Jürn Schmelzer

Size and rate dependence of crystal nucleation in single tin drops by fast scanning calorimetry

The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops has been studied via differential fast scanning calorimetry. The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.

Kinetics of first-order phase transitions in adiabatic systems

Abstract Based on thermodynamic investigations a general scenario and a kinetic description of the process of first-order phase transitions in adiabatically closed systems, starting from metastable initial states, is developed. It is shown that, in analogy to isothermal constraints, three main stages of the transition may be distinguished: a first stage of dominating nucleation and simultaneous growth of the already formed supercritical clusters, a second stage of independent growth of the clusters, their number being nearly constant, and a third stage of competitive growth, of Ostwald ripening. The change of the temperature of the system due to the latent heat of the transition can be considered hereby as an additional depletion effect. It leads to an increase of the critical size of the clusters and thus to a significant decrease of the nucleation rate, compared with isothermal conditions, especially for relatively large initial supersaturations. Further, it may result also in variations of the stable heterogeneous equilibrium state—that is, configurations of stable clusters in the otherwise homogeneous medium. In particular, for a one-component system under a constant external pressure it makes the existence of such a state possible and results therefore in a qualitative change of the whole course of the phase transition from independent nucleation and growth to the three-stage scenario as characterized above. A theoretical description of the independent growth of the drops and of Ostwald ripening under adiabatic conditions is developed. The results are compared with growth processes in isothermal systems and both quantitative and possible qualitative differences are discussed. Further, they are applied to an interpretation of molecular-dynamics simulations of first-order phase transitions in adsorbed layers.

Temperature fluctuations and the thermodynamic determination of the cooperativity length in glass forming liquids

The aim of this paper is to decide which of the two possible thermodynamic expressions for the cooperativity length in glass forming liquids is the correct one. In the derivation of these two expressions, the occurrence of temperature fluctuations in the considered nanoscale subsystems is either included or neglected. Consequently, our analysis gives also an answer to the widely discussed problem whether temperature fluctuations have to be generally accounted for in thermodynamics or not. To this end, the characteristic length-scales at equal times and temperatures for propylene glycol were determined independently from AC calorimetry in both the above specified ways and from quasielastic neutron scattering (QENS), and compared. The result shows that the cooperative length determined from QENS coincides most consistently with the cooperativity length determined from AC calorimetry measurements for the case that the effect of temperature fluctuations is incorporated in the description. This conclusion indicates that-accounting for temperature fluctuations-the characteristic length can be derived by thermodynamic considerations from the specific parameters of the liquid at glass transition and that temperature does fluctuate in small systems.

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, Tammanns 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.

Nucleation and growth in freely expanding gases

A model is developed for the description of clustering processes in first-order phase transformations in freely expanding gases. The theory results in a set of first-order differential equations describing the evolution of the cluster size distribution, the time dependence of the thermodynamic parameters of the system like particle density, pressure, temperature as well as of the rate of expansion of the gas. The model considerations do not require as a basic preposition the assumption of an isentropic expansion of the gas. Therefore, based on the theoretical approach developed, the effect of clustering on the entropy and other thermodynamic state functions of the system can be studied in detail. Solutions of the set of equations are given and possible applications (expansion of atomic, molecular and nucleonic gases) are discussed.