Adsorption excluded volume effect

In the following paper, the possibility of equilibration of the primarily adsorbed portions of polymer was analyzed [20]. The surface coupling constant (k0) was introduced to characterize the polymer-surface interaction. The constant k0 includes an electrostatic interaction term, thus being k0 > 1 for polyelectrolytes and k0 1 for neutral polymers. It was found that, theoretically, the adsorption characteristics do not depend on the equilibration processes for k0 > 1. In contrast, for neutral polymers (k0 < 1), the difference between the equilibrium and non-equilibrium modes could be considerable. As more polymer is adsorbed, excluded-volume effects will swell out the loops of the adsorbate, so that the mutual reorientation of the polymer chains occurs. 

Features of polyelectrolyte adsorption are that both the adsorbance and the thickness can be easily varied by changing the concentration of added salt as well as pH in bulk solution since such changes cause variation of the electrostatic repulsions of polyelectrolyte chains adsorbed, i.e., the excluded volume effect. 

For adsorption of nonionic polymer, Hoeve (15) and Jones-Richmond (16) attempted to incorporate the excluded-volume effect into the expansion factor, respectively. They suggested that the thickness of the adsorbed layer in good and 0 solvents should be taken at the same adsorbance and molecular weight3 respectively. We may calculate the expansion factor at the bulk NaPSS concentration of 0.02 g/lOOml, since the adsorbances are almost the same for the respective NaCl concentrations, as seen from Figure 5. 

The theoretical description of excluded volume effects on the adsorption from good solvents is still unsatisfactory. The scaling theory for polymer adsorption has not yet been subject to experimental tests. 

Surface-bound, neutral, hydrophilic polymers such as polyethers and polysaccharides dramatically reduce protein adsorption [26-28], The passivity of these surfaces has been attributed to steric repulsion, bound water, high polymer mobility, and excluded volume effects, all of which render adsorption unfavorable. Consequently, these polymer modified surfaces have proven useful as biomaterials. Specific applications include artificial implants, intraocular and contact lenses, and catheters. Additionally, the inherent nondenaturing properties of these compounds has led to their use as effective tethers for affinity ligands, surface-bound biochemical assays, and biosensors. 

Several papers compare the properties of sulfobetaine (meth)acrylic polymers. NMR spectra and solution properties of 23a and 23b [59,60] are correlated with data from the corresponding polycarbobetaines [26]. The photophysical and solution properties of pyrene-labeled 23c were studied in terms of fluorescence emission. Addition of surfactants induces the formation of mixed micelles in aqueous solution [61]. Excluded volume effects of the unlabeled polymer were measured by light scattering [62], its adsorption on silica was studied by adsorbance measurement and ellipsometry [62,63], and the electrostimulated shift of the precipitation temperature was followed at various electric held intensities [64]. Polysulfobetaines may accelerate interionic reactions, e.g., oxidation of ferrocyanide by persulfate [65]. The thermal and dielectric properties of polysulfobetaines 23d were investigated. The flexible lateral chain of the polymers decreased Tg, for which a linear relationship with the number of C atoms was shown [66,67]. 

An increase in diffusion rates occurs as a consequence of increasing protein bulk concentration (Patino et al., 1999 Home and Patino, 2003 Baeza et al., 2004a). Excluded volume effects can have an effect similar to increasing protein concentration because of the increased thermod)mamic activity of the protein in the bulk solution — that would perform as a more concentrated one (Carp et al., 1999) — and can lead to an enhancement of protein adsorption at fluid interfaces (Tsapkina et al., 1992). 

Two diverse views of non-specific adhesion processes form the bases for contemporary theories introduced to rationalize observations of colloidal stability and flocculation in solutions of macromolecules (see 16-18 for general reviews). The first view is based on adsorption and cross-bridging of the macromolecules between surfaces. Theories derived from this concept indicate a strong initial dependence on concentration of macromolecules there is a rapid rise in surface adsorption for infinitesimal volume fractions (32) followed by a plateau with gradual attenuation of surface-surface attraction because of excluded volume effects in the gap at larger volume fractions (19-20). The interaction of the macroinolecule with the surface is assumed to be a snort range attraction proportional to area of direct contact. The second - completely disparate - view of non-specific adhesion is based on the concept that there is an exclusion or depletion of macromolecules in the vicinity of the surface, i.e. no adsorption to the surfaces. Here, theory shows that attraction is caused by interaction of tne (depleted) concentration profiles associated with each surface which leads to a depreciated macrornolecular concentration at the center of the gap. The concentration... 

The literature presents many studies on coil dimensions of synthetic polymers in mixed solvents. Most investigations involve liquid mixtures composed of a good and a poor solvents for the polymer. The action of mixed solvents has been reported to change coil dimensions, not only because of excluded volume effect or due to the interactions existing between the two liquids but also due to the preferential adsorption of one of the solvent by the polymer. 

The transition concentrations separating the concentration domain chain flexibility aspects, excluded volume effects and total and preferential adsorption coefficients of the same system have been discussed. 

The Kratky-Porod formula may not be applicable for long molecules with L Ip, for which excluded volume interactions should be taken into account. Intramolecular excluded volume effects result from repulsion between segments within the same molecule, which result in an increase of the end-to-end distance. These effects are particularly strong for 2D systems, which demonstrate an increased density of segments and do not permit chain crossings. Both methods require complete visualization of a statistical ensemble of single molecules in order to determine L, 0, and (R ). In addition, they assume the observation of molecules in their natural state, in which molecules are not constrained and freely fluctuate around their equilibrium conformation. The concurrent effects of adsorption, solvent evaporation, and capillary forces can, however, lead to kinetically trapped conformations. The question arises whether and under what conditions an equilibrium 2D conformation can be achieved. 

The product f-F is usually referred to in chromatography of column flow as the retardation factor, Fr (Giddings, 1965). In a polymer flood, there are therefore two competing effects on the retardation factor adsorption, tending to make Fr> 1, and velocity enhancement, which tends to make Fr< 1. Note that if Fr = 1, then it is probable that there are no adsorption or excluded-volume effects however, it could be that they fortuitously cancel. 

Experimental effluent profiles may be fitted directly to the analytic form of Equation 7.15, provided that the solute experiences only dispersion, equilibrium linear reversible adsorption and/or excluded-volume effects. Figure 7.2 shows an analytical fit to the experimental effluent profile of a tracer flood indicating that only dispersion occurs in this case. In some experimental situations, however, the analytic form in Equation 7.15 is inadequate to describe the observed effluent profiles, and other phenomena need to be considered, as discussed in the following section. 

Adsorption of material, for example polymer, will always have the same gross effect on the position of the effluent compared with that of an inert tracer. The effluent will be retarded relative to the tracer (i.e. it will appear later) because of the retention process, although this also depends on the magnitude of the IPV/excluded volume effect—the product of quantities / F—as discussed in Section 7.2.1. Considering the case of a linear adsorption isotherm (i.e. adsorption, T, is linear with c) when there is no IPV/excluded volume effect (/= ), the retardation factor, Fr, as defined in Equation 7.12, is greater than unity. Hence, the component velocity of the adsorbed/retained species will be less than that of an inert tracer by the factor 1/Fr whereas the tracer travels at the same average velocity as the fluid. 

The development of adsorption theory provides the explanation of the macromolecule behavior in the adsorption layer and provides the basis of arguments on the experimental results. A few theoretical models, describing the adsorbed macromolecule, are widely used now. Self-consistent field theory or mean field approach is used to calculate the respective distribution of trains, loops, and tails of flexible macromolecule in the adsorption layer [22-26]. It allows one to find the segment density distribution in the adsorption layer and to calculate the adsorption isotherms and average thickness of the adsorption layer. Scaling theory [27-29] is used to explain the influence of the macromolecule concentration in the adsorption layer on the segment density profile and its thickness. Renormalization group theory [30-33] is used to describe the excluded volume effects in polymer chains terminally attached to the surface. The Monte Carlo method has been used for the calculation of the density profile in the adsorption layer [33-35]. 

Some GPC analysts use totally excluded, rather than totally permeated, flow markers to make flow rate corrections. Most of the previously mentioned requirements for totally permeated flow marker selection still are requirements for a totally excluded flow marker. Coelution effects can often be avoided in this approach. It must be pointed out that species eluting at the excluded volume of a column set are not immune to adsorption problems and may even have variability issues arising from viscosity effects of these necessarily higher molecular weight species from the column. 

Thus, there are two limitations of the pycnometric technique mentioned possible adsorption of guest molecules and a molecular sieving effect. It is noteworthy that some PSs, e.g., with a core-shell structure, can include some void volume that can be inaccessible to the guest molecules. In this case, the measured excluded volume will be the sum of the true volume of the solid phase and the volume of inaccessible pores. One should not absolutely equalize the true density and the density measured by a pycnometric technique (the pycnometric density) because of the three factors mentioned earlier. Conventionally, presenting the results of measurements one should define the conditions of a pycnometric experiment (at least the type of guest and temperature). For example, the definition p shows that the density was measured at 298 K using helium as a probe gas. Unfortunately, use of He as a pycnometric fluid is not a panacea since adsorption of He cannot be absolutely excluded by some PSs (e.g., carbons) even at 293 K (see van der Plas in Ref. [2]). Nevertheless, in most practically important cases the values of the true and pycnometric densities are very close [2,7],... 

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