Expansion behavior

One of the biggest challenges in this industry is the wide variety of substrates that can be encountered for any given application. Not only can the materials be substantially different in their chemical make up, but they may also be quite different in surface roughness, surface curvature and thermal expansion behavior. To help adhesion to these substrates, preparation of the surface to be bonded may be critical. This preparation may be as simple as a cleaning step, but may also include chemical priming and sanding of the surface. 

Mori M and Hiei Y. Thermal expansion behavior or titanium-doped La(Sr)Cr03 solid oxide fuel cell interconnects. J. Am. Ceram. Soc. 2001 84 2573-2578. 

Tests of a graphite-reinforced polyimide composite (C6000/PMR15) did not show any effect of radiation exposure (1 MEV electrons 6x109 rad total dose) on the thermal expansion behavior (14). DMA curves for unirradiated and irradiated composites were essentially identical over the temperature range of the thermal expansion measurements. 

To assess the effect of elastomer degradation on composite performance, additional composites were fabricated with the same 121°C cure epoxy without any addition of the elastomer (211. The expansion behavior of the modified epoxy composite was similar to the toughened material. For electron doses less than 10 rads the CTE of the toughened and untoughened composites were essentially the same which suggests that the epoxy matrix and not the elastomeric component controls the thermal expansion behavior. 

Tschatifeser, P. and Parker, S.C. (1995) Thermal expansion behavior of zeolites and AIPO4S. J. Phys. Chem., 99, 10609-10615. 

Because of the structural variety possible with polyimides, many smdies have sought to understand their structure-property relationships, often focusing on one specific target property. Such studies have included those aimed at understanding thermal expansion behavior, optical properties electronic structure, dielectric constant and loss, PTIR analysis, adhesion, water absorption, and molecular ordering, as well as others. The references cited... 

The CTE of 6FDA/TFDB is a little higher than that of PMDA/ODA. The former has a high CTE because the main chains contain bent hexafluoroisopro-pylidene units. We discuss the thermal expansion behavior of GFDA/TFDB in the next section, comparing it with the low-thermal-expansion fluorinated polytmide PMDA/TFDB. In addition, the refractive index of GFDA/TFDB, 1.556 at... 

We have attempted to review briefly the volume expansion work and to introduce our most recent experimental findings. Needless to say we have not arrived at a theoretical model to explain the anomalous volume expansion behavior. It has been our objective to stimulate and whet the experimental and theoretical appetites of others to pursue a logical deduction and interpretation of these findings. 

A thermally induced residual stress. The origin of the residual stresses is a mismatch of thermal expansion behaviors among the components. Rigid connection of each component with different thermal expansion coefficients causes residual stresses. For example, the electrolyte and electrodes are fabricated and connected at a high temperature. If the thermal expansion behaviors are not identical among the components, residual stresses will occur in the cell at room temperature. For stacks, similar residual stresses will occur by a mismatch of thermal expansion behavior among cells and other stack components. 

Typical materials for the electrolyte are YSZ, samaria doped ceria (SDC), and LaGaC>3. The intrinsic property of the thermal expansion behavior of an electrolyte depends only on the material species. However, the other mechanical properties (Young s modulus, Poisson s ratio, and strength) depend on the morphology through the manufacturing processes. Accordingly, the reported mechanical properties are not unique. The reported thermal expansion coefficient (TEC) and other mechanical properties for the electrolyte materials are listed in Table 10.1. 

The origin of chemically induced stresses is a change of the lattice distance of materials due to changes in the physical state. For example, it is known that the lattice constant of LaCrCL increases under a reducing atmosphere [3], On the basis of the analogy between the thermal expansion and chemical expansion, the chemical expansion behavior can be simulated along with the thermal expansion behavior. 

Thus Equation (10.33) is solved as the new equilibrium equation. To calculate the thermal expansion behavior of the model, the thermal expansion coefficient is necessary as the calculating parameter. If the temperature of the model is even, the initial temperature and the final temperature are used as just a calculating parameter. If a temperature distribution exists in the model, the temperature distribution data is dispensable for the stress calculation. The temperature is firstly calculated by a CFD and the calculated data is used as the boundary condition in the stress calculation. If the thermal expansion coefficient is temperature dependent, the temperature dependence must be considered in the calculation. Here the temperature data at the nodes is transferred from STAR-CD to the ABAQUS. 

In addition to the occurrence of the residual stress, cells warp toward the cathode side because of the mismatch of the thermal expansion behavior between the electrolyte and anode. Thus, the deformations of cells at room temperature are also... 

A numerical model to simulate the lattice expansion behavior of the doped lanthanum chromites under a cell operating condition has been proposed, and the deformation of the lanthanum chromite interconnectors has been calculated [33], In the model, the sample deformation is calculated from the profile of the oxygen vacancy concentration in the interconnector. Under a practical cell operation, the oxygen vacancy concentration in the interconnector distributes unevenly from the air side to the fuel side. The distribution of the oxygen vacancy concentration in the interconnector depends on both the temperature distribution in the interconnector and the profile of the oxygen partial pressure at the interconnector surface. Here, a numerical model calculation for the expansion behavior of the LaCrC>3 interconnector under a practical cell operation is carried out, and the uneven distribution of... 

Yakabe, H., Hishinuma, M. and Yasuda, I., Static and transient model analysis on expansion behavior of LaCiO under an oxygen potential gradient, Journal of The Electrochemical Society 147, 2000, 4071. 

At a foaming time of 30 s, the differences in expansion behavior become more evident. The increase in SBM content leads to an increasing foam density for all foaming temperatures. Besides the previously mentioned reduction of the glass transition temperature of the more viscous PPE phase by the selective blending with PS, subsequently reducing the stabilization effect, the fine blend structure is responsible... 

The expansion behavior of carboxylic latex particles can be studied by several methods (10). The present comparison was made using a sedimentation method which involved the measurement of particle sedimentation rates in an ultracentrifuge at various degrees of neutralization. Assuming the change in particle volume is equal to the volume of water absorbed, an expanded particle settles slower, as its density decreases, according to the equation ... 

Figure 13. The effect of nonuniform polymerization on the expansion behavior of carboxylic emulsion polymers. The power feed example was prepared using the monomer feed profile illustrated in Figure 12 ((%) uniform feed power feed).

If this hypothesis is right, the specific volumes that characterize the RAF and MAF have to be essentially different below the crystallization temperature. Figure 17 exhibits a sketch to illustrate this point. This sketch basically shows a hypothetical thermal-expansion behavior associated with the RAF and MAF for PET, crystallized at some arbitrary crystallization temperature, Tc. Above Tc, in the equilibrium melt, only one phase occurs, i.e. the specific volumes for the RAF and MAF are the same. If vitrification of the RAF occurs at Tc, the slope of specific volume versus temperature for this fraction should change at Tc, and become characteristic of the glassy state in the temperature interval below Tc. In the same manner for the MAF, the slope of specific volume versus temperature, below Tc, should continue to be the same as for the equilibrium melt and change only at the real Tg. Therefore, if room temperature (25 °C) is considered as the reference, the specific volume for the RAF at 25 °C must be larger than that for the MAF. The same reasoning would lead to the anticipation that the specific volume of the RAF will be a direct function of Tc. 

Expansion in each dimension is the same. This would only be true for isotropic materials, that is, those with a cubic crystal structure, or glass. Polycrystalline materials with non-isotropic crystalline grains would also generally demonstrate a direction independent expansion behavior, due to the averaging effect of the random orientation of their grains. 

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