Average Chain Dimensions

CALCULATION OF AVERAGE DIMENSIONS FOR VARIOUS POLYMER CHAIN STRUCTURES... 

The chemical structure of a polymer chain determines its statistical properties, such as its average dimensions in space and its flexibility. These parameters, in turn, affect various properties of a network consisting of these chains. A detailed understanding of the single chain is therefore important in this regard. 

We could say quite generally that the average dimension of a chain is linear in the link length but is some function of N, f(TV) ... 

A further expansion of the average dimensions of the coil results when one assumes that rotation around single bonds is not free but is still independent of the rotation around the adjacent bonds. Let us take as an example a polyethylene chain On the base of each of the two cones of formula 70, three positions are identified, T, G", and G, differently populated according to the energy difference E = Eq — Ej and the temperature. The characteristic ratio is then written ... 

The Monte-Carlo method is utilized to investigate the conformational distribution in the central section of a PIB decamer at various temperatures. It is checked that a six-state RIS model based on the two matrices P and Pj constitutes a description of the conformational distribution in PIB. The Monte-Carlo results are in excellent agreement with the experimental data on the average dimensions of PIB chains, as well as with the molecular scattering functions of this polymer in solution and in bulk. 

N 110 "Spatial Configurations of Polynucteotide Chains. II. Conformational Energies and the Average Dimensions of Polyribonucleotides"... 

Smith, Ciferri and Hermans (159) have used a similar series expansion as Wang and Guth but followed the — in our opinion preferable — HFW-type derivation (see Section III-l). It may be recalled that in the HFW treatment, only the average dimensions of the chains are required to follow the macroscopically imposed strain. Introducing again the A and B factors (see Eq. III-9), their result reads ... 

The average dimensions, or other statistical properties of the polymeric chains, are then calculated, allowing for the relative probabilities of the rotational states and making full allowance for the mutual interdependence of adjacent pairs of bond rotational states. Parameters required for the models are normally obtained from molecular structure data and from experimental information relating to the statistical conformations of the polymeric chains. Further references to rotational isomeric state models will be made later. 

The unperturbed average dimensions of polyacrylate chains would thus be only slightly dependent upon ionic strength, the characteristic ratio, value at 15° ranging from about 11 to 13 going from... 

If the universal constancy of is accepted, it is possible to calculate the average dimensions of polymer molecules in solution merely from knowledge of their intrinsic viscosities and molecular weights. More particularly, it is possible to calculate the natural, or unperturbed, dimensions of the polymer chain from the knowledge of intrinsic viscosity in a theta solvent [28,29]. 

In this Section, the general characteristics of the conformation of a polymer molecule in solution are considered. The general model for a linear polymer molecule in solution is based on a randomly coiled, flexible chain, the average form of which possesses spherical symmetry. The distribution of chain ends about the center of this sphere is further supposed to be Gaussian. Since the total number of conformations which the macromolecule may adopt is exceedingly large, only an average dimension can... 

The maximum energy released during the primary opening of such a microcrack with average dimensions about 100 A (average diameter of microfibril) is about 10" erg if one takes for the chain E =... 

Any physical property of a polymer molecule that depends on its conformation can ordinarily be expressed as a function of some sort of average dimension. The polymer dimension that is most often used to describe its spatial character is the displacement length, which is the distance from one end of the molecule to the other. For the fully extended chain, this quantity is referred to as the contour length. Given the extremely large number of possible conformations and number of chains, a statistical average, such as the root-mean-square end-to-end distance, (rj), is required to appropriately express this quantity. 

---