Density, equilibrium adsorption polymer

Adsorption and electrokinetic effects of amino acids, solid-aqueous interface, 311-26 Adsorption density, equilibrium PAA at various pH values, 299f PAA on hematite, 304f SDS with and without polymer, 298f,303f... 

Since the adsorbed molecules are in exchange equilibrium with the rest of the sorbed molecules, a is in effect the average dynamic packing density of the molecules immobilized by adsorption to the accessible monomer units of crosslinked polymer at liquid saturation. If the relationship expressed by Eq. 14 is indeed correct as... 

When using more active emulsifiers of the C-10 type (Yeliseyeva, 1966) the effective rate and the equilibrium value of adsorption increase in the polymerization of polar monomers, which reduces the intensity of the processes of initial flocculation. Moreover, in this case the charge density is not the only stabilizing factor it is su(f>lemented by the enthalpy factor which arises from hydration of oxyethylenic chains of emulsifier molecules. The presence of these emulsifiers creates conditions that enable tbe obtain-ment of polar polymer latexes of high stability. 

The GC route is particularly attractive for it requires no a priori information on the polymer. With the exception of X-ray measurements, most methods of measurement involve a comparison of some property of the polymer, such as density, with that of the totally amorphous or crystalline material. Furthermore neither the mass of polymer in the column nor the flow rate of carrier gas need to be measured since a ratio of retention volumes is computed in Eq. (21). It should be added, however, ttiat for the successful application of the method it is essential that the measured retention volumes correspond effectively to equilibrium bulk sorption, both above and below. Low molecular weight compounds are known to exhibit apparently similar discontinuities in retention diagrams at their melting points but this is to be ascribed to a change in retention mechanism, from surface adsorption for the solid to bulk sorption for the liquid stationary phase. For a detailed discussion of retention characteristics of low molecular weight substances near their transition temperatures the reader is referred to a recent review by McCrea (8J). 

Henry constant for absorption of gas in liquid Free energy change Heat of reaction Initiator for polymerization, modified Bessel functions, electric current Electric current density Adsorption constant Chemical equilibrium constant Specific rate constant of reaction, mass-transfer coefficient Length of path in reactor Lack of fit sum of squares Average molecular weight in polymers, dead polymer species, monomer Number of moles in electrochemical reaction Molar flow rate, molar flux Number chain length distribution Number molecular weight distribution... 

Other lattice polymer efforts have been based on the self-consistent fleld theory of Scheutjens and Fleer (150,151). This approach differs from previously posed statistical theories for chain molecules in that the partition function is expressed in terms of the distribution of chain conformations rather than the distribution of segment densities. The equilibrium distribution of chain (ie model protein) conformations is thus calculable. Quantities predicted using this approach include the force between parallel plates coated with protein (152,153), the adsorption isotherm (154,155), and the segmental density distribution (154-157). 

The grand canonical ensemble describes a system of constant volume, but capable of exchanging both energy and particles with its environment. Simulations of open systems under these conditions are particularly useful in the study of adsorption equilibria, surface segregation effects, and nanoscopically confined fluids and polymers. Under these conditions, the temperature and the chemical potentials jti,- of the freely exchanged species are specified, while the system energy and composition are variable. This ensemble is also called the jx VT ensemble. In the case of a one-component system it is described by the equilibrium probability density... 

In all these eases one has a constrained equilibrium situation, where the polymer eonfigurations and thus the density profile can adjust only with the constraint that the total adsorbed polymer exeess stays constant. This case has been first considered by de Gennes [45] and he found that two fully saturated adsorbed layers will strongly repel each other if the total adsorbed amount of polymer is not allowed to decrease. The repulsion is mostly due to osmotic pressure and originates from the steric interaction between the two opposing adsorption layers. It was experimentally verified in a series of force-microscope experiments on PEO layers in water (which is a good solvent for PEO)[48j. 

In this section, we discuss how our measurement may or may not reflect the three factors commonly attributed to the out-of-equilibrium state of thin polymer films, namely reduced entanglement density, residual stress and on-going chain adsorption to the substrate surface. 

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