Langmuir adsorption isotherm polymers

For polymeric membranes filled with absorptive fillers, sorption in the filler occurs in accordance with the Langmuir adsorption isotherm while Henry s law governs that in the polymer matrix. This kind of sorption isotherm is designated as type-II isotherm. 

Langmuir adsorption isotherm Pendant drop method Sanchez approximation Surface tension of polymer blends Surface tension of random copolymers... 

Interestingly, while the adsorption of polyelectrolytes onto BaS04 does not conform to the usual assumptions of the Langmuir adsorption isotherm model, the Langmuir model nevertheless provides a good fit to these experimental results as it does in many other cases of polymer adsorption. The Langmuir adsorption isotherm can be written in linear form as shown in Equation 1. 

This section will deal with the above interfacial aspects starting with the equilibrium aspects of surfactant adsorption at the air/water and oil/water interfaces. Due to the equilibrium aspects of adsorption (rate of adsorption is equal to the rate of desorption) one can apply the second law of thermodynamics as analyzed by Gibbs (see below). This is followed by a section on dynamic aspects of surfactant adsorption, particularly the concept of dynamic surface tension and the techniques that can be applied in its measurement. The adsorption of surfactants both on hydrophobic surfaces (which represent the case of most agrochemical solids) as well as on hydrophilic surfaces (such as oxides) will be analyzed using the Langmuir adsorption isotherms. The structure of surfactant layers on solid surfaces will be described. The subject of polymeric surfactant adsorption will be dealt with separately due to its complex nature, namely irreversibility of adsorption and conformation of the polymer at the solid/liquid interface. 

Figure 7.8 Adsorption of polymers following the Langmuir adsorption isotherm. The adsorption typically increases with increasing polymer molecular weight. When polymers are used as steric stabilizers, high molecular weight polymers at full coverage (i.e. the plateau area) should be preferred (see also Chapter 12)...

Many adsorption phenomena especially of surfactants, polymers, proteins and the chemical adsorption of gases on solids can be well represented by the Langmuir adsorption isotherm. This equation can be expressed in a suitable linear form and we can obtain the two parameters of the model, of which one is the concentration or volume at maximum (full) coverage or the so-called monolayer coverage. Knowledge of this monolayer coverage and of the specific surface area of the solid can help us estimate the surface area occupied by a molecule at the interface and thus the amount needed for stabilization. The specific solid surface area can be obtained from gas adsorption measurements on the same solid. 

Before our theory was fully developed, extensive work by J. Koral in cooperation with R. Ullman (15) confirmed in detail and with considerable accuracy all previously known features. They ascertained, in addition, the particulars of the adsorption isotherms for a number of polymers and dispersed adsorbates and established the remarkable degree to which most isotherms could be approximated by 2-parameter equations, like Langmuir s isotherm for monolayers of small molecules. They found the dependence of the adsorption on MW to be weak and determined the area per adsorbed molecule. 

Many systems that definitely do not conform to the Langmuir assumptions —the adsorption of polymers, for example —nevertheless display experimental isotherms that resemble Figure 7.16. Although these can be fitted to Equation (67), the significance of the constants is dubious. Therefore the Langmuir equation is often written as... 

Type G is a high-affinity adsorption isotherm. The molecules bind so strongly that no rest can be detected in the solution or gas phase. The difference to the Langmuir type is quantitative not qualitative. It is often observed for polymer or proteins adsorbing from solution. 

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. 

A Ithough the adsorption of polymers onto solid surfaces has been thor-oughly studied (I), relatively few studies can be found in the literature on the adsorption of proteins onto polymer surfaces. In 1905, Landsteiner and Uhliz (2) discussed the interaction of serum proteins with synthetic surfaces. Blitz and Steiner (3) showed that albumin adsorption onto solid surfaces increased with increasing albumin concentration and that adsorption was nearly irreversible. Hitchcock reported (4) that adsorption of egg albumin onto collodion membranes followed a Langmuir isotherm with maximum adsorption occurring near the isoelectric point. Later, Kemp and Rideal (5) reported that protein adsorption onto solids conforms with Langmuir adsorption. 

We obtained adsorption kinetic data and isotherm curves by determining the amount of protein adsorbed onto polymers by internal reflection IR spectroscopy which gave good reproducibility (19). The adsorption character was consistent with the Langmuir adsorption type and adsorption vs. time curves showed the expected plateau usually found in macro-molecular adsorption. A competitive adsorption study is being carried... 

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-... 

Similar adsorption data have also been reported for the adsorption isotherms of many compounds in various systems. For example, the adsorption data of several jS-blockers, particularly those of propranolol acquired in a 1 to 7000 relative concentration range, on an immobilized cellulase. Cel 7A, fit very well to the bi-Langmuir model, as illustrated in Figure 3.13 [47,55]). The enantioselective site was identified as a pair of amino acid residues in the tunnel formed by the main chain of the protein. The parameters of the isotherm depend on the pH as illustrated in Figure 3.14. A bi-Langmuir model was also found to accoimt well for the separation of pairs of enantiomers on polymers molecularly imprinted with one of the enantiomers [56]. Note, however, that there are also many systems in which the adsorption isotherms of enantiomers are not accounted for by a bi-Langmuir model showing that enantioselectivity is often achieved by a complex... 

The Langmuir-type isotherm can be used (Lakatos et al., 1979), as it is in UTCHEM, to describe polymer adsorption. The Langmuir-type isotherm is given by... 

Li (2007) observed that the adsorption of a hydrophobically associating water-soluble polymer, AP-2, did not follow the Langmuir-type isotherm. Figure 5.37 shows that the adsorption increased to a maximum and then decreased as the polymer concentration was increased. The reason is probably that the hydrophobic polymer has an adsorption layer of multiple molecules on rock surfaces. When the polymer concentration is increased, the adsorption layer becomes thicker because of more adsorption. When the polymer concentration is further increased, the molecular interaction in the liquid is stronger than that between the adsorbed molecules and rock surfaces. Then the adsorbed molecules may leave the rock surfaces and redissolve into the liquid. Thus, the adsorption decreases. 

To relate the triiodide concentration in solution to the oxidation of the polymer, an approach based on a Langmuir-like adsorption isotherm has been used... 

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