Nonisothermal Nucleation Research Articles

Manipulation of non-isothermal crystallization kinetics of poly(lactic acid) composite film by a novel nucleating agent

As a type of renewable and biodegradable polymer, poly(lactic acid) (PLA) has been widely used in various fields. However, its weak crystallization ability deteriorates the properties of the final product. In this work, a novel nucleating agent (MWCNTs@CeO2), multi-walled carbon nanotubes (MWCNTs) decorated with ceria (CeO2), was synthesized using the hydrothermal method and subsequently used to manipulate the non-isothermal crystallization kinetics and nucleation behavior of PLA. The results show that MWCNTs@CeO2 can act as an effective nucleating agent to accelerate the crystallization rate of PLA by reducing the half-crystallization time. In non-isothermal crystallization kinetics, the Avrami equation modified by Jeziorny cannot accurately describe the non-isothermal crystallization behavior of PLA and PLA/MWCNTs@CeO2 composite films, whereas the Mo method can. Furthermore, it is found that the addition of MWCNTs@CeO2 does not change the crystal structure of PLA, but increases the nucleation and growth rate of PLA, thereby promoting its crystallization.

Multiscale approach to the theory of nonisothermal homogeneous nucleation.

Molecular dynamics (MD) of the Lennard-Jones cluster in the environment of supersaturated vapor at fixed temperature and density is used for the investigation of nonisothermal nucleation. The results allow one to single out different processes occurring at different time scales, the Ornstein-Uhlenbeck fluctuations at the short time scale and a combination of slow diffusion and drift of the fluctuation packet that represents a cluster, at the long time scale. The multiscale approach is developed, in which a separate treatment of different time scales makes it possible to consider strongly correlated cluster size and temperature. This reduces the nonisothermal cluster evolution to a one-dimensional problem. The fluctuation packet drift velocity and diffusivity are calculated based on the cluster microscopic thermophysical parameters determined in this work from MD data for isothermal clusters. The proposed approach is consistent with the results of our MD simulation.

A constant number Monte Carlo approach to examine Non-Isothermal nucleation and growth in a limited vapor system

Nucleation and growth are the central reactions in gas phase nanomaterial synthesis reactors. When particles collisionally grow, latent heat release occurs, which can lead to particle elevated thermal energies, and in turn greatly affect particle size distribution evolution. Unfortunately, particle heating during growth is difficult to probe experimentally, and atomistic scale simulations accounting for heating are computationally expensive. Here, we devise a constant number Monte Carlo simulation approach to study particle growth, permitting growing particles to be in thermal non-equilibrium with their gaseous surroundings. To examine how non-isothermal effects influence particle growth, we studied the nucleation of gold particles in a closed system with high initial saturation ratio and variable background gas temperatures. Particles evolve by condensation, coagulation, and evaporation. The model also incorporates collisional or dissociative latent to sensible heat conversion, heat transfer between particles and surrounding gas, and black body radiation, which are difficult to incorporate in traditional population balance studies. Simulations clearly demonstrate how the system temperature, pressure, initial saturation ratio, heat transfer rate affect the particle size distribution evolution, thermal energy distributions, and the inferred system nucleation rates. Using Jaccard and Frobenius similarities, we also developed metrics of the “non-isothermalness” of particle evolution processes by comparing non-isothermal nucleation size distributions with their isothermal counterparts. We find that a simple dimensionless ratio between gas cooling rate to condensational heating rate can serve as a guide in evaluating the necessity of non-isothermal heat transfer model in gas phase synthesis reactions.

Enthalpy effect on the kinetics of concurrent nucleation and chemical aging of aqueous organic aerosols: The stage of thermal relaxation

The size and composition distribution of an ensemble of aqueous organic droplets, evolving via nucleation and concomitant chemical aging, may be affected by the latent heat of condensation and enthalpy of heterogeneous chemical reactions, so the temperature of the droplet may deviate from the air temperature and thus become an independent variable of its state (additional to its size and composition variables). Using the formalism of the classical nucleation theory, we derive a partial differential equation for the temporal evolution of the distribution of an ensemble of such droplets with respect to all their variables of state via Taylor series expansions of the corresponding multidimensional discrete equation of balance, describing the material and heat exchange between droplets and air. The resulting kinetic equation goes beyond the framework of the Fokker-Planck approximation with respect to the temperature variable. A hierarchy of time scales of nonisothermal nucleation and concomitant chemical aging of aqueous organic aerosols is established and an analytical description of their thermal relaxation stage is developed, allowing one to estimate the characteristic time of the establishment of the equilibrium distribution of aerosol particles with respect to their temperatures. Theoretical results are illustrated with numerical calculations for the concurrent nucleation and chemical aging of model aqueous hydrophilic-hydrophobic organic aerosols in air.

Numerical analysis method for intra-stage non-equilibrium two-phase condensing flow in wet steam turbine and its application

To improve the numerical calculation performance of the intra-stage wet steam non-equilibrium condensing flow in a wet steam turbine, this paper proposed a numerically modified wet steam non-equilibrium condensation (NEC) model by considering the interphase heat and mass transfer in the Euler/Euler coordinate system. The model was developed based on nucleation kinetics, and the expressions of the critical droplet formation free energy and the nucleation rate were given. First, combining the experimental data, the non-isothermal effect nucleation model was modified by the surface tension coefficient method. Then, the low-pressure modified droplet growth model, which is suitable for describing any range of Knudsen numbers, was employed to calculate the droplet surface heat and mass transfer process, and the steam/liquid two-phase control equations and the turbulence model were presented. Meanwhile, the parameter transfer and coupling problem between the vapor and liquid phases was solved. Subsequently, the modified model and the original model were adopted to solve the wet steam condensing flow at the 1D Moses-Stein nozzle numerically, and the results showed that the modified model could calculate the distribution characteristics of pressure and droplet radius more accurately and fit the experimental results better. Afterward, the characteristicsof the non-equilibrium condensing flow of wet steam in the steam turbine cascade were investigated. Finally, combined with the experimental result on the pressure distribution in the steam turbine plane static cascade, the validity of the proposed numerically modified model was further verified, which provided a theoretical basis for the high-accuracy numerical analysis of the condensing flow in the nuclear power wet steam turbine cascade.

Nonisothermal nucleation in the gas phase is driven by cool subcritical clusters

Nucleation of clusters from the gas phase is a widely encountered phenomenon, yet rather little is understood about the underlying out-of-equilibrium dynamics of this process. The classical view of nucleation assumes isothermal conditions where the nucleating clusters are in thermal equilibrium with their surroundings. However, in all first-order phase transitions, latent heat is released, potentially heating the clusters and suppressing the nucleation. The question of how the released energy affects cluster temperatures during nucleation as well as the growth rate remains controversial. To investigate the nonisothermal dynamics and energetics of homogeneous nucleation, we have performed molecular dynamics simulations of a supersaturated vapor in the presence of thermalizing carrier gas. The results obtained from these simulations are compared against kinetic modeling of isothermal nucleation and classical nonisothermal theory. For the studied systems, we find that nucleation rates are suppressed by two orders of magnitude at most, despite substantial release of latent heat. Our analyses further reveal that while the temperatures of the entire cluster size populations are elevated, the temperatures of the specific clusters driving the nucleation flux evolve from cold to hot when growing from subcritical to supercritical sizes and resolve the apparent contradictions regarding cluster temperatures. Our findings provide unprecedented insight into realistic nucleation events and allow us to directly assess earlier theoretical considerations of nonisothermal nucleation.

Influencia de etilcelulosa en una mezcla multicomponente (monopalmitato de sorbitan-aceites vegetales) sobre las propiedades fisicoquímicas de organogeles

The modification of vegetable oils from liquid to solid state gel type is achieved by organogelation, the first phenomenon experienced is nucleation that can be spectrophotometrically evaluated and obtain thermodynamic properties. The objective of the work was to evaluate the solid formation from nucleation to macroscopic properties of the mixture: sorbitan monopalmitate and ethyl cellulose in canola, olive and coconut vegetable oils. Nucleation kinetics, solid growth analysis, oscillatory rheology characterization, thermal properties by differential scanning calorimetry and microstructural formation by optical microscopy were evaluated. Non-isothermal nucleation kinetics indicated short induction times for canola and prolonged in coconut, the inclusion of ethyl cellulose involved a more compact solid formation in the systems, without modifying the growth parameters, the coconut organogel was more sensitive to thermal changes. Non-isothermal nucleation kinetics are useful for determining the thermodynamic properties of organogels and the closest to thermodynamic equilibrium, the inclusion of ethyl cellulose being decisive; same that does not influence formation speed and solid growth. The multicomponent gels obtained showed that the structural differences depend on the concentration of the mixture that includes ethyl cellulose, presenting more compact structures and thereby more resistant gels. Keywords: nucleation, organogelation, ethyl cellulose, vegetable oils.

Methane hydrate nucleation on water—methane and water—decane boundaries

The nucleation of methane hydrate in water – methane and two-layer water – decane – methane systems was studied using thermal analysis under methane pressure. The nucleation processes in the systems under consideration were represented as empirical survival curves. The effect of aggregate state of guest-rich phase on the methane hydrate nucleation process was evaluated. The experiments were carried out at constant supercooling (19.7 °C). The two-step shape of experimental survival curves was observed in the both studied systems. Based on the data obtained and literature data, it was assumed that in the case of Teflon containers steady-state methane hydrate nucleation occurred at interfaces of water – methane and water – decane saturated with methane while non-isothermal nucleation with a higher rate may be caused by the presence of a small quantity of microimpurities in the initial samples or two-step mechanism of the methane hydrate nucleation process. The comparison of the observed periods of non-stationarity during which nucleation rate takes constant value and calculated nucleation rates showed that the presence of a liquid phase rich with the hydrate-forming component promotes a steadier nucleation of the methane hydrate in the quiescent reactor and facilitates the formation of clusters in the surface layer (water – decane).

Nonisothermal Nucleation in the Solid Solution CuCl in Glass: Temperature Range of the Formation of Supercritical Nuclei of CuCl Phase

It is established both experimentally and by calculations that the nuclei of CuCl phase do not form in the solid solution of CuCl in the glass at the temperature Tu ≥ 600°C. At the temperature of 500°C, nuclei do not form due to a low diffusion coefficient. In the temperature range of 500–600°C maximums of the flow of new clusters and the critical radius are almost at the same temperature. The supersaturation is minimal in the area of maximum. The experimental dependence of the formation rate of CuCl clusters on temperature is in a good agreement with the calculated one. It is shown that the concentration of nuclei, its average radius, and the width of distribution by radii can be effectively controlled using the cooling “on the top.” The narrow distributions of CuCl clusters in the glass with the relative half-width of about 3.7% are obtained.

Nucleation rates of droplets in supersaturated steam and water vapour–carrier gas mixtures between 200 and 450 K

We compare experimental nucleation rates for water vapour in various carrier gases, estimated nucleation rates for steam, and nucleation rates obtained from molecular simulations. The data for steam are deduced from empirical adjustments of the classical nucleation theory developed by various authors to reproduce pressure and optical data for condensing steam flows in converging-diverging nozzles and turbine stages. By combining the data for nucleation in carrier gases and the data for steam nucleation, an unprecedented temperature range of 250 K is available to study the temperature dependence of nucleation rate. Original results of molecular dynamic simulations for TIP4P/2005 force field in the NVE (system constrained by number of particles, volume and energy) conditions are provided. Correction of classical nucleation theory for non-isothermal nucleation conditions is applied to experimental and simulated data. The nucleation rate data for steam follow a similar temperature trend as the nucleation rate data for water vapour in carrier gases at lower temperatures. The ratio of observed nucleation rates to classical nucleation theory predictions decreases more steeply with temperature than the empirical correlation by Wölk et al. ( J Chem Phys 2002; 117: 4954–4960). On the contrary to experimental data, the ratios of nucleation rates computed from molecular simulations to classical nucleation theory predictions do not show a significant temperature trend.

Effect of molar mass on enthalpy relaxation and crystal nucleation of poly (l-lactic acid)

The effect of the chain length/molar mass of poly (l-lactic acid) (PLLA) on the formation of homogeneous crystal nuclei below and above the glass transition temperature (Tg) has been analyzed by fast scanning chip calorimetry, employing Tammann’s nuclei development method. It has been found that the kinetics of crystal nucleation below Tg is independent on the chain length within the investigated range of molar masses from about 60 to 600kDa, similar as the kinetics of enthalpy relaxation. In contrast, at temperatures well above Tg there is detected that crystal nucleation is slower in samples of higher molar mass. This observation is confirmed by non-isothermal nucleation experiments which showed that suppression of nucleation occurs on cooling at rates of 200, 100, and 30K/s in samples with molar masses of around 60, 100, and 600kDa, respectively. The different effect of molar mass on crystal nucleation in the glass and well above Tg is discussed in terms of the length-scale of required chain-mobility and of the critical size of nuclei.

Nonisothermal nucleation in a solid solution of CuCl in glass: Concentration effect upon heating of the solid solution

The influence of the heating rate of a solid solution of CuCl in glass on the size distribution of the produced CuCl nanoparticles is studied. The distribution curves of CuCl nanocrystals are determined by the method of exciton-thermal analysis. It is established that the concentration of CuCl nanoparticles increases by ten times upon slowing the sample heating process from 2 to 60 min, while the mean radius of particles decreases almost twice. The concentration of CuCl nanoparticles passes through a maximum in the process of heating the sample. The numerical simulation of the nucleation upon slow heating of a solid solution showed that the formation of the concentration maximum of the new phase clusters is determined by a rapid increase in the critical radius owing to an increase in temperature and decrease in the solution supersaturation. As a result, the formation of new phase nuclei ceases at a certain temperature, and a part of the previously formed clusters dissolves.

The concentration effect at nonisothermal nucleation under conditions of solid-solution heating

The influence of the heating rate of a solid solution up to the temperature of isothermal annealing on the distribution of CuCl particles by radii has been studied using the example of a solid solution of CuCl in glass. The study of changes in the distribution of particle radii in the CuCl phase has been performed using exciton-thermal analysis. It has been found that, with slow (60 min) heating of the sample to 650°C, the concentration of nucleates in the CuCl phase first increases rapidly and, then, the concentration decreases. The decrease in concentration is explained by the rapid growth of the critical radius with temperature and depletion of the solution. As follows from numerical simulation, the nucleation in a solution of CuCl in glass under conditions of slow heating is in good agreement with the experimental data.

Effect of Ag nanoparticle embedment on electroactive phase nucleation of PVDF and PVDF-HFP under non-isothermal condition: A comparative study

Silver nano-particle embedded polyvinylidene fluoride (PVDF) and poly (vinylidene fluoride– hexafluoropropylene) (PVDF-HFP) was prepared by in-situ chemical reaction. The formation of silver nanoparticles was confirmed by UV–vis spectroscopy and HR-TEM image analysis. The weight percentage of silver nano-particle was estimated by thermogravimetric analysis (TGA). Nonisothermal melt-crystallization kinetics and nucleation of molten polymers were analyzed by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). Different parameters coming from the DSC data recommended that silver nano-particle enhanced the molecular chain mobility of molten PVDF during its crystallization but for PVDF-HFP it hindered the chain mobility. The values of effective activation energies, calculated by the differential isoconventional method supported the results. Fourier transform infrared spectroscopy (FT-IR) and melting thermograms of different samples concluded that silver nano-particles helped to form polar β- phase of molten PVDF during crystallization but it was ineffective for PVDF-HFP.

Exciton-thermal analysis of nonisothermal nucleation in solid solution of CuCl in glass

The work presents results of investigation of nucleation of CuCl nanocrystals in glass by method of exiton-thermal analysis (ETA) which is based on measuring the optical absorbance of CuCl phase in sample under heating up to the melting temperature of CuCl nanocrystals. The melting temperature of nanoparticle depends on its radius. Therefore analysis of curve of melting CuCl phase allows to determine distribution curve of nanoparticles on their radii. By the method of ETA the features of variation of CuCl nanoparticles distributions in glass when changing regime of sample annealing (nonisothermal nucleation) were studied. For example, by reducing the heating rate of the sample the concentration of particles of CuCl phase increases considerably while reducing average radius.

Experimental Test of Tammann's Nuclei Development Approach in Crystallization of Macromolecules

Abstract Prediction of the supermolecular structure and with that of properties of crystallizable polymers requires in-depth knowledge about the crystallization behavior, in particular the temperature-dependence of the nucleation kinetics. Typically, at low supercooling of the melt the nucleation rate/nuclei density often is assessed by optical microscopy, through an analysis of the evolution of the spherulitic superstructure. This approach fails if the nuclei density is too high, or if nuclei formation is not followed by growth due to chain-mobility constraints. In such cases, Tammann's two-stage crystal nuclei development method can be applied. It includes the formation of crystal nuclei at high supercooling of the melt, and their detection at higher temperature, after their growth to crystals. Though initially developed for analysis of low molecular mass compounds, this approach has recently also successfully been employed for analysis of the nucleation behavior of polymers, which is demonstrated here on the examples of poly (L-lactic acid) (PLLA), and poly (∊-caprolactone) (PCL). While in case of PLLA the ability to gain information about isothermal and non-isothermal nucleation is explained, in case of PCL new information about the thermal stability of nuclei is presented. The importance of such analyses in the context of understanding structure formation of polymers at processing-relevant cooling conditions is discussed.

Kinetic model of non-isothermal crystal nucleation with transient and athermal effects

A kinetic model of primary homogeneous non-isothermal crystal nucleation with transient and athermal effects is developed. For comparison, steady-state and transient isothermal nucleation rates are considered. Kinetic equation for the development of cluster size distribution provides the basis for the model. Transient effects are characterized by the longest relaxation time which increases with temperature at low and moderate undercooling. In isothermal conditions, nucleation rate is controlled by thermal mechanism; in non-isothermal conditions, there appears also athermal mechanism. Closed-form analytical formula for the development of transient cluster size distribution in single-relaxation-time approximation is derived for non-isothermal processes, as well as thermal and athermal nucleation rates and total number of nuclei produced in a cooling or heating run. The transient term contributes to isothermal nucleation kinetics the more the higher is temperature. Under non-isothermal conditions, the relaxation time contributes to the nucleation kinetics by the product with the cooling/heating rate. Considerable transient effects should be expected for the relaxation times as long as 102–105 s. Contribution of thermal nucleation to the concentration of nuclei is inversely proportional to the temperature rate, while the contribution of athermal nucleation depends on the temperature interval of cooling or heating. Our kinetic model indicates similarities in the nucleation mechanisms in polymers and metals undergoing crystallization. Example computations are presented for molten indium and a linear polymer—polyhydroxybutyrate (PHB). A low-temperature limit is predicted for the nucleation mechanism in PHB, while for indium the mechanism is active in the entire temperature range.

Crystal nucleation in random l/d-lactide copolymers

Poly (l-lactic acid) (PLLA) and its random copolymers with small amount of d-isomer co-units but identical mass-average molar mass of 120kDa were analyzed regarding the non-isothermal and isothermal crystallization and nucleation behaviors. First, it was confirmed that the gross crystallization rate and crystal growth rate decrease with increasing d-isomer content in the chains. In extension to earlier work, the isothermal analysis of the crystallization rate was completed by determination of critical cooling rates to suppress ordering of the melt. While in case of the PLLA homopolymer the melt needs to be cooled faster than 0.5Ks−1 in order to suppress crystallization, the critical cooling rate is lowered by about one order of magnitude to 0.05Ks−1 in case of a copolymer with 4% d-isomer co-units. However, even if the melt is cooled faster than the critical cooling rate to suppress crystallization, nuclei formation still occurs in a specific cooling-rate range depending on the d-isomer content, ceasing only on cooling about two orders of magnitude faster than the critical cooling rate to suppress crystallization. The observation of slower nuclei formation at non-isothermal conditions in PLLA containing d-isomer co-units is confirmed by isothermal nucleation experiments.

Effect of an aryl amide derivative on the crystallization behaviour and impact toughness of poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) and aryl amide derivative (TMB-5) blends were prepared by melt blending. It was found that TMB-5 shows a significant nucleation effect on PET and especially the non-isothermal nucleation efficiency reached up to 80.7% at a very low content of 0.6 wt% TMB-5. The effects of TMB-5 on the crystallization behavior and mechanical properties of PET were systematically investigated. DSC results show that crystallization temperature of PET apparently increased by nearly 20 °C with the addition of 0.6 wt% TMB-5 during the cooling process. A remarkable acceleration in the crystallization rate of PET was achieved as analyzed using the Avrami equation. Wide angle X-ray diffraction (WAXD) and polarized optical microscopy (POM) results show that the addition of TMB-5 remarkably increases the crystallinity and nuclei density of PET. Small angle X-ray scattering (SAXS) measurements reveal that the long period of PET decreased and lamellar thickness increased with an increase in TMB-5 content. The impact strength of PET was greatly enhanced by the addition of TMB-5, and a toughening mechanism was proposed.

Nonisothermal nucleation in the CuCl solid solution in glass: Nucleation under continuous cooling of the solid solution

The processes of nonisothermal nucleation in the CuCl solid solution in glass under continuous cooling from 700 to 500°C have been investigated. It has been shown that, in the studied cooling modes, regardless of the cooling rate, two distributions of CuCl nanoparticles with radii in the ranges of 8–20 and 2.5–3.5 nm in the absence of particles with intermediate radii are formed. The simulation of the nucleation under continuous cooling of the solid solution has revealed some features in the kinetics of the formation of two distributions of nanoparticles that differ significantly in size. It has been found that, under specific conditions, there can arise one wide distribution (strongly overlapping distributions). The role of a change in the critical radius during the nonisothermal nucleation (cooling of the solid solution) in the formation of a binary distribution has been demonstrated.