Adam-Gibbs Theory Research Articles

Kinetic criterion for triple-shape memory effect in amorphous polymers undergoing heterogeneous glass transitions

The triple-shape memory effect (triple-SME) in amorphous polymers arises from the heterogeneous glass transitions of different components. However, due to the complex composition and structural relaxation of triple-shape memory polymers (triple-SMPs), existing models struggle to characterize the shape memory temperature range for each component and its dependence on thermal history. This presents a challenge in developing a kinetic criterion to judge the occurrence of the triple-SME. To address this issue, we propose a kinetic phase transition model to predict the shape memory temperature range for each transition phase in triple-SMPs under different thermal histories. By combining the Tool-Narayanaswamy-Moynihan (TNM) model with the Adam-Gibbs theory, the effect of cooling rate during programming on subsequent triple-SME is investigated. Subsequently, the effectiveness of the proposed model is evaluated by applying it to predict the shape memory performance and thermomechanical behavior of SMPs with dual- and triple- SMEs under different thermal histories. Using this modeling strategy enables the calculation of the critical isothermal shape recovery time for each transition phase under different thermal histories, effectively preventing shape recovery overlap. Consequently, the proposed model is expected to provide theoretical guidance for designing SMPs with triple-SME and promoting their application in engineering.

A phase transition model in dual-amorphous water undergoing liquid–liquid transition

An in-depth understanding of liquid–liquid phase transition (LLPT) in condensed water will gain insight into anomalous behaviors of dual-amorphous condensed water. Despite numerous experimental, molecular simulation, and theoretical studies, it is yet to achieve a widely accepted consensus with convinced evidence in the condensed matter physics for two-state liquid–liquid transition of water. In this work, a theoretical model is proposed based on the Avrami equation, commonly used to describe first-order phase transitions, to elucidate complex homogeneous and inhomogeneous condensation from high-density liquid (HDL) water to low-density liquid (LDL) water for both pure and ionic dual-amorphous condensed water. This model unifies the coupling effects of temperature and electrolyte concentration based on the new theoretical framework. The Adam–Gibbs theory is then introduced to characterize the synergistic motion and relaxation behavior of condensed water. Variations in the configurational entropy under electrostatic forces are further explored, and an analytical 2D cloud chart is developed to visualize the synergistic effect of temperature and electrolyte concentration on the configurational entropy of ionic water. The constitutive relationships among viscosity, temperature, and electrolyte concentration are derived to analyze their synergistic effects under different condensation fractions of LDL and HDL. The Stokes–Einstein relation and free volume theory are further used to analyze diffusion coefficients and densities (or apparent density) during both pure and ionic LLPT. Finally, theoretical results obtained from these models are compared with experimental results reported in literature to validate the accuracy and applicability of the proposed models, which offer significant benefits and advancements in effectively predicting physical property changes of dual-amorphous condensed water.

Tuning the Dynamic Fragility of Polymers by Metallic Ions: The Interplay of Coordination Strength

High-Tg polymers generally exhibit high dynamic fragility (m). Here, we propose to design striking polymeric materials with low m but high Tg by introducing ionic coordination. The enthalpy relaxation of poly(vinylpyrrolidone)/metal chloride complexes was investigated to elucidate the influences of the coordination strength on Tg and m. Findings reveal that Tg increases with the addition of metallic ions, while m decreases for weakly coordinated complexes (Li+) and moderate systems (Zn2+ and Mg2+). Meanwhile, m increases continuously for strongly coordinated systems (La3+). Further experiments revealed that m is well correlated to heat capacity jump ΔCp and enthalpy hysteresis ΔHR as predicted by Adam–Gibbs theory. Ionic coordinated polymers with low m but high Tg can be achieved only when ΔHR changes more than Tg·ΔCp, suggesting that the enthalpy change plays a leading role in the activation free energy of segmental cooperative rearrangement. These results not only add new evidence of the thermodynamic link to dynamic fragility but also help clarify the mechanism of the independent tuning of Tg and m.

Yielding mechanisms for mechano-chemo-thermal couplings in amorphous shape memory polymer undergoing molecular entanglement

Shape memory polymers (SMPs) have good properties of recovering their original shape in the presence of an external stimulus. However, the thermodynamic behaviors behind the yielding effects on mechano-chemo-thermal shape-memory effect (SME) are yet to be explored. In this study, molecular entanglement theory is employed to develop a thermodynamic model in terms of glass transition temperature. Based on the Arrhenius equation and Adam–Gibbs theory, an extended yield model is formulated to investigate the synergistic coordination of yield stress and stored strain energy on mechano-chemo-thermal SME and relaxation behavior in the amorphous SMPs. Furthermore, the effectiveness of this model is demonstrated by applying it to predict thermomechanical and mechano-chemo-thermal shape-recovery behaviors of the SMP, and the theoretical results are well validated by the experimental data reported in the literature. This study explores the working principle of stored strain energy in terms of molecular entanglement and yield stress, and describes a constitutive relationship between molecular entanglement and mechano-chemo-thermal coupling thermodynamics in the amorphous SMP.

Structural origin of thermal shrinkage in soda-lime silicate glass below the glass transition temperature: A theoretical investigation by microsecond timescale molecular dynamics simulations.

Microscopic dynamical features in the relaxation of glass structures are one of the most important unsolved problems in condensed matter physics. Although the structural relaxation processes in the vicinity of glass transition temperature are phenomenologically expressed by the Kohlrausch-Williams-Watts function and the relaxation time can be successfully interpreted by Adam-Gibbs theory and/or Narayanaswamy's model, the atomic rearrangement, which is the origin of the volume change, and its driving force have not been elucidated. Using the microsecond time-scale molecular dynamics simulations, this study provides insights to quantitatively determine the origin of the thermal shrinkage below Tg in a soda-lime silicate glass. We found that during annealing below Tg, Na ions penetrate into the six-membered silicate rings, which remedies the acute O-O-O angles of the energetically unstable rings. The ring structure change makes the space to possess the cation inside the rings, but the ring volume is eventually reduced, which results in thermal shrinkage of the soda-lime silica glass. In conclusion, the dynamical structural relaxation due to the cation displacement evokes the overall volume relaxation at low temperature in the glassy material.

Dynamic coordination of miscible polymer blends towards highly designable shape memory effect

Miscible polymer blends offer great designability on shape memory effect (SME) with adjustable mechanical properties and stimuli-responsiveness, by simply changing the constituent compositions. However, the thermodynamics understanding behind those SMEs on miscible polymer blends are yet to be explored. This paper describes an approach to achieve highly designable SMEs with adjustable glass transition temperature (Tg) and width of glass transition zone by dynamically coordinating components in miscible blends. An extended domain size model was formulated based on the Adam-Gibbs theory and Gaussian distribution theory to study the synergistic coordination of component heterogeneities on conformational entropy, glass transition and relaxation behavior of the miscible blend. The effectiveness of model was demonstrated by applying it to predict dual- and triple-SMEs in miscible polymer blends, where the theoretical results show good agreements with the experiment results. We expect this study provide an effective guidance on designing advanced miscible polymer blends based on the SME.

The relation between molecular dynamics and configurational entropy in room temperature ionic liquids: Test of Adam-Gibbs model.

In this communication, the Adam-Gibbs model connecting molecular dynamics with configurational entropy is tested for the first time for ionic liquids. For this purpose, we investigate simultaneously the shear viscosity η and configurational entropy Sc of an aprotic ionic liquid: 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm TFSI). Comparing the Sc data obtained by the combination of Vogel-Fulcher-Tammann and Adam-Gibbs equations to the Sc points determined directly from the calorimetric experiment, good agreement is found in the entire supercooled liquid region. These results indicate the validity of the Adam-Gibbs model in materials with electrostatic interactions being dominated. These important findings not only generalize the applications of the Adam-Gibbs theory but also provide an opportunity to gain insight into the relationship between thermodynamics and molecular dynamics in ionic liquids.

Do String-like Cooperative Motions Predict Relaxation Times in Glass-Forming Liquids?

The Adam-Gibbs theory of glass formation posits that the growth in the activation barrier of fragile liquids on cooling emerges from a loss of configurational entropy and concomitant growth in "cooperatively rearranging regions" (CRRs). A body of literature over 2 decades has suggested that "string-like" cooperatively rearranging clusters observed in molecular simulations may be these CRRs-a scenario that would have profound implications for the understanding of the glass transition. The central element of this postulate is the report of an apparent zero-parameter relationship between the mass of string-like CRRs and the relaxation time. Here, we show, based on molecular dynamics simulations of multiple glass-forming liquids, that this finding is the result of an implicit adjustable parameter-a "replacement distance". This parameter is equivalent to an adjustable exponent within a generalized Adam-Gibbs relation, such that it tunes the entire functional form of the relation. Moreover, we are unable to find any objective criterion, based on the radial distribution function or the cluster fractal dimension, for selecting this replacement distance across multiple systems. We conclude that the present data do not establish that string-like cooperative rearrangements, as presently defined, are predictive of segmental relaxation via an Adam-Gibbs-like physical model.

Collective and cooperative dynamics in transition domains of amorphous polymers with multi-shape memory effect

The multi-shape memory effect (multi-SME) in amorphous shape memory polymers (SMPs) linked with collective and cooperative rearrangements and accommodation of monomeric segments leads to the generation of complex thermodynamic modes. In this study, an extended domain size model is initially formulated to describe variations in temperature-dependent relaxation behavior and domain transitions in amorphous SMPs. According to the Adam–Gibbs theory, a cooperative model is employed to identify the principle role of domain size in the collective dynamics of multi-SMEs in amorphous SMPs. The phase transition theory is then combined with the multi-branch Kelvin model to describe the collective and cooperative relaxation behavior of the SMPs with multiple transition domains. It is shown that the proposed model is able to characterize the thermomechanical transitions and multiple shape recovery processes. Finally, the model is applied to predict the shape recovery behavior of SMPs with triple- and quadruple-SMEs, respectively, and the theoretical results are well validated by the experimental results.

On Measuring the Characteristic Length of the Cooperative Molecular Dynamics in the Glass-Forming Liquids

An analysis of the methods for measuring the characteristic length of the cooperative molecular dynamics in glass-forming liquids is submitted. The equations and methods for measuring the size of the cooperatively rearranging regions in post Adam-Gibbs theories are compered, and it is proved that they give one and the same number, but with different interpretation for the relaxed molecular units. The interpretation that the rearranging units defined by Wunderlich are smallest structural units, named beads, is supported by the predicted “universal” value for the cooperatively rearranging range at the glass-transition temperature, as well as from a precise modeling for the relaxations by the generalized entropy theory. It has been found that the characteristic length estimated by random first order transition theory, as well as by the “four-point” dynamic susceptibility method, measured as the number of the bead’s diameters coincide with the length of the cooperatively rearranging region in Adam-Gibbs theory extended at the molecular level.

Relations between the sub-molecula and the cooperative scales in the molecular dynamics of the glass-forming liquids

The molecules of the supercooled liquids in the cooperative molecular dynamics are partitioning to specific dynamic units, known as “beads”. The beads have been defined as the smallest units, forming the heat capacity of the supercooled liquids. The beads appear as a sub-molecular scale in the dynamics of the glass-forming liquids. In the Adam-Gibbs theory the number of molecules, rearranging simultaneously, has been defined as the size of the cooperative rearranging region and these regions form the second larger molecular scale in molecular dynamics. Due to a noticeable discrepancy in estimating the number of beads in the molecules by the empirical rules as well as by theoretical models the relations between these two scales are not well known. Recently, a new thermodynamic method for estimating the number of the beads in the molecules and a rule for the examination of their temperature dependence have been suggested. By these methods 48 low-molecular supercooled liquids are investigated and the relations between these two molecular scales and the structure of the molecules have been found. The estimated number of configuration beads is compared with the number of the structural units (the chemical groups, the ions and the atoms), with the assigned number by the empirical rules and with the ones calculated, based on a Lennar-Jones model of the random first order transition theory. A constant and two kinds of temperature dependence of the number of the beads in the molecules of different liquids have been revealed. A molecular basis, forming the fragility of the supercooled liquids, has been found. From the results obtained, the investigated liquids are classified in several groups following the logical line in the formation of the beads.

Looking at the dynamical heterogeneity in a supercooled polymer system through isoconfigurational ensemble

The dynamic correlations that emerge in a polymer system in supercooling conditions have been studied using molecular dynamic simulations. It is known that when a glass former approaches the glass transition temperature, the dynamics of the system (in terms of the mobilities of the particles) not only significantly slows down but also becomes more heterogeneous. Several theories relate this slowing down to increasing spatial (structural) correlations, for example, through the onset of cooperative relaxation regions in the Adam-Gibbs theory. In this work, we employ Pearson's coefficient in the isoconfigurational ensemble (ICE) which allows us to study the dynamic correlations of the monomers in the ICE and establish the relation between the structure of the monomers and its dynamic behavior. Similar to what happens with mobility, monomers with highest correlation are clustered, and the clustering increases with decreasing temperature. An interesting result is that regions with high ICE dynamic correlation are not coincident with highly mobile or immobile regions. These results represent a new approach to the study of dynamic heterogeneity that emerges in glass forming liquids, complementing the more traditional characterization in terms of mobility. The methodology proposed in this work that characterize the connected dynamic regions to structural causes can represent an alternative way to observe the cooperative relaxation regions.

Utilization of high entropy alloy characteristics in Er-Gd-Y-Al-Co high entropy bulk metallic glass

In the present study, we carefully evaluate the role of high entropy alloy (HEA) characteristics on glass-forming ability (GFA) and mechanical responses in a newly developed Er-Gd-Y-Al-Co high entropy bulk metallic glass (HE-BMG) by comparison with the Er-Al-Co and Er-Y-Al-Co bulk metallic glasses (BMGs). The addition of multiple rare-earth elements (REs) to Er-Al-Co BMG results in both higher fragility according to Adam-Gibbs theory and slower crystallization kinetics according to confusion principle. Based on these mutual competitions, the Er18Gd18Y20Al24Co20 HE-BMG can be successfully fabricated up to 5 mm in diameter for glass formation. In particular, the HE-BMG exhibits unexpected structural bias and more fragile manner via preferential covalent bonding of Co-Al and various RE-Al clusters, which leads to larger deviation from the typical BMGs' behavior in the relation between fragility and elastic properties. Furthermore, the HE-BMG effectively retards crystallization kinetics, which was confirmed by exceptionally sluggish nanocrystallization of multi-precipitates from metastable liquid and longer post-recalescence plateau duration in cooling curve of solidification from stable liquid. Indeed, the increased structural instability due to HEA characteristics (preferential short-range order and sluggish crystallization) in HE-BMGs reduces cut-off size of self-organized shear avalanches and increases the number of chaotic shear avalanches, which can distribute the applied strain more homogeneously, resulting in enhanced intrinsic ductility. Consequently, these results provide a guideline on how to design HE-BMGs with promising properties by utilizing HEA characteristics, and thus can give us a strategy for bridging BMG and HEA.

Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy

Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. Here, we report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four-point space-time correlation function demonstrates a growing dynamic correlation length, ξ, upon cooling of the liquid toward the glass transition temperature. ξ as a function of the relaxation time τ are in good agreement with Adam-Gibbs theory, inhomogeneous mode-coupling theory and random first-order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near-surface layer with order of magnitude shorter relaxation time than inside the bulk.

Energy-Renormalization for Achieving Temperature Transferable Coarse-Graining of Polymer Dynamics.

The bottom-up prediction of the properties of polymeric materials based on molecular dynamics simulation is a major challenge in soft matter physics. Coarse-grained (CG) models are often employed to access greater spatiotemporal scales required for many applications, but these models normally experience significantly altered thermodynamics and highly accelerated dynamics due to the reduced number of degrees of freedom upon coarse-graining. While CG models can be calibrated to meet certain properties at particular state points, there is unfortunately no temperature transferable and chemically specific coarse-graining method that allows for modeling of polymer dynamics over a wide temperature range. Here, we pragmatically address this problem by "correcting" for deviations in activation free energies that occur upon coarse-graining the dynamics of a model polymeric material (polystyrene). In particular, we propose a new strategy based on concepts drawn from the Adam-Gibbs (AG) theory of glass formation. Namely we renormalize the cohesive interaction strength and effective interaction length-scale parameters to modify the activation free energy. We show that this energy-renormalization method for CG modeling allows accurate prediction of atomistic dynamics over the Arrhenius regime, the non-Arrhenius regime of glass formation, and even the non-equilibrium glassy regime, thus allowing for the predictive modeling of dynamic properties of polymer over the entire range of glass formation. Our work provides a practical scheme for establishing temperature transferable coarse-grained models for predicting and designing the properties of polymeric materials.

Does fragility of glass formation determine the strength of Tg-nanoconfinement effects?

Nanoscale confinement has been shown to alter the glass transition and associated mechanical and transport properties of glass-forming materials. Inspired by expected interrelations between nanoconfinement effects, cooperative dynamics in supercooled liquids, and the "fragility" (or temperature-abruptness) of the glass transition, it is commonly expected that nanoconfinement effects on Tg should be more pronounced for more fragile glass formers. Here we employ molecular dynamics simulations of glass formation in the bulk and under nanoconfinement of model polymers in which we systematically tune fragility by several routes. Results indicate that a correlation between fragility and the strength of nanoconfinement effects is weak to modest at best when considering all systems but can appear to be stronger when considering a subset of systems. This outcome is consistent with a reanalysis of the Adam-Gibbs theory of glass formation indicating that fragility does not necessarily track in a universal way with the scale of cooperative motion in glass-forming liquids. Finally, we find that factors such as composition gradients or variability in measurement sensitivity to different parts of the dynamic gradient have the potential to significantly confound efforts to identify trends in Tg-nanoconfinement effects with variables such as fragility, emphasizing the importance of employing diverse data sets and multiple metrologies in the study of this problem.

Structural evolution on medium-range-order during the fragile-strong transition in Ge15Te85

Using synchrotron X-ray scattering, we investigate liquid Ge15Te85 spanning a wide temperature range from near Tg to the melt, and demonstrate that the density anomaly and fragile-strong transition are not only related to short-range-order (SRO) structural change (e.g. Peierls-like distortion), but also accompanied by a remarkable development of medium-range-order (MRO). The latter manifests as an emerging pre-peak in total structure factor S(Q) and atomic pair correlations on the length scale of ∼8 Å in the real space G(r) function. The results highlight the role of medium-range structural ordering in the evolution of the configurational entropy which, according to the Adam-Gibbs theory, can be linked to the fragile-strong transition (FS-transition). Based on the relation between structure and liquid dynamics, the FS-transitions at high pressures are examined in terms of experimental data and the Ehrenfest relation. This work identifies the length scale for the atomic correlations in MRO structural evolutions and presents a structural approach to exploring liquid dynamics, which may be useful for investigating relevant phase-change alloys.

The glass transition and interfacial dynamics of single strand fibers of polymers.

We investigate the glass transition and interfacial dynamics of single strand fibers of flexible polymers by employing molecular dynamics (MD) simulations along with a coarse grained model. While the polymer fiber has drawn significant attention due to its applicability in tissue engineering and stretchable electronics, its dynamic properties, especially the glass transition temperature (Tg), are yet to be understood at the molecular level. For example, there has been a controversy on the effect of the polymer fiber radius (R) on Tg: Tg decreased with a decrease in R for some polymer fibers, whereas Tg of other polymer fibers was not sensitive to R. In this article, we estimate the bond relaxation time of polymers and evaluate both Tg and fragility (m) as a function of R. We illustrate that Tg of the polymer fiber decreased with a decrease in R monotonically and also that the values of Tg follow faithfully the empirical equation proposed by Keddie et al. as a function of R, which was successfully employed to fit the values of Tg of both polyvinyl alcohol (PVA) fibers and polyethylene (PE) fibers. We also find that the dynamics of polymers at the interface between a polymer fiber and air is faster than that of polymers at the center. By employing Adam-Gibbs theory, we show that the fast interface dynamics of polymer fibers should influence the cooperative motion of monomers, which should be responsible for the decrease in Tg for smaller values of R. Near the interface there are more mobile monomers that participate in the cooperative motions of polymers. Interesting is that due to the curved surface (unlike flat polymer films) the cooperative motion of monomers is anisotropic in polymer fibers.

Sub-molecular dynamics in liquids and polymers

An extension of Adam-Gibbs theory at its molecular level is proposed. New relations, measuring the number of the configurations within the cooperatively rearranging regions, are found. By these relations the transformation of activated-hopping to free-diffusion dynamics can be observed as a measurement of the number of the sub-molecular dynamic units, known in the literature as “beads”. Two new methods for measuring the number of the beads in the molecules have been found. One of the methods used the thermodynamics results, and the second one used both the thermodynamics and relaxation ones. The measured number of beads in the twelve liquids is compared with the measuring by other theories. The evolution of the liquid state by measuring the number of the configurations within the cooperatively-rearranging regions is presented. With the suggested equations, the molecular level of Adam-Gibbs theory becomes a completed theory, permitting all molecular quantities, in the theory, to be measured by experimental results.

Revising the formulization of the Narayanaswamy equation using the Adam-Gibbs theory

Hodge's formulization of the Tool-Narayanaswamy-Moynihan (TNM) equation from the Adam-Gibbs (AG) theory was re-evaluated. The non-linearity parameter (x) and the apparent activation energy (Δh*) of the TMN equation were re-derived. Compared with the original derivations, the revised values of x and Δh* were better correlated with experimental results. Of particular importance, the revised theoretical x correctly predicts the experimental trend of x for the cooling rate of polystyrene, whereas the original derivation predicted an opposite trend. Furthermore, the new derivation establishes a strong relationship between the fragility coefficient (m) and the x of a material. The relationship correlates well with the experimental values for a wide range of materials. Ultimately, the revised equations for x and Δh* more precisely reveal the theoretical foundation of the phenomenological TNM equation, as it relates to structural relaxation of polymeric materials.