Chain contraction

In the semidilute solution, blobs do not feel the excluded volume by the other blobs. Therefore, a chain of blobs takes a conformation of an ideal chain consisting of A/gjv blobs of size Its radius of gyration in the semidilute solution at monomer density p is estimated as 

In the semidilute solution, R the same as the ideal chain. The chain keeps contracting with an increasing p by effectively decreasing the monomer size of the 

This equation has an asymptote identical to Eq. 4.30, but the scaling exponent of -1/8 is not reached in the range shown. Apparently, longer chains are needed to observe the exponent. 

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Ionization of the carboxyl groups is accompanied by binding of the cations. But if counterions are site-bound the charge on the carboxyl groups is neutralized and chain contraction results. A special case is that of the polyacid which adopts a contracted form because the close association of hydrogen ions with carboxyl groups results in a neutral chain. 

The floe rupture model may also be used to explain the maximum observed in versus temperature (figure 5). According to equation (4) Tg = f (< > H) Eg, where f(2H) is the collision frequency term. Although Eg increases with increase of temperature, f(< > H) is a decreasing function of temperature as a result of decrease of solvency of the dispersing medium which leads to the contraction of the adsorbed layer (13). The increase of Eg with increase of temperature initially outweighs any reduction of f (< > H), but at higher temperatures, the reduction in f (4> j ) as a result of chain contraction may exceed the increase in Eg and this results in reduction in the measured Tg. 

The higher reactivity of the PVMI-Co(III) complex is attributed to the electrostatic domain of the polymer complex, as in the above PVP system. When the PVMI chain contracts, the charge density in the polymer domain increases and the reaction rate also increases. On the other hand, when the polymer chain expands, the electrostatic domain is weakened, which produces a fall in reactivity. These results confirm that the conformation of the polymer complex is closely related to the strength of its electrostatic domain and to the reaction rate. The effects of the polymer chain on reactivity are to be understood not only in terms of static chemical environment but also as dynamic effects which vary with the solution conditions, e.g. pH, ionic strength, solvent composition, temperature, and so on. 

Dynamic Monte Carlo simulations were first used by Verdier and Stockmayer (5) for lattice polymers. An alternative dynamical Monte Carlo method has been developed by Ceperley, Kalos and Lebowitz (6) and applied to the study of single, three dimensional polymers. In addition to the dynamic Monte Carlo studies, molecular dynamics methods have been used. Ryckaert and Bellemans (7) and Weber (8) have studied liquid n-butane. Solvent effects have been probed by Bishop, Kalos and Frisch (9), Rapaport (10), and Rebertus, Berne and Chandler (11). Multichain systems have been simulated by Curro (12), De Vos and Bellemans (13), Wall et al (14), Okamoto (15), Kranbu ehl and Schardt (16), and Mandel (17). Curro s study was the only one without a lattice but no dynamic properties were calculated because the standard Metropolis method was employed. De Vos and Belleman, Okamoto, and Kranbuehl and Schardt studies included dynamics by using the technique of Verdier and Stockmayer. Wall et al and Mandel introduced a novel mechanism for speeding relaxation to equilibrium but no dynamical properties were studied. These investigations indicated that the chain contracted and the chain dynamic processes slowed down in the presence of other polymers. 

Atomic and molecular displacement under constraint. Thermal expansion and compressibility are large and anisotropic. Sometimes structural data have been extrapolated from the room temperature (RT) down to low temperature (LT) simply by considering changes in lattice dimensions. This has led to disappointing results since, even in the absence of a phase transition, molecular shapes and orientations may change substantially. Similarly, if we find an isostatic pressure at room temperature whose effect is equivalent to a given temperature decrease at ambient pressure for, say, the chain contraction, the equivalence will not usually match for, say, the... 

Figure 36.3. Pleated sheet structure (hefa arrangement) proposed by Pauling for silk fibroin. Chains contracted to make room for small side chains. Adjacent chains head in opposite directions hydrogen bonding between adjacent chains.

The above observations are in agreement with studies on chain contraction of sodium polymethacrylate (NaPMA) in the presence of Ca2+ and Cu2+ counterions [25]. Static and quasi-elastic light scattering measurements indicate that a PMA chain contracts but does not have a compact spherical structure close to the precipitation threshold. 

In these deep quenches, one observes a variety of other interesting effects that have not been considered by theory so far the tendency to avoid unfavorable contacts between chains as fast as possible leads to a chain contraction during very early stages after the quench (Fig. 38). This interpretation is corroborated by a direct study of the time-dependence of different types of nearest-neighbor contacts [155]. This reduction in coil size also leads to a decrease of the effective self-diffusion constant of the chains with time after the quench. We refer the reader to the original literature [155] for further details. It is quite clear, that with respect to simulations of spinodal decomposition of polymers only modest first steps could be taken, but this work already has yielded stimulating insight into various effects that need to be considered in the future. 

Effects of Ionic Strength. Figure 13 illustrates the effect of NaCl concentration on intrinsic viscosity for each terpolymer. Of course, this experiment should demonstrate only the effects of added electrolyte on individual chain contraction or expansion. The chains with sufficient monomer pairs exhibit increases in viscosity as expected with addition of NaCl. The best chain expansion is seen for the 5-5 sample, which is rapidly solvated with increasing ionic strength. The 5-10 sample shows some typical polyelectrolyte behavior because it has an excess of macroanions at pH 7. 

Peng et al. [130] used the complexation of the HPAM chains in CaCl2 aqueous solution to investigate the complexation-induced transition from intra-chain contraction to interchain association over a wide range of the hydrolysis degrees and Ca++ concentrations as well as the structure of the HPAM/Ca " ... 

As seen in Table 2.1, the change in C > with temperature is small. Polyethylene chains contract on heating since the shorter gauche conformations become more numerous at higher temperatures because of energetic considerations. This chain contraction with increasing temperature was previously discussed in this chapter (Section 2.7). 

According to Lacks and Rutledge, the increase in entropy associated with chain contraction makes a minor contribution (c. 25%) to the negative axial thermal expansion. In the following, all the major investigations carried out on the thermal expansion of polymer liquid crystals, particularly TPLCs, are given in detail. The dependence of oCi on temperature and draw ratio is also discussed. 

Also, when copolymers of polystyrene and 4-(methacryloyl-amino)azobenzene containing 2.2-6.5% of the latter are irradiated in a cyclohexane soluticMi with 15 flashes of 347 nm of Ught. The polymeric chains contract [221], This occurs at a high rate per second as a consequence of isomerization. At a later stage, several hundred seconds after the flash, there is evidence of polymer aggregation and precipitation [221], In addition, when azobenzene residues are introduced into the main chain of poly(dimethylsiloxane), reversible solution viscosity changes can be obtained by irradiation with ultraviolet light [221],... 

Ilg. 7J2. Explanation of the stress relaxation after large step strain, (a) Before deformation the conformatian of the fnimitive chain is in equilibrium (r = —0). (b) Immediately after deformation, the primitive chain is in the afiindy deformed conformation (t = -1-0). (c) After time Tj, the primitive chain contracts along the tube and recovers the eqi brium contour length (t Tj,). (d) After the time Xj, the primitive chain leaves the deformed tube by reptation (t Xa). The oblique lines indicates the deformed part of the tube. Reproduced from ref. 107. 

Viovy et argued that as the contour length of the surrounding primitive chain contracts, there will be an extra relaxation by the release of the topological constraints. They proposed a theory which gives a slightly different relaxation behaviom for Though this proposal... 

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