Phase diagram of model anisotropic particles with octahedral symmetry

We computed the phase diagram for a system of model anisotropic particles with six attractive patches in an octahedral arrangement. We chose to study this model for a relatively narrow value of the patch width where the lowest-energy configuration of the system is a simple cubic crystal. At this value of the patch width, there is no stable vapour-liquid phase separation, and there are three other crystalline phases in addition to the simple cubic crystal that is most stable at low pressure. Firstly, at moderate pressures, it is more favourable to form a body-centred cubic crystal, which can be viewed as two interpenetrating, and almost non-interacting, simple cubic lattices.Secondly, at high pressures and low temperatures, an orientationally ordered face-centred cubic structure becomes favourable. Finally, at high temperatures a face-centred cubic plastic crystal is the most stable solid phase.Comment: 12 pages,10 figure

The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry

The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centred-cubic crystal becomes more stable than the body-centred-cubic crystal, and at higher temperatures a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centred-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centred-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centred-cubic crystal and between the fluid and the diamond crystal show that, at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.Comment: 15 pages, 13 figure

Homogeneous nucleation of a non-critical phase near a continuous phase transition

Homogeneous nucleation of a new phase near a second, continuous, transition, is considered. The continuous transition is in the metastable region associated with the first-order phase transition, one of whose coexisting phases is nucleating. Mean-field calculations show that as the continuous transition is approached, the size of the nucleus varies as the response function of the order parameter of the continuous transition. This response function diverges at the continuous transition, as does the temperature derivative of the free energy barrier to nucleation. This rapid drop of the barrier as the continuous transition is approached means that the continuous transition acts to reduce the barrier to nucleation at the first-order transition. This may be useful in the crystallisation of globular proteins.Comment: 6 pages, 1 figur

Lattice model of gas condensation within nanopores

We explore the thermodynamic behavior of gases adsorbed within a nanopore. The theoretical description employs a simple lattice gas model, with two species of site, expected to describe various regimes of adsorption and condensation behavior. The model includes four hypothetical phases: a cylindrical shell phase (S), in which the sites close to the cylindrical wall are occupied, an axial phase (A), in which sites along the cylinder's axis are occupied, a full phase (F), in which all sites are occupied, and an empty phase (E). We obtain exact results at T=0 for the phase behavior, which is a function of the interactions present in any specific problem. We obtain the corresponding results at finite T from mean field theory. Finally, we examine the model's predicted phase behavior of some real gases adsorbed in nanopores

Recent Developments in Modeling Heteroepitaxy/Heterogeneous Nucleation by Dynamical Density Functional Theory

Crystallization of supersaturated liquids usually starts by epitaxial growth or by heterogeneous nucleation on foreign surfaces. Herein, we review recent advances made in modeling heteroepitaxy and heterogeneous nucleation on flat/modulated surfaces and nanoparticles within the framework of a simple dynamical density functional theory, known as the phase-field crystal model. It will be shown that the contact angle and the nucleation barrier are nonmonotonous functions of the lattice mismatch between the substrate and the crystalline phase. In continuous cooling studies for substrates with lattice mismatch, we recover qualitatively the Matthews–Blakeslee mechanism of stress release via the misfit dislocations. The simulations performed for particle-induced freezing will be confronted with recent analytical results, exploring thus the validity range of the latter. It will be demonstrated that time-dependent studies are essential, as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Using Interviews in CER Projects: Options, Considerations, and Limitations

Interviews can be a powerful chemistry education research tool. Different from an assessment score or Likert-scale survey number, interviews can provide the researcher with a way to examine and describe what we cannot see, aspects such as feelings, thoughts, or explanations of thinking or behavior. Most people have no doubt seen countless interviews on TV news and talk shows. These sessions might convey interviewing as a spontaneous, easy, and straightforward process. However, using interviews as a meaningful research tool requires considerable thought, preparation, and practice. This chapter provides a general introduction to the use of interviews as a tool within a chemistry education research context. The chapter provides a general introduction to the use of interviews as a research tool including how to plan, conduct, and analyze interviews. It highlights important considerations for designing and conducting fruitful interviews, provides examples of different ways in which interviews have been used effectively in chemistry education research, and supplies additional references for the reader who wants to delve more deeply into particular topics

The importance of context: an exploration of factors influencing the adoption of student-centered teaching among chemistry, biology, and physics faculty

Background: Research at the secondary and postsecondary levels has clearly demonstrated the critical role that individual and contextual characteristics play in instructors’ decision to adopt educational innovations. Although recent research has shed light on factors influencing the teaching practices of science, technology, engineering, and mathematics (STEM) faculty, it is still not well understood how unique departmental environments impact faculty adoption of evidence-based instructional practices (EBIPs) within the context of a single institution. In this study, we sought to characterize the communication channels utilized by STEM faculty, as well as the contextual and individual factors that influence the teaching practices of STEM faculty at the departmental level. Accordingly, we collected survey and observational data from the chemistry, biology, and physics faculty at a single large research-intensive university in the USA. We then compared the influencing factors experienced by faculty in these different departments to their instructional practices. Results: Analyses of the survey data reveal disciplinary differences in the factors influencing adoption of EBIPs. In particular, the physics faculty (n = 15) had primarily student-centered views about teaching and experienced the most positive contextual factors toward adoption of EBIPs. At the other end of the spectrum, the chemistry faculty (n = 20) had primarily teacher-centered views and experienced contextual factors that hindered the adoption of student-centered practices. Biology faculty (n = 25) fell between these two groups. Classroom observational data reflected these differences: The physics classrooms were significantly more student-centered than the chemistry classrooms. Conclusions: This study demonstrates that disciplinary differences exist in the contextual factors teaching conceptions that STEM faculty experience and hold, even among faculty within the same institution. Moreover, it shows that these differences are associated to the level of adoption of student-centered teaching practices. This work has thus identified the critical need to carefully characterize STEM faculty’s departmental environment and conceptions about teaching before engaging in instructional reform efforts, and to adapt reform activities to account for these factors. The results of this study also caution the over generalization of findings from a study focused on one type of STEM faculty in one environment to all STEM faculty in any environment

El Conocimiento Didáctico del Contenido en ciencias: estado de la cuestión

This paper gives a descriptive overview of the literature related to Pedagogical Content Knowledge - PCK - in the sciences. It is expected that this review can contribute to a better understanding of PCK, pointing out what has been investigated about this concept. Specifically, we analyze: a) how PCK is defined, what are its main features and how it has been appropriated by teachers; b) the relationship between PCK, knowledge of the contents to be taught and students learning; c) how PCK was actually used in teachers' training and teachers' evaluation; and, d) the scientific areas in which PCK has been studied. It concludes that PCK is an essential tool for improving the quality of teacher training