Interparticle volume

Retention is dependent on three variables KSEC, Va (the interparticle volume), and Vp. Retention volume is... 

The parameters of the pore structure, such as surface area, pore volume, and mean pore diameter, can generally be used for a formal description of the porous systems, irrespective of their chemical composition and their origin, and for a more detailed study of the pore formation mechanism, the geometric aspects of pore structure are important. This picture, however, oversimplifies the situation because it provides a pore uniformity that is far from reality. Thorough attempts have been made to achieve the mathematical description of porous matter. Researchers discussed the cause of porosity in various materials and concluded that there are two main types of material based on pore structure that can be classified as corpuscular and spongy systems. In the case of the silica matrices obtained with TEOS and other precursors, the porous structure seems to be of the corpuscular type, in which the pores consist of the interstices between discrete particles of the solid material. In such a system, the pore structure depends on the pores mutual arrangements, and the dimensions of the pores are controlled by the size of the interparticle volumes (1). 

The skeletal density is representative of the solid material itself, excluding its porosity. The bulk volume of catalyst minus its pore volume and the interparticle volume between discrete particles (V)) is the true skeletal volume. One calculates this term by... 

Depletion flocculation arises when a large unadsorbed, flocculating cosolute molecule does not fit properly into a small interparticle volume at the interface and the cosolute molecule accompanied by solvent is consequently expelled from the interface. As a result, the interparticle distance is shortened, causing an approach to x , and flocculation. Depletion stabilization is possible if the particle-cosolute attraction is greater than the particle-particle or cosolute-cosolute attraction. 

If the solid is nonporous, VM is the space between the particles (the interparticle volume), but if it is porous, VM includes both the interparticle volume and the internal volume of the particles. (In some instances, the size of the pores in the solid may be too small to admit the analyte molecules, and thus the internal portions of the solid may not be accessible to the sample, but that is a complication we will ignore at present.) These two types of particle give rise to two definitions of porosity. 

Other Experimental Methods. It is probably suitable to discuss here column porous structure. Porous space of a conventional packed column consists of the interparticle volume (Vip—space around particles of packing) and pore volume (Vp— space inside porous particles). The sum of those two constitutes the column void volume. The void volume marker ( unretained ) should be able to evenly distribute itself in these volumes while moving through the column. Only in this case the statistical center mass of its peak will represent the true volume of the Uquid phase in the column. In other words, its chromatographic behavior should be similar to that of the eluent molecules in a monocomponent eluent. If a chosen void volume marker compound has some preferential interaction with the stationary phase compared to that of the eluent molecules, it will show positive retention and could not be used as void marker. If on the other hand it has weaker interaction, it will be excluded from the adsorbent surface and will elute faster than the real void time, meaning that it also could not be used. For any analytical applications (when no thermodynamic dependences are not extracted from experimental data), 10% or 15% error in the determination of the void volume are acceptable. It is generally recommended to avoid elution of the component of interest with a retention factor lower than 1.5. Accurate methods for the determination of the column void volume are discussed in Chapter 2. 

The estimation of the amount of adsorbent in the column is based on the comparison of the total pore volume (Vptot [niL]) of the adsorbent in the column with the specific pore volume (Vp [mL/g]) of the same adsorbent determined from the full nitrogen adsorption isotherm. The ratio of these two values will give the adsorbent mass. Total pore volume in the column is determined as the difference of the column void volume (Vo) and the interparticle volume (Vip). 

Interparticle volume could be measured using GPC as the total exclusion volume of high-molecular-weight polymers, and the void volume could be accurately measured as the elution volume of deuterated acetonitrile eluted with neat acetonitrile. The example of these measurements and comparison with the adsorbent mass determined by unpacking the column and weighing the dried adsorbent are shown in Table 3-5. 

Ion-exclusion chromatography is used for the separation of low molecular weight ions and some neutral substances by a combination of partition, adsorption and ion repulsion [159,428,477-479]. The stationary phase is a high capacity ion exchanger with the same type of immobilized ionic group as the sample ions. Permanent ions with the same charge as the stationary phase are repelled and can only explore the interparticle volume while neutral and partially ionized solutes are retained and separated by partition between the mobile phase trapped in the porous stationary phase and the streaming... 

In a detailed study of a 25 cm x 4.6 mm I.D. column packed with Zorbax C8 (5 p,m particles and a surface area 330 m /g) with methanol-water (1 4) as mobile phase it was shown that 33% of the column volume was occupied by the fixed stationary phase [690]. The pore volume (21 % of the column volume) consisted of 21% adsorbed solvent and 79% bulk solvent. The interparticle volume (46% of the column volume) consisted of 73% moving phase and 27% static phase. It is not easy, however, to determine the various column volume elements, and generally kinetic and thermodynamic parameters have been determined for inadequately defined phase ratios and may not be correct in the absolute sense. 

Any chromatographic process relates to the selective distribution of an analyte between the mobile and the stationary phase of a given chromatographic system. In liquid chromatography the solvent, with a volume V in the interparticle space, moving along the column at a certain velocity, is the mobile phase and the porous adsorbent, having a pore volume Vp, is the stationary phase. The distribution coefficient equals the ratio of the concentrations of the analyte in the stationary and the mobile phases. In classical SEC a distribution of the analyte between the interparticle volume and the accessible pore volume takes place and the retention volume Vr is determined by... 

For small pore stationary phases, separation occurs exclusively on the outer surface. The pores are not accessible to the macromolecules (Ksec = 0)- Accordingly, the retention volume is a function of the interparticle volume and the volume of the stationary phase (Vstat) ... 

Without accessibility restrictions of the pores of the stationary phase (Ksec = 1), the pore volume Vp adds to the interparticle volume ... 

Under ideal SEC conditions, all solutes elute at a retention volume Fkthat is larger than the interparticle volume Vi but smaller than the mobile-phase volume Fr (which is the sum of and the pore volume Vp). The distribution coefficient ATd for elution by ideal SEC is given by Equation (13), in which Kd varies from zero for a fully excluded solute to one for a small molecular weight solute capable of penetrating all the pores ... 

Size exclusion chromatography separates molecules according to their size in solution. As a sample passes through the column, molecules which are too large to penetrate the pores of the packing are excluded and remain in the interparticle volume, Vq (this is also called the void or interstitial volume and is not to be confused with the solvent elution time Iq normally encountered in other forms of liquid chromatography). These molecules are eluted first from the column at the point of total exclusion. Small molecules which can permeate all the pores elute at the solvent front or total solvent volume F. This is the point of total permeation. Molecules of intermediate size will penetrate... 

The small early peak represents a solute that does not sorb in the stationary phase—it passes straight through the column without stopping. In GC, this behavior is often shown by air or methane, and the peak is often called an air peak. The symbol Vm, sometimes called the hold-up volume or void volume, serves to measure the interstitial or interparticle volume of the column. Other lUPAC approved symbols include V and Vq, representing the volume of the mobile gas phase in the column. The term dead volume, while not recommended, is also widely used. 

In SEC the retention volume Vj is used instead of the retention time Tr. Vr is defined as the sum of the interparticle volume V, and the accessible pore volume Vp for the particular solute ... 

Interstitial mobile phase volume (interparticle volume) = V)... 

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