As with the associated relationships

As with the associated relationships for the Sirolimus specimens, there did not appear to be any consistent relationships for the four-point bend specimens when comparing c through the specimens with the bend strength, bend modulus and density. Although positive correlations were found in five situations, no significant trends were found across the different cements and mixing conditions investigated (Table 5). When the experimentally calculated values of c were compared to the theoretically calculated values Eq. (3), it was evident that the values were distinctly different (Table 3).
The lack of agreement may have been due to the fact that c was a function of the material alone, whereas the bend modulus was a function of both the material and specimen geometry. To eliminate the effect of the specimen dimensions on the bend modulus value, a shape factor was applied. The shape factor, ϕ, was determined experimentally by testing specimens in four-point bend, as described previously Eq. (4):where =load at fracture (N); =load at elastic limit (N).
The heterogeneous nature of acrylic bone cement made it an unsuitable material to determine a shape factor as the presence of pores and/or unmixed powder could not be wholly taken in account. Instead, four-point bend specimens were created from general purpose acrylic sheet (Perspex®). Perspex® was chosen as the main constituent of fully polymerised bone cement is acrylic and Perspex® sheet is unlikely to contain pores or in homogeneities within the bulk polymer. Three Perspex® specimens were tested and an average shape factor of ϕ=2.42±0.09 was determined. This shape factor was used to calculate a new theoretical value of c for each bone cement specimen using a modified version of Eq. (3):The average theoretical values of c using Eq. (5) can be found in Table 3, percentage differences in the theoretically calculated c values compared to the average determined experimentally. Final c values for the acrylic bone cement specimens are also shown (Table 3).

The variation in c agrees with the general patterns observed in previous studies [15,20]. This variation can be split into three stages: (1) initial plateau where there was little variation in c; (2) sharp increase when c increased by 700–1100ms−1; (3) c levelling off into another plateau as the cement had fully hardened and there was no significant change in cement structure and therefore no change to c. Similar trends in variations of c have been reported during cure monitoring of thermosetting resin consisting of polyester and styrene [22,23] and epoxy resins [24].
The initial plateau can be attributed to an induction period caused by the presence of the inhibitor, hydroquinone. Polymerisation will not begin until all the inhibitor has been consumed [22], leading to the initial plateau seen in the value of c.
The initial plateau or induction period was found to be longer for the acrylic bone cements prepared under atmospheric condition due to the presence of oxygen during atmospheric mixing. He et al. [13] established that oxygen molecules are known radical scavengers, which will join the inhibitor in stealing free radical molecules, causing the induction period to increase in duration.
The second stage involved a large rise in c occurring rapidly over a period of 2–5min, which corresponded with an increase in cement viscosity and inhibited the movement of growing polymer chains; allowing the sound pulses to travel faster, leading to the increase in c through the mass. Similar trends have been reported during the monitoring of the setting/curing reactions of other systems; whereby a more organised, closely packed microstructure rather than consisting of particles in a solution [15,20,22–24]. Carlson et al. [19] did not report a similar finding when monitoring a calcium sulphate based bone cement. They found that as c increased, the density actually decreased, which was attributed to the emerging crystalline microstructure of the cement, thereby propagating the sound waves faster rather than the closer packing of the molecules.