Conformation of the Molecular Chain

The picture presented so far of the polyethylene chain being of a linear zig-zag geometry is an idealised one. The conformation of a molecular chain is in fact random provided that the bond tetrahedral angle remains fixed. This is best illustrated by considering a piece of wire with one bend at an angle of 109° 28 as shown in Fig. A.5a. 

If the horizontal arm is rotated about its axis, the other arm will form a cone of revolution. On the polyethylene molecule, the bent wire is similar to the carbon backbone of the chain with carbon atoms at positions 1, 2 and 3. Due to the rotation of the bond 2-3, atom 3 may be anywhere around the base of the cone of revolution. Similarly the next bond will form a cone of revolution with atom 3 as the apex and atom 4 anywhere around the base of this cone. Fig. A.5(b) illustrates how the random shape of the chain is built up. The hydrogen atoms have been omitted for clarity. 

In practice the picture can take on a further degree of complexity if there is chain branching. This is where a secondary chain initiates from some point along the main chain as shown in Fig. A.6. In rubbers and thermosetting materials these branches link up to other chains to form a three dimensional network. 

So far the structure of polymers has been described with reference to the material with the simplest molecular structure, i.e. polyethylene. The general principles described also apply to other polymers and the structures of several of the more common polymers are given below. 

Polymers can also be produced by combining two or more different monomers in the polymerisation process. If two monomers are used the product is called a copolymer and the second monomer is usually included in the reaction to enhance the properties of the polymer produced by the first monomer alone. It is possible to control the way in which the monomers (A and B) link up and there are four main configurations which are considered useful. These are  

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An increased yield stress is required [62] in order to reverse the unfavourable conformations of the molecular chains that develop during annealing. This explanation is supported by the energy changes observed in annealed polymers. The enthalpy difference, as determined by DSC was AH = 1.8 J/g (Sect. 4.2), whereas the additional work required for yielding in an annealed sample was... 

The transition state was shown to have a four-centered nonplanar structure and the product showed a strong jS-agostic interaction.59 Molecular-mechanics (MM) calculations based on the structure of the transition state indicated that the regioselectivity is in good agreement with the steric energy of the transition state rather than the stability of the 7r-complex. The MM study also indicated that the substituents on the Cp rings determine the conformation of the polymer chain end, and the fixed polymer chain end conformation in turn determines the stereochemistry of olefin insertion at the transition state.59... 

Independent of the contact geometry, the calculations also demonstrated that the introduction of gauche defects resulted in a decrease of the bridge conductance by a factor of 10, as compared to an all-trans alkanedithiol chain (see Fig. 14b, triangles). Due to variations in the number and positions of gauche defects, as well as various contact geometries, the molecular junctions can exhibit conductance values up to two orders of magnitude below the conductance values of an all-trans conformation of the alkyl chain. 

Combining 2D-NOESY and 2D-ROESY NMR experiments with molecular modelling protocols, Kuhn and Kunz32 have been able to study the saccharide-induced peptide conformational behaviour of the recognition region of Ll-Cadherin. The detailed conformational analysis of this key biomolecule not only proves that the saccharide side chain exerts a marked influence on the conformation of the peptide chain, but also that the size and type of the saccharide indeed strongly affects the conformation of the main chain. 

The secondary structure describes the molecular shape or conformation of the polymer chain. For most linear polymers this shape approaches a helical or pleated skirt (or sheet) arrangement depending on the nature of the polymer, treatment, and function. Examples of secondary structures appear in Figure 2.13. 

Cyclic oligomers with x - 2-9 are found to be present in poly(1,3-dioxolane) samples prepared by monomer-polymer-equilibrations using boron trifluoride diethyl etherate as catalyst. The molecular cyclization equilibrium constants 7fx are measured and the values are in agreement with those calculated by the Jacobson-Stockmayer theory, using an RIS model to describe the statistical conformations of the corresponding chains and assuming that the chains obey Gaussian statistics. 

Methods used to obtain conformational information and establish secondary, tertiary, and quaternary structures involve electron microscopy, x-ray diffraction, refractive index, nuclear magnetic resonance, infrared radiation, optical rotation, and anisotropy, as well as a variety of rheological procedures and molecular weight measurements. Extrapolation of solid state conformations to likely solution conformations has also helped. The general principles of macromolecules in solution has been reviewed by Morawetz (17), and investigative methods are discussed by Bovey (18). Several workers have recently reexamined the conformations of the backbone chain of xylans (19, 20, 21). Evidence seems to favor a left-handed chain chirality with the chains entwined perhaps in a two fold screw axis. Solution conformations are more disordered than those in crystallites (22). However, even with the disorder-... 

The haemoglobin molecule (Hb) has a molecular weight of about 64000. Four subunits can be identified, each consisting of a polypeptide chain to which is attached a porphyrin group (Fig. 8.6), with an iron atom near its centre. The iron atom is in the II oxidation state (high-spin d6) and is further bonded to a nitrogen atom from an amino-acid residue below the porphyrin ring. The conformation of the polypeptide chain prohibits... 

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