Thermodynamic-Kinetic Precipitation Modeling. A Case Study: The Amorphous Calcium Carbonate (ACC) Precipitation Pathway Unravelled

Nine accurate experimental data sets on amorphous calcium carbonate (ACC) formation in dilute solution were collected varying temperature and pH. The entire precipitation process is described using a complete thermodynamic-kinetic model. The thermodynamic model includes two new complex chemical interactions whereas the kinetic model is based on the discretized population balance approach. Saturation, primary particles size distribution, average secondary particles size, nucleation, and growth rates, as well as a number of additional parameters on the ACC precipitation reaction, are reported. The excellent agreement among experiments, calculated results, and literature data demonstrates that a complete thermodynamic kinetic model can significantly contribute toward the understanding of a plausible pathway for precipitating systems. In this case study, the classical nucleation theory, which includes homogeneous nucleation, "true" secondary nucleation, and diffusion limited growth events, is able to completely describe the entire precipitation process. The calculated surface (gamma) and cohesion (beta) energies range from 28 to 35 and 30 to 42 mJ m(-2), respectively, as a function of pH and temperature. Clusters or prenucleation entities act as spectators and are not directly involved in the solid formation pathway. The general methodological approach presented can be readily applied to other solid phase formation processes.

Atmospheric heterogeneous reactions of chlorine and bromine containing molecules

Arnaud Aguzzi

This thesis deals with a laboratory study of heterogeneous reactions involving bromine and chlorine containing reservoir species on alkali salt substrates which are relevant to the marine boundary layer, and on ice substrates which are relevant to the lower stratosphere. The aim is to obtain reliable data on uptake coefficients γ and reaction mechanisms for the sake of extrapolation of results obtained in the laboratory to atmospheric conditions. The experiments have been performed in a Teflon coated Knudsen flow reactor equipped with a quadrupole mass spectrometer. The reactions of BrONO2 with solid alkali halides have been studied at ambient temperature. The initial uptake coefficients γ0 of BrONO2 on NaCl and KBr substrates are γ0 = 0.31 ± 0.10 and γ0 = 0.32 ± 0.09, respectively. For NaCl substrates BrCl, Br2 and HCl and for KBr both Br2 and HBr are observed as products. HCl and HBr result from the interaction of NaCl and KBr, respectively, with HNO3 generated in the hydrolysis of BrONO2 with H2O condensed on the salt sample. Using NaCl we observed Br2 which is formed from heterogeneous BrONO2 decomposition occurring on solid KBr samples. Halogen exchange reactions are competing with hydrolysis and decomposition which also take place on non-reactive salts (NaNO3, Na2SO4). A high rate of initial uptake (0.2 ≤ γ0 ≤ 0.4) and a Br2 yield on the order of 50 % are observed on non-reactive salts with a closed mass balance for Br2. The ClONO2-salt system has been reinvestigated. Experiments on NaCl, KBr (reactive salts) and on NaNO3 and Na2SO4 (non-reactive salts) have been performed. The hydrolysis of ClONO2 was not observable in contrast to heterogeneous decomposition which occurred on non-reactive salts with a Cl2 yield of (25 ± 5) %. Calculations have been performed using a 0-D box model in order to observe the effects of heterogeneous chemistry on sea salt in the marine boundary layer. Chlorine and bromine chemistry is activated by heterogeneous reactions occurring on NaCl and KBr which are the sole sources of chlorine and bromine in the model. Simulations performed with chlorine heterogeneous chemistry and gas phase chemistry indicate: 1) Denitrification of the troposphere (NOy converted to solid nitrates). 2) Increase of the oxidative capacity of the troposphere by the release of Cl atoms. When bromine chemistry is added to the model, the recombination reaction of NO2 with BrO leads to an increase of tropospheric denitrification through formation of BrONO2. Calculations show that at high [NOx], the most important bromine reservoir is BrONO2, while at low [NOx] HOBr is the most important bromine reservoir. The uptake of HNO3 on ice, solid sulfuric acid solutions and solid ternary solutions (STS) has been investigated at 180 to 211 K. The uptake coefficient γ decreases from 0.30 at 180 K to 0.06 at 211 K. The Arrhenius representation shows two distinct regimes. The first at low temperatures (180-190 K) shows a constant value γ of 0.3, whereas the second regime at T > 195 K corresponds to an activation energy of Ea = -7 ± 1 kcal/mol. At a fixed temperature, γ is independent of [HNO3] thus confirming a rate law first order in [HNO3]. The γ values of HNO3 on H2SO4/H2O solid solutions linearly decreases from 0.20 (0.10) at 10 wt % H2SO4 to 0.05 (0.03) at 98 wt % H2SO4 at 180 K (200K). The γ values of HNO3 with STS of H2SO4/HNO3/H2O is equal to 0.10 ± 0.03 in the temperature range 185-195 K at conditions where the composition of the interface was held constant at the given temperature by adding an external flow of H2O. Br2O hydrolysis on ice surfaces occurs rapidly in the chosen temperature range of 180 to 210 K. At a fixed temperature the uptake kinetics follow an apparent first order rate law in [Br2O]. The observed negative temperature dependence leads to an activation energy Ea for heterogeneous hydrolysis of -2.3 ± 0.6 kcal/mol. These facts point towards a complex reaction mechanism implying that the interaction of Br2O with ice is not an elementary reaction. BrONO2 hydrolysis has been measured on bulk (B), condensed (C) and single crystal (SC) ice in the temperature range 180-210 K. On all types of ice, HOBr and Br2O are observed as products. At a fixed temperature the rate law is first order in [BrONO2] with γ ≈ 0.3 at 180 K. The observed negative temperature dependence leads to an activation energy Ea for the hydrolysis of BrONO2 on pure ice of -2.0 ± 0.2, -2.1 ± 0.2 and -6.6 ± 0.3 kcal/mol on (C), (B) and (SC) ice, respectively, pointing towards different kinetics of BrONO2 on these different types of ice. Doping the ice samples with HBr leads to the formation of Br2, preceded by BrONO2 hydrolysis. The Arrhenius representation corresponds to an activation energy of Ea = -1.2 ± 0.2 kcal/mol. We investigated the structural properties of the near-surface region of various types of HX (X = Cl or Br) doped ice. Basically, we studied the time dependent [HX] in the interface region using the fast reaction titration XONO2 + HX → X2 + HNO3. These experiments reveal that HX is located near the surface of the substrate in a well defined region of thickness I. The HX molecules composing the interface are immediately available for the titration reaction, whatever the flow of XONO2. In the temperature range 190-200 K, we measured a value of IHCl = 43 ± 16, 250 ± 50 and 444 ± 120 nm for (SC), (C) and (B) ices, respectively and IHBr = 110 ± 15 nm on (C) ice at 205K. Finally, we assessed the bulk diffusion coefficient for HX, DHX by modeling our results according to Fick's laws of diffusion. We obtained values of DHCl = 4.5·10-15 - 1.0·10-12 cm2/s at 190 K and DHBr = (6.5 ± 3.0)·10-15 cm2/s at 205 K.

EPFL2001

Study of the kinetics of condensation and evaporation of water vapor over atmospherically relevant pure and doped ice films

Christophe Eric Ludovic Delval

This thesis presents the different steps in the development of a multiple diagnostic experimental setup and the results concerning the kinetics of condensation and evaporation of water over pure ice, as well as ice films doped with a known amount of atmospheric trace gases. The goal of this project is to obtain reliable data concerning the evaporative flux, Jev [molec cm-2 s-1], and the concomitant rate of condensation, kcond [s-1], of H2O molecules in the presence of an ice film. A further aim of this work is the detailed investigation of the impact on the aforementioned kinetic processes of the deposition of atmospherically relevant trace gases such as hydrogen chloride (HCl), hydrogen bromide and nitric acid (HNO3) under well defined conditions including those that are representative of the atmosphere. The new experimental apparatus consisting of a stainless steel reactor may be used under three different regimes, namely static, stirred flow and dynamic condition which correspond to equilibrium, low rate of pumping and molecular flow, respectively. The separation of the kinetics into individual processes is principally afforded by the application of these 3 regimes. First, using a combination of the first two regimes, we have measured Jev and γ of H2O in the case of pure as well as HCl- or HBr-doped ice in the range 190-240 K. The resulting Arrhenius expressions for pure ice are: in the presence of an average mole fraction of HCl, ΧHCl, in the range 3.2·10-5 to 6.4·10-3 we have found: and for ΧHBr at a HBr mole fraction smaller than 6.4·10-3 was found, where R=1.987 cal mol-1 K-1. Owing to the rate separation, γ applies to an individual rate process and should be called an accommodation rather than an uptake coefficient. Of utmost importance is the fact that during most of the ice film evaporation the vapor pressure remained that of pure ice even in the presence of small amounts of HCl or HBr on the order of a fraction to several formal monolayers. This is consistent with the enthalpies of sublimation that may be derived following the relation ΔHsubl0 = Econd - Eev. It leads to different thermochemical parameters A (pre-exponential factor) and E values (energy of activation) for the three cases that are identical within experimental uncertainty. In addition, FTIR spectroscopy of the ice films involved in these experiments in transmission have revealed that different species such as amorphous HCl·H2O mixtures or the crystalline HCl·6H2O hexahydrate are formed depending on the doping protocol. These two species significantly affect the temporal change of Jev each in a different manner. For the sake of precision and accuracy of the kinetic results, a quartz crystal microbalance (QCM) was subsequently added to the experimental apparatus and used as a substrate for ice film growth. The development of a QCM-based device for the investigation of the kinetic processes of ice films at atmospherically relevant temperatures was a challenge we have successfully surmounted whereas previously published attempt had given barely convincing results. The Arrhenius representation of the zero order evaporative flux Jev (molec cm-2 s-1) of H2O from pure ice displays a discontinuity at 193±2 K that could be observed owing to the accuracy and precision of the QCM measurements. It leads to: In addition, γ of H2O onto ice was found to be lower than 0.5 for temperatures below 240 K in contrast to the value of 1.0 which is often encountered in the literature. Subsequently, the deposited ice films have been doped with HNO3 using different protocols depending on parameters such as temperature, rate of deposition of HNO3 onto ice as well as number ofHNO3 molecules deposited. The reproducible and quantitative dosing of the doping gas was key to the quality of the results. This study has shed light on a complex interplay between several of these parameters that affect the continuous decrease of Jev during ice evaporation. Using atmospherically relevant conditions in the doping of ice by HNO3 we have observed crystalline α-NAT being most likely the first species that forms in/on ice films. During most of the evaporation of the ice film doped with known amounts of HNO3 we have checked that the vapor pressure over the ice film remains that of pure ice. Finally, HCl-doped ice films have been investigated in experiments that are complementary to the first set in order to verify that HCl doping has a similar impact on the change of Jev of H2O in the presence of small albeit known amounts of HCl. The doping protocol is a fundamental parameter determining the decrease of Jev with H2O evaporation time of doped ice films. In summary, we have developed from scratch a new experimental apparatus that allows the separation of the kinetic processes of condensation and evaporation of pure as well as doped ice films using multiple diagnostics under the same experimental conditions which was heretofore not attainable. The main result for pure ice films is that the uptake coefficient, γ of H2O on ice is always lower than approximately 0.5 for atmospherically relevant temperatures. Its negative temperature dependence has been confirmed. An accurate control of the doping protocol has allowed us to observe that for a fraction to a few monolayers of the doping gases, HCl, HBr and HNO3, the nature of the aforementioned protocol is the predominant factor influencing the continuous temporal decrease of Jev and γ during doped ice film evaporation. Of utmost importance is the fact that the vapor pressure over the doped ice films remains that of pure water ice during almost all of the evaporation process. These results may be of importance in atmospheric modeling for determining the lifetime of ice particles involved in clouds in regions that are undersaturated in the vapor pressure of H2O over ice. In this way the physical process of evaporation affects the importance of heterogeneous chemistry of atmospheric trace gases on ice substrates representative of Cirrus clouds, aviation induced Cirrus clouds and contrails as well as type II PSC's.

EPFL2004

Empirical Kinetic Models for Tryptic Whey-Protein Hydrolysis

Antoine Margot, Albert Renken

Enzymic hydrolyses of naturally occurring protein sources represent complex reactions at a molecular level because of the specificity pattern of proteases and the composition of the substrates involved. In addition, rather global criteria are in practical use for describing the extent of protein hydrolysis. Therefore, mechanistically based kinetic modelling may not be applicable under these circumstances. For practical purposes it is often sufficient to use a descriptive mathematical model, which leads to a reliable interpolation of the experimental data. Empirical models are proposed for the kinetics of the limited tryptic whey-protein hydrolysis. These models are identified by fitting profiles of the fraction of soluble protein (non-protein nitrogen, NPN) as a function of operating time of discontinously operated stirred-tank reactors. Models with at least four parameters are required in order to describe profiles obtained at temperatures at which strong enzyme inactivation is observed. A simple model of only two parameters based on a kinetics with exponential decrease of the activity with increasing fraction of soluble protein is sufficient to simulate the tryptic digestion of whey-protein in batch reactors under conditions of moderate enzyme inactivation applicable for temperatures lower than 60 degrees C.