Solvent-excluded volumes

Solvent-excluded surfaces correlate with the molecular or Connolly surfaces (there is some confusion in the literature). The definition simply proceeds from another point of view. In this c ase, one assumes to be inside a molecaile and examines how the molecule secs the surrounding solvent molecules. The surface where the probe sphere does not intersect the molecular volume is determined. Thus, the SES embodies the solvent-excluded volume, which is the sum of the van der Waals volume and the interstitial (re-entrant) volume (Figures 2-119. 2-120). 

The solvent-excluded volume is a molecular volume calculation that finds the volume of space which a given solvent cannot reach. This is done by determining the surface created by running a spherical probe over a hard sphere model of molecule. The size of the probe sphere is based on the size of the solvent molecule. 

Polymer Solutions in Good Solvent Excluded Volume Effect... 

We can reasonably assume two major contributions to the difference in specific volume between the unfolded and folded states of a protein. The first contribution is that arising from the decrease in solvent-excluded volume when the tightly, but of course not perfectly, packed protein folded structure is disrupted. Water molecules enter this volume, thereby decreasing the overall volume of the protein solvent system. The magnitude of this contribution is a specific property of the protein, both in its folded and unfolded state. The second contribution arises from the change in the volume of the water molecules that hydrate the newly exposed protein surface area, relative to their volume in the bulk. Much of our present understanding of the contribution of differential hydration volume has come from recent studies of model compounds and proteins based on PPC. This technique, developed by Brandts and coworkers [17] and recently reviewed by us [16,18], is based on the measurement of the heat released or absorbed upon small (e.g., 0.5 MPa) pressure... 

In theta solvents, excluded volume effects vanish and flexible molecular chains behave as phantom chains (1). The characteristic ratio Cn = where (r )o is the mean square end-to-end distance of a... 

The volume of space bounded by the solvent-accessible molecular surface is called the solvent-excluded volume because it is the volume of space from which solvent is excluded by the presence of the molecule when the solvent molecule is also modelled as a hard sphere. Moreover, the interstitial volume is the volume consisting of packing defects between the atoms that are too small to admit a probe sphere of a given radius in practice, it is calculated as the difference between the solvent-excluded volume and the van der Waals volume. An analytical method was developed by Connolly able to calculate the solvent-excluded volume [Connolly, 1983b] several other numerical and analytical approaches have been proposed. 

Steric descriptors and/or -> size descriptors representing the volume of a molecule. The volume of a molecule can be derived from experimental observation such as the volume of the unit cell in crystals or the molar volume of a solution or from theoretical calculations. In fact, analytical and numerical approaches have been proposed for the calculation of molecular volume where the measure depends directly on the definition of - molecular surface-, -> van der Waals volume and -> solvent-excluded volume are two volume descriptors based on van der Waals surface and solvent-accessible surface, respectively. 

This procedure is based on the use of unique sphere, with its tesserae defined in terms of a number of spherical triangles (from 60 to 940) derived by partition of the pentakisdodecahedron faces. The sphere is deformed to mimick the molecular shape, taking into account solvent excluded volume. The number of tesserae is automatically increased only in the portions of the surfaces where it is needed, keeping the shape of a curvilinear triangle. The gain in computational times reaches a 100 factor for the largest molecules. 

Keywords Macroions, layering, thin colloidal films, solvent excluded volume effects, struc-... 

The radius R is dependent on the solvent. Where the polymer is represented as an ideal, freely jointed chain, no account is taken of the effect of the solvent. This represents the borderline case between a poor and good solvent. Here, each link is in a random direction with respect to its neighbors and the end-to-end distance is proportional to aN where a is the effective monomer length. This distance is much smaller than the molecular length aN and is characteristic of the molecular radius R. For the more common case of a chain in a good solvent, excluded volume effects must be considered, and where this volume is of the order of it can be shown that (de Gennes 1979, 1990)... 

The non-polar contribution to the free energy of solvation includes van der Waals solute-solvent interactions and the cost of cavity formation. The cost of cavity formation can be modeled effectively with a term that is simply proportional to the solvent accessible surface area or the solvent excluded volume [28-30]. Often, van der Waals interactions are not considered separately, but new formalisms have been suggested to include such contributions effectively [31]. Recently, it was also recognized that the length-scale dependence of non-polar interactions may further complicate the development of accurate implicit non-polar models [32]. It is clear that further studies will be needed to identify the optimal implicit non-polar formalism. 

The zero mode is the self-diffusion of the center of mass whose diffusion coefficient is given by the Stokes-Einstein relation D = k TIN. The time Tj will be proportional to the time required for a chain to diffuse an end-to-end distance, that is, R )/D = t N b lk T. This means that for time scales longer than Tj the motion of the chain will be purely diffusive. On timescales shorter than Tj, it will exhibit viscoelastic modes. However, the dynamics of a single chain in a dilute solution is more complex due to long-range forces hydrodynamic interactions between distant monomers through the solvent are present and, in good solvents, excluded volume interactions also have to be taken into account. The correction of the Rouse model for hydrodynamic interaction was done by Zimm [79]. Erom a mathematical point of view, the problem becomes harder and requires approximations to arrive at some useful results. In this case, the translational diffusion coefficient obtained is... 

The Connolly solvent-excluded volumes (the volume contained within the contact molecular surface) of the probe molecules are 269 A, 392 A, and 515 A for FDM, FDMDG, and FDMTG, respectively. It is clear that increasing the volume of the probe molecule lowers the overall mass transport, thereby decreasing the oxidative current, but increases the selectivity as evidenced by the greater normalized current ratio (AZ/Z s). 

Let us start with a solution of chains (polymerization index A ) in a good solvent (excluded volume parameter i = a (1 - 2 ) > 0). The chains repel each other, and this is reflected in the existence of a positive osmotic pressure II. 

Among the surface calculation approaches tested (cf. [2]), the analytically accurate programs MSRoll [21] and, in particular, SIMS [22] turned out to yield the most reasonable results for protein envelopes in terms of molecular and accessible surfaces, in addition to the possibility to create a smooth molecular dot surface required for application of advanced hydration modeling strategies and values for the solvent-excluded volume. The input to both programs can be influenced by the values used for r dbe (usually approx. 1.45 A), and in the case of SIMS also by the dot density, t/dot (in A ), chosen. 

It is to be noted that, as the size exponent increases from 1/2 to 3/5 due to polymer-solvent excluded volume interactions, the chain extends more inside the pore for the same values of Dp and N, while maintaining the one-dimensional nature of/ n for strong confinements. 

Wss being the solvent-solvent excluded volume parameter. Like monomer-solvent electrostatic interactions, we ignore the solvent-ion electrostatic interactions so that Hsj = 0 for j = c, +, — due to the point-like sizes of the ions, which exhibit zero excluded volume. Also, taking ion-ion interactions to be purely electrostatic in nature, we can write... 

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