Fletcher's spherical substrate model [J. Chem. Phys. 29, 572 (1958)] is a basic model for understanding the heterogeneous nucleation phenomena in nature. However, a rigorous thermodynamic formulation of the model has been missing due to the significant complexities involved. This has not only left the classical model deficient but also likely obscured its other important features, which would otherwise have helped to better understand and control heterogeneous nucleation on spherical substrates. This work presents a rigorous thermodynamic formulation of Fletcher's model using a novel analytical approach and discusses the new perspectives derived. In particular, it is shown that the use of an intermediate variable, a selected geometrical angle or pseudocontact angle between the embryo and spherical substrate, revealed extraordinary similarities between the first derivatives of the free energy change with respect to embryo radius for nucleation on spherical and flat substrates. Enlightened by the discovery, it was found that there exists a local maximum in the difference between the equivalent contact angles for nucleation on spherical and flat substrates due to the existence of a local maximum in the difference between the shape factors for nucleation on spherical and flat substrate surfaces. This helps to understand the complexity of the heterogeneous nucleation phenomena in a practical system. Also, it was found that the unfavorable size effect occurs primarily when R<5r( *) (R: radius of substrate and r( *): critical embryo radius) and diminishes rapidly with increasing value of R/r( *) beyond R/r( *)=5. This finding provides a baseline for controlling the size effects in heterogeneous nucleation.

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Anthropogenic climate change threatens ecosystem functioning. Soil biodiversity is essentialfor maintaining the health of terrestrial systems, but how climate change affects the richness and abundance of soil microbial communities remains unresolved. We examined the effects of warming, altered precipitation and annual biomass removal on grassland soil bacterial, fungal and protistan communities over 7 years to determine how these representative climate changes impact microbial biodiversity and ecosystem functioning. We show that experimental warming and the concomitant reductions in soil moisture played the predominant role in shaping microbial biodiversity by decreasing the richness of bacteria (9.6%), fungi (14.5%), and protists (7.5%). Our results also show positive associations between microbial biodiversity and ecosystem functional processes such as gross primary productivity and microbial biomass. We conclude that the detrimental effects of biodiversity loss might be more severe in a warmer world. MAINBiodiversity, the variety of genes, species, and ecosystems which constitute life on our planet 1 , is dramatically affected by human alterations of global environment 2 . Biodiversity underscores healthy ecosystem functions and assures the production of essential goods, services, and benefits to society, such as climate regulation, landscape stability, fibers, and food production 1 . However, such benefits are threatened by the unprecedented biodiversity loss 3,4 caused by anthropogenic global environmental changes like climate warming, altered precipitation patterns, and land use changes 5 . Studies demonstrate that biodiversity loss impairs the functioning of natural ecosystems * *

A simple, sensitive and reliable reversed phase Rapid Resolution Liquid Chromatography (RRLC) method was developed and validated for six biologically active compounds (salidroside, tyrosol, rosarin, rosavin, rosin and rosiridin) in Rhodiola rosea L. roots and powder extracts. The method uses a Phenomenex C18 (2)-HST column at 40 o C with a neutral gradient system mobile phase (H 2 O and acetonitrile), a flow rate of 1.0 mL/min, and UV detection wavelengths set at 205 and 254 nm, simultaneously. Baseline separation of the six active compounds was achieved within 8 minutes. The average percentages of rosavins (rosarin, rosavin, and rosin) in authentic R. rosea roots and root powder extracts were quantitatively determined and a characteristic R. rosea roots RRLC profile was established. The RRLC method is accurate and sensitive; in addition, it effectively increases the sample analysis throughput compared with conventional HPLC.