A modern approach to the Heckel Equation: The effect of compaction pressure on the yield pressure of ibuprofen and its sodium salt

Despite being heavily criticised in the literature the most widely used and accepted compaction equation is the Heckel equation proposed by Heckel in 1961. Its presence in literature for 55 years is due to the ease in which it can distinguish between plastic and brittle materials. Achieving the correct balance of plastic and brittle materials in a formulation is critical to ensure adequate tablet strength is achieved therefore classifying materials using the Heckel equation is attractive. Despite the importance of this understanding, especially in the design and manufacture of direct compression formulations, there are no set analytical testing standards or materials classification guidelines. Instead many workers have attempted to develop techniques for the measurement and classification of a materials deformation but there is still confusion and contradiction present in this field. In this study we repot on report the effect of compaction pressure on the yield pressure of ibuprofen and its sodium salt. Ibuprofen and its sodium salt were selected as models for study due to the availability of comparative literature yield pressure values. The reported variation in yield pressure can be significant e.g, ibuprofen which has literature values of 21-1139 MPa. This study proposes an approach to determine yield pressure from the Heckel equation using a linear regression method. The full linear regression methodology utilised is described and is used to report the yield pressure of ibuprofen and its sodium salt dihydrate. This technique reveals the most representative compaction pressure in order to derive yield pressure to be 121 MPa. The yield pressure of ibuprofen and its sodium salt have been shown to increase with increasing compaction pressure. The reported values lie between 52-78 MPa for ibuprofen and 48-75 MPa for ibuprofen sodium dihydrate. The slightly lower reported yield pressure values for ibuprofen sodium suggest increased plasticity which could be attributed to the water contained within the structure acting as a plasticiser

Economic analysis of community solar heating systems that use annual cycle thermal energy storage

The economics of community-scale solar systems that incorporate a centralized annual cycle thermal energy storage (ACTES) coupled to a distribution system is examined. Systems were sized for three housing configurations: single-unit dwellings, 10-unit, and 200-unit apartment complexes in 50-, 200-, 400-, and 1000-unit communities in 10 geographic locations in the United States. Thermal energy is stored in large, constructed, underground tanks. Costs were assigned to each component of every system in order to allow calculation of total costs. Results are presented as normalized system costs per unit of heat delivered per building unit. These methods allow: (1) identification of the relative importance of each system component in the overall cost; and (2) identification of the key variables that determine the optimum sizing of a district solar heating system. In more northerly locations, collectors are a larger component of cost. In southern locations, distribution networks are a larger proportion of total cost. Larger, more compact buildings are, in general, less expensive to heat. For the two smaller-scale building configurations, a broad minima in total costs versus system size is often observed

Analysis of community solar systems for combined space and domestic hot water heating using annual cycle thermal energy storage

A simplified design procedure is examined for estimating the storage capacity and collector area for annual-cycle-storage, community solar heating systems in which 100% of the annual space heating energy demand is provided from the solar source for the typical meteorological year. Hourly computer simulations of the performance of these systems were carried out for 10 cities in the United States for 3 different building types and 4 community sizes. These permitted the use of design values for evaluation of a more simplified system sizing method. Results of this study show a strong correlation between annual collector efficiency and two major, location-specific, annual weather parameters: the mean air temperature during daylignt hours and the total global insolation on the collector surface. Storage capacity correlates well with the net winter load, which is a measure of the seasonal variation in the total load, a correlation which appears to be independent of collector type