SUBRUTINA DE INICIALIZACIÓN DE COMUNICACIÓN CAN.

Water adsorption on the surface of crystalline solids at a certain temperature and vapour pressure is most commonly fitted to either the BET or its extension the GAB adsorption isotherm (as mentioned previously). In case of amorphous solids however, water is known to be absorbed into amorphous regions rather than being adsorbed. To fit data of water absorption into amorphous materials or amorphous regions, the BET equation or the GAB equation have been used. It is considered to be useful in estimating Wn,. Hancock and Zografi (1993) argue however that in the case of amorphous solids, these mathematical models are basically used as they fit data quite well rather than being able to advance our understanding of the molecular processes occurring as water is taken up into amorphous solids. It clearly does not take into account the significant plasticizing effect of water or any structural changes in the solid taking place as water is absorbed. This is a disadvantage in relying on the BET equation to demonstrate water absorption

profile in amorphous solids. In the case of amorphous solids Wm does not indicate monolayer coverage but rather reflects the polarity of the solid, the higher the polarity the higher the value of Wm (Buckton, 1995a). For amorphous solids, Wf is substituted with the term Wg indicating the amount of water needed to convert the amorphous solid from the glassy rigid state to the rubbery state. The significance of Wg being a critical point is quite clear from knowing the greater molecular mobility accompanying the rubbery state relative to the glassy state, which will lead to a significant increase in water uptake above

Wg. In the case of Wm, the significance in amorphous materials is not as clear but it was shown that for water-PVP system, the ratio of Wg to Wm over 100° range is quite constant indicating that Wm is related to the plasticizing effect of water (Zografi and Hancock, 1994). Basic solution theories have been used to model data and to achieve a better understanding of water vapour absorption into amorphous solids. This is based on the idea that the water absorption process by amorphous solids is completely analogous to the solution process. Two theories are considered here:

1.3.2.4.1 THE FLORY- HUGGINS THEORY:

This theory is based on the assumption that the solution process is driven by a minimum free energy requirement. A form of the equation that gives the partial pressure of the solvent as a function of the solvent content is a frequently used form of the equation (Hancock and Zografi, 1993).

P/Po = c|)i exp {(1 - 1/x) 02 + X 02^} ... Equation. 1.9

Where P/Po is the partial pressure of the solvent, 0i and 02 are the volume fractions of the solvent and the polymer respectively; x is the ratio of the molar volumes of the solvent and the polymer and % is the Flory-Huggins polymer-solvent interaction parameter (a constant). This constant ranges from 0 (good solvent) to 0.5 (poorer solvent). The validity of the Flory-Huggins model for predicting water vapour absorption into amorphous pharmaceutical solids was tested by comparing the predicted isotherm with experimental data from the literature (Hancock and Zografi, 1993). Poly(vinylpyrrolidone) (PVP K30)- water system at 30 °C was used as the model to test for agreement with Flory-Huggins model. It was noted that there is an overall agreement between experimental data and predicted isotherm especially when the amount of water vapour sorbed is sufficient to plasticize the sample and convert it from the glassy to the rubbery state where

significantly greater amounts o f water will be taken up by the amorphous solid sample. This is not surprising since this theory was derived for non-polar polymer-solvent systems at high solvent concentrations, which are not met by PVP absorbing small amounts o f water in the glassy state. It can thus be concluded that this is a suitable model to predict behaviour o f the amorphous solid material in the rubbery state upon exposure to water though is less suitable to predict behaviours in the glassy state which is maintained at low partial vapour pressures provided that the temperature o f experiment is kept below Tg o f the sample mix (Figure 1.11). It has to be mentioned though that the glassy region is the region o f interest for most pharmaceutical applications since samples will almost always be dried and then stored at lower vapour pressures.

0.6

^

Vapour pressure, p/po

Figure 1,11 Comparison o f data fitting o f PVP K30 to both Vrentas model and Flory-

Huggins model at 30 (•) Data; (....) Vrentas equation; ( ----) Flory-Huggins

equation. Adapted from Hancock and Zografi (1990).

1.3.2.4.2 THE VRENTAS THEORY:

Vrentas proposed that the sorption o f a penetrant by a polymer results in a nonideal hole free volume increase. Nonideal, in the sense that, the net hole free volume o f the polymer/water system in the glassy state is less than what would be predicted by simple addition o f the hole free volumes o f the two independent components. This net excess loss in hole free volume is due to local rearrangement o f the glassy polymer as the penetrant enters the system and interacts with the polymer (Hancock and Zografi, 1993). Vrentas equation is very similar to Flory-Huggins equation but with the addition o f the term exp/ as shown below:

Where/ = {MiW2^ (Cpg - Cp) (dTgm/dwi) ((T/Tgm) -1)}/RT

Where Mi is the molecular weight of the solvent, w% and w% are the penetrant mass fraction and the polymer mass fraction respectively, Cpg and Cp are the heat capacities of the mix in the glassy state and the rubbery state respectively, dTgm/dwi is the change in Tg of the mixture with varying penetrant mass fraction, R is the universal gas constant and T is the experimental temperature. It can be noted that the term /includes all those factors that reflect the change in structure of the polymer-penetrant mixture below the glass transition temperature. It can further be commented that all components of this term are constant at any given experimental temperature except for dTgm/dwi, hence it is this term that is most critical in determining the shape of the isotherm below Tg. A significant change in the value of dTgVdwi would produce a large shoulder of the isotherm in the region of Wm. This shoulder is not predicted by the Flory-Huggins model, which basically deals with the rubbery state. Thus, the value of the Vrentas model is that it enables the prediction of sorption isotherms for polymers in both the glassy and the rubbery states as water is absorbed as can be seen in Figure 1.11. It should be noted that at T = Tg the Vrentas equation reduces to the Flory-Huggins equation.

1.3.3 EFFECT OF ADDITIVES OTHER THAN WATER ON Tg OF