Attached chains

It should be pointed out that Tanaka (1977) has derived the first order perturbation theory result for the expansion factor a, for tails in near 0-conditions. The result 

It is illuminating to compare the third-power type of equation for free chains and for tails. These both follow the general formula 

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One may wonder to what extent our predictions for hard spheres apply to a system of soft particles in a polymer solution. A definite answer to this question cannot be given at the moment since numerical data for the depletion of free polymer chains in the neighbourhood of a surface with terminally attached chains are not yet available. Some qualitative features for such a system have been discussed using scaling arguments (24). We may expect that the depleted amount of polymer is, at least in some cases, less than near a hard surface, giving rise to weaker attraction. Both the destabilization concentration (J) and the restabilisation concentration (<(> ) could be much lower. Experimental observations support this qualitative conclusion (1-5). 

The concentrations of the two forms, P and Q, of the cosubstrate may be regarded as approximately uniform within the film containing the enzyme molecules, the attaching chains, and the ferrocene and ferricenium moieties. Under such conditions, the current may be expressed by... 

Irregular polymers in which polymer or oligomer chains are attached to the main chain (as in graft copolymers) are named as follows. The attached polymer or oligomer chains are considered to be substituents to the main chain and named in the same way as regular polymers [1] or irregular polymers (cf Rules 1 and 2) but without the suffix -yl. The atom in the attached chains nearest to the point of attachment to the main chain is given the locant 1. 

The simulation of polymer chains attached at one end to an inert interface ("tails") Is described, using a combination of Monte-Carlo techniques and the RIS scheme. Four types of chains that exhibit different structural and geometrical characteristics are examined PE, POM, POE, and PDMS. The overall effects on the conformation of the attached chains arising from the presence of the interface are qualitatively similar. The chains are significantly extended, as measured by the mean square displacement, in the direction normal to the interface, but essentially unaffected parallel to the interface. A comparison Is made of intramolecular excluded volume with excluded volume arising from an impenetrable interface. It is shown that the two types of excluded volume exhibit qualitatively different effects on the conformation. 

Graft polymers can be made in great profusion by attaching chains of one kind of polymer to the middle of another. A particularly simple but uncontrollable way of doing this is to knock groups off a polymer chain with x-ray or y radiation in the presence of a monomer. The polymer radicals so produced then can grow side chains made of the new monomer. 

LC phases usually corresponds to at least the number of attached chains [258]. Moreover, no SmA phases were observed for non-fluorinated polycatenar mesogens, whereas chain fluorination obviously enables the formation of SmA phases, which are most probably of the de Vries type. It seems that non-fluorinated polycatenars are mainly stabilized by core-core interactions, whereas the mesophase stabilization by the fluorophobic effect retains the layer structure even if core-core interactions are relatively weak. 

B. Li, E. Ruckenstein Statistical thertnodynamics of end-attached chain monolayers, JOURNAL OF CHEMICAL PHYSICS 106 1 (1997) 280-288. 

In this paper, a physical picture equivalent to those of Leermakers and Scheutjens10,12 and Cantor13 is employed. However, a more simple generator-matrix methodology is used to examine the effects of the intramolecular interactions, the nearest-neighbor bond correlations, and the intermolecular interactions on the structural properties of end-attached chain monolayers. While equivalent to that developed in Refs. 10 and 12, the method is more simple and compact, and hence more convenient from a computational point of view. 

We consider a two-dimensional mixture which contains N end-attached chains and N0 solvent molecules and employ the simple cubic lattice model for its representation. The lat-... 

Now, take these chains at random and attach them to R-A molecules until they all have attached chains. Because large, small and intermediate size chains are combined into larger molecules at random, the molecular weight distribution narrows. This can... 

The molecular area per alkyl chain is approximately 0.25 nm which is a value often found in X-ray structures of hydrocarbon chains. These results indicate that the higher generation dendrimer have a more flat conformation because in that case all the attached chains can count for the observed molecular area. 

As far as the fluctuation dynamics of an end-attached chain is concerned, a characteristic length is defined as the size of the thermal fluctuation of the tube which is given by ... 

We have investigated the way the typical features of Fig. 4 to 6 were dependent on the molecular characteristics of the system, i.e. the molecular weight of the polymer melt, Mw(P), the molecular weight of the surface anchored chains, Mw(N), and the surface density of surface attached chains, a parameter which is only qualitatively under control through the contact angle of dodecane with the surface. 

Finally, for higher flow regimes attached chains are completely elongated and disentangled from the bulk polymer. Slippage is then easy, wall stress is again proportional to slip velocity and friction is similar to that which could be obtained with ideal surface. 

Figure 3.18. Monolayers of physisorbed homopolymers at low coverage (a and b) and at high coverage (c). Diagram (d) shows a so-called brush of end-attached chains at high grafting density, where the hairs are forced to stretch.

Polymer brush systems are theoretically and experimentally of great interest as the change in the conformational entropy of the attached chains and... 

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