Langmuir-type dependence

The basic premise of the dual-sorption theory is that a glassy polymer contains microvoids, or holes created during the process of cooling the polymer below its glass transition temperature. Therefore, gas molecules can either dissolve in the bulk polymer or go into these holes. Consequently, glassy polymers have a high gas solubility due to the availability of dual-sorption modes. It is found that gas dissolution in the matrix follows Henry s law, whereas that in the holes displays a Langmuir-type dependence. Thus, at equilibrium, the total gas concentration in the polymer can be separated into a normal sorption term c, and a hole contribution [65] ... 

Specific adsorption of ions (probably anions) of the electrolyte phase on the metal also should depend on the metal. Assuming a Langmuir-type equilibrium, one has22 for ions of charge qt and solution concentration c,... 

The data set given in Fig. 9.6 shows a rate dependence on [HS ] this part of the figure reflects the initial linear "Langmuir" type on the adsorption equilibrium ... 

If the surface complex is the chromophore, then the photochemical reductive dissolution occurs as a unimolecular process alternatively, if the bulk iron(III)(hydr)-oxide is the chromophore, then it is a bimolecular process. Irrespective of whether the surface complex or the bulk iron(IIl)(hydr)oxide acts as the chromophore, the rate of dissolved iron(II) formation depends on the surface concentration of the specifically adsorbed electron donor e.g. compare Eqs. (10.11) and (10.18). It has been shown experimentally with various electron donors that the rate of dissolved iron(II) formation under the influence of light is a Langmuir-type function of the dissolved electron donor concentration (Waite, 1986). 

This result indicates a hyperbolic dependency of [rsurf] on [/] when CEC K,c Kiex [co-ion] (i.e., a Langmuir type isotherm, Section 9.2). 

According to the Langmuir-type adsorption model, a differential equation for time dependence of the amount of FeCp-X adsorbed on the droplet (m) is given as... 

Sensitization of Ti02 nanosized particle films soaked in water was tried by dissolving a sensitizer and a sacrificial electron donor (EDTA) in the water phase (Fig. 19.7). Photocurrent was strongly dependent on the concentration of Ru(bpy)32+, reaching saturation at higher concentrations beyond 2 mM. By analysis of the photocurrent-vs.-concentration curve, a Langmuir-type adsorption of the dye was suggested. 

The compositional dependence of the volume of hydrates is solely in the vo term. The compositional dependence was assumed to be a Langmuir type expression that accounts for a guest molecules repulsive nature with each hydrate... 

Figure 9.9 shows how BET isotherms depend on the parameter C. For high values of C the binding of vapor molecules directly to the surface, is strong compared to the intermolecular interaction. Therefore, at least for low pressures, a Langmuir type of adsorption is obtained. Only at high pressures do the molecules start to form multilayers. For low values of C the... 

The dependence of the distribution coefficient of the protein on an ion-exchanger with regard to protein and salt concentration [K(Cm, /)] can be empirically described by the following equation assuming a Langmuir-type adsorption behavior for the protein ... 

Equilibrium between solution and adsorbed or sorbed phases is a condition commonly used to evaluate adsorption or sorption processes in soils or soil-clay minerals. As previously stated, equilibrium is defined as the point at which the rate of the forward reaction equals the rate of the reverse reaction. Two major techniques commonly used to model soil adsorption or sorption equilibrium processes are (1) the Freundlich approach and (2) the Langmuir approach. Both involve adsorption or sorption isotherms. A sorption isotherm describes the relationship between the dissolved concentration of a given chemical species (adsorbate) in units of micrograms per liter (pg L 1), milligrams per liter (mg L-1), microequivalents per liter (pequiv L-1), or millimoles per liter (mmol L-1), and the sorbed quantity of the same species by the solid phase (adsorbent) in units of adsorbate per unit mass of adsorbent (solid) (e.g., pg kg-1, mg kg-1, peq kg-1, or mmol kg 1) at equilibrium under constant pressure and temperature. Sorption isotherms have been classified into four types, depending on their general shape (Fig. 4.13) ... 

The discussion in the Introduction led to the convincing assumption that the strain-dependent behavior of filled rubbers is due to the break-down of filler networks within the rubber matrix. This conviction will be enhanced in the following sections. However, in contrast to this mechanism, sometimes alternative models have been proposed. Gui et al. theorized that the strain amplitude effect was due to deformation, flow and alignment of the rubber molecules attached to the filler particle [41 ]. Another concept has been developed by Smith [42]. He has indicated that a shell of hard rubber (bound rubber) of definite thickness surrounds the filler and the non-linearity in dynamic mechanical behavior is related to the desorption and reabsorption of the hard absorbed shell around the carbon black. In a similar way, recently Maier and Goritz suggested a Langmuir-type polymer chain adsorption on the filler surface to explain the Payne-effect [43]. 

If we pursue the model of the catalytic surface as a collection of a fixed number of sites S capable of forming chemical bonds with adsorbed species, then we may expect to find that substances which can compete for the catalytic sites may inhibit the reaction. Furthermore, the effectiveness of the inhibition will depend on the relative pressures of the two adsorbates as well as their sorption constants on the surface. Let us consider as an example the simple Langmuir-type sorption of two sorbates A and B on a surface of S° sites ... 

The rate is first order in total metal and, depending on conditions, approximately first order in monomer. Note that eqn 10.89 is in terms of liquid-phase monomer concentration if the monomer must be supplied from a gas phase, as in SHOP, Langmuir-type absorption may produce a tendency toward saturation kinetics. 

Figure 14 The ion-exchange isotherms for uni-univalent ion-exchange reactions (left) and the In dependence (right) of various types of reaction on X, (a) Langmuir type, (b) selectivity reversal, (c) anti-Langmuir type, (d) incomplete exchange, (e) hysteresis loop. (From M. Abe, in Ion Exchange Processes Advances and plications (A. Dyer, M. J. Hudson, and P. A. Williams, eds.). The Royal Society of Chemistry, Science Park, Cambridge, UK, p. 199, 1993. With permission.)...

Adsorption of albumin, y-globulin, and fibrinogen from single solutions onto several hydrophobic polymers was studied using internal reflection IR spectroscopy. The adsorption isotherms have a Langmuir-type form. The calculated rate and amount of protein adsorbed was dependent on the polymer substrate and the flow rate of the solution. Competitive adsorption experiments were also investigated to determine the specific adsorption of each I-labelled protein from a mixture of proteins. Platelet adhesion to these proteinated surfaces is discussed in relation to a model previously proposed. 

Our studies (19) indicated that proteins were readily adsorbed from aqueous solution onto hydrophobic polymer surfaces with Langmuir type adsorption and that the rate of adsorption toward a plateau surface concentration depends on the polymer nature. In the study of competitive adsorption from a protein mixture solution (20), fibrinogen and y-globulin adsorb onto FEP very rapidly compared with PEUU and SR. Therefore, the FEP surface in contact with blood has more acceptor sites for platelet adhesion than does the PEUU or SR surface. 

Early work (Kemp and Rideal, 1934 Lindau and Rhodius, 1935) showed that the concentration dependence of adsorption followed a Langmuir-type isotherm, and recent studies have confirmed this in many cases (Dillman and Miller, 1973 Brash and Lyman, 1969). Thus the adsorbed film is believed to be monomolecular and its concentration is frequently found to approach a plateau value as the solution concentration is increased, consistent with the saturation of available sites. In addition to the plateau value concentration (capacity), two other quantities, the thickness of the adsorbed film and the initial slope of the isotherm are often used to characterize polymer adsorption. The thickness data supplements interfacial concentrations to give clues about molecular conformation. For proteins, the interfa-... 

At pH 7 5, a Langmuir type adsorption isotherm, consistent results for different solid to liquid ratios, at pH 5 5 the course of adsorption isotherms depends on tlie solid to liquid ratio... 

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