Technology Selection

occurs. This transfer of stress is continued until the particle ruptures or is pulled out. Bridging is at times purposely introduced (glass slide in this investigation) into concrete by adding small fibres to serve as bridges across the surface of the cracks. Some of the commonly used fibres are steel, polypropylene, aramide and glass fibres (Crane & Charles, 1997). The propagation of the main crack is occasionally terminated by a large internal void; this toughening mechanism is termed crack tip blunting. When a crack tip propagates into a void, the tip of the crack becomes blunt and an extra amount of energy is needed to propagate the crack with a blunt tip. When the main crack splits into two cracks, the toughening mechanism of crack branching is introduced into the specimen. More energy is needed to propagate two cracks through concrete than it does to propagate one crack.

These toughening mechanisms take place amongst one another and absorb a part of the energy being introduced into a concrete specimen by an external force or movement. The fracture mode of a cementitious material relates very closely to the nature of fracture process that takes place in that material, based on the understanding of the conditions under which a number of toughening mechanisms can occur in a given material, it may be possible to control the fracture mode by tailoring the material microstructure (Crane & Charles, 1997).

For naturally reinforced cement composite processing, it is of more practical relevance to understand and predict the thermal decomposition of the reinforcing based on the simplified kinetic scheme and parameters under specific process temperature of natural reinforcer composite. However, there have been few fundamental studies in this field.

Moreover, the reported values of kinetic parameters for natural reinforcer were in a large range, e.g., activation energy for pure cellulose from 100 and 250kJ/mol (Malek, 1992).

This variability was primarily caused by different kinetic schemes used and pre-assumption of the reaction function and reaction order in kinetic modeling process. The suitable kinetic models for natural fibers remain to be developed (Malek, 1992). A method proposed by Málek and his co-workers allows fairly reliable kinetic analysis and interpretation of non-isothermal TG-DTG data (Malek, 1992; Malek et al., 2001).

2.14.1 Theoretical Approach of Thermal Decomposition

The fundamental rate equation used in all kinetic studies is generally described as (Malek et al. 2001):

(2.3)

Where k is the rate constant and k, f(α) is the reaction model, a function depending on the actual reaction mechanism. Eq. (2.3) expresses the rate of conversion, dα/dt, at a constant temperature as a function of the reactant concentration loss and rate constant. In this study, the conversion rate α is defined as (Liu and Fan, 1998):

(2.4)

where W0, Wf and Wt are time, initial and final weights of the sample respectively, the rate constant k is generally given by the Arrhenius equation (Liu & Fan, 1998):

Comment [Kingsley12]: Something is missing here.

(2.5)

where E is the apparent activation energy(Kj/mol) , R is the gas constant (8.314J/K.mol), A is the pre-exponential factor (s^-1), T is the absolute temperature (K). The combination of Eqs.

(2.3) and (2.5) gives the following relationship (Liu and Fan, 1998):

(2.6)

For a dynamic TGA process, introducing the heating rate, β= Dt/dt into Eq. (2.6), Eq. (2.7) is obtained

(2.7)

Eqs.(2.6) and (2.7) are the fundamental expressions of analytical methods to calculate kinetic parameters on the basis of TGA data. The most common “model-free” methods used in this study are summarized in Table 2.4. The Friedman method is the isoconversional method, which directly leads to -Ea/R for a given value of α by plotting the term ln(dα/dt) against 1/T.

In the Kissinger method, is in (β/T²p) plotted against 1/Tp for a series of experiments at different heating rates with the peak temperature, Tp, obtained from the DTA curve.

The isoconversional Flynn-Wall-Ozawa (F-W-O) method is the integral method, which leads to -Ea/R from the slope of the line determined by plotting log(β) against 1/T at any certain conversion rate. The modified Coats-Redfern method is a multi-heating rate application of the Coats-Redfern equation. Plotting the left hand side for each heating rate versus 1/T at that heating rate gives a family of straight lines of slope -Ea/R. The full solution is to be done iteratively by first assuming a value of Ea and then recalculating the left hand side until convergence occurs. Here, a quick solution, however, is also available by moving into the intercept and assuming that it is a constant.

Table 2.3 Kinetic methods used in evaluating activation energy in this study (Liu and Fan, 1998).

2.14.2 Modelling of thermally activated reactions

In many cases, DTA/TGA data obtained for composites have been analysed in a purely qualitative manner, i.e. by relating the presence of endothermic or exothermic effects to particular reactions without attempting to obtain quantitative information on these reactions, their progress, or the mechanisms involved. Quantitative analysis is more often performed for isothermal experiments as compared to linear heating experiments. This is related to the availability of isothermal models, which are mathematically simpler than their non-isothermal equivalents (Liu & Fan, 1998).

The type of modeling of thermally activated reactions that has been used in conjunction with DTA, or that can be applied to DTA/TGA, is of a broad and diverse nature. Modelling approaches can mostly be classified as one of four types (Malek et al., 2001):

i. Generic analysis models, which are models that use relatively simple expressions that provide the fraction;

ii. Transformed as a function of time or reaction rate as a function of fraction transformed, and that are applicable to a wide range of reactions;

iii. Simplified physically based models, which are models that are specifically based on considerations of the physical or chemical process, often with adjustable process-related parameters, such as impingement parameters that allow some flexibility in

Comment [Kingsley13]: Does this need to change to percent as well?

analyzing data; and

iv. Simulations, which are models that make predictions, often using extensive computer time, with all models of parameters being fixed appeared ove r the past 10 years and that are suited for analysis of thermally activated reactions in polymer-based composites.

A general objective of the modelling of thermally activated reactions by generic analysis methods and physically based methods is the derivation of a “complete description of the progress of a reaction that is valid for any thermal treatment, be it isothermal, by linear heating or any other non-isothermal treatment. In the case of physically based methods, an additional aim is to be able to use the analysis to understand the processes involved in the reaction. At the outset, it should be realized that for many reactions these objectives are daunting, especially for solid state reactions, any given reaction might progress through a range of mechanisms and intermediate stages, all of which will, in general, have a different temperature dependency (Malek et al., 2001).