Unperturbed Coils

In this section an unperturbed coil refers to the condition of immobilized solvent in the interior of the molecular domain. This is a hydrodynamic criterion and leads to Eq. (9.42). 

In earlier chapters an unperturbed coil referred to molecular dimensions as predicted by random flight statistics. We saw in the last chapter that this thermodynamic criterion is met under 0 conditions. 

The exponent can vary from v=0.33 for hard spheres up to v=1.0 for rigid rods. For linear chains v=0.5 refers to unperturbed coil dimensions in -solvents and v=0.588 [6] to good solvent conditions. Equation (37) maybe re-writ-ten by expressing the molar mass as a function of the radius of gyration, i.e.. 

In some specific cases, dissolved macromolecules take up the shape predicted by the above theories of isolated chain molecules. In general, however, the interaction between solvent molecules and macromolecules has significant effects on the chain dimensions. In poor solvents, the interactions between polymer segments and solvent molecules are not that much different from those between different chain segments. Hence, the coil dimensions tend towards those of an unperturbed chain if the dimension of the unperturbed coil is identical to that in solution, the solution conditions are called conditions (ff solvent, temper-... 

We fch.ua take the segment size smaller and. smaller, at the same time increasing the number of segments so as to keep the unperturbed coil size rv constant. Thus... 

For the purpose of determination of the temperature coefficient for unperturbed dimensions of copolymer 3 (Table 1), [r ] values were measured in the same solvent (toluene) at different tempe-ratures. In accordance with the Shtockmayer-Fixman method, Kg=(/M)1/2xF0 values was deter-mined using the least-square technique. The temperature coefficient of unperturbed dimensions was calculated from the values obtained at different temperatures (Table 6) using the relation, suggested in the work [45] dinldT = 2/3x1 n A/ t//-. The coefficient of unperturbed coil dimension (dlnldl), determined for copolymer 3 (Table 1), equals 0.85xl0 3 deg"1 [44],... 

A reversible transition from a swollen to unperturbed coil and further to a more compact globule-like conformation of polystyrene on cooling its diluted solutions in cyclohexane below the -temperature is well documented by viscosimetric measurements [142, 144], determination of... 

It seems appropriate to discuss here the probabUity of interpenetration of polystyrene coils in the model networks. As already mentioned, according to the theoretical considerations of Flory [138] and De Gennes [139], polymeric coils in an amorphous solid state retain unperturbed dimensions. Since the volume fraction of the polymer in an unperturbed coil under -conditions is weU known to be very smaU, only about 2%, the transition from swoUen coils to solid state has to be accompanied by the replacement of aU solvent molecules with fragments of other polymeric molecules. In other words, theoretical notions predict extremely high mutual interpenetration of the polymeric chains in bulk state. Indeed, in order to maintain the coil dimension that is characteristic for a -solution, the coil must accommodate, on removing the solvent, a 50- to 100-fold amount of alien polymeric matter. In the 1970s this problem was discussed in fiiU [149-165], The authors of the tailor-made networks also took part in the discussion. 

In analogy to previous results [107, 114—120], all PS films on such substrates turned out to be metastable and ruptured upon annealing at elevated temperatures. The number density of holes increased rapidly with decreasing film thickness [107]. We concentrated on the shape of these holes and its evolution with time at temperatures above about 103°C. Complementary experiments indicated, however, that hole formation was also possible at lower temperatures [162]. As discussed previously [4, 17], hole formation may also reflect the relaxation of internal tensions induced during sample preparation and caused by confining the polymers to films thinner than the size of the unperturbed coil. 

The expansion factor is unity for an unperturbed coil. The larger a/ , the greater is the expansion and the better the solvent is for the polymer. 

The steric hindrance parameter o measures the hindrance to rotation about main chain bonds, and, so, is a measure of the thermodynamic flexibility of the coiled molecule. It can be calculated from the radius of gyration of unperturbed coils via Equations (4-29) and (4-27) if the bond length, valence angle, and number of main chain bonds is known. 

The persistence length model therefore describes the whole spectrum from the more rodlike oligomers (small j) to the well-developed coils (large y). However, the model ignores the finite thickness of the chain, and so it only holds strictly for unperturbed coils. The error due to the finite thickness may be neglected when the persistence length is much greater than the chain thickness. 

The first term on the right-hand side of Equation (4-51) is a characteristic constant for the unperturbed coil, as can be seen from equation (4-26). Since (Rg oIM is Si function of the hindrance parameter a, it is a measure of the short-range interactions. Conversely, the slope contains the constant... 

An important length-scale associated with polymer solutions is the root-mean-square radius of the polymer coil in the solution. For an unperturbed coil, this is known as the unperturbed radius of gyration, / g, and is given by the following (1) ... 

Unperturbed coil dimensions in solution are equal with those of macromol-ecirles in amorphous sohd state. 

Beyond the screening length the volume exclusions have been completely screened out due to the interpenetration of polymer coils. Therefore, the chain can be regarded as an unperturbed coil formed by blobs with the unit size and then... 

According to this intramolecular-nucleation model, when the melt of long-chain macromolecules is quenched to low temperatures for fast crystallization, each macromolecule may perform multiple local intramolecular nucleation events and hence will be included in several lamellae or several positions of the same lamellae, with only little changes of their unperturbed coil-size scaling. At each position, intramolecular nucleation yields folded-chain clusters. This picture is quite consistent with Hoffman s proposition of a variable-cluster model for the conformation of macromolecules in the semi-crystalline state [50[. 

The same approximation gives the difference between the free energies of a globule and an unperturbed coil without excluded-volume effects... 

Both the theoretical and experimental studies have shown the macromolecule sizes near the critical point to be comparable with the size of an unperturbed coil at the tf-state, and /M. 

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