Free volume effect polymer chain ends

Van Meerwall E, Grigsby J, Tomich D, Van Antverp R (1982) Effect of chain-end free volume on the diffusion of oligomers. J Polym Sci Polym Phys Ed 20(6) 1037-1053 Van Vleck JH (1932) The Theory of electric and magnetic susceptibilities. Oxford University Press, London... 

The molecular weight and molecular weight distribution of polymers affects the volume fraction of chain ends and hence the free volnme of the polymer and, consequently, determines the chain mobility and crystallisation. It also determines the number of acidic end gronps that can participate in hydrolysis and their possible catalytic effect. Overall, the molecular weight affects both the chemical and physical properties of a polymer." ... 

Another critical note that should be put forward about the quenching studies is that the polymer chain end, either a phosphorophore or a quencher, is not the same as in a free-radical polymerization. If segmental diffusion is indeed the rate-determining step, then it is implicitly assumed that the segmental mobility is not influenced by the nature of this chain end. Up to now, there is no unambiguous evidence to prove this assumption and, as segmental diffusion is influenced by parameters such as chain flexibility, steric hindrance, excluded volume effects etc., common sense would decline this assumption. 

It is shown that the present model for a polymer network as a copolymer of chain ends, chain segments and branch points provides a workable hypothesis, from which useful conclusions can be derived. To arrive at a set of consistent expressions, the mixing rules for free volumes of copolymers and polymer mixtures had to be reformulated. Where possible, these results have been checked with data from the literature on the effects of chain ends and branch points on T. Thus it was shown that a unified free volume theory for polymer solutions, copolymers, or polymer networks exists which is in agreement with most experimental data. 

Repulsive forces between Fe oxide particles can be established by adsorption of suitable polymers such as proteins (Johnson and Matijevic, 1992), starches, non-ionic detergents and polyelectrolytes. Adsorption of such polymers stabilizes the particles at electrolyte concentrations otherwise high enough for coagulation to occur. Such stabilization is termed protective action or steric stabilization. It arises when particles approach each other closely enough for repulsive forces to develop. This repulsion has two sources. 1) The volume restriction effect where the ends of the polymer chains interpenetrate as the particles approach and lose some of their available conformations. This leads to a decrease in the free energy of the system which may be sufficient to produce a large repulsive force between particles. 2) The osmotic effect where the polymer chains from two particles overlap and produce a repulsion which prevents closer approach of the particles. 

How do we take into account the contribution of dangling chains to Tg In linear polymers, we know that chain ends carry on a free volume excess and, thus, play a plasticizing effect that can expressed through a copolymer law ... 

This reflects the effect of the greater number of chain ends at lower molar mass resulting in a larger local free volume and thus a lower Tg. While this relation hold well for linear polymers, there are exceptions linked to the nature of the end groups, e.g. when they are ionic or hydroxyl groups, and also when cyclics are studied. McKenna (1989) considers in more detail these and other factors which may affect Tg. The effect of crosslinking, which is important for reactive processing of both elastomers and three-dimensional networks, is considered in a later section. 

Branches present in small numbers on a polymer chain are known to decrease Tg. This effect also can be explained using. the free volume concept. Since branches give rise to chain ends, the above arrSfysis of the effect of molecular weight on Tg can be extended to branching. Thus, if the total number ends per chain is y, then by the analysis as given above one may write... 

In a blend solution, the interaction parameter x of the Flory-Huggins theory is zero (the chain end effect is negligible) and independent of temperature. Otherwise, a temperature-dependent x can lead to a thermorhe-ologically complex behavior of the polymer solution sj tem, which would disallow the apphcation of the time-temperature superposition principle. A theoretical analysis indicates that if M M2, the system is free of the excluded volume effect that will cause the component-two chain to expand in other words, the chain coil remains Gaussian. Here, we consider polystyrene blend solutions with Mi slightly smaller than Mg (= 13,500 for polystyrene). In such a system, the condition M > M2 can be easily satisfied. Furthermore, the solvent, being chains of more than ten Rouse... 

A simple titeory. The original idea of Flory for calculating the rize of a polymer is to consider the balance of two effects a repulsive excluded volume interaction which tends to swell the polymer, and the elastic energy ariring from the chain connectivity u ch tends to shrink the polymer. This idea can be put into a partially simple form of theory. Consider the free energy of a chain whose end-to-end vector is fixed at R. This is given by... 

Milner (61) addressed the energetics of polymer brushes. In this case neighboring polymer chains need to avoid one another. This volume exclusion effect provides the driving force for the chains to extend out into the solution. However, the problem is also different from the one chain bonding two particles, above, because one end of the chain is free. Milner also included a correction term for surface tension effects. He concluded that excess energies in the range of 8 to 10 kT were reasonable for many brush conformations. 

---