Schematic representation volume

Figure 9.2 (a) Schematic representation of a unit cube containing a suspension of spherical particles at volume fraction [Pg.589]

Fig. 7. Schematic representation of hydration causing crack propagation in a wedge test specimen. The increase in volume upon hydration induces stresses at the crack tip that promote crack growth 19,391.

The results of the micromechanics studies of composite materials with unidirectional fibers will be presented as plots of an individual mechanical property versus the fiber-volume fraction. A schematic representation of several possible functional relationships between a property and the fiber-volume fraction is shown in Figure 3-4. In addition, both upper and lower bounds on those functional relationships will be obtained. 

Figure 35. Schematic representation of the reversible variation of volume associated with the electrochemical switching of polypyrrole. Changes in free volume are mainly due to two effects electrostatic repulsions between fixed positive charges and exchange of cations, anions, and solvent molecules between the polymer and the solution. (Reprinted from T. F. Otero, H.-J. Grande, and J. Rodriguez, J. Phys. Chem. 101, 3688, 1997, Figs. 1, 3,6, 7, 13. Copyright 1997. Reprinted with the permission of the American Chemical Society.)...

Figure 4 Schematic representation of a small section of a diffusion profile illustrating the application of Fick s law to determine the concentration change in the central volume element as a result of the fluxes (F) across the two planes at L and R (see text for details).

Figure 5. A schematic representation of superposed steady-state reservoirs of constant volumes Vi (fractional crystallization is omitted in this schema). At steady-state, Vi/xi=V2/x2=..., where x is the residence time. This is analogous to the law of radioactive equilibrium between nuclides 1 and 2 Ni/Ti=N2/T2=...A further interest of this simple model is to show that residence times by definition depend on the volume of the reservoirs.

Fig. 27. A schematic representation of the seven transmembrane helical peptide chains (A-G) viewed from inside the cell. The numbering denotes the first and last amino acid residues. The proton channel is believed to be the volume between helices C, D, F and G...

Schematic representation of differential volume element of plug flow reactor.

Consider the schematic representation of a continuous flow stirred tank reactor shown in Figure 8.5. The starting point for the development of the fundamental design equation is again a generalized material balance on a reactant species. For the steady-state case the accumulation term in equation 8.0.1 is zero. Furthermore, since conditions are uniform throughout the reactor volume, the material balance may be... 

Fig. 7 Schematic representation of moisture transfer between solid components A and B with (a) headspaces isolated from one another and (b) headspaces allowed to equilibrate. Ra and Rb = initial relative humidities above A and B VA and VB = headspace volumes above A and B Rf and VT = final relative humidity and headspace volume above A and B. (From Ref. 95.)...

Figure 23.7 Schematic representation of control volume for material balance for bubbling-bed reactor model...

The experimental constant-pressure heat capacity of copper is given together with the Einstein and Debye constant volume heat capacities in Figure 8.12 (recall that the difference between the heat capacity at constant pressure and constant volume is small at low temperatures). The Einstein and Debye temperatures that give the best representation of the experimental heat capacity are e = 244 K and D = 315 K and schematic representations of the resulting density of vibrational modes in the Einstein and Debye approximations are given in the insert to Figure 8.12. The Debye model clearly represents the low-temperature behaviour better than the Einstein model. 

Fig. 19 TEM image of toroidal micelles from a PAA-PMA-PS triblock copolymer (A). This sample was cast from a solution with 0.1 wt% PAA99-PMA73-PS66 triblock copolymer, a THF water volume ratio of 1 2, and an amine acid molar ratio of 0.5 1 by addition of 2,2-(ethylenedioxy)diethylamine. The cast film was negatively stained with uranyl acetate. A schematical representation of theses micelles is also shown (B). Reprinted with permission from [279], Copyright (2004) American Association for the Advancement of Science...

Figure 9. Schematic representation of the acrylic chambers used for treatment of P815 cells with DC. Chambers are connected in series by filter-paper bridges, and fitted with platinum electrodes in their extremities. In this system, cell suspensions can be exposed directly to the anodic reactions (AC) or cathodic reactions (CC) or to electric current without contact with the electrodes, in the intermediary chamber (IC). Internal volume 3 cm3. After Veiga et al.62...

Figure 12.18 Schematic representation of a linear motor powered by light Adapted from V. Balzani, A. Credi and M. Venturi, Light-powered molecular-scale machines , Pure and Applied Chemistry Volume 75, No. 5,541-547 International Union of Pure and Applied Chemistry IUPAC 2003...

Fig. 4.7 A schematic representation of a cationic displacement along a polymeric chain above its Tg. (a) An initial activated step (ft) allows the formation of an interstitial pair, the migration of which (c) and (d) is assisted by local free volume redistribution.

Figure 5.3. Schematic representation of a free expansion. A small valve separating the two chambers in (a) is opened so that the gas can msh in from left to right. The initial volume of the gas is Vi, and the final volume is V2.

Figure 14. Schematic representation of the diffusion process of particles in a conductor composed of L cells of volume AV between two particle reservoirs, A and B.

Fig. 1.8 Schematic representation of a gas-source mass spectrometer for stable isotope measurements, P denotes pumping system, V denotes a variable volume...

This highly sensitive calorimeter needs to be connected to a sensitive volumetric system in order to determine accurately the amounts of gas or vapor adsorbed. A schematic representation of the whole assembly is shown in Figure 13.4 [147]. The volumetric determination of the adsorbed amount of gas is performed in a constant-volume vessel linked to a vacuum pump. The apparatus consists of two parts the measuring section equipped with a capacitance manometer, and the vessels section that includes the cells placed in the calorimeter (a sample cell in which the adsorbent solid is set, and an empty reference cell). 

FIGURE 16.12 Schematic representation of the LC LCD procedure (adsorption retention mechanism with a narrow barrier of adsorli injected in front of sample). Large volume of sample is depicted. The sample contains two polymers exhibiting different adsorptivities. The fast (SEC-like) elution of adsorbing polymer is hindered by the barrier of adsorli while the non-adsorbing species are freely eluted in the exclusion mode. Four stages of the process are shown. The peak focusing is demonstrated. 

FIGURE 16.13 Schematic representation of separation of a block copolymer poly(A)-block-poly(B) from its parent homopolymers poly(A) and poly(B). The elnent promotes free SEC elntion of all distinct constitnents of mixtnre. The LC LCD procednre with two local barriers is applied. Poly(A) is not adsorptive and it is not retained within colnmn by any component of mobile phase and barrier(s). At least one component of barrier(s) promotes adsorption of both the homopolymer poly(B) and the block copolymer that contains poly(B) blocks, (a) Sitnation in the moment of sample introdnction Barrier 1 has been injected as first. It is more efficient and decelerates elntion of block copolymer. After certain time delay, barrier 2 has been introdnced. It exhibits decreased blocking (adsorption promoting) efficacy. Barrier 2 allows the breakthrongh and the SEC elution of block copolymer but it hinders fast elution of more adsorptive homopolymer poly(B). The time delay 1 between sample and barrier 1 determines retention volume of block copolymer while the time delay 2 between sample and barrier 2 controls retention volume of homopolymer poly(B). (b) Situation after about 20 percent of total elution time. The non retained polymer poly(X) elutes as first. It is followed with the block copolymer, later with the adsorptive homopolymer poly(B), and finally with the non retained low-molar-mass or oligomeric admixture. Notice that the peak position has an opposite sign compared to retention time or retention volume Tr. 

Fig. 20. Schematic representation of the s, p, d and f partial contributions to the total energy of electrons in the conduction band of a light actinide metal. The different R s denote the radial extension of the different contributing orbitals. R (f-included) and R 2n-f refer to the equilibrium volumes when the 5 f electrons are itinerant and when they are non-binding (from Ref. 77)...

Figure 21.6. Schematic representation of the relative phase-space volumes available to reactant, transition state, and product. A plane located at the most constricted place has the highest prohahility of being crossed only once by a molecular trajectory, which is the location of the transition state.

Fig. 7. Schematic representation of four procedures commonly used to sample a field in stereo-logical analysis. These procedures have been used to study the porous structure of collagen-GAG matrices [74] and yield values for average pore diameter, pore volume fraction and other features. In this illustration, a phase A (cross-hatched) is embedded in a continuous phase B (white background). A Random point count B systematic point count C areal analysis D lineal analysis. (Reprinted from [64] with permission).

A schematic representation of a laboratory apparatus for CDJP is given in Figure l.l.l. In principle, the reacting solutions are introduced into a constant temperature chamber at desired flow rates by means of peristaltic pumps. The predetermined volume of solutions in the reactor may contain stabilizing, reducing, or other agents, or it may be used to control the reaction pH. 

FIG. 4.3 Schematic representation of a concentric-cylinder viscometer (a) geometry of a cup and bob and (b) volume element within a liquid gap. 

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