Elasticity entropic

Crosslinked polymers are rather peculiar materials in that they never melt and they exhibit entropic elasticity at elevated temperatures. The present review on the influence of crosslink density is structured around model polymers of uniform composition but with widely varying numbers of crosslinks. The degree of crosslinking in the polymers was verified by use of the theory of rubber elasticity. 

Although the basic concept of macromolecular networks and entropic elasticity [18] were expressed more then 50 years ago, work on the physics of rubber elasticity [8, 19, 20, 21] is still active. Moreover, the molecular theories of rubber elasticity are advancing to give increasingly realistic models for polymer networks [7, 22]. 

Fig. 3.1. Young s moduli E of the polymers A, B, C, D in the rubbery state against absolute temperature T (test frequency 0.01 Hz). Entropic elasticity is indicated by the proportionality of E to T [11]...

Urry, D.W., Entropic elastic processes in protein mechanisms. 1. Elastic structures due to an inverse temperature transition and elasticity due to internal chain dynamics, J. Prot. Chem., 7, 1-34, 1988. 

The entropic elasticity of a single polymer chain is treated similarly to the statistical mechanical property of gas molecules. Now, let us compare gas molecules to children moving around freely... 

FIGURE 21.1 Drawing to help explain entropic elasticity. (From Saito, N., Polymer Physics [in Japanese], Syokabo, Tokyo, Japan, 1967.)... 

The large deformability as shown in Figure 21.2, one of the main features of rubber, can be discussed in the category of continuum mechanics, which itself is complete theoretical framework. However, in the textbooks on rubber, we have to explain this feature with molecular theory. This would be the statistical mechanics of network structure where we encounter another serious pitfall and this is what we are concerned with in this chapter the assumption of affine deformation. The assumption is the core idea that appeared both in Gaussian network that treats infinitesimal deformation and in Mooney-Rivlin equation that treats large deformation. The microscopic deformation of a single polymer chain must be proportional to the macroscopic rubber deformation. However, the assumption is merely hypothesis and there is no experimental support. In summary, the theory of rubbery materials is built like a two-storied house of cards, without any experimental evidence on a single polymer chain entropic elasticity and affine deformation. 

ENTROPIC ELASTICITY OF A SINGLE POLYMER CHAIN 21.2.1 Brief Introduction... 

In this chapter, AFM palpation was introduced to verify the entropic elasticity of a single polymer chain and affine deformation hypothesis, both of which are the fundamental subject of mbber physics. The method was also applied to CB-reinforced NR which is one of the most important product from the industrial viewpoint. The current status of arts for the method is still unsophisticated. It would be rather said that we are now in the same stage as the ancients who acquired fire. However, we believe that here is the clue for the conversion of rubber science from theory-guided science into experiment-guided science. AFM is not merely high-resolution microscopy, but a doctor in the twenty-first century who can palpate materials at nanometer scale. 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

Bustamante C, Marko JF, Siggia ED et al (1994) Entropic elasticity of X-phage DNA. Science 265 1599-1600... 

Ortiz C, Hadziioannou G. Entropic elasticity of single polymer chains of poly(methacrylic acid) measured by atomic force microscopy. Macromolecules 1999 32 780-787. 

Due to the chain architecture and the large size of the macromolecules, the wetting behaviour of polymer liquids can be different from that of simple liquids. The effect becomes particularly strong when the dimension of the liquid phase, e.g. film thickness and droplet diameter, approaches the dimension of the polymer coil. In addition to the spreading coefficient and the surface pressure effects, entropic elasticity of the polymer chain provides a strong contribution to the free energy for a constant volume V0=Ad ... 

Trombitas, K., Greaser, M., and Labeit, S. (1998b). Titin extensibility in situ Entropic elasticity of permanently folded and permanently unfolded molecular segments. 

Most of the physical properties of networks in the rubbery state can be linked to two groups of quantities that characterize respectively, the equilibrium entropic elasticity and the relaxation kinetics (linked to the segmental mobility). 

Remark As previously stated, the above theory is the simplest one. There are other physical approaches of entropic elasticity, especially the theory of phantom networks (Queslel and Mark, 1989), in which the crosslinks freely fluctuate around their mean position. The above relationship then becomes ... 

Summary In this chapter, a discussion of the viscoelastic properties of selected polymeric materials is performed. The basic concepts of viscoelasticity, dealing with the fact that polymers above glass-transition temperature exhibit high entropic elasticity, are described at beginner level. The analysis of stress-strain for some polymeric materials is shortly described. Dielectric and dynamic mechanical behavior of aliphatic, cyclic saturated and aromatic substituted poly(methacrylate)s is well explained. An interesting approach of the relaxational processes is presented under the experience of the authors in these polymeric systems. The viscoelastic behavior of poly(itaconate)s with mono- and disubstitutions and the effect of the substituents and the functional groups is extensively discussed. The behavior of viscoelastic behavior of different poly(thiocarbonate)s is also analyzed. 

Rejection of protein adsorption to the outermost grafted surface is attributed to a steric hinderance due to the tethered chains. A grafted surface in contact with an aqueous medium, a good solvent of the chains, has been identified to have a diffuse structure [67]. Reversible deformation of tethered chains due to invasion of mobile protein molecules into the layer would lead to a repulsive force which is governed by the balance of entropic elasticity of the chains and osmotic pressure owing to the rise in the segment concentration. The overlapped repulsive force would prevent the direct contact of protein molecules with the substrate surface. 

C. Bustamante, J.F. Marko, E.D. Siggia, S. Smith, Entropic elasticity of lambda-phage DNA. Science 265, 1599-1600 (1994)... 

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