Ryshkewitch- Duckworth

Application of Ryshkewitch-Duckworth Equation Prediction of Tensile Strength... 

Pharmaceutical tablets are made from a number of components, and each component contributes to the tablet s final properties. Therefore, it is important to study the physical properties of the individual components and their mixture rules in order to predict the mechanical properties of the final tablet. Tensile strength is one of the crucial properties that assess mechanical strength the most common method for measuring tensile strength is the diametrical compression test discussed above (110). In this section the application of the Ryshkewitch-Duckworth equation to the analysis of tensile strength of mixtures will be discussed (151,152). 

Ryshkewitch (152) investigated the tensile strength of porous sintered alumina and zirconia and showed that the logarithm of the tensile strength is inversely proportional to the porosity. Based upon this, Duckworth (151) developed an equation that correlates tensile strength and porosity, which is called the Ryshkewitch-Duckworth equation ... 

Keywords Ryshkewitch-Duckworth equation, compaction, tableting, surface free energy, adhesion, tablet porosity... 

Over the past several decades the Ryshkewitch-Duckworth equation has been discussed a number of times. Recently, the Ryshkewitch-Duckworth equation has been discussed by Doelker [2], Barraleta et al [8]., Nyongesa and Aduda [9] as well as by Tye et al. [10]. The literature suggests that the Ryshkewitch-Duckworth equation has been successfully applied to a variety of systems that have applications both to pharmaceutical science and to other disciplines. 

The importance of the Ryshkewitch-Duckworth equation is that it suggests that porosity is a measure of the outcome of the tableting process. Tablets of the same porosity have the same mechanical properties even though they might have been made on vastly different tablet presses operating at different speeds. 

The Ryshkewitch-Duckworth equation is an empirical equation. Andersson has, however, offered a theoretical explanation [11]. Knudsen [12] also comments on the Ryshkewitch-Duckworth equation and associates the increase in tensile strength with an increase in the smface area of contact and the k parameter to the difficulty of creating contact area, k is expected to be temperature dependent. 

In an earlier paper, Wu et al. [20] proposed a model to calculate the radial tensile strength of tablets from the Ryshkewitch-Duckworth parameters of... 

Combining Equation (16.17) and the Ryshkewitch-Duckworth equation (Equation (16.3)) yields the following relation. 

Equation (16.18) indicates that the Ryshkewitch-Duckworth parameters for a powder composed of several components may be calculated from the Ryshkewitch-Duckworth parameters of the individual components using the following relations. 

Figure 16.1 Ryshkewitch-Duckworth plots for dicalciuin phosphate, lactose and sodium dodecyl sulfate (SDS) at several dwell times. As suggested in earher publications [22] no dwell time dependence is noted If data are missing for a given dwell time then tablets were not formed at this dwell time. Points represent data for individual tablets.

Ryshkewitch-Duckworth Equation as a Predictor of the Tensile Strength of Binary Mixtures... 

The tensile strengths of binary mixtures are shown in Figures 16.1-8. In general, the results conform to the proposed model and the Ryshkewitch-Duckworth equation. Specifically, the tensile strengths of tablets when plotted against porosity follow an exponential dependence. Furthermore, the dependences of k and show the proper dependence on SDS volume fraction, k follows a linear dependence with volume fraction and t follows an exponential dependence with volume fraction. 

Figure 16.4 Ryshkewitch-Duckworth parameters for lactose and sodium dodecyl sulfate mixtures. Results conform to the proposed model and Equations (16.19) and (16.20). The 90% confidence interval of the least squares fit is indicated by the dashed lines. The solid line is the least squares fit to the data points.

Figure 16.6 Ryshkewitch-Duckworth plots for starch and mannitol mixtures with sodium dodecyl sulfate (SDS)...

Figure 16.10 Tablet tensile strength versus porosity for two individual components (drug compound and PEG 8000) of the formulation discussed in Figure 16.9 [23]. Circles-neat compounds. Squares - wet granulations. Dashed line - prediction using Ryshkewitch-Duckworth parameters for neat compound.

Figures 16.1-3 show Ryshkewitch-Duckworth plots for dicalcium phosphate or lactose mixtures with sodium dodecyl sulfate as well as the Ryshkewitch-Duckworth plots for each of the pure components. As previously observed by Wu et al. [20] and Tye et al. [10] no dependence on dwell time was noted. We did note that tablets were not formed for some materials when short dwell times, comparable to production conditions, were used. Presumably, insufficient time is given for viscoelastic deformation of the materials that is, in part, responsible for adhesion. Viscoelestic recovery upon decompression may also contribute to lamination of tablets on decompression. Figures 16.1-3 and Figme 16.6 show the importance of tablet porosity to tablet tensile strength. Porosity should be considered a measure of the outcome of the tableting process.

Figures 16.4,16.5,16.7 and 16.8 showthe dependence of the Ryshkewitch-Duckworth parameters, and k, on volume fraction of sodium dodecyl...

In this paper the compaction of several common pharmaceutical excipients blended with sodium dodecyl sulfate is investigated. Furthermore, a model based on the principles of adhesion science is proposed for calculation of tablet radial tensile strength as a function of tablet porosity for powders composed of several materials. The data indicate that the model, indeed, allows for the calculation of tablet tensile strength from the Ryshkewitch-Duckworth parameters of the component materials. 

Here we have demonstrated the essential features of a proposed model for determining tablet tensile strength from the properties of the component materials. The dependence of the Ryshkewitch-Duckworth parameters with tablet composition is consistent with the proposed model. Furthemore, the relation between particle surface free energy and tablet tensile strength is consistent with the available data. Calculations of the type discussed can be used to improve the efficiency of the formulation process. The model presented here is a step toward achieving quality by design in the pharmaceutical industry. 

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