Determination of the optimal conditions

The optimum conditions are determined using the Minitab Response Optimiser. Response optimisation is useful to determine optimum operating conditions. It helps to identify the combination of input variable settings that jointly optimise a single response or a set of responses. This is useful when we need to evaluate the impact of multiple inputs on a response.

Once an optimisation plot has been created, the input variable settings can be changed. For response surface designs, the factor levels can be adjusted. Input variable settings on the optimisation plot can be change for many reasons (Minitab Inc, 2007), including:

 To search for input variable settings with a higher composite desirability

 To search for lower-cost input variable settings with near optimal properties

 To explore the sensitivity of response variables to changes in the design variables

 To “calculate” the predicted responses for an input variable setting of interest

 To explore input variable settings in the neighbourhood of a local solution

Figure 4.1 shows an optimisation plot: each factor (column) is plotted against the response and composite desirability (rows). The vertical red lines on the graph and the red numbers displayed at the top of a column show the current factor level settings. The horizontal blue lines and numbers represent the responses for the current factor level. The optimal solution serves as the starting point for the plot. This optimisation plot allows us to interactively change the input variable settings to perform sensitivity analyses and attempt to improve on the initial solution. For each new set of input variables, the optimisation plot is redrawn and the predicted response and desirability are recalculated. The optimisation plot allows us to shows how the factors affect the predicted responses.

72 Cur High Low 1.0000D Optimal d = 1.0000 MaximumModulus y = 1210.8586 1.0000 DesirabilityComposite 5.0 9.0 60.0 100.0 175.0 195.0 Speed Time Temperat [175.0] [100.0] [6.9394]

Figure 4.1 Optimisation plot

Temperature: Decreasing temperature moved Young’s modulus towards its maximum. This

effect is attributed to PLA were found to be highly sensitive to heat, especially at temperatures higher than 190 °C (Jamshidi et al., 1988, Garlotta, 2001).

For the effect of temperature on nanocomposites, the results reported in the literature are relatively controversial. Kwak et al. (2002) reported a better dispersion of organoclay in polyethylene at higher temperature (230 C instead of 170 C). Modesti et al. (2005, 2006) obtained better results at lower temperature (170 C instead of 200 C), but for polypropylene. In fact, it seems that, beside the nature of the nanocomposite considered, the temperature cannot be considered independently of the other parameters such as screw speed (Tillekeartne et al., 2003). As temperature increases, viscosity decreases, and thus the stress necessary to break the clay aggregates decreases. At the same time, diffusion is improved, which can help to intercalate and exfoliate the platelets. In addition, a temperature too high could cause a degradation of the organoclay intercalants, leading to a collapse of the interlayer galleries and decreased intercalation (Mederic et al., 2006).

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Speed: Increasing speed moved Young’s modulus towards its maximum. Generally speaking,

it is well admitted in the literature that an increase in screw speed leads to a better dispersion. This effect has been observed on different systems, including nanocomposites based on polyamide (Cho and Paul, 2001, Incarnato et al., 2003), polyethylene (Kwak et al., 2002), and polypropylene (Modesti et al., 2005, Modesti et al., 2006, Lertwimolnun and Vergnes, 2005). It can be explained by the fact that a higher shear rate allows to break the agglomerates in smaller aggregates, enhancing polymer–clay interactions by making the entire surface of layers available for the polymer (Beyer, 2002, Lertwimolnun and Vergnes, 2007). This suggests that the optimum speed at these factor conditions is above the range trialled in this study.

Time: Increasing time first increased then decreased Young’s modulus. It reached a maximum

within the range of times trialled, so the optimum is around 7 minutes for these factor conditions. Figure 4.1 show that Young’s modulus has a high coefficient for Time*Time, that is, it increases quadratically with time.

Denault and coworkers (2006) reported that long compounding time and high compounding temperature can lead to organoclay degradation in a polymer nanocomposite. Bourbigot et al. (2008) also reported that longer times accompanied by higher shear lead to the reagglomeration of the platelets.

Optimum conditions: The Minitab Response Optimiser calculated that modulus is maximized

when temperature is at the lowest setting, speed is at the highest setting and time is at a mid- point (Temperature =175 C, Speed =100 rpm and Time =7 min).

However the optimum conditions to maximise Young’s modulus appear to be beyond the range of factors trialled in this study. The optimum temperature may be lower than 175 C and the optimum speed may be higher than 100 rpm while the optimum time is clearly around 7 min (Figure 4.1). Hence the Response Optimiser is not the best approach when the optimum is outside the experimental range. An empirical model based on the best fit to the data can be used to predict an optimum point beyond the measured range. Once the optimum is found, the accuracy of the model can be improved if desired, by repeating the experiments at a wider range of conditions.

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According to the best fit model to the data, the maximum Young’s modulus was predicted to be 1210 MPa at a temperature, speed and time of 175 C, 100 rpm and 7 min. The model was tested for robustness by making samples at the predicted optimum mixing conditions, then the measured modulus was compared with the prediction. The modulus of a sample made at the optimum conditions was 1240 MPa, which is higher 2.4 % than predicted by the best fit model. This difference is not significant at a 95 % confidence level. Hence the agreement between the measured and predicted response is considered to be reasonable, and the model is considered robust.

The optimum modulus (1240 MPa) is also 7.8 % higher than the average modulus for the BBD runs (1150 MPa), so it is significant at the 99 % confidence level. Hence making samples at optimised conditions improved the modulus significantly.

This is in reasonable agreement with other studies of optimum process conditions for polymer nanocomposites. Jollands and Gupta (2010) reported the optimum mixing conditions 185 C, 80 rpm and 7 min. The small differences may be attributed to different mixer and/or material grade. Bourbigot et al. (2008) reported a mixing study for PLA/clay nanocomposites with 3 % Closite® 30B using a DSM twin screw micro extruder at various speeds and residence times. A DSM micro extruder has a recirculating channel so that residence time can be controlled. They produced samples at 25, 50, and 100 rpm at 185 C and residence time of 1 – 15 min under a nitrogen blanket. They reported the optimum conditions were ‘‘high shear stress’’ (100 rpm) for 1 min, then low shear stress (25 rpm) for an additional 5 min. The differences to this study may also be attributed to different equipment and PLA material grade and that temperature was not varied. Hasook and coworkers (2008) reported a mixing study for intercalated PLA/clay nanocomposites with 5 % and 10 % organoclay using a TSE co- rotating twin screw extruder at two speeds. They produced samples at 180 C and 65 and 150 rpm, and found better properties at the higher speed. The differences to this study may also be attributed to different equipment and PLA material grade and residence time was not controlled.

Although numerical optimisation along with graphical analysis can provide useful information, it is not a substitute for subject matter expertise. Relevant background information, theoretical principles, and knowledge gained through observation or previous experimentation needs to be considered when applying these methods (Minitab Inc, 2007).

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It should be noted that determination of the optimum conditions is specific for this one nanocomposite material in this one mixing configuration. When different materials or mixers are used then the optimum conditions will also change.