Dimensions of macromolecules

Polymers differ from small molecules in that the space-filling dimensions of macromolecules are not fixed. This has some important consequences, one of which is that certain polymers behave elastically when they are deformed. The nature of this rubber elasticity and its connection with changes in the dimensions of elastomeric polymers are explored in this and the subsequent section of this chapter. 

In spite of the considerable difference in experimental and theoretical results obtained by different authors for the dimensions of macromolecules of aromatic polyamides, these results indicate a sharp asymmetry of the macromolecules. It should be pointed out, for the sake of comparison, that for flexible chain polymers the Kuhn segment amounts to only 20-50 A. For example, for an aromatic polyamide which does not exhibit coaxial rotation of the bonds, poly(m-phenylene isophtalamide), the Kuhn segment is equal to 50 A, i.e. it is 10-15 times as small as that for its para-analog. 

To measure the dimension of macromolecules is a very delicate task. However, the dimension is a primary parameter needed to understand the physical properties of a macromolecule. We have described two experimental methods, MALS and SEC, to measure sY on-line to a SEC system. 

Similarly, the hydrodynamic size of polymer coils, expressed as the radius of gyration under the critical conditions, also depends on the eluent nature [67]. Thus, the critical conditions can not be related to a specific molecular conformation of PS and the hydrodynamic dimensions of macromolecules with the same molar mass are different in various mixed mobile phases corresponding to CEEC. 

Equation 10 shows that in the small coverage limit the dimension of macromolecules covered with surfactant increases slightly with a. In the high coverage limit, a complex is described as a wormlike chain with persistent length... 

The behaviour of diluted solutions is related to the relation between the viscosity and the chain characteristics (structure, configuration, conformation, etc). Usually, the polymer solutions are treated as two-phase systems, consisting from mechanical elements, the macromolecules, immersed into a continuous media, the solvent. For long time, it was considered that the solvent acts to the polymer macromolecules in the same manner in which a fluid exerts forces about a small particle suspended in it. However, the extension of this model to the polymer solution is not adequate since, the ratio between the dimensions of macromolecules and those of solvent molecules essentially differs by that between the dimensions of a solid immersed particle and solvent molecules. On the other side, the flexible macromolecules, randomly coiled, can not be assimilated with the solid particles and therefore the typical relations applied to solid suspensions in liquids can not be used in this case. 

Another technique to study the dimensions of macromolecules on the basis of their charge properties is electric birefringence. In flow birefringence macromolecules were aligned with the help of hydrodynamic shear. In electric birefringence an electric field is used to align the macromolecules and the alignment is determined by the electrical properties of the molecules. 

Hiller, A. Wall, F.T. Wheeler, D.J. Statistical computation of mean dimensions of macromolecules. J. Chem. Phys. 1954, 22, 1036. 

The shape and dimension of macromolecules in the adsorption layer depend on the nature of polymer, surface, and solvent quahty. 

H. Polymolecularity Correction Factors for the Determination of the Dimensions of Macromolecules... 

Deteimination of Unperturbed Dimensions of Macromolecules VII / 241 TABIE 70. POLYMOLECULARITY CORRECTION FACTORS AND FOR BURCHARD-STOCKMAYER -FIXMAN PROCE-... 

---