Polymer overlap

The keen observer may have noticed that modern methods of additive analysis in polymers overlap with those in allied areas (Figure 10.4) rubber [150,151], paints [152,153] and coatings [152], adhesives [153], inks [153], food [154], impregnated paper and faced paperboard [155], etc. Clearly, tool-boxes will differ to some extent, as do the analytes. 

However, polymer coils overlap and dominate most of the physical properties of semidilute solutions (such as viscosity). Thus, adding a very small amount of polymer to a solvent can create a liquid with drastically different properties than the solvent. This unique feature of polymer overlap is due to their open conformations. Linear polymers in solution are fractals with fractal dimension I) < 3. In semidilute solutions, both solvent and other chains are found in the pervaded volume of a given coil. The overlap parameter P is the average number of chains in a pervaded volume that is randomly placed in the solution ... 

Consider a monodisperse melt of randomly branched polymers with N Kuhn monomers of length b. Randomly branched polymers in an ideal state (in the absence of excluded volume interactions) have fractal dimension D = 4. Do these randomly branched polymers overlap in a three-dimensional monodisperse melt ... 

Hint What would be the iV-dependence of density if monodisperse randomly branched polymers overlapped in the melt ... 

PAGE 14 End of the first paragraph replace is necessary with arises In practice this ambiguity arises because polymer overlap occurs over a range of concentrations. ... 

On the other hand, for fixed p, the polymer overlap increases with M the interval of p, corresponding to dilute solutions, becomes smaller and smaller. Consequently, measuring the osmotic pressure as a function of concentration cannot serve to determine the mass M of polymers with high molecular masses. 

Before the emergence of the isotopic labelling methods and of the neutron-scattering technique, it hardly seemed possible to separate the contributions Hl(q) and Hn q). Thus, very little has been said concerning these functions in the case of solutions with polymer overlap. However, they are directly related in the case of polymer liquids (a limiting case). Then, the structure function H q) becomes identical to the global structure function H q) of the system. In agreement with the assumption that the system can be considered as... 

The definition of this apparent correlation length can be extended to dilute regimes, in which case app gives g/V3 (see eqn (2.72)). The behaviour of app is entirely different in dilute solutions and concentrated solutions. In dilute solutions, lapp dincreases with the molecular weight and the excluded volume, while in concentrated solutions app — I is independent of the molecular weight and decreases as a function of concentration and excluded volume (see eqn (5.36)). The reason can be easily understood from Fig. 5.1 once polymers overlap each other, the excluded volume interaction tends to make the concentration homogeneous. 

The upper solid curve in Fig. 3a is a plot of Eq. (4) with /2//1 =0.11. The equation for the non-adsorption mixture fits the data well. Our previous study of the same system also suggests that the PEP polymer does not adsorb onto the colloidal spheres. The two end-functionalized polymers are found to be partially adsorbed onto the colloidal surfaces. The lower solid curve in Fig. 3a is a fit to Eq. (8) with ao = 0.21. In the range 0 < a < 24, ao is found to be independent of the molar ratio u. In this range of a , the overall polymer concentration P2 is below the polymer overlap concentration. The zwitterion-PEP data can also be fitted to Eq. (8) with a constant ao = 0.18. The dashed curve in Fig. 3b is a plot of Eq. (8) with a = 1 (complete adsorption). One can immediately see from Fig. 3 that the measured y(u ,ao) for our end-functionalized polymers lies in-between the non-adsorption and complete adsorption curves. 

Experimental work on the determination of the depletion layer thickness commenced in this period. The depletion thickness S of polystyrene at a nonadsorbing glass plate was measured using an evanescent wave technique by Aflain et al. [120]. The value found for S was indeed close to the radius of gyration of the polymer. Ausserre et al. [121] measured the depletion thickness of xanthan (a polysaccharide) at a quartz waU below and above the polymer overlap concentration. In dilute solutions, below overlap, S was close to the radius of gyration of... 

In this section we consider the phase behaviour of dispersions containing spherical colloids and interacting polymer chains in a common solvent. For small polymer-to-colloid size ratios, q < 0.4, the relevant part of the phase diagram hes below the polymer overlap concentration ((j>p < 1). Then accounting for interactions between the polymers is not essential to properly describe the phase diagram and it is still sufficient to approximate the polymer-induced osmotic pressure by the ideal gas law as assumed within free volume theory [18]. However, for >0.4, the polymer concentrations where phase transitions occur are of the order of and above the polymer overlap concentration in that case interactions between the polymer segments should be accounted for. 

Above the polymer overlap concentration we enter the semi-dilute regime (Fig. 4.7c). The length scale over which the polymer segments are correlated is denoted as correlation length Below overlap (p<(p ) this quantity is the coil size Rg which depends only on M (and solvency). Above overlap

q> ) we have the famous De Gennes scaling law [40]... 

Three types of blend crystallization are distinguished (1) simultaneous of both components (2) in the presence of molten second component and (3) in the presence of solid second component. The case (1) takes place when ranges of the crystallization temperatures, T, of the two polymers overlap and their crystallization rates are similar their mixed spherulites usually have additive physical properties. For the case (2), Paul and Barlow predicted five crystallization patterns (i) no effect (ii) retardation (iii) delay (iv) acceleration and (v) crystallization of a... 

Protein molecular weights also have a substantial effect on the protein network structure. They also determine the presence of molecular overlapping, leading to the formation of physical nodes. As is the case for odier polymers, overlapping could occur beyond a critical molecular weight (generally around 10" g.mol ), overlapping is possible and the material properties are stable. 

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