Derive a simplified version of the above model that


Determining the Effect of Process Parameters on the Size of Chitosan Microspheres

Background.

Immobilized enzymes have great importance in industrial bioprocesses especially in food, nutritional and pharmaceutical technologies. When immobilized the generally expensive biocatalysts can be used repeatedly in several batches, or the process can be carried out continuously (e.g. in a fluidized-bed reactor). Enzymes are generally immobilized on solid support particles with a size usually ranging from some hundred micro meters to several millimetres. Particles of several hundred microns can be separated without difficulty, and they have enough surface area for the efficient immobilization of enzyme molecules and to contact them effectively with the substrate. Chitosan is a suitable substance for the support particles for enzyme immobilization in the above size range because of its beneficial properties: i.e. it is non-toxic, biocompatible and biodegradable. In addition, after suitable treatment its reactive amino and hydroxyl groups offer a good enzyme coupling efficiency.

Experimentation and Data Collection.

Chitosan particles can be obtained by several methods such as precipitation, emulsion crosslinking, spray-drying, ionotropic gelation, emulsion-droplet coalescence and reverse micellar methods. n-Hexadecane was bought from Fluka Chemie GmbH (Buchs, Switzerland). n-Hexane, ethanol, sunflower oil, glutaraldehyde (25% aqueous solution) were supplied by Reanal Ltd. (Budapest, Hungary). All chemicals used in this work were of analytical grade.

The chitosan microspheres were prepared by the w/o emulsion crosslinking method, but replacing the highly volatile petroleum ether with the more friendly n-hexadecane. The oil phase was composed of 40% (v/v) sunflower oil and 60% (v/v) n-hexadecane. Adequate quantities of chitosan were dissolved in 2% (w/w) aqueous solution of acetic acid to obtain in 0.5, 1.0 and 1.5% (w/w) solutions, respectively.

Emulsification was carried out by adding 4cm3 chitosan solution drop wise to 40cm3 oil phase containing various amounts of Tween 80 surfactant under continuous stirring. The rotation speed of the paddle stirrer was varied in the range of 500 and 1750 min-1. After stirring for 30 minutes, different quantities of 25% (w/w) aqueous glutaraldehyde were added to the emulsion to solidify the droplets and then to harden the resultant particles by crosslinking. The quantity of glutaraldehyde was varied between 1.0 and 5.0% (w/w) relative to the weight of the aqueous chitosan solution. After addition of the crosslinking agent the mixture was further stirred for one hour, then the formed microspheres were filtered out and washed with n-hexane and ethanol sequentially. The size measurement of micro particles was carried out by Malvern 2600c type laser diffraction particle size analyser. The mean particle diameter data used for this study was determined from the volumetric size distributions of the samples. Morphological investigation of particles was carried out by optical microscope and Philips XL30 ESEM scanning electron microscope using this latter in the environmental mode.

All experimental work was carried out at the University of Pannonia and to investigate the effect of the above process parameters, 2 experiments was carried in which the composition and viscosity of the oil phase and the type of surfactant were not changed.

Experiment 1.

The first step was to identify whether the stirring rate was an important process variable. Thus a traditional change one variable at a time experiment was carried out. Twenty tests were carried out at a stirring rate of 1000 rpm and twenty tests were carried out at a stirring rate of 500 rpm. In all these tests the levels for Tween 80 concentration, Chitosan concentration and glutaraldehyde concentration were held fixed at 1.5%, 1%, and 3% respectively. The particle sizes for each of these tests are shown in Sheet1 of the Data Sheet .


Experiment 2.
This was the biggest experiment consisting of forty three different tests. In this experiment the effect of 4 process parameters (stirring rate, Tween 80 concentration, Chitosan concentration and glutaraldehyde concentration) on particle size was studied. These test conditions and the corresponding particle sizes are shown in Sheet2 of the Data Sheet.

Objectives.
You are required to write a mini project that carries out a detailed statistical investigation on the experimental data discussed above. The project should provide an answer as to what processing conditions produce chitosan microspheres with particle size suitable as biocatalyst supports.
When writing this mini project, structure it in a way that allows you to cover and address all the following questions and issues in a way that reveals a progressively greater understanding of the two experimental data sets.

1. Describe the sources of variability present in each data set of Experiment 1. Then using appropriate data displays, describe each data set in Experiment 1, highlighting any similarities or differences that may exist between the 2 stirring rates.

2. Using the data sets collected in Experiment 1, construct an appropriate parametric and non-parametric test to assess the claim that the typical particle size is not the same for each rate of stirring. When writing up your analysis of this claim state any assumptions that need to be made in conducting these tests and if appropriate carry out tests to validate these assumptions. Discuss also the advantages and disadvantages of each test.

3. Using the data set collected in Experiment 2 and the technique of multiple least squares, estimate β the parameters of the following second order response surface model:

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where Y is particle size, X1 is the stirring rate, X2 is the Tween 80 concentration, X3 is the Chitosan concentration, and X4 is the glutaraldehyde concentration. ε is the prediction error or residual.
When writing up your analysis of this model, describe how well this model fits the data, which variables are statistically significant (important) and what meanings can be attached to the β parameters. State any assumptions that need to be made is assessing such statistical significance, and if appropriate carry out tests or construct scatter plots to validate these assumptions.

4. Derive a simplified version of the above model that includes only the statistically significant variables.

When writing up your analysis, describe how well this simplified model fits the data, the meaning of the parameters, the degree of accuracy achievable when predicting the particle size using this simplified model (as described by a 95 confidence interval on an actual v prediction plot). Use the model to find the process conditions required for small (< 0.25 mm) and large particle sizes (> 0.53 mm), making full use of any suitable 2D or 3D scatter plots to explain these conditions.

Attachment:- data.xlsx

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