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We reconsider a recently proposed design for smart responsive brushes, which is based on a conformational transition in very dilutely embedded block copolymers with a surface active block (Qi et al., Macromolecules 53, 5326, 2020). Under certain conditions, the transition acquires an unusual character: it remains very sharp, but the barrier separating the adsorbed and desorbed states disappears completely. We show that these features are very robust with respect to changing almost all system parameters: the lengths of the inert and active blocks of the minority chain, the brush length, its density, and its polydispersity. The only relevant condition is that the inert block of the minority chain is long enough to extend outside the brush density profile. We develop an analytical theory that predicts the relevant characteristics of the transition and verify it with Monte Carlo simulations. We also show that the surprising universality of the transition properties is rooted in an underlying connection to the force-induced desorption transition, which is known to combine the features of the first- and second-order transitions with a pretransition fluctuation growth accompanied by phase coexistence.

Recently, a new design for switch sensors has been proposed that exploits a conformational transition of end-grafted minority adsorption-active homopolymers in a monodisperse polymer brush [Klushin...

Biological materials, such as bones, teeth and mollusc shells, are well known for their excellent strength, modulus and toughness1–3. Such properties are attributed to the elaborate layered microstructure of inorganic reinforcing nanofillers, especially two-dimensional nanosheets or nanoplatelets, within a ductile organic matrix4–6. Inspired by these biological structures, several assembly strategies—including layer-by-layer4,7,8, casting9,10, vacuum filtration11–13 and use of magnetic fields14,15—have been used to develop layered nanocomposites. However, how to produce ultrastrong layered nanocomposites in a universal, viable and scalable manner remains an open issue. Here we present a strategy to produce nanocomposites with highly ordered layered structures using shear-flow-induced alignment of two-dimensional nanosheets at an immiscible hydrogel/oil interface. For example, nanocomposites based on nanosheets of graphene oxide and clay exhibit a tensile strength of up to 1,215 ± 80 megapascals and a Young’s modulus of 198.8 ± 6.5 gigapascals, which are 9.0 and 2.8 times higher, respectively, than those of natural nacre (mother of pearl). When nanosheets of clay are used, the toughness of the resulting nanocomposite can reach 36.7 ± 3.0 megajoules per cubic metre, which is 20.4 times higher than that of natural nacre; meanwhile, the tensile strength is 1,195 ± 60 megapascals. Quantitative analysis indicates that the well aligned nanosheets form a critical interphase, and this results in the observed mechanical properties. We consider that our strategy, which could be readily extended to align a variety of two-dimensional nanofillers, could be applied to a wide range of structural composites and lead to the development of high-performance composites. Layered nanocomposites fabricated using a continuous and scalable process achieve properties exceeding those of natural nacre, the result of stiffened matrix polymer chains confined between highly aligned nanosheets.

By performing coarse-grained molecular dynamics simulations, we study the effect of crosslinking and chain uncrossability on the microphase behaviors and mechanical properties of the double-network gels. The double-network systems can be viewed as two separate networks interpenetrating each other uniformly, and the crosslinks in each network are generated, forming a regular cubic lattice. The chain uncrossability is confirmed by appropriately choosing the bonded and nonbonded interaction potentials. Our simulations reveal a close relation between the phase and mechanical properties of the double-network systems and their network topological structures. Depending on the lattice size and the solvent affinity, we have observed two different microphases: one is the aggregation of solvophobic beads around the crosslinking points, which leads to locally polymer-rich domains, and the other is the bunching of polymer strands, which thickens the network edges and thus changes the network periodicity. The former is a representation of the interfacial effect, while the latter is determined by the chain uncrossability. The coalescence of network edges is demonstrated to be responsible for the large relative increase in the shear modulus. Compressing and stretching induced phase transitions are observed in the current double-network systems, and the sharp discontinuous change in the stress that appears at the transition point is found to be related to the bunching or debunching of the network edges. The results suggest that the regulation of network edges has a strong influence on the network mechanical properties.

Within the framework of a dynamic self-consistent field theory, we study the effect of the correlations in a small scale on polymer dynamics, adopting the semiflexible homopolymer blends as the model system. This is accomplished by taking the pair correlation function of ideal semiflexible chains as the Onsager coefficient and the Debye function as an approximation to the Onsager coefficient. Relying on the difference of the two pair correlation functions in the small-scale region, we can identify the effect of small-scale correlations. In the equilibrium state, with the chain length growing, the interface width has a continuous transition from the contour length to radius of gyration. The investigation of interfacial evolution and chain orientation reveals that strong small-scale correlations would accelerate the small-scale dynamic process. We also expect that such a small-scale effect should be highlighted in the process where microscopic phase separation happens.

Using self-consistent field theory, we investigate the stretching-induced microphase separation in an irreversibly cross-linked polymer network composed of diblock copolymer chains and estimate its...

Nanocomposite fibers have attracted intensive attentions owing to their promising applications in various fields. However, the fabrication of nanocomposite fibers with super toughness and strong strength under mild conditions remains a great challenge. Here we present a facile flow-induced assembly strategy for the development of super-tough and strong nanocomposite fibers with highly ordered carbon nanotubes (CNTs), which can be induced by directional and fast flow on a grooved hydrogel surface. The prepared nanocomposite fibers show excellent mechanical properties, with a tensile strength up to 643± 27 MPa and toughness as high as 77.3±3.4 MJ m−3 at ultimate strain of 14.8±1.5%. This versatile and efficient flow-induced alignment strategy represents a promising direction for the development of high-performance nanocomposites for practical applications.

Energy-dissipation elastomers relying on their viscoelastic behavior of chain segments in the glass transition region can effectively suppress vibrations and noises in various fields, yet the operating frequency of those elastomers is difficult to control precisely and its range is narrow. Here, we report a synergistic strategy for constructing polymer-fluid-gels that provide controllable ultrahigh energy dissipation over a broad frequency range, which is difficult by traditional means. This is realized by precisely tailoring the relaxation of confined polymer fluids in the elastic networks. The symbiosis of this combination involves: elastic networks forming an elastic matrix that displays reversible deformation and polymer fluids reptating back and forth to dissipate mechanical energy. Using prototypical poly (n-butyl acrylate) elastomers, we demonstrate that the polymer-fluid-gels exhibit a controllable ultrahigh energy-dissipation property (loss factor larger than 0.5) with a broad frequency range (10−2 ~ 108 Hz). Energy absorption of the polymer-fluid-gels is over 200 times higher than that of commercial damping materials under the same dynamic stress. Moreover, their modulus is quasi-stable in the operating frequency range., In most cases the frequency range of a damping material is adapted to a specific application. Huang et al. design a gel filled with a polymeric fluid that bypasses this problem and offers an unusually broad window over which vibrational energy is effectively dissipated.

Using self-consistent field calculations, we examine the effect of brush polydispersity on conformational transitions of single adsorption-active diblock copolymer chains embedded in inert polydisperse brushes. To represent the polydispersity, we adopt the continuous Schulz–Zimm chain length distributions, and three typical distributions are chosen such that a wide range of polydispersity is covered. A phase diagram of the diblock copolymer switches has been constructed showing that the first order phase transitions occupy a larger space in the case of polydisperse brushes. We further characterize these first order phase transitions by specifying their transition points, transition widths and transition barriers, where the latter two are particularly important as they determine the performance of the polymer switches. Our calculation indicates that polydispersity has different effect on the switching behavior depending on the lengths of both the active block and the inert block of the copolymer switch chain. In general, polydispersity improves the switching performance in the case of short active blocks, i.e. shorter or not very longer than the average length of the brush chains, and the corresponding energy barrier is smaller than a few kBT. In contrast, monodisperse brushes have the advantages when these two blocks are particularly long, i.e., lower transition barriers and fast switching. Notably, when the inert block approaches the average length of the brush chains, the transition barrier becomes almost zero in any case for monodisperse brushes, while a large finite value is still observed for that in polydisperse brushes. The complex interplay between the brush polydispersity and the switch behavior is attributed to the wide-range repulsions generated by the polydisperse brushes.

We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of the mobility coefficient, $\Lambda(r,r')$, which relates the thermodynamic driving force on monomers at position $r'$ to the motion of monomers at position $r$. A first approach based on the Green-Kubo formalism turns out to be impractical because of a severe plateau problem. Instead, we propose to extract the mobility coefficient from an effective characteristic relaxation time of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblock copolymer melts. The DDFT results are in very good agreement with the data from corresponding fine-grained simulations., Comment: Some typos corrected compared to published version (Eqs. (32) and (38))

We study the effect of polydispersity on the compression and interpenetration properties of two opposing polymer brushes by numerical self-consistent field approach and by analytical theory. Polydispersity is represented by an experimentally relevant Schulz–Zimm chain-length distribution. We focus on three different polydispersities representing sharp, moderate, and extremely wide chain length distributions and derive approximate analytical expressions for the pressure–separation curves, Π(D). We study the brush interpenetration and quantify it in terms of the overlap integral, Γ, representing the number of interbrush contacts, and interpenetration length, δ. For the case of moderate densities where the equation of state is dominated by the second virial term with coefficient υ, we demonstrate that the pressure, the overlap integral, and the interpenetration length are related by a simple equation, Π/kBT = υΓ/δ, where kBT represents the thermal energy. We propose a scaling form for δ(D) for the three poly...

Macromolecules densely end-grafted to a planar solid surface form a polymer monolayer (brush). It is known that, in a good solvent, the density profile of monodisperse brushes parabolically decays on moving away from the plane. Using the analytical theory and computer simulation methods, we studied the structure of a polydisperse brush from homopolymers, for which molecular-mass distribution is set by the Schulz–Zimm distribution. It is found that, at a polydispersity index of 1.143, the polymer brush in a good solvent has a linear density profile. In this brush, the average distance of chain ends to the grafting plane is proportional to the square of their contour length. If any chain of the brush is chemically modified so that it will be able to adsorb on the grafting surface, then the adsorption of this chain inside the brush will proceed via a discontinuous first-order phase transition with the bimodal distribution of the order parameter (free end height). This transition has unusual features: the energy of adsorption corresponding to the midpoint of the transition is proportional to the contour length of the adsorbing chain N, the sharpness of the transition is proportional to N2, and the height of the barrier separating adsorbed and desorbed states is proportional to N3. The predicted dependences are verified by computer simulation.

Using self-consistent field theory, we study the effect of reversible cross-linking on the nucleation behavior of a binary polymer blend where only one of the components is able to form cross-links. To control the total number of cross-links and their distribution, we introduce a position-dependent cross-linking probability function that is characterized mainly by two parameters, the magnitude and the width. In the weakly cross-linked region, where the product of the magnitude and width, I, is small, the nucleation behavior is classical-like and the profile of the free energy excess is unimodal. In contrast, in the strongly cross-linked region, the profile of the free energy excess becomes bimodal, and the free energy minimum specifies a metastable nucleus. In a certain I, the free energy barrier for the metastable nucleus turns to be negative, which means it becomes more stable. In both cases, the free energy barrier of the critical nucleus is lower than that without cross-linking, indicating that cross-linking always facilitates nucleation although the dynamic behavior may be different when a metastable nucleus is involved during the nucleation process. The free energy analysis demonstrates that the interaction energy rather than the entropy is responsible for the properties of the critical nucleus. Our study provides an easy alternative way for the control of the nucleation behavior and may attract practical interest.

Dynamic density functionals (DDFs) are popular tools for studying the dynamical evolution of inhomogeneous polymer systems. Here, we present a systematic evaluation of a set of diffusive DDF theories by comparing their predictions with data from particle-based Brownian dynamics (BD) simulations for two selected problems: Interface broadening in compressible A/B homopolymer blends after a sudden change of the incompatibility parameter, and microphase separation in compressible A:B diblock copolymer melts. Specifically, we examine (i) a local dynamics model, where monomers are taken to move independently from each other, (ii) a nonlocal "chain dynamics" model, where monomers move jointly with correlation matrix given by the local chain correlator, and (iii,iv) two popular approximations to (ii), namely (iii) the Debye dynamics model, where the chain correlator is approximated by its value in a homogeneous system, and (iv) the computationally efficient "external potential dynamics" (EPD) model. With the exception of EPD, the value of the compressibility parameter has little influence on the results. In the interface broadening problem, the chain dynamics model reproduces the BD data best. However, the closely related EPD model produces large spurious artefacts. These artefacts disappear when the blend system becomes incompressible. In the microphase separation problem, the predictions of the nonlocal models (ii-iv) agree with each other and significantly overestimate the ordering time, whereas the local model (i) underestimates it. We attribute this to the multiscale character of the ordering process, which involves both local and global chain rearrangements. To account for this, we propose a mixed local/nonlocal DDF scheme which quantitatively reproduces all BD simulation data considered here., Comment: 17 pages, 9 figures, Macromolecules, 2017

We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense such that particles can switch their level of resolution on the fly. The switching of resolution is controlled by a tuning function which can be chosen at will according to the geometry of the system. As an application, the hybrid scheme is used to study the kinetics of interfacial broadening of a polymer blend, and is validated by comparing the results to the predictions from pure Brownian dynamics and pure local dynamics calculations., Comment: 10 Pages, 5 Figures

We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable walls as particles keeping the configuration details, and chains in the bulk region as continuous density fields. Polymers can switch resolutions on the fly, controlled by an inhomogeneous tuning function. By properly choosing the tuning function, the representation of the system can be adjusted to reach an optimal balance between physical accuracy and computational efficiency. The hybrid simulation reproduces the results of a reference particle simulation and is significantly faster (about a factor of 3.5 in our application example).

We investigate the effect of polymer length dispersity on the properties of self-assembled micelles in solution by self-consistent field calculations. Polydispersity stabilizes micelles by raising the free energy barriers of micelle formation and dissolution. Most importantly, it significantly reduces the size fluctuations of micelles: Block copolymers of moderate polydispersity form more uniform particles than their monodisperse counterparts. We attribute this to the fact that the packing of the solvophobic monomers in the core can be optimized if the constituent polymers have different length., 4 main figures and 4 supplementary figures. Manuscript accepted for publication in Physical Review Materials

Hydrogels with multiscale structured surface have attracted significant attention for their valuable applications in diverse areas. However, current strategies for the design and fabrication of structured hydrogel surfaces, which suffer from complicated manufacturing processes and specific material modeling, are not efficient to produce structured hydrogel surfaces in large area, and therefore restrict their practical applications. To address this problem, a general and reliable method is reported, which relies on the interplay between polymer chain diffusion and the subsequent freezing-induced gelation and microphase separation processes. The basic idea is systematically analyzed and further exploited to manufacture gel surfaces with gradient structures and patterns through the introduction of temperature gradient and shape control of the contact area. Moreover, the formed micro/nanostructured surfaces are exemplified to work as capillary systems and thus can uplift the liquid spontaneously indicating the potential application for anti-dehydration. It is believed that the proposed facile and large-area fabrication method can inspire the design of materials with various functionalized surfaces.

We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force $F$ applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition, and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static and the dynamic behavior of chains with different length $N$ are very well described by a scaling Ansatz with the scaling parameters $(\varepsilon - \varepsilon^*) N^\phi$ (adsorption transition) and $(F-F^*) N^\nu$ (loop-stretch transition), respectively, where $\phi$ is the crossover exponent of the adsorption transition, and $\nu$ the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the Ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes., Comment: 14 pages, 10 figures

We study the effective interaction between two parallel rod-like nanoparticles in swollen and collapsed polymer brushes as a function of penetration depth by 2D self-consistent field calculations. In vertical direction, the interaction is always attractive. In lateral direction, the behavior under good and poor solvent conditions is qualitatively different. In swollen brushes (good solvent), nanoparticles always repel each other. In collapsed brushes (poor solvent), we identify two different regimes: an immersed regime, where the nanoparticles are fully surrounded by the brush, and an interfacial regime, where they are located in the interface between brush and solvent. In the immersed regime, the lateral interactions are repulsive, in agreement with previous theoretical predictions. In the interfacial regime, they are governed by the deformations of the interface and tend to be attractive. This implies that the nature of nanoparticle interactions can be manipulated by changing the solvent condition. The influence of particle size and grafting density are also briefly discussed.

Based on theoretical analysis, the effect of polydispersity on particle penetration into polydisperse polymer brushes is investigated. Three different polydispersities representing sharp, moderate, and extremely wide chain length distributions are chosen, since the corresponding explicit expressions of brush density at these polydispersities are available. To simplify the discussion, this study is restricted to spherical particles of small size which ensure that the particle insertion only causes local conformational perturbations. By analyzing the particle distribution, it is found that polydispersity always facilitates particle penetration. This prediction is confirmed by analyzing the surface fluctuations of the brushes. Interestingly, uniform scaling relations are observed for particles penetrating into monodisperse and moderately polydisperse brushes. The uniformity predicted by monodisperse and moderately polydisperse brushes originates from the same asymptotic behavior of their densities approaching the brush edge. This indicates that polydispersity brings significant influence only at high polydispersities.

We study the effect of polydispersity on the structure of polymer brushes by analytical theory, a numerical self-consistent field approach, and Monte Carlo simulations. The polydispersity is represented by the Schulz-Zimm chain-length distribution. We specifically focus on three different polydispersities representing sharp, moderate and extremely wide chain length distributions and derive explicit analytical expressions for the chain end distributions in these brushes. The results are in very good agreement with numerical data obtained with self-consistent field calculations and Monte Carlo simulations. With increasing polydispersity, the brush density profile changes from convex to concave, and for given average chain length $N_n$ and grafting density $\sigma$, the brush height $H$ is found to scale as $(H/H_{\mathrm{mono}}-1)\propto(N_w/N_n-1)^{1/2}$ over a wide range of polydispersity indices $N_w/N_n$ (here $H_{\mathrm{mono}}$ is the height of the corresponding monodisperse brush. Chain end fluctuations are found to be strongly suppressed already at very small polydispersity. Based on this observation, we introduce the concept of the brush as a near-critical system with two parameters (scaling variables), $(N_{n}\sigma^{2/3})^{-1}$ and $(N_w/N_n-1)^{1/2}$, controlling the distance from the critical point. This approach provides a good description of the simulation data. Finally we study the hydrodynamic penetration length $l_\mathrm{p}$ for brush-coated surfaces in flow. We find that it generally increases with polydispersity. The scaling behavior crosses over from $l_\mathrm{p}\sim N_\mathrm{n}^{1/2}\sigma^{-1/6}$ for monodisperse and weakly polydisperse brushes to $l_\mathrm{p}\sim N_{n}^{2/3}$ for strongly polydisperse brushes., Comment: 21pages, 9 figures. Accepted for publication in Macromolecues

Using a combination of analytical theory, Monte Carlo simulations, and three dimensional self-consistent field calculations, we study the equilibrium properties and the switching behavior of adsorption-active polymer chains included in a homopolymer brush. The switching transition is driven by a conformational change of a small fraction of minority chains, which are attracted by the substrate. Depending on the strength of the attractive interaction, the minority chains assume one of two states: An exposed state characterized by a stem-crown-like conformation, and an adsorbed state characterized by a flat two-dimensional structure. Comparing the Monte Carlo simulations, which use an Edwards-type Hamiltonian with density dependent interactions, with the predictions from self-consistent-field theory based on the same Hamiltonian, we find that thermal density fluctuations affect the system in two different ways. First, they renormalize the excluded volume interaction parameter $v_\mathrm{\tiny bare}$ inside the brush. The properties of the brushes can be reproduced by self-consistent field theory if one replaces $v_\mathrm{\tiny bare}$ by an effective parameter $v_{\mathrm{\tiny eff}}$, where the ratio of second virial coefficients $B_{\mathrm{\tiny eff}}/B_\mathrm{\tiny bare}$ depends on the range of monomer interactions, but not on the grafting density, the chain length, and $v_\mathrm{\tiny bare}$. Second, density fluctuations affect the conformations of chains at the brush surface and have a favorable effect on the characteristics of the switching transition: In the interesting regime where the transition is sharp, they reduce the free energy barrier between the two states significantly. The scaling behavior of various quantities is also analyzed and compared with analytical predictions., Comment: 15 pages, 14 figures

We propose a design for polymer-based sensors and switches with sharp switching transition and fast response time. The switching mechanism involves a radical change in the conformations of adsorption-active minority chains in a brush. Such transitions can be induced by a temperature change of only about ten degrees, and the characteristic time of the conformational change is less than a second. We present an analytical theory for these switches and support it by self-consistent field calculations and Brownian dynamics simulations., Highlighted as APS focus story in Physics 7, 83 (2014)

In metastable polymer blends, nonclassical critical nucleus is not a drop of stable phase in core wrapped with a sharp interface, but a diffuse structure depending on the metastability. Thus, forming a critical nucleus does not mean the birth of a new phase. In the present work, the nonclassical growing dynamics of the critical nucleus is addressed in the metastable polymer blends by incorporating self-consistent field theory and external potential dynamics theory, which leads to an intuitionistic description for the scattering experiments. The results suggest that the growth of nonclassical critical nucleus is controlled by the spinodal-decomposition which happens in the region surrounding the nucleus. This leads to forming the shell structures around the nucleus.

Based on a modified expression of the rate of the convective constraint release, we present a new contour-variable model of constitutive equations in which the non-uniform segmental stretch and the non-Gaussian chain statistical treatment of the single chain are considered to describe the polymer chain dynamics and the rheological behavior of an entangled system composed of linear polymer chains. The constitutive equations are solved numerically in the cases of steady shear and transient start-up of steady shear. The results indicate that the orientation and stretch, as well as the tube survival probability, have strong dependence on the chain contour variable, especially in the high-shear-rate region. However, the inclusion of the non-uniform features in the constitutive models has little modification comparing with the uniform models in determining the rheological properties both qualitatively and quantitatively., 26 pages, 13 figures

The formation of interface from an initial sharp interface in polydisperse A/B blends is studied using the external potential dynamic method. The present model is a nonlocal coupling model as we take into account the correlation between segments in a single chain. The correlation is approximately expressed by Debye function and the diffusion dynamics are based on the Rouse chain model. The chain length distribution is described by the continuous Schulz distribution. Our numerical calculation indicates that the broadening of interface with respect to time obeys a power law at early times, and the power law indexes are the same for both monodisperse and polydisperse blend. The power law index is larger than that in the local coupling model. However there is not a unified scaling form of the broadening of the interface width if only the interfacial width at equilibrium is taken into account as the characteristic length of the system, because the correlation makes an extra characteristic length in the system, and the polydispersity is related to this length., Comment: 15 pages, 5 figures

The effect of polydispersity on nucleation in a metastable mixture of polydisperse polymer A and monodisperse polymer B is studied using self-consistent field theory. We adopt the continuous Schulz chain length distribution to describe the polydispersity of species A. The results show that the free energy barrier, as well as many other properties of the critical nucleus, is sensitive to the polydispersity, especially in the highly polydisperse case. This should be attributed to the fact that longer chains have stronger tendencies toward nucleation. As a result, the distribution of the volume fraction as a function of chain length in the nucleus becomes different from that in the bulk. The chain length, which corresponds to the maximum contribution to the volume fraction in the nucleus, becomes larger than the number-average chain length. Meanwhile, the interface between the critical nucleus and the parent metastable bulk phase broadens. This phenomenon is obvious when the polydispersity is high.