Desorption-adsorption transition

In adsorption, the solvent always plays a double role, affecting both lateral interactions between the adsorbate molecules and determining the effective interaction between the surface and the adsorbate. For polymers, this means that they adsorb strongly from some solvents, whereas from others they do not at all. As a consequence, mixed solvents can give rise to an adsorption/desorption transition the polymer is desorbed by a so-called displacer. 

An adsorption-desorption transition is illustrated schematically in Figure 1, where we plot a displacement isotherm, i.e. the adsorbed amount of a polymer as a function of the composition of a mixture of solvent and displacer. At the left in Figure 1, where the concentration of displacer is low, the polymer surface excess is positive. As we increase the proportion of displacer in the mixture, we observe a decrease in the adsorbed amount. At a certain composition the adsorbed amount of polymer becomes zero. The concentration at which the polymer surface excess just vanishes will be denoted as the critical displacer concentration cr. Beyond 4>cr, the surface excess of the polymer is negative (and very small if the polymer concentration is low). 

Figure 5. TLC retention factor Rp for poly(methyl methacrylate) on silicagel, as a function of the elution strength of binary solvent (carbontetrachloride, CCl )/ displacer (1,4-dioxane) mixtures. Note the steep increase in Rj, at Efj w 0.38, indicating a sharp adsorption/ desorption transition.

Bouchaud and Vannimenus [54] were the first to apply RSRG techniques on fractals to study the linear polymers near an attractive substrate. They showed that the known phenomenology of the adsorption -desorption transition is well-reproduced on fractals, and different critical exponents can be evaluated exactly. The values of the exponent for HB 2,2) and HB 2,3) fractals were found to be 0.5915 and 0.7481 respectively. They also showed that for a container of fractal dimension D and adsorbing surface d, 0 has lower and upper bounds ... 

Brun has extended the concept of LCCC to the cases of statistical copolymers as well as porous stationary phases with heterogeneous surfaces (viz., surfaces with both inert and active groups) [ 162]. The theory predicted that a statistical copolymer with narrow CCD always possesses a single adsorption-desorption transition point and behaves like a homopolymer with a single energy of interaction between the effective monomer units and the active groups at the surface. If copolymer has a broad CCD, each compositionally homogeneous fraction has its own adsorption-desorption threshold. 

In the next section, we present the results of this approach for polyelectrolyte adsorption onto planar, cylindrical, and spherical surfaces. This is possible because the equation for the Green function reduces, in the corresponding separable coordinates, to a one-dimensional equation comparable to (32) in the ground-state approximation. We confirmed that the WKB applicability condition Q x)/Q x) < 1 is satisfied for aU three geometries. The approach applies particularly well above the adsorption-desorption transition, whereas it naturally fails in the proximity of the zero-potential point xq at which Q(xo) = 0. 

Probability distributions pj (%, /Jm) for the 179-mer in solvent with s=1 (a) near the layering transition horn AC1 to AGe at 1 >= 0.34 and (b) near the adsorption-desorption transition from AE1 to DE at 1 2.44. Both transitions are expected to be reai phase transitions in the thermodynamic iimit and iook first-order-iike. From [302]. 

Abstract. A model of the conformational transitions of the nucleic acid molecule during the water adsorption-desorption cycle is proposed. The nucleic acid-water system is considered as an open system. The model describes the transitions between three main conformations of wet nucleic acid samples A-, B- and unordered forms. The analysis of kinetic equations shows the non-trivial bifurcation behaviour of the system which leads to the multistability. This fact allows one to explain the hysteresis phenomena observed experimentally in the nucleic acid-water system. The problem of self-organization in the nucleic acid-water system is of great importance for revealing physical mechanisms of the functioning of nucleic acids and for many specific practical fields. 

To specify these transition probabilities we make the further assumption that the residence time of a particle in a given adsorption site is much longer than the time of an individual transition to or from that state, either in exchange with the gas phase in adsorption and desorption or for hopping across the surface in diffusion. In such situtations there will be only one individual transition at any instant of time and the transition probabilities can be summed, one at a time, over all possible processes (adsorption, desorption, diffusion) and over all adsorption sites on the surface. To implement this we first write... 

Faghoni F, Goddard WA. 2005. Energetics of hydrogen coverage on group VIII transition metal surfaces and a kinetic model for adsorption/desorption. J Chem Phys 122 014704. 

N2 adsorption-desorption isotherms and pore size distribution of sample II-IV are shown in Fig. 4. Its isotherm in Fig. 4a corresponds to a reversible type IV isotherm which is typical for mesoporous solids. Two definite steps occur at p/po = 0.18, and 0.3, which indicates the filling of the bimodal mesopores. Using the BJH procedure with the desorption isotherm, the pore diameter in Fig. 4a is approximately 1.74, and 2.5 nm. Furthermore, with the increasing of synthesis time, the isotherm in Fig. 4c presents the silicalite-1 material related to a reversible type I isotherm and mesoporous solids related to type IV isotherm, simultaneously. These isotherms reveals the gradual transition from type IV to type I. In addition, with the increase of microwave irradiation time, Fig. 4c shows a hysteresis loop indicating a partial disintegration of the mesopore structure. These results seem to show a gradual transformation... 

Reversible transition of penta- and octahedrally coordinated Al species into tetrahedral Al after hydrothermal treatment is confirmed by FTIR measurements of NH3 adsorption/desorption. They show a reformation of Bronsted sites. The concentration of BS rises to 50% and more with respect to the initial value. This reformation of BS can be explained by an re-hydroxylation of the internal surface. 

Let us study now a stochastic model for the particular a+ib2 -> 0 reaction with energetic interactions between the particles. The system includes adsorption, desorption, reaction and diffusion steps which depend on energetic interactions. The temporal evolution of the system is described by master equations using the Markovian behaviour of the system. We study the system behaviour at different values for the energetic parameters and at varying diffusion and desorption rates. The location and the character of the phase transition points will be discussed in detail. 

The studies of Ertl and co-workers showed that the reason for self-oscillations [142, 145, 185-187] and hysteresis effects [143] in CO oxidation over Pt(100) in high vacuum ( 10 4 Torr) is the existence of spatio-temporal waves of the reversible surface phase transition hex - (1 x 1). The mathematical model [188] suggests that in each of the phases an adsorption mechanism with various parameters of CO and 02 adsorption/desorption and their interaction is realized, and the phase transition is modelled by a semi-empirical method via the introduction of discontinuous non-linearity. Later, an imitation model based on the stochastic automat was used [189] to study the qualitative characteristics for the dynamic behaviour of the surface. 

Within the frameworks of the lattice gas model it is reasonable to classify the elementary processes by the number of sites m, which a given process occurs on, i.e., one- and two-site cases. In the first case the changing parameter is the occupancy state of one site. The processes such as these include isomerization associated with changes in the internal degrees of freedom of the adspecies (ZA- ZB, i.e., transition of the adspecies from state A to state B), adsorption-desorption of the atoms and nondissociating molecules (A + Z- ZA), reaction according to the collision mechanism (A + ZB ->ZD + C, Eley-Rideal s-type mechanism). It should be remembered that ZA, Z and A denote adspecies A, empty lattice site and species A in the gaseous phase, respectively. 

A similar interpretation holds for the preexponential factor of the rate constants for the dissociative adsorption, desorption, reaction between the adspecies and their migration. The CM is distinguished by the fact that the preexponential factor is dependent on the properties of the starting reagents only and is independent of the transition state whereas the rate constant depends on the activation barrier height, which is governed by the transition state energy. 

For definiteness, consider barrierless adsorption-desorption reaction (2). In the variational TST, the position qf of transition complex TCad in the reaction path (see Figures 9.1 and 9.2) corresponds to a maximum of the Helmholtz free energy cf(qr) of the trial transition complex TCad( r) considered as a function of the reaction coordinate. 

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