The structure of montmorillonite intercalated with [Al13O4(OH)24+x(H2O)12−x](7−x)+ cations ( for short), where x = 0, 2 and 4, has been studied using the Cerius2 modeling environment. The Crystal Packer module used in the present study takes into account only the nonbonded interactions between the silicate layer and the Keggin cations. Minimization of the total sublimation energy led to the following conclusions: the structure of the interlayer (that is, the orientation of Keggin cations and the basal spacing) depends on the charge of cations (that is, on the degree of hydrolysis, x). The values of basal spacings in the range 19.38–20.27 Å have been obtained, depending on the charge and arrangement of cations in the interlayer. The dominating contribution to the total sublimation energy comes from the electrostatic interactions. Translations of cations along the 2:1 layers give only small fluctuations of the total sublimation energy and basal spacings. No preference for the position of cations in the interlayer of montmorillonite was found during translation along the 2:1 layers. This result confirmed the inhomogeneous distribution of cations in the interlayer and turbostratic stacking of layers.

Investigation of the organization of interlayer water and cations in smectite is a permanent topic in clay science for environmental science, civil engineering, materials science, and industrial applications. Experimental X-ray (or neutron) diffraction methods and molecular simulations are key techniques to probe the organization of the smectite structure at a similar molecular length scale. The combination of both of these experimental and numerical methods represents a complementary approach to reveal the structural heterogeneity of real samples, design and model a wide range of smectite structures, and validate the simulation results through comparison with experimental data.

This paper first revisits establishment of the original interlayer model as developed in the 1930s for the organization of water and ions in the smectite structure using X-ray diffraction (XRD) techniques. Then, based on a simplified approach, key theoretical tools are provided to calculate XRD pattern 00l reflections for a periodic smectite structure with a wide range of interlayer compositions and organizations using conventional spreadsheet software. In addition to educational purposes, this theoretical description is used to describe the principal parameters governing the positions and intensities of experimental XRD 00l reflections. This calculation toolbox is also used to determine better the layer-to-layer distances considered in molecular simulations and to validate these simulations through a detailed collation procedure using experimental data.

Recent examples of the application of such a procedure to collate experimental diffraction data and molecular simulations are presented for the specific case of deciphering the molecular organization of interlayer water and cations in the different smectite hydrates (mono-, bi-, and tri-hydrated layers). The extension of this approach to the interlayer refinement of organo-clays is also detailed, and perspectives regarding the characterization of other lamellar compounds are discussed.

Understanding protein–inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein–surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time- and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein–surface interactions and discuss the successes and limitations of current approaches.

In Markov Chain Monte Carlo (MCMC) simulations, thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the probability distribution function, known from the partition function of equilibrium state. As the stochastic error of the simulation results is significant, it is desirable to understand the variance of the estimation by ensemble average, which depends on the sample size (i.e., the total number of samples in the set) and the sampling interval (i.e., cycle number between two consecutive samples). Although large sample sizes reduce the variance, they increase the computational cost of the simulation. For a given CPU time, the sample size can be reduced greatly by increasing the sampling interval, while having the corresponding increase in variance be negligible if the original sampling interval is very small. In this work, we report a few general rules that relate the variance with the sample size and the sampling interval. These results are observed and confirmed numerically. These variance rules are derived for the MCMC method but are also valid for the correlated samples obtained using other Monte Carlo methods. The main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them.

We propose a derivation of a nonequilibrium Langevin dynamics for a large particleimmersed in a background flow field. A single large particle is placed in an ideal gasheat bath composed of point particles that are distributed consistently with thebackground flow field and that interact with the large particle through elasticcollisions. In the limit of small bath atom mass, the large particle dynamics converges inlaw to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni, D. Dürrand S. Kusuoka, J. Stat. Phys. 55 (1989) 649–693. D. Dürr,S. Goldstein and J. Lebowitz, Z. Wahrscheinlichkeit 62(1983) 427–448. D. Dürr, S. Goldstein and J.L. Lebowitz. Comm. Math. Phys.78 (1981) 507–530.] and provides extensions to handle the nonzerobackground flow. The derived nonequilibrium Langevin dynamics is similar to the dynamicsin [M. McPhie, P. Daivis, I. Snook, J. Ennis and D. Evans, Phys. A299 (2001) 412–426]. Some numerical experiments illustrate the useof the obtained dynamic to simulate homogeneous liquid materials under shear flow.

Multilink robot arms are geometrically similar to chain molecules. We investigate the performance of molecular simulation methods, combined with stochastic methods for optimization, when applied to problems of robotics. An efficient and flexible algorithm for solving the inverse kinematic problem for redundant robots in the presence of obstacle's (and other constraints) is suggested. This “Constrained Kinematics/Stochastic Optimization” (CKSO) method is tested on various standard problems.