Marco Normativo 1 A Nivel Internacional.

5. Fracture toughness, R. a (MPa) 4 -h D M eO 6- 2- BuO PrD 45 50 55 60 65 y s (mNm-1)

Figure 4.2.5. Relationship between surface energy and tensile strength for the alkyl p-hydroxybenzoates.

A relationship between such properties and surface energy might be expected, because as Ys increases, the work of cohesion, Wc, (w here W c =2Ys) increases and therefore, the interaction between particles

Chapter 4 Surface Energies 180

would also be expected to increase. A graph of these five properties as a function of surface energy (calculated using the harmonic mean equation, using contact angle data analysed by method (a)), are shown in figures 4.2.5 - 4.2.9. 1500 1000- Py (MPa) 500- 4-hD Et&Buin Ys (mNm-1)

Figure 4.2.6. Relationship between surface energy and mean yield pressure for the alkyl p-hydroxybenzoates.

The best correlation (see table 4.2.24) is between ys and critical stress intensity, Kjc and fracture toughness, R. This would be expected as these are the two mechanical properties (as well as critical stress energy release rate) which reflect the toughness of a material (e.g. Newton et al.y 1993). The other parameters provide information about the relative plastic or elastic nature of the powder. The critical strain energy release rate is also an indicator of toughness and since Gjc is equivalent to 2yg, (e.g. Mashadi, 1988) for brittle, elastic materials, a good correlation between Gjc and surface energy would be expected. However, if the

elastic/plastic nature varied, then a deviation from linearity would be seen. 0.4 M e O 4-hO 0.3 - EtO 0.2- 0.1- PrO 65 45 50 55 60 Ys (mNm*l)

Figure 4.2.7. Relationship between surface energy and the critical stress intensity for the alkyl p-hydroxybenzoates.

M eO 12.5- BuO 1 0- 4-hO EtO 7.5- PrO 2.5 45 50 55 60 65 Ys (mNm-l)

Figure 4.2.8. Relationship between surface energy and critical strain energy release rate for the alkyl p-hydroxybenzoates.

Chapter 4 Surface Energies 182

( Nm )

Ys (mNm-l)

Figure 4.2.9. Relationship between surface energy and fracture toughness for the alkyl p-hydroxybenzoates.

It is well recognised (e.g. Mashadi, 1988) that standardisation of experimental procedures is of paramount importance for the testing of the mechanical properties of powders. However, since these data were obtained by the same operator, this factor should not affect the data and therefore, does not provide an explanation for the deviation from linearity, for some of these relationships.

Table 4.2.24. To show the correlation coefficients (r^) for the relationship between surface energy and several mechanical properties.

Property r2 O (MPa) 0.510 Py (MPa) 0.674 Kic (MNm-3/2) 0.770 Gic ( Nm-l 1 0.627 R ( Nm ) 0.884

As m entioned previously, the correlation coefficients in table 4.2.24. are for th e rela tio n sh ip betw een surface energy obtain ed u sin g the harmonic m ean equation. To evaluate the four theories available for estim a tin g surface free energy the correlation coefficients for the relationship w ith critical stress intensity, K jc and fracture toughness, R, using each theory is shown in table 4.2.25. The results indicate that the geometric and harmonic m ean equations provide the b est models, w hilst Wu's equation of state, provides the worst model.

Table 4^.25. To show the range correlation o f coefficients (r^ obtained for the relationship between surface ffiee energy and two mechanical properties.

Equation of state Equation of G eom etric H a rm o n ic Property (N eu m an n )* r2 state (Wu)* r2 m ean equation r2 m ean equation r2 Kic(MNm-3/2) 0.618 0.597 0.775 0.770 R ( Nm ) 0.844 0.823 0.862 0.884

The unexpected behaviour of methyl p-hydroxybenzoate has been noted co n tin u o u sly throughout th is work. In particu lar, th e surface p rop erties (con tact angle and surface energy) and m ech an ical properties (m ean yield pressu re and fracture to u g h n ess). This phenomena will be discussed in more detail in section 6.3.

Chapter 4 Surface Energies 184

4.3. CONCLUSIONS.

U sin g a combination of the findings of previous workers and data obtain ed in th is study, the follow ing conclusions can be draw n concerning the choice of theory selected to calculate surface energies from contact angle data,

1. N eum ann's equation of state is not suitable for pharm aceutical

system s, which are frequently polar in nature. Although, th is theory can be used to provide the rank order o f the surface en ergies of m a teria ls, w here contact angle data a g a in st only one liq u id are available.

2. Little work had been carried out using Wu's equation of state. It was

considered here due to its comparative simplicity. However, data clearly shows that this approach is unsuitable for pharmaceutical system s. 3. The geometric and harmonic m ean theories are clearly th e m ost appropriate, in term s of the extent of inform ation and accuracy of information provided. Although, the drawbacks of these theories should still be considered and where possible the sam e two liquids should be u sed for all m aterials under in vestigation . The harm onic m ean equation would appear to be the m ost suitable as, in accordance w ith observation made by Wu (1973), (comparing calculated and experim ental data), the surface energy obtained is generally greater and m odels the system more accurately.

3. The acid/base approach has previously been shown to be the m ost