Small solute molecules

This model then leads us through a thicket of statistical and algebraic detail to the satisfying conclusion that going from small solute molecules to polymeric solutes only requires the replacement of mole fractions with volume fractions within the logarithms. Note that the mole fraction weighting factors are unaffected. 

Next let us consider the light scattered by liquids of low molecular weight compounds. We are actually not directly interested in this quantity per se, but in scattering by solutions-polymer solutions eventually, but for now solutions of small solute molecules. The solvent in such a solution does scatter, but, in practice, the intensity of light scattered by pure solvent is measured and subtracted as a blank correction from the scattering by the solution. 

If the solute molecules are so large that they are completely excluded from the gel, Kd = 0. In this case, the solute passes through the column entirely in the mobile phase, and its elution volume equals the void volume V0. Small solute molecules that can freely penetrate the gel pores will have a Kd value of 1 here, Ve = V0 + Vf. Between these two extremes lie all solutes that can enter the gel phase to various, limited extents these will have Kd values lying between 0 and 1, and elution volumes between V0 and V0 + Vt, with both Kd and Ve increasing as the molecular size of the solute decreases. 

For contrast variation the EL.O content of a solution has to be replaced by D20. Usually a series of samples is prepared with varying EL.O/D.,0 ratios. For each solution in the series, there must be a buffer with exactly the same composition of aqueous phase, induding small solute molecules and ions. The exchange of IL,0 for D20 is usually performed by dialysis, and so the last dialysis must be taken to equilibrium. 

The stationary phase in SEC is a highly porous substrate whose pores are penetrated best by small solute molecules. Because larger solute molecules are unable to enter as deeply into the pores, they will travel further down the column in the same time. The largest molecules, which are totally excluded from the pores, are eluted first from the column. Because the solvent molecules are usually the smallest, they are normally the last to be eluted. The rest of the solute molecules are eluted between these two extremes, at a time dependent on their ability to penetrate into the pores. In SEC, therefore, unlike other chromatographic methods, the entire sample often is eluted before the solvent dead time peak, t0, as shown in Figure 2.13.53... 

Osmosis is the selective passage of particular components of a solution through a semipermeable membrane. Usually, it is the solvent that passes through the membrane, because the solute is blocked. However, some membranes also allow small solute molecules to pass through as well and only block the passage of macromolecular solute molecules. The osmotic pressure of a solution is the pressure difference produced at equilibrium across the membrane, with the solution on one side of the membrane and pure solvent on the other side. As shown in Fig. 4, the reduced activity of the solvent in solution is compensated for by an increase in the pressure of the solution ... 

Microporous membranes can be used in a manner similar to reverse osmosis to selectively allow small solute molecules and/or solvents to pass through the membrane and to prevent large dissolved molecules and suspended solids from passing through. Microfiltration refers to the retention of molecules typically in the size range from 0.05 to 10 pm. Ultrafiltration refers to the range from 1 to 100 nm. To retain even smaller molecules, reverse osmosis, sometimes called hyperfiltration, can be used down to less than 2 nm. 

In the Snyder approach to gradient optimization the characteristics of the individual solutes are largely neglected. The optimum shape of the gradient is determined by the phase system and the optimum slope is usually estimated from simple rules for the retention behaviour of the solutes (e.g. assuming S = 7 for small solute molecules as we did above). Only the initial and the final conditions are adapted to the requirements Of the sample. 

For so-called regular solutions, in which small solute molecules disperse randomly among like-size solvent molecules, AS° can be taken as zero [14]. The enthalpy change AH% for transferring (mixing) pure solute of molar volume Vi into solvent p at high dilution is approximately [14]... 

Macromolecules often have a number of sites for interactions and binding of the solute or ligand molecules. For example, hemoglobin in the blood binds oxygen at certain sites. Surface charges on the molecules also affect the diffusion. Therefore, the presence of macromolecules and small solute molecules in solutions may affect Fickian-type diffusion. Most of the experimental data on protein diffusivities have been extrapolated to very dilute or zero concentration since the diffusivity is often a function of concentration. Table 6.4 shows diffusivities of some proteins and small solutes in aqueous solutions. The diffusion coefficients for the macromolecules of proteins are on the order of magnitude of 5 X 10 11 m2/s. For small solute molecules, the diffusivities are around 1 X 10 9 m2/s. Thus, macromolecules diffuse about 20 times slower then small molecules. 

Dialysis a phenomenon in which a semipermeable membrane allows transfer of both solvent molecules and small solute molecules and ions. (17.6)... 

Because of its apolar interior, the lipid bilayer is a barrier to diffusional equilibration of solutes between the two aqueous compartments that it separates. The ability of most small solute molecules (50 < molecular weight < 300) to cross the bilayer is directly proportional to their ability to partition into hexadecane or olive oil from an aqueous solution (58), which is an observation first made by Overton (59) and is often referred to as Overton s Law. Permeation of lipid bilayers by small polar molecules and ions seems to occur via one or a combination of both of two mechanisms depending on the nature of the permeants and the nature of the bilayers. First, a solubility-diffusion mechanism treats the bilayer as a slab of liquid hydrocarbon sandwiched between two bulk aqueous compartments. The permeant must partition into the bilayer slab from one of the aqueous compartments, diffuse across it, and leave by dissolving into the second aqueous compartment. In this case, the permeability coefficient, P, is given by ... 

In this equation compared to Equation 6.1, the osmotic pressure, AIT, of the feed solution and a reflexion coefficient, tr, have been introduced to account for the counter flux due to the difference in concentration of small solutes (molecule or ion) between the feed phase and the permeate phase. 

The free-energy and chemical potentials of the solvent is slightly altered from the case of small solute molecules (Flory, 1970) ... 

These results support the assertion that plasticization will affect the mobility of small solute molecules embedded within. However, there is a significant caveat in using these results to confirm that plasticization may also be linked to the reactivity of small solutes embedded within the matrix. As shovm by Simatos et al. (1981), one would expect the increased... 

For an understanding of protein-solvent interactions it is necessary to explore the modifications of the dynamics and structure of the surrounding water induced by the presence of the biopolymer. The theoretical methods best suited for this purpose are conventional molecular dynamics with periodic boundary conditions and stochastic boundary molecular dynamics techniques, both of which treat the solvent explicitly (Chapt. IV.B and C). We focus on the results of simulations concerned with the dynamics and structure of water in the vicinity of a protein both on a global level (i.e., averages over all solvation sites) and on a local level (i.e., the solvent dynamics and structure in the neighborhood of specific protein atoms). The methods of analysis are analogous to those commonly employed in the determination of the structure and dynamics of water around small solute molecules.163 In particular, we make use of the conditional protein solute -water radial distribution function,... 

Are the water (and small solute) molecules associated with protein surfaces squeezed out of the interfacial region upon complex formation ... 

For a molecular species completely excluded, Ve = V0 and KD is zero. For small solute molecules which can enter all the pores, KD = 1. Separation, therefore, occurs only where solute molecules obey the condition 0 < Kd < i. 

How can one then decide on the choice of the dielectric boundary One possibility is to benchmark PB calculations against explicit-solvent molecular dynamics (MD) simulations. Most of such efforts have been limited to small solute molecules [20-22]. However, it has been shown that the difference between MS and vdW results for electrostatic solvation energies depends on solute size [23]. Therefore parameterization on small solutes (either against explicit-solvent MD results or against experimental data) may not be reliable for calculating electrostatic contributions to protein-protein and protein-nucleic acid binding. 

To understand how steric exclusion differs from the other forms of chromatography, refer to Equation 21.4. In this context, V a and Va are referred to as the void volume and the total pore volume, respectively. The distribution coefficient depends on the molecular weight of the sample and on the pore size of the packing. The equilibrium established in exclusion chromatography is described by Equation 21.1 ATx is defined by Equation 21.2. In a true permeation process, assuming all pores to be accessible to a small solute molecule, and = 1- If none of the pores... 

Since it is well known that at least part of the Cu of ceruloplasmin undergoes cyclic reduction by substrate and oxidation by molecular oxygen (88), the availability of the various Cu binding sites to small solute molecules is of importance. One of the first observations which suggested that at least part of the Cu was... 

In particular, it has been suggested that the highly ordered structure of these salts may contain voids, and that these voids can accommodate small solute molecules. Furthermore, since the chains present on the cations are flexible they can move more rapidly than the whole cation, permitting a rapid diffusion of solutes from one void to another [18]. The formation of cavities (voids) in ionic liquids has been recently studied via Monte Carlo simulations [19]. Analysis of cavity size distribution functions shows that ionic liquids exhibit a large tendency to form cavities, a property which seems to be correlated to the attractive interactions between ions and, particularly, to the tendency of the ions to associate into ion aggregates. 

Entangled difiusion of small solute molecules within the pores of... 

In osmosis a semipermeable membrane prevents transfer of all solute particles. A similar phenomenon called dialysis occurs at the walls of most plant and animal cells. However, in this case the membrane allows transfer of both solvent molecules and small solute molecules and ions. One of the most important applications of dialysis is the use of artificial kidney machines to purify the blood. The blood is passed through a cellophane tube, which acts as the semipermeable membrane. The tube is immersed in a dialyzing solution (see Fig. 17.17). This washing solution contains the same concentrations of ions and small molecules as blood but has none of the waste products normally removed by the kidneys. The resulting dialysis of waste products cleanses the blood. 

PMF. Understanding PMF is of great importance in biology and chemistry, in such phenomena as aggregation, cluster formation, protein folding, and protein-DNA interaction, to name a few. When large hydrophobic solutes are present in water, then they introduce a distortion in the HB network around them. Therefore, two hydrophobic solutes can interact with each other even when they are far apart, at the scale of solvent molecular diameter. Such large-scale distortion of the water structure is not present for small solute molecules, such as methane, which can be easily accommodated within the water structure. 

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