Cliff Woodward

A Debye–Hückel theory for electrostatic interactions in proteins

The site–site Ornstein–Zernike equation with a simple mean spherical closure is used to study electrostatic interactions of proteins. Using a Debye–Huckel approximation for the correlation functions of the bulk electrolyte and a simple basis expansion for the protein–salt direct correlation functions, we obtain a very simple variational expression for the electrostatic component of the excess chemical potential of a protein in an electrolyte solution. The predictions of the theory are tested on a model of the protein calbindin D9k. Our calculations for calcium binding affinities and protein acidity constants are found to be in excellent agreement with the results of computer simulations.

Aggregation of Calcium Silicate Hydrate Nanoplatelets

We study the aggregation of calcium silicate hydrate nanoplatelets on a surface by means of Monte Carlo and molecular dynamics simulations at thermodynamic equilibrium. Calcium silicate hydrate (C-S-H) is the main component formed in cement and is responsible for the strength of the material. The hydrate is formed in early cement paste and grows to form platelets on the nanoscale, which aggregate either on dissolving cement particles or on auxiliary particles. The general result is that the experimentally observed variations in these dynamic processes generically called growth can be rationalized from interaction free energies, that is, from pure thermodynamic arguments. We further show that the surface charge density of the particles determines the aggregate structures formed by C-S-H and thus their growth modes.

CV EXTREMA ON ISOTHERMS FOR SIMPLE FLUIDS AND WHY THEY EXIST

We review experimental results for the locus in the temperature–density plane of isothermal Cv (constant volume heat capacity) extrema of Ar, Kr and Xe, and published Percus–Yevick and simulation equations of state. It is likely that the locus of Cv maxima terminates at the critical point. We report new long (960 million Monte Carlo steps), 864 particle simulations of the heat capacity for the truncated Lennard-Jones potential (cutoff=2.5σ) near the liquid coexistence line, and establish directly that the locus of Cv minima intersects the coexistence line. On the basis of calculations and simulations for model systems, we induce that previously reported Cv extrema are caused by the interplay of three physical effects that we term, “aggregation,” “caging,” and “soft-core penetration.” We test our hypothesis by carrying out calculations for a one-dimensional, nearest-neighbor, infinite-chain, truncated interaction model with the following potentials: Lennard-Jones, Lennard-Jones with hard core, Lennard-Jone...

The growth of charged platelets

Growth models of charged nanoplatelets are investigated with Monte Carlo simulations and simple theory. In a first model, 2-dimensional simulations in the canonical ensemble are used to demonstrate that the growth of a single weakly charged platelet could be limited by its own internal repulsion. The short range attractive interaction in the crystal is modeled with a square well potential while the electrostatic interactions are described with a screened Coulomb potential. The qualitative behavior of this case can also be described by simply balancing the attractive crystal energy with the screened Coulomb repulsion between the crystal sites. This repulsion is a free energy term dominated by counterion entropy and of course reduced by added salt. For a strongly coupled system, that is with high charge density and divalent counterions as in calcium silicate hydrate, the main product of cement hydration, the screened Coulomb approximation becomes inadequate and the growth behavior has to be described with the full primitive model. In this case, the energetic interactions become relatively more important and the entropy of the system plays a minor role. As a consequence, the electrostatic interactions gradually become less of a hindrance for aggregation and in extreme cases electrostatics actually promote the growth. This is manifested as an increased aggregation with, for example, increasing surface charge density. In the presence of divalent calcium ions and at the high negative surface charge density typical for calcium silicate hydrate, electrostatic interactions are not a hindrance for an infinite growth of the particles. By combining experimental and simulated data we can show that the limited sized platelets found in cement paste is due to a very fast nucleation rate compared to the growth rate.

Heat capacity extrema on isotherms in one‐dimension: Two particles interacting with the truncated Lennard‐Jones potential in the canonical ensemble

Exact expressions are obtained for the heat capacity of a two‐particle one‐dimensional system interacting with the truncated, unshifted Lennard‐Jones potential subject to periodic boundary conditions and the minimum image convention in the Gibbs canonical ensemble. Numerical calculations show that along isotherms the heat capacity exhibits maxima and minima as a function of density comparable to those found for three‐dimensional models and experimental systems. For the present system, at very low temperatures, the maximum in the heat capacity arises because of a competition between low energy, which drives the particles towards the potential minimum, and high entropy, which drives the particles past the truncation distance where the force of interaction vanishes. The minimum arises because the range of integration in the partition function no longer is effectively infinite at sufficiently high densities. As the temperature rises, the locus of the maxima and the locus of the minima in the temperature–densi...