Cooperative Rearranging Region Research Articles

Influence of Chemical Composition and Structure on the Cooperative Fluctuation in Supercooled Glass-Forming Liquids.

The kinetics of the glass transition and the characteristic size of the fluctuating spatio-temporal domains in supercooled glass-forming liquids, i.e., the Cooperatively Rearranging Regions (CRR), were measured upon cooling over a broad range of cooling rates using Differential Scanning Calorimetry (DSC) and chip-based Fast Scanning Calorimetry (FSC). The investigations were conducted on a selection of fragile glass formers (fragility indices between 80 and 140), with a large variance in the atomic or molecular structure but comparable thermal glass transition temperatures Tg, with the aim of evaluating the influence of chemical composition and structure on the CRR size and the associated temperature fluctuation. The selected materials are two polymers (poly(vinyl acetate) (PVAc), poly(lactic acid) (PLA)) as well as the simplest chalcogenide glass-former (selenium). It turned out that the CRR size plotted against the reduced temperature T/Tg follows the same trend, irrespective of the considered glass-former.

Highlighting the interdependence between volumetric contribution of fragility and cooperativity for polymeric segmental relaxation.

The blurring around the link between the isobaric fragility and the characteristic size of cooperative rearranging region for glass-forming liquids has been cleared up by considering volumetric and thermal contributions of the structural relaxation. The measurement of these contributions is carried out for three amorphous thermoplastic polymers using broadband dielectric spectroscopy under pressure, providing an understanding of the link between isobaric fragilities, glass transition temperatures, and microstructures. The cooperative rearranging region (CRR) volume is calculated as a function of pressure using the extended Donth's approach, and the values are compared with the activation volume at the glass transition under different isobaric conditions. By combining these different results, a link between the chemical structure and the influence of pressure/temperature on the molecular mobility can be established. Furthermore, this study shows also a strong correlation between the activation volume, leading to the volumetric contribution of the isobaric fragility, and the CRR volume. Finally, this work highlights the influence of inter- and intra-molecular interactions on thermal and volumetric contributions of the isobaric fragility as a function of pressure.

Statistical model of synchronized cooperative motion in glass-forming liquids

This paper presents a theoretical framework describing the tendency for synchronized positional rearrangements of any two structural species in a multicomponent glass-forming liquid. Such correlated motions are especially important as the glass-forming liquid approaches the glass transition. It is established that the expected cage-breaking probability of a structural unit is proportional to the dynamical propensity of the structural unit calculated via the isoconfigurational ensemble method. This theoretical framework supports the notion that spatial heterogeneities in composition result in dynamical heterogeneities, enabled by synchronized positional rearrangements. Using this model, an alkali borosilicate glass is investigated as an example, and results indicate that structural species with large differences in enthalpy might inhibit the expansion of cooperative rearranging regions and increase the number of such regions. The physical impact on relaxation time distribution and configurational entropy are also discussed.

Physical property characterizations of natural rubber nanocomposites through experimental techniques, models and CRR concept

AbstractIn this research, the combinations of silica (SiO2), with either graphite (GR) or graphene oxide (GO), are studied as hybrid reinforcements of natural rubber (NR). Whereas individual improvements of rigidity, strength or ductility can be obtained depending on the composition, a synergistic reinforcement is specifically evidenced after addition of GO/SiO2 with a 3:1 ratio. For this formulation, both strength and modulus drastically increase while keeping the strain at break at a decent level. From the confrontation of all tensile tests results with theoretical reinforcement models, a good correlation between the experimental data and the Guth Gold model is observed, which reveals that the mechanical properties should essentially be governed by the filler/matrix interactions. This assumption has been discussed through the cooperative rearranging region (CRR) concept, by analyzing the calorimetric response of the nanocomposites at the glass transition. Not only the 3:1 GO/SiO2 composition is the only one for which the glass transition clearly shifts to higher temperatures, its CRR average size is also the lowest in comparison with reference NR. This result, interpreted as the signature of the most efficient intercalation of the fillers, matches well with the steep strain hardening recorded for this nanocomposite.

Determination of cooperatively rearranging regions in a binary glass former

Cooperative motions are important for understanding the divergence of viscosity of glassy materials at a finite temperature, since the elementary process of the structural relaxation occurs within the smallest cooperative region as suggested by Adam and Gibbs. On the basis of the definition of a cooperatively rearranging region (CRR) by Adam and Gibbs and by Odagaki, we determine the size of CRR for the Kob–Andersen model as a function of temperature using molecular dynamics simulations. We first confine particles in a spherical region and, varying the radius of that region, we determine the CRR size as the smallest radius of the region in which particles can change their relative positions. The size of the CRR increases as the temperature is reduced and seems to diverge below the glass transition temperature. The temperature dependence of the number of particles in the CRR obeys the equation derived from the Adam–Gibbs relation and the Vogel–Fulcher–Tammann equation.

Probing excitations and cooperatively rearranging regions in deeply supercooled liquids

Upon approaching the glass transition, the relaxation of supercooled liquids is controlled by activated processes, which become dominant at temperatures below the so-called dynamical crossover predicted by Mode Coupling theory (MCT). Two of the main frameworks rationalising this behaviour are dynamic facilitation theory (DF) and the thermodynamic scenario which give equally good descriptions of the available data. Only particle-resolved data from liquids supercooled below the MCT crossover can reveal the microscopic mechanism of relaxation. By employing state-of-the-art GPU simulations and nano-particle resolved colloidal experiments, we identify the elementary units of relaxation in deeply supercooled liquids. Focusing on the excitations of DF and cooperatively rearranging regions (CRRs) implied by the thermodynamic scenario, we find that several predictions of both hold well below the MCT crossover: for the elementary excitations, their density follows a Boltzmann law, and their timescales converge at low temperatures. For CRRs, the decrease in bulk configurational entropy is accompanied by the increase of their fractal dimension. While the timescale of excitations remains microscopic, that of CRRs tracks a timescale associated with dynamic heterogeneity, {t}^{*} sim {tau }_{alpha }^{0.8}. This timescale separation of excitations and CRRs opens the possibility of accumulation of excitations giving rise to cooperative behaviour leading to CRRs.

An extended shoving model for dynamic fluctuation of glass transition in amorphous polymer towards cooperative shape-memory effect

Phase transition theory is a powerful approach to study shape-memory effect (SME) and dynamic relaxation behaviour in amorphous shape-memory polymers (SMPs) undergoing glass transition processes. However, previous studies are mostly limited to building-up of experimental models, mainly due to poor understanding of dynamic fluctuation of glass transition. In this study, the dynamic fluctuation of glass transition in the amorphous SMPs, whose thermodynamic SME is governed by the phase transition theory, was investigated using a shoving model. A constitutive relationship between potential energy and cooperatively rearranging region (CRR) volume is firstly developed to explore the working principle of phase transition in the thermodynamic SME of amorphous SMPs, based on the shoving model and Adam–Gibbs domain size model. The effect of CRR volume on the phase transition is further formulated using the strain function, and then employed to develop a constitutive stress–strain equation based on the extended Maxwell model. The working principles of cooperative SME and dynamic relaxation behaviours have been explored and discussed. Finally, the effectiveness of the analytical results obtained using the proposed model has been verified using the experimental results of amorphous SMPs reported in literature.

A coupling model for the cooperative actuation mechanism of thermochemically responsive shape memory polymers

Thermochemically responsive shape memory polymers (SMPs) have attracted great interest in biomedical applications such as drug-releasing capsules and implantable medical stents, because body temperature can drive their shape recovery behaviors. However, it is difficult to determine the configurational dynamics of polymer segments due to the complexities of environmental stimuli (e.g. solute concentration, temperature change, and solvent diffusion). Besides, the cooperative actuation mechanism behind the thermochemical-driven shape memory effect (SME) is still poorly understood. In this study, we describe the effects of temperature and solvent absorption on conformational rearrangements in SMPs using the size change of cooperative rearrangement region (CRR) derived from the Adam–Gibbs model. The quasi-lattice model is further combined with Fick’s second law to characterize the kinetic diffusion behavior of solvent molecules in the CRR. The dependences of dual- and quadruple-SMEs in amorphous SMPs on immersion time, solution concentration, and programming temperature are quantitatively investigated using the proposed model. The theoretical results are also compared with experimental data and a good agreement is achieved. The proposed model is expected to provide theoretical guidance for understanding the working mechanism of thermochemically responsive SMPs and advancing their engineering applications.

Heterogeneity and Memory Effect in the Sluggish Dynamics of Vacancy Defects in Colloidal Disordered Crystals and Their Implications to High-Entropy Alloys.

Vacancy dynamics of high-density 2D colloidal crystals with a polydispersity in particle size are studied experimentally. Heterogeneity in vacancy dynamics is observed. Inert vacancies that hardly hop to other lattice sites and active vacancies that hop frequently between different lattice sites are found within the same samples. The vacancies show high probabilities of first hopping from one lattice site to another neighboring lattice site, then staying at the new site for some time, and later hopping back to the original site in the next hop. This back-returning hop probability increases monotonically with the increase in packing fraction, up to 83%. This memory effect makes the active vacancies diffuse sluggishly or even get trapped in local regions. Strain-induced vacancy motion on a distorted lattice is also observed. New glassy properties in the disordered crystals are discovered, including the dynamical heterogeneity, the presence of cooperative rearranging regions, memory effect, etc. Similarities between the colloidal disordered crystals and the high-entropy alloys (HEAs) are also discussed. Molecular dynamics simulations further support the experimental observations. These results help to understand the microscopic origin of the sluggish dynamics in materials with ordered structures but in random energy landscapes, such as high-entropyalloys.

Multiscale Analysis of Segmental Relaxation in PC/PETg Multilayers: Evidence of Immiscible Nanodroplets

This work highlights the influence of layer thicknesses on glass transition and molecular mobility in polycarbonate (PC) and poly(ethylene terephthalate glycol) (PETg) multilayered films obtained by the layer-multiplying coextrusion process. By combining modulated temperature scanning calorimetry (MT-DSC) and dielectric relaxation spectroscopy (DRS) measurements, the average values of the cooperative rearranging region (CRR) size in a wide range of relaxation times and temperatures have been calculated. The size reduction from micro- to nanoscale is accompanied by a significant deviation of the structural and dynamical properties compared to the bulk. Furthermore, we have evidenced significant differences in PETg and PC behaviors: PETg plays the role of a “hard-confined” polymer, while PC behaves as a “free-confined” polymer, implying opposite variations of the glass transition temperature. The determination of the relaxation parameters for each individual polymer has been possible even for very low layer thicknesses (below 10 nm), for which the multilayer structure is not observed. This result shows that even when PETg and PC are brought into very intimate contact, they maintain their own structural behavior and segmental relaxation, suggesting the formation of immiscible nanodroplets when the multilayer structure disappears.

Segmental Relaxation Dynamics in Amorphous Polylactide Exposed to UV Light

AbstractThe degradation of polylactide (PLA) under UV exposure is investigated in terms of cooperativity and kinetic fragility at the glass transition. In the first part, possibly coexisting degradation mechanisms are evoked from the interpretation of the infrared spectroscopy analyses. Furthermore, the reduction of PLA chain length, owing to photolytic scissions predominant over local crosslinks, is assessed from chromatography, and confirmed by the shift of the glass transition temperature toward lower temperature. Modulated temperature thermogravimetric analysis (MT‐TGA) also shows that the activation energy needed to initiate thermal degradation falls after UV exposure. In the second part, the impact of UV‐induced degradation on the cooperative rearranging region (CRR) size and the kinetic fragility, respectively, calculated thanks to calorimetric and dielectric measurements, is discussed. Despite the assumed concomitance of several degradation mechanisms, it is observed that the glass transition, the kinetic fragility, and the CRR size decrease together with the exposure time. Moreover, it is found that the data align well on another trend depicting the change in the relaxation properties caused by plasticization of PLA. Thus, the variations of segmental relaxation properties caused by UV may be related to the increase of free volume linked to the damaging of the PLA structure.

Elastic response of Carbon Black reinforced polyester based composites using micromechanical models: Role of interphase

Carbon-based reinforcements have been widely reported in improving mechanical properties of polymers. However, still few studies exist on the incorporation of the interphase as a result of the interfacial interactions into analytical prediction tools. To better understand the effect of interfacial interphase, this study compares and correlates the experimental mechanical response of polyester based composites filled with carbon black (CB) with the elastic behavior obtained from the micromechanical models. Mold cast composites of polyester reinforced with 0 wt%–10 wt% of CB were fabricated. To determine the length of cooperative rearranging region (CRR) as a measure of the interphase, thermal studies focusing on the variations in the specific heat capacity or the relaxation strength of the composites around the glass transition temperature ( Tg) range were performed using a thermodynamical model. Micromechanical models such as the Halpin-Tsai and Tandon-Weng were used to determine the Young’s modulus with respect to the CB wt% and diameter as well as the interphase thickness and modulus. The results exhibited the sensitivity of the models to the existence of the interphase as a secondary mechanism, which was correlated to the cross-link density and interfacial bonding. The impact results showed the decrease in the impact resistance upon the addition of higher filler loadings ascribed to the destroyed bonding at the interface and CBs agglomeration confirmed by morphological studies. The research results can be further utilized in the explanation of the changes in the elastic response of carbon-based reinforced thermosetting composites emphasizing the key role of interphase.

Investigation of Carbon Black/ Polyester Micro-composites: An Insight into Nano-size Interfacial Interactions

In the micro/nanomaterial reinforced composites, interfacial interactions at the interface of filler/polymer lead to the formation of a third layer called interphase as the secondary reinforcing mechanism. The interphase may be formed due to local adsorption of polymer chains at the interface, mechanical interlocking, and interdiffusion of polymer chains. Since the interactions govern the load transfer at the filler/polymer interface, they play a key role in the mechanical response of reinforced composites. However, there exist only a few well-established and validated studies in the description of the interfacial interactions presented in thermosetting composites. This research aims at the understanding of correlations amongst the mechanical properties of thermosetting polyester composites reinforced with 0-15 wt. % of carbon black (CB) focusing on the nano-size cooperative rearranging region (CRR). To estimate the length of CRR, thermal analysis of the variations in the specific heat capacity or the relaxation strength within the glass transition temperature (Tg) range was measured using a thermodynamic model. A nano-size CRR of 10 nm on average was estimated and correlated to the enhanced impact and toughness behavior of the specimens. The results suggested the presence of softer interphase based on the Tg values influenced by the CBs agglomeration level and cross-linking density, which in turn governs the mechanical response of the composites. The methodology introduced in this study can be used in the explanation of changes in mechanical and physical properties of reinforced composites with a focus on the underlying role of nano-size interfacial interactions.

Glassy feature in melts of 3-dimensional architectured polymer blends

3-dimensional architectured polymers, for example, giant molecules, present distinct dynamics from chain-like polymers and are coarse-grained as soft-clusters. There is a critical number of beads, above which their melts cannot relax under thermal energy and become cooperative glass. To reveal the role of dispersity, we study the dynamics of binary blends of giant molecules with the same glass transition temperature by rheological experiments and by molecular dynamics simulations. The large component of the blend, OPOSS24 or 141335, contains more beads than the critical number and forms cooperative glass, while the small component contains less beads than the critical number. The gradual change of volume fraction allows us to fine-adjust the average number of beads. An abrupt slowdown happens only if the volume fraction of the large component reaches 80%. Both experimental and simulated data can be described by a Vogel–Fulcher–Tammann-like equation against volume fractions with only one fitting parameter. The divergent relaxation times can also be rewritten as a function of the average number of beads. Such abrupt dynamic slowdown has to be induced by the glass-like cooperative dynamics. The cooperative glass state may only be reached when the majority of giant molecules or generally speaking, soft-clusters, are large enough. If we regard binary blends of soft-clusters as large and small cooperative rearranging regions, this may provide a direct approach to glass problems and may shed light on our understanding.

The Relationship between Free Volume and Cooperative Rearrangement: From the Temperature-Dependent Neutron Total Scattering Experiment of Polystyrene.

Although many theories have been proposed to describe the nature of glass formation, its microscopic picture is still missing. Here, by a combination of neutron scattering and molecular dynamics simulation, we present the temperature-dependent atomic structure variation of polystyrene at the glass formation, free volume and cooperative rearrangement. When it is close to glass formation, the polymer is confined in tubes, whose diameter is the main chain–main chain distance, in a “static cage” from its neighbors. This definition can not only account for the kinetic pathway dependence of Williams-Landel-Ferry (WLF) free volume, but also be testified in a set of six polymers. However, the free volume which allows a monomer to move cannot be found in any frame of its real-space image. Monomers, thus, have to move cooperatively to be out of the cage. During glass formation, dynamic heterogeneity develops, and string-like cooperative rearrangement region (CRR) grows over a long range of time and length scales. All of these CRRs tend to walk through loose “static cages”. Our observation unifies the concepts of free volume and cooperative rearrangement. The former is a statistical average leading to a polydisperse “static cage” formation; while a loose “static cage” provides the way that CRRs move.

Molecular and micro-scale heterogeneities in Raman modes of a relaxing polymer glass

We have used Raman spectroscopy to study relaxation dynamics at two different length scales, molecular level and micro-scale in order to probe the presence of cooperative rearranging regions in a polymer glass. Response to slow thermal cycles and fast quench through the glass transition temperature (T g) is analyzed for film and unprocessed forms of polyvinyl acetate (PVAc). In PVAc film, enhanced disorder and molecular mobility lead to peak broadening by about a factor of 10 compared to unprocessed PVAc. Thermal cycles (10 K min−1) produce hysteresis in integrated Raman peak intensity (loop area ). values of film are two orders of magnitude more than unprocessed, indicating more configurational mosaics with higher interfacial energy dissipations. Ageing after 60 K min−1 quench manifests as heterogeneous molecular dynamics of film Raman modes with significant peak-width variations, differentiating high mobility and low mobility modes. Two-dimensional mapping of film Raman modes after quench reveal micro-scale clusters of average size ≈250 molecules having fractal boundaries with fractal dimension d f = 1.5, resembling d f of percolation clusters below percolation threshold. During thermal cycling and relaxation after a quench, cooperative segmental dynamics with large correlations between skeletal C–C stretch and side branch modes is observed. The observations are analyzed in the context of the random first order transition theory of glasses, which attributes heterogeneous relaxations in glasses to the presence of clusters of variable configurational states.

Fragility of short‐chain poly(lactic acid)s derivatives by combining dielectric spectroscopy and fast scanning calorimetry

AbstractLow‐molecular‐mass bio‐polyesters, such as lactic acid oligomers, constitute a growing category of plasticizers for poly (lactic acid), since they show good compatibility and are respectful of the environment. This study focuses on the glass transition of a series of oligomers with different molecular weights, with the aim of investigating how their associated dynamics occur. Dielectric and calorimetric results are combined to study the molecular mobility in a large temperature range. In comparison with poly (lactic acid), the oligomers exhibit a lower fragility index and smaller cooperative rearranging regions. Among oligomers, the fragility is clearly dependent on the molecular weight, whereas the variations of the cooperativity are subtler.

Promoting Interfacial Interactions with the Addition of Lignin in Poly(Lactic Acid) Hybrid Nanocomposites.

In this paper, the calorimetric response of the amorphous phase was examined in hybrid nanocomposites which were prepared thanks to a facile synthetic route, by adding reduced graphene oxide (rGO), Cloisite 30B (C30B), or multiwalled carbon nanotubes (MWCNT) to lignin-filled poly(lactic acid) (PLA). The dispersion of both lignin and nanofillers was successful, according to a field-emission scanning-electron microscopy (FESEM) analysis. Lignin alone essentially acted as a crystallization retardant for PLA, and the nanocomposites shared this feature, except when MWCNT was used as nanofiller. All systems exhibiting a curtailed crystallization also showed better thermal stability than neat PLA, as assessed from thermogravimetric measurements. As a consequence of favorable interactions between the PLA matrix, lignin, and the nanofillers, homogeneous dispersion or exfoliation was assumed in amorphous samples from the increase of the cooperative rearranging region (CRR) size, being even more remarkable when increasing the lignin content. The amorphous nanocomposites showed a signature of successful filler inclusion, since no rigid amorphous fraction (RAF) was reported at the filler/matrix interface. Finally, the nanocomposites were crystallized up to their maximum extent from the glassy state in nonisothermal conditions. Despite similar degrees of crystallinity and RAF, significant variations in the CRR size were observed among samples, revealing different levels of mobility constraining in the amorphous phase, probably linked to a filler-dimension dependence of space filling.

Structural dependence of the molecular mobility in acetylated starch

In this study, the molecular mobility of acetylated starch (AS) with degree of substitution (DS) 1.5 and 3, representing partial and complete substitution of hydroxyl groups with acetyl groups, was investigated. The glass transition region and the onset of long-range cooperative molecular motions were examined using temperature-modulated-DSC (TMDSC). A potential analogy between the relaxation time of hole formation and the α-relaxation time was observed. The deviation in the temperature dependence of the α-relaxation time from the Arrhenius relationship, obtained with the fragility index, revealed differences according to DS. The cooperative rearranging region (CRR) characteristics differed according to DS and estimation method. Smaller size of the CRR for AS with DS 3 compared to AS with DS 1.5 suggest disruption of hydrogen bonds at high acetylation level. TMDSC experimental data at moderate temperature and predictions and SS-NMR results at ambient temperature, indicate different mobility of AS according to DS and temperature conditions.

Local Dynamics of Excitations in Glassy Liquids

In this study, we propose new elementary processes of the excitation dynamics in glassy liquids, which trigger the structural rearrangement in a local and isolated region known as the cooperative rearrangement region. We identify the existence of primary particles which facilitate local dynamics by using a machine learning technique and a time series analysis. The local soft domains are established by a few soft particles that hop between local energy basins. While particles in contact with these primary soft particles respond non-linearly, other particles not in direct contact with them respond linearly as elastic materials.