Gibbs-Thomson Effect Research Articles

The single freezing episode of early-age cementitious composites: Threshold properties of cement matrix ensuring the frost resistance

The freezing is recognized as one of the most dangerous phenomena jeopardizing the durability of cement-based materials. In this work, the cementitious material exposed to a single freezing event after 1, 2, 3, 7, 14, 21, and 28 days of hydration was investigated. The change of mechanical parameters, e.g. compressive strength and Young’s modulus, due to individual water crystallization was determined. Water freezing in cement paste proceeds at depressed temperature, which can be calculated using Gibbs-Thomson equation. The change of the in-pore ice content profile in temperature domain along with hydration was calculated using differential scanning calorimetry and was related with the degradation of mechanical properties. The two dominant mechanisms inducing water freezing can be recognized in cement paste: gradual ice penetration and ice nucleation. The change of microstructure along with hydration was monitored using mercury porosimetry. These observations allowed to determine the threshold properties which provide the resistance of cementitious materials to the single freezing at early age. The research was supplemented with isothermal calorimetry and XRD data of the applied binder.

Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles

Abnormal melting point depression of metal nanoparticles often occurs in heterogeneous catalytic reactions, which leads to a reduction in the stability of reactive nanoclusters. To study this abnormal phenomenon, the original and surface-energy modified Gibbs–Thomson equations were analyzed in this work and further modified by considering the effect of the substrate. The results revealed that the original Gibbs–Thomson equation was not suitable for the particles with radii smaller than 10 nm. Moreover, the performance of the surface-energy modified Gibbs–Thomson equation was improved, and the deviation was reduced to (−350−100) K, although further modification of the equation by considering the interfacial effect was necessary for the small particles (r < 5 nm). The new model with the interfacial effect improved the model performance with a deviation of approximately −50 to 20 K, where the interfacial effect can be predicted quantitatively from the thermodynamic properties of the metal and substrate. Additionally, the micro-wetting parameter αw can be used to qualitatively study the overall impact of the substrate on the melting point depression.

Melting simulations of poly(ethylene oxide) nanocrystals in amorphous environments

The embedded model has been proposed for simulating melting process of the semicrystalline polymer with a low crystalline fraction. This approach is exemplarily applied to the multiscale coarse-grained (CG) model of poly(ethylene oxide) (PEO) of 14 monomers per chain. When continuously heated to a high temperature, the nanocrystal undergoes great conformational change and disassembly in order. While the specific volume and potential energy of the semicrystalline polymer system capture only glass-rubber transition of amorphous chains, the interaction energy or contact number between the nanocrystal and its amorphous environment allows for precisely identifying glass transition temperature (Tg) and equilibrium melting point (Tm) at the same time. Furthermore, the so-simulated Tg is insensitive to the lateral dimension of the nanocrystal whereas the so-simulated Tm linearly decrease with the inverse of the lateral dimension by the variant of Gibbs-Thomson equation. The extrapolated Tg and Tm for the nanocrystal with infinite lateral dimension compare well with the referenced data. The proposed scheme is quite competitive to the previous ones for a quick and accurate prediction of the Tm of a crystallizing polymer.

Supercooled nano-droplets of water confined in hydrophobic rubber.

Hydrophobic elastomers are capable of absorbing a small amount of water that forms droplets around hydrophilic sites. These systems allow the study of confinement effects by a hydrophobic environment on the dynamics and thermodynamic behaviour of water molecules. The freezing-melting properties and the dynamics of water inside nano-droplets in butyl rubber are affected, as revealed by differential scanning calorimetry (DSC) and deuterium nuclear magnetic resonance (2H-NMR). Upon cooling down, all water crystalizes with a bimodal droplet population (da = 3.4 nm and db = 4.4 nm) in a temperature range associated with the droplet size distribution. However, the melting temperature is not shifted according to the Gibbs-Thomson equation. The relative decrease of the 2H-NMR longitudinal magnetization is not a single exponential and, by inverse Laplace transformation, it was deduced to be bimodal in agreement with the DSC measurements (T1,a ∼ 10 ms and T1,b ∼ 200 ms). The deduced correlation time of molecular reorientation is longer than that of bulk water and the behaviour with temperature follows the Vogel-Fulcher-Tammann (VFT) equations with a changing fragility as the droplet size is reduced when reducing hydration.

Thermodynamic Characterization of Planar Shapes and Curves, and the Query of Temperature in Black Holes

The purpose of this research is to characterize shapes in thermodynamic terms, namely, in terms of total energy, dissipative energy, entropy, and temperature. As case studies, polygons and some well-known curves were taken, and they were characterized using physical terms. The relation between entropy and curvature was elucidated, and the black hole surface gravity and temperature were criticized and reinterpreted from this point of view. Particular energy attributions were evaluated by comparing the position of any edge of a polygon (i.e. its angle with the horizontal axis) with a broken crystal surface. Energies of all edges were added up at all positions between 0˚ - 360˚. In regular polygons, the total energy decreases with the increase of the number of edges. Entropy increases in the reverse order, and the increase of the number of edges increases entropy. It implies that the circle has the lowest energy but the highest surface entropy. In curves (circle, sine-curve, spiral, and exponential curve), the total energy, dissipative energy, and entropy all depend on amplitude and also on specific variables. Black hole entropy expressed in terms of the surface area is a configurational entropy and not thermal entropy; therefore, it does not involve a varying temperature term. The surface gravity of a black hole is connected to acceleration and thus to curvature. To relate it with the temperature needs to be reinterpreted, because, surface gravity behaves like an attractive force not exactly like temperature. Hawking radiation is still possible, but the black hole does not get warmer as it evaporates. Material loss from the black hole gets faster as its radius decreases due to the curvature effect, i.e. by a mechanism similar to the Gibbs-Thomson effect.

Gibbs-Thompson Effect as Driving Force for Liquid Film Migration

Liquid film migration is of great practical importance in materials engineering. The phenomenon depends on thermal gradients and coherency strain, but no single driving mechanism seems capable of justifying all experimental observations. On the other hand, the inevitable capillarity effects are often indeterminable due to the unknown three-dimensional geometry of the system. Here, we present evidence of liquid film migration governed primarily by the Gibbs-Thomson effect through a microstructural setup of cylindrical interfaces designed to allow clear interpretation and modeling. The experiment relies on the strong oxygen-gettering ability of tantalum fibers dispersed in a tungsten matrix and on field-enhanced diffusivity provided by pulse plasma compaction. Tantalum scavenges residual oxygen present in the W powder and, as a result, oxide films grow around the fibers. These oxide tubes, in liquid state during sintering, migrate toward the fiber axis and become surrounded by external rims of metallic Ta. An analytical description of the film evolution is implemented by combining the incoming O flux with capillarity driven migration. P ossible contributions from other mechanisms are examined and the r elevance of the Gibbs-Thomson effect to liquid film migration is established .

How the shift in the phase transition temperature influences the evolution of crystals during the intermediate stage of phase transformations

The influence of the phase transition temperature shift on the growth dynamics of a polydisperse ensemble of spherical crystals in metastable melts and solutions is studied. This shift is connected with the Gibbs–Thomson effect and the attachment kinetics of atoms at the phase transition interfaces of evolving crystals. The nonlinear model of kinetic and balance equations with allowance for the particle “diffusion” term is solved analytically. The obtained solution is compared with the case when this temperature shift is not taken into account. It is shown that the Gibbs–Thomson and attachment kinetics effects slightly accelerate the system desupercooling for a single-component titanium melt. This shifts the particle-size distribution function and changes the shape of its tail, which is responsible for the concluding stage of Ostwald ripening.

Homogeneous water nucleation: Experimental study on pressure and carrier gas effects.

Homogeneous nucleation of water is investigated in argon and in nitrogen at about 240 K and 0.1 MPa, 1 MPa, and 2 MPa by means of a pulse expansion wave tube. The surface tension reduction at high pressure qualitatively explains the observed enhancement of the nucleation rate of water in argon as well as in nitrogen. The differences in nucleation rates for the two mixtures at high pressure are consistent with the differences in adsorption behavior of the different carrier gas molecules. At low pressure, there is not enough carrier gas available to ensure the growing clusters are adequately thermalized by collisions with carrier gas molecules so that the nucleation rate is lower than under isothermal conditions. This reduction depends on the carrier gas, pressure, and temperature. A qualitative agreement between experiments and theory is found for argon and nitrogen as carrier gases. As expected, the reduction in the nucleation rates is more pronounced at higher temperatures. For helium as the carrier gas, non-isothermal effects appear to be substantially stronger than predicted by theory. The critical cluster sizes are determined experimentally and theoretically according to the Gibbs-Thomson equation, showing a reasonable agreement as documented in the literature. Finally, we propose an empirical correction of the classical nucleation theory for the nucleation rate calculation. The empirical expression is in agreement with the experimental data for the analyzed mixtures (water-helium, water-argon, and water-nitrogen) and thermodynamic conditions (0.06 MPa-2 MPa and 220 K-260 K).

Macrosegregation and thermosolutal convection-induced freckle formation in dendritic mushy zone of directionally solidified Sn-Ni peritectic alloy

Compared with the growing applications of peritectic alloy, none research on the freckle formation during peritectic solidification has been reported before. Observation on the dendritic mushy zone of Sn-36 at.%Ni peritectic alloy during directional solidification at different growth velocities shows that the freckles are formed in two different regions: region I before peritectic reaction and region II after peritectic reaction. In addition, more freckles can be observed at lower growth velocities. Examination on the experimental results demonstrates that both the temperature gradient zone melting (TGZM) and Gibbs-Thomson (G–T) effects have obvious influences on the morphology of dendritic network during directional solidification. The current theories onKI Rayleigh number Ra characterizing the thermosolutal convection of dendritic mushy zone to predict freckle formation through the maximum of Ra can only explain the existence of region I while the appearance of region II after peritectic reaction cannot be predicted. Thus, a new Rayleigh number RaP is proposed in consideration of evolution of dendritic mushy zone by both effects and peritectic reaction. Theoretical prediction of RaP also shows a maximum after peritectic reaction in addition to that before peritectic reaction, thus, agreeing well with the freckle formation in region II. In addition, more severe thermosolutal convection can be predicted by the new Rayleigh number RaP at lower growth velocities, which further demonstrates the reliability of RaP in describing the dependence of freckle formation on growth velocity.

Growth Kinetics of Planar Nanowires

An approximate analytic equation is derived that describes the law of elongation of a semiconductor nanowire (NW) growing via the vapor–liquid–solid (VLS) mechanism in a substrate plane. Various growth regimes are theoretically analyzed as dependent on NW radius R and epitaxial deposition conditions. It is established that the growth rate of planar NWs can be controlled either by the Gibbs–Thomson effect (in the case of small catalyst droplet dimensions) or by the diffusion of adatoms from the substrate surface (for increasing radius of the crystal). Dependence of the diffusion-controlled growth rate on radius R obeys the R–m law, where the power exponent takes the values of 1, 3/2, or 2 depending on the character of surface diffusion.

Comparative Study of VC, NbC, and TiC Interphase Precipitation in Microalloyed Low-carbon Steels

Interphase precipitation behavior of VC, NbC, and TiC during isothermal ferrite transformation in a series of microalloyed low-carbon steels with various amounts of carbide-forming alloying elements was comparatively investigated. Through the quantification by three-dimensional atom probe, the dispersion of alloy carbides formed by interphase precipitation was found to be higher in number density and smaller in size with more addition of carbide-forming elements or at lower transformation temperature. Moreover, although the dispersion of NbC and TiC was relatively finer than that of VC with the same amount of alloy addition, larger driving force for precipitation was necessary to obtain the same number density of NbC and TiC as that of VC. This deviation can be explained by the difference in amount of bulk alloy addition as well as interfacial energy between ferrite and alloy carbide, the latter of which was confirmed through the analysis based on Gibbs–Thomson effect.

Preparation and thermophysical properties of three-dimensional attapulgite based composite phase change materials

• Attapulgite based three-dimensional carriers were prepared via “grafting from” method. • Pore size of 3D network can be adjusted by chain length and functional groups of connecting molecule. • SA/TATP have excellent thermal property and thermal reliability. • Melting point and melting latent heat of SA/TATP decrease with the decrease of TATP pore size. • Higher grafting rate of the carrier results in the larger thermal energy storage capacity. Aiming to reveal the relationship between the thermophysical properties of shape-stabled phase change materials (PCMs) with the structure of its matrix, a series of stearic acid/three-dimensional attapulgite (SA/TATP) composite PCMs were fabricated by vacuum impregnation method using TATP as matrix, which prepared via “grafting from” method and employed attapulgite (ATP) as raw material, diphenylmethane diisocyanate (MDI) as modifying agent and amines as linking molecules. The structure of carriers, thermophysical properties of the composite PCMs were analyzed, and the relationship between the thermophysical properties of SA/TATP and characteristics of the carrier were also studied. The results indicated that the thermophysical properties of the composite PCMs were improved significantly due to the introduce of organic bonding agents and the formation of three-dimensional network in the matrix. The latent heat of SA/TATP can be up to 136.81 J/g without leakage, and the maximum thermal conductivity of SA/TATP is 0.4215 W/m•K. The melting temperature and melting latent heat of the composite PCMs degenerate with the decrease of the pore size of the carriers. The relationship between the melting phase transition temperature, melting latent heat of SA/TATP and pore size of TATP can be descripted by the Gibbs–Thomson equation. In addition, the melting enthalpy of SA/TATP is positively associated with the grafting rate of the carrier.

An effective method to calculate atomic movements in 3D objects with tuneable stochasticity (3DO-SKMF)

We present an effective computer simulation method, called 3D object stochastic kinetic modelling framework (3DO-SKMF), to calculate atomic movements in 3D objects including surface segregation and Gibbs–Thomson effect (surface curvature). Objects with any kind of shapes can easily be considered thanks to the flexibility and versatility of the model and code. Accordingly, the model and the computer code can be used in a wide variety of applications: nanoparticles, nanorods, nanotubes, nanopillars, etc. To increase the versatility of the model, it includes stochastic noise in a tuneable manner. This means that if the noise level is zero, the model is completely deterministic (mean-field), whereas by increasing the noise level the result gets closer and closer to that obtained by a kinetic Monte Carlo calculation. This allows us to calculate processes with activation barriers. Besides demonstrating the capabilities of the model, we also reproduce an experimental result showing decomposition of Ag–Cu nanoparticles. Program summaryProgram title: 3DO-SKMFCPC Library link to program files:http://dx.doi.org/10.17632/776b7txmhv.1Licensing provisions: CC BY NC 3.0Programming language: ISO CNature of problem: Atomistic simulation of nano-objects with free surfaces by calculating occupation probabilities. The model includes surface segregation and Gibbs–Thomson effect (surface curvature).Solution method: Numerical solution of a system of differential equations with taking into account the conservation of matter. The number of equations is equal to the number of lattice sites in a 3D lattice.Additional comments including restrictions and unusual features: The model contains parameters that can be determined from macroscopic measurements, still in the background it follows an atomistic approach. Note that the provided code is written for nanospheres (hollow and solid), nanowires and nanotubes, however objects with any kind of shapes can easily be considered. Due to the flexibility of the code, with minor change of initialization, any 3D object can be simulated. The published code uses the face centred cubic lattice (fcc), its modification for other lattices is, however, straightforward.

Analysis on fluid permeability of dendritic mushy zone during peritectic solidification in a temperature gradient

Compared with the growing applications of peritectic alloys, none research on the fluid permeability K of dendritic network during peritectic solidification has been reported before. The fluid permeability K of dendritic network in the mushy zone during directional solidification of Sn-Ni peritectic alloy was investigated in this study. Examination on the experimental results demonstrates that both the temperature gradient zone melting (TGZM) and Gibbs-Thomson (G–T) effects have obvious influences on the morphology of dendritic network during directional solidification. This is realized through different stages of liquid diffusion within dendritic mushy zone by these effects during directional solidification. The TGZM effect is demonstrated to play a more important role as compared with the G–T effect during directional solidification. Besides, it is shown that the evolution of dendrite network is more complex during peritectic solidification due to the involvement of the peritectic phase. Through the specific surface SV, analytical expression based on the Carman–Kozeny model was proposed to analyze the fluid permeability of dendritic mushy zone in directionally solidified peritectic alloys. In addition, it is interesting to find a rise in permeability K after peritectic reaction in both theoretical predication and experimental results, which is different from that in other alloys. The theoretical predictions show that this rise in fluid permeability K after peritectic reaction is caused by the remelting/resolidification process on dendritic structure by the TGZM and G–T effects during peritectic solidification.

Investigation on morphology evolution of secondary branch during peritectic solidification in a temperature gradient through morphology characteristic: Experimental measurement and prediction

Despite the obvious influence of the secondary branch on final microstructure and properties of alloy, investigation on the morphology variation of it during solidification is not enough. On the basis of a parameter ϕ, the morphology evolution of it during peritectic solidification was analyzed. Experimental measurements on two peritectic alloys: Sn–Ni and Sn–Mn show that ϕ first decreases then turns to increase with solidification time. The minimum of ϕ during peritectic solidification is found after peritectic reaction. Further examination shows that ϕ first decrease because it is mainly determined by the growth of secondary branch before peritectic reaction. Then, it is mainly dependent on the radius of secondary branches since the growth space for them is obviously restricted after peritectic reaction. Further analysis shows that the continuous increase of ϕ with solidification time after peritectic reaction is caused by the remelting/resolidification process by both the Gibbs-Thomson (G-T) and temperature gradient zone melting (TGZM) effects on secondary branch. It was also confirmed that the remelting/resolidification process by the G-T effect is less important as compared with that by the TGZM effect. As a result, resolidification on both the front and back edges of thicker secondary branches leads to the “V”-type variation of ϕ during peritectic solidification. The analytical prediction in which the influences of these effects are taken into account shows reasonably agreement with the experimental measurement.

Extension and Limits of Cryoscopy for Nanoconfined Solutions.

This work investigates the phase behavior of aqueous solutions of glycerol confined in MCM-41 and SBA-15 nanoporous matrixes by calorimetry. Limitations due to overfilling and eutectic freezing are prevented by the absence of an external liquid reservoir and by the glass-forming property of glycerol. Consequently, the stability of nanoconfined ice in equilibrium with aqueous solutions is studied over a wide range of compositions. In confinement, a large temperature depression of the liquidus line is observed. A thermodynamic model accounting simultaneously for the cryoscopic and the Gibbs-Thomson effects gives a consistent view of the phase diagram for large pores (Rp = 4.15 nm). For smaller pores (Rp = 1.8 nm), it reveals that the water activity strongly deviates from the bulk solution with the same composition, indicating the possible role of concentration heterogeneities in determining the onset of ice freezing in strongly nanoconfined solutions.

Freezing of partly saturated cementitious materials – Insight into properties of pore confined solution and microstructure

The main object of the presented research was to investigate properties of water confined in hardened cement paste with w/c ratio equal to 0.5. The experimental analysis was conducted by means of differential scanning calorimetry on samples containing various moisture content which reflected the equilibrium with ambient air of RH = 11%, 54%, 75%, 84%, 93%, 97%, and 100%. Consequently, the relation between temperature and ice content was provided for partly saturated samples. The recorded thermograms consisted of two main peaks which clearly separated the transitions of liquid confined in capillary pores from that within gel ones. Concerning the molecules migration during freezing the ions concentration in gel pores for various moisture content was increasing. The analysis also involved the phase transition hysteresis between melting and freezing of partially saturated cement paste. It was established that apart from different interfacial curvatures, changeable concentrations of ions contained in pore solution can serve as a supplementary explanation of the hysteresis. Hence, we also investigated how the presence of ions affected the phase transition temperature of pore solution and final ice content in cementitious materials. The arguments for underestimating the pore size of cement-based materials using the Gibbs-Thomson equation were provided.

Restriction or acceleration: Investigation on the remelting/resolidification process during Sn–Ni peritectic solidification in a temperature gradient

In this work, extensive remelting/resolidification process induced by diffusion on the secondary dendrite arms in the mushy zone was confirmed in a Sn–Ni peritectic alloy. Examination on the dependence of λ2 on local solidification time showed that the remelting/resolidification process on secondary dendrite arm by the Gibbs-Thomson effect was restricted at the initial of peritectic reaction. Then, this restriction turns to disappear as directional solidification proceeds. Experimental observation shows that the remelting/resolidification on secondary dendrite arm could be attributed to both the Gibbs-Thomson and temperature gradient zone melting (TGZM) effect. Further analysis showed that this remelting/resolidification process was complicated in peritectic alloys due to interaction between peritectic reaction and the TGZM effect by the imposed temperature gradient. It was found that the influence of peritectic reaction on the remelting/resolidification process was different at different stages of solidification. The restriction or acceleration of the Gibbs-Thomson effect by peritectic reaction at different stages of solidification was clarified by diffusion-controlled analytical model describing the remelting/resolidification process. The dependence of the remelting/resolidification process on secondary dendrite arm on solidification time can be attributed to the interaction between peritectic reaction, the Gibbs-Thomson and TGZM effects.

The Gibbs-Thomson effect in the evolution of particulate assemblages in a metastable liquid

The influence of the phase transition temperature shift on surfaces of spherical particles (the Gibbs-Thomson effect) evolving in a metastable liquid on the evolution of particulate assemblages is studied. The integro-differential model of kinetic and balance equations describing the phase transition process at the intermediate stage is analytically solved. It is shown that the temperature shift substantially influences the particle-size distribution function and the desupercooling/desupersaturation dynamics in a metastable liquid. Namely, the metastability degree reduces slowly and the distribution function is higher and shifted to smaller particle radii with allowance for the Gibbs-Thomson effect. The main conclusion is that this effect must be taken into account when considering the nucleation and growth of small particles at the intermediate stage of phase transition processes in a metastable liquid.

Кинетика роста планарных нитевидных нанокристаллов

A kinetic equation is obtained which describes the elongation rate of planar semiconductor nanowires growing via the vapor-liquid-solid mechanism in the substrate plane. Theoretical analysis of different regimes depending on the nanowire radius and epitaxial conditions shows that planar growth of nanowires can be limited by either the Gibbs-Thomson effect in a catalyst droplet (for small droplet size) or surface diffusion of adatoms (for larger nanowire radii. Diffusion-like dependence of the growth rate on the nanowire radius R has the form R^(-m), where the power exponent equal 1, 3/2 or 2 depending on the mechanism of surface diffusion transport.