Conformational Statistics Research Articles

The conformational statistics of pectic acid

AbstractThe effect of random insertions of 1,2‐linked a‐ and β‐L‐rhamnose units on the characteristic ratio of a 1,4‐linked poly‐a‐D‐galacturonic acid molecule was investigated. In each case the characteristic ratio decreases dramatically as the proportion of rhamnose units is increased, the effect being more marked with the β sugar than with the a sugar. The effect is interpreted in terms of kinks which are introduced into the chain by the insertion of the rhamnose units.

Molecular Theories of Rubberlike Elasticity and Polymer Viscoelasticity

Abstract The foundation for nearly all the molecular theories of the physical properties of polymers was laid in 1934 when Guth and Mark and Kuhn first recognized the role of configurational entropy of polymer chains. By virtue of ability of their segments to rotate with respect to each other along the chain backbone, macromolecules are capable of assuming a myriad of conformations. It is this long, flexible chain nature of polymer molecules that provides us a link in interpreting the macroscopic physical properties in terms of microscopic molecular dynamics. In this review we shall demonstrate the utilization of conformational statistics in the formulation of molecular theories for two important aspects of the mechanical properties of polymers. The first part deals with the equilibrium elastic response of a crosslinked rubberlike network. A simplified derivation will be given on the basis of the entropic approach. Some of the underlying assumptions will then be examined, and the contribution of internal energy to rubber elasticity scrutinized. The second part describes the transient viscoelastic properties of linear polymers in solution and in bulk. Limitations of the model will be assessed and its applications to experimental data explored. It should be pointed out that a number of reviews are available in the literature both for elasticity and viscoelasticity of polymers. The present work is not an exhaustive review of these fields, but rather concentrates on the more recent developments not previously discussed. The emphasis will be placed upon polymers in the bulk state, although solution properties will be mentioned where appropriate.

Conformational Statistics of 1,3- and 1,4-Linked Homopolysaccharides

Conformational Statistics of 1,3- and 1,4-Linked Homopolysaccharides

Conformational energy calculations on alginic acid. II. Conformational statistics of the copolymers

AbstractConformational energy maps have been calculated for α‐D‐mannuronic acid (1–4) α‐L‐guluronic acid and for α‐L‐guluronic acid (1–4) β‐D‐mannuronic acid. These have been used, together with maps previously calculated for the homomonomeric dimers, to estimate the characteristic ratios and Kuhn lengths of the alternating copolymer and of a stochastic copolymer similar in composition to that extracted from L. digitata.The results show that the alternating copolymer is less extended than either homopolymer. Kuhn lengths calculated for the stochastic copolymer agree well with experimental results on high ionic strength solutions of alginate isolated from L digitata.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 4. Calculation of cyclic trimer content of poly(ethylene terephthalate)

The equilibrium concentration of cyclic trimer in poly(ethylene terephthalate) ( pet) melts is calculated by the Jacobson and Stockmayer theory using rotational isomeric state models to describe the conformational statistics of the corresponding linear chains. The Williams and Flory rotational isomeric state model of pet is used for the calculations, together with a model which incorporates structural information made available by a recent study of internal rotation in ethyl formate. This latter model takes into account all the intramolecular interactions within monomeric units by considering interactions that depend on rotations about monads, diads and triads of skeletal bonds. The models define 26244 discrete conformations for the acyclic trimer (CO.C 6H 4.CO.O.CH 2.CH 2.O) 3. The probability that such a chain will intramolecularly cyclize is calculated by computing the total number of conformations that have terminal atoms in close proximity for ring closure, each conformation being accorded a statistical weight based on molecular structural information relating to low molecular weight analogues and on estimates of the steric and electrostatic attractions and repulsions between non-bonded atoms of the chain. The rotational isomeric state models predict the cyclic trimer content of pet melts at 570 K to be 0.1–0.5% by weight (compared with the experimental value of 1·4%) and they give values of the ratio [ 〈r 2〉 0 M ] ∞ of the unperturbed mean-square end-to-end distance of pet to its molecular weight of 0.9–0.6Å 2(g mol.wt.) −1 at 303K (compared with the experimental value of 1·0).

Behavior of Macromolecules on the Phase Boundary. II. Conformational Statistics of the Linear Chain in a Pore

The pseudodiffusion equation with a term added by the author to describe the effect of the field of force has been employed in the calculations of the partition function and equilibrium concentration of a dilute solution of linear polymer in pores, the walls of which are formed by a swollen gel and are therefore partly permeable to chainlike macromolecules. The effect of surface forces near the walls of the pores has also been considered. In this way, Casassa's equilibrium theory of gel permeation chromatography (GPC) formulated for pores with inert impermeable walls has been generalized. To simplify the calculations, a quasistationary approximation has been proposed and employed. The equilibrium concentration difference between a pore and the bulk phase of solution is a result of two antagonistic phenomena; i.e., of the decrease in the number of conformations in the walls of the pore, and of attractive adsorption forces. Its sign depends on the values of the following expressions: (d / b)2(φA / kT), φA / φG, and (ν − 1)d / (L − d), where d is the thickness and φA is the potential of the layer of adsorption forces, b is the length of the chain segment, φG is the potential characterizing the interaction of the linear polymer with the gel, L is the radius of the pore, and ν is the geometric characteristic of the pore (ν = 1 for a plane-parallel pore, ν = 2 for a cylinder, ν = 3 for a sphere).

A random-walk model for hydrocarbon-type chains with short-range correlations

The conformational statistics of a normal alkane-type chain is studied by describing a random walk on a diamond lattice. The progress of the chain is governed by two probability parameters. The mathematical methods of a Markoff chain are used to calculate the expected square of the end-to-end distance for an oriented chain. The problem of excluded volume is not considered.

MOLECULAR THEORIES OF RUBBER-LIKE ELASTICITY AND POLYMER VISCOELASTICITY

Abstract The foundation for nearly all the molecular theories of the physical properties of polymers was laid in 1934 when Guth and Mark [I], and Kuhn [21 first recognized the role of configurational entropy of polymer chains. By virtue of ability of their segments to rotate with respect to each other along the chain backbone, macromolecules are capable of assuming a myriad of conformations. It is this long, flexible chain nature of polymer molecules that provides us a link in in terpreting the macroscopic physical properties in terms of microscopic molecular dynamics. In this review we shall demonstrate the utilization of conformational statistics in the formulation of molecular theories for two important aspects of the mechanical properties of polymers. The first part deals with the equilibrium elastic response of a cross-linked rubber -like network. A simplified derivation will be given on the basis of the entropic approach. Some of the underlying assumptions will then be examined, and the contribution...

Dielectric dispersion in solutions of flexible polymers

Abstract