Investigating Granule Compression Dynamics: A Heckel Plot Approach to Optimize Crushing Strength in Tablet Formulations

Tablet manufacturing is a critical process in the pharmaceutical industry, where the quality and mechanical properties of the final product directly influence its therapeutic efficacy and patient compliance (1). One of the key factors in determining tablet quality is the behaviour of granules under compression. The compression process transforms granules into compact structures by applying mechanical forces that reduce porosity and induce deformation. Understanding these deformation mechanisms and their impact on porosity is essential for optimizing tablet strength and ensuring consistency in production (2) Granule deformation during compression occurs in distinct stages, including initial particle repacking, elastic deformation, plastic deformation, and brittle fracture. The initial stage focuses on rearranging particles to reduce bulk volume, followed by elastic deformation, where particles undergo temporary shape changes. As compression pressure increases, plastic deformation becomes dominant, leading to permanent changes in particle structure and the formation of strong interparticle bonds. In some cases, harder granules experience brittle fracture, producing fragments that enhance packing efficiency. These deformation mechanisms directly affect the porosity of the tablet, which is a measure of the void spaces within the compacted mass (3). Porosity is a critical parameter in tablet formulation as it influences mechanical strength, disintegration, and dissolution profiles. Higher porosity generally indicates weaker tablets, while reduced porosity reflects improved compactness and strength. By understanding and controlling porosity, pharmaceutical scientists can design tablets with desired properties, ensuring optimal drug delivery and patient satisfaction (4).  One of the most widely used models for studying granule deformation and its relationship to porosity is the Heckel equation. This empirical equation establishes a linear relationship between the logarithm of the inverse of porosity and the applied compressional pressure. The Heckel plot, derived from this equation, provides valuable insights into the mechanical behaviour of granules, including their deformation characteristics and the quality of the resulting tablet (3).

The Heckel equation is given as:

Log1/E= K_yP +K_r ----------------- (1)

Key parameters of the Heckel equation, such as the slope (K_y) and intercept (K_r?), offer quantitative measures of the material's yield pressure and initial packing stage, respectively (3). The slope (K_y) is particularly significant as it correlates with the crushing strength of the tablet, a vital attribute that determines its ability to withstand mechanical stresses during handling, storage, and transportation. A steeper slope indicates higher plastic deformation potential and stronger tablets, while a gentler slope suggests harder materials with lower compressibility. The intercept (K_r) provides insights into the initial porosity (E) of the powder mass, reflecting the efficiency of particle packing before the onset of significant deformation (3). Values of porosity can be calculated from:

E= 100[1- 4w/?_t.?.D^2.H]------------------- (2)

Where, D= tablet diameter, w= weight of tablet mass, ?t= True density & H= thickness of tablet (3) This study aims to explore the deformation behaviour of granules during compression, analyze the impact of porosity on tablet properties, and utilize the Heckel plot to calculate crushing strength. By investigating the role of different binders and formulation parameters, this research seeks to provide a comprehensive understanding of the compression process and its implications for tablet manufacturing. The findings will aid in optimizing formulation strategies, ensuring high-quality and reliable pharmaceutical products.

MATERIALS AND METHODS

MATERIALS

Hydroxypropyl methyl cellulose (E 5 LV Premium), Lactose(Monohydrate), Ethyl cellulose, Starch, PVPK30 and Magnesium Stearate Precipitated were purchased from Loba Chemie Pvt. Ltd. (Mumbai, India). Talc was purchased from Indian Drug House (Sonarpur, India).

Preparation of granules and compression of tablets

The wet granulation method was used to prepare 5 batches of tablets each from two different formulations (F1 and F2), as depicted in table I. HPMC, EC and lactose were sifted through sieve no. #44 to ensure uniform particle size, then mixed using geometric dilution. A slurry was prepared with half the amount of binders and added to the powder mixture to create a wet mass. The wet mass was then passed through sieve no. #22 and dried in the hot air oven for 10 minutes at 50°C so that the moisture content remains 2-4%. The resulting granules were further reduced in size using sieve no.#22, and then blended with magnesium stearate and talc for proper lubrication (5). Finally, the granules were compressed using an 11 mm flat punch on an automatic tablet punching machine (CREATE CIB-4) to produce 650 mg tablets. The compression was done at 5 different compressional force (65 kN, 70 kN, 75 kN, 80 kN and 85 kN).

Table 1: Formula for preparation of granules of two different formulations F1 and F2

Tablet thickness, diameter, weight and true density

The thickness and diameter of the tablets were determined using a digital Vernier caliper (Aqmezzure IP54) (6). The weight of the tablets were measured using digital weighing balance (WENSAR PBG-700). The true density of the tablets were determined using a Helium Pycnometer (True density meter) (Smart Instruments Co. Pvt. Ltd.) (7).

RESULTS AND DISCUSSIONS

Porosity of tablets

The prepared tablets of both the formulations (F1 and F2) were evaluated for their thickness, diameter, weight and true density. From these, the porosity of tablets(E) were calculated as shown in table II and table III.

Table II: Porosity of tablets of formulation F1

Table III: Porosity of tablets of formulation F2

Construction of Heckel plot

From the value of porosity (E), Log E^-1 was calculated and the Heckel Plot was constructed by plotting compressional force against Log E^-1 (3) (Figure 1a and 1b).

Analysis of crushing strength from Heckel plot

Compressional force plotted against Log E^-1 for two formulations F1 and F2 show linearity above 85% compressional force. From the plots, by regression analysis, the slope which is related to the crushing strength of tablets and intercept which is related to initial packing stage i.e., initial porosity were determined. It was observed from the plots that in case of the F1, the slope was 0.002 and intercept was -0.143, whereas in case of F2, the slope was 0.003 and intercept is -0.241. The larger value of slope in case of F2 indicated that the crushing strength of tablet formulated by using PVP K30 as binder was greater than that of the tablets formulated by using starch as binder and thus the tablets formed were harder. Larger intercept in case of F1 indicated that its initial porosity was greater than that of F2.