Polymers, glassy

We note that in both of these PP and PC cases the potential-energy functions used for the model were based on experimentally determined densities at 233 K for 

Modulus (GPa) Energy technique Force technique Experimental 

PP and 293 K for PC. Thus, they had already incorporated the appropriate anharmonic temperature dependence of these polymers. 

Semi-crystalline polymers such as polyethylene, polypropylene, and polyamide (Nylon-6), obtained by solidification from the melt, as discussed in Section 2.6.5 are nano-composites made up of chain-folded highly anisotropic crystalline 

Subscripts a, b, c denote parallel axes to the a, b, c orthorhombic crystal axes. 

Since the molecular crazing criteria require a substantial amount of detailed information about the molecular structure of the solid polymer and no clear correlation to the macroscopic phenomena observed experimentally exists, phenomenological criteria analogous to those for shear yielding were proposed. The 

Shear yielding in the form of a quasi-homogeneous,bulk process can contribute substantially to the crack resistance of a polymeric solid. On the other hand, however, localized shear yielding in the form of shear micro-bands is befleved to be a precursor of brittle fracture in many semicrystalline and glassy thermoplas- 

Strain rate, test temperature and the thermal history of the specimen all affect the appearance of shear bands in a particular glassy polymer [119]. The differences in morphology of shear bands was proposed to be due to different rates of strain softening and the rate sensitivity of the yield stress. Microshear bands tend to develop in polymers with a small deformation rate sensitivity of Oy and when relatively large inhomogeneities exist in the specimen before loading. This is sometimes characterized by a factor e j, introduced by Bowden in the form [119]  

The parameter has a value of 0.11 for PMMA at room temperature and 0.2 for PS at 80 °C. In both cases, diffuse shear bands develop. Reducing the test temperature to about 70 °C, Osj, for PS decreased to about 0.016 and sharp, well defined shear bands were developed. 

Interestingly, the contribution of diffuse shear bands to the total deformation of the specimen is large, despite relatively low deformation existing in them. On the other hand, large plastic deformation in microshear bands does not contribute so substantially to the total deformation of the specimen. It appears that a small deformation over a large volume has a much larger effect on crack resistance than a large deformation within a small volume. 

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Mangipudi V S ef a/1996 Measurement of interfacial adhesion between glassy polymers using the JKR method Macromoi. Symp. 102 131-43... 

In glassy polymers tire interactions of tire penetrant molecules witli tire polymer matrix differ from one sorjDtion site to anotlier. A limiting description of tire interaction distribution is known under tire name of tire dual-soriDtion model [, 60]. In tliis model, tire concentration of tire penetrant molecules consists of two parts. One obeys Henry s law and tire otlier a Langmuir isotlienn ... 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

Kotelyanskii M, Wagner N J and Paulaitis M E 1996 Building large amorphous polymer struotures atomistio simulation of glassy polymers Macromolecules 29 8497- 506... 

Interfacial polymerization membranes are less appHcable to gas separation because of the water swollen hydrogel that fills the pores of the support membrane. In reverse osmosis, this layer is highly water swollen and offers Httle resistance to water flow, but when the membrane is dried and used in gas separations the gel becomes a rigid glass with very low gas permeabiUty. This glassy polymer fills the membrane pores and, as a result, defect-free interfacial composite membranes usually have low gas fluxes, although their selectivities can be good. 

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

Table 10 contains some selected permeabiUty data including diffusion and solubiUty coefficients for flavors in polymers used in food packaging. Generally, vinyUdene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation whereas the polyolefins are poor barriers. Comparison to Table 5 shows that the large molecule diffusion coefficients are 1000 or more times lower than the small molecule coefficients. The solubiUty coefficients are as much as one million times higher. Equation 7 shows how to estimate the time to reach steady-state permeation t if the diffusion coefficient and thickness of a film are known. 

For glassy polymers, sorption isotherms are more complex and hysteresis oetween the pressurization and depressurization steps may... 

The moduli of metals, ceramics and glassy polymers below Tq reflect the stiffness of the bonds which link the atoms. Glasses and glassy polymers above are leathers, rubbers or viscous liquids, and have much lower moduli. Composites have moduli which are a weighted average of those of their components. 

Fig. 22.4. The random walk of o chain in a polymer melt, or in a solid, glassy polymer means that, on average, one end of the molecule is -yJn)A away from the other end. Very large strains (=4) are needed to straighten the molecule out.

Because the rubber is not too compatible it exists in droplets, rather than in a molecular scale mixture with the glassy polymer. 

HAWARD, R. N., (Ed.), The Physics of Glassy Polymers, Applied Science, London (1973) JENKINS, A. D., (Ed.)., Polymer Science, North-Holland, Amsterdam (1972)... 

Crystalline structures have a much greater degree of molecular packing and the individual lamellae can be considered as almost impermeable so that diffusion can occur only in amorphous zones or through zones of imperfection. Hence crystalline polymers will tend to resist diffusion more than either rubbers or glassy polymers. 

The process of blending with another glassy polymer to raise the heat distortion temperature is not restricted to polycarbonate, and the polysulphones are obvious candidates because of their higher Tg. One blend has been offered (Arylon T by USS Chemicals) which has a higher softening point than the ABS-polycarbonates. 

Johnson and coworkers [6], in their original paper on the JKR theory, reported the measurements of surface energies and interfacial adhesion of soft elastomeric materials. Israelachvili and coworkers [68,69], and Tirrell and coworkers [62, 63,70,88-90] used the SFA to measure the surface energies of self-assembled monolayers and polymer films, respectively. Chaudhury and coworkers [47-50] adapted the JKR technique to measure the surface energies and interfacial adhesion between self-assembled monolayers. More recently, Mangipudi and coworkers [55] modified the JKR technique to measure the surface energies of glassy polymers. All these measurements are reviewed in this section. 

Pa, would deform appreciably under the action of loads comparable to the pull-off force given by Eq. 16. It is for this reason that the JKR type measurements are usually done on soft elastic materials such as crosslinked PI rubber [45,46] or crosslinked PDMS [42-44,47-50]. However glassy polymers such as polystyrene (PS) and PMMA are relatively hard, with bulk moduli of the order of 10 Pa. It can be seen from Eq. 11 that a varies as Thus, increasing K a factor of... 

The aim of this chapter is to describe the micro-mechanical processes that occur close to an interface during adhesive or cohesive failure of polymers. Emphasis will be placed on both the nature of the processes that occur and the micromechanical models that have been proposed to describe these processes. The main concern will be processes that occur at size scales ranging from nanometres (molecular dimensions) to a few micrometres. Failure is most commonly controlled by mechanical process that occur within this size range as it is these small scale processes that apply stress on the chain and cause the chain scission or pull-out that is often the basic process of fracture. The situation for elastomeric adhesives on substrates such as skin, glassy polymers or steel is different and will not be considered here but is described in a chapter on tack . Multiphase materials, such as rubber-toughened or semi-crystalline polymers, will not be considered much here as they show a whole range of different micro-mechanical processes initiated by the modulus mismatch between the phases. 

The micro-mechanical processes will be presented next, followed by the models used to describe them. The predictions of the models will then be compared with results obtained using well-defined coupling chains. Application of the models to the joining of dissimilar polymers will then be described. Finally welding of glassy polymers will be considered. 

Models of chain pull-out in glassy polymers without crazing... 

When the stress that can be bom at the interface between two glassy polymers increases to the point that a craze can form then the toughness increases considerably as energy is now dissipated in forming and extending the craze structure. The most used model that describes the micro-mechanics of crazing failure was proposed by Brown [8] in a fairly simple and approximate form. This model has since been improved and extended by a number of authors. As the original form of the model is simple and physically intuitive it will be described first and then the improvements will be discussed. 

Micro-mechanical processes that control the adhesion and fracture of elastomeric polymers occur at two different size scales. On the size scale of the chain the failure is by breakage of Van der Waals attraction, chain pull-out or by chain scission. The viscoelastic deformation in which most of the energy is dissipated occurs at a larger size scale but is controlled by the processes that occur on the scale of a chain. The situation is, in principle, very similar to that of glassy polymers except that crack growth rate and temperature dependence of the micromechanical processes are very important. 

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