Elasticity enthalpic

In 2005, Hugel et al. reported the enthalpic elasticity with high-accuracy of a monomer of three kinds of polymers (Fig. 2), which was calculated at the MP2 level of theory [47]. The modulus of the monomer was nonlinear and can be expressed in a polynomial expansion ... 

We have now reviewed three types of behaviour the enthalpic elasticity of rigid polymers at temperatures below Tg, the entropic elasticity of polymers at temperatures above Tg- -40°C and the viscous response of uncrosslinked polymers in the molten state. When examining the various states of polymer materials, we emphasised analogies between temperature and time behaviour. This naturally leads us to consider the viscoelastic character exhibited by polymers under certain conditions, particularly in the region of the glass transition. 

The stress-strain curve in Fig. 7.24a shows a linear region corresponding to enthalpic elasticity, followed by a slightly curved region in which local deformation processes (referred to as preplastic) lead to a reduction in modulus. Brittle fracture then occurs, perpendicular to the load direction. 

Entropic and Enthalpic Elasticity. In recent years, SFM approaches and complementary force-sensing approaches, such as biomembrane probe and laser optical trap techniques, have been perfected to an extent that the study of individual (bio)macromolecules have become feasible as routine experiments in many... 

Miscellaneous Forces. Force measurements on polymer surfaces or between chemically modified SFM tips and polymer surfaces yielded important insight into fundamental force vs separation distance relationships for, eg, polymer colloidal particles (207), mechanochemical behavior of individual macromolecules (see section Entropic and Enthalpic Elasticity) (87-96,99), but also adhesion information directly relevant for practical applications, such as electrochemically controlled adhesion (208) or toner particle-rubber interactions relevant for xerographic applications (209,210). 

LSCEs offer numerous new aspects to the field of polymer science due to their exceptional physical properties. With respect to mechanical behavior, LSCEs are unique soft crystals. Mechanical fields not only bias the state of LC order but also cause exceptional reorientation behavior, which impressively modifies the mechanical response. If the LC phase stmeture additimially exhibits one-dimensional positional long-range order, conventional entropic elasticity exists solely in two dimensions, while the third dimension is determined by the enthalpic elasticity of the LC order. 

ENTHALPIC AND ENTROPIC CONTRIBUTIONS TO RUBBER ELASTICITY THE FORCE-TEMPERATURE RELATIONS... 

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]. 

However, Noolandi (1991) has noted that eqn 6.7 only contains elastic contributions to the reduction in interfacial tension, and not the major contribution from enthalpic terms which are included in the expression derived by Noolandi and Hong (eqn 6.10). Noolandi (1991) argues that the major reduction in interfacial tension arises from the energetically favoured orientation of the copolymer blocks in their compatible homopolymers. 

The adsorbed layers between the particles may interpenetrate and so give a local increase in the concentration of polymer segments. Depending on the balance between polymer-polymer and polymer-dispersion medium interactions, this may lead to either repulsion or attraction by an osmotic mechanism. Enthalpic and entropic changes will be involved. If interpenetration takes place to a significant extent, elastic repulsion will also operate. 

These effects have been observed for both aqueous and non-aqueous media and good correlation between the point of incipient flocculation and the 0-temperature is well established112. The transition from stability to instability usually occurs over a very narrow temperature range (1 or 2 K). Enthalpic stabilisation tends to be the more common in aqueous media and entropic stabilisation the more common in non-aqueous media. Owing to the elastic effect, aggregation into a deep primary minimum does not take place (as is possible with lyophobic sols) and redispersion takes place readily on reverting to better than 0-solvent conditions. 

To understand elastic mechanical properties, the discussion of the storage of energy of deformation provides a powerful approach. Dynamic mechanical measurements at higher strain on filled silicone elastomers show that the energy of deformation may be related to an entropic and an enthalpic part. The entropic part is mainly due to the restriction of the conformational space of the polymer chain by the presence of the solid silica particles. Whereas the enthalpic part of the energy of deformation is related to... 

VII. Enthalpic and Entropic Contributions to Rubber Elasticity Force-Temperature Relations Vtn. Direct Determination of Molecular Dimensions IX. Single-Molecule Elasticity References... 

Another model frequently used to describe the polymer chain is WLC. In WLC model, a polymer is treated as a homogenous string of constant bending elasticity. Both entropic and enthalpic contributions are combined in this model [6,61]. Scheme 30.3b shows the WLC model and the relationship between force and the extension of a WLC is shown as follows ... 

We conclude that elastomer elasticity has entropic origins, whilst rigid polymer and metal elasticity are enthalpic. They are therefore of quite different nature. 

Besides the introduction of an enthalpic contribution, the elastic energy terms of the spheres or cylinders located at lamellar interfaces have to be changed in the corresponding expressions for spheres or cylinders in a diblock copol5mier For a lamellar B block, there is no gain of conformational entropy upon mixing of the A and C blocks within this simple model. In addition the mixing entropy of the jimction points Sj at the AB and BC interfaces has to be considered as another... 

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