1-3-1 Thermogravimetric analysis, TGA[13]
Thermogravimetric analysis (TGA) was the study of weight changes of a specimen as a function of temperature. The technique is useful strictly for transformations involving the absorption or evolution of gases from a specimen consisting of a condensed phase. Typical TG specimen powder or liquid was placed on a refractory pan, often porcelain or
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platinum. The pan, in the hot zone of the furnace, is suspened from a high precision balance. A thermocouple is in close proximity to the specimen but not to interface with the free float of the balance. The balance was electronically compensated so that the specimen pan does not move when the specimen gain or loss weight.
If reactive gases are passed through the specimen chamber or gases are released by the specimen, the chamber containing the balance is often maintained at a slightly more positive pressure via compressed air or inert gas; this is in order to protect the balance chamber and its associated electronic components from exposure to corrosive gases.
Sometime were shown the figure is the numerical derivative TG trace (DTG), which is a smoothed plot of the instantaneous slope of the specimen mass with respect to time. DTG does not contain any new information, however it clearly identifies the temperature at which mass loss is at maximum “the DTG peak”. Superimposed transformations, which are seen only as subtle slope changes in a TG trace appear more clearly shown as DTG peaks. Comparison of DTG data with DTA data of the same material shows striking similarity for those transformations with an associated weight change. Thus, combining DTA and DTG traces is useful for differentiating the types of transformations depicted by the DTA trace.
Thermogravimetric analysis that provide for a spell of constant temperature of a specimen once the non-steady heating is over give the most correct results. They are used to determine key physical and chemical properties of individual substances. The percentage difference was calculated as:
- 9 - The results of thermogravimetric analysis cast doubts over the validity of a number of experimental investigations in which the reference temperature for the data obtained was that of the furnace space rather than the specimen temperature. Note than an intensification of heating did not lead to a proportional increase in the temperature of specimens Tsp which leveled out at an ultimate value peculiar to every substance.
Dynamic thermal analysis of thermal decomposition was investigated by thermogravimetric analysis. Depending on the importance and goals of investigation, one may call upon various types of heaters:
convective heaters, lasers, plasma gun and a whole range of burners and furnaces. The derivatographs manufactured produce TG and DTG curves, which make it possible to determine the thermal effects of decomposition, complete with the decomposition rate records ω& =ω(t).
The most common approach to describing the kinetics of isothermal decomposition is to consider it as a homogeneous one-stage chemical reaction: substance; k is reaction rate constant at a given temperature; w=M/M0. By integrating blow equation one can obtain an analytical expression describing the kinetic curves of decomposition. At n = 1:
) ( 0exp−kt
=ω
ω (1.4) The constant of integration, w0, is determined by the initial condition,
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0
0 ω
ωt= = . It is not much more difficult to obtain solutions at n≠1.
One-stage chemical reaction between gases and solutions sometimes follow fairly well the empirical Arrhenius equation in relatively narrow ranges of temperature: Where, k0 is pre-exponential factor; E is activation energy.
The equation includes the Boltzmann constant e−E/RT which has a physical meaning in rate calculations for gas-phase reactions, according to the theonection that a more elaborate temperature dependence of the rate of chemical reactions was derived from this theory [14]:
) the number of particles produced when an activated complex is being formed which has great bearing on polymer systems.
The physical irrelevance of apparent characteristics is evident in activation energy changing with temperature and depending on the extent of conversion, pre-exponential factor is, in turn, often time-dependent and differeing from its theoretical value of 1012 s-1.
The theory of absolute rates of chemical reactions forms the groundwork of blow equation within the strict framework of rigorous limitations the most important of which are:
1. the reaction should be homogenous and occur in a gas medium;
2. the starting compound should be in equilibrium with its activated complex;
3. temperature and all other parameters are constant;
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4. the reaction does not alter the Maxwell-Boltzmann equilibrium distribution;
Non-isothermal decomposition of solid substances fails to meet these requirements to a lesser or greater extent. It is a heterogeneous process developing at phase boundaries. This equilibrium between an initial substance and its activated complex is broken by the loss of vibration stability of oscillators in three-dimensional and liner crystals.
Kinetic equations of heterogenous decomposition of solids were shown at Table 1-2. The equations cited may describe intricate kinetic curves more than exponential equations, yet they fall short of taking into account certain factors of nonisothermal heating such as homogeneous nucleation.
The thermodynamic feasibility of such nucleation is well established and experimentally verified for metastable liquids[15].
Responding to the practical need to have simple analytical relationships for TG curves, many researchers are determined to apply equations derived for isothermal conditions to the kinetics of decomposition during monotonic heating. The KEKAM equation, which incorporated the Arrhenius law, will then become:
] At constant heating rate:
) To describe the non-isothermal kinetics of decomposition of condensed substances, many also adopt the One-stage chemical reaction equation:
- 12 - The TG curves of linear polymers while quantitatively different from calculated curves are qualitatively the same at low heating rates. More complex substances such as coals and thermosets do not evince even a qualitative agreement with calculated plots at high heating rates.
1-3-2 Differential thermal analysis, DTA[13]
Differential Thermal Analysis DTA, can provide the some material information during thermal processing. The temperatures of transformations as well as the thermodynamics and kinetics of a process may be determined using DTA. The DTA information of material were glass transition, crystallization temperature, melting temperature, and any reaction about exothermic and endothermic during thermal processing.
The Differential Thermal Analysis (DTA), measures the difference in temperature between a sample and reference which are exposed to the same heating schedule via symmetric placement with respect to the furnace. The reference material is any substance, with about the same thermal mass as the sample, which undergoes no transformations in the temperature range of interest. The temperature difference between sample and reference is measured by the differential thermocouple in which one junction is in contact with the underside of the reference crucible. The sample temperature is measured via the voltage across the appropriate screw terminals and similarly for the reference temperature; generally only one or the other is recorded.
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The material sample undergoes a transformation, the single will either absorb, means endothermic, or release, means exothermic, heat.
Usually the melting of solid material will absorb heat, where that thermal energy is used to promote the phase transformation. The DTA will detect that the sample is cooler than the reference, and will indicate the transformation as the endothermic on the plot of differential temperature (∆T) versus time.
In order to analyze the differential heating curve, it is convenient to write down a formal expression for the rate at which heat is transferred into and out of the sample or reference cell.
) Here dq/dt is the rate at which heat is received by the reference material and sample material, respectively. Kr and Ks are heat transfer coefficients between the materials and the furnace wall. They are made as nearly identical as possible by choice of reference material and design of cell and furnace. Sigma is the heat transfer coefficient between the cells, and alpha is the heat loss to the outside environment. Tw, Tr, Ts and T0 are the temperature of the furnace wall, reference and sample materials, and external environment, respectively.
Next use can be made of the identity dt For the sample it is convenient to segregate the portion of the increased heat content arising from phase change, writing
- 14 - Here Cs is the heat capacity of the cell plus its contents, while ∆H is the heat of the transformation and df/dt is its time rate of occurrence under the conditions of the experiment, f being the fraction of the sample transformed at any time t.
For reaction kinetics in DTA, the temperature distribution in the differential thermal analysis specimen holders obeys the general heat flow equation. Where T is the temperature, t the time, k the thermal conductivity, σ the density, c the specific heat, and dq/dt the rate of heat generation due to a chemical reaction per unit volume of sample. No heat effects occur in the reference sample, so the temperature distribution in the reference is given by: The differential temperature is the difference in temperature of the centers of the two samples. The differential temperature, θ, is then given by This equation it is seen that when d2q/dt2, the derivative of the rate of heat absorption, is zero, dθ/dt is also zero. Since the rate of heat absorption is proportional to the rate of reaction, the equation states that the peak differential deflection occurs when the reaction rate is a maximum. So the results of the differential thermal study agree with
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results obtained isothermally except in some specific cases.
1-3-3 Stress and Strain Rheometers[16]
Rheology is the science of deformation and flow. It is a branch of physic since the most important variables come from the field of mechances: forces, deflections and velocities. All forms of shear behavior, which can be described rheologically in a scientific way, can be viewed as lying in between two extremes: the flow of idealviscous liquids on one hand and the deformation of idealelastic solids on the other. The behavior of all real materials is based on the combination of both the viscous and the elastic portion and therefore, it is called viselastic.
Rheometry is the measuring technology used to determine rheological data. The emphasis here is on measuring system, instruments and analysis methods. Both liquids and solids can be investigated using rotational and oscillatory rheometers. Viscosity curves are usually plotted with γ& on the x-axis and η on the y-axis. When measuring at shear rates γ& < 1 1/s, it is important to ensure that the measuring point duration is long enough. This is especially true for high-viscosity samples which are tested at very low shear rates. Otherwise start effects or time-dependent transition effects are obtained, this means the transient viscosity instead of the desired steady-state viscosity is measured. When γ& >1 1/s, transient effects only influence samples with pronounced viscoelastic properties. Therefore, for liquids with low or medium viscosities the duration of t=5 s is sufficient in most cases for each measuring point.
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However, transient effects should always be expected for polymers at shear rates γ& < 1 1/s.
Rotational tests are performed to characterize viscous behavior and evaluated viscoeleastic behavior, creep tests, relaxation tests and oscillatory tests are performed. In all fluids, there are frictional forces between the molecules and, therefore, they display a certain flow resistance which can be measured as viscosity. The dynamic viscosity is sometimes used for η. However, many rheologists also use this term to describe either the complex viscosity measured in oscillatory tests or the real part of the complex viscosity. The inverse value of viscosity is referred to as fluidity ψ and following as:
η
ϕ[1/pas]=1/ (1.17) For rotational tests, the different types of flow behavior were presented and their rheological background was explained using, for example, Newton’s law or other viscosity functions which depend on the structure of the sample. A normal test for shear rate tests, the speed or shear rate is set and controlled. This tests method with controlled shear rate is usually selected when specific flow velocities of technical processes have to be simulated. The viscosity curves are usually poltted with γ& on the x-axis and η on the y-axis.
To know the structure decomposition and regeneration were measured by thixotropy and rheopexy which are shear rate step function test. For measurements like this, three test intervals are preset:
1. Rest phase under low-shear conditions during the time period between
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t0 and t1. The aim is to achieve a fairly constant η value for the whole first interval, since it is then used as the reference value for the third interval;
2. Load phase under high-shear condition during the time period between t1 and t2 in order to decompose the structure of the sample;
3. Phase after removing the load under low-shear conditions during the time period between t2 and t3, under the same shear conditions as in the first interval to facilitate regeneration of the structure.
The extent of thixotropy is given as the change in viscosity Δη, which is calculated as the difference between the maximum viscosity.
Here, ηmin is taken at the time point t2 and ηmax at the point t3. The formula were Δη=ηmax−ηmin. And the total thixotropy time is the time difference between the end of the structural decomposition phase and the time point at which the maximum value ηmax is reached after structural regeneration. The total thixotropy time were analyzed as the period of time required for the structure to reach the state of complete regeneration in the third test interval. The testing and analysis method that flow curve with hysteresis area for determining thixotropic and rheopectic behavior were now outdated, although it is still used for QC tests in some industrial laboratories. The hysteresis area was determined by taking the difference between the following two areas: the area between the upward curve and the γ axis, and the area between the downward curve and the γ& axis.
Sample with positive area value were referred to as thixotropic and those with negative values as rheopectic.
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For viscoelastic behavior, a viscoelastic material shows viscous and elastic behavior simultaneously. For viscous portion behaves accorded to Newton’s law, and elastic portion behaves accorded to Hooke’s law. The behavior of viscoelastic liquid can be illustrated using the combination of a spring and a dashpot in serial connection. Both components can be deflected independently of each other. The extent of the reformation represents the elastic portion, and the extent of permanently remaining deformation corresponds to the viscous portion. So the deformation process is irreversible, as the sample has changed its form at the end of the process because its reformation is not complete. Therefore, the material behaves essentially as a liquid and is referred to as a viscoelastic or Maxwell liquid due to the above-mentioned properties.
For an elastic deformation you apply the Hook’s law to rheology:
Shear Stress A
= F
τ , and the deformation τ =G*γ . The reasons of viscoelasticity were entanglement in polymers and structure or network of an emulsion. Always used the oscillation test to give the extension of the measuring range, non destructive methode, and analyses data of the material structure and monitoring of time or temperature-depending changes. The oscillation were used the change of direction for input shear stress τ then give the elastic reaction for deformation γ and 00 phase shift for elastic response or 900 viscous response. Separation in elastic and viscous components was: So to define the complex mouulus:
- 19 - The oscillatory test included some methods as simple oscillation, time curve for ageing, curing and gelation, and sweep experiment for frequency, amplitude and temperature, and preshear oscillation for structure recovery, and multiwave for monitoring material changes. The stress sweep test was determination of the linear-visco-elastic range for material stability and yield point. The G’ and G” are independent from stress or deformation. All stress sweeps can be presented either as function of stress or strain. For material stability, the critical stress from the stress sweep is used as characteristic value. The frequency sweep was investigated materials response to impact or gradual load and usually applied at material condition, impact resistance, damping properties and mouth feeling. The frequency sweep was obtained the material characterization of gel, paste and liquid material structure. Usually the behaviors were obtained the viscous at low frequency and elastic at high frequency.
Moreover, the time temperature sweeps were observed of change of material properties due to different initiators for material aging, gelation, fusion, curing, crosslinking and degradation. The multiple creep tests were see the slope value deviating from zero and applied for leveling, sagging and stability. Modeling test was described the material functions
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as mathematical equation. Relaxation test was known the non linear equations incorporate coefficients, which are known as relaxation times.
- 21 - Reference
1. D. Lochun, E. Zeira and R. Menize., Electronic Components and Technology Conference., (2002).
2. S. Molesa, D. R. Redinger, D. C. Huang, and V. Subramanian., Mat.
Res. Soc. Symp. Proc., 769, (2003).
3. J. Kabachinski., Biomedical Instrumentation and Technology., March/April, (2005).
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Ying-Chang Hung “Thermal-decomposition and crystallization behaviour of coupling agents for silver paste application”
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Component. Package. Manuf. Tech. B., 19(2) (1996).
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16. H. P. Le., J. Image. Sci. Tech., 42(1) (1998).
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Table 1-1. Metal electrical conductivity and thermal conductivity properties
Electrical conductivity
(μΩ∙cm)
Thermal conductivity
(W/mK)
Electrical conductivity
(μΩ∙cm)
Thermal conductivity
(W/mK)
Ag 1.59 427.0 Fe 9.71 25.1
Cu 1.67 398.0 Pt 10.6 71.4
Au 2.35 315.0 Pd 10.8 75.5
Al 2.66 237.0 Sn 11.0 66.6
Zn 5.92 121.0 Cr 12.9 90.3
Ni 6.84 90.5 Pb 20.6 35.2
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Table 1-2. Kinetic equations of heterogenous decomposition of solids
Basic Factors Function
Two-dimensional motion of an interface Three-dimensional motion of an interface Linear diffusion
Three-dimensional diffusion Prout-Tompkins’ mechanism Avrami-Erofeev’s mechanism
Ultimate decomposition temperature Tu1
2
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Figure 1-1. A typical RFID System.
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Figure 1-2. The diagram of Parelec Inc innovative 2-step low curing and roll-to-roll printing metal ink process [6].,
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