Free chains

Flory (1953) has presented a celebrated theory of the excluded volume effect that relates the expansion factor to the thermodynamic properties of the polymer-solvent system. Basically what Flory calculated was the free energy of mixing of polymer segments with solvent that is associated with the expansion of the coil dimensions in a good solvent. Such expansion is opposed, however, by the loss of configurational entropy of the chain. The latter corresponds, of course, to an elastic contractive force. Expansion proceeds until the two opposing effects are in equilibrium. Flory s result was 

In these equations, A/=molecular weight, Xi= interaction parameter, V2=partial specific volume of the polymer, Ki =molar volume of the solvent and r o=unperturbed rms end-to-end dimensions. 

Note that for polymer in the bulk, is very large. This means that Cm 0 just as it is if X1 =i- Accordingly, a = 1 in the melt, a result that is identical with that for a 0-solvent. The expansion factor a increases slowly without limit with increasing molecular weight M. 

There has been a proliferation of theories of the excluded volume problem using a variety of methods to decouple the many-bodied problem. Their results can be summarized crudely by 

Comparison of equations (4.27) and (4.28) shows that the Flory theory in near 0-solvents predicts a numerical coefficient (2.6) that is too large by most a factor of 2. Stockmayer (1955 1960) has therefore suggested that Flory s original equation should be arbitrarily adjusted so that 

---

Similarly to LB films, the order of alkanetliiols on gold depending on temperature has been studied witli NEXAFS. It was observed tliat tire barrier for a gauche confonnation in a densely packed film is an order of magnitude higher tlian tliat of a free chain [48]. 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

Chains of polybutadiene were trapped in the network formed by cooling a butadiene-styrene copolymer until phase separation occurred for the styrene, effectively crosslinking the copolymer. At 25°C the loss modulus shows a maximum which is associated with the free chains. This maximum occurst at the following frequencies for the indicated molecular weights of polybutadiene ... 

FIG. 22 (a) Log-log plot of the scaling function vs C = upper curves refer to the mean-square end-to-end distance, R, while the lower ones show results for i g. (b) The same vs scaling variable N "Region I— free chains, II—crossover, and III—renormaUzed free chains. The slope 0.6 corresponds to l cross = 0.78. [20]... 

One of the signatures of densely tethered chains is expressed in Eq. 5, namely the linear variation of L with N. This stands in marked contrast with free chains where excluded volume interaction produces, at most, an R N3/5 distortion from the R N1/2 unperturbed dimensions. Tethered layers are stretched and this is the origin of their interesting behavior. 

The linearity of L with N is maintained at the theta point. Relative to Eq. 5, the chains have shrunk by a factor of (a/d),/3 but the linear variation indicates that the chains are still distorted at the theta point and characteristic dimensions do not shrink through a series of decreasing power laws as do free chains [29-31]. Experimentally, Auroy [25] has produced evidence for this linearity even in poor solvents. Pincus [32] has recently applied this type of analysis to tethered polyelectrolyte chains, where the electrostatic interactions can produce even stronger stretching effects than those that have been discussed for good solvents. Tethered polyelectrolytes have also been studied by others [33-35],... 

A more accurate analysis of this problem incorporating renormalization results, is possible [86], but the essential result is the same, namely that stretched, tethered chains interact less strongly with one another than the same chains in bulk. The appropriate comparison is with a bulk-like system of chains in a brush confined by an impenetrable wall a distance RF (the Flory radius of gyration) from the tethering surface. These confined chains, which are incapable of stretching, assume configurations similar to those of free chains. However, the volume fraction here is q> = N(a/d)2 RF N2/5(a/d)5/3, as opposed to cp = N(a/d)2 L (a/d)4/3 in the unconfined, tethered layer. Consequently, the chain-chain interaction parameter becomes x ab N3/2(a/d)5/2 %ab- Thus, tethered chains tend to mix, or at least resist phase separation, more readily than their bulk counterparts because chain stretching lowers the effective concentration within the layer. The effective interaction parameters can be used in further analysis of phase separation processes... 

The importance of polydispersity is an interesting clue that it may be possible to tailor the weak interactions between polymer brushes by controlled polydispersity, that is, designed mixtures of molecular weight. A mixture of two chain lengths in a flat tethered layer can be analyzed via the Alexander model since the extra chain length in the longer chains, like free chains, will not penetrate the denser, shorter brush. This is one aspect of the vertical segregation phenomenon discussed in the next section. 

For density values g > 0.92 g/cm3 the deformation modes of the crystals predominate. The hard elements are the lamellae. The mechanical properties are primarily determined by the large anisotropy of molecular forces. The mosaic structure of blocks introduces a specific weakness element which permits chain slip to proceed faster at the block boundaries than inside the blocks. The weakest element of the solid is the surface layer between adjacent lamellae, containing chain folds, free chain ends, tie molecules, etc. 

Regiodefects are less readily incorporated into crystallites than defect-free chain sequences. In semicrystalline polymers, increasing levels of misinsertion result in reduced crystallinity. This can affect numerous physical properties, resulting in reduced modulus, lower heat distortion temperature, and decreased tensile strength. 

To follow the crystallization of kebabs around a shish, the dynamics of 10 short chains (N = 180) near a preformed shish (from 7 chains of length N = 500) were followed at T = 9.0, by fixing the center of mass of the shish. The initial position of the short free chains was chosen at random in a cylinder around the shish, with radius 30ro and a height of 60ro. Each rim started with different initial conditions. Figure 29 shows one such initial state. 

The distribution of the thi monomer in molecular chains or in the whole polymer should affect the perfection of the vulcanizate network, free chain ends or the uncross-linked parts in the polymer making no contribution to the tensile strength but acting as a plasticizer of like structure as the polymer. 

Here x=qNb/6=qR where Ru is the radius of an undeformed Gaussian random flight chain. I deriving Eq. 10, the sum in Eq. 7 is replaced by an integral. The effect of the free chain segments, exclusive of the position of the junctions appears in the first two terms in the exponential. The deformations of the chains depend on the constraints on the junctions. Results are immediately derivable from Eq. 10. 

The polarized emission experiments on partially photooxidized aligned PF films indicate that the emission from the keto defects exhibits a somewhat smaller polarization ratio than the blue emission from the defect-free chains [263]. This observation was explained with the support of quantum mechanical calculations, which showed that the polarization of the fluorenone emission is influenced by local disorder [263]. 

The second theory is the Keele theory proposed by Plesch and Westermann [2, 4, 5] in which the propagation reaction is seen as a ring-expansion during which no free chain-end is formed ... 

Fd h = 0) should increase as when the chain concentration increases. A very different picture is predicted in the case of adsorbing polymers [49]. The layer of adsorbed chains may be partially interpenetrated by free chains in the bulk and therefore the range and strength of the attraction are not determined by the solution concentration. Instead, they are rather sensitive to the coverage and thickness of the adsorbed chains which depend essentially on the solvent quality and on the mean chain length in the dilute regime. 

It is believed that the surface structure of the porous packing material plays an important role. The presence of the free chain ends of styrene-divinylbenzene copolymer may prevent the movement of the macromolecules in the pore. 

It is possible that either Me has increased by degradation of the network structure or the resin is internally plasticized by free chain ends. If Me has increased, then the modulus in the rubbery plateau region for irradiated specimens should be less than that of a control. As discussed above, E (Tg+40) decreases up to a dose of 5000 Mrads. Between 5000 and 10,000 Mrads, E (Tg+40) increases but remains 6% below the control. For the 73/27 and 80/20 samples (10,000 Mrads) which have been sorbed/desorbed, E (Tg+40) is 18.5% greater than the control. 

The most noticeable property change is a decrease in the glass transition temperature of the epoxy resin as a function of absorbed dose. The decrease in Tg is due to plasticization by degradation products and free chain ends from chain scission. 

The morphologies of the large ionic clusters observed in these simulations rather suggest free chain end folding to produce rudimentary lattice structure as a possible pre transitional mechanism. 

The chain transfer by alcoholysis involves the attack of ROH on a propagating Pd-acyl to give a free chain, bearing at least an ester-end group, and a Pd-hydride species, which re-initiates the chain growth by insertion of ethene (Scheme 7.15a). 

---