Daan Frenkel

Gibbs’s monumental article on the equilibrium of heterogeneous substances contains a paradoxical sentence stating that, for a crystallite in equilibrium with a fluid, the chemical potential of the solid will not be equal to that of the fluid if the surface free-energy density differs from the mechanical surface-tension. How can this be? After all, in chemical equilibrium, the chemical potential of any species should be the same throughout the system. This “second Gibbs paradox” has intrigued many authors. In the present paper, I sketch my interpretation of the approach of Gibbs and that of Mullins [J. Chem. Phys. 81, 1436–1442 (1984)], which accounts for the possibility of vacancies and interstitials. I argue that a consistent treatment of point defects in a critical nucleus is essential for clarifying the meaning of the chemical potential of the nucleus. My paper lacks the rigor of Gibbs or Mullins but will hopefully be more accessible for scientists who think primarily in terms of atoms and molecules. In my attempt, I am motivated by a quote that is sometimes attributed to Paul Valéry: “The glass must be absolutely transparent for one to perceive the mud at the bottom.”

In his Equilibrium of Heterogeneous Substances Gibbs seems to suggest that the chemical potential of a crystal nucleus need not be equal to that of the coexisting fluid. In the field, Gibbs's statement has been something of a hot potato. I argue that a consistent treatment of point defects in the critical nucleus is essential for clarifying the meaning of the chemical potential of the nucleus. In the end -- as always -- Gibbs was right.

The immune system exploits a wide range of strategies to combine sensitivity with selectivity for optimal response. We propose a generic physical mechanism that allows tuning the location and steepness of the response threshold of cellular processes activated by multivalent binding. The mechanism is based on the possibility to modulate the attraction between membrane receptors. We use theory and simulations to show how tuning interreceptor attraction can enhance or suppress the binding of multivalent ligand-coated particles to surfaces. The changes in the interreceptor attraction less than the thermal energy k _B T can selectively switch the receptor-clustering and activation on or off in an almost step-wise fashion, which we explain by near-critical receptor density fluctuations. We also show that the same mechanism can efficiently regulate the onset of endocytosis for, e.g. , drug delivery vehicles.

We present molecular dynamics simulations to study the thermodynamics of nanobubbles trapped at the mouth of narrow slit pores. Except when the slit dimensions are comparable to typical molecular sizes, the predictions of macroscopic thermodynamic theory are recovered by our simulations. Our simulations confirm that in this case, the internal pressure of stable nanobubbles is independent of the bubble radius and the surface tension and only depends on the bulk properties of the solute-containing solution, i.e., the chemical potential balance. However, in the case of extreme confinement, the pressure is not a suitable quantity to describe the thermodynamics of the bubbles, while the balance of the chemical potentials is.

Correction for ‘The Lennard-Jones potential: when (not) to use it’ by Xipeng Wang et al., Phys. Chem. Chem. Phys., 2020, 22, 10624–10633, https://doi.org/10.1039/C9CP05445F.

Self-replication of amyloid fibrils via secondary nucleation is an intriguing physicochemical phenomenon in which existing fibrils catalyze the formation of their own copies. The molecular events behind this fibril surface-mediated process remain largely inaccessible to current structural and imaging techniques. Using statistical mechanics, computer modeling, and chemical kinetics, we show that the catalytic structure of the fibril surface can be inferred from the aggregation behavior in the presence and absence of a fibril-binding inhibitor. We apply our approach to the case of Alzheimer’s A β 42 amyloid fibrils formed in the presence of proSP-C Brichos inhibitors. We find that self-replication of A β 42 fibrils occurs on small catalytic sites on the fibril surface, which are far apart from each other, and each of which can be covered by a single Brichos inhibitor.

Self-replication of amyloid fibrils via secondary nucleation is an intriguing physicochemical phenomenon in which existing fibrils catalyse the formation of their own copies. The molecular events behind this fibril surface-mediated process remain largely inaccessible to current structural and imaging techniques. Using statistical mechanics, computer modelling, and chemical kinetics, we show that the catalytic structure of the fibril surface can be inferred from the aggregation behaviour in the presence and absence of a fibril-binding inhibitor. We apply our approach to the case of Alzheimer’s A β ₄₂ amyloid fibrils formed in the presence of proSP-C Brichos inhibitors. We find that self-replication of A β ₄₂ fibrils occurs on small catalytic sites on the fibril surface, which are far apart from each other, and each of which can be covered by a single Brichos inhibitor.