Heckel plots

Fig. 17 Athy-Heckel plots (a) material undergoing plastic deformation (b) material undergoing brittle fracture.

One can analyze the data from this type of work to classify materials with respect to their brittle fracture or plastic deformation tendencies or behavior [1,10]. Examples of Heckel plots are shown in Figure 3. This technique has also been used to follow bead compaction with modifications of the Heckel equation to account for rheological behavior [8]. 

Tablet porosity vs. force curve to visualize the densification process Heckel plots to quantitate the densification process and characterize materi-...

Figure 3 Heckel plots for (A) microcrystalline cellulose and (B) an MCC/lactose mixture.

Figure 4 A full-cycle Heckel plot for an experimental material, with densification, compression, and decompression phases noted.

The equation of Heckel is the most extensively used model and the underlying porosity-pressure plot is called a Heckel plot (Figure 18). The equation for the linear compression process follows fist-order kinetics (Table 7). Heckel... 

Despite this critique of the Heckel equation, the analysis of Heckel plots has been intensively used for the description of powder compression [128, 133-136], Gabaude et al. [136] stated that the analysis is quite useful when defining preconditions exactly and apply correct displacement measurement. 

Since the development of the equation, it has been tried to derive further information from it. Rees and Rue [129] determined the area under the Heckel plot. Duberg and Nystrom [137] used the nonlinear part for characterization of particle fracture. Paronen [138] deduced elastic deformation from the appearance of the Heckel plot during decompression. Morris and Schwartz [139] analyzed different phases of the Heckel plot. Imbert et al. [134] used, in analogy to Leuenberger and Ineichen [14], percolation theory for the compression process as described by the Heckel equation. Based on the Heckel equation, Kuentz and Leuenberger [135,140] developed a new derived equation for the pressure sensitivity of tablets. 

Tsardaka and co-workers [102,141,142] presented the Heckel plot with dependence on time and analyzed deformation in combination with elastic recovery. Additional areas to describe plasticity were determined from two-dimensional (2D) plots [129], Finally, the three-dimensional (3D) model [143, 144] was developed by fitting a plane to a 3D data plot on the basis of normalized time, pressure, and porosity according to Heckel. 

Paronen, P. (1986), Heckel-plots as indicators of elastic properties of pharmaceuticals, Drug Dev. Ind. Pharm., 12,1903-1912. 

Tsardaka, K. D., Rees, J. E., and Hart, J. R (1988), Compression and recovery behaviour of compacts using extended Heckel plots, J. Pharm. Pharmacol., 40,73P. 

The Heckel plot allows an interpretation of the mechanism of bonding. A nonlinear plot with small value for its slope (a small Heckel constant) indicates that the material undergoes fragmentation during compression. When the plot is linear, it indicates that the material undergoes plastic deformation during compression. 

Information from Heckel plots indicates that anhydrous citric acid is predominantly fragmented during compression. The elastic deformation and consequently the elastic recovery during decompression are low. " ... 

Typically, displacement measurements during compaction are used to define relationships between compaction force/pressure and the resulting tablet porosity/ density. Heckel plots have been derived from the density-pressure relationship and have been frequently presented in the literature. Fig. 18 is an example of a Heckel plot, where the tablet porosity values are plotted as a function of compaction pressure. The shape of the Heckel plot has been used to describe the type of... 

However, the real problem with Heckel plots is identifying a truly rectilinear section. When pressure-porosity diagrams were first devised, instrumented... 

FIGURE 23 Heckel plots for binary mixtures of microcrystal-linc cellulose. Source Adapted from Ref. 48. 

FIGURE 6 A typical Heckel plot showing three phases of particle deformation during in-die method. Source Adapted from Ref. 180. 

The main utility of Heckel plots arises from their ability to identify the predominant deformation behavior of the material. The relationship is mostly used to distinguish between substances that consolidate by fragmentation and those that consolidate by plastic deformation. 

Empirical evidence shows that materials with low mean yield pressures undergo plastic deformation, whereas, tableting materials with high mean yield pressure have a tendency to be brittle and consolidate via fragmentation. Based on Heckel plots and the compaction behavior of materials can be classified into three types. A, B, and C (Fig. 6) (88,89). 

Considering the several limitations of the Heckel equation (lack of correlation between the mean yield pressure and the plasticity of a material, clear identification of the linear region of a Heckel plot etc.), recently, a new relationship using the Gurnham equation was propo.sed to characterize the deformation behavior of pharmaceutical material by Zhao et al. (94). This relationship was introduced in chemical engineering by Gurnham and Mas.son (95). They proposed that the rate of applied pressure is directly proportional to the apparent density of a given mass of material (94). Thus,... 

Pharmaceutical powders do not produce perfect straight lines, and the type of deviation provides information about the compaction behaviour of the material. A typical Heckel plot for a pharmaceutical powder is illustrated in Figure 11.9. A straight-line portion is obtained over a certain pressure range with a negative deviation at low pressures and a positive deviation at high pressures. 

The effect of compression speed on the yield pressure of a material has been suggested as a method of determining the time-dependent nature of materials compression properties (Roberts and Rowe 1985). Heckel plots are produced at two punch velocities, 0.03 and 300 mm sec, and the yield pressures determined. The strain rate sensitivity (SRS) is calculated as ... 

While Heckel plots are able to distinguish between plastic and fragmenting mechanisms, they do not readily distinguish between plastic and elastic deformation. The data presented in Table 11.4 would suggest that microcrystalline cellulose and starch 1500 have very similar properties, yet the elastic nature of starch and its derivative products is well documented in the literature. Additional methods are, therefore, required to measure elasticity. 

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