Entropic interactions

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

AG is always negative, and the decrease in free energy can be due to adsorption effects (change in AH) or entropic interactions (change in AS). AS is always operating when the polymer chain cannot occupy all possible conformations in a pore (confined space) due to the limited size of the pore relative to the size of the macromolecule. In a real... 

As has been pointed out, both entropic and enthalpic interactions affect the chromatographic behavior of macromolecules. They are adjusted to the required type of separation by selecting appropriate stationary and mobile phases. In a third mode of liquid chromatography of polymers, liquid chromatography at the critical condition (LCCC) (Entelis etal., 1985,1986 Pasch, 1997), the adsorptive interactions are fully compensated by entropic interactions. This mode is also referred to as liquid chromatography at the critical point of adsorption. Hence, TAS is equal to AH and therefore, AG becomes zero. K is 1 irrespective of molar mass and, consequently, homopolymer molecules of different molar masses coelute in one chromatographic... 

Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,... 

To extract a value of the step-mobility h from the grating relaxation experiments [12], we must evaluate the strength of the step-step interaction y. Computational work suggests that ydue to elastic interactions between Si(OOl) steps is 0.2 eV run [29], while, we estimate that the entropic interaction is 10 times larger. (We use a step stiffness P calculated from the geometric mean of P for Sa and Sb steps given in Ref [30] P, 0.03 eV mn-. ) Therefore, entropic repulsion should dominate, and... 

Jusufi A, Likos CN, Lowen H. Counterion-induced entropic interactions in solutions of strongly stretched, osmotic polyelectrolyte stars. J Chem Phys 2002b 116 11011-11027. 

A practically useful predictive method must provide quantitative process prediction from accessible physical property data. Such a method should be physically realistic and require a minimum number of assumptions. A method which is firmly based on the physics of the separation is likely to have the widest applicability. It is also an advantage if such a method does not involve mathematics which is tedious, complicated or difficult to follow. For the pressure driven processes of microfiltration, ultrafiltration and nanofiltration, such methods must be based on the microhydrodynamics and interfacial events occurring at the membrane surface and inside the membrane. This immediately points to the requirement for understanding the colloid science of such processes. Any such method must account properly for the electrostatic, dispersion, hydration and entropic interactions occurring between the solutes being separated and between such solutes and the membrane. 

Extending this idea one step further, bacteria may have evolved to produce extracellular polymeric substances (EPSs) in order to make mineral surfaces more favorable for attachment. This would be an important evolutionary step, especially if the earliest bacteria utilized minerals for respiration and nutrition.25 According to the present model, oxides other than quartz also have unfavorable entropic interactions with the head group PL (AS°adsi < 0). EPSs should then be exuded on the surfaces of many oxide (and silicate) minerals. As discussed above, quartz is the most harmful, so greater production of EPSs should be expected on quartz, all other factors being equal. Consistent with this hypothesis, the nature of the substrate and of the bacterial surfaces does, in fact, affect the amount of EPS produced.60-62 The idea that surfaces become more hydrophilic by bacterial attachment also underlies the biobeneflciation of ores during mineral separation by floatation. 

Hydrophobic effects are thus of practical interest. If we accept the goal of a simple, physical, molecularly valid explanation, then hydrophobic effects have also proved conceptually subtle. The reason is that hydrophobic phenomena are not tied directly to a simple dominating interaction as is the case for hydrophilic hydration of Na+, as an example. Instead hydrophobic effects are built up more collectively. In concert with this indirectness, hydrophobic effects are viewed as entropic interactions and exhibit counterintuitive temperature dependencies. An example is the cold denaturation of globular proteins. Though it is believed that hydrophobic effects stabilize compact protein structures and proteins denature when heated sufficiently, it now appears common for protein structures to unfold upon appropriate cooling. This entropic character of hydrophobic effects makes them more fascinating and more difficult. 

One explanation that can be offered to explain the two Tc values obtained for PMA at low values of a is that they represent the independent rotation of small clusters of the polymer chain. The larger value of (approximately 50 ns) can be associated with a rotating spherical cluster of radius 3.8 nm and of polymer molecular weight equal to 19000. Rotating units of similar size have been observed when the probes 9-methylanthracene and 9,10-DMA are solubilized in the PMA hypercoil structure (15,16) and when the more polar fluorescent probes Rhodamine B ( ) and 1,8-anilinonaphthalene sulfonic acid (1,8-ANS) (28) are bound to PMA for a value of a equal to 0. The smaller rotating unit present in PMA and PAA whose value of Tj, is approximately equal to 5 ns (which corresponds to particles whose radii are approximately equal to 2 nm) may arise from the rotation of a small section of the chain which is just sufficient to surround the 9,10-DMA probe and protect it from unfavourable entropic interactions with water. This shorter T, was... 

Reduction in configurational entropy of the chains on significant overlap. This is referred to as elastic (entropic) interaction, and is given by the expression ... 

Elastic interaction occurs when the displacement fields from steps substantially superpose. Atoms located in the vicinity of steps tend to relax stronger compared to those farther away. The resulting displacements or lattice distortions decay with increasing distance perpendicular to the steps. Atoms situated in between two steps experience two opposite forces and cannot fully relax to an energetically more favorable position as would be the case with quasiisolated steps. The line dipoles at steps are due to Smoluchowski smoothing [160] and interact electronically. Only dipole components perpendicular to the vicinal surface lead to repulsion whereas parallel components would lead to attractive interaction. The dipole-dipole interaction seems to be weaker than the elastic one. For instance, steps on vicinal Ag(lll) have weak dipoles as was shown in a theoretical study [161]. Entropic interaction is due to the condition that steps may not cross and leads to an effective repulsive potential, the weakest interaction type. This contribution is always present and results from the assumption that cavities under the surface are unstable. Experiments and theory investigating steps on surfaces were recently reviewed [162]. 

In real LAC only a fraction of the pores of the stationary phase is accessible and, therefore, entropic interactions must be assumed. Accordingly, the distribution... 

In conclusion, ideal SEC and ideal LAC are extremes of the same principle. In the real SEC and LAC modes, retention responds to both enthalpic and entropic interactions, and only the predominance of one of these interactions decides which mode is operating. Accordingly, real SEC and real LAC can be regarded as mixed mode chromatographic methods. With chemically heterogeneous polymers, effects are even more dramatic because exclusion and adsorption act differently on molecules of different composition. 

In a more general sense, the size exclusion mode of liquid chromatography relates to a separation regime, where entropic interactions are predominant and TAS > AH. In the reverse case, AH > TAS, separation is mainly directed by enthalpic interactions. As both separation modes in the general case are affected by the macromolecule size and the pore size, a certain energy of interaction may be introduced, characterizing the specific interactions of the monomer unit of the macromolecule and the stationary phase, e is a function of the chemical composition of the monomer unit, the composition of the mobile phase of the chromatographic system, and the temperature. 

The most frequently apphed technique for the separation of polymers, namely size-exclusion chromatography (SEC), is based on the well-balanced interactions between the column material, the solvent, and the polymer sample. In order to achieve a complete separation according to size, and also to determine reliable polydispersity values, enthalpic interactions between the sample and column material must be excluded, as only entropic interactions lead to SEC separation. This is not always possible in the case of dendritic polymers which, being multifunctional architectures, have interactions with the column material that are effectively predestined. It has been repeatedly observed that this problem is more severe for higher molar mass products. An example of aromatic hb polyesters with different... 

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