Homogeneous Crystal Nucleation Research Articles

3D visualization reveals the cooling rate dependent crystallization near a wall in dense microgel systems.

Controlled crystallization, melting and vitrification are important fundamental processes in nature and technology. However, the microscopic details of these fundamental phenomena still lack understanding, in particular how the cooling rate and presence of a wall influence the crystal nucleation and glass formation. Thermoresponsive microgels provide the possibility to study phase transitions at the single-particle level, owing to the ability to tune the particle size with temperature. In this study, we employ composite microgels consisting of a hard core and a crosslinked poly(N-isopropyl acrylamide-co-methacrylic acid) shell to study the crystallization of dense suspensions of soft colloids near a wall using confocal microscopy. We investigate the effect of the cooling rate on the fluid-to-solid transition close to the sample wall. The structures formed during cooling range from glassy in the case of a rapid temperature quench to crystalline when a slow cooling rate is used. Detailed analysis of the final structure reveals that the cooling rate also sets the degree of alignment of the crystal domains with the wall as a result of a balance between homogeneous and heterogeneous crystal nucleation. The results presented here yield valuable insight into the microscopic details of temperature-controlled crystallization near a wall. This understanding will help pave the way towards optimal crystallization conditions for microgel applications.

Homogeneous Organic Crystal Nucleation Rates in Solution from the Perspective of Chemical Reaction Kinetics

It is demonstrated for 11 different combinations of organic solutes and solvents that the supersaturation dependence of homogeneous organic crystal nucleation rates from solution can be predicted from the solubility, bar a single empirical rate constant, when it is assumed that nucleation takes place in reversible aggregates of solvated solutes formed in supersaturated solutions. Reversible solute aggregation represents natural solute density fluctuations that take place in any solute/solvent system. For thermodynamically ideal solutions, the steady state size distribution, and thus the population of reversible aggregates in supersaturated solution, can be predicted quantitatively from the overall solute concentration by a simple mathematical expression. Supersaturation creates an excess of reversible aggregates with sizes exceeding that of the largest aggregate in saturated solution. It is shown that the number of these excess aggregates is proportional to experimental homogeneous nucleation rates, suggesting a rate equation for homogeneous nucleation that has only one empirical parameter, namely, a rate constant specific to the solute/solvent combination. This rate constant can be determined from standard nucleation rate data. The system-specificity of homogeneous nucleation rates thus appears to be encoded solely in a rate constant for the transformation of the large excess aggregates into crystal nuclei. The driving force for triggering nucleation events in these aggregates is likely the extremely high local supersaturation, which provides the conditions for spatiotemporally aligned bond-breaking (e.g., de-solvation) and bond-forming (e.g., solute–solute bonding) events that create stable crystal nuclei. The possible influence of heterogeneous nucleation by solid impurities is considered.

In-situ observation of homogeneous nucleation of colloidal crystals formed with attractive interactions under density-matching conditions

Colloidal crystals formed with attractive interactions are used for in-situ observations of homogeneous nucleation processes in density-matched dispersion. We found globular and plate-like polycrystalline clusters stably suspended in the dispersion. Both clusters rotated randomly and moved freely with suspending in the dispersion. They were probably formed through homogeneous nucleation processes.

Transient nucleation driven by solvent evaporation.

We theoretically investigate homogeneous crystal nucleation in a solution containing a solute and a volatile solvent. The solvent evaporates from the solution, thereby continuously increasing the concentration of the solute. We view it as an idealized model for the far-out-of-equilibrium conditions present during the liquid-state manufacturing of organic electronic devices. Our model is based on classical nucleation theory, taking the solvent to be a source of the transient conditions in which the solute drops out of the solution. Other than that, the solvent is not directly involved in the nucleation process itself. We approximately solve the kinetic master equations using a combination of Laplace transforms and singular perturbation theory, providing an analytical expression for the nucleation flux. Our results predict that (i) the nucleation flux lags slightly behind a commonly used quasi-steady-state approximation. This effect is governed by two counteracting effects originating from solvent evaporation: while a faster evaporation rate results in an increasingly larger influence of the lag time on the nucleation flux, this lag time itself is found to decrease with increasing evaporation rate. Moreover, we find that (ii) the nucleation flux and the quasi-steady-state nucleation flux are never identical, except trivially in the stationary limit, and (iii) the initial induction period of the nucleation flux, which we characterize as a generalized induction time, decreases weakly with the evaporation rate. This indicates that the relevant time scale for nucleation also decreases with an increasing evaporation rate. Our analytical theory compares favorably with results from a numerical evaluation of the governing kinetic equations.

RSeeds: Rigid Seeding Method for Studying Heterogeneous Crystal Nucleation

Heterogeneous nucleation is the dominant form of liquid-to-solid transition in nature. Although molecular simulations are most uniquely suited to studying nucleation, the waiting time to observe even a single nucleation event can easily exceed the current computational capabilities. Therefore, there exists an imminent need for methods that enable computationally fast and feasible studies of heterogeneous nucleation. Seeding is a technique that has proven to be successful at dramatically expanding the range of computationally accessible nucleation rates in simulation studies of homogeneous crystal nucleation. In this article, we introduce a new seeding method for heterogeneous nucleation called Rigid Seeding (RSeeds). Crystalline seeds are treated as pseudorigid bodies and simulated on a surface with metastable liquid above its melting temperature. This allows the seeds to adapt to the surface and identify favorable seed-surface configurations, which is necessary for reliable predictions of crystal polymorphs that form and the corresponding heterogeneous nucleation rates. We demonstrate and validate RSeeds for heterogeneous ice nucleation on a flexible self-assembled monolayer surface, a mineral surface based on kaolinite, and two model surfaces. RSeeds predicts the correct ice polymorph, exposed crystal plane, and rotation on the surface. RSeeds is semiquantitative and can be used to estimate the critical nucleus size and nucleation rate when combined with classical nucleation theory. We demonstrate that RSeeds can be used to evaluate nucleation rates spanning many orders of magnitude.

Formation of imperfect crystals in poly(ε-caprolactone) at high melt-supercooling

• Fast scanning calorimetry permits homogeneous crystal nucleation in PCL. • Crystallization of PCL near the glass transition yields non-lamellar, imperfect crystals. • Low-temperature crystallization of PCL suppresses spherulitic crystal growth. Poly(ε-caprolactone) (PCL) was crystallized at high melt-supercooling in a fast scanning chip calorimeter, with this instrumentation needed to reach the temperature range of homogenous crystal nucleation by fast cooling the melt. Subsequently, after slow heating the polymer to ambient temperature, the semicrystalline morphology and X-ray structure were evaluated. Nucleation and crystallization at low temperature yields a featureless structure at the micrometer-length scale, indicating non-spherulitic crystal growth. Images of the nanometer-scale structure suggest presence of irregular grown short lamellae or particle-like domains, and the absence of sharp peaks in the X-ray scattering pattern indicates formation of small or defective crystals. In conclusion, due to the high nuclei density, crystallization of PCL near the glass transition leads to formation of imperfect crystals, and slow heating to ambient temperature does not allow their reorganization to yield long-range orthorhombic order, typically observed on crystallization at low melt-supercooling.

Radiation-Induced Nucleation and Growth of CaSi2 Crystals, Both Directly during the Epitaxial CaF2 Growth and after the CaF2 Film Formation.

The radiation-induced phenomena of CaSi2 crystal growth were investigated, both directly during the epitaxial CaF2 growth on Si (111) and film irradiation with fast electrons on Si (111) after its formation, while maintaining the specified film thickness, substrate temperature and radiation dose. Irradiation in the process of the epitaxial CaF2 film growth leads to the formation of CaSi2 nanowhiskers with an average size of 5 µm oriented along the direction <110>. The electron irradiation of the formed film, under similar conditions, leads to the homogeneous nucleation of CaSi2 crystals and their proliferation as inclusions in the CaF2 film. It is shown that both approaches lead to the formation of CaSi2 crystals of the 3R polymorph in the irradiated region of a 10 nm thick CaF2 layer.

Liquid ordering induced heterogeneities in homogeneous nucleation during solidification of pure metals

Homogeneous crystal nucleation is prone to formation of defects and often experiences heterogeneities, the inferences of which are crucial in processing crystalline materials and controlling their physical properties. It has been debated in literature whether the associated heterogeneities are an integral part of the homogenous nucleation. In this study by integrating a probabilistic approach with large-scale molecular dynamics simulations based on the most advanced high-temperature interatomic potentials, we attempt to address the ambiguity over the sources and mechanisms of heterogeneities in homogenous nucleation during solidification of pure melts. Different classes of structured metals are investigated for this purpose, including face-centered cubic aluminum, body-centered cubic iron, and hexagonal close-packed magnesium. The results reveal, regardless of the element type or the solidified crystal structure, that the densification process of liquid metals is accompanied by short-range orderings of atoms prior to the formation of crystals, controlling the heterogeneities during homogenous nucleation.

How to quantify and avoid finite size effects in computational studies of crystal nucleation: The case of homogeneous crystal nucleation.

Finite size artifacts arise in molecular simulations of nucleation when critical nuclei are too close to their periodic images. A rigorous determination of what constitutes too close is, however, a major challenge. Recently, we devised rigorous heuristics for detecting such artifacts based on our investigation of how system size impacts the rate of heterogeneous ice nucleation [S. Hussain and A. Haji-Akbari, J. Chem. Phys. 154, 014108 (2021)]. We identified the prevalence of critical nuclei spanning across the periodic boundary, and the thermodynamic and structural properties of the liquid occupying the inter-image region as indicators of finite size artifacts. Here, we further probe the performance of such heuristics by examining the dependence of homogeneous crystal nucleation rates in the Lennard-Jones (LJ) liquid on system size. The rates depend non-monotonically on system size and vary by almost six orders of magnitude for the range of system sizes considered here. We confirm that the prevalence of spanning critical nuclei is the primary indicator of finite size artifacts and almost fully explains the observed variations in rate. Proximity, or structuring of the inter-image liquid, however, is not as strong of an indicator due to the fragmented nature of crystalline nuclei. As a result, the dependence of rate on system size is subtle for the systems with a minuscule fraction of spanning critical nuclei. These observations indicate that our heuristics are universally applicable to different modes of nucleation (homogeneous and heterogeneous) in different systems even if they might be overly stringent for homogeneous nucleation, e.g., in the LJ system.

Multiple pathways in NaCl homogeneous crystal nucleation.

NaCl crystal nucleation from metastable solutions has long been considered to occur according to a single-step mechanism where the growth in the size and crystalline order of the emerging nuclei is simultaneous. Recent experimental observations suggest that significant ion-ion correlations occur in solution and that NaCl crystals can emerge from disordered intermediates which is seemingly at odds with this established view. Here, we performed biased and unbiased molecular dynamics simulations to analyse and characterise the pathways to crystalline phases from solutions far into the metastable region. We find that large liquid-like NaCl clusters emerge as the solution concentration is increased and a wide distribution of crystallisation pathways are observed with two-step nucleation pathways-where crystalline order emerges in dense liquid NaCl regions-being more dominant than one-step pathways to phase separation far into the metastable region. Analyses of cluster size populations and the ion pair association constant show that these clusters are transient, unlike the thermodynamically stable prenucleation cluster solute species that were suggested in other mineralising systems. A Markov state model was developed to analyse the mechanisms and timescales for nucleation from unbiased molecular dynamics trajectories in a reaction coordinate space characterising the dense regions in clusters and crystalline order. This allowed calculation of the committor probabilities for the system to relax to the solution or crystal states and to estimate the rate of nucleation, which shows excellent agreement with literature values. From a fundamental nucleation perspective, our work highlights the need to extend the attribute 'critical' to an ensemble of clusters which can display a broad range of structures and include sizeable disordered domains depending upon the reaction conditions. Moreover, our recent simulation studies demonstrated that carbon surfaces catalyse the formation of liquid-like NaCl networks which, combined with the observations here, suggests that alternative pathways beyond the single-step mechanism can be exploited to control the crystallisation of NaCl.

Two-step crystal nucleation kinetics: Solution of the master equation

The master equation of two-step nucleation is numerically solved with parameters characterizing isothermal homogeneous nucleation of ice crystals and water droplets in steam below the water freezing temperature. The time dependences of the crystal and droplet size distributions and nucleation rates as well as of the nucleation rate of ice crystals in the droplets are determined at different constant supersaturations. The stationary values of these nucleation rates are obtained in a wide supersaturation range. It is found that when the crystallization of the water droplets is slower than their growth, the stationary rate of two-step crystal nucleation is orders of magnitude lower than the corresponding stationary rate of one-step crystal nucleation. As to the stationary nucleation rate of the water droplets, it is practically unaffected by the ice crystals nucleating and growing in both the droplets and the steam. Finally, the delay times of the different nucleation processes are determined and it is found that at both low and high supersaturations the delay time of the two-step crystal nucleation is negative because of the presence of high initial peak in the nonstationary rate of this process. The results obtained provide unprecedented mechanistic insight into the kinetics of two-step crystal nucleation.

Effect of dispersed water on the paraffin crystallization and deposition of emulsified waxy crude oil via dissipative particle dynamics

The gelation of emulsions is a notorious problem during the transportation of crude oil. In this study, the impact of dispersed water on the paraffin crystallization behavior in waxy crude oil was investigated using the mesoscopic dissipative particle dynamic method. The results indicated that water cuts affect the nucleation of wax crystals. The homogeneous nucleation of waxy crystals is important in systems when the water cuts are lower than the critical value (47.75 mol% of the studied systems), whereas heterogeneous nucleation becomes dominant when the water cuts are larger than the critical value. In addition, the water accelerates the nucleation and build-up of the crystal structure. Furthermore, the wax appearance temperature of the system experiences a steady increase when the water cut is lower than the critical value. The wax appearance temperature increases abruptly when the water cuts are larger than the critical value. This indicates that the injection of water further deteriorates the low-temperature rheological behavior of the emulsions. The critical water cut also impacts the competitive capture relationship between the water molecules and paraffin molecules.

Kinetics of homogeneous crystal nucleation of polyamide 11 near the glass transition temperature

Kinetics of homogeneous crystal nucleation of polyamide 11 near the glass transition temperature

New Insights into Crystallization of Heterophasic Isotactic Polypropylene by Fast Scanning Chip Calorimetry.

The crystallization kinetics of metallocene-catalyzed heterophasic isotactic polypropylene composed of a matrix of isotactic polypropylene (iPP) and rubbery particles made of random ethylene–propylene copolymers (EPC), often denoted as heterophasic iPP copolymers, was analyzed as a function of the cooling rate and supercooling in nonisothermal and isothermal crystallization experiments, respectively. Fast scanning chip calorimetry (FSC) allowed assessing crystallization at processing-relevant conditions, and variation of the content (0–39 wt %) and composition (0–35 wt % propylene counits) of the EPC particles revealed qualitatively new insight about mechanisms of heterogeneous crystal nucleation. For neat iPP homopolymer, the characteristic bimodal temperature dependence of the crystallization rate due to predominance of heterogeneous and homogeneous crystal nucleation at high and low temperatures, respectively, is reconfirmed. At high temperatures, in heterophasic iPP, the here studied ethylene-(C2)-rich EPC particles accelerate crystallization of the iPP-matrix, with the acceleration or nucleation efficacy correlating with the EPC-particle content. The crystallization time reduces by more than half in presence of 39 wt % EPC particles. An additional nucleating effect of the EPC particles on iPP-matrix crystallization is detected after their crystallization, suggesting that liquid/rubbery particles are less effective than solid/semicrystalline particles in affecting crystallization of the surrounding iPP-matrix. At low temperature, homogeneous crystal nucleation in the iPP-matrix outpaces all heterogeneous nucleation effects, and the matrix-crystallization rate is independent of the sample composition. The obtained results lead to the conclusion that the crystallization kinetics of iPP can be affected significantly by the content and composition of EPC particles, even towards superfast crystallizing iPP grades.

Critical assessment of the alleged failure of the Classical Nucleation Theory at low temperatures

The Classical Nucleation Theory allegedly fails to describe the temperature dependence of the homogeneous crystal nucleation rates below the temperature of maximum nucleation, Tmax. Possible explanations for this suspected breakdown have been advanced in the literature. However, the simplest hypothesis has never been tested, that it is a byproduct of nucleation datasets that have not reached the steady-state regime. In this work, we tested this possibility by analyzing published nucleation data for oxide supercooled liquids, using only nucleation and viscosity data measured in samples of the same glass batch that also have satisfied a steady-state regime test. Furthermore, all the uncertainty and regression confidence bands were computed and considered. Having this rigorous protocol, among the 6 datasets analyzed, we only found weak evidence supporting the existence of the nucleation break in 2 datasets. Our collective results thus indicate that the break at Tmax is not a common feature of all glass-formers.

Steady-State Crystal Nucleation Rate of Polyamide 66 by Combining Atomic Force Microscopy and Fast-Scanning Chip Calorimetry

Homogeneous crystal nucleation in polyamide 66 (PA 66) was studied by a combination of atomic-force microscopy (AFM) and fast-scanning chip calorimetry (FSC), with a specific experimental setup all...

Fingerprints of homogeneous nucleation and crystal growth in polyamide 66 as studied by combined infrared spectroscopy and fast scanning chip calorimetry

Homogenous crystal nucleation and growth in polyamide 66 (PA66) are followed in situ by means of a combination of FTIR spectroscopy and fast scanning chip calorimetry (FSC). Therefore, a novel setup with a calorimetry chip equipped with an IR-transparent SiN membrane was developed, which enables to examine IR spectroscopic and FSC experiments on the identical specimen. Because of the small amount of sample material (~ 100 ng), it is possible to achieve heating and cooling rates up to 5000 Ks−1, and hence to quench the sample into a fully amorphous state without quenched-in homogeneous crystal nuclei. Annealing the film then allows to determine the onset of homogenous nucleation and crystal growth by means of FSC, whereas molecular interactions are unraveled by FTIR spectroscopy. It is demonstrated that different moieties of PA66 respond distinctly during crystallization; far-reaching interactions such as hydrogen bonding are established prior to onset of short-range steric hindrance.Graphical Crystal nucleation and growth are followed in situ by means of a combination of FTIR spectroscopy and fast scanning chip calorimetry. For this purpose a novel IR-transparent chip enables to examine both measurements on the identical specimen, while heating and cooling rates up to 5000 Ks−1 and hence quenching into a fully amorphous state can be achieved

Specific Features of Structure Transformation and Properties of Amorphous-Nanocrystalline Alloys

This work is devoted to a brief overview of the structure and properties of amorphous-nanocrystalline metallic alloys. It presents the current state of studies of the structure evolution of amorphous alloys and the formation of nanoglasses and nanocrystals in metallic glasses. Structural changes occurring during heating and deformation are considered. The transformation of a homogeneous amorphous phase into a heterogeneous phase, the dependence of the scale of inhomogeneities on the component composition, and the conditions of external influences are considered. The crystallization processes of the amorphous phase, such as the homogeneous and heterogeneous nucleation of crystals, are considered. Particular attention is paid to a volume mismatch compensation on the crystallization processes. The effect of changes in the amorphous structure on the forming crystalline structure is shown. The mechanical properties in the structure in and around shear bands are discussed. The possibility of controlling the structure of fully or partially crystallized samples is analyzed for creating new materials with the required physical properties.

Dominant Effect of Heterogeneous Dynamics on Homogenous Crystal Nucleation in Supercooled Liquids

Understanding the microscopic (molecular) mechanism of crystal nucleation remains intangible. For instance, it is still impossible to predict in which regions of a supercooled liquid nucleation will occur. Moreover, allegedly the Classical Nucleation Theory fails to describe the homogeneous crystal nucleation rates below the glass transition temperature. In this mini-review article, we revisit, critically comment, and link some highly selected recent studies using examples of an oxide glass-former, water, and a metallic alloy on the largely neglected effect of dynamic heterogeneities on crystal nucleation.

Effects of hydrogen-bonding density on polyamide crystallization kinetics

We employed Flash DSC1 apparatus for fast-scan chip-calorimeter measurement in a broad temperature range to compare the isothermal crystallization rates among six polyamide/nylon (PA) samples, i.e. PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12. The double parabolic curves of crystallization half-time versus crystallization temperature revealed that PA 46 crystallizes relatively fast due to its high hydrogen-bonding density favoring thermodynamic driving forces for crystallization in the high temperature region, while PA 1012 and PA 12 crystallize relatively fast due to their low hydrogen-bonding densities favoring short-range diffusion for crystallization in the low temperature region. Furthermore, the cross-over temperatures between two parabolic curvatures of six samples follow their sequences in hydrogen-bonding density, and the Avrami indexes reveal a potential switching in the modes between heterogeneous and homogeneous crystal nucleation.