Thermal shape fluctuations of a two-dimensional compressible droplet.

Analysis of thermal capillary waves on the surface of a liquid usually assumes incompressibility of the bulk fluid. However, for droplets or bubbles with submicronic size, or for epithelial cells whose out-of-plane elongation can be modeled by an effective 2D bulk modulus, compressibility of the internal fluid must be taken into account for the characterization of their shape fluctuations. We present a theoretical analysis of the fluctuations of a two-dimensional compressible droplet. Analytical expressions for area, perimeter and energy fluctuations are derived and compared with Cellular Potts Model (CPM) simulations. This comparison shows a very good agreement between theory and simulations, and offers a precise calibration method for CPM simulations.

Specific Surface Area Determination for Microporous/Mesoporous Materials: The Case of Mesoporous FAU-Y Zeolites.

A methodology for determining the micropore, mesopore, and external surface areas of hierarchical microporous/mesoporous materials from N2 adsorption isotherms at 77 K is described. For FAU-Y zeolites, the microporous surface area calculated using the Rouquerol criterion and the Brunauer-Emmett-Teller (BET) equation is in accord with the geometrical surface determined by the chord length distribution method. Therefore, BET surface area ( SBET) is the well representative of micropore surface areas of microporous materials and of total surface area of microporous/mesoporous materials. Mechanical mixtures of mesoporous MCM-41 and microporous FAU-Y powders of known surface areas were used to calculate the respective surface areas by weighted linear combination and the results were compared to the values obtained by the t-plot method. The first slope of the t-plot determined the mesopore and external surface areas ( Smes+ext). The linear fit of the first slope is in general in the range 0.01 < p/ p0 < 0.17 and contains the volumes and relative pressures at which all micropores are filled ( p/ p0 > 0.10). Overestimation of Smes+ext values was evident and appropriate corrections were provided. External surface areas ( Sext) were obtained from the second slope of the t-plot, without noting an overestimation of Sext, thus allowing the determination of mesopore surface areas ( Smes) by difference. Micropore surface areas were calculated by subtracting Smes+ext from the total surface area, SBET. As an example, this methodology was applied to characterize a family of hierarchical microporous/mesoporous FAU-Y (FAUmes) synthesized from H-FAU-Y (H-Y, Si/Al = 15) using C18TAB as the surfactant and different NaOH/Si ratios (0.05 < NaOH/Si < 0.25). By increasing the NaOH/Si ratio in the synthesis of FAUmes, it was shown that as the micropore surface area decreases, the mesopore surface area increases, whereas the micropore and mesopore surface area remains constant. This methodology allows accurate characterization of the surface areas of microporous/mesoporous materials.

Validity of the t-plot method to assess microporosity in hierarchical micro/mesoporous materials.

The t-plot method is a well-known technique which allows determining the micro- and/or mesoporous volumes and the specific surface area of a sample by comparison with a reference adsorption isotherm of a nonporous material having the same surface chemistry. In this paper, the validity of the t-plot method is discussed in the case of hierarchical porous materials exhibiting both micro- and mesoporosities. Different hierarchical zeolites with MCM-41 type ordered mesoporosity are prepared using pseudomorphic transformation. For comparison, we also consider simple mechanical mixtures of microporous and mesoporous materials. We first show an intrinsic failure of the t-plot method; this method does not describe the fact that, for a given surface chemistry and pressure, the thickness of the film adsorbed in micropores or small mesopores (< 10σ, σ being the diameter of the adsorbate) increases with decreasing the pore size (curvature effect). We further show that such an effect, which arises from the fact that the surface area and, hence, the free energy of the curved gas/liquid interface decreases with increasing the film thickness, is captured using the simple thermodynamical model by Derjaguin. The effect of such a drawback on the ability of the t-plot method to estimate the micro- and mesoporous volumes of hierarchical samples is then discussed, and an abacus is given to correct the underestimated microporous volume by the t-plot method.

Molecular simulation of adsorption and transport in hierarchical porous materials.

Adsorption and transport in hierarchical porous solids with micro- (~1 nm) and mesoporosities (>2 nm) are investigated by molecular simulation. Two models of hierarchical solids are considered: microporous materials in which mesopores are carved out (model A) and mesoporous materials in which microporous nanoparticles are inserted (model B). Adsorption isotherms for model A can be described as a linear combination of the adsorption isotherms for pure mesoporous and microporous solids. In contrast, adsorption in model B departs from adsorption in pure microporous and mesoporous solids; the inserted microporous particles act as defects, which help nucleate the liquid phase within the mesopore and shift capillary condensation toward lower pressures. As far as transport under a pressure gradient is concerned, the flux in hierarchical materials consisting of microporous solids in which mesopores are carved out obeys the Navier-Stokes equation so that Darcy's law is verified within the mesopore. Moreover, the flow in such materials is larger than in a single mesopore, due to the transfer between micropores and mesopores. This nonzero velocity at the mesopore surface implies that transport in such hierarchical materials involves slippage at the mesopore surface, although the adsorbate has a strong affinity for the surface. In contrast to model A, flux in model B is smaller than in a single mesopore, as the nanoparticles act as constrictions that hinder transport. By a subtle effect arising from fast transport in the mesopores, the presence of mesopores increases the number of molecules in the microporosity in hierarchical materials and, hence, decreases the flow in the micropores (due to mass conservation). As a result, we do not observe faster diffusion in the micropores of hierarchical materials upon flow but slower diffusion, which increases the contact time between the adsorbate and the surface of the microporosity.

Quasistatic rheology of soft cellular systems using the cellular Potts model.

Soft cellular systems, such as foams or biological tissues, exhibit highly complex rheological properties, even in the quasistatic regime, that numerical modeling can help to apprehend. We present a numerical implementation of quasistatic strain within the widely used cellular Potts model (CPM). The accuracy of the method is tested by simulating the quasistatic strain of two-dimensional dry foams, both ordered and disordered. The implementation of quasistatic strain in CPM allows the investigation of sophisticated interplays between stress-strain relationship and structural changes that take place in cellular systems.

Balancing Accuracy and Cost of Confinement Simulations by Interpolation and Extrapolation of Confinement Energies.

Improvements to the confinement method for the calculation of conformational free energy differences are presented. By taking advantage of phase space overlap between simulations at different frequencies, significant gains in accuracy and speed are reached. The optimal frequency spacing for the simulations is obtained from extrapolations of the confinement energy, and relaxation time analysis is used to determine time steps, simulation lengths, and friction coefficients. At postprocessing, interpolation of confinement energies is used to significantly reduce discretization errors in the calculation of conformational free energies. The efficiency of this protocol is illustrated by applications to alanine n-peptides and lactoferricin. For the alanine-n-peptide, errors were reduced between 2- and 10-fold and sampling times between 8- and 67-fold, while for lactoferricin the long sampling times at low frequencies were reduced 10-100-fold.

Assessment of Mutational Effects on Peptide Stability through Confinement Simulations.

The evaluation of free energy differences between specific states of a system is of fundamental interest in the study of (bio)chemical systems. Herein, we examine the use of the recently introduced confinement method (CM) to evaluate relative free energy changes upon protein/peptide mutations. CM is a path-independent technique that involves the transformation of a configurational state of the system into an ideal crystal permitting the direct computation of free energy differences. We illustrate the method by evaluating the differential stabilities between native and mutant sequences of a model peptide that has been extensively characterized by experimental approaches, the GB1 hairpin. We show a good correlation between calculated and experimental relative stabilities and discuss other possible applications of this method in the context of complex molecular conversions.