Subject polymer chains

A polymer chain can be approximated by a set of balls connected by springs. The springs account for the elastic behaviour of the chain and the beads are subject to viscous forces. In the Rouse model [35], the elastic force due to a spring connecting two beads is f= bAr, where Ar is the extension of the spring and the spring constant is ii = rtRis the root-mean-square distance of two successive beads. The viscous force that acts on a bead is... 

This kind of perfect flexibility means that C3 may lie anywhere on the surface of the sphere. According to the model, it is not even excluded from Cj. This model of a perfectly flexible chain is not a realistic representation of an actual polymer molecule. The latter is subject to fixed bond angles and experiences some degree of hindrance to rotation around bonds. We shall consider the effect of these constraints, as well as the effect of solvent-polymer interactions, after we explore the properties of the perfectly flexible chain. Even in this revised model, we shall not correct for the volume excluded by the polymer chain itself. 

Coating solutions often exhibit a mixture of viscous and elastic behavior, with the response of a particular system depending on the stmcture of the material and the extent of deformation. Eor example, polymer melts can be highly elastic if a polymer chain can stretch when subjected to deformation. 

The statistical properties of polymer chains in a quenched random medium have been the subject of intensive investigations during the last decades, both theoretically [79-89] and experimentally [90-96], because diffusion in such media is of great relevance for chromatography, membrane separation, ultrafiltration, etc. 

Terminal bonding of a polymer chain to a surface is a subject of great academic and industrial interest. Eastmond et al. [63] used Mn2(CO)io and Re2(CO)io pho-... 

A final class of multifunctional initiators is based on the use a (muUi)functional polymer and a low molecular weight redox agent. Radicals on the polymer chain arc generated from the polymer bound functionality by a redox reaction. Ideally, no free initiating species are formed. The best known of this class are the polyol-redox and related systems. Polymers containing hydroxy or glycol and related functionality are subject to one electron oxidation by species such as ceric ions or periodate (Scheme 7.23).266,267 Substrates such as cellulose,... 

Highly branched polymers, polymer adsorption and the mesophases of block copolymers may seem weakly connected subjects. However, in this review we bring out some important common features related to the tethering experienced by the polymer chains in all of these structures. Tethered polymer chains, in our parlance, are chains attached to a point, a line, a surface or an interface by their ends. In this view, one may think of the arms of a star polymer as chains tethered to a point [1], or of polymerized macromonomers as chains tethered to a line [2-4]. Adsorption or grafting of end-functionalized polymers to a surface exemplifies a tethered surface layer [5] (a polymer brush ), whereas block copolymers straddling phase boundaries give rise to chains tethered to an interface [6],... 

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. 

The yield or efficiency of cross-linking is also dictated by the hydrostatic pressure to which the polymer is subjected during irradiation [76]. The increase in G(X) is due to an enhancement of chain-reaction cross-linking furthered by a closer proximity of the polymer chains. 

The conformation of polymer chains in an ultra-thin film has been an attractive subject in the field of polymer physics. The chain conformation has been extensively discussed theoretically and experimentally [6-11] however, the experimental technique to study an ultra-thin film is limited because it is difficult to obtain a signal from a specimen due to the low sample volume. The conformation of polymer chains in an ultra-thin film has been examined by small angle neutron scattering (SANS), and contradictory results have been reported. With decreasing film thickness, the radius of gyration, Rg, parallel to the film plane increases when the thickness is less than the unperturbed chain dimension in the bulk state [12-14]. On the other hand, Jones et al. reported that a polystyrene chain in an ultra-thin film takes a Gaussian conformation with a similar in-plane Rg to that in the bulk state [15, 16]. 

If we were to have an isolated polymer chain with a single nuclear spin attached to each segment (the marked chain) crosslinked into an unmarked network, the second moment of the NMR line of that spin species would carry information relating to the separation of chain segments, and to their relative orientation with respect to the field direction. If the network were to be subjected to a bulk deformation, these geometrical parameters would be altered, and hence we would expect a corresponding change in the value of the experimentally measured... 

The structure of hydrogels that do not contain ionic moieties can be analyzed by the Flory Rehner theory (Flory and Rehner 1943a). This combination of thermodynamic and elasticity theories states that a cross-linked polymer gel which is immersed in a fluid and allowed to reach equilibrium with its surroundings is subject only to two opposing forces, the thermodynamic force of mixing and the retractive force of the polymer chains. At equilibrium, these two forces are equal. Equation (1) describes the physical situation in terms of the Gibbs free energy. 

Lee, J.J. Fuller, G.G. "Elllpsometry Studies of Adsorbed Polymer Chains Subjected to Flow", submitted to Macromolecules. 

Principle of Minimum Internal Conformational Energy. The conformation of a polymer chain in a crystal approaches one of the minima of the internal conformational energy, which would be taken by an isolated chain subjected to the restrictions imposed by the equivalence principle. 

The chemistry of compounds containing Si-Si bond(s) is an intriguing subject in the field of organosilicon chemistry because Si-Si bonds have unique physical and chemical properties. The reactivities of Si-Si bonds is often compared with those of carbon-carbon double bonds. The current interest in polysilanes in material science stems from the fact that they exhibit unusual properties implying considerable electron delocalization in the polymer chain [62]. This section concerns with the unique elecrochemical properties of compounds containing Si-Si bonds (Sect. 2.4). 

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