Lamellar strength

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Table 13 is a representative Hst of nickel and cobalt-base eutectics for which mechanical properties data are available. In most eutectics the matrix phase is ductile and the reinforcement is britde or semibritde, but this is not invariably so. The strongest of the aHoys Hsted in Table 13 exhibit ultimate tensile strengths of 1300—1550 MPa. Appreciable ductiHty can be attained in many fibrous eutectics even when the fibers themselves are quite britde. However, some lamellar eutectics, notably y/y —5, reveal Htde plastic deformation prior to fracture. 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

Structured laundry liquids are currently available in Europe and were recently introduced in the United States [50,51]. These products typically contain high levels of surfactants and builder salts, as well as enzymes and other additives. In the presence of high ionic strength, the combination of certain anionic and nonionic surfactants form lamellar liquid crystals. Under the microscope (electron microscope, freeze fracturing) these appear as round droplets with an onion-like, multilayered structure. Formation of these droplets or sperulites permits the incorporation of high levels of surfactants and builders in a pourable liquid form. Stability of the dispersion is enhanced by the addition of polymers that absorb onto the droplet surface to reduce aggregation. 

Similar types of lamellar morphologies were observed for triblock copolymers of diphenylsiloxane and dimethylsiloxane having 40 wt% polydiphenylsiloxane, using electron microscopy, 47-148>. The lamellae thickness was approximately equal to the chain length of the rigid polydiphenylsiloxane blocks. These copolymers showed elastomeric properties comparable to those of conventional silica-reinforced, chemically crosslinked silicone rubbers. Tensile tests yielded an initial modulus of 0.5-1 MPa, tensile strength of 6-7 MPa and ultimate elongation between 400 and 800 %. 

In conclusion, it can be suggested that the lamellar spacing of miktoarm-star copolymers is controlled by two parameters (i) the molecular weight of the corresponding AB diblock, which also controls the segregation strength, and (ii) the functionality of the central core. 

Here scalar order parameter, has the interpretation of a normalized difference between the oil and water concentrations go is the strength of surfactant and /o is the parameter describing the stability of the microemulsion and is proportional to the chemical potential of the surfactant. The constant go is solely responsible for the creation of internal surfaces in the model. The microemulsion or the lamellar phase forms only when go is negative. The function/(<))) is the bulk free energy and describes the coexistence of the pure water phase (4> = —1), pure oil phase (4> = 1), and microemulsion (< ) = 0), provided that/o = 0 (in the mean-held approximation). One can easily calculate the correlation function (4>(r)(0)) — (4>(r) (4>(0)) in various bulk homogeneous phases. In the microemulsion this function oscillates, indicating local correlations between water-rich and oil-rich domains. In the pure water or oil phases it should decay monotonically to zero. This does occur, provided that g2 > 4 /TT/o — go- Because of the < ), —<(> (oil-water) symmetry of the model, the interface between the oil-rich and water-rich domains is given by... 

Crystalline regions of polymers can be represented as combinations of folded chains forming lamellar structures. Amorphous regions are less ordered than crystalline regions. Additional orientation of polymer chains occurs. This results in increased strength in the order of the orientation. 

KP and v can, in contrast to kp, not be determined via the concentration gradient for binary and ternary mixed micelles, because for the calculation of the Nemstian distribution a constant CMC and an almost constant partial molar volume must be assumed. The calculation of aggregation constants of simple bile salt systems based on Eq. (4) yields similar results (Fig. 8b). Assuming the formation of several concurrent complexes, a brutto stability constant can be calculated. For each application of any tenside, suitable markers have to be found. The completeness of dissolution in the micellar phase is, among other parameters, dependent on the pH value and the ionic strength of the counterions. Therefore, the displacement method should be used, which is not dependent on the chemical solubilization properties of markers. For electrophoretic MACE studies, it is advantageous for the micellar constitution (structure of micelle, type of phase micellar or lamellar) to be known for the relevant range of concentrations (surfactant, lipids). 

Fig. 13 Effect of an electric field on the lamellar distance of a block copolymer solution, (a) 2D scattering pattern of a 50 wt% solution of SI51 dissolved in THF for different electric field strengths, (b) Dependence of the lamellar distance d of parallel (filled circles) and perpendicular (open circles) aligned lamellae, with respect to the electric field lines, on the electric field strength for the same solution, (c) Proposed chain stretching effect for lamellae aligned parallel to the field lines. Adapted with permission from Nature Materials [57]. Copyright (2008) Nature Publishing Group...

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