can be a versatile strategy in optimizing the ligand-receptor binding in nanofluidic transportation towards advantageous biomedical applications.

Janus Nanoparticles Enable Entropy-Driven Mixing of Bicomponent Hydrogels

Mixing incompatible polymers in water to form homogeneous hydrogels possessing both hydrophilic and lipophilic components is challenging due to high enthalpic penalty and negligible entropic gain in total Gibbs free energy. Here we performed dissipative particle dynamics simulations and machine learning to uncover the influence of Janus nanoparticles on immiscible polymer mixtures with high water content and to predict the phase behavior of bicomponent hydrogels. An intriguing transition from kinetically arrested demixing to spontaneous mixing was observed with increasing particle concentration and decreasing particle size. The analysis reveals that the mixing is driven by a significant entropic gain of small nanoparticles being well dispersed in aqueous solvent of high-volume fraction. This finding highlights an entropy-driven mixing mechanism for nanocomposite bicomponent hydrogels. Supervised machine learning algorithms were used to establish a microstructure phase diagram with respect to particle concentration and radius, in which homogeneous, percolated, clustered, and separated phases, as well as corresponding phase boundaries, were clearly identified.

Theoretical Study of the Optimal Design of a UV-Controllable Smart Surface Decorated by a Hybrid Azobenzene-Containing Polymer Layer

Although grafting polymers onto surfaces is widely suggested for designing smart systems, optimizing the performance of such systems is not simple. In this article, we investigate an azo-polymer-based smart surface using the single-chain-in-mean-field theory. Through the numerical simulations, we study the adhesion/erasion transition of the system and show that the performance of the smart surface can be characterized by the difference between the effective nanoparticle-surface interactions in the UV-on and UV-off states. Further exploring the optimization of the smart surface, we find that the distribution function of the receptor can have typical bimodal characteristics, which is crucial for optimizing the position of the azo-bond along the azo-polymer, f. Moreover, the presence of the homopolymer is also essential for the optimal performance of the smart surface, and we build a reference map for the good combinations of f and the homopolymer design f_homo.

Dissipative Particle Dynamics Simulations of a Protein-Directed Self-Assembly of Nanoparticles

Design and fabrication of multifunctional porous structures play key roles in the development of high-performance energy storage devices. Our experiments demonstrated that nanostructured porous components, such as electrodes and interlayers, generated from the protein-directed self-assembly of nanoparticles can significantly improve the battery performances. The protein-directed assembly of nanoparticles in solution is a complex process involving the complicated interactions among proteins, particles, and solvent molecules. In this paper, we investigate the effects of coating proteins and specific solvent environments on the assembled porous structures. Comprehensive dissipative particle dynamics (DPD) simulations have been implemented to explore the molecular interactions and uncover the fundamental mechanisms in a gelatin-directed self-assembly of carbon black particles under different solvent conditions. Our simulations show that compact triple-strand "rod-like" structures are formed in water while loose curved "sheet-like" structures are formed in an acetic acid/water mixture. The structural difference is mainly due to the redistribution of the charges on the gelatin side chains under specific acid-solvent conditions. The strong and flexible "sheet-like" structures lead to a homogenous porous structure with high porosity and with large functionalized surfaces. Our simulations results can reasonably explain the experimental observations; this work demonstrates the great potential of DPD as a powerful tool in guiding future experimental design and optimization.

Entropic Effects in Polymer Nanocomposites

Polymer nanocomposite materials, consisting of a polymer matrix embedded with nanoscale fillers or additives that reinforce the inherent properties of the matrix polymer, play a key role in many industrial applications. Understanding of the relation between thermodynamic interactions and macroscopic morphologies of the composites allow for the optimization of design and mechanical processing. This review article summarizes the recent advancement in various aspects of entropic effects in polymer nanocomposites, and highlights molecular methods used to perform numerical simulations, morphologies and phase behaviors of polymer matrices and fillers, and characteristic parameters that significantly correlate with entropic interactions in polymer nanocomposites. Experimental findings and insight obtained from theories and simulations are combined to understand how the entropic effects are turned into effective interparticle interactions that can be harnessed for tailoring nanostructures of polymer nanocomposites.

Morphology evolution of Janus dumbbell nanoparticles in seeded emulsion polymerization

Emulsion polymerization is a versatile approach to produce different polymeric nanoparticle morphologies, which can be useful in a variety of applications. However, the detailed mechanism of the morphology formation is not entirely clear. We study the kinetics of nanoparticle morphology evolution during a seeded emulsion polymerization using both experimental and computational tools. Lightly crosslinked polystyrene seeds were first synthesized using dispersion polymerization. Then the seed particles were swollen in tert-butyl acrylate and styrene monomers, and subsequently polymerized into nanoparticles of dumbbell and multilobe morphologies. It was discovered that both the seed and final particle morphology were affected by the methanol concentration during the seed synthesis. Systematically adjusting the methanol amount will not only yield spherical seed particles of different size, but also dumbbell particles even without the second monomer polymerization. In addition to methanol concentration, morphology can be controlled by crosslinking density. The kinetics studies revealed an interesting transition from multilobe to dumbbell geometries during the secondary polymerization. Based on the results, a nucleation-growth model has been proposed to describe the morphology evolution and verification was offered by computer simulation. The key discovery is that nanoparticle morphology can be kinetically controlled by diffusion of the protrusions on the seed particles. The condition of seed synthesis and crosslinking density will drastically change the seed and final nanoparticle morphology.

How Implementation of Entropy in Driving Structural Ordering of Nanoparticles Relates to Assembly Kinetics: Insight into Reaction-Induced Interfacial Assembly of Janus Nanoparticles

The ability to understand and exploit entropic contributions to ordering transition is of essential importance in the design of self-assembling systems with well-controlled structures. However, much less is known about the role of assembly kinetics in entropy-driven phase behaviors. Here, by combining computer simulations and theoretical analysis, we report that the implementation of entropy in driving phase transition significantly depends on the kinetic process in the reaction-induced self-assembly of newly designed nanoparticle systems. In particular, such systems comprise binary Janus nanoparticles at the fluid-fluid interface and undergo phase transition driven by entropy and controlled by the polymerization reaction initiated from the surfaces of just one component of nanoparticles. Our simulations demonstrate that the competition between the reaction rate and the diffusive dynamics of nanoparticles governs the implementation of entropy in driving the phase transition from randomly mixed phase to intercalated phase in these interfacial nanoparticle mixtures, which thereby results in diverse kinetic pathways. At low reaction rates, the transition exhibits abrupt jump in the mixing parameter, in a similar way to first-order, equilibrium phase transition. Increasing the reaction rate diminishes the jumps until the transitions become continuous, behaving as a second-order-like phase transition, where a critical exponent, characterizing the transition, can be identified. We finally develop an analytical model of the blob theory of polymer chains to complement the simulation results and reveal essential scaling laws of the entropy-driven phase behaviors. In effect, our results allow for further opportunities to amplify the entropic contributions to the materials design via kinetic control.

Interfacial Targeting of Sessile Droplets Using Electrospray

We report on the use of electrospray atomization to deliver nanoparticles and surfactant directly to the surface of sessile droplets. The particles delivered to the target droplet remained adsorbed at its interface since they arrived solvent-free. Upon complete evaporation, the interface of the target drop was mapped to the underlying substrate, forming a nanoparticle deposit. The use of electrospray permitted the exploration of the interfacial particle transport and the role of surfactants in governing particle motion and deposit structure. When no surfactant was present in the sprayed solution, there was no observable convection of the interfacial particles. When Tween 80, a high-molecular-weight surfactant, was added to the sprayed solution, the surface flow was similarly suppressed. Only when small surfactants (e.g., sodium dodecyl sulfate) were present in the sprayed solution was Marangoni flow, directed toward the droplet apex, induced at the interface. This flow drove the interfacial particles to the apex of the target droplet, creating a particle-dense region at the center of the final deposit. We found that small surfactants were capable of desorbing from the interface at a sufficiently high rate relative to the evaporation time scale of the target droplet. Once inside the drop, the desorbed surfactant was convected to the contact line where it accumulated, inducing a surface tension gradient and a solutal Marangoni flow. Numerical modeling using the lattice Boltzmann-Brownian dynamics method confirmed this mechanism of particle transport and its relationship to deposit structure. The use of sacrificial targets combined with electrospray may provide a unique capability for building colloidal monolayers with organized structure in a scalable way.

Supramolecular multicompartment gels formed by ABC graft copolymers: high toughness and recovery properties

We conceptually design multicompartment gels with supramolecular characteristics by taking advantage of amphiphilic ABC graft copolymers. The ABC graft copolymers contain a solvophilic A backbone and solvophobic B and C grafts, where the C grafts interact with each other via hydrogen bonds. The mechanical properties of supramolecular multicompartment gels under uniaxial tension are studied by coupling dissipative particle dynamics simulations with the nonequilibrium deformation technique. The results show that the supramolecular multicompartment gels exhibit high toughness and recovery properties, while their stiffness is maintained. Due to the physical origin, the superior mechanical properties of supramolecular gels have a tight relation with the structural relaxation of grafts and the association-disassociation dynamics of hydrogen bonds. In addition, the toughness of the multicompartment gels can be further tuned by adjusting the strength and directivity of the hydrogen bonds. The present work unveils the physical origin of the distinct mechanical properties of supramolecular gels, which may provide useful guidance for designing functional gels with superior toughness.

Light triggered interfacial damage self-healing of poly(p-phenylene benzobisoxazole) fiber composites

The interfacial microcracks in the resin matrix composites are difficult to be detected and repaired. However, the self-healing concept provides opportunities to fabricate composites with unusual properties. In the present study, photothermal conversion Ag-Cu₂S nanoparticles were immobilized onto poly(p-phenylene benzobisoxazole) (PBO) fibers via a polydopamine chemistry. Benefitting from the photothermal effects of Ag-Cu₂S, the obtained PBO fibers (Ag-Cu₂S-PBO) efficiently converted the light energy into heat under Xenon lamp irradiation. Then, single PBO fiber composites were prepared using thermoplastic polyurethane as the matrix. It was found that the interfacial damage caused by single fiber pull-out was simply self-healed by Xe light irradiation. This wonderful interfacial damage self-healing property was mainly attributed to the in situ heating generation via photothermal effects of Ag-Cu₂S in the composite interface. This paper reports a novel strategy to construct advanced composites with light-triggered self-healing properties, which will provide inspiration for preparing high performance composite materials.

Tailoring Interfacial Nanoparticle Organization through Entropy

The ability to tailor the interfacial behaviors of nanoparticles (NPs) is crucial not only for the design of novel nanostructured materials with superior properties and of interest for many promising applications such as water purification, enhanced oil recovery, and innovative energy transduction, but also for a better insight into many biological systems where nanoscale particles such as proteins or viruses can interact and organize at certain interfaces. As a class of emerging building blocks, Janus NPs consisting of two compartments of different chemistry or polarity are ideal candidates to generate tunable and stable interfacial nanostructures because of the asymmetric nature. However, precise control over such interfacial nanostructures toward a controllable order and even responses to various external stimuli still remains a great challenge as the interfaces do not simply serve as a scaffold but rather induce complex enthalpic and entropic interactions. In this Account, we focus on our efforts on exploiting entropy strategies based on computational design to tailor the spatial distribution and ordering of NPs at the interfaces of various systems. First, we introduce the physical principle of entropic ordering, being the theoretical basis of entropy-directed interfacial self-assembly. The typical types of entropy, which have been harnessed to manipulate the interfacial NP organization, are then summarized, including conformational entropy, shape entropy, and rotational and vibrational entropy. Next, we describe the emerging pathways in the development of novel environmentally responsive systems which involve the use of entropy to access the stimuli-responsive behaviors of interfacial nanostructures. Taking one step further, how molecular architectures can be tailored to tune the entropic contributions to the interfacial self-assembly is demonstrated, through identifying the effects of various intrinsic properties of block segments, such as chain length and stiffness, on entropy-governed precise organization of Janus NPs at block copolymer interfaces. Finally, we detail some key factors for tailoring interfacial organization through entropy. In summary, entropy strategies offer a promising and abundant framework for precisely programming the structural organization of NPs at interfaces. We discuss future directions to signify the framework in tailoring the interfacial organization of NPs. We hope that this Account will promote further efforts toward fundamental research and the wide applications of designed interfacial assemblies in new types of functional nanomaterials and beyond.

Physical principles of graphene cellular interactions: computational and theoretical accounts

Clarifying the physical principles of graphene cellular interactions is critical for the wider application of graphene-based nanomaterials in nanomedicine. This review highlights the advances in computational and theoretical accounts for this emerging field.