Determination of key parameters of nucleation from optical investigations of mesoscopic models
Final Report Abstract
Over the last ten years the present project was concerned with nucleation and growth in colloidal model systems of various kind. Our extensive studies have mapped out the regions in parameter state of colloids, where Classical Nucleation Theory (CNT) can or cannot be safely applied. As it turned out, CNT is problematic in a number of cases but gives an valuable parameterization in the case of charged sphere colloids. There, we successfully established a route to obtain the key parameters of nucleation and compared them those of metals. Nucleation rates and growth velocities can now be reliably measured from optical experiments including USAXS in the range of J(n) = (106-1019)s-1m-3. Here, n is the number density. Important supplementary information on the nucleation scenario is obtained from small angle light scattering and various newly established microscopic techniques. Measurements may become problematic, if two crystal polymorphs are present, or multiple scattering becomes excessively strong. In all other cases, we now have thoroughly tested, reliable protocols available to obtain both nucleation rates, J(n) and growth velocities v(n). Only for hard spheres (HSs) the melt-crystal difference in chemical potential, ∆µ. is known analytically. We have shown that it can be experimentally determined from measurements of the growth velocity in systems showing reaction controlled growth (charged spheres and hard spheres above coexistence). This also works well in binary mixtures and HS-polymer mixtures as long as fractionation processes are avoided. For strongly charge regulated systems additional measurements of the density dependent charge are necessary. To further obtain non-equilibrium nucleus-melt interfacial free energies, γ and kinetic prefactors, J0, two CNT-based schemes were found to work well. One utilizes a fit of a modified CNT expression to the J(n) data, the other employs a two parameter fit in an Arrhenius-type plot of ln(γ) vs. 1/(n∆µ)2. This is particularly useful for salt dependent measurements or if no estimate of the effective diffusion coefficient is available. Both procedures work well for most systems. CNT cannot be applied, if nucleation proceeds from a dense piling of compacted amorphous precursors, because the relevant ∆µ is still unknown, this excludes the use of CNT for HS far above coexistence (φ ≥ 0.565), for attractive HS, and fractionating systems. For all other systems, a simple, yet powerful extrapolation scheme is now available to estimate several key parameters of nucleation from a plot of the reduced interfacial free energy σ(n) = γn-2/3 vs. ∆µ. These include the equilibrium reduced interfacial free energy, σ0, the entropy of fusion, ∆SF and the enthalpy of fusion ∆HF. For HS, the CNT-based values of σ0 compare well with values derived from equilibrium simulations. For several different charged sphere systems and one binary mixture, the derived values range between those of HS and of metals. We find a close correlation of σ0 to ∆SF which here was tuned utilizing particles of different size polydispersity. This implies that slightly unlike spheres crystallize much faster. We further obtained the first systematic experimental estimate of the bcc Turnbull coefficient as CT,bcc = 0.31(3). This value appears to be much smaller than the fcc coefficient and is in very good agreement with values for bcc crystallizing metals obtained from simulations from computer simulation.
Publications
- Optical experiments on a crystallizing hard-sphere–polymer mixture at coexistence, Phys. Rev. E 81, 051401 (2010)
A. Stipp, H. J. Schöpe, T. Palberg, T. Eckert, R. Biehl, E. Bartsch
- Polymer induced changes of the crystallization scenario in suspensions of hard sphere like microgels, J. Chem. Phys. 136, 234906 (2012)
R. Beyer, S. Iacopini, T. Palberg and H. J. Schöpe
(See online at https://doi.org/10.1063/1.4729562) - Polymer-Enforced Crystallization of a Eutectic Binary Hard Sphere Mixture, Soft Matter 8, 627-630 (2012)
A. Kozina, P. Diaz-Leyva, E. Bartsch, T. Palberg
(See online at https://doi.org/10.1039/c1sm06699d) - Charged colloidal model systems under confinement in slit geometry – A new setup for optical microscopic studies Rev. Sci. Instr. 84, 063907 (2013)
A. Reinmüller, H. J. Schöpe, T. Palberg
(See online at https://doi.org/10.1063/1.4811719) - Colloids as model systems for metals and alloys: a case study of crystallization, Euro. Phys. J. Special Topics 223, 591-608 (2014)
D. M. Herlach
(See online at https://doi.org/10.1140/epjst/e2014-02111-5) - Coupling between bulk- and surface chemistry in suspensions of charged colloids, J. Chem. Phys. 140, 124904 (2014)
M. Heinen, T. Palberg, H. Löwen
(See online at https://doi.org/10.1063/1.4869338) - Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives, J. Phys.: Condens. Matter 26, 333101 (2014)
T. Palberg
(See online at https://doi.org/10.1088/0953-8984/26/33/333101) - Nucleation and crystal growth in a suspension of charged colloidal silica spheres with bi-modal size distribution studied by time-resolved ultrasmall-angle X-ray scattering, J. Chem. Phys. 141, 214906 (2014)
W. Hornfeck, D. Menke, M. Forthaus, S. Subatzus, M. Franke, H.-J. Schöpe, T. Palberg, J. Perlich, and D. Herlach
(See online at https://doi.org/10.1063/1.4902904) - From Nuclei to Micro- Structure in Colloidal Crystallization: Investigating Intermediate Length Scales by Small Angle Laser Light Scattering, J. Chem. Phys. 143, 064903 (2015)
R. Beyer, M. Franke, H. J. Schöpe, E. Bartsch and T. Palberg
(See online at https://doi.org/10.1063/1.4928370) - Equilibrium interfacial energies and Turnbull coefficient for bcc crystallizing colloidal charged sphere suspensions. Phys. Rev E 93, 022601 (2016)
T. Palberg, P. Wette, D. M. Herlach
(See online at https://doi.org/10.1103/PhysRevE.93.022601)
