Flexible chain concentrated

FIG. 11 Adsorbed amount as a function of bulk concentration for a non-interacting (empty symbols) and adsorbing (full symbols) wall. Diamonds and triangles correspond to a system with semi-rigid chains, circles and squares for flexible chains [28]. 

Usually, dilute polymer solutions are isotropic systems, i.e. macromolecular chains can exist in these solutions independently of each other with a random distribution of orientations of the long axes of coils. The solutions of flexible-chain polymers remain isotropic when the solution concentration increases whereas in concentrated solutions of macromolecules of limited flexibility the chains can no longer be oriented arbitrarily and some direction of preferential orientations of macromolecular axes appears, i.e. the mutual orientations of the axes of neighboring molecules are correlated. This means that... 

Hence, Flory s theory offers an objective criterion for chain flexibility and makes possible to divide all the variety of macromolecules into flexible-chain (f > 0.63) and rigid-chain (f < 0.63) ones. In the absence of kinetic hindrance, all rigid-chain polymers must form a thermodynamically stable organized nematic phase at some polymer concentration in solution which increases with f. At f > 0.63, the macromolecules cannot spontaneously adopt a state of parallel order under any conditions. 

Figure 2. Mechanism of PDH. The three different subunits of the PDH complex in the mitochondrial matrix (E, pyruvate decarboxylase E2, dihydrolipoamide acyltrans-ferase Ej, dihydrolipoamide dehydrogenase) catalyze the oxidative decarboxylation of pyruvate to acetyl-CoA and CO2. E, decarboxylates pyruvate and transfers the acetyl-group to lipoamide. Lipoamide is linked to the group of a lysine residue to E2 to form a flexible chain which rotates between the active sites of E, E2, and E3. E2 then transfers the acetyl-group from lipoamide to CoASH leaving the lipoamide in the reduced form. This in turn is oxidized by E3, which is an NAD-dependent (low potential) flavoprotein, completing the catalytic cycle. PDH activity is controlled in two ways by product inhibition by NADH and acetyl-CoA formed from pyruvate (or by P-oxidation), and by inactivation by phosphorylation of Ej by a specific ATP-de-pendent protein kinase associated with the complex, or activation by dephosphorylation by a specific phosphoprotein phosphatase. The phosphatase is activated by increases in the concentration of Ca in the matrix. The combination of insulin with its cell surface receptor activates PDH by activating the phosphatase by an unknown mechanism.

In general, the factor by which G is reduced depends on Me, f, chain stiffness, and the initial concentrations of reactive groups obtainable in bulk, in a manner which still needs to be resolved in detail. However, for bulk reaction mixtures, the moduli of networks with relatively flexible chain structures can be reduced by a factor of five below those expected for network formation in the absence of pre-gel intramolecular reaction. 

Cyclisation of long-chain molecules is a field where theory has far preceded experiment. In his pioneering treatment of flexible chains in terms of the freely-jointed chain model, Kuhn (1934) derived for the local concentration Ceff of one chain end in the neighbourhood of the other (see p. 7) expression (56) where Aa is Avogadro s number and Ceff is given in moles per... 

Each of the examples mentioned above behave slightly differently and these differences are due to the detailed structure. In each case the hydrocarbon groups associate via hydrophobic bonding but HMHEC for example can show a critical concentration threshold for this to occur. HEUR on the other hand tends to associate at all concentrations. This is due to accessibility of the hydrophobes as they are at the ends of very flexible chains. In HMHEC, however, we have a much stiffer chain with the hydrophobes spread randomly along it. It is therefore a more difficult process to bring these together to form network nodes. HP AM conforms more closely to HMHEC than HEUR but, as we have groups of hydrocarbon chains at each modification site, it associates somewhat more readily. 

When the two monomers are linked by a short flexible chain, intramolecular excimers can be formed. This process is still diffusion-controlled, but in contrast to the preceding case, it is not translational it requires a close approach between the two molecules via internal rotations during the excited-state lifetime. Equations (4.44), (4.45), (4.47) to (4.49) are still valid after replacing k [M] by k because intramolecular excimer formation is independent of the total concentration. Estimation of the local fluidity of a medium can be achieved by means of probes capable of forming intramolecular excimers (see Chapter 8). 

The general conclusion of the mentioned works was that the appearance of the jump on the dependences of network volume on the composition of the solvent or on temperature is reached only at some definite content of ionic groups in the network chains. For neutral networks with flexible chains, the collapse is usually not observed. Exceptions to this rule were reported for poly(isopropylacrylamide) (PIPAA) [16], poly(vinylcaprolactam) and poly-(2-vinylpyrrolidone) [17] gels. The specific feature of these systems is that the transition takes place in structured solvents water or concentrated aqueous solutions of aluminium sulfate. 

Williams begins with Fixman s equation (220) for the stress contributed by intermolecular forces in flexible chain systems. The theory assumes that the polymer concentration is high enough that intermolecular interactions control the stress. The shear stress contributed by polymer molecules in steady shear flow is expressed in the form... 

There is some similarity between Ferry s treatment of concentrated systems (14), (123) [eq. (4.4)] and Cerf s just mentioned approach. In both cases the normal coordinate transformation is assumed to be possible along the lines given for infinitely dilute solutions of kinetically perfectly flexible chains (Rouse, Zimm). Only afterwards, different external (Ferry) or internal (Cerf) friction factors are ascribed to the various normal modes. 

This result is contrary to that found in the solution proposed by Heller and coworkers, of attaching the mediator to the enzyme on a flexible chain (49), and adsorbing die modified species on an electrode in a polyelectrolyte. In this instance the O2 induced decrease in signal was constant with glucose concentration. 

In a comparison study of the values of flow birefringence An and the viscosity t of a polymer solution it is often possible to simplify the experimental procedure so as to avoid the determinations of the characteristic values of [n] and [tj] by determining the quantity An/g (i - tjq) at finite solution concentration instead of the ratio [n]/[7j]. Here is the viscosity of the solvent and the value of g(rj - t o) - At characterizes the effective shearing stress in solution introduced by the dissolved polymer. Many experimental data show that for a flexible-chain polymer in the absence of the macroform effect the ratio An/At, which may be called the shear optical coefficient , is independent of solution concentration, and, also, over a wide range of molecular weights, of chain length ... 

For rigid-chain polymers An/Ar is also independent of solution concentration. This can be seen in Fig. 12 in which the experimental poonts for solutions of the same polymer at different concentrations fall on the same curve illustrating the dependence of An on At. This coincidence holds for both flexible-chain polyisobutylene (Curve 1) and rigid-chain nitrocellulose (Curve 2). 

The properties of the surplus segment probability p and the effective constraint coordination number z are less well established. It seems possible that p will dep d on polymer species to some extent, since loop projection may be easier for a more locally flexible chain. Weak dependences on concentration and temf rature are likely for the same reason. On the other hand, z characterizes the topology on a fairly large scale and therefore may be virtually a universal constant. Diese however are only some speculations. Values of p and z can be established by various experiments, p from the elastic properties of networks and also from the relaxation of star polymers, z from relative relaxation rates of linear and star molecules in liquids and networks and also from measurements of diffusion rates of stars in linear chain liquids. The adequacy of the... 

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