Entropy spring model

An entropy spring model for the degradation of Young s modulus... 

Wang, Y., Han, X., Pan, J., Sinka, C., 2010. An entropy spring model for the Young s modulus change of biodegradable polymers during biodegradation. Journal of the Mechanical Behavior of Biomedical Materials 14—21. 

A model network can thus be schematized by an ensemble of spring-suspended beads the elastic chains act as entropy springs, and they connect beads of constant — as yet unknown — functionality. 

In the Rouse model to be discussed below, each Kuhn segment is subdivided into a bead (where the segment mass is concentrated) and a massless spring . The elasticity of these springs is based on the conformational entropy of the segments which depends on how far they are stretched. This bead/spring model is characterized by the following basic parameters partially also illustrated in Fig. 6. 

PEG in hexadecane behaves like an ideal entropy spring and is therefore well described by a FJC model. In water, marked deviations are observed in the region from 20 to 200 pN, which are caused by the dismption of a suprastructure stabilized by water bridges. Again, this molecular fingerprint is reversible and thus in thermodynamic equilibrium. 

The early molecular theories of rubber elasticity were based on models of networks of long chains in molecules, each acting as an entropic spring. That is, because the configurational entropy of a chain increased as the distance between the atoms decreased, an external force was necessary to prevent its collapse. It was understood that collapse of the network to zero volume in the absence of an externally applied stress was prevented by repulsive excluded volume (EV) interactions. The term nonbonded interactions was applied to those between atom pairs that were not neighboring atoms along a chain and interacting via a covalent bond. 

In 1953 Rouse published a paper to describe theoretically the flow of polymers in dilute solutions. The polymer molecule is assumed to exist as a statistical coil and is subdivided into N submolecules. Each submolecule is thought of a solid bead. The beads behave as Gaussian chains and their entropy-elastic recovery can be described by a spring with a spring constant hkT/cP-, where a is the average end-to-end distance of a submolecule and k is the Boltzmann constant. The model is shown in Figure 8.9. 

The classical models of rubber elasticity reduce the elastic properties to a study of entropic springs. In the phantom model the EV interaction only gives the volume conservation, while in the affine deformation model it also is responsible for the affine position transformation of the crosslinks. Otherwise the entropic forces and the excluded volume interactions and consequently the entanglements, as they are a result of the EV interaction, completely decouple from the chain elasticity. The elasticity is entirely determined by the strand entropy. It is obvious that this is a... 

In another research, the thermo-mechanical behavior of SMPs was described by both linear and nonlinear viscoelastic theories [4]. In this woik four element mechanical units consisting of spring, dashpot and frictional device were used to derive a constitutive differential equation. In order to determine the material properties by a constitutive differential equation the modulus, viscosity and other parameters were assumed to decay exponentially with temperature. Liu et al. [5] developed a constitutive equation for SMPs based on thermodynamic concepts of entropy and internal energy. They adopted the concept of frozen strain and demonstrated the utility of the model by simulating the stress and strain... 

---