materials science experiments as a tool for learning

Journal of Materials Education Vol. 37 (1-2): 59-84 (2015)

MATERIALS SCIENCE EXPERIMENTS AS A TOOL FOR LEARNING AND APPLYING HIGH SCHOOL MATHEMATICS Natalija Budinski a, Djurdjica Takaci b, Mirjana Jovicic c, Jelena Pavlicevicc, Ivan Ristic c, Nevena Vukic c, Vesna Teofilovic c,Mladjan Popovic d High School “Petro Kuzmjak”, 25233 Ruski Krstur, Serbia; nbudinski@yahoo; Faculty of Natural Sciences, Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovica 5, 21000 Novi Sad, Serbia; c Faculty of Technology, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia; d Faculty of Forestry, University of Belgrad, Kneza Viseslava 1, 11000 Belgrad, Serbia a

b

ABSTRACT We discuss a new educational approach for teaching Materials Science and Engineering (MSE). MSE can be introduced to high school students via classes of Mathematics. We describe how such students are introduced to MSE experiments by scientists from the Faculty of Technology of the University of Novi Sad. Subsequently, students share their experiences with their peers. Application of our approach accomplishes at least two objectives. First, students see Applied Mathematics via demonstrated connections between Mathematics and MSE. Second, MSE appears on their radar when they reach the stage of choosing their major at the college level and thus their future professions. This is important since most high school students do not get in contact with exhibitions of the Materials Research Society or with other MSE related activities of professional societies. Keywords: materials science, mathematical model, high school mathematics

INTRODUCTION The latest educational research emphasizes the importance for students to build models in a wider context instead of working only with those, which are provided by textbooks. The advantage of this approach is that students can review models that have been built in the school context and compare them to those built in the scientific context in order to explain ideas, objects, phenomena or similar systems. It cannot be done by following a rigid algorithm

in the classroom, but rather by understanding what a model represents 1-3 . The knowledge about models and the process of modeling is becoming a way of developing scientific understanding4. According to Chamizo5 it is necessary to rethink the meaning of science we are teaching and how much it transforms our students’ attitudes towards knowledge. In this paper, we report implications of a modeling-based approach that has been carried out at the Faculty of Technology, University of

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Budinski, Takaci, Jovicic, Pavlicevic, Ristic, Vukic, Teofilovic and Popovic

Novi Sad and high school “Petro Kuzmjak” in Ruski Krstur, Serbia. During this specific project, high school students (age 17-18) worked collaboratively with materials scientists. Six students took part in scientific experiments related to materials preparation. All of them had advanced knowledge in mathematics and chemistry. They were introduced to the project’s experiments by the scientific staff of the Faculty of Technology. Those scientists provided lectures about chemical kinetics, materials science, and connections between mathematics and chemistry. The methodology and the significance of the scientific experiment they had been working on at the time were also explained and the students were trained in making the scientific measurements and observations. The training has only an educational purpose and served to illustrate scientific methods to the students. Six students, involved in this research, transferred their new knowledge about chemical kinetics and mathematics to their peers in the high school “Petro Kuzmjak”. Under the guidance of their instructors, the students have prepared several presentations where they explained the realworld application of mathematics in chemical kinetics and Materials Science to their peers in high school. Guided by the educational theoretical framework6-15 the designed process is theoretically and empirically grounded. It consists of strategy instructions that describe the teaching process in detail and provides educational affect in gaining new knowledge such as the benefits of modeling material experiments. The Aim The aim of our work was to develop the teaching strategies for learning mathematical concepts through models of chemical kinetics related to Materials Science and Engineering. Materials Science and, more specifically, Polymer Engineering are disciplines suitable for introducing students to the scientific method. Examples from Materials Science can show to

students, not only how materials behave, but also reasons for their behavior11. The basic idea of the approach that will be described in this paper is to present concepts from Materials Science to high school students and teach them how to determine reaction kinetics during material preparation using their mathematical knowledge. Choosing scientific experiments related to materials that cover real-world situations is of interest to the students, and engages them in the multidisciplinary approaches of Materials Science and mathematical modeling. Furthermore, those high school students who were included in Materials Science modeling made presentations to the other students in order to illustrate the significance of applying high school mathematics and science in general. This is a unique approach in which the high school students can broaden their perspective of how to use their knowledge. Having experienced new ways of learning mathematics and science, students should be able to transfer these techniques to their future education and work. The proposed educational model differs from traditional educational strategies. The connection between mathematical modeling and chemical kinetics was made comprehensible for high school students by giving them firsthand experience in the polymer laboratory at the Department of Materials Engineering, at the Faculty of Technology. The chemical reaction dynamics during the polymer preparation was simulated and visualized in order to explore a given mathematical model. The mathematical topics such as functions, particularly exponential functions, slopes, differential and integral calculus were examined. From an instructional point of view, the science (chemistry in particular) has mathematical implications. Educators point out the importance of connecting mathematics and science in the school, even though they are separate subjects. Unfortunately, connecting mathematics and chemistry is difficult for students16.

Journal of Materials Education Vol. 37 (1-2)

Materials Science Experiments as a Tool for Learning and Applying High School Mathematics

CONNECTION BETWEEN HIGH SCHOOL MATHEMATICS AND MATERIAL SCIENCE This paper describes the methods in which four types of experimental work related to material synthesis have been presented to high school students. Students were given lectures about the fundamentals of Materials Science and the significance of planned experimental work. They were introduced to Materials Science experiments related to selected material types known to students, from everyday life (rubber, wooden products, sportswear, printing ink, furniture parts or coatings). Four experiments related to Materials Science are described in detail in the last section of the paper. Those experiments were: 1) explain the reaction kinetics of polyurethane (PU) formation using the differential scanning calorimetry (DSC) method for the assessment of the optimal condition for production; 2) introduce the students to printing technology with an experiment concerning the cross-linking of printing inks. The formation of polymer networks based on resins, from liquid monomers or oligomers, involves a complex combination of chemical and physical events, which can be followed by the DSC method. 3) study the reaction kinetics of epoxy resin materials based on 2,2-Bis(4-glycidyloxyphenyl) propane DGEBA and thermoplastic polyurethanes prepared from aliphatic hexamethyelene-diisocyanate (HDI), polycarbonate diol and 1,4-Butanediol (BD) as the chain extender with a montmorillonite dispersion as a catalyst; 4) curing performances of urea-formaldehyde (UF) resin. All experiments produced DSC data that could use applied mathematics to analyze and interpret the results. The introduction section started with the experiments, which examined the influence, in curing of polyurethanes, of isocyanate type on catalyzed and noncatalyzed reaction on network formation with castor oil. This experiment is described in the section Materials Science experiments as the first example17. Students are introduced to isocyanates as potentially

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dangerous irritants to the eyes and the respiratory tract, despite their relatively low acute toxicities. Polyurethanes have variable curing times, and the presence of free isocyanates in foams vary accordingly. We used this example to introduce the students to the differential scanning calorimetry (DSC) method and instruments. In this example, DSC has been used to examine polyurethane formation reactions. The lecturer illustrated operational details about DCS, e.g., how to prepare samples and obtain the measurements. The DSC method is a thermo analytical technique in which the difference in the amount of heat required to increase the temperature of a sample and a non-reactive reference material is measured as a function of temperature. Both the sample and reference are maintained at nearly the same temperature throughout the experiment. Generally, the temperature program for a DSC analysis is designed in such a way that the sample holder temperature increases linearly as a function of time. The reference sample should have a welldefined heat capacity over the range of temperatures to be scanned. The basic principle underlying this method is that when the sample undergoes a physical or chemical transformation such as phase transitions, more or less heat will need to flow to it than the reference to maintain both at the same temperature. Whether more or less heat must flow to the sample depends on whether the process is endothermic or exothermic, respectively. For example, as the solid sample melts to a liquid it will require more heat flowing to the sample to increase its temperature at the same rate as the reference. This is due to the absorption of heat by the sample as it undergoes the endothermic transition from solid to liquid. Likewise, as the sample undergoes exothermic processes less heat is required to raise the sample temperature. By observing the difference in heat flow between the sample and reference, DSC instruments are able to measure the amount of heat absorbed or released during such transitions. It is widely used in industrial settings as a quality control instrument due to


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its applicability in evaluating sample purity and for studying polymer curing. Curing of polymers results in formation of thermosets, a widely used class of materials including polyurethanes as well as epoxies that are important among the thermosets18,19. There were already prepared samples in the laboratory and the students used those materials to determine thermochemical data. The lecturer explained that the results of the measurements by the DSC are usually presented as data plots, which directly connect this experiment to mathematics. In the lecture students are given DSC data plots to investigate. For example, the results from the second experiment was about printing technology and cross-linking kinetics for offset ink linked to a real-world situation of printing, which is interesting to students because of printed items; for example, books or news papers in everyday situations. Students got the DSC curves and their task was to determine the maximum values or peak temperatures from the DSC curves. As the Faculty of Technology scientists introduced the students the Materials Science basic techniques, in the following examples we put stress on the mathematical concepts and modeling in Materials Science. Table 1 shows the chemical concepts that can be used for learning mathematical concepts regarding the experimental study of thermally activated material synthesis and property changes. Mathematical techniques are illustrated with chemical examples taken from the experiments chosen. The first, important mathematical concepts that can be learned from the chemical experiment are functions. During the experiment in chemistry the independent variable (x) is producing a change in another dependent variable (y). Mathematically, that is presented as y = f(x) . In that form, chemical experiments can be used as a real-world context to illustrate the concept of functions. If we want students to explore a particular function, we can choose the appropriate chemistry model. For example, we

Table 1. Connection between chemical and mathematical concepts in material preparation. Chemical concept

Mathematical concept

Rate constant, Arrhenius equation

Definition of a function in general Linear, exponential and logarithmic function Growth or decline of function Function graph Plotting and fitting curves Inverse functions

Order of reaction

Derivative introduction Composition of the function Derivation, Chain rule Extremes of the function

OzawaFlynn-Wall model

Integration, definite integral

can use the Arrhenius equation to analyze the properties of exponential functions.

Ea k = A  e RT 

(1)

This equation defines the rate constant as an exponential function, where k represents the rate constant (in unit of s-1for 1st order rate constant or M-1s-1for 2nd order rate constant) A is pre-exponential (frequency) factor, Ea is activation energy [J/mol], R is gas constant (8.314 J/molK), T is temperature [K]. It can be seen that the rate constant varies exponentially with temperature and activation energy. The activation energy Ea is the minimum energy that must be input to a chemical system with potential reactants to cause a chemical reaction, and may also be defined as the minimum energy required for starting a reaction. Activation energy can be defined as the height of the energy barrier separating the minimum of the reactants and reaction product's potential energy. For a reaction to proceed at a reasonable rate there should be an appreciable number of molecules with energy equal to or greater than the activation energy. At a more



advanced level, the Ea term is best regarded as an experimentally determined parameter that indicates the sensitivity of the reaction rate to temperature. Mathematically, when the activation energy increases, the rate decreases, or as the temperature increases, the rate increases. This property can be used for observing the growth and decline of the function. If we give the rate constant for the reaction and temperature dependence, students can plot the graph and determine the activation energy. For the purpose of easier calculations, natural logarithms are used. The logarithmic function is the inverse function to the exponential, so this fact can be used to review the inverse function properties. That leads students to the equation

lnk = 

Ea 1  + lnA R T

(2)

The (Eq.2) is linear, where: y = lnk , The slope of the line is

m= 

Ea R

(3)

1

The independent variable is T , and lnA is the intersection with the y axis. This linear function is much easier to deal with and from it the activation energy can be obtained from the formula Ea = m  R . The second important concept that can be learned by observing a real-world chemistry situation is differential calculus. Transformations of matter and energy are connected with physical and chemical changes. Scientists are usually concerned with the quantitative relationship between the change and the rate of change. Changes in chemical reactions can be used for introducing students to derivatives. Combining the equations, students have to understand the concept of a composite function. Students are learning about the application of derivatives in order to determine the maximum of the function. In the calculations the chain rule can be applied. The third important

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mathematical concept is integration. Students can derive models by applying rules of integration and apply definite integrals. In the third lesson students closely examine the mathematical models used in Materials Science and broaden their knowledge to calculus and its application. By the calculus we mean differentiation and integration, which are important mathematical concepts. To illustrate these concepts with applications to real-world examples enhances the students understanding and brings to light the importance of the multidisciplinary approach. In order to introduce students to mathematical and kinetic models, students had a third lesson, which was connected with the third experiment in the section Materials Science Experiments as Educative Lessons. That experiment was examining the analysis of hybrid material preparation. In this lesson, the attention was paid to the investigation of montmorillonit dispersion in epoxy/amine systems20. Improvement of thermal stability and mechanical properties of an epoxy/amine system can be achieved by addition of organically modified montmorillonite (MMT). Depending on the nature of the organic ions intercalated in the interface, the modified MMT can catalyze a reaction or react with prepolymer or crosslinking agent. A series of epoxy/amine (epoxy based on 2,2-Bis(4glycidyloxyphenyl) propane (DGEBA) and amine (Jeffamine D-230)) samples with different montmorillonite content (0, 3, 5 and 10 wt. %) were prepared. The curing of obtained modified systems was carried out by differential scanning calorimetry (DSC), using a dynamic regime at three different heating rates: 5, 10 and 20 °C/min. Based on the obtained DSC curves (Figure 1) it can be noticed that by increasing montmorillonite content the temperature of maximum curing rate was decreased, as followed by the change of DSC curves (kinetics and mechanism of curing reaction). The calculations in this experiment are performed using isoconversional models (Ozawa-Flynn-Wall, Kissinger-Akahira-Sunose and Friedman).


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Figure 1. DSC curves of the curing at the heating rate 10 °C/min 20 As students were introduced to the DSC method previously only technically, in this lesson we wanted to analyze the DSC method through mathematics and kinetics. The lesson started with revising the fact that the difference in heat

flow of samples (DGEBA/Jeffamine D-230 with 0, 3, 5 and 10 wt. % montmorillonite content) and a reference (empty DSC pan hermetically sealed) at the same temperature is observed as a function of temperature. Students



have learned about the constant rate definition in mathematical lessons in school, so they noted dH heat flow as dt . The lecturer added the fact that it can be measured in units

J W  and gs g

asked the students to note heat flow as the difference between the sample and reference. Students have written that as

ΔdH  dH   dH  =  .   dt  dt  samle  dt  reference Graphically, it is explained with the example of DSC curve obtained in the mentioned scientific experiment in Figure 1. DSC curves of the curing at the heating rate 10 °C/min are given in Figure 1. From the presented curves (Figure 1) it can be seen that a single broad peak is obtained in all experiments. The lecturer pointed out the maximum of the DSC curves. The position of the maximum represents the biggest curing rate and depends on montmorillonite in the reaction. The temperature of the maximum in the curing curves increases with decreasing of the montmorillonite content. It can be seen from Figure 1 that the increase of montmorillonite, reaction is shifted to lower temperatures. The difference in curve shapes means that there are changes in kinetic parameters. The lecturer pointed out that the marked area would be the curing degree. As students were familiar with the integral, they came to the conclusion that there are integrals involved. They have learned in school that the definite integral of a function represents the area of the space bound by its graphs. Easily, they have concluded that the overall heat of the reaction is H =



dH  dt . dt

The lecturer revealed to students that the curing

H

degree is defined as a ratio α= ΔH and posted some problems for students. The main problem was revealing the underlying mathematics in the kinetics for curing,

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crystallization and the thermally activated reactions. Students have to use mathematical concepts mentioned in the table to derive mathematical models used in materials science experiments. The lecturer mentioned the Arrhenius equation, which some students were familiar with. What they did not know, that if they combine it with the previous fact of curing degree and composition of the function, it would lead them to the more sophisticated models. The curing reaction can be described by a rate equation, which is a rate function with the degree of curing, noted as α and Eq. 2.

dα = k  ( 1  α) n dt

(4).

The lecturer explained that the previous equation describes, for example, the disappearance of epoxy functional groups or appearance of chemical bonds, in a curing reaction, where 1-α represents the epoxy group concentration and n represents the order of the reaction21. Thus, the above Eq.1 and Eq. 3. can be combined as

E  a dα = A  e RT  ( 1  α) n dt

(5)

When it was told to the students that the curing reaction rate reaches a maximum at the temperature where the DSC curve displays the peak, one of the students explained that if we want to calculate the maximum of the function we have to find the derivative. The derivative of the curve is calculated in order to obtain the maximum of the function. Students made the following calculations:

E    a   d  A  e RT  ( 1  α) n  dα   d( )  dt =  dt dt


and

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E E      a  a   dT   dα E  A  e RT  ( 1  α) n a 2    A  e RT n( 1  α) n1  =0 RT  dt    dt       dT The lecturer added that n( 1  α) n1 is a number close to unity and dt =β represents heating rate, which is constant. Students applied that to the previous expression and obtained the following equation:

ln

β AR E a = ln − 2 E a RT T

(6)

The lecturer also added that the most commonly used equation to describe the reaction rate in the non-isothermal curing is as presented below:  d (7)  A  e RT f ( ) dT  dT  K   where β is the heating rate       , α is the curing degree, A is the pre-exponential factor, dt  s    Ea



Ea is the activation energy [J/mol], R is the universal gas constant [8.314 J/molK], t is the reaction time [s] and T is the reaction temperature [K]. The function f(α) represents the mathematical expression of the kinetic model. The isoconversional models are based on the assumption that the reaction rate at a given degree of conversion is only a function of the temperature. In this case, the conversion-dependence functions f ( ) or g ( ) are not required. From those equations several isoconversional models are derived. Those are: -

Ozava-Flynn-Wall 22:

 A  Ea  E   2.315  0.4567 a logβ = log RT  R  g α  

(8)

where: g α  is a function of degree of curing attained, or reaction in general. Students manipulated the integral and determined the following function: α

g α  =  0

E E  a  a t dα = A  e RT dt = A  e RT t f α  0

(9)

Therefore, for different heating rates at a constant degree of conversion  T  , a linear relationship is observed by plotting log  vs.

1 , and the activation energy (Ea) is obtained as slope of the T

straight line. -

Kissinger-Akahira-Sunose model based on the Coats-Redfern approximation23, which is described by Eq. 10:

 R  A  Ea      ln  2   ln  T   Ea  g    RT

(10)

1    vs. 2  T T 

Therefore, if Kissinger’s assumptions are correct, a plot of ln 


(Eq. 10) should be

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linear and the activation energy might be obtained from the slope 

lnβ

- Friedman24

Ea . R

E dα = lnA + lnf α   a dt RT

(11)

 

where: f α  = 1  α  , where n is the order of reaction. For α=const., the plot ln   n

1 d   vs. , T dT 

obtained from thermograms recorded at several heating rates should be a straight line whose slope allows the evaluation of the activation energy. At the end of the lecture it was concluded that mentioned models are called isoconversional and they are assuming that the speed of the reaction for the degree of conversion is dependent only on temperature. In this case, the conversion-dependence function ( f ( ) or g ( ) ) is not required. Based on the obtained DSC curves, it can be noticed that by increasing montmorillonite content the temperature of maximum curing rate was decreased, followed by the change of DSC curves (kinetics and mechanism of curing reaction). Based on obtained values for the kinetic parameters 20 it is determined that montmorillonite presence affects the mechanism and curing kinetics of epoxy/amine systems, as well as the structure and final properties of prepared nanocomposites.

CLASSROOM FEEDBACK After visiting the polymer laboratory at the Faculty of Technology, high school students prepared presentations with the guidance of a mathematics teacher. The presentations showed the different aspects of connection between Materials Science and mathematics. For example, a student presenter introduced peers to the DSC operation and used the DSC data analysis to explore properties of exponential function in the form of Arrhenius equation (Eq.1). This analysis was connected with the inverse logarithmic function (Eq. 2) and linear functions. The properties of linear functions were analyzed through isoconversional models. For determining functions results in the data analysis students used educational software Geogebra25. Geogebra is free educational software suitable for high school mathematics. Students use Geogebra in mathematics class on a regular basis and they accepted the challenge very well. Some of the presentations are published on the schools’ web sites and in the school paper. In the following text we will describe two students’ presentations. The first student chose to talk about a real world situation of urea-formaldehyde (UF) resins used in the wood processing industry. The UF resins present the most common thermosetting adhesives used for the production of interior wood based panels. The presenter chose the scientific experiment, which evaluates the influence of different wood species on the UF adhesive curing behavior26. This example itself was very interesting to students since the town where the school is settled is producing wood furniture. The scientific experiment incorporated the wood flour of beech, fir and poplar, representing the three industrially important wood species growing in Serbia. The experiment is described in detail in the section Materials Science Experiments as the Educational Examples as the fourth example. The student took the original data from the scientific experiment for peak temperatures (Tp, [C]) at the different heating rates (β, [C/min]) obtained with differential scanning calorimetry (DSC). The data, as was shown by the student in the presentation, for the control UF adhesive (without the addition of wood flour) and for the UF adhesive mixes with wood flour are presented in Table 2.


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Table 2. Maximum temperature of the curing reaction of the control UF adhesive sample and different UF adhesive mixes with wood extracts β, [C/min]

UF adhesive

UF+beech

UF+fir

UF+poplar

5

85.6

88.6

87.1

98.4

10

95

97.5

95.6

108.5

15

101.3

103.2

101.9

113

20

105

107.2

106.1

117.2

After introducing the temperature data, the student posed the real world problem. The problem was to compare the activation energy of the curing reaction of the "pure" UF adhesive and of the UF adhesive mixes with wood flour. In the real situation, during the hot pressing phase in the production of wood based panels, the UF adhesive is in the immediate contact with the wood particles, and hence it is mixed with the low molecular weight chemical components, being extracted from the wood material. In such conditions, the pH value of wood extracts may interfere with the curing reaction of UF adhesive. This subtle influence may prove significant on the industrial scale, and in this experiment it may be observed through the changes in the activation energy of the given UF adhesive mix with wood flour. To calculate the activation energy, students used mathematical model Eq. 6. At that point, the teacher pops in a comment that the model has a linear form. The slope is Eq. 3. Students who were listening to the lecture put in the data from the Table 2 in Geogebra and tried to find a linear model that would fit. It could be done by using Geogebra commands FitLinear or Analyze Data. Once the students got models, it was easy to calculate the activation energy. The mathematical model for calculating activation energy for UF adhesive is shown in Figure 2. The solutions for other samples are

Figure 2. The interfaces of the program Geogebra during the modeling.



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following the same path. As the presenter was familiar with the scientific results, peers’ results were accepted. They were very close to the results in the experiment. The results deviated due to rounding the numbers, using educational software instead of professional and conducting calculations in the high school classroom. The work of students is shown in Figure 2. The second student presenter chose the real world situation of examining the modification of epoxy resins by addition of thermoplastic-segmented aliphatic polyurethanes with good elastic properties. The experiment is described in detail in the section Materials Science Experiments as Educational Examples as the third experiment26. The reasons for choosing this example were various. The complex modification of epoxy resin by polyurethane addition, in order to improve their mechanical and thermal properties, could be interesting research approach for the students since epoxy resins have wide range of possible application in different industrial fields. Also, aliphatic polycarbonatebased polyurethanes are very interesting materials since they possess good biocompatibility and biostability, enhanced elastic properties and low temperature flexibility, chemical and heat resistance. They have been used in various applications, as protective coatings, industrial and building materials, for medical equipment and artificial tissues27. This experiment was significant and educational for the students to realize how it is possible to affect on the curing mechanism of epoxy resins, in order to tailor their end-use properties. After the introduction to the significance of the experiment, the student presented one integral method called Ozawa–Flynn–Wall27. The mathematical model is in the form of the Eq. 8. It is the model that he learned at the Faculty of Technology. He pointed out that the task of the scientific experiment was to compare obtained values of energy of activation of the curing reaction of modified epoxy resins with the same parameters and properties of unmodified resins. In order to tackle the problem he presented some data from the experiment to his peers. In Table 3, he presented the maximum temperatures of epoxy curing, determined from the DSC experiments. The given the example is for curing of epoxy resin modified with 15 wt. % of thermoplastic polyurethanes containing 20 wt. % of hard segments. All students noticed that the maximum temperature of epoxy curing is shifted to higher values when increasing the heating rate. Table 3. Maximum temperatures of curing of epoxy resins modified with 15wt.% of thermoplastic polyurethanes containing 20 wt.% of hard segments, applying three different heating rates during DSC experiments27 Sample code

Heating rate, β (°C/min)

Tmax (°C)

DGEBA/Jeffamine D-2000/PC-PU20

5

168

DGEBA/Jeffamine D-2000/ PC-PU20

10

177

DGEBA/Jeffamine D-2000/ PC-PU20

20

190

1

If we observe the plot of a graph where is log β vs. T we will get a straight line whose slope allows evaluation of the activation energy. The presenter derived the following expression:

slope =

E  0.4567 R

This method will allow students to determine activation energy independently. He also added that the conversion in this case is constant. Once the students got data, they entered it in the Geogebra sheets Journal of Materials Education Vol. 37 (1-2)

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and easily obtained linear models and activation energies, as in the previous example. Then students were able, from a practical point of view, to determine the complexity of polyurethane presence effect on the final properties of epoxy hybrid materials, and, in this way, to suggest their possible application as coatings with improved mechanical and thermal characteristics. The complex modification of epoxy resins by polyurethane addition, in order to improving their mechanical and thermal properties, was a very interesting research approach for the students since epoxy resins have a wide range of possible application in different industrial fields. Also, the structure of aliphatic polycarbonate-based polyurethanes consists of hard and soft segments (Figure 3). They are very interesting materials since they possess good biocompatibility and biostability, enhanced elastic properties and low temperature flexibility, chemical and heat resistance. They have been used in various applications, as protective coatings, industrial and building materials, and for medical equipment and artificial tissues28.

Figure 3. Schematic illustration of aliphatic thermoplastic polycarbonate-based polyurethanes containing soft and hard segments28 This experiment was significant and educative for the students in order to realize how it is possible to effect at the curing mechanism of epoxy resins, in order to tailor their end-use properties. The influence of different polyurethane weight content and different hard segments of elastomers on curing of modified epoxy systems was studied in the experiments. From the practical point of view, using the illustrated example, students had a possibility to determine the complexity of polyurethane presence effect on the final properties of epoxy hybrid materials, and, in this way, to suggest their possible application as coatings with improved mechanical characteristics. Students were surprised with the fact that there is so much underlying mathematics in Materials Science and Engineering. They positively accepted the new educational approach, because as they say, they were familiar with most of the mathematics. Also they were surprised that all the formulas and equations had meaning in real life. One student said that he is an average student, but after the presentation he saw that science is arising from everyday life problems. He would never think that the exponential functions and elastomeric materials have something in common. Also, he had a chance to learn more about Materials Science in general. During the presentation students were encouraged to explore functions connected with the scientific experiments. Another student said that she is very good in mathematics and chemistry, but usually in school connections are not made between the two disciplines. Visiting the Faculty of Technology and taking part in scientific experiments provided her science insight. Science is multidisciplinary and requires teamwork in her opinion. That is what makes her very happy because she would like to be a scientist and combine different knowledge that she gained during her education.



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Interactive displays and models of basic principles, properties, and phenomena of materials science are a very good teaching tool29. That is the reason why students accepted the new approach very well and showed great interest. They explored, collaborated and contributed to the promotion of materials science in high school. In the beginning it did not look like an easy task, but in the end the teachers’, scientists’ and students’ efforts provided excellent feedback and opened new possibilities in high school education.

MATERIAL SCIENCE EXPERIMENTS AS EDUCATIONAL EXAMPLES This part describes four scientific experiments related to materials science. Students were introduced to the basics of these experiments adjusted to the high school level. Data, diagrams and calculations d applied by the experimental scientist were shown to students. The link between technology and mathematics was highlighted, as well as application to real life. Experiments were chosen to raise interest about materials science among high school students. The first example The aim of the first lesson was to explain the reaction kinetics of polyurethane (PU) formation using the differential scanning calorimetry (DSC) method for the assessment of the optimal condition for production of materials17. The influence of isocyanate type on catalyzed and non-catalyzed reactions based on stoichiometric balance of NCO and OH groups was studied. Students are informed about basic principles for structuring of PU materials. PU includes materials that incorporate the carbamate group (NHCOO) as well as other functional groups, such as ester, amide, ether, and urea. In addition to the linear thermoplastic polyurethanes based on difunctional reactive components, branched or cross-linked thermoset polyurethane materials are based on reactants with higher functionality. Segmented polyurethanes have good impact strength and excellent processibility, but limited thermal stability. Permanent PU networks have higher thermal stability but sometimes lower impact strength. The better properties are obtained with isocyanates with higher functionality, or with higher functional polyols. The preparation of PU based on vegetable oils is very complex and thus for industrial production of this materials it is important to determine the optimal temperature for polymerization and finally to obtain materials with the proper mechanical properties. The use of renewable materials as polyol component has been a steeply rising trend. There are a limited number of naturally occurring vegetable oils, which contain the unreacted OH groups. The natural triglyceride of fatty acids castor oil (Figure 4) is produced directly from a plant source, other oils require chemical transformation.

Figure 4. The structure of castor oil The data of isocyanates used here and mechanical properties of obtained polyurethanes are given in Table 4. The reaction was carried out in bulk as a one-step process. Before the synthesis the castor oil was dried in the vacuum, 4 hours at 70 °C in water bath. In a three-neck glass reactor equipped with a magnetic stirrer and thermometer was placed in the castor oil. The temperature was kept at


72


Table 4. The data for used isocyanates and for the mechanical properties of obtained polyurethanes Isocyanate

Tensile NCO content NCO group reactivity strength [%] [MPa]

Elongation at break [%]

37.8

Primary NCO group is more reactive than the secondary

0.891

130

Diisocyanate 2,4-TDI

48.3

The 4-position is four times more reactive than the 2position.

0.693

100

Diisocyanate HDI

49.9

NCO groups of equal reactivity

0.485

155

Polyisocyanate HDIt (Bayhydur 3100)

17.1

Functionality 3,1

0.217

132

Diisocyanate IPDI

70 °C. The addition of isocyanate was done under rigorous stirring. The reactive mixture was cast into preheated silicon mold and cured in an oven at 110 °C during 12h. Isocyanate and polyol were mixed in glass immersed in an ice bath in order to prevent chemical reaction before DSC measurements. 2-3 mg of reaction mixture was sealed in DSC pans by hermetic press. The glass with reactive mixture was stored in a refrigerator at a temperature lower than 5 °C to prevent reaction of network formation. Stress-strain experiments were performed on a tensile testing machine (Instron 1122) at 25 °C. For each data point, five specimens were tested, and the average value was taken. The tensile strength and elongation at break were calculated as:

Fm A0 l  %   100% l0

m 

(11) (12)

where: Fm is the force measured at the break, A0 is the cross-section area (mm2), l0 is the original length of the specimen, Δl is the change of length. Thermograms for curing of reactive systems based on IPDI are given in Figure 5. Thermograms of non-catalyzed reactions with different isocyanates are given in Figure 6. The obtained data for assessed reaction rate temperature maxima are given in Table 5. The activation energy is the minimum energy that must be input to a chemical system with potential reactants to cause a chemical reaction. It is the minimum energy required to start a reaction. In our experiments the determined Ea for catalyzed reaction was in the interval from 51 to 64 kJ mol -1, and for reaction without catalyst in the interval from 35 to 60 kJ mol-1. At heating rate 20 ºC/min it was obtained that Ea for catalyzed reactive system with aromatic TDI was 44.6 kJ/mol. The smallest value was obtained for catalyzed system with polyisocyanate HDIt 39.7 kJ/mol, and the highest was for the catalyzed system based on HDI 45.3 kJ/mol. The order of reaction was in the region from 0.87 to 1.39. For non-catalyzed reactive system based on TDI the conversion degree of 90% was reached for 35 minutes at 120 ºC. For catalyzed systems the same conversion degree was reached at 50 ºC. It is obvious that the catalyst reduced the activation energy. As the activation energy can be defined as the height of the



73

energy barrier separating the minimum of the reactants and reaction products potential energy for a reaction to proceed at a reasonable rate, there should exist an appreciable number of molecules with energy equal to or greater than the activation energy.

Figure 5. DSC thermograms for catalysed and noncatalysed reactive systems based on IPDi obtained at different heating rate.


74


Figure 6. DSC thermograms for non catalysed system based on different diisocyanate and polyisocyanate Bayhydur HDIt (bay). The reaction rate temperature maxima are noticed

Table 5. The data for Ea and n determined at different heating rate for catalysed and non catalysed samples based on different isocyanates. The reaction rate temperature maxima T max was assessed at heating rate 20 °C/min Ea Ea Ea [kJ/mol] [kJ/mol] [kJ/mol]

T max (°C)

Sample

n

n

n

Heating rate (°C/min)

5

10

20

5

10

20

20

IPDI no catalyst

1.10

1.13

0.87

39.8

52.6

55.1

191.34

2,4-TDI no catalyst

0.98

1.08

0.90

40.3

41.3

51.3

166.13

HDI no catalyst

1.24

1.21

1.31

51.2

52.3

57.9

182.23

HDIt no catalyst

1.08

0.95

0.97

46.3

59.9

64.6

196.23

IPDI catalyst

0.94

0.96

1.15

30.1

38.9

44.7

104.00

2,4-TDI catalyst

1.08

0.92

1.27

31.1

34.9

44.6

88.95

HDI catalyst

0.99

1.06

0.97

38.4

41.1

45.3

60.27

HDIt catalyst

1.39

1.29

1.25

34.8

35.4

39.7

70.41



75

The second example The second lesson was to introduce the students to printing technology. The real-world situation of printing is interesting to students because of the presence of printed items; for example, books or newspapers in everyday situations. Students were involved with an experiment concerning the crosslinking of printing inks. The formation of polymer networks based on resins, from liquid monomers or oligomers, involves a complex combination of chemical and physical events, which can be followed by the DSC method. Because the ink’s viscosity is effected by temperature, printing presses must carefully regulate the temperature of the ink and control the tendency of ink to lose viscosity from friction-generated heat in the ink train. There has been a great demand for coating compositions having high curing speed. Particularly, the demand for the improvement of printing speed has been increasing along with the development of the printing technology. With the increase in the demand for higher printing speed, the serious demand for the drying speed of printing inks has been growing. From room temperature and in less than a few minutes, a liquid mixture of relatively low molar mass components is transformed into a material with a supramolecular architecture in the form of printing films. Dynamical measurements with different heating rates gave parameters for designing the real processes in order to get prints with the necessary resolution. In this experiment conditions of the DSC instrument were organized to obtain parameters of the real printing process in order to determine optimum curing temperature for three different types of commercial printing inks. The typical curing scan of printing inks is shown in Figure 7. This thermogram was characterized by the temperature of the deviation from the baseline (T1), the extrapolated onset curing temperature (Te), the exothermal peak position (Tp), the temperature of full conversion of reaction of the exothermal (T2), and the heat of curing (ΔH). The results for different types of commercial inks are summarized in Table 6. For isothermal measurements temperatures were 115 °C, 95 °C and 75 °C. From the dynamic ramp program with heating rate 10 °C/min it was assessed that the cross-linking reaction was completed when the temperature reached 120 °C (Figure 8). In this study the registrated values of T1, Te, Tp, and T2 are shifted to higher temperature. According to the Kissinger 30 and Ozawa31 Sample: V-sunchemical_crna D:...\V-sunchemical_crna28012009.001 methods, the activation of the exothermic reactions File: were obtained from registrated Size: 6.3400energies mg Operator: jelena DSC Method: Ramp

Run Date: 28-Jan-2009 10:40 Instrument: DSC Q20 V23.10 Build 79

0.00 Tp

Heat Flow (W/g)

-0.05

-0.10

Te T1

T2

-0.15

-0.20 40 Exo Up

60

80

100

120

Temperature (°C)

140

160 Universal V4.3A TA Instruments

Figure 7. DSC scan of printing ink cross-linking obtained with heating rate 10 °C/min


76


Table 6. Reported data from DSC curing thermograms for different printing inks obtained with heating rate of 10 °C/min Printing inks

T1 [°C]

Te [°C]

Tp [°C]

T2 [°C]

ΔH [J/g]

Cinkarna

155.98

161.10

164.85

172.35

5.97

Expertink black

97.70

105.90

118.05

142.54

58.61

Sunchemical

101.22

103.78

110.09

129.32

23.34

0.2

––––––– sunchemical 20C/min –––– sunchemical 15C/min ––––– · sunchemical 10C/min

0.1 118.36°C

Heat Flow (W/g)

0.0 100.16°C 110.07°C

-0.1

-0.2

-0.3

-0.4 50 Exo Up

100

150

Temperature (°C)

200 Universal V4.3A TA Instruments

Figure 8. Dynamic DSC thermograms of ink sample cross-linking obtained with different heating rates thermograms measured with different heating rates. Two relationships among activation energy (Ea), heating rates (β) and temperatures of exothermic peak (Tp), established as (Eq.12) and (Eq. 13), were utilized. The Ea of the cross-linking reactions were determined from the slopes of the plots of

  ln  2 T  p

  vs. 1 (Eq. 12) and ln   vs. 1 (Eq. 13) respectively. We used the following models:  Tp Tp      d ln  2    T p  E 1.052 E a d ln     a (1331) and (1432)  R R  1   1  d  d  T  T   p  p

The calculated activation energy of Sunchemical sample composition was 20.32 and 26.631 kJ/mol from Kissinger’s and Ozawa’s methods, respectively. The values of the activation energies from the two methods were similar, and the values from Ozawa’s method were a little larger than those from


77


Kissinger’s method. Students explored data obtained in these experiments. Also the illustrations of cross-linking reaction of coating on the substrate and film formation after cross-linking were shown to students. The third example The aim of this experiment was to study the reaction kinetics of epoxy resin materials based on 2,2Bis(4-glycidyloxyphenyl) propane DGEBA and thermoplastic polyurethanes prepared from aliphatic hexamethyelene-diisocyanate (HDI), polycarbonate diol and 1,4-Butanediol (BD) as the chain extender. In the first step the polyurethanes were synthesized in a bulk using the catalyst. The soft segment content SSC was 80, 75 and 70 mass%. In the next step the modified epoxy materials were prepared by reaction of the homogenized melt of thermoplastic polyurethane and epoxy resin using polyoxypropylenediamine (Jeffamine D-2000) as crosslinker. The weight fraction of PU in the reaction mixture was varied (5, 10 and 15 mas. %). The curing reaction was monitored at three heating rates in the temperature interval from ambient to 300 °C. Kinetic parameters of crosslinking reaction were estimated using Friedman differential kinetic procedure and two integral procedures (Kissinger–Akahira–Sunose, Ozawa–Flynn–Wall). With the decrease of soft segments content in polyurethanes added in higher concentration into epoxy matrix, the temperature of curing ratio maximum was shifted to lower values. The addition of polyurethanes retarded the curing process due to decreased mobility of reactants. It was concluded that the influence of slow diffusion is more pronounced in the presence of polyurethanes based on polycarbonateadiol. Results are shown in Table 7. The influence of different polyurethane weight content and hard segments in elastomers on curing of modified epoxy systems was studied. In order to obtain kinetic parameters of the curing reaction, DSC data were analyzed using one differential kinetic model (Friedman) and two integral methods (Ozawa–Flynn–Wall and Kissinger–Akahira–Sunose)27. Figure 9 presents the influence of Table 7. The effect of soft segments content 20, 25 and 30 mass %) in prepared PU samples on the curing of modified epoxy systems with different content of PU (5, 10 and 15 mass %) Sample code

Heating rate, β [°C/min]

SSC of PU [wt.%]

5

10

20

Enthalpy, ΔH [J/g]

DGEBA/D2000/-

80.4

105.5

103.1

PU weight content [wt. %] 5

10

15

5

10

15

5

10

15

Enthalpy, ΔH [J/g] DGEBA/D2000/PU80

80

106.8

109.8

107.1

111.6

123.1

115.3

117.8

135.1

119.4

DGEBA/D2000/PU75

75

111.2

114.6

117.8

119.1

127.0

143.2

124.5

148.0

152.7

DGEBA/D2000/PU70

70

128.7

115.8

119.3

140.4

129.1

149.9

167.7

161.4

168.3


78


Figure 9. The activation energy dependence on the conversion degree of hybrids, obtained by applying Ozawa–Flynn–Wall, Kissinger-Akahira-Sunose and Friedman isoconversional model, for system DGEBA/Jeffamine D-2000 modified with a) 0 mass % b) 5 mass % c) 10 mass % and d) 15 mass % of polyurethane with 75 % of soft segments27



79

different polyurethane content (0, 5, 10 and 15 mas. %) on the activation energy for the curing reaction of epoxy resin modified by the addition of polycarbonate-diol-based polyurethane with 75 % of soft segments (PC-PU25). The differences of activation energy were noticed in the second part of the epoxy curing characterized by significant increase of activation energies values. The students could conclude that the presence of polyurethane elastomer slowed down the curing reaction due to decreased mobility of reactant molecules, and that the effect of slow diffusion is more pronounced by addition of segmented polyurethanes, which confirmed their effect on the mechanism of epoxy curing. As an example of the influence of polyurethane addition on the mechanical properties of modified epoxy resins, tensile strength and elongation at break of epoxy samples modified with weight content of polyurethane with 75% of soft segment is shown in Table 8. On the basis of shown results and presentation, it is noticeable that increasing the weight content of polyurethane in an epoxy matrix, the tensile strength of modified epoxy was improved. The elongation at break of prepared modified epoxy samples was significantly higher in regard to unmodified epoxy resins, due to the present of flexible soft segment chains in polyurethane elastomer. Table 8. Mechanical properties of unmodified epoxy resin crosslinked with Jeffamine D-2000 and modified ones by polycarbonate diol based polyurethanes with 75. % of soft segment27 PU75 content Tensile strength, σ [MPa] [wt. %]

Elongation at break, ε [%]

DGEBA/D2000/PU75

-

0.41

36

DGEBA/D2000/PU75

5

0.43

232

DGEBA/D2000//PU75

10

0.45

229

DGEBA/D2000//PU75

15

0.56

107

The fourth example The fourth example addressed the problem of curing performances of urea-formaldehyde (UF) resin26. For that purpose, the UF adhesive mixes were prepared with the addition of wood flour of beech, fir and poplar in the quantity of 10% (by oven dry weight per UF adhesive dry matter) and with the addition of ammonium chloride as catalyst (0.2% by oven dry weight). The control UF adhesive sample for the DSC measurements included only the addition of catalyst. In order to calculate the activation energy of the UF adhesive systems, DSC scans were performed at four different heating rates (5, 10, 15 and 20 °C/min). Figure 10 presents the characteristic DSC scans of UF adhesive and UF adhesive mixes with wood flour (beech, fir and poplar) obtained at the heating rate of 10 °C/min. It could be noticed that the peak temperatures (T p) of UF adhesive mixes with wood flour were shifted to the right (i.e. higher temperature levels) suggesting that all three wood species used have interfered in the curing reaction of UF adhesive. In that aspect, the poplar has the most retarding effect. The results of the activation energy, calculated using Kissinger-AkahiraSunose kinetics models are presented in Table 9. Interestingly, the UF adhesive mix with poplar


80


Figure 10. DSC thermograms for the curing of the UF adhesive and its mixes with wood flour obtained at a heating rate of 10 °C/min in the presence of catalyst NH4Cl (0.2 %)

Table 9. Peak temperatures and activation energy for the curing reaction of UF and UF/wood flour mixes obtained by DSC measurements at different heating rates Peak temperature Tp [°C]

Function

Energy of activation Ea [kJ/mol]

Heating rate [°C/min]

5

10

15

20

-

-

UF adhesive

85.6

94.6

101.3

105.0

y = 8.83x – 14.46 R2 = 0.998

73.4

UF + beech

87.8

97.8

102.7

106.8

y = 9.28x – 15.54 R2 = 0.9978

77.2

UF + fir

87.5

97.1

103.6

107.0

y = 8.85x – 14.37 R2 = 0.9978

73.6

89.8

100.2

106.2

110.6

y = 8.54x – 13.34 R2 = 0.9997

71.0

UF poplar

+



wood flour resulted in the lowest activation energy, suggesting the beneficial effect of this wood species, and contradicting the previous results for the peak temperature (Tp) data. This might be explained by the increased porosity of the poplar wood. Density of the polar was 0.34 g/cm3 in comparison to the 0.65 g/cm3 of beech wood. Having in mind that the same amount of wood flour per unit weight was added, this means that the volume and the specific surface of the poplar wood flour were significantly higher than that of the beech wood. This may have affected the absorption processes and the phase change of the UF adhesive at the surface of wood particles, which all might have influenced the curing reaction. In that aspect, the homogeneous solution of UF adhesive when mixed with poplar wood flour could become a heterogeneous system, meaning that the UF adhesive has transformed from the continuous into dispersive phase. Presumably, the UF adhesive may disperse on many spots on the surface of wood flour. The curing reactions of each spot will progress as for the bulk UF adhesive, but they will not be able to link effectively with each other.

AN OVERVIEW This paper contributes to one of the goals of secondary education of science and mathematics. That is to prepare students for future study or professional activities in the fields of mathematics, science and technology. Students should enrich their epistemological views of models and modeling in the early stage33. We described how contemporary scientific achievements and results from materials science experiments can illustrate the application of mathematics in a real context. The mathematical concepts were illustrated through analysis of data from scientific experiments. Learners are capable of performing at higher intellectual levels when they are guided by an experienced individual and asked to work in

81

collaborative situations. While investigating scientific phenomena, students receive information not only from an experienced person, like a scientist, teacher or capable peer, but from their own performances, i.e. experientially working through the data analysis and interpretation, e.g. modeling. That raises students’ awareness about their skills deficiencies and makes them think about how to improve their knowledge. Guidance by a scientist, teacher or peer will bring additional experiences that will lead to improvements in their knowledge34. Therefore, in this paper we dealt with the teaching-learning process, which can engage students in Materials Science through the familiar context of high school mathematics. Introducing students to Materials Science at an early age can contribute to their choice of a future job in this field. This approach is excellent background for future studies in the field of technology. Students explore multidisciplinary topics, which is rarely the case in the traditional education. They learn how to approach problems, how to work collaboratively and how to share their new experiences with other students. They become acquainted with a wide range of phenomena and get a close look at the science underlying those observations. Students showed positive attitudes toward this unique educational approach, thus, our goal is to make this kind of collaboration a regular practice in order to discover future materials scientists, which will know how to work in teams, approach a problem from different perspectives and link various disciplines. This kind of learning and teaching will enhance the educational practice.

ACKNOWLEDGEMENT The authors would like to express their gratitude to the Ministry of Education, Science and Technological Development of the Republic of Serbia (Project III45022) for financial support.


82


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10. P. Galbraith, G. Stillman, J. Brown and I. Edwards, Facilitating middle secondary modelling competencies. In C. Haines, P., Galbraith, W., Blum, & S. Khan, (Eds.), Mathematical modelling: Education, engineering and economics (pp. 130-140), Horwood, Chichester, UK:(2007) 11. M. Hess, ‘Integration of materials science in the education of high school teachers in and advanced course program’, Journal of Materials Education, 33 (3-4) 141 (2011) 12. G. Kaiser and B. Schwarz, ‘Mathematical modelling as bridge between school and university’. Zentralblatt für Didaktik der Mathematik 38 196 (2006) 13. S. J. Lamon, W. A. Parker and S. K. Houston Mathematical modelling: A way of life, Horwood, Chichester (2003) 14. J. Mason, Modelling: Where is the centre of gravity of-when modelling?, in J. Matos, W. Blum, S. Houston and S. Carreira (Eds.) Modelling and mathematics Education: ICTMA 9 applications in science and technology, (39-61), Horwood, (Chichester, UK,(2001) 15. S. McKenney, N. Nieveen and J. van den Akker, “Design research from a curriculum perspective”, in J. van den Akker, K. Gravemeijer, S. McKenney & N. Nieveen (Eds.), Educational design research, Routledge, London (2006) 16. M. Potgieter, A. Harding and J. Engelbrecht, ‘Transfer of algebraic and graphical thinking between mathematics and chemistry’, Journal of Research in Science Teaching, 45(2), 197 (2008) 17. Z. Bjelovic, I. S. Ristic, J. BudinskiSimendic, M. Jovicic, J. Pavlicevic, B. Pilic and S. Cakic, ‘Investigation of formation kinetics of polyurethanes based on different types of diisocyanates and castor oil’, Hem. Ind., 66(6) 841 (2012) 18. B. Bilyeu, W. Brostow and K. P. Мenard, ‘Epoxy thermosets and their applications’ I. Chemical Structures, J. Mater. Ed., 21, 281 (1999)



19. B. Bilyeu, W. Brostow and K. P. Мenard, ‘Epoxy thermosets and their applications’ II. Thermal analysis, J. Mater. Ed., 22, 107 (2000) 20. M. Jovičić, O. Bera, J. Pavličević, V. Simendić, R. Radičević, ‘The influence of montmorillonite content on the kinetics of curing of epoxy nanocomposites’, Hem. Ind., 66 (6) 863-870 (2012) 21. B. Bilyeu, W. Brostow and K. P. Мenard, J. Mater. Ed., 23, 189 (2001) 22. T. Ozawa, J. Therm. Anal. Calorim, 2, 301-324 (1970) 23. T. Akahira, T. Sunose, Res. Rep. Chiba. Inst. Technol. 16, 22–31 (1971) 24. H.L Friedman, J. Polym. Sci. 6. 183–195 (1964) 25. M. Hohenwarter, J. Hohenwarter, Y. Kreis and Z. Lavicza, Teaching and learning calculus with free dynamic software Geogebra, 11th International Congress on Mathematical Education, Monterrey, Nuevo Leon, Mexico (2008) 26. M. Popović, J. Budinski-Simendić, J.Miljković, J. Pavličević, and I. Ristić, ‘Curing Characteristics of Low Emission Urea-Formaldehyde Adhesive in the Presence of Wood, Wood Research 56 (4) 589 (2011) 27. J. Pavličević, M. Jovičić, V. Simendić, O. Bera, R. Radičević, and M. Špírková, ‘Modification of epoxy resins with thermoplastic segmented polycarbonatebased polyurethanes’, Hemijska industrija, in press

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DOI:10.2298/HEMIND130904086P (2014) 28. A. Eceiza, M. Larranag, K. de la Caba, G. Kortaberria, C. Marieta, M. A. Corcuera, and I. Mondragon, ‘Structure–property relationships of thermoplastic polyurethane elastomers based on polycarbonate diols’, J Appl Polym Sci, 108,:3092-3103 (2008) 29. J. Pavličević, M. Špírková, O. Bera, M. Jovičić, B. Pilić, S. Baloš and J. BudinskiSimendić, ‘The influence of ZnO nanoparticles on thermal and mechanical behavior of polycarbonate-based polyurethane composites’, Composites Part B: Engineering, 60, 673-679 (2014). 30. H.E. Hagg Lobland, Strange Matter: Student impressions of a museum exhibit by the Materials Research Society, J. Mater. Ed. 27, 29-32 (2005) 31. H.E. Kissinger, Analytical Chemistry, 29, 1702-1706 (1957) 32. T. Ozawa, Thermochimica Acta, 356 173180 (2000) 33. Prins G., Teaching and Learning of Modelling in Chemistry Education. Authentic Practices as Contexts for Learning. Freudenthal Institute for Science and Mathematics Education, Utrecht University – FIsme wetenschappelijke bibliotheek, nr. 63, (2010). 34. M. I. Mustafa and L. Trudel, International Journal of Advanced Computer Science and Applications, 4(9) 124 (2013)


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materials science experiments as a tool for learning

materials science experiments as a tool for learning

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