Theory of Sorption Hysteresis in Nanoporous Solids: II. Molecular condensation

Motivated by the puzzle of sorption hysteresis in Portland cement concrete or cement paste, we develop in Part II of this study a general theory of vapor sorption and desorption from nanoporous solids, which attributes hysteresis to hindered molecular condensation with attractive lateral interactions. The classical mean-field theory of van der Waals is applied to predict the dependence of hysteresis on temperature and pore size, using the regular solution model and gradient energy of Cahn and Hilliard. A simple "hierarchical wetting" model for thin nanopores is developed to describe the case of strong wetting by the first monolayer, followed by condensation of nanodroplets and nanobubbles in the bulk. The model predicts a larger hysteresis critical temperature and enhanced hysteresis for molecular condensation across nanopores at high vapor pressure than within monolayers at low vapor pressure. For heterogeneous pores, the theory predicts sorption/desorption sequences similar to those seen in molecular dynamics simulations, where the interfacial energy (or gradient penalty) at nanopore junctions acts as a free energy barrier for snap-through instabilities. The model helps to quantitatively understand recent experimental data for concrete or cement paste wetting and drying cycles and suggests new experiments at different temperatures and humidity sweep rates.Comment: 26 pages, 10 fig

Constitutive Model for Material Comminuting at High Shear Rate

The modeling of high velocity impact into brittle or quasibrittle solids is hampered by the unavailability of a constitutive model capturing the effects of material comminution into very fine particles. The present objective is to develop such a model, usable in finite element programs. The comminution at very high strain rates can dissipate a large portion of the kinetic energy of an impacting missile. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate is enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a high-rate shear strain of forming particles. For simplicity, the shape of these particles in the plane of maximum shear rate is considered to be regular hexagons. The rate of release of free energy density consisting of the sum of this energy and the fracture energy of the interface between the forming particle is minimized. The particle sizes are assumed to be distributed according to Schuhmann's power law. It is concluded that the minimum particle size is inversely proportional to the (2/3)-power of the shear strain rate, that the kinetic energy release is to proportional to the (2/3)-power, and that the dynamic comminution creates an apparent material viscosity inversely proportional to the (1/3)-power of the shear strain rate.Comment: 13 pages, 2 figure

Model B4 : multi-decade creep and shrinkage prediction of traditional and modern concretes

To improve the sustainability of concrete infrastructure, engineers face the challenge of incorporating new concrete materials while pushing the expected design life beyond 100 years. The time-dependent creep and shrinkage response of concrete governs the serviceability and durability in this multi-decade time frame. It has been shown that current prediction equations for creep and shrinkage underestimate material deformations observed in structures outside of a laboratory environment. A new prediction model for creep and shrinkage is presented that can overcome some of the shortcomings of the current equations. The model represents an extension and systematic recalibration of model B3, a 1995 RILEM Recommendation, which derives its functional form from the phenomena of diffusion, chemical hydration, moisture sorption, and the evolution of micro-stresses in the cement structure. The model is calibrated through a joint optimization of a new enlarged laboratory test database and a new database of bridge deflection records to overcome the bias towards short-term behavior. A framework for considering effects of aggregates, admixtures, additives, and higher temperatures is also incorporated

Attractive forces in microporous carbon electrodes for capacitive deionization

The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nm), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by meanfield theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.Comment: 19 page