Stiff Polymer Networks Research Articles

Simple Approach for a Self-Healable and Stiff Polymer Network from Iminoboronate-Based Boroxine Chemistry

Despite offering robust mechanical properties, polymer networks suffer from a lack of recyclability, reshaping, and healability. Designing stiff and remendable polymer networks that can repair unde...

Tailoring the mechanical properties by molecular integration of flexible and stiff polymer networks.

Designing a multiple-network structure at the molecular level to tailor the mechanical properties of polymeric materials is of great scientific and technological importance. Through the coarse-grained molecular dynamics simulation, we successfully construct an interpenetrating polymer network (IPN) composed of a flexible polymer network and a stiff polymer network. First, we find that there is an optimal chain stiffness for a single network (SN) to achieve the best stress-strain behavior. Then we turn to study the mechanical behaviors of IPNs. The result shows that the stress-strain behaviors of the IPNs appreciably exceed the sum of that of the corresponding single flexible and stiff network, which highlights the advantage of the IPN structure. By systematically varying the stiffness of the stiff polymer network of the IPNs, optimal stiffness also exists to achieve the best performance. We attribute this to a much larger contribution of the non-bonded interaction energy. Last, the effect of the component concentration ratio is probed. With the increase of the concentration of the flexible network, the stress-strain behavior of the IPNs is gradually enhanced, while an optimized concentration (around 60% molar ration) of the stiff network occurs, which could result from the dominant role of the enthalpy rather than the entropy. In general, our work is expected to provide some guidelines to better tailor the mechanical properties of the IPNs made of a flexible network and a stiff network, by manipulating the stiffness of the stiff polymer network and the component concentration ratio.

The influence of disorder on deformations in semiflexible networks

We present a model that assesses the different elastic responses of a semiflexible network, which either (i) is constrained to deform in an affine way or (ii) is permitted to thermally fluctuate and deviate from affine response. The thermal, non-affine response of the network is achieved using a Metropolis Monte Carlo algorithm with dynamic step size. We find that non-affine deformations soften the network dramatically at low strains and make the eventual nonlinear strain stiffening far more pronounced. We show that the effect of these non-affine deformations are very sensitive to the degree variation in the lengths of filaments connecting cross-links. Where there is high variation, non-affine deformations allow internal stresses to relax, giving rise to a smaller range of tensile forces in filaments and a dramatic reduction of network stiffness. This highlights that non-affine deformations are crucial in small strain response of stiff polymer networks.

The Localization Model of Rubber Elasticity

AbstractWhile the unusual elastic properties of rubbery polymer materials have been studied for literally centuries, a quantitative theoretical description of these properties in terms of molecular structural parameters remains a challenging task. Classical network elasticity theories are based on the concept of flexible volumeless network chains fixed into a network in which there are no excluded volume, or even topological, interactions between the chains and where the chains explore accessible configurations by Brownian motion. In this type of model, the elasticity of the deformed network derives from the entropic changes in this idealized network arising from a deformation of the network junction positions. The shortcoming of this approach is clear from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to an exploration of their local molecular environments. The imposition of a deformation of these solid rubbery materials then necessitates a consideration of how local molecular packing constraints become modified under deformation and the impact of these changes on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult problem, but we focus on the simple ‘localization model’ of rubber elasticity introduced by Gaylord and Douglas (GD), which provides an attractive and mathematically simple minimal model for the network elasticity of rubbers having strong intermolecular interactions in the dense polymer state. GD assume that the network chain segments are localized at the network junctions, as in classical elasticity theory, but they also consider the chains to be localized along their contours by a local harmonic potential arising from inter‐particle packing interactions, as in atoms in a simple harmonic crystal. This is the familiar Edwards‐De Gennes ‘tube’ model of polymers in the condensed state. The existence of the tube means that the entropy of the network chains is reduced relative to chains without this constraint, but the crucial problem is how this entropy change becomes modified as the material becomes deformed. GD approach this problem by first observing that both the volume of the material and the network chains are essentially invariant under deformation so they require that the dimensions of the confining tube to also be a deformation invariant where this constraint is applied at a segmental level. The properties of the resulting ‘localization model’ of elasticity of dry and swollen rubbers are summarized and some extensions of the model to describe chain finite extensibility and stiff polymer networks are briefly summarized.

Development of minimal models of the elastic properties of flexible and stiff polymer networks with permanent and thermoreversible cross-links

We review the elasticity of flexible and stiff polymer networks with permanent cross-links and synthesize these results into a unifying polymer chain network model. This framework is then used to address how the network elasticity becomes modified when the network cross-linking is thermoreversible in nature, changes in the stability of the network with deformation, and the effect of a variable rate of network deformation on the non-linear elastic response. Comparisons are made between this class of simplified network models with elasticity measurements performed on flexible chain and stiff fiber networks, both with permanent and associative cross-links. Although these network models are highly idealized, they are apparently able to capture many aspects of the elastic properties of diverse real networks.

Effective-medium approach for stiff polymer networks with flexible cross-links

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective-medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.

Nonlinear Elasticity of Composite Networks of Stiff Biopolymers with Flexible Linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.

Nonaffine rubber elasticity for stiff polymer networks

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams, stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces ("stretching"). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of "floppy modes"-low-energy bending excitations that retain a high degree of nonaffinity. The length scale characterizing the emergent nonaffinity is given by the "fiber length" lf, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.

Large amplitude light-induced motion in high elastic modulus polymer actuators

Well-defined gradients in molecular alignment have been used as tools to generate large amplitude, light-induced deformations in stiff polymer networks. These systems are reversible, monolithic and based on a simple one-step self-assembly process. To fabricate the actuators, diacrylate dopants containing azobenzene moieties were blended with liquid crystalline diacrylate hosts and photopolymerized in a twisted configuration. The resulting twisted networks were heavily crosslinked with room temperature elastic moduli on the order of 1 GPa. Regardless of the temperature with respect to the glass transitions, subsequent exposure to UV radiation induced anisotropic expansion/contraction, and simple variations in geometry were used to generate uniaxial bending or helical coiling deformation modes. Because mechanical energy is directly related to elastic modulus, these systems are expected to provide significantly greater work output than contemporary polymer actuator materials.

Elasticity of stiff polymer networks.

We study the elasticity of a two-dimensional random network of rigid rods ("Mikado model"). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidity percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where the elasticity is dominated by bending deformations.

Transport of penetrants in the macromolecular structure of coals III. Dynamic swelling of stiff polymer networks that simulate the coal structure

AbstractThe structure of three cross‐linked polymers containing naphthalenic rings in their backbone structure was investigated by dynamic swelling and thermal analytic techniques. It was determined that the pyridine and n‐proplyamine transport in microparticles (40 μm) of these polymers was non‐Fickian, often approaching case II transport and sometimes even supercase II transport. The thermal analysis showed relatively stable structures up to about 350°C.