Chain stiffness factor

Typical physical property-area correlations obtained in these studies are shown in Figs. 1 and 2. In Figure iP the distance between chain entanglements, (in terms of the number of chain atoms) is plotted as a function of area. In Figure 2p the physical property plotted is the chain stiffness factor, cr, where = f f is the ratio of the mean-square end-to-end distance of the chain in the unperturbed condition to that which the same chain would have if it were a "freely-rotating" chain. 

The glass transition temperature of a random copolymer usually falls between those of the corresponding homopolymers since the copolymers will tend to have intermediate chain stiffness and interchain attraction. Where these are the only important factors to be considered a linear relationship between Tg and copolymer composition is both reasonable to postulate and experimentally verifiable. One form of this relationship is given by the equation... 

In general, the factor by which G is reduced depends on Me, f, chain stiffness, and the initial concentrations of reactive groups obtainable in bulk, in a manner which still needs to be resolved in detail. However, for bulk reaction mixtures, the moduli of networks with relatively flexible chain structures can be reduced by a factor of five below those expected for network formation in the absence of pre-gel intramolecular reaction. 

Several factors related to chemical structure are known to affect the glass transition tempera lure. The most important factor is chain stiffness or flexibility of the polymer. Main-chain aliphatic groups, ether linkages, and dimethylsiloxane groups build flexibility into a polymer and lower Tg Aliphatic side chains also lower Tg, (he effect of the length of aliphatic groups is illustrated by the methacrylate series (4,38) ... 

Hybrid membranes composed of poly(vinyl alcohol) (PVA) and tetraethylorthosilicate (TEOS), synthetised via hydrolysis and a co-condensation reaction for the pervaporation separation of water-isopropanol mixtures has also been reported [32], These hybrid membranes show a significant improvement in the membrane performance for water-isopropanol mixture separation. The separation factor increased drastically upon increasing the crosslinking (TEOS) density due to a reduction of free volume and increased chain stiffness. However, the separation factor decreased drastically when PVA was crosslinked with the highest amount of TEOS (mass ratio of TEOS to PVA is 2 1). The highest separation selectivity is found to be 900 for PVA TEOS (1.5 1 w/w) at 30°C. For all membranes, the selectivity decreased drastically up to 20 mass % of water in the feed and then remained almost constant beyond 20 mass %, signifying that the separation selectivity is much influenced at lower composition of water in the feed. 

In the glass transition region, both structural scales play a significant role and their effects cannot be dissociated. The crosslinking effect (macro-molecular scale) on Tg, is an increasing function of the chain stiffness, which is under the dependence of molecular scale factors (essentially aromaticity). 

E is also independent of chain stiffness and chain interactions, these factors play a role in the height of the glass-rubber transition temperature and the melting point. A stiffer chain, therefore, does not result in a stiffer polymer except, sometimes, in an indirect way, namely when stiff chains enable the formation of high orientation, such as in liquid-crystalline polymers (see 4.6). 

In reality the interactions between polymer and solvent molecules, which determine the solution viscosity, are very complicated and dependent on a great number of parameters. The literature mentions the solubility parameters of polymer and solvent, polymer chain stiffness, free volume of the solution, etc. In principle, all these factors should be taken into account in predicting the viscosity of a polymer solution. However, the available experimental data are insufficient for this purpose. 

The factor Cw> the Flory characteristic ratio of the actual end-to end distance to that predicted on the basis of a random flight model, obviously depends on chain stiffness or bond rotational freedom (Equation 8-11). 

A rough correlation exists between Tg and T for crystal lizable polymers, although the molecular mechanisms that underly both transitions differ. Any structural feature that enhances chain stiffness will raise Tg, since this is the temperature needed for the onset of large-scale segmental motion. Stronger intermolecular forces will also produce higher Tg s. Tliese same factors increase T, as described on page 382, in connection with Eq. (11-1). 

Q is the scattering vector and t 2 is the half-peak time of the dynamic structure factor, the larger is the chain stiffness, the smaller is the value of which may be as small as 2. 

Structural and compositional factors, the most fundamental of which are chain stiffness and interchain cohesive forces. These factors will be discussed further in Section 6.B. 

The correlation for Tg was developed by analyzing the dataset for relationships between the polymeric structure and the two important physical factors summarized in Section 6. A, namely chain stiffness and cohesive forces. Chain stiffness is, admittedly, a somewhat nebulous concept, which has been quantified in different ways by different authors. It is hoped that the reader will agree that the manner in which this key physical factor will be incorporated into our correlation for Tg makes sense at an intuitive level. 

The number of rotational degrees of freedom in the side groups, and the relative ease of rotational motions of the side groups, also affect the chain stiffness. If two side groups have equal volumes, but one of them is much less flexible than the other one, the use of the less flexible side group will normally result in a greater enhancement of chain stiffness. The structural parameter xg accounts for these factors, and is determined by the following rules ... 

The effects of tacticity on Tg are associated intimately with its effects on chain stiffness, which was shown earlier to be a key factor in determining Tg. These effects are difficult to quantify entirely in terms of empirical quantitative structure-property relationships, and require instead examining chain stiffness from a computationally more sophisticated perspective. 

Recently the study of the dilute solution behavior of polymacromonomer, a limiting case of graft copolymer where each repeat unit carries a grafted chain, has been initiated. The main interests are focused on the dependence of conformation and size of the whole molecule on factors such as nature of the backbone and side chain, molecular weight of backbone and grafts, solvent interactions with respect to both components, and chain stiffness induced on the backbone due to the high grafting density and its dependence on the aforementioned factors [310-313]. 

The primary factors governing mesophase formation for cellulose derivatives is not only chain stiffness, but also the type and degree of substitution, the molar mass of the polymer, as well as the solvent and the temperature [103]. Among the water-soluble cellulose biopolymers, HPC is still the most investigated derivative (it forms stable and easy to handle mesophases) and as such will... 

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