E. H. Chimowitz

Quantum confinement in nanoscale silicon: The correlation of size with bandgap and luminescence

The optical properties of silicon nanocrystallites of known sizes, present in supercritically dried porous silicon films of porosities as high as 92%, have been measured by a variety of techniques. The bandgap and luminescence energies have been measured as a function of size for the first time. The bandgap increases by more than 1 eV due to quantum confinement. The peak luminescence energy which also shifts to the blue is increasingly Stokes shifted with respect to the bandgap, as the size decreases. The measured bandgap is in agreement with realistic theories and the Stokes-shift between bandgap and luminescence energies coincides with the exciton binding energy predicted by these theories. These results demonstrate unambiguously and quantitatively the role of quantum confinement in the optical properties of this indirect gap semiconductor.

A molecular thermodynamic model for adsorption equilibrium from supercritical fluids

Abstract Using, the Bragg-Williams approximation for interaction between the molecules of a lattice gas, a phenomenological two-parameter statistical-mechanical model is studied for adsorption of pure and multicomponent gases at low pressures on a variety of surfaces. The model is also used for the correlation and prediction of adsorption data from high-pressure, supercritical carbon dioxide in contact with octadecyl silica (ODS) and alumina (Alox-T), as stationary phases, respectively. The model appears to correlate and predict the data at both low and high pressures quite well, for the systems studied, and should be useful for engineering purposes. The low-pressure data were obtained from various sources in the literature while the high-pressure supercritical-fluid data came from our laboratory. The two parameters in the model characterize the adsorbate-adsorbent potential well-depth, and adsorbate-adsorbate interactions, respectively.

A new representation for retention time in supercritical fluid chromatography

Abstract A new equation is given for describing the column retention time of species in a supercritical fluid chromatograph (SFC). The simplicity of this representation is such that the plot of the capacity factor versus density is predicted to be linear on log-log coordinates. Experimental capacity factor data are presented that confirm this hypothesis. As a result, the prediction and correlation of capacity factor data in SFC are made considerably easier when compared to the usual PT representation.

Optical Properties of Free-Standing Ultrahigh Porosity Silicon Films Prepared by Supercritical Drying

Highly luminescent free-standing porous silicon thin films of excellent optical quality have been manufactured by using electrochemical etching and lift-off steps combined with supercritical drying. One to 50 μm thick free-standing layers made from highly (p + ) and moderately (p) Boron doped single crystal silicon (c-Si) substrates have been produced with porosities (P) up to 95 %. The Fabry-Perot fringes observed in the transmission and photoluminescence (PL) spectra are used to determine the refractive index. At the highest P the index of refraction is below 1.2 from the IR to 2 eV. The absorption coefficients follow a nearly exponential behavior in the energy range from 1.2 eV and 4 eV. The porosity corrected absorption spectra of free-standing films made from p type c-Si substrates are blue shifted with respect to those prepared from p + substrates. For P > 70 % a blue shift is also observed in PL. At equal porosities the luminescence intensities of porous silicon films made from p + and p type c-Si are different by one order of magnitude.

Optimal control of molecular resolution in supercritical-fluid chromatography with density programming

Abstract A technique which allows the a priori determination of optimal density programs for supercritical-fluid chromatography (SFC) is proposed. This new approach is meant to supersede heuristic methods for optimizing molecular resolution in SFC. The analysis is based upon optimal control theory applied to the treatment of molecular resolution in fixed beds with supercritical mobile phases. The optimal dynamic trajectories for the process operating conditions are found by solving the optimal control problem as posed here. A comparison with published data for a seven-component separation illustrates the concepts and shows that the method proposed has the potential for establishing optimal separation strategies in SFC.

An algorithm for the simulation of density-programmed supercritical fluid chromatography

Abstract An analysis and an algorithm are provided for simulating molecular resolution in multicomponent separations using density programmed supercritical fluid chromatography (SFC). Numerical results are compared to recently published results for a seven component separation, and are shown to provide an accurate representation of the system behavior. Various density program strategies are simulated to illustrate the potential of this technology for optimizing separations.

Local thermodynamic models for high pressure process calculations

Abstract This paper discusses the local thermodynamic model concept in the context of high pressure chemical processes where equations of state are usually required for performing thermodynamic property evaluations. Functional forms for local K-value models are developed by simplifying the rigorous equations governing fluid phase equilibria. The local models have imbedded adjustable parameters that are evaluated by regression against either experimental data or thermodynamic properties calculated with more rigorous theoretically based models. During the course of the calculations the parameters in the local models are updated periodically, thereby ensuring that the local models continually provide accurate values for thermodynamic properties. Use of the concepts for process calculations is demonstrated in an example problem.

Analysis of modal reduction techniques for the dynamics of general tridiagonal systems

Abstract An analysis and algorithm are provided for developing modal reduced-order models for general tridiagonal system dynamics. A number of new results are presented including a set of bounding equations for the dominant system time constant and an error measure that enables one to determine the suitability of the reduced-order model with regard to both its mathematical form and order. The model reduction algorithm provided in this work provides fast, reliable estimates of the parameters required for the reduced-order models. In addition, the eigenvalue bounding equations provide conservative estimates of the domain in which the dominant system time constant must lie. These bounds provide the maximum error in the value for the dominant system time constant evaluated with our technique. Finally, the use of the error measure quantity defined in this work is shown to be of value in evaluating issues related to model suitability.

A variational formulation and numerical solution of the optimal resolution problem in supercritical fluid chromatography

Abstract In this paper we propose a formulation of an optimal resolution problem in supercritical fluid chromatography (SFC) using variational theory. In the recent supercritical fluid literature there has been interest in the enhanced selectivity properties of near-critical fluids used as mobile phases in SFC. As the near-critical thermodynamic retrograde region is traversed, selectivity increases dramatically, often with respect to similar molecular species which are of most interest in separations technology. However, column retention times in the retrograde region tend to be maximal and as a result resolution and speed of processing, both desirable objectives, are in conflict here. The purpose of the optimal control formulation is to resolve this conflict according to a prespecified objective function. The numerical solution of the optimization problem provided here shows that there is significant potential for optimizing system performance. The calculations were done using a molecular thermodynamic model for species adsorption that in our previous experimental work was shown to be accurate for predicting retention time characteristics in SFC columns. Thus the insights gained from this computational study will be useful in future experimental investigations.

Diffusion in dilute binary fluids confined in porous structures near the solvent critical point

We analyze diffusion in dilute binary fluids confined within porous media near the critical point of the solvent species. Both ordered and random confining structures are considered. At the solvent critical point solvent dynamics are quiescent, a consequence of the critical slowing-down phenomenon predicted by theory. Solute diffusion, however, remains finite at these conditions, which we have characterized in terms of a system-invariant quantity we define as Ω. In specific situations Ω can also be related to scaling results in pure, homogeneous fluids, a result we illustrate with simulation data for a lattice–gas system. The implications of these theoretical concepts for both short-time dynamics and the practical situation involving diffusion through porous membranes are discussed and illustrated with computer simulation data. The simulations are carried out using a recently proposed relaxation-dynamics simulation algorithm that appears to be ideally suited for dynamical simulations in near-critical systems.