Theory interpenetrating

The above argument shows that complete overlap of coil domains is improbable for large n and hence gives plausibility to the excluded volume concept as applied to random coils. More importantly, however, it introduces the notion that coil interpenetration must be discussed in terms of probability. For hard spheres the probability of interpenetration is zero, but for random coils the boundaries of the domain are softer and the probability for interpenetration must be analyzed in more detail. One method for doing this will be discussed in the next section. Before turning to this, however, we note that the Flory-Huggins theory can also be used to yield a value for the second virial coefficient. 

As described in Sect. 2.4, SCF calculations are useful in determining local details of density profiles. A more local examination of profiles is indeed necessary to study the question of interpenetration in more detail. The analytical SCF theory [56, 57] shares with the adapted Alexander model embodied in Eq. 35 the characteristic of impenetrability. The full numerical SCF theory is necessary to... 

Simha [53] made the first attempts to model the transition from a dilute to a concentrated solution. He assumed that in the range from lscaling laws a theory has been developed which allows for the prediction of the influence of Mw c and the solvent power on the screening length [54,55]. This theory is founded on the presumption that above a critical concentration, c, the coils overlap and interpenetrate. Furthermore it is assumed that in a thermody-... 

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are ... 

Comparison of Theory and Experiment. The expression for the free energy of interpenetration of sterically stabilized particles may be obtained by combining Equations 2, 3 and 6. Using these expressions can be calculated as a function of both... 

The information available on aqueous polymer blends is qualitative in nature because of the lack of a suitable theory to interpret the experimental observations. Mixed gels can be comprised of an interpenetrating network, a coupled network (as discussed above), or a phase-separated network [2]. The latter is the most common as the blends have a tendency to form two phases during gelation. In such cases the miscibility and thermodynamic stability have to be empirically investigated and proper conditions for miscible blends identified. This involves a phase diagram study as is described in [3]. 

Fig. 14. Dependence of the interpenetration function R on the number of arms in star molecules. The full line represents the result of the renormalization group theory [90], the data points refer to measurements [77]. Reprinted with permission from [77]. Copyright [1983] American Society...

FIG. 1. Three stages in the interaction between a mucoadhesive polymer and mucin glycoprotein according to the interpenetration theory. 

The diffusion theory states that interpenetration and entanglement of polymer chains are additionally responsible for bioadhesion. The intimate contact of the two substrates is essential for diffusion to occur, that is, the driving force for the interdiffusion is the concentration gradient across the interface. The penetration of polymer chains into the mucus network, and vice versa, is dependent on concentration gradients and diffusion coefficients. It is believed that for an effective adhesion bond the interpenetration of the polymer chain should be in the range of 0.2-0.5 pm. It is possible to estimate the penetration depth (/) by Eq. (5),... 

The influence of surfactant structure on the nature of the microemulsion formed can also be predicted from the thermodynamic theory by Overbeek (17,18). According to this theory, the most stable microemulsion would be that in which the phase with the smaller volume fraction forms the droplets, since the osmotic term increases with increasing i. For w/o microemulsion prepared using an ionic surfactant, the hard sphere volume is only slightly larger than the water volume, since the hydrocarbon tails of the surfactant may interpenetrate to a certain extent, when two droplets come close together. For an oil in water microemulsion, on the other hand, the double layer may extend to a considerable extent, depending on the electrolyte concentration... 

Until recently, the theory did not allow the configuration of the positive state to be described, due to entry/exit DNAs interpenetration upon application of the positive constraint to the loop. A recent development [63] takes the DNA impenetrability into account and deals with the resulting DNA self-contacts, which were allowed to slide freely, following the needs of the energy minimization process. 

The examples summarized above are but indicative of the increasing body of evidence in support of the chemical bonding theory, and of the role of the silane organofunctional group in the formation of covalent bonds at the coupling agent/ matrix interphase by reaction or by co-polymerization with the formation of an interpenetrating polymer network. 

Several analytical techniques have been used to characterize the polymer/ silane coupling agent interphase. Culler et aL [2] used Fourier transform infrared (FT-IR) spectroscopy to characterize the chemical reactions at the matrix/silane interphase of composite materials. They correlated the extent of reaction of the resin with the coupling agent (as determined by FT-IR) with the extent of interpenetration. Culler et al. [2] have also used observations of improved resistance of the interphase region to solvent attack as indirect evidence to support the interpenetrating network theory. 

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