Polymer chains, configuration

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

Figure 7.4 Polymer chain configurations at crystallite surfaces ...

Although the general picture can be drawn, several problems must be solved that arise from the interaction of polyelectrolytes (polycation and polyanion) with ions (MV2+ and EDTA). These interactions bring about changes in polymer chain configuration. This effect is manifested by the... 

The simplest mechanisms leading to the dispersion (spreading) of a zone s molecules can be described by the classical random-walk model [9], as noted in Section 5.3. However this model does not fully account for the complexities of migration. It gives, instead, a simple approximation which inherits the most essential and important properties (foremost of all the randomness) of the real migration process. The random-walk model has been used in a similar first-approximation role in many fields (chemical kinetics, diffusion, polymer chain configuration, etc.) and is thus important in its own right. 

Figure 2-2 Polymer chain configurations of atactic, isotactic and syndiotactic polymers.

Proton NMR spectroscopy has been used fruitfully for many years in the analysis of polymer chain configuration (i). The proton solution spectra (2) for poly(methyl-n-propylsilylene) (PMPS), poly(methyl-n-hexylsilylene) (PMHS), poly(methyl-n-dodecylsilylene) (PMDS), and poly(di-n-hexylsil-ylene) (PDHS) are shown in Figure I, At this high field (11.75 T), the res-... 

Flory, P. j. Treatment of the effect of excluded volume and deduction of unperturbed dimensions of polymer chains. Configurational parameter for cellulose derivatives. Makromol. Chem. 98, 128 (1966). 

Peterlin-Tschoegl Method. The Zimm theory is constructed on the assumption that the polymer chain configurations follow a Gaussian distribution and hence the average distance between the i-th and the j-th elements satisfies a relation... 

Tip 2 Chain stereoregularity and active sites. In free radical polymerization, polymer chain configuration and MWD are often independent of initiator type and initiation mechanism, depending strongly on reaction temperature, initiation rate, and monomer concentration. One can, therefore, often predict chain stereoregularity and MWD without a detailed knowledge of the initiation mechanism. 

Fig. 5.2 Schematic representation of functional polymer chains configured on a cubic lattice. The darker cubes indicate a lattice site occupied by a functional end group, and the lighter cubes are occupied by polymer chain segments (a) illustrates a chain with a low-energy attractive end group, (b) depicts a nonfunctional polymer with neutral end groups. Reproduced with permission from [54]...

Figures 9 and 10 show that both the low-shear relative viscosity and the power-law index approached limiting values with increasing NaCl concentration. These results indicate that there is a lower limit for the hydrodynamic radius for the polymer chain beyond which all the charges on the polymer chain are completely shielded with the cations. Increasing NaCl concentration further will not change the polymer chain configuration and, as a result, the relative viscosity of the polymer solution remains constant. Figures 9 and 10 also show that the limiting values for the relative viscosity and the power-law index are functions of polymer concentration.

P. Love, R. Sugimoto and Yoshino. The NMR spectrum of poly(3-alkylthiophene)s and polymer chain configuration. Jpn. J. Appl. Phys., Part 2 27(8), L1562-L1564 (1988). 

The first question is impossible to answer because there are far too many possibilities at the molecular level, as we have just seen with polymer chain configuration. With regards to their physical state, however, they do, collectively, have a fixed ... 

Constructing and equilibrating molecular-level polymer configurations are described in detail in the literature [129-135]. Such techniques are important because much longer times than can be achieved in practice are required in order to equilibrate the entire chain, starting from a random configuration in a room-temperature simulation. The objective of those methods is to ensure that representative polymer chain configurations are used for the sorption and diffusion calculations. 

The quantity P is a constant for a given series of polymer homologs. Equations (5.19a) and (5.19b) are Flory s theory to describe the polymer chain configuration, de Gennes commented that because of the assumption of Gaussian distribution with respect to R )q, Flory s theory is still intrinsically a random-flight chain in nature. 

Statistical-mechanical treatments of polymer adsorption at a planar surface have been pursued extensively using both analytical and Monte Carlo techniques. These procedures place polymer chain configurations in a one-to-one correspondence with random walk configurations on a lattice. While the analytical methods are limited to massless segments, and the Monte Carlo techniques are restricted to relatively short chains because of computational limitations, both provide results capable of experimental verification. The restriction to dilute solutions and non-interacting adsorbed molecules has been circumvented in recent theoretical treatments of concentrated pol3nner solutions. 

Cornell was a scientifically exciting place in the 1940s. Debye was leading a good corps of researchers in many directions. Since the random coil model was now an accepted paradigm, Debye explored the quantitative aspects of polymer chain configurations. He related the mean-square end-to-end distance and the... 

The solvent molecules are not modelled explicitly in a BD model. The forces applied on each repeat unit from the solvent molecules are collisions and frictions. They can be virtually expressed by the friction term (thermodynamics drag term) and the noise term (Brownian force term) in Equation [8.32] or [8.33] for different polymer chain configuration models. 

---