Volume exclusion

This was precisely the point where a was defined to equal unity, so it is entirely appropriate that inter- and intramolecular exclusion volumes are effectively zero under the same conditions. 

Components of a highly short chain branched (scb) waxymaize and a more long chain branched (Icb) amylomaize were separated on the semipreparative Sephacryl S-1000 system. Both samples contained high dp components that eluted in the exclusion volume, but the percentage of these components was quite different 90% for the scb waxymaize starch and approximately 10% for the Icb amylomaize starch (Fig. 16.6). The degree of polymerization averages for these samples was determined utilizing the previously established linear... 

Fig. 5. Probabilities pn of observing n water-oxygen atoms in spherical cavity volumes v. Results from Monte Carlo simulations of SPC water are shown as symbols. The parabolas are predictions using the flat default model in Eq. (11). The center-to-center exclusion distance d (in nanometers) is noted next to the curves. The solute exclusion volume is defined by the distance d of closest approach of water-oxygen atoms to the center of the sphere. (Hummer et al., 1998a)... 

In addition, branched chain compounds have been developed consisting of a functional group or a reactive group followed by a PEG4 chain, which then leads to three branches each having an mPEG arm on them. Such compounds are expected to provide large exclusion volumes in aqueous solution to surround, protect, and solubilize modified molecules. 

V0 = Retention volume for a non-retained component (or exclusion volume), and... 

Assuming an exclusion volume of 5 ml per column allows construction of Table I from Equation 1. Table I lists the bandwidth in microliters as a function of column plate number and the number of columns in series. The data assume that the plate number may be generated at total exclusion, as well as at total permeation actual measurements made using the smaller pore size column si ibstantiate this. 

Polymer gel GPC columns packed with 10-pm gels can exhibit efficiencies of 12,000 to 16,000 plates depending on the pore size. Single columns of this type produce bandwidths from 160 to 180 pi. As columns are coupled in series, bandwidth increases as the square root of the number of columns, as may be seen from Equation 1. Plate number doubles, but so does the exclusion volume. The 5-pm gel columns typically achieve 20,000 to 24,000 plates, and are represented by the bottom two rows of the table. The implications of the bandwidth values in Table I will be discussed below. 

Surprisingly enongh, the above processes are very fast and separation of macromolecnles on this principle can be considered an equilibrium process. The precise measurements of retention volumes of polymers under conditions of their partial pore permeation in absence of enthalpic interaction did not reveal practically any effect of the eluent flow rate [55]. On the contrary, in a review, Aubert and Tirrell [66] have demonstrated that the SEC exclusion volumes can be flow rate dependent due to both anomalous and physical effects. The former are caused by... 

Fig. 6. Elution profiles of three alkyl 2-acetamido-2-deoxy- -D-glucopyranosides 4a (a. n=8 b. n=ll c. n=14) in gel filtration chromatography on sepharose 4B (exclusion 2.10 Da, exclusion volume 10 mL) monitored by and radioactivity countings (normed to 1.0 for reason of convenience). ( ) H countings of H-labelled phosphatidyl choline (x) C...

What is the total exclusion volume for the column (i.e. the interstitial volume), and what is the volume of the pores (the intraparticle volume) ... 

The radial distance distribution in simple atomic and molecular fluids is determined essentially by the exclusion volume of the particles. Zemike and Prins [12] have used this fact to construct a one-dimensional fluid model and calculated its radial distance correlation function and its scattering function. The only interaction between the particles is given by their exclusion volume (which is, of course, an exclusion length in the one-dimensional case) making the particles impenetrable. The statistical properties of these one-dimensional fluids are completely determined by their free volume fraction which facilitates the configurational fluctuations. 

In contrast to that model, we generated statistical homogeneous defect structures with a broken coordination number of next neighbors. The exclusion volume of the segments should be accounted for. To our knowledge, there is no mathematical method that allows one to describe the radial distance distribution of such structures analytically. It must be calculated on a computer by generating the structure steadily. 

The packing fraction is given by the ratio (exclusion volume/total volume). 

The essential step to simulate a realistic short range order region with our model is to occupy the local segment exclusion volume with the mean electronic density of the chain segments yielding the correlation cylinders introduced in Sect. 2. 

In the case of the PE melt, the largest part of the configuration entropy is included in the variety of chain conformations. In our model of the PE melt, these chain conformations cause the diameter of the correlation cylinders in which the chain segments are embedded to fluctuate. This leads necessarily to distance fluctuations of next neighbor segments because of steric hindrance of the local segment exclusion volume. Therefore, the inter- and intramolecular distance correlations cannot be discussed independently. 

Ksec = 0 when the molecule hydrodynamic radius is higher than the mean pore diameter. KSEC is 1 with small molecules, which can easily penetrate into the pores. The most important parameters influencing resolution are the pore volume, pore size distribution, and particle size. The separation domain is between the exclusion volume Va and the inclusion volume ( V0 + Vp). 

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