Elasticity of networks with permanent and thermoreversible cross-links
- PDF / 692,238 Bytes
- 12 Pages / 612 x 792 pts (letter) Page_size
- 117 Downloads / 205 Views
1234-QQ04-01
Elasticity of networks with permanent and thermoreversible cross-links Jack F. Douglas Polymers Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 Abstract: Simplified models of flexible chain and stiff fiber networks are introduced to address how the network elasticity becomes modified when the cross-linking is thermoreversible in nature and changes in the stability of the network with deformation. These idealized models apparently able to capture many aspects of the elastic properties of real networks. INTRODUCTION Synthetic and natural networks of polymers and self-assembling molecules are ubiquitous in manufacturing and biology, and the study of network elasticity has a long and distinguished scientific history [1]. The theory of flexible polymer networks has received particular attention, but even in this case the quantitative role of interchain interactions in the dry rubber state (the socalled “entanglement” effect) has been slow to develop and the topic remains one of scientific and technological interest [1]. Networks of stiff fibers have seen a large upsurge of interest recently because many networks of biological origin (and thus many biological materials) are comprised of such networks, which have an elasticity quite distinct from their flexible network counterparts. Specifically, the elasticity of flexible polymer networks is characterized at moderate deformations by strain softening and positive normal stresses while stiff fiber networks often exhibit strain stiffening and negative normal stresses [2,3]. The elasticity of these classes of networks could thus not be more different from each other. Moreover, many real networks are comprised of network junctions or cross-links that involve a reversible association-dissociation process so that the junctions are not fixed for all time, although their time-averaged number may be an invariant. Deforming these associating networks then leads to diverse complicating effects such as the breakdown of the network and subsequent slow recovery following the cessation of an applied stress, a dependence of the elastic response on the rate of network deformation, temperature and the concentration of associating species, as well as other thermodynamic parameters that influence network stability. Finally, flexible and semi-flexible networks can also exhibit strong strain stiffening effects associated with the limited extensibility of the chains, which itself can lead to large changes of elasticity at large network deformation. ELASTICITY OF POLYMER NETWORKS WITH PERMANENT JUNCTIONS Networks of flexible cross-linked chains (‘rubber’) A minimal statistical mechanical model of rubber elasticity must incorporate three main features of the network chains: 1) A connected network of flexible chains [4-6], 2) ‘Entanglement’ constraints [7-9], 3) Finite volume of chains [10]. The localization model (LM) of rubber elasticity is a minimal model that directly addresses these effects and we briefly summarize the essential ideas of this mode
Data Loading...
