Elasticity Of Polymer Networks Research Articles

Influence of swelling on the elasticity of polymer networks cross-linked in the melt state: Test of the localization model of rubber elasticity.

The elasticity of polymer networks, formed by cross-linking high molecular mass polymers in the melt state and then swollen by a solvent, involves contributions from both the presence of cross-link network junctions and the interchain interactions associated with the combined effect of excluded volume interactions and topological constraints that become modified when the network is swollen. We test the capacity of the previously developed localization model of rubber elasticity, a mean field "tube model," to describe changes in elasticity observed in classical experimental studies of the mechanical properties of this type of network. In order to obtain a satisfactory comparison to the experiments, it was found to be necessary to account for the independently observed tendency of the network junctions to become localized in the network with appreciable swelling, as well as the interchain interactions emphasized in previous discussions of the localization model.

Fabrication and Photothermal Actuation Performances of Electrospun Carbon Nanotube/Liquid Crystal Elastomer Blend Yarn Actuators.

Liquid crystal elastomers (LCEs) are a kind of polymer network that combines the entropic elasticity of polymer networks and the mesogenic unit by means of mild cross-linking. LCEs have been extensively investigated in various fields, including artificial muscles, actuators, and microrobots. However, LCEs are characterized by the poor mechanical properties of the light polymers themselves. In this study, we propose to prepare a carbon nanotube/liquid crystal elastomer (CNT/LCE) composite yarn by electrospinning technology and a two-step cross-linking strategy. The CNT/LCE composite yarn exhibits a reversible shrinkage ratio of nearly 70%, a tensile strength of 16.45 MPa, and a relatively sensitive response speed of ∼3 s, enabling a fast response by photothermal actuation. The research disclosed in this article may provide new insights for the development of artificial muscles and next-generation smart robots.

Liquid crystal polymer actuators with complex and multiple actuations.

Deformable liquid crystal polymers (LCPs), which exhibit both entropic elasticity of polymer networks and anisotropic properties originating from ordered mesogens, have gained more and more interest for use as biomedical soft actuators. Especially, LCP actuators with controllable mesogen alignment, sophisticated geometry and reprogrammability are a rising star on the horizon of soft actuators, since they enable complex and multiple actuations. This review focuses on two topics: (1) the regulation of mesogen alignment and geometry of LCP actuators for complex actuations; (2) newly designed reprogrammable LCP materials for multiple actuations. First, basic actuation mechanisms are briefly introduced. Then, LCP actuators with complex actuations are demonstrated. Special attention is devoted to the improvement of fabrication methods, which profoundly influence the available complexity of the mesogen alignment and geometry. Subsequently, reprogrammable LCP actuators featuring dynamic networks or shape memory effects are discussed, with an emphasis on their multiple actuations. Finally, perspectives on the current challenges and potential development trends toward more intelligent LCP actuators are discussed, which may shed light on future investigations in this field.

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions.

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

Rubber elasticity of polymer networks in explicitly non-Gaussian states. Statistical mechanics and LF-NMR inquiry in hydrogel systems

We present a statistical mechanics theory of rubber-like elasticity in swollen and unswollen polymer networks characterized by explicitly non-Gaussian distribution functions (Laplace’s, Cauchy’s, and continuous Poisson’s in the exponential limit). An important outcome is the derivation of new families of statistical and mechanical laws, including a discussion of energy functions of strain invariants, which are reasonably simple for a model comparison with available data on polymer networks. Accordingly, a theoretical–experimental approach based on LF-NMR was devised to identify the most likely end-to-end length distribution in an arbitrary network. When this strategy is applied to agar 1 %, alginate 1 %, and scleroglucan 2 % hydrogels, it turns out that the end-to-end distribution should be never regarded as Gaussian even if, as in agar and scleroglucan systems, the normal statistics is the best among those here regarded. Remarkably, Poisson’s distribution is proved instead to be the most realistic for the alginate hydrogel.

Cytoskeleton-inspired artificial protein design to enhance polymer network elasticity.

Reducing topological network defects to enhance elasticity in polymeric materials remains a grand challenge. Efforts to control network topology, primarily focused on crosslinking junctions, continue to underperform compared to theoretical estimations from idealized networks using affine and phantom network theories. Here, artificial protein technology was adapted for the design of polymer-network hydrogels with precisely defined coil-like and rod-like strands to observe the impact of strand rigidity on the mechanical properties of polymeric materials. Cytoskeleton-inspired polymer-network hydrogels incorporated with rod-like protein strands nearly tripled the gel shear elastic modulus and relaxation time compared to coil-like protein strands, indicating an enhanced effective crosslinking density. Furthermore, asymmetric rod-coil protein designs in network strands with an optimal rod:coil ratio improved the hydrogel relaxation time, enhancing the stability of physical macromolecular associations by modulating crosslinker mobility. The careful design of strand rigidity presents a new direction to reduce topological defects for optimizing polymeric materials.

Emergence of tissue-like mechanics from fibrous networks confined by close-packed cells.

The viscoelasticity of the crosslinked semiflexible polymer networks-such as the internal cytoskeleton and the extracellular matrix-thatprovide shape and mechanical resistance against deformationis assumed to dominate tissue mechanics.However, the mechanical responses of soft tissues and semiflexible polymer gels differ in many respects. Tissues stiffen in compression but not in extension1-5, whereas semiflexible polymer networks soften in compression and stiffen in extension6,7. In shear deformation, semiflexible polymer gels stiffen with increasing strain, but tissues do not1-8. Here we use multiple experimental systems and a theoretical model to show that a combination of nonlinear polymer network elasticity and particle (cell) inclusions is essential to mimic tissue mechanics that cannot be reproduced by either biopolymer networks or colloidal particle systems alone. Tissue rheology emerges from an interplay between strain-stiffening polymer networks and volume-conserving cells within them. Polymer networks that soften in compression but stiffen in extension can be converted to materials that stiffen in compression but not in extension by including within the network either cells or inert particles to restrict the relaxation modes of the fibrous networks that surround them. Particle inclusions also suppress stiffening in shear deformation; when the particle volume fraction is low, they have little effect on the elasticity of the polymer networks. However, as the particles become more closely packed, the material switches from compression softening to compression stiffening. The emergence of an elastic response in these composite materials has implications for how tissue stiffness is altered in disease and can lead to cellular dysfunction9-11. Additionally, the findings could be used in the design of biomaterials with physiologically relevant mechanical properties.

Counting Secondary Loops Is Required for Accurate Prediction of End-Linked Polymer Network Elasticity.

To predict and understand the properties of polymer networks, it is necessary to quantify network defects. Of the various possible network defects, loops are perhaps the most pervasive and yet difficult to directly measure. Network disassembly spectrometry (NDS) has previously enabled counting of the simplest loops-primary loops-but higher-order loops, e.g., secondary loops, have remained elusive. Here, we report that the introduction of a nondegradable tracer within the NDS framework enables the simultaneous measurement of primary and secondary loops in end-linked polymer networks for the first time. With this new "NDS2.0" method, the concentration dependences of the primary and secondary loop fractions are measured; the results agree well with a purely topological theory for network formation from phantom chains. In addition, semibatch monomer addition is shown to decrease both primary and secondary loops, though the latter to a much smaller extent. Finally, using the measured primary and secondary loop fractions, we were able to predict the shear storage modulus of end-linked polymer gels via real elastic network theory (RENT).

Experimental Observation of Two Features Unexpected from the Classical Theories of Rubber Elasticity.

Although the elastic modulus of a Gaussian chain network is thought to be successfully described by classical theories of rubber elasticity, such as the affine and phantom models, verification experiments are largely lacking owing to difficulties in precisely controlling of the network structure. We prepared well-defined model polymer networks experimentally, and measured the elastic modulus G for a broad range of polymer concentrations and connectivity probabilities, p. In our experiment, we observed two features that were distinct from those predicted by classical theories. First, we observed the critical behavior G∼|p-p_{c}|^{1.95} near the sol-gel transition. This scaling law is different from the prediction of classical theories, but can be explained by analogy between the electric conductivity of resistor networks and the elasticity of polymer networks. Here, p_{c} is the sol-gel transition point. Furthermore, we found that the experimental G-p relations in the region above C^{*} did not follow the affine or phantom theories. Instead, all the G/G_{0}-p curves fell onto a single master curve when G was normalized by the elastic modulus at p=1, G_{0}. We show that the effective medium approximation for Gaussian chain networks explains this master curve.

Contribution of Entanglements to Polymer Network Elasticity

Trapped entanglements, cross-linker functionality, and elastically effective chains are the sources of elasticity of polymer networks and gels. However, despite more than 80 years of theoretical and experimental research in this field, still little is known about their relative contribution to network elasticity. In this work, we use double quantum nuclear magnetic resonance (DQ NMR) experiments to characterize the elasticity of model polymer networks prepared with cross-linkers of mixed functionality and control of structural defects. An order parameter that condensates the elastic response within the theoretical framework of the entangled phantom theory for rubber elasticity was identified. Standard lore dictates that low molecular weight precursors for the elastically active chains leads to a negligible contribution of trapped entanglements. Here we show that the contribution of trapped entanglements may equal the contribution coming from elastically active material and that it is independent of networ...

Odd–Even Effect of Junction Functionality on the Topology and Elasticity of Polymer Networks

The junction functionality of polymer networks is a key design variable to tune the material properties through changing the network connectivity. Here, we perform a Monte Carlo simulation to study the topology and elasticity of end-linked polymer networks constructed by junctions with different functionalities. The effect of junction functionality on the topological structure of the network displays both universal features and odd–even effects. For all junction functionalities, the primary loop fraction shows a linear dependence on the dimensionless product of concentration with single chain pervaded volume. The slopes of the lines exhibit strong odd–even alternation: primary loops are formed more frequently for junctions with an odd number of functional groups. The secondary loop fraction has a maximum when plotted against the normalized primary loop fraction, where the value of the maximum also shows odd–even alternation. The topological information obtained through Monte Carlo simulation is then incor...

Classical Challenges in the Physical Chemistry of Polymer Networks and the Design of New Materials.

Polymer networks are widely used from commodity to biomedical materials. The space-spanning, net-like structure gives polymer networks their advantageous mechanical and dynamic properties, the most essential factor that governs their responses to external electrical, thermal, and chemical stimuli. Despite the ubiquity of applications and a century of active research on these materials, the way that chemistry and processing interact to yield the final structure and the material properties of polymer networks is not fully understood, which leads to a number of classical challenges in the physical chemistry of gels. Fundamentally, it is not yet possible to quantitatively predict the mechanical response of a polymer network based on its chemical design, limiting our ability to understand and characterize the nanostructure of gels and rationally design new materials. In this Account, we summarize our recent theoretical and experimental approaches to study the physical chemistry of polymer networks. First, our understanding of the impact of molecular defects on topology and elasticity of polymer networks is discussed. By systematically incorporating the effects of different orders of loop structure, we develop a kinetic graph theory and real elastic network theory that bridge the chemical design, the network topology, and the mechanical properties of the gel. These theories show good agreement with the recent experimental data without any fitting parameters. Next, associative polymer gel dynamics is discussed, focusing on our evolving understanding of the effect of transient bonds on the mechanical response. Using forced Rayleigh scattering (FRS), we are able to probe diffusivity across a wide range of length and time scales in gels. A superdiffusive region is observed in different associative network systems, which can be captured by a two-state kinetic model. Further, the effects of the architecture and chemistry of polymer chains on gel nanostructure are studied. By incorporating shear-thinning coiled-coil protein motifs into the midblock of a micelle-forming block copolymer, we are able to responsively adjust the gel toughness through controlling the nanostructure. Finally, we review the development of novel application-oriented materials that emerge from our enhanced understanding of gel physical chemistry, including injectable gel hemostats designed to treat internal wounds and engineered nucleoporin-like polypeptide (NLP) hydrogels that act as biologically selective filters. We believe that the fundamental physical chemistry questions articulated in this Account will provide inspiration to fully understand the design of polymer networks, a group of mysterious yet critically important materials.

Quantifying the impact of molecular defects on polymer network elasticity.

Elasticity, one of the most important properties of a soft material, is difficult to quantify in polymer networks because of the presence of topological molecular defects in these materials. Furthermore, the impact of these defects on bulk elasticity is unknown. We used rheology, disassembly spectrometry, and simulations to measure the shear elastic modulus and count the numbers of topological "loop" defects of various order in a series of polymer hydrogels, and then used these data to evaluate the classical phantom and affine network theories of elasticity. The results led to a real elastic network theory (RENT) that describes how loop defects affect bulk elasticity. Given knowledge of the loop fractions, RENT provides predictions of the shear elastic modulus that are consistent with experimental observations.

Bending a beam by a generalized ideal elastomeric gel

A hybrid beam with a gel layer bonded on the top of an elastic non-swellable substrate has been commonly adopted to make various sensors and actuators. Usually, different models need to be developed for the hybrid beam when different gels are used in the system. In this article, based on the generalized ideal elastomeric gel model, we formulate a unified relationship between the swelling of hydrogels and the bending curvature of the elastic beam, which is independent of specific swelling mechanisms of gels. We further illustrate that the equations derived in the article can be used to validate the ideal elastomeric gel model and measure the elasticity of polymer networks of the gels.

Synthesis and Characterization of Liquid Crystal Elastomer

The thermal and mechanical properties of Liquid Crystal Elastomers (LCEs) were characterized using various techniques for understanding of their physical behavior. The material used for investigation was synthesized by us, using Finklemann procedure, with proper cross linking density in nematic phase. The material is found to have unique coupling between anisotropicorder of liquid crystal component and elasticity of polymer network. The chemical structures were confirmed by Fourier Transform Infrared (FTIR) Spectroscopy and Scanning Electron Microscopy (SEM). Fabry Perot Scattering Studies (FPSS), Thermo gravimetric Analysis (TGA) and Differential Scanning Calorimatory (DSC) were used to study thermal properties. The mechanical properties were studied using force sensor. Our investigation shows that this synthesized Liquid Crystal Elastomer has ability of spontaneous change as a function of temperature and mechanical force, which shows it as a unique class of soft material.

A Molecular Thermodynamic Model for Restricted Swelling Behaviors of Thermo-sensitive Hydrogel

A molecular thermodynamic model was developed for describing the restricted swelling behavior of a thermo-sensitive hydrogel confined in a limited space. The Gibbs free energy includes two contributions, the contribution of mixing of polymer and solvent calculated by using the lattice model of random polymer solution, and the contribution due to the elasticity of polymer network. This model can accurately describe the swelling behavior of restricted hydrogels under uniaxial and biaxial constraints by using two model parameters. One is the interaction energy parameter between polymer network and solvent, and the other is the size parameter depending on the degree of cross-linking. The calculated results show that the swelling ratio reduces significantly and the phase transition temperature decreases slightly as the restricted degree increases, which agree well with the experimental data.

Effect of swelling and deswelling on the elasticity of polymer networks in the dilute to semi-dilute region

The Obukhov model is known as the model describing the dependence of the elastic modulus of polymer networks on the concentration and solvent class. In the Obukhov model, the Panyukov model, which assumed the Hooke's law of elasticity, was adopted for describing the elastic energy of a network strand. In this study, we for the first time extended both models from the semi-dilute to concentrated region to the dilute to semi-dilute region. To evaluate the extended model, we used Tetra-PEG gel, which has near-ideal network structure, as a model system. The experimental results are well described by the extended model. It is strongly suggested that the Panyukov model and the Obukhov model are valid in dilute to semi-dilute good solvent systems.

Molecular thermodynamic model for swelling behavior and volume phase transition of multi-responsive hydrogels

A new molecular thermodynamic model for swelling behavior and volume phase transition of multi-responsive hydrogels was developed. The swelling behavior of hydrogels results from three contributions, the mixing of polymer network and solvent, the elasticity of polymer network and the ionic effect containing Donnan equilibrium of ions distributed inside and outside hydrogels and electrostatic interactions between the charges carried by the polymer network and the counter ions. Two kinds of model parameters are included; they are the interaction energy parameters between polymer network and solvent or between the two solvents, and a size parameter which is the molecular mass of the network between two cross-linking points. They should be determined from the experimental swelling curves of hydrogels. It is shown that this model can describe the swelling behavior and volume phase transitions of pH-sensitive and ion-sensitive hydrogels by using fewer model parameters comparing with other models. The different swelling behaviors such as shrinking at low pH and swelling at high pH, swelling at low pH and shrinking at high pH, shrinking at middle pH and swelling at both low pH and high pH, the swelling behaviors of pH- and temperature-sensitive hydrogels or temperature- and solvent-sensitive hydrogels, can be satisfactorily described.

Nonaffine Displacements in Flexible Polymer Networks

The validity of the affine assumption in model flexible polymer networks is explored. To this end, the displacements of fluorescent tracer beads embedded in polyacrylamide gels are quantified by confocal microscopy under shear deformation, and the deviations of these displacements from affine responses are recorded. Nonaffinity within the gels is quantified as a function of polymer chain density and cross-link concentration. Observations are compared with current theories of nonaffinity in random elastic media. We note that the mean-squared nonaffine deviation is proportional to the square of the applied strain in the linear elasticity regime, as per theoretical predictions. The measured degree of nonaffinity in the polyacrylamide gels suggests the presence of structural inhomogeneities which likely result from heterogeneous reaction kinetics during gel preparation. In addition, the macroscopic elasticity of the polyacrylamide gels is confirmed to behave in accordance with standard models of flexible polymer network elasticity.

A Hexagonal Pillar Array of Thermo-responsive Soft Actuators Prepared by Nanoimprinting

ABSTRACTThermo-responsive actuation (thermomechanical effects) based on nematic liquid crystal elastomers (LCEs) have become a research priority in the preparation of soft actuators. Nematic LCEs combine the anisotropic features of liquid crystal phases with the rubber elasticity of polymer network. When heated at nematic to isotropic phase transition temperature (N-to-I temp.), a uniaxial thermomechanical deformation of LCEs will undergo at nearly constant volume due to a change of LC director order. Recently, an array of the micro-sized LCE pillars related to such thermomechanical effects have been successfully constructed through a soft lithography technology (i.e., replica molding). The prepared LCE pillars are mono-dispersive and micro-sized. They also possess N-to-I temp. higher than 100°C, largely limiting the available application. By contrast, the present study will report a hexagonal array of nano-sized thermo-responsive pillar actuators that are able to contract and expand in response to temperature changes around a lower N-to-I temp. is manufactured via using reactive rod-like liquid crystal and ultraviolet nanoimprinting technology. According to atomic force microscope (AFM) observation, a hexagonal array of pillars can be easily constructed by nanoimprinting and a responsive surface with a thermo-stimuli-driven roughness change is achieved. The room-temperature AFM scans quantitatively represent the single pillar shows a diameter of ca. 270 nm and 140 nm in depth, and the pitch meaning the averaged inter-pillar distance is measured as ca. 425 nm, thus lying in a nano-sized range. Furthermore, temperature-variable AFM is also utilized to demonstrate the pillar behaves as a thermally-stimulated nano-sized actuator. In our case, when heated above N-to-I phase transition temperature (ca. 65°C), it is clearly observed that the pillar diameter is expanded in the order of over 12-15 % and then reversibly contracted in response to temperature drop.