Moduli foams

Superabsorbents. Water-sweUable polymers are used extensively in consumer articles and for industrial appUcations. Most of these polymers are cross-linked acryUc copolymers of metal salts of acryUc acid and acrylamide or other monomers such as 2-acrylamido-2-methylpropanesulfonic acid. These hydrogel forming systems can have high gel strength as measured by the shear modulus (134). Sometimes inorganic water-insoluble powder is blended with the polymer to increase gel strength (135). Patents describe processes for making cross-linked polyurethane foams which contain superabsorbent polymers (136,137). 

Composites can be created ia which the core optimizes desired physical properties such as modulus, whereas the outer layer optimizes surface coasideratioas aot inherent ia the core material. SoHd outer—foam core can provide composites with significant reductions ia specific gravity (0.7). Dry blowiag ageats can be "dusted" onto the peUets orHquid agents iajected iato the first transitioa sectioa of the extmder. 

Density and polymer composition have a large effect on compressive strength and modulus (Fig. 3). The dependence of compressive properties on cell size has been discussed (22). The cell shape or geometry has also been shown important in determining the compressive properties (22,59,60,153,154). In fact, the foam cell stmcture is controlled in some cases to optimize certain physical properties of rigid cellular polymers. 

Strengths and moduli of most polymers increase as the temperature decreases (155). This behavior of the polymer phase carried over into the properties of polymer foams and similar dependence of the compressive modulus of polyurethane foams on temperature has been shown (151). 

Tensile strength and modulus of rigid foams have been shown to vary with density in much the same manner as the compressive strength and modulus. General reviews of the tensile properties of rigid foams are available (22,59,60,131,156). 

Those stmctural variables most important to the tensile properties are polymer composition, density, and cell shape. Variation with use temperature has also been characterized (157). Flexural strength and modulus of rigid foams both increase with increasing density in the same manner as the compressive and tensile properties. More specific data on particular foams are available from manufacturers Hterature and in References 22,59,60,131 and 156. Shear strength and modulus of rigid foams depend on the polymer composition and state, density, and cell shape. The shear properties increase with increasing density and with decreasing temperature (157). 

Tensile Strength and Elongation. The tensile strength of latex mbber foam has been shown to depend on the density of the foam (149,177) and on the tensile strength of the parent mbber (177,178). At low densities the tensile modulus approximates a linear relation with density but kicreases with a higher power of density at higher densities. Similar relations hold for polyurethane and other flexible foams (156,179,180). 

Rheology. The rheology of foam is striking it simultaneously shares the hallmark rheological properties of soHds, Hquids, and gases. Like an ordinary soHd, foams have a finite shear modulus and respond elastically to a small shear stress. However, if the appHed stress is increased beyond the yield stress, the foam flows like a viscous Hquid. In addition, because they contain a large volume fraction of gas, foams are quite compressible, like gases. Thus foams defy classification as soHd, Hquid, or vapor, and their mechanical response to external forces can be very complex. 

Fig. 4. Schematic representation of a two-dimensional model to account for the shear modulus of a foam. The foam stmcture is modeled as a coUection of thin films the Plateau borders and any other fluid between the bubbles is ignored. Furthermore, aH the bubbles are taken to be uniform in size and shape.

Although aH these models provide a description of the rheological behavior of very dry foams, they do not adequately describe the behavior of foams that have more fluid in them. The shear modulus of wet foams must ultimately go to zero as the volume fraction of the bubbles decreases. The foam only attains a solid-like behavior when the bubbles are packed at a sufficiently large volume fraction that they begin to deform. In fact, it is the additional energy of the bubbles caused by their deformation that must lead to the development of a shear modulus. However, exactly how this modulus develops, and its dependence on the volume fraction of gas, is not fuHy understood. 

Industrially, polyurethane flexible foam manufacturers combine a version of the carbamate-forming reaction and the amine—isocyanate reaction to provide both density reduction and elastic modulus increases. The overall scheme involves the reaction of one mole of water with one mole of isocyanate to produce a carbamic acid intermediate. The carbamic acid intermediate spontaneously loses carbon dioxide to yield a primary amine which reacts with a second mole of isocyanate to yield a substituted urea. 

Another difference between hot and cold elastomeric SBR latices is that hot types are carried to < 90% conversion and not normally shortstopped. The cold latices are usually shortstopped at ca 60—80% conversion. Again the desired physical properties of the contained copolymer are responsible for these differences. Cold latices are used in applications where the modulus, eg, in foam, or retention of physical properties at high filler loadings, eg, in fabric backing, are required. The cold latices are generally suppHed at a higher soHds concentration than the hot series because of these uses. 

In the manufacture of highly resident flexible foams and thermoset RIM elastomers, graft or polymer polyols are used. Graft polyols are dispersions of free-radical-polymerized mixtures of acrylonitrile and styrene partially grafted to a polyol. Polymer polyols are available from BASF, Dow, and Union Carbide. In situ polyaddition reaction of isocyanates with amines in a polyol substrate produces PHD (polyhamstoff dispersion) polyols, which are marketed by Bayer (21). In addition, blending of polyether polyols with diethanolamine, followed by reaction with TDI, also affords a urethane/urea dispersion. The polymer or PHD-type polyols increase the load bearing properties and stiffness of flexible foams. Interreactive dispersion polyols are also used in RIM appHcations where elastomers of high modulus, low thermal coefficient of expansion, and improved paintabiUty are needed. 

Ultem PEI resins are amber and amorphous, with heat-distortion temperatures similar to polyethersulfone resins. Ultem resins exhibit high modulus and ate stiff yet ductile. Light transmission is low. In spite of the high use temperature, they are processible by injection mol ding, stmctural foam mol ding, or extmsion techniques at moderate pressures between 340 and 425°C. They are inherently flame retardant and generate Httie smoke dimensional stabiUties are excellent. Large flat parts such as circuit boards or hard disks for computers can be injection-molded to maintain critical dimensions. 

Now for some real numbers. Table 3.1 is a ranked list of Young s modulus of materials - we will use it later in solving problems and in selecting materials for particular applications. Diamond is at the top, with a modulus of lOOOGPa soft rubbers and foamed polymers are at the bottom with moduli as low as 0.001 GPa. You can, of course, make special materials with lower moduli - jelly, for instance, has a modulus of about 10 GPa. Practical engineering materials lie in the range 10 to 10 GPa - a... 

At small strains the cell walls at first bend, like little beams of modulus E, built in at both ends. Figure 25.10 shows how a hexagonal array of cells is distorted by this bending. The deflection can be calculated from simple beam theory. From this we obtain the stiffness of a unit cell, and thus the modulus E of the foam, in terms of the length I and thickness t of the cell walls. But these are directly related to the relative density p/ps= t/lY for open-cell foams, the commonest kind. Using this gives the foam modulus as... 

Real foams are well described by this formula. Note that foaming offers a vast range of modulus p/Ps can be varied from 0.5 to 0.005, a factor of 10, by processing, allowing E to be varied over a factor of 10 . ... 

Fig. 26.4. Young s modulus for wood depends mainly on the relative density p/p,. That along the groin varies os p/p, that across the groin varies roughly os like polymer foams.

The transverse modulus is lower partly because the cell wall is less stiff in this direction, but partly because the foam structure is intrinsically anisotropic because of the cell shape. When wood is loaded across the grain, the cell walls bend (Fig. 26.5b,c). It behaves like a foam (Chapter 25) for which... 

Today polyether foam with a density of less than half that of rubber latex foam is widely used as a cushioning material. Polyester foams, although tending to be more expensive, continue to have a number of outlets, particularly where a high initial modulus is desirable. In addition to miscellaneous upholstery applications... 

Throne has reported that the relationship between foam modulus and density can be generalised to other properties such as tensile strength, fatigue strength, creep properties as well as shear and compression modulus. Thus if X is the general material property then... 

A sheet of chopped strand mat-reinforced polyester is 5 mm thick and 10 mm wide. If its modulus is 8 GN/m calculate its flexural stiffness when subjected to a point load of 200 N midway along a simply supported span of 300 mm. Compare this with the stiffness of a composite beam made up of two 2.5 mm thick layers of this reinforced material separated by a 10 mm thick core of foamed plastic with a modulus of 40 MN/m. ... 

Flexural modulus is the force required to deform a material in the elastic bending region. It is essentially a way to characterize stiffness. Urethane elastomers and rigid foams are usually tested in flexural mode via three-point bending and tite flexural (or flex ) modulus is obtained from the initial, linear portion of the resultant stress-strain curve. 

Comprehensive evaluation of the results shows that the adsorption and desorption of alkanesulfonates, and other surfactants too, is diffusion-controlled. The dilatation modulus increases with increasing number of carbons because of the enhanced intermolecular interaction. This information is particularly significant in, for instance, foams. 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

The responses chosen all relate to important foam properties. We believed that yi, the emulsion droplet size, determines y2, the cell size in the resultant foam, and we wished to determine whether this is true over this range of formulations. The foam pore size ys should determine the wetting rate y7, so these responses could be correlated, and yg, the BET surface area, should be related to these as well. The density y and density uniformity ys are critical to target performance as described above, and ys, the compressive modulus, is an important measure of the mechanical properties of the foam. 

Temperature dependence of the elastic modulus of the rigid urethane foam. 

We prepare force versus compression plots in a similar fashion to force versus elongation plots. We generally perform compressive testing over a much more limited range of strain than tensile testing. Samples typically take the form of thick pads, which do not break in the same manner as tensile specimens. The limit of compressive strain can approach 100% for low density foams, but is much less for other samples. The most common property that we obtain from this mode of testing is compressive modulus. 

Define compressive modulus. Why is this property commonly performed on materials such as foams and rubbers ... 

The complex interfacial dilational modulus ( ) is a key fundamental property governing foam and emulsion stability. It is defined as the interfacial tension increment (da) per unit fractional interfacial area change (dA/A) i.e.,... 

Figure 9.28 shows the relation of the relative modulus (Ktf Kp) to the relative density (Pf/Pp) of neat PLA and PLA-based nanocomposite foams, taken in the directions parallel (A) and perpendicular (B) to the flow. 

To clarify whether the modulus enhancement of the nanocomposite foams was reasonable, Equation (9.7) proposed earlier by Kumar [66] was applied to estimate the relative moduli with various foam densities ... 

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