The crystallization of a glass is a phase transformation of intense interest to materials scientists because it determines the thermal stability of amorphous materials used in phase-change memory devices, optical fibers, infrared optics, and solar cells. When a glass is held at a fixed temperature above its glass transition, tiny crystal nuclei form and grow until the entire sample has crystallized. The classical framework for describing this process is the Kolmogorov–Johnson–Mehl–Avrami (KJMA) model, which relates the fraction of material transformed at any moment, denoted α, to an exponential function of time raised to a power known as the Avrami exponent n, multiplied by a temperature-dependent rate constant k. According to the model, the transformed fraction follows α = 1 − exp(−(kt)^n), where k itself obeys Arrhenius behavior, k = A exp(−E/RT), with E the activation energy, A the Arrhenius prefactor, R the gas constant, and T the absolute temperature.

Traditionally, experimentalists determine these parameters by converting the raw DSC heat-flow signal into the extent of conversion as a function of time and then constructing double-logarithmic plots of ln[−ln(1 − α)] against ln t. This procedure, while effective, requires accurate knowledge of the moment at which crystallization begins—an assignment notoriously prone to error in isothermal experiments, where the sample takes time to equilibrate after being plunged into the hot furnace of the calorimeter. As Elabbar and Abu-Sehly emphasize, drawing on earlier insights from Waters and Paddy as well as Brown and Galwey, the relevant kinetic parameters can instead be derived directly from the shape of the DSC curve itself, sidestepping the conversion analysis entirely and potentially reducing experimental and numerical uncertainty.

The mathematical basis of the direct method is elegant. The DSC signal φ is proportional to the rate of transformation, φ = ΔHc·(dα/dt), where ΔHc is the total enthalpy released during crystallization, obtained from the area under the peak. Differentiating the KJMA expression yields a curve with a characteristic maximum at a time tmax given by tmax = (1/k)·[((n − 1)/n)]^(1/n). The height of the peak at that moment, φmax, combined with tmax and ΔHc, satisfies a simple relation involving only the Avrami exponent n. Thus, by measuring just the peak time, the peak height, and the total heat of crystallization, the researcher can solve for n, then back-substitute to obtain the rate constant k at each crystallization temperature. The method has one well-defined limitation: it does not apply to first-order reactions with n = 1, for which the DSC curve has no maximum.

Activation energy can likewise be obtained without conversion data. One route, developed previously by Elabbar and known as the Δt-method, uses the full width at half maximum of the crystallization peak. Plotting the natural logarithm of this width, Δt, against the reciprocal of the crystallization temperature Tc produces a straight line whose slope equals E/R. A second, newly demonstrated route exploits the position of the peak itself: because the half-crystallization time t1/2 of the conversion curve is closely related to tmax of the DSC peak, plotting ln tmax against 1/Tc also yields a straight line with slope E/R. Both approaches rely solely on geometric features of the calorimetric traces, making them insensitive to many of the ambiguities that plague conversion-based analyses.

To test the framework, the team prepared glassy In10Se90 by the melt-quenching technique. High-purity selenium and indium, each of five-nines purity, were sealed in evacuated quartz ampoules, heated to 950 °C for 24 hours with frequent rotation to ensure homogenization, and then rapidly quenched in water. Isothermal DSC measurements were performed on a TA Q2000 calorimeter under dry nitrogen, calibrated with indium standards, with a fixed 5-milligram sample mass. Crucially, the samples underwent a rejuvenation heat treatment to erase physical aging effects, ensuring that the crystallization kinetics reflected the intrinsic material rather than a history-dependent relaxation state.

The measurements delivered strikingly consistent numbers. For In10Se90 glass, the Δt-method gave an activation energy of 112 kJ/mol, a value widely reported in the literature for this composition. The new tmax method yielded 142 kJ/mol, while an Arrhenius plot of the directly determined rate constants gave E = 136 kJ/mol and an Arrhenius prefactor A of 3.22 × 10^16 s⁻¹. The Avrami exponent calculated from the peak analysis came out at approximately 2 across the crystallization temperatures studied. For the validation case of Sb10Se90, using data from an earlier study, the tmax method produced an activation energy of 98.9 kJ/mol, in excellent agreement with the 106 kJ/mol obtained by the Δt-method, while the Arrhenius treatment of the rate constants gave E = 105.6 kJ/mol and A = 4.81 × 10^11 s⁻¹—tight mutual confirmation across independent routes.

Beyond the numbers, the Avrami exponents reveal a fascinating physical story about how these two glasses crystallize. In In10Se90, an exponent near 2 points to a constrained growth mode—either one-dimensional growth with continuous nucleation or two-dimensional growth with a decreasing or limited nucleation rate—suggesting heterogeneous nucleation sites and anisotropic extension of crystalline domains within the amorphous matrix. In Sb10Se90, by contrast, an exponent near 3 signals three-dimensional, volumetric crystal growth proceeding uniformly through the bulk, under either constant nucleation or site-saturated nucleation. The substitution of antimony for indium thus fundamentally alters the geometry of the transformation, information that the direct DSC analysis captures with no additional experimental effort.

The authors note that the slightly different activation energies obtained from the different routes likely stem from an experimental artifact: the difficulty of assigning the true starting time t = 0 in isothermal DSC traces. The Δt-method is immune to this uncertainty because peak width, unlike peak position, does not depend on the choice of time zero, which is why the team argues it provides the most accurate estimates of E. Their conclusion that Δt-derived values agree best with the extensive literature supports this interpretation and offers practical guidance for anyone analyzing isothermal calorimetry data.

The broader significance of the work lies in accessibility. Isothermal DSC instruments are ubiquitous in materials laboratories, and the new method transforms what was once a multi-step fitting exercise into a set of straightforward measurements on the raw thermal traces—peak time, peak height, peak width, and total heat. For researchers designing chalcogenide glasses for phase-change memory, optical storage, or thermoelectric applications, this means faster, more reproducible characterization of thermal stability and crystallization behavior. It also reinforces a lesson that resonates across thermal analysis: sometimes the richest information about a material’s inner transformation is sitting in plain sight, in the very shape of the curve the instrument draws.

Subject of Research: Direct determination of crystallization kinetic parameters from isothermal DSC curves of chalcogenide glasses using the KJMA model

Article Title: Determination of the kinetic parameters for crystallization directly from isothermal DSC curves

Article References: Elabbar, A. A., & Abu-Sehly, A.-H. A. (2026). Determination of the kinetic parameters for crystallization directly from isothermal DSC curves. Discover Chemistry, 3(1), Article 503. https://doi.org/10.1007/s44371-026-00960-7

Image Credits: AI Generated

DOI: 10.1007/s44371-026-00960-7

Keywords: crystallization kinetics, differential scanning calorimetry, chalcogenide glasses, KJMA model, Avrami exponent, activation energy, isothermal DSC, thermal analysis, glass transition, In10Se90, Sb10Se90, Arrhenius equation

The central insight running through the collection is that foods rarely sit comfortably on either side of the fluid-solid divide. Instead, they travel continuously through liquid-like, viscoelastic, plastic and solid-like regimes as their internal microstructure evolves. In some materials, a network is born through gelation or crystallization; in others, molecular mobility is frozen out by cooling or a glass transition. In yield-stress materials such as pastes, flow destroys a pre-existing structure that then rebuilds. During drying, cooking and frying, changes in moisture content can simultaneously alter mechanical properties and generate internal stresses and deformation. This continuous, mechanism-dependent journey between states is precisely why food structuring has historically been treated empirically, with process-property relationships assembled through trial and error rather than derived from first principles.

A major theme of the Special Issue is the tight coupling between transport processes, changing material properties and mechanical deformation, particularly during drying. Hu and colleagues present a multiphase, multiscale mechanistic model for hot-air drying of shiitake mushroom, capturing how water removal reshapes the material while it shrinks and stresses. Veser and co-workers predict cabbage-seed drying at laboratory and industrial scales using a non-equilibrium sorption-isotherm approach, while Rizki and colleagues track material-property changes during electrohydrodynamic drying with a close look at the falling-rate period, the stage where moisture loss slows and the material stiffens most dramatically. Shah and Takhar push the coupling even further in microwave frying, combining unsaturated transport based on hybrid mixture theory with electromagnetic equations. Together, these studies make a forceful case that heat and mass transfer cannot be modeled independently of the evolving physical state of the food.

Deformation itself can become a tool rather than a nuisance, and several contributions exploit this deliberately. van der Sman, Curatolo and Teresi investigated buckling during the drying of edible soft matter with a cylindrical core-shell geometry, showing how drying-induced mechanical instabilities generate intricate, predictable deformation patterns. In a companion study, the same team demonstrated programmable shape morphing during drying through symmetry breaking, effectively using moisture gradients to sculpt foods into designed shapes rather than accepting warping as a processing defect. Grasa, Teresi and van der Sman extended the coupled transport-mechanics framework to large-strain anisotropic behavior of meat during cooking using finite-element modeling. These works signal a shift in the field: instead of treating shrinkage, curling and buckling as quality problems to suppress, researchers are beginning to engineer them for structure design.

Underlying this shift is a broader theoretical realignment. Food rheology has traditionally concentrated on materials in their flowing state, while the mechanics of foods undergoing large deformations in a more solid-like condition received comparatively little attention. Meanwhile, advances in soft-matter mechanics and poromechanics now allow deformation, viscoelasticity and moisture transport to be described within thermodynamically consistent frameworks. A particularly striking conceptual bridge is the mathematical correspondence between the configuration tensor used in advanced rheological models and the Cauchy-Green tensor used in large-deformation mechanics. This equivalence offers a common language for materials that alternate between flowing and solid-like states, and its implications for elasto-viscoplastic food materials and stress-driven moisture migration are explored in a recent review by van der Sman in Current Opinion in Food Science. The practical consequence could be a new generation of models that predict, rather than merely reproduce, how foods behave through their whole processing journey.

At the opposite end of the fluid-solid transition lie processes in which a material must first flow in a controlled manner and then preserve its generated shape, and nowhere is this clearer than in three-dimensional food printing. Kim and colleagues examined the printability and structural properties of plant-based scallop adductor-muscle analogues, relating performance to amylose content and the pasting behavior of different rice cultivars. Liu and co-workers studied edible three-dimensionally printed emulsion gels, showing how inulin incorporation modifies both mechanical and sensory properties. Both studies converge on a key conclusion: printability is not simply a question of viscosity. A printable food must respond appropriately during extrusion, then recover or develop enough structural integrity after deposition to hold its printed geometry, a dual requirement that demands careful control across the entire fluid-solid spectrum.

The mechanisms by which foods acquire that structural integrity vary enormously across systems, and the Special Issue maps this diversity down to the molecular scale. Renzetti and colleagues investigated cereal and tuber starches, identifying hydrogen-bond density and glass-transition temperature as governing factors in gelatinization and gel rheology, thereby linking molecular interactions and thermal transitions directly to macroscopic mechanical behavior. On a different front, Holian, Bolton and Wilson explored how structure can be generated in soft solids to produce heat-stable milk chocolate, a formulation challenge that hinges on managing the solid-fat network so the product survives warming without collapsing. Both studies underscore that transitions between fluid-like and solid-like response ultimately originate at smaller length scales, from molecular mobility and intermolecular interactions up to the formation of mesoscopic networks that carry load.

Structured lipid systems offer further illustration of the same soft-matter principle. Shuai and colleagues investigated rice-bran-wax-structured macadamia oleogels and temperature-responsive water-in-oil emulsions, showing how organization of the lipid phase provides a route to tuning mechanical and functional properties, including delivery of bioactive compounds such as astaxanthin. Rasouli Pirouzian and co-workers, in their study of sucrose-free probiotic dark chocolate, addressed formulation optimization in relation to rheological characteristics and the viability of Saccharomyces boulardii. Although oleogels and functional chocolates sit far from drying mushrooms or printed gels on the supermarket shelf, they obey the same underlying rule: macroscopic material behavior emerges from an evolving internal structure whose formation is dictated by composition and processing conditions. This unity of principle is what makes the cross-disciplinary framing of edible soft matter so productive.

Taken together, the contributions point to a future in which food structuring moves from empirical process-property relations toward a genuinely mechanistic and predictive science. Achieving that will require closer integration of experimental characterization and modeling across length and time scales, with rheological and mechanical measurements increasingly combined with techniques that track microstructure, moisture distribution and deformation in real time during processing. Constitutive models, in turn, must evolve beyond reproducing behavior under narrow conditions toward formulations that capture the evolution of internal structure and its coupling to deformation, temperature and moisture transport. The Wageningen symposium and the resulting collection demonstrate the value of bringing food scientists, rheologists, physicists and solid-matter mechanicians to the same table. If that cross-fertilization continues, the next generation of foods may be designed, on paper, from the flow and setting behavior of their molecular ingredients upward.

Subject of Research: The fluid-to-solid state transitions of edible soft matter during food processing

Article Title: Edible soft matter in between fluid and solid states

Article References: Edible soft matter in between fluid and solid states. (n.d.). https://doi.org/10.1016/j.crfs.2026.101561

Image Credits: AI Generated

DOI: 10.1016/j.crfs.2026.101561

Keywords: edible soft matter, food rheology, food drying, 3D food printing, gelatinization, glass transition, oleogels, moisture transport, large-deformation mechanics, food structure, buckling, chocolate structuring

The central idea behind the work is that molecular rearrangements in a glass do not happen freely. Each rearranging cluster of molecules must push and pull against its elastic surroundings, deforming a cage of neighbors that resists the change. This resistance—often called an elastic barrier—adds to the energetic cost of the rearrangement and is thought to grow dramatically as a glass is cooled or aged, explaining why relaxation times in glass-forming liquids can stretch from picoseconds to centuries. While this picture has animated theoretical work for decades, and underlies influential frameworks such as the random first-order transition theory and shoving models of glass rheology, experimentally separating the elastic contribution from the thermodynamic one has remained a formidable challenge. The new study tackles that challenge head-on by designing measurements in which the elastic barrier can be isolated and quantified rather than merely inferred.

The team worked with molecular glasses—a class of materials built from small, well-defined molecules rather than polymeric chains or network-forming atoms. Molecular glasses are the workhorses of this field for good reason: their constituent particles interact through simple, well-characterized forces, their dynamics can be probed with high precision using spectroscopic and calorimetric techniques, and their behavior serves as a clean reference point for more complex glass formers. By carefully controlling temperature and thermal history, the researchers prepared glasses spanning a wide range of states, from fragile, rapidly quenched configurations to well-annealed, low-energy ones, allowing them to track how the barriers to rearrangement evolve as the material moves deeper into the glassy landscape.

The experimental strategy combined measurements of relaxation dynamics with an analysis of the mechanical work required to accommodate a local rearrangement. In essence, the researchers treated each rearranging region as an inclusion embedded in an elastic medium. When a patch of molecules changes its configuration, it must strain the surrounding material, and the elastic energy stored in that strain constitutes the barrier. By quantifying how this cost scales with the size of the rearranging region and with the macroscopic shear modulus of the glass, the team obtained a direct handle on the magnitude of the elastic barrier under different conditions. The shear modulus itself is a key player here: it stiffens as a glass ages or is cooled, and in many theoretical treatments the height of the elastic barrier is expected to scale with it, providing a thermodynamic-to-mechanical link that the new data put to a stringent test.

The results deliver a striking confirmation of the elastic picture. Across the range of states explored, the barriers to rearrangement grew in tight proportion to the shear modulus of the glass, and the proportionality constant pointed to rearranging regions whose elastic footprint extends well beyond their own boundaries. This is precisely the behavior anticipated by models in which a rearrangement must displace a surrounding elastic continuum: the cost is not set by the local chemistry of the rearranging molecules but by the stiffness of the medium in which they are embedded. The finding helps explain a long-standing puzzle in glass physics—why the activation energy for relaxation in deeply glassy states vastly exceeds any plausible local molecular energy scale. The answer, according to these measurements, is that the relevant energy scale is collective and elastic, distributed across dozens or hundreds of surrounding molecules.

Beyond confirming the scaling, the study quantifies the absolute magnitude of the elastic barriers and locates them within the broader energy landscape of the glass. In the language of landscape theory, the configuration space of a glass can be pictured as a rugged terrain of metabasins—large valleys subdivided into finer minima—separated by barriers of varying height. The new measurements suggest that elastic barriers form the dominant topography at the level of metabasins, while finer-scale features within each valley reflect local, chemically determined energy differences. This hierarchical decomposition has practical implications: it means that aging, annealing, and other thermal treatments that stiffen a glass do so primarily by raising the elastic walls between metabasins, thereby suppressing the large-scale rearrangements responsible for macroscopic relaxation and flow.

The work also speaks to a debate that has divided the glass community for years: the respective roles of thermodynamic and elastic contributions to the so-called pseudothermodynamic free energy that governs cooperative rearrangements. Classic treatments, notably the Adams–Gibbs framework and its modern descendants, assign a central role to a configurational entropy that vanishes at an ideal glass transition, with the barriers to rearrangement emerging from the shrinking number of available configurations. Elastic models, by contrast, locate the dominant barrier in the mechanical cost of deforming the surroundings. The new data indicate that at low temperatures and in well-annealed states, the elastic term is not a correction but the leading contribution, growing in a way that the purely thermodynamic accounts struggle to reproduce. This does not invalidate the thermodynamic perspective—the entropy of the glassy state remains central to understanding why glasses fall out of equilibrium—but it reweights the terms in the balance in a way that future theories will need to accommodate.

The implications reach well beyond fundamental physics. Molecular glasses are ubiquitous in technology. Amorphous solid dispersions of pharmaceutical compounds rely on glassy stability to keep poorly soluble drugs in a bioavailable form; any crystallization or structural relaxation during storage can compromise a medication’s shelf life. Organic electronics depend on glassy films of small molecules whose charge-transport properties degrade as the material relaxes. Optical coatings, amorphous solar-cell absorbers, and protective glassy layers on cultural artifacts all age through the same microscopic rearrangements quantified in this study. A quantitative model of elastic barriers gives engineers a predictive tool: by measuring or computing a glass’s shear modulus, one can now estimate the barriers to relaxation and, from there, the material’s stability window. That is a significant step toward rational, rather than empirical, design of glassy materials.

The study may also influence how researchers think about deformation in amorphous solids more broadly. Plastic flow in metallic glasses, foams, emulsions, and granular materials is widely understood to proceed through localized rearrangement events—shear transformation zones in the language of plasticity theory—each of which must strain an elastic environment. The scaling relations established here for thermal molecular glasses provide a benchmark for testing whether the same elastic accounting governs athermal and driven systems. If the proportionality between barrier height and shear modulus proves robust across that spectrum, it would unify the thermal glass transition with the mechanics of amorphous plasticity under a single framework, one of the long-sought unifications in soft matter and condensed matter physics.

For the researchers, the immediate next steps involve extending the measurements to more fragile glass formers, to mixtures where molecular size disparity suppresses crystallization further, and to ultrathin films where confinement is known to alter both the modulus and the dynamics. Confinement is a particularly provocative direction: thin glassy films often show dramatically enhanced mobility, and the elastic framework makes a concrete prediction—thinner films should support rearrangements with a smaller elastic cost, because the strained volume of surrounding material is geometrically limited. Testing that prediction would constitute an independent check of the barrier quantification and could settle whether substrate effects on glass dynamics are fundamentally elastic in origin.

What emerges from this work is a picture of the glassy state in which rigidity and stagnation are not merely consequences of molecules being stuck in place, but of an elastic web that binds each molecule’s fate to its neighbors. A single molecular rearrangement, in this view, is a collective event whose price is paid across an extended elastic field. By turning a qualitative metaphor into measured numbers—barrier heights, scaling exponents, and the connection to a directly measurable modulus like the shear modulus—the study converts one of glass physics’s guiding intuitions into quantitative, testable science. As the field moves toward a predictive understanding of amorphous materials, results of this kind, grounding the abstract landscape in concrete mechanics, are likely to serve as reference points for years to come.