Distribution of polymer segments

Thus we may retain the root-mean-square end-to-end distance as a measure of the size of the random-coiling polymer chain, and the parameter jS required to characterize the spatial distribution of polymer segments (not to be confused with the end-to-end distribution) can be calculated from It should be noted that the r used here... 

Since branched chains like LDPE have many chain ends, it is customary to use the radius of gyration, S, as a measure of the distribution of polymer segments. The radius of gyration is the distance of a chain end from the polymer s center of gravity rather than a measure of the RMS. Both measures are statistically related. 

Figure 3 presents the distribution of polymer segments between the two plates for various distances. The distribution of the... 

Among other topics that can now be studied are the distribution of polymer segments at an interface, the dynamics of water adsorbed in clays and lamellar liquid crystals, and, using the more recent technique of neutron spin echo , the diffusion of colloidal particles and its dependence on particle concentration. 

Writing Gj gCR) in terms of the distribution of polymer segments (R) (the probability of finding monomer j in R when i is at the origin), we can rewrite Equation 18.37 as... 

Fig. 6.3. Sketch of the experimental geometries to illustrate for elliptically polarized x-rays the orientation of the major horizontal Eh and minor vertical E component of the electrical field vector for parallel (A) and perpendicular (B) orientation of the film surface with respect to the rubbing direction (4-a direction). (C) Relationship between the sample frame x,y,z) and the molecular frame x, y, z ), in which the molecular distribution of polymer segments at the film surface has at least twofold symmetry about all three orthogonal axes.

The distribution of polymer segments between trains, loops, and tails may be adjusted when the polymer-covered surfaces encounter each other and this, in turn, may interfere with the steric stabilization mechanism. The polymers best performing as stabilizers are block copolymers made of two kinds of monomers that are clustered in long sequences of one kind. The sequence of the one kind of monomer should have a high affinity for adsorption and, hence, firm attachment at the surface, whereas the sequence of the other type should prefer to stay in solution giving extended loops and tails. With homopolymers, affinity for the sorbent surface and extension into the solution are compromising tendencies. 

Kurata and Yamakawa (1958) criticized McMillan and Mayer s theory for lack of experimental support and Rory and Krigbaum s theory for their assumption of Gaussian distribution of polymer segments around the center of the mass. The introduction of the factorization approximation does not help much. As a result, Flory and Krigbaum s theory underestimates the molecular weight dependence of A2. For Kurata and Yamakawa, the excluded volume effect has a non-Gaussian character with respect to the chain configuration. Kurata and Yamakawa s approach, however, basically follows the same line as that of McMiUan and Mayer. 

From this description of polymer configurations, a full characterization of the adsorption process clearly requires a knowledge of the amount of polymer adsorbed per unit area of the surface, T (mol m or mg m ), the fraction of segments in close contact with the surface, p, and the distribution of polymer segments, p z), from the surface towards the bulk solution. We also must know how far the seg-... 

In summary, electrokinetic measurements combined with an advanced theory for soft surfaces is an effective tool for the comprehensive characterisafion of switchable hydrogel coatings. The accessible physicochemical parameters (distribution of polymer segment density, charge density, hydrodynamic softness, interphasial dilfuseness) complanent the results as obtained by techniques like ellipsometry or indenter measur ents. 

Figure 1. Illustration of a cap-and-gown model for the radial distribution of polymer segment volume fraction in a micelle, The micellar core is described as the cap and the diffuse outer layer as the gown. The relative sizes of the cap (radius a) and the gown (Gaussian width cr) are related by the PEO to PPO volume ratio. The water penetration profile is complementary to the polymer segment distrubution.

In many circumstances it is possible to extend the range of measurements with neutrons to cover more than this low Q limit, and then more detailed models of the structure must be evaluated. Debye [22] has derived a result for the scattering from a Gaussian distribution of polymer segments appropriate to a random polymer coil which is of the form ... 

Flory-Krigbaum Theory A theory of dilute polymer solutions which describes the distribution of polymer segments as clusters of segments separated by regions of pure solvent. A model for this structure is used which takes account of the excluded volume within the coils. 

The thickness of an adsorbed polymer layer, together with the quality of the solvent, are the important parameters determining the magnitude of the steric barriers in colloid stabilization. As the distribution of polymer segments away from a surface is approximately exponential, the thickness measured may depend on the technique used. The influence of various parameters on adsorbed-layer thickness is discussed below. 

For full characterization of the process of adsorption, it is necessary to know the amount of polymer adsorbed per unit area of the snrface, the fraction of segments in close contact with the surface, and the distribution of polymer segments. 

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