Conformational States in Polymers

The barriers separating the three conformational states have heights several times the thermal energy, kT, which means that the lifetime in a given state will be much longer than the vibration periods within the well. The quantity k is Boltzmann s constant. The sequence of bond conformations at a given instant defines the rotational isomeric state of the chain. 

Helfand and co-workers investigated the various transitions among the conformational states by means of computer simulations (3031) and by applications of a kinetic theory (32-34). This analysis yielded the details of the long periods of motion near the bottom of the conformational wells, and the occa- 

One surprising finding was that the transitions frequently occur in pairs, cooperatively. Immediately following the transition of one bond, a strong increase in the transition rate of its second-neighbor bonds was found. The intermediate bond usually remained unchanged. Thus the transitions might be 

The significance of this observation arises from the geometric properties of the two transitions. In both cases the first two and last two bonds translate relative to each other in opposite directions. Except for the central bond, the final state of each bond is parallel to its initial state. The cooperative pair transitions of equations (2.37) and (2.38) greatly reduce the motion of the long tail chains attached to the rotating segment, and hence the frictional resistance that the tails would present to the transition (28). 

The trans-gauche transitions underlie the diffusional motions of de Gennes (Section 5.4), the Shatzki transition (Section 6.4.1), and the glass transition itself. 

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This chapter would not be complete without a further discussion of the various conformational states in polymers (28-34). The rotational potential energy diagram (Figure 2.11) (23) indicates three stable positions or conformations— the trans, the gauche plus, and the gauche minus. 

The synthesis of optically active polymers was tackled with the purpose not only of clarifying the mechanism of polymerization and the conformational state of polymers in solution, but also to explore the potential of these products in many fields as chiral catalysts, as stationary phases for chromatographic resolution of optical antipodes, for the preparation of liquid crystals, and so on. 

The fragments of macromolecules with ordered cholesterol group sequences, that are formed in bad solvents, may serve as nuclei of supermolecular order in films, obtained from these solvents. Structural and optical studies have shown that PChMA-11 films produced by solvent evaporation display different properties those obtained from chloroform and toluene solutions (small relaxation times, see Table 17) are optically isotropic, and those obtained from heptane solutions (large relaxation times, see Table 17) are optically anisotropic, what reflects the differences in conformational state of polymeric chains in these films. Contrary to the optically isotropic films, a high degree of side branch ordering characterizes optically anisotropic films, which is confirmed by X-ray studies. The observed difference of LC polymer structure in the bulk is thus the consequence of their different conformational state in solution this reveals some possibilities for the control of LC polymer structure at the initial steps of mesophase nucleation in solutions. 

If the interaction forces between polymer and solvent molecules can be neglected (the so-called -solution) the polymer molecule is in an unperturbed conformational state. In this situation, the molecular dimensions and the limiting viscosity number can be predicted rather accurately. For a normal dilute polymer solution, however, only approximate values of these quantities can be estimated. 

C, the dipolar interaction is not responsible for the large peak width for the amorphous phase in this case. The chemical shift is affected by the conformation of the polymer. In the amorphous phase, the polymer chain takes several con-formers or makes rapid transitions between a number of conformational states. In this case, the distribution of the conformation contributes to the peak width of the amorphous phase. 

In addition, conformational disorder in polymer crystals may give rise to point and line defects which are tolerated in the crystal lattice at a low cost of free energy as kinks [104,105], jogs [106,107] and dislocations [108,109]. Such crystallographic defects arise whenever portions of chain adopt conformations different from the conformation assiuned by the chains in the crystal state [99], and have been widely discussed in the literature, in the case of polyethylene [108,109] and some aliphatic polyamides [99,106]. Point and... 

Now let s look at the quantity xab- This quantity appears for many different processes in solution, or at interfaces, or for conformational changes in polymers. The exchange parameter xab describes the energetic cost of beginning with the pure states of A and B and transferring one B into a medium of pure A s and one A into a medium of pure B s (see Figure 15.6) ... 

Again we assume that the polymer can be in one of two conformational states in equilibrium... 

Long-chain molecules can exist in either one of two states. These are characterized by the conformation of the individual molecular chains and their organization relative to one another. The liquid state is the state of molecular disorder. In this state, the individual chains adopt a statistical conformation, commonly called the random coil. The centers of mass of the molecules are arranged randomly relative to one another in this situation. All the thermodynamic and stmctural properties observed in this state are those which are commonly associated with a liquid, although usually a very viscous one. This state exhibits the characteristic long-range elasticity. The liquid state in polymers is also commonly called the amorphous state. 

Wobser, G., Blasenbrey, S. (1970) Structural and conformational calculation in polymers. 2. Ideal crystal and defective state (bundle model) in polyethylene. Kolloid-zeitschrift, 241, 985. 

The rotational isomeric state approximation, which is a convenient procedure for dealing with the conformational states of polymers, was introduced by Flory. Each molecule is treated as existing only in... 

Polymer molecules are found in a preferred conformational state in crystals. The experimental techniques for determining the preferred conformation are mainly X-ray and electron diffraction. The difficult determination of the crystal unit cell must be followed by further molecular mechanical modelling to establish the exact chain conformation. 

In what kind of conformational state are polymers in a (i) good solvent, dilute solution (ii) theta solvent, dilute solution (iii) good solvent, semi-dilute solution (iv) molten state ... 

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