Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces

Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally-shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, {\beta}-tin, and high- pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces.Comment: Article + supplementary information. 23 pages, 10 figures, 2 table

Вариации метана в атмосфере Антарктиды в 2009–2017 гг. по данным наземных и спутниковых измерений

The article presents the results of systematic measurements (2009−2017) of the total column abundances of methane (TC_CH4 ) and the column-averaged concentration (X_CH4 ) at the Antarctic station Novolazarevskaya. Solar radiation is recorded in the range 2990 – 3006 cm–1 using a diffraction spectrometer with 0.2 cm–1 resolution. The inverse task CH4 total column determining is achieved using the SFIT4 v0.9.4.4 code. The analysis shows that during the measurement period the average TC_CH4 was (3.4±0.8).1019 molecules/cm2 during the measurement period, and the average X_CH4 is (1663±34) ppbv. TC_CH4 trend is (4.5±2.2).1015 molecules/cm2 /month, and X_CH4 trend is (0.28 ± 0.11) ppbv/month. The average TC_CH4 values and trend at Novolazarevskaya are in good agreement with the measurements by the Brucker120HR instrument at the Arrival Heights station. Seasonal variations of atmospheric methane have the maximum in October–November and the minimum in May–July. The trends of surface methane concentrations at Sywa, the Halley station and the Amundsen-Scott South Pole station are 0.59 – 0.61 ppbv/month and exceed the trend of the column-averaged concentration at Novolazarevskaya and AIRS trends for the troposphere (0.24 – 0.32) ppbv/month, due to a decrease in the maximal values of TC_CH4 in the period after 2014. The closest agreement of X_CH4 variations at Novolazarevskaya with AIRS data is observed at the levels of 150–200 hPa. Significant semiannual harmonics varied with height are characteristic of CH4 variations according to the AIRS data. The interference of annual and semiannual harmonics leads to the appearance of two maxima in the seasonal variations of methane with relative position to each other varies with height. The statistical model is developed for all the series considered. It approximates the trend, annual and semi-annual components of CH4 oscillations.The authors have no competing interests.Представлены результаты систематических измерений (2009–2017 гг.) общего содержания и средней по высоте концентрации метана на ст. Новолазаревская. Рассчитанные значения линейных трендов и параметров внутригодовых колебаний атмосферного метана сопоставлены с данными анализа вариаций приземных концентраций метана на станциях Сёва (Sywa), Халли (Halley Station) и Амундсен-Скотт (Amundsen-Scott South Pole Station), общего содержания метана на станции Арривал-Хайтс (ArrivalHeights), а также спутниковыми данными AIRS. Средние значения и тренд общего содержания метана на ст. Новолазаревская и ст. Арривал-Хайтс хорошо согласуются. Для периода измерений 2009–2014 гг. тренд средней по высоте объемной концентрации метана на ст. Новолазаревская совпадает в пределах погрешности с трендом приземных концентраций метана на станциях Сёва, Халли и Амундсен-Скотт, однако в 2015–2016 гг. согласно данным ст. Новолазаревская, Арривал-Хайтс и спутниковым данным наблюдалось замедление роста концентраций метана. Для вариаций средней по высоте объемной концентрации на ст. Новолазаревская и концентрации метана по данным AIRS, наряду с годовыми колебаниями, характерны значительные полугодовые вариации. Для всех рассмотренных рядов построена статистическая модель, которая аппроксимирует трендовую, годовую и полугодовую составляющие колебаний СН4.Авторы заявляют об отсутствии конфликта интересов

Controlling the growth of "ionic" nanoparticle supracrystals

Dimensions and quality of supracrystals self-assembling from oppositely charged nanoparticles (NPs) can be controlled by changing the relative nanoparticle concentrations, NP polydispersity, and pH. In particular, excess nanoparticles of either polarity terminate the self-assembly process at desired stages by forming charged, stabilizing shells around the growing aggregates. In this way, average supracrystal sizes can be varied from several micrometers down to tens of nanometers. While larger crystals precipitate from the growing solution, those smaller than ca. 400 nm are soluble. The experimentally observed threshold size for solubility agrees with arguments based on the DLVO theory

Modeling of electrodynamic interactions between metal nanoparticles aggregated by electrostatic interactions into closely-packed clusters

This paper is a theoretical and experimental study of the optical properties of binary aqueous suspensions containing metal nanoparticles (NPs) coated with charged organics. If all nanoparticles bear charges of the same polarity, the NPs do not aggregate, and the solutions are stable. Under these circumstances, optical response of the mixture is a linear combination of the optical responses of the individual components. In contrast, when the NPs are oppositely charged, they aggregate into clusters, whose optical properties cannot be understood without taking into account electrodynamic coupling between the constituent NPs. To model such aggregates, we present two theoretical approaches: (i) an exact analytical model accounting for the granularity of the NPs and (ii) an approximation, in which the aggregates are represented as spherosymmetric core-and-shells. Both models reproduce optical spectra recorded experimentally and give physically reasonable estimates of the aggregates' internal structure and composition

Precipitation of Oppositely Charged Nanoparticles by Dilution and/or Temperature Increase

Mixtures of oppositely charged nanoparticles (NPs) exhibit anomalous solubility behavior and precipitate either upon dilution or upon temperature increase. Precipitation is reversible and can be explained by a thermodynamic model that accounts for changes in the electrostatic interactions due to the adsorption/desorption of counterions from the surface of the NPs. Specifically, decreasing the salt concentration via dilution Or increasing the temperature causes dissociation of counterions from the NP surfaces, increasing the magnitude of electrostatic interactions between NPs and resulting in their precipitation. Model predictions of NP solubility are in quantitative agreement with the experimental observations. Such predictions are of practical importance for the preparation of "patchy" electrostatic coatings and ionic-like NP supracrystals

Studying the thermodynamics of surface reactions on nanoparticles by electrostatic titrations

For nanoparticles coated with binary SAMs (m-SAM NPs) containing charged or ionizable molecules, the relative equilibrium constants and the difference in the free energies of absorption of the m-SAM's components can be obtained in a straightforward way by titrating such NPs with oppositely charged nanoparticle "standards" until precipitation at the point of overall electroneutrality