Transition adsorption

The solution to this model for a deep bed indicates an increase in velocity of the fluid-phase concentration wave during breakthrough. This is most dramatic for the rectangular isotherm—the instant the bed becomes saturated, the fluid-phase profile Jumps in velocity from that of the adsorption transition to that of the fluid, and a near shocklike breakthrough curve is obseived [Coppola and LeVan, Chem. Eng. Sci.,36, 967(1981)]. 

According to the scaling theory of the adsorption transition [2,35], one expects for e near e. in the limit A oo a power law behavior... 

The adsorption transition also shows up in the behavior of the chain linear dimension. Fig. 6(a) shows the mean-square gyration radii parallel, i gl, and perpendicular, to the adsorbing plate. While these components do not differ from each other for e for e > ej i g strongly increases whereas Rh decreases. In the first case (non-adsorbed chain) oc oc N as a dilute solution in a good solvent in the bulk. For adsorbed chains R /N 0 for oo because the thickness is finite it is controlled by the distance e- e from the adsorption threshold, but does not diverge as N oo. The adsorbed chain follows in fact a... 

The principle of the liquid chromatography under critical conditions (LC CC) was elucidated in Section 16.3.3. The mutual compensation of the exclusion—entropy and the interaction—enthalpy-based retention of macromolecules can be attained when applying in the controlled way the interactions that lead to either adsorption or enthalpic partition. The resulting methods are called LC at the critical adsorption point (LC CAP) or LC at the critical partition point (LC CPP), respectively. The term LC at the point of exclusion-adsorption transition (LC PEAT) was also proposed for the procedures employing compensation of exclusion and adsorption [161]. It is anticipated that also other kinds of enthalpic interactions, for example the ion interactions between column packing and macromolecules can be utilized for the exclusion-interaction compensation. 

In these hybrid simulations, coupling happened through the boundary condition. In particular, the fluid phase provided the concentration to the KMC method to update the adsorption transition probability, and the KMC model computed spatially averaged adsorption and desorption rates, which were supplied to the boundary condition of the continuum model, as depicted in Fig. 7. The models were solved fully coupled. Note that since surface processes relax much faster than gas-phase ones, the QSS assumption is typically fulfilled for the microscopic processes one could solve for the surface evolution using the KMC method alone, i.e., in an uncoupled manner, for a combination of fluid-phase continuum model parameter values to develop a reduced model (see solution strategies on the left of Fig. 4). Note again that the QSS approach does not hold at very short (induction) times where the microscopic model evolves considerably. 

Both theories of single-chain adsorption, described above, ignore a very important effect—the loss of conformational entropy of a trand due to its proximity to the impenetrable surface. Each adsorption blob has jb contacts with the surface and each strand of the chain near these contacts loses conformational entropy due to the proximity effect. In order to overcome this entropic penalty, the chain must gain finite energy E er per contact between a monomer and the surface. This critical energy Ecr corresponds to the adsorption transition. For ideal chains Ecr A E. The small additional free energy gain per contact kT6 should be considered in excess of the critical value Ecr,... 

The thickness ads of an adsorbed ideal chain decreases rapidly as the adsorption energy E is increased above the adsorption transition E. ... 

This in fact denotes the location of a continuous adsorption transition at which the layer grows to infinity. The scaling results for the adsorption behavior of... 

Table 9. Summary of experimental results obtained for halogen adsorption transition metals. The colttrtm headings are the same as defined for Table 1. on the smfaces of hep ...

Another interesting question is the effect of chain stiffness on polymer adsorption. It has been found [34] that increase of p —> oo causes a crossover in the character of the adsorption transition from second order (for finite 7p) to first order as diverges. This finding is compatible with mean field theories [35]. However, a complication that has not been analyzed before is the finding that the persistence length is not only dependent on the bending potential, but also depends on the distance from the adsorption transition [34]. 

There are different possibilities for how the forced translocation can be effected. For example, Milchev at al. [74, 75] studied the possibility that the monomer-membrane interaction is attractive on the tram side, while it is assumed to be repulsive on the cis side. Assuming that a few monomers of a chain have already passed through the pore and experience the favorable membrane-monomer interaction on the tram side, two questions that are asked are (1) How likely is it that the rest of the chain will follow from the cis to the tram side, depending on chain length N and the distance T/Tc — 1 from the adsorption transition that happens on the tram side at T = Tc (2) How does the time needed for complete translocation depend on these parameters ... 

Liquid chromatography at the critical condition (LCCC) is performed at the elution-adsorption transition. It can be used to separate macromolecules with different functionalities such as chains with different chain ends or to separate linear chains from cycles. LCCC was used [77] to separate cycles from linear chains in poly(bisphenol-A-carbonate) PC. Figure 45.20 contains the LCCC trace. The trace is bimodal, with two bands, Z1 and Z2. The MALDI spectrum of Z1 displayed a large number of peaks, ranging approximately from 2.0 to 10 kDa, due to PC chains terminated with n-butyl on one side or on both sides. The MALDI spectrum of Z2 was far less crowded. It is made of cycles and one can note the systematic absence of linear chains. This implies that the LCCC separation is perfect. 

LC-PEAT Liquid chromatography at the point of exclusion-adsorption transition... 

The chromatographic separation of polymers by liquid chromatography under critical conditions (LCCC), also referred to as liquid chromatography (LC) at the critical point of adsorption, LC in the critical range or LC at the point of exclusion-adsorption transition, has attracted significant attention within polymer community. Russian scientists using TLC [1-3] and later LC [4,5] have been the first experimentally identify critical conditions. At the critical conditions polymers of a given kind are eluted independently from their molar mass (for example. Fig. 1 [6]). 

The crossover exponent, polymer conformation in the vicinity of the adsorption threshold, kBTa/[wan- Defining a scaled distance, Ts 1 - TJT, from the adsorption transition, one finds for the number of contacts with the substrate a scaling law of the form ... 

Figure 4. The relationship between temperature, water content, and stability (after Franks, F.f In a dilute aqueous suspension, a biochemically active molecule is structural stabile but is vulnerable to a wide range of environmental degradative forces such as hydrolysis, oxidation and racemization. In a surface immobilized or dehydrated state, a biochemically active molecule achieves peater kinetic stability at a cost of thermodynamic instability. From a dilute state (A) through supersaturation (S) with progressive water loss on the way to a solid glassy state (B), a biochemcially active molecule passes through a thermodynamically defined (entropic loss of water and enthalpy of adsorption) transition zone (stippled) where irreversible conformational changes may occur. We have observed that the disaccharides used to fabricate Aquasomes appear to stabilize biochemically active molecules in this zone during surface-induced dehydration. The dashed line represent the freeze-drying pathway between the eutectic point and Tg.

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