Kinetics of strain-induced crystallization in natural rubber: A diffusion-controlled rate law

A Water Balloon as an Innovative Energy Storage Medium

Soft rubbery materials are capable of withstanding large deformation, and stretched rubber contracts when heated. Additionally, rubber balloons exhibit non-monotonic pressure-volume curves. These unique properties have inspired numerous ingenious inventions based on rubber balloons. To the authors' knowledge, however, it is surprising that these properties have not inspired any study that exploits the elasticity of rubber balloons for energy storage. Motivated by these, this study examines the performance of water balloons as energy storage media. In each experiment, a single water balloon is implemented using a flat membrane, and it is subject to repeated inflation, heating, deflation, and cooling. Inflating the balloon deposits energy into it. The heating simulates the recycling of waste heat. The balloon delivers work during its deflation. Finally, the cooling completes the energy-storage cycle. The performance is evaluated in terms of the balloon's transferred energies, efficiencies, and service life. Simple as it is, a water balloon is actually an impressively efficient energy storage medium. The efficiency is 85-90% when a water balloon stores and releases energy at room temperature. Recycling waste heat can boost a balloon's efficiency beyond 100%, provided that the cost of the heat is negligible so that the heat is not taken as part of the input energy. However, heating shortens the service life of a balloon and reduces the total energy it can accommodate. By running fatigue tests on balloons, this study reveals the trade-off between a water balloon's efficiency and its longevity. These results shall serve as a useful guide for implementing balloon-based mechanical devices not limited to energy-storage applications.

Geometric thermodynamics of strain-induced crystallization in polymers

Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity, the Riemannian curvature, which was used to extract information on the nature of interactions between molecules in fluids, ideal gases, and other open systems. In this article, we examine the implications of this curvature in a nonequilibrium thermodynamic system where relaxation is sufficiently slow so as not to invalidate the local equilibrium hypothesis. The nonequilibrium system comprises a rubbery polymer undergoing strain induced crystallization. The curvature is found to impart information on a spurious isochoric energy arising from the conformational stretching of already crystallized segments. This unphysical component perhaps arises as the crystallized manifold is considered Euclidean with the stretch measures defined via the Euclidean metric. The thermodynamic state associated with curvature is the key to determine the isochoric stretch and hence the spurious energy. We determine this stretch and propose a form for the spurious free energy that must be removed from the total energy in order for the correct stresses to be recovered.

Strain-induced self-assembly of crystallites in elastomers

We propose a model of strain-induced crystallization in elastomers, combining Flory's original work with a description of crystallization adopted from the theory of micellar solutions. The experimentally observed hysteresis appears in the model due to a continuous, unidirectional change of the free energy difference between straightened polymer sections which occur isolated and those which are aggregated. The model yields good qualitative and even semiquantitative agreement with measurements of crystallization in natural rubber at variable cross-link density, strain amplitude, and temperature. The attendant description of the stress hysteresis is less good but still qualitatively correct.

The recovery of nano-sized carbon black filler structure and its contribution to stress recovery in rubber nanocomposites

The hierarchical structural evolution of natural rubber (NR) filled with different contents of nanoscale carbon black (CB) (10 phr-CB10 and 50 phr-CB50) after first loading and recovering for different times was investigated by X-ray nano-CT, wide-angle X-ray scattering (WAXS) and solid state NMR techniques. The CB filler structures as captured by X-ray nano-CT recover gradually with increasing recovering time, but the filler network with different CB contents shows dramatically different structure evolution. For CB10, limited by the filling content, CB particles mainly induces a hydrodynamic effect in spite of deformation or recovering. For CB50, the CB filler forms a 3D connected network, partially destructed during deformation, and the destructed part can be partially recovered during recovery. This suggests that the connected CB filler structure mainly acts as a network reinforcement, whereas the destructed part can induce a hydrodynamic effect. The different effects induced by different CB filling contents are also reflected by the NR matrix, which is reflected by the onset strains εc of strain-induced crystallization (SIC) of NR as captured by WAXS. For CB10, εc remains almost constant, i.e. εc = ca. 1.49, while that of NR with CB50 slightly decreases from initial ca. 1.12 to 0.96 with increasing recovering time up to 50 h. Also, the bound rubber fraction and entangled rubber network remain unchanged after deformation and under different recovery time as detected by the magic sandwich echo (MSE) FID and proton multiple quantum (MQ) NMR. These results demonstrate the key role of the CB filler network in determining the stress-softening behavior of reinforced rubber.

In situ characterization of strain-induced crystallization of natural rubber by synchrotron radiation wide-angle X-ray diffraction: construction of a crystal network at low temperatures

Strain-induced crystallization (SIC) of natural rubber (NR) at descending temperatures as low as -60 °C is systematically investigated by in situ synchrotron radiation wide-angle X-ray diffraction (SR-WAXD) measurement. The detailed structural evolution of NR during SIC is studied in the strain-temperature space, where up to four regions are defined depending on the SR-WAXD results. In region I, the molecular chains begin to be oriented under tensile loading. The onset of crystallization happens in the very beginning of region II, and the NR crystal acts as a new physical cross-linking point to form a crystal network, namely the series model. The further increment of crystallinity (> ca. 8%) leads to the transition of the crystal network from the series model to the parallel model in region III. The crystal network is finally accomplished in region IV, where the crystallinity remains almost constant. Interestingly, regions III and IV exist only in the intermediate-temperature zone II (-40 °C to -10 °C), which are missing in zones I (-10 °C to 25 °C) and III (-60 °C to -40 °C). This suggests that sufficient crystallinity (χ_II-III > ca. 8%) is required to form the parallel model. The new crystal network provides a deep understanding of SIC of NR considering the microscopic features, i.e. oriented amorphous component, the onset of crystallization and crystallinity evolution and its correlation with the macroscopic stress-strain curve.

Thermodynamics and mechanics of stretch-induced crystallization in rubbers

The aim of the present paper is to provide a quantitative prediction of the stretch-induced crystallization in natural rubber, the exclusive reason for its history-dependent thermomechanical features. A constitutive model based on a micromechanism inspired molecular chain approach is formulated within the context of the thermodynamic framework. The molecular configuration of the partially crystallized single chain is analyzed and calculated by means of some statistical mechanical methods. The random thermal oscillation of the crystal orientation, considered as a continuous random variable, is treated by means of a representative angle. The physical expression of the chain free energy is derived according to a two-step strategy by separating crystallization and stretching. This strategy ensures that the stretch-induced part of the thermodynamic crystallization force is null at the initial instant and allows, without any additional constraint, the formulation of a simple linear relationship for the crystallinity evolution law. The model contains very few physically interpretable material constants to simulate the complex mechanism: two chain-scale constants, one crystallinity kinetics constant, three thermodynamic constants related to the newly formed crystallites, and a function controlling the crystal orientation with respect to the chain. The model is used to discuss some important aspects of the micromechanism and the macroresponse under the equilibrium state and the nonequilibrium state involved during stretching and recovery, and continuous relaxation.

A comparison of the abilities of natural rubber (NR) and synthetic polyisoprene cis-1,4 rubber (IR) to crystallize under strain at high strain rates

Strain induced crystallization (SIC) of a natural rubber (NR) and a synthetic rubber (IR) with a high amount of cis-1,4 units (98.6%) is studied, thanks to in situ wide angle X-ray (WAXS) experiments at room temperature performed in a large range of strain rates. During stretching at a low strain rate (4.2 × 10(-3) s(-1)), SIC in IR occurs at a larger stretching ratio than in NR. As a result, the crystallinity index at a given stretching ratio is lower in IR than in NR, in spite of the similar crosslink densities of the chains involved in the crystallization in both materials. This lower ability for crystallization in IR is attributed to the presence of branching along its backbone and its lower stereoregularity. Conversely, dynamic experiments performed at high strain rates (10(1)/10(2) s(-1)) show for both materials a similar ability to crystallize. This unexpected result is confirmed by monotonic tensile tests performed in a large range of strain rates. The reason is thermodynamic: the chain extension plays a predominant role compared to the role of the microstructure defects when the strain rate is high, i.e. when the kinetics of the crystallite nucleation forces the crystallization to occur at a large stretching ratio. A thermodynamic model enables qualitative reproduction of the experimental results.