HYDROLYSIS MODEL

Equations 9-14 provide the framework for combining either of the two surface hydrolysis models that were presented with any of the four electric double layer models to define the interface model completely and to solve for all unknown potentials, charges, and surface concentrations. In the following section some specific limiting cases are considered. 

Diprotic Surface Groups. Most of the recent research on surface hydrolysis reactions has been interpreted in terms of the diprotic surface hydrolysis model with either the triple layer model or the constant capacitance model of the electric double layer. The example presented here is cast in terms of the constant capacitance model, but the conclusions which are drawn apply for the triple layer model as well. 

Figure 7. Covariability between values of C and Kd yielding best fit of diprotic surface hydrolysis model with constant capacitance model to titration data for TiC>2 in 0.1 M KNOj (Figure 5). The line is consistent with Equation 29. The crosses represent values of C and log found from a nonlinear least squares (NLLS) fit of the model to the data, with the value of capacitance imposed in all cases the fit was quite acceptable. The values of and C found by Method I (Figure 6) also fall near the line consistent with Equation 29. The agreement between these results supports the use of the linearized model (Equation 29) for developing an intuitive feel for surface reactions.

This model was applied to the same data for batch and flowthrough systems with and without acid addition as for the previous two models, and some of the xylan conversion predictions calculated from the data and concentration predictions via Eq. 8 are summarized in Figs. 5 and 6 for batch and flowthrough systems, respectively. Tables 4 and 2 present the parameters and the SSE values for the branched pore model, respectively. Overall, although some data are better matched than others, hemicellulose hydrolysis models based on mass transfer alone can predict performance in batch and flow systems as well as, if not better than, reaction-only models. In addition, the changes in mass transfer coefficient with flow are consistent with expectations for a mass transfer model but not for strictly a chemical reaction. 

The measured equilibrium constants for this stepwise deprotonation scheme for Mo and W have been collected from the literature in [56]. They show that Mo is more hydrolyzed than W, and that the deprotonation sequence for Mo and W at pH = 1 reaches the neutral species M02(0H)2(H20)2. Assuming the deprotonation processes for the Sg compounds to be similar to those of Mo and W, Equations (6-9), V. Pershina and J.V. Kratz performed fully relativistic density-functional calculations of the electronic structure of the hydrated and hydrolyzed structures for Mo, W, and Sg [56]. By use of the electronic density distribution data, relative values of the free energy changes and by use of the hydrolysis model [29,30], constants of hydrolysis reactions (6-9) were defined [56]. These results show hydrolysis of the cationic species to the neutral species to decrease in the order Mo>W>Sg which is in agreement with the experimental data on hydrolysis of Mo and W, and on Sg [55] for which the deprotonation sequence may end earlier with a cationic species such as SgO(OH)3(H20)2+ that is sorbed on the cation-exchange resin. 

This slight change in the water adsorption rate is probably due to the difference in water uptake between pure binder (used in this study) and the binder within PBX 9501 which is surrounded by HMX. As seen in Figure 8, good agreement is observed between the hydrolysis model and the experimental molecular weight hydrolysis data for several humidity s. 

Figure 8. Comparison of the experimental data (open markers) with hydrolysis model (solid line) for Estane/NP/Irganox at 70°C at given humidity.

The experimental data for molecular weight and L/Lo agree well with the hydrolytic degradation predictive model for Estane as shown in Figure 10. Ongoing experimental work validating the Estane hydrolysis model for Estane binder will contribute to providing a robust lifetime prediction for PBX 9501 explosives. 

Keywords. Cellulases, Cellulose, Hydrolysis, Model Mechanism, Structure, Kinetics... 

Gupta, A.R. and Venkataramani, B., Sorption of uranyl ions on hydrous oxides. A new surface hydrolysis model. Bull. Chem. Soc. Jpn, 61, 1357, 1988. 

Tables 1 and 2 list the complete set of mass balance equations for the hydrolysis model and the SSF model. Dilution due to cell growth was not included in the model, nor was a cell mass balance. As cells were grown to maximal exponential phase before the batch runs and the fermentation was 90% complete in 5 h or less, any maintenance or growth requirements were neglected, and yield coefficients were used to determine the conversion yield for each reaction rate.

The following seleeted constant was derived from the fit of the overall hydrolysis model (see Appendix D). 

Figure V-8 SIT plot for log, (V.6) in perchlorate media. The symbols (o) denote the reported values of the equilibrium constants, established according to the hydrolysis models of the corresponding references. These original interpretations are not consistent with the overall hydrolysis model (Appendix D) selected by this review, represented by the solid straight line (and the 95% confidence limits denoted by the dashed lines).

Due to a different choice in a solubility constant for Zr(OH)4(am aged), the proposed constant is inconsistent with the present hydrolysis model. Using a solubility constant of log, (Zr(OH)4(am aged), Im NaC104) = - (5.55 0.2) a model-consistent stability constant ... 

The principal dimeric hydrolysis species of Zr in aqueous solutions is reported to be Zr, (OH)j [99VEY] as obtained from potentiometric and solubility data. However, the overall hydrolysis model has been found to be inconsistent with the presence of dimeric species. The re-evaluation of the original data of [99VEY] indicates that the proposed dimer, Zr, (OH)j, is most likely the tetramer Zr, (OH) 5 (see Appendix A and Appendix D). 

These complexes have not been included explicitly in the hydrolysis model, but if present as a significant fraction in the experiments in chloride solutions, their impact on solution chemistry is implicitly included in the CF interaction parameters. 

One of the major difficulties in evaluating Zr complexation constants is the unavoidable coexistence with hydroxo species over all pH regions of interest. Therefore, any determination of stability constants for complex formation with ligands other than OH critically depends on the quality and precision of the stability constants assigned to the hydrolysis. This is particularly true in the carbonate system where OH and CO3 concentrations will co-vary with pH. In the course of the review, it became evident that all Zr-carbonate constant determinations found in the literature relied on a hydrolysis model that differs from that selected in this review. Consequently, all constant determinations had to be re-evaluated. Due to the limited information provided by most references (missing raw data, insufficient declaration of experimental conditions), or because of the inherent unsuitability of the data, a meaningful reinterpretation was possible only in a few cases (mainly for potentiometric titrations). Table V-37 is a compilation of the Zr-carbonate complexation constants reported in the... 

Because of the incorrectness of the hydrolysis model used in [72DER], we were forced to re-evaluate these solubility data in terms of the hydrolysis model defined and accepted in this review. In contrast, the (precise) determination of the conditional carbonic acid dissociation constants in 1 M NH4NO3 could be taken without modification and were applied in our re-evaluation. The following constants were determined by [72DER] ... 

As shown in Figure A-23, these solubility measurements are close to the results of [66B1L/BRA2] and of other similar studies (see also Figure D-2 in this review). Hence, they are reasonably consistent with the hydrolysis model selected in this review for aqueous species and log Ar° ((V. 17), 298.15 K) = -(3.24 0.10) for Zr(OH)4(am, fresh). The latter constant, though not selected in the present review, is a calculated average corresponding to the apparent maximum solubility for fresh amorphous Zr(OH)4(s) (see Section V.3.2.2.2) and is used here for the re-evaluation of the solubility data in the presence of carbonate. 

Table A-16 Solubility data of [72DER] for Zr(OH)4(s) in the presence of carbonate and results of calculations based on the hydrolysis model selected in this review. The molalities of COj", Zr[C03] and Zr were calculated using Eqs. (A.9), (A.10) and (A.l 1), respectively.

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