Segment concentration, mean

Figure 2. The bound fraction, , as a function of mean segment concentration, < >j, in an interfacial region of width equal to 5d (6 lattice planes).

Figure 7. The distribution of chain segment density, at 8 = 0.75, in an interfacial region with M = 6. The various curves correspond to the same values of mean segment concentration as in Figure 5.

For situations of overlapping chains, where lateral fluctuations in the segment concentration become rather small, mean-field descriptions become appropriate. The most successful of this type of theoiy is the lattice model of Scheutjens and Fleer (SF-theoiy). In chapter II.5 some aspects of this model were discussed. This theory predicts how the adsorbed amount and the concentration profile 0(z) depend on the interaction parameters and x and on the chain length N. From the statistical-thermodynamic treatment the Helmholtz energy and, hence, the surface pressure ti can also be obtcdned. When n is expressed as a function of the profile 0(z), the result may be written as ... 

A polymer chain at an interface is subject to a potential t/(r), which in general is composed of two components. There is an external component that arises directly from the effects of the wall. To this must be added an internal potential which reflects the mean field experienced by one segment due to the physical presence of all other segments. In the mean field approximation, this latter potential is simply proportional to the segment concentration c(r)... 

So what has been gathered from the computer simulations of selfavoiding walks It appears that the conformational properties of a polymer coil are quite significantly affected by the excluded volume. The coils become looser, and the fiuctuations in the segment concentration become more severe. The mean-square size of the coil increases. Moreover, the mean-square end-to-end distance R now depends differently on the number of segments in the chain. Instead of the familiar N (which we... 

In Section 6.6, we used the same sort of argument for an ideal polymer.) The same thing can be said about the mean concentration of the segments in the coil, n N/V t N / (cf. (6.14)). At first glance, you may think it implies that a polymer with excluded volume is always ideal. Indeed, if the segment concentration is so low, their encounters are very rare, and one can be tempted to neglect them. On the other hand, we know that the coil is very pliable, and its elastic modulus is small. 

Adopting the so-called mean-field approximation means in our context ignoring of correlations or = = c. The segment concentration c within the coil is ... 

In terms of sc>gment density (Equation 224), the screening length in semidiliite. solutions is equivalent to the distance from a certain fixed segment, where the local segment concentration Co(0 becomes equal to the mean c over all the solution. 

In the approximation of ideal chains being in the mean field of the potential r) owing to the presence of other chains (Edwards, 1966 de Gennes, 1979), the segment concentration near the point f given V (i ) is small falls according to... 

Polarization equations of the type (14.35) or (14.38) contain the mean values of true current density. However, the rate-determining step is more often concentrated at just a few segments of the electrode the true working area changes continuously and an exact determination of this area is practically impossible. This gives rise to difficulties in an interpretation of polarization data. 

The concentration gradient terms, dC/dZ, both in and out of segment n, can be approximated by means of their finite-differenced equivalents. Substituting these into the component balance equation, gives... 

The conventional concentration of benzalkonium chloride in eyedrops is 0.01%, with a range of 0.004-0.02% [111]. While uptake of benzalkonium chloride itself into ocular tissues is limited [113], even lower concentrations of benzalkonium chloride have been reported to enhance corneal penetration of other compounds including therapeutic agents [93,112,114]. The differential effect of this preservative on the cornea compared to the conjunctiva can be exploited to target a drug for corneal absorption and delivery to the posterior segment of the eye [115]. Its use has been proposed as a means of delivering systemic doses by an ocular route of administration [116]. 

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