Void volume, definition

Thus, there are two limitations of the pycnometric technique mentioned possible adsorption of guest molecules and a molecular sieving effect. It is noteworthy that some PSs, e.g., with a core-shell structure, can include some void volume that can be inaccessible to the guest molecules. In this case, the measured excluded volume will be the sum of the true volume of the solid phase and the volume of inaccessible pores. One should not absolutely equalize the true density and the density measured by a pycnometric technique (the pycnometric density) because of the three factors mentioned earlier. Conventionally, presenting the results of measurements one should define the conditions of a pycnometric experiment (at least the type of guest and temperature). For example, the definition p shows that the density was measured at 298 K using helium as a probe gas. Unfortunately, use of He as a pycnometric fluid is not a panacea since adsorption of He cannot be absolutely excluded by some PSs (e.g., carbons) even at 293 K (see van der Plas in Ref. [2]). Nevertheless, in most practically important cases the values of the true and pycnometric densities are very close [2,7],... 

Density Types Density Definitions Solid Material Volume Volumes in Definition Closed- Open- Interparticle Pore Pore Void Volume Volume Volume ... 

Adsorption model of HPLC retention mechanism allows clear definition of the column void volume as the total volume of the liquid phase in the column, but this model requires the use of the surface-specific retention and the correlation of the HPLC retention with the thermodynamic (and thus energetic) parameters, which is not well-developed. This model requires the selection of the standard state of given chromatographic system and relation of all parameters to that state. 

When a liquid or a gas occupies a volume, it may be assumed to fill the volume completely. On the other hand, when solid particles occupy a volume, there are always spaces (voids) among the particles. The porosity or void fraction of a bed of particles is the ratio (void volume)/(totai bed volume). The bulk density of the solids is the ratio (mass of solids)/(iotaI bed volume), and the absolute density of the solids has the usual definition, (mass of solids)/(volume of solids). 

Solvent interaction model for normal-phase liquid chromatography. The solvent-interaction model of Scott and co-workers (Scott and Kucera, 1979) assumes that the analyte partitions between the bulk mobile phase and a layer of solvent absorbed onto the stationary phase. The quantitative description of the relationship between retention and the composition of the mobile phase in the solvent-interaction model requires the definition of the void volume corrected retention volume (V), which is related to the retention volume (F ) and the void volume (Fq) by... 

Column dimensions—length (L) and column inner diameter (dc or i.d.)— control column performance (N, speed, sensitivity, sample capacity) and its operating characteristics (flow rate, back pressure). Designations of various column types based on column inner diameters and their associated characteristics are shown in Table 3.1. Note that void volume, sample capacity, and operating flow rate are proportional to (dc)2, while detection limit, or sensitivity, is inversely proportional to (dc)2. Note also that prep columns (>10mm i.d.), microbore (micro columns (<0.5 mm i.d.) will require specialized HPLC instruments (see Chapter 4). There is a definitive trend toward the increased use of shorter and smaller inner diameter analytical columns due to their higher sensitivity performance and lower solvent usage.9"11 This trend will be explored later. 

Porosity or voidage of a packed bed of powder is defined as the volume of the voids within the bed (i.e. the volume occupied by air) divided by the total (overall) volume of the bed. The void volume includes the pores within the particles if they are porous. The pores in the particles can, however, be excluded from the definition, particularly if the application is in fluidized beds or flow through packed beds because the pores in the particles are in those cases not available to the flow. 

The term reaction rate denotes the rate of a reaction in a general way. We now define it specifically as the moles reacting per unit of reaction space per unit time. The reaction space can be the empty volume of the reacting space, void volume of the catalyst bed, volume of the catalyst, weight of the catalyst, surface area of the catalyst, or volume of one or all of the phases present in a heterogeneous system. Where time is concerned, its definition depends on the type of reactor used. There are essentially two broad classes of reactors batch and flow. In a batch reactor, time (0 corresponds to the elapsed time from the start of a run. In a flow reactor, it is given by... 

Despite this, and for a variety of reasons, the definition of space time is not always as clear as one would like and researchers often settle for some fairly arbitrary, often murky, quantity to represent the space time. This leads to differences in reported rates that make reliance on literature values of rates, not to mention the utility of rate parameters, quite unsatisfactory. For example, in a PFR packed with inert material, the volume of the reactor in space time calculations should be the void volume between the packing particles, not the volume of the empty reactor. It is not clear that this is the definition used in all cases of reported data. 

However, the void area fraction is equivalent to the void volume fraction, based on equation (21-76) and the definition of intrapellet porosity Sp at the bottom of p. 555. Effectiveness factor calculations in catalytic pellets require an analysis of one-dimensional pseudo-homogeneous diffusion and chemical reaction in a coordinate system that exploits the symmetry of the macroscopic boundary of a single pellet. For catalysts with rectangular symmetry as described above, one needs an expression for the average diffusional flux of reactants in the thinnest dimension, which corresponds to the x direction. Hence, the quantity of interest at the local level of description is which represents the local... 

Another definition is based on the void volume of the reactor [2], which corresponds to... 

Column effects. In order to establish optimal operating conditions, it is useful to consider the effects of system parameters on the resolution characteristics of an HDC system. HDC has been described as a chromatographic method with very low capacity but very high efiBciency. For example, the calibration curves show that the spectrum of sizes from less than 100 nm to greater than 300 nm is encompassed in less than about 5% of the column void volume. On the other hand, the theoretical plate count corresponding to the marker peak is typically in the range of several thousand per foot. Comparisons in terms of the specific resolution factor, enable a more precise analysis, since both the separation factor and peak dispersion are included in its definition. A simple form for the specific resolution between two particle populations of diameter Dpi and Dp2 is [11]. 

Because the definition of the adjusted retention volume was given above, and a related definition of the corrected retention volume was given in Chapter 2 (equation 4), we ought to make sure that these two are not confused with one another. Each has its own particular definition the adjusted retention volume, Fr is the retention volume excluding the void volume (measured from the methane or air peak) as shown in equation 9 the corrected retention volume, Vg, is the value correcting for the compres-... 

Equation [3.18] assumes that the extra-column volume Vg is negligible. However, there are two definitions of void volume, and thus also of the capacity ratio of a solute. The two void volumes are called the thermodynamic and the dynamic void volumes and they are not equal (Scott, www.chromatography-online.org) the two void volumes and capacity ratios are used for different purposes. Equations [3.16-3.18] incorporate the thermodynamic dead volume and all further discussion in this chapter assumes this definition. 

Before focusing on some of the simpler solutions of such a system to develop an understanding of the single solute separation capabilities of a fixed-bed adsorption process, we will provide a few more definitions for a packed adsorbent bed in general. The density of the solid material of the adsorbent particles is p. The bulk density of the adsorbent bed pi, is related to the void volume e of the packed bed, solid material density p and the porosity of the particle Ep via... 

Therefore, a somewhat arbitrary reference pressure must be chosen for defining the total volume. The void volume of carbon black at a pressure of 0.18 MPa was chosen to be the reference in this case. This level for the reference pressure has a practical significance in that it is lower by one order of magnitude than the pressure exerted by the rotor blade of an internal mixer. Accepting this definition of void volume, the degree of penetration into the void volume, PEN, in Table 3.3, becomes a good measure of the degree of compaction. Under the present set of experimental conditions 30-35% of the void volume was penetrated by the elastomer. 

We may begin by describing any porous medium as a solid matter containing many holes or pores, which collectively constitute an array of tortuous passages. Refer to Figure 1 for an example. The number of holes or pores is sufficiently great that a volume average is needed to estimate pertinent properties. Pores that occupy a definite fraction of the bulk volume constitute a complex network of voids. The maimer in which holes or pores are embedded, the extent of their interconnection, and their location, size and shape characterize the porous medium. 

GL 18] ]R 6a]]P 17/Using the same experimental conditions and catalysts with the same geometric surface area, the performance of micro-channel processing was compared with that of a fixed-bed reactor composed of short wires [17]. The conversion was 89% in the case of the fixed bed the micro channels gave a 58% yield. One possible explanation for this is phase separation, i.e. that some micro channels were filled with liquids only, and some with gas. This is unlikely to occur in a fixed bed. Another explanation is the difference in residence time between the two types of reactors, as the fixed bed had voids three times larger than the micro channel volume. It could not definitively be decided which of these explanations is correct. 

Pores are found in many solids and the term porosity is often used quite arbitrarily to describe many different properties of such materials. Occasionally, it is used to indicate the mere presence of pores in a material, sometimes as a measure for the size of the pores, and often as a measure for the amount of pores present in a material. The latter is closest to its physical definition. The porosity of a material is defined as the ratio between the pore volume of a particle and its total volume (pore volume + volume of solid) [1]. A certain porosity is a common feature of most heterogeneous catalysts. The pores are either formed by voids between small aggregated particles (textural porosity) or they are intrinsic structural features of the materials (structural porosity). According to the IUPAC notation, porous materials are classified with respect to their sizes into three groups microporous, mesoporous, and macroporous materials [2], Microporous materials have pores with diameters < 2 nm, mesoporous materials have pore diameters between 2 and 50 nm, and macroporous materials have pore diameters > 50 nm. Nowadays, some authors use the term nanoporosity which, however, has no clear definition but is typically used in combination with nanotechnology and nanochemistry for materials with pore sizes in the nanometer range, i.e., 0.1 to 100 nm. Nanoporous could thus mean everything from microporous to macroporous. 

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