Mechanics of Polymers

In this section, we describe the mechanical properties of a class of materials that continues to grow in terms of use in structural applications. As issues related to energy consumption and global warming continue to increase demands for lightweight, recyclable materials, the development of new polymers and the characterization of recycled polymers will continue to dominate research and development efforts in this area. 

Despite the similarities in brittle and ductile behavior to ceramics and metals, respectively, the elastic and permanent deformation mechanisms in polymers are quite different, owing to the difference in structure and size scale of the entities undergoing movement. Whereas plastic deformation (or lack thereof) could be described in terms of dislocations and slip planes in metals and ceramics, the polymer chains that must be deformed are of a much larger size scale. Before discussing polymer mechanical properties in this context, however, we must first describe a phenomenon that is somewhat unique to polymers—one that imparts some astounding properties to these materials. That property is viscoelasticity, and it can be described in terms of fundamental processes that we have already introduced. 

As the term implies, viscoelasticity is the response of a material to an applied stress that has both a viscous and an elastic component. In addition to a recoverable elastic response to an applied force, polymers can undergo permanent deformation at high strains, just as was the case for metals and some glasses, as described previously. The mechanism of permanent deformation is different in polymers, however, and can resemble liquid-like, or viscous flow, just like we described in Chapter 4. Let us first develop two important theoretical models to describe viscoelasticity, then describe how certain polymers exhibit this important property. 

Recall from Eq. (5.10) that the shear strain can be related to the shear stress through the shear modulus, G, according to Hooke s Law, where we now add subscripts to differentiate the elastic quantities from the viscous quantities  

This relation can be differentiated with respect to time and solved for the strain rate  

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Roulin-Moloney A C 1989 Fractography and failure mechanisms of polymers and composites (London Elsevier)... 

Pearson, J.R. A., 1985. Mechanics of Polymer Processing, Applied Science Publishers, Barkings, Essex, UK. 

Other aspects of stabilization of acetal resins are briefly discussed under processing and fabrication. Reference 15 provides a more detailed discussion of the mechanism of polymer degradation. 

J. G. WiUiams, fracture Mechanics of Polymers, Ellis Horwood, Chichester, UK, 1984. 

The principal mechanism of polymer degradation during aging is the acid-catalyzed cleavage of the ether linkage in the backbone. The acid acceptor. 

Some of these findings are in agreement with the observation of Chaudhury and Whitesides [47], In an extension of these studies, Tirrell and coworkers [62,63,70, 88-90] studied the contact mechanics of polymer surfaces using the SFA. 

Creton, C., Kramer, E.J., Hui, C.-Y. and Brown, H.R., Failure mechanisms of polymer interfaces reinforced with block copolymers. Macromolecules, 25, 3075-3088 (1992). Boucher et al., E., Effects of the formation of copolymer on the interfacial adhesion between semicrystalline polymers. Macromolecules, 29, 774-782 (1996). 

Pearson, J.R.A. Mechanics of Polymer Processing, Elsevier Applied Science, London (1985) Throne, J.L. Plastics Process Engineering, Marcel Dekker, New York (1979)... 

K. Schwetlick, Mechanisms of Polymer Degradation and Stabilization (G. Scott, ed.), Elsevier Science Publishers, New York, Chap. 2, (1990). 

Williams JG (1984) Fracture mechanics of polymers. Ellis Horwood, Chichester, p 46... 

G. C. Arridge, Mechanics of Polymers, Clarendon Press, Oxford, 1975. 

Burnett, G. M., Mechanism of Polymer Reactions, Interscience, New York 1954,... 

Applications Desorption chemical ionisation has proven potential in the analysis of thermally labile, nonvolatile and polar compounds [40,67,68], for the identification of unknown polymers and the study of the thermal degradation mechanisms of polymers. Considering the overall ease of DCI operation, the capability of analysing nonvolatile compounds, and the selectivity provided by choosing different reagent gases, DCI has found surprisingly few practitioners in the analysis of polymer additives. 

In the classical Lauritzen-Hoffman theory for the mechanism of polymer crystal growth [106], it is assumed that the observed lamellar thickness corresponds to those crystallites that happen to have the largest growth velocity. However, this picture is hard to reconcile with the experimental observation that the thickness of polyethylene single crystals can be modulated by varying the temperature at which they are grown [117,118]. In fact, simulations by Doye et al. [119,120] suggest that the observed lamellar thickness does... 

In the world of molecular simulation, it would be more conventional to consider that the present model is a coarse grained model of real polymers, where the real time-scale is much longer than that of the present MD simulation time-scale. However, we did not intend to make a coarse grained model. The crystallization of polymers was shown to be rather universal. Various kinds of polymers, either fast crystallizing or slow crystallizing, were known to follow the same scheme with respect to the molecular mechanism of crystallization. So we studied this simple model expecting that the present model would also follow the same crystallization scheme and show the general molecular mechanisms of polymer crystallization. 

Acknowledgements The present work was supported by the Grant-in-Aid of Scientific Research on Priority Areas, Mechanism of Polymer Crystallization (No. 12127206), from the Ministry of Education, Science, and Culture, Japan. 

The molecular weight (M) dependence of the steady (stationary) primary nucleation rate (I) of polymers has been an important unresolved problem. The purpose of this section is to present a power law of molecular weight of I of PE, I oc M-H, where H is a constant which depends on materials and phases [20,33,34]. It will be shown that the self-diffusion process of chain molecules controls the Mn dependence of I, while the critical nucleation process does not. It will be concluded that a topological process, such as chain sliding diffusion and entanglement, assumes the most important role in nucleation mechanisms of polymers, as was predicted in the chain sliding diffusion theory of Hikosaka [14,15]. 

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

J G. Williams, Fracture Mechanics of Polymers. Wiley, New York. 19H4. 

B. Fu, E. Bakker, J.H. Yun, V.C. Yang, and M.E. Meyerhoff, Response mechanism of polymer membrane-based potentiometric polyion sensors. Anal. Chem. 66, 2250-2259 (1994). 

Hikosaka, M., Watanabe, K., Okada, K. and Yamazaki, S. Topological Mechanism of Polymer Nucleation and Growth - The Role of Chain Sliding Diffusion and Entanglement. Vol. 191, pp. 137-186. 

This reaction is very exothermic (A// —180 to —200kJ mol-1) and, therefore, seems to be very probable from the thermochemical point of estimation. The pre-exponential factor is expected to be low due to the concentration of the energy on three bonds at the moment of TS formation (see Chapter 3). To demonstrate that this reaction is responsible for the oxidative destruction of polymers, PP and PE were oxidized in chlorobenzene with an initiator and analyzed for the rates of oxidation, destruction (viscosimetrically), and double bond formation (by the reaction with ozone) [131]. It was found that (i) polymer degradation and formation of double bonds occur concurrently with oxidation (ii) the rates of all three processes are proportional to v 1/2, (iii) independent of p02, and (iv) vs = vdbf in PE and vs = 1.6vdbf in PP (vdbf is the rate of double bond formation). Thus, the rates of destruction and formation of double bonds, as well as the kinetic parameters of these reactions, are close, which corroborates with the proposed mechanism of polymer destruction. Therefore, the rate of peroxyl macromolecules degradation obeys the kinetic equation ... 

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