V---t curves

In Chapter 4, it was emphasized that the surface of an adsorbent is never covered with an adsorbed film of uniform depth but rather with stacks of 

Shull assumed that the adsorbate molecules were packed one on top of the other in the film and deduced the monolayer depth to be 4.3 A for nitrogen. A more realistic assumption is that the film structure is close-packed hexagonal, leading to a monolayer depth of 3.54 A as shown by equation (8.23). Therefore, as stated previously, the statistical depth t of the adsorbed film is 

If the volume adsorbed on a surface of area S is expressed as the corresponding liquid volume, then 

Lippens and deBoer have shown that a plot of the volume adsorbed versus t calculated from equation (8.24) will yield a straight line of slope S X 10 from which the surface area can be calculated. Plots of this nature are termed V-t curves and generally give surface areas comparable to BET values provided that multilayer adsorption and not condensation into the pores takes place. 

It is convenient to categorize pores into several size ranges. The largest pore radii amenable to analysis by the Kelvin equation are about 1000 A which corresponds to relative pressures near 0.99. Pores with radii greater than this are termed macropores . Dubinin calls pores in the Kelvin range, from about 15 to 1000 A, transitional and pores with radii less than about 15 A micropores . The failure of V-t plots to pass through the origin has led to the postulation of submicropores with radii less than about 7 A. 

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Fig. 5.4 Voltage-time curve for a p-type silicon electrode anodized galvanostatically at 0.1 mA cm"2 in 10% acetic acid. Silicon electrodes were removed from the electrolyte after various anodization times (filled circles) and the thickness of the anodic oxide was measured by ellipsometry (open circles). The curvature of the sample was monitored in situ and is plotted as the value of stress times oxide thickness (filled triangles). The bar graph below the V(t) curve shows a proposed formation mechanism. Galvanostatically a...

Figure 8.7 illustrates three types of V-t curves. Curve X results from multilayer adsorption in the absence of any condensation into pores. Curve Y shows that condensation into pores commences where the slope starts to increase. The upward deviation from a straight line reflects the increased uptake due to condensation in larger pores. Curve Z results when narrow pores are filled at low relative pressures by multilayer adsorption, thereby reducing the available surface for continued adsorption. 

Figure 9.5 V-t curve from Figure 9.4 (from reference 82).

Take i0 = 10-6 A cm-2 at 25°C. Explore the appropriate time and potential range to form a galvanostatic transient relation with the parameters stated. (Note The so-called "rise time of the potential is about 4C R, where R = dV/ddt. Calculate the full V—t curve to 99% of the steady state. (Bockris)... 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

In Fig. 4 the experimental isobaric volume temperature curve of the 1-l.c. 4-hexyloxybenzoic acid 4 -hexyloxyphenylester is shown, which possesses a nematic phase 37,38). Two phase transformations are indicated by the jumps of the V—T curve the isotropic to nematic and, at lower temperatures, the nematic to crystalline transformation. As well known, both transformations are of first order and obey the Clausius-Clapeyron equation. 

In comparison to a conventional polymer and l.c. mentioned above, we will now discuss the PVT behavior of a l.c. side chain polymer, which has linked mesogenic moieties as side chains, and is very similar to the previous monomer. The experimental results are shown in Fig. 5. It is obvious, that the phase behavior of the l.c. polymer differs from that of a 1-l.c. and amorphous polymer. At high temperature we observe a transformation from the isotropic polymer melt into the l.c. phase, indicated by the jump in the V(T) curve. At low temperatures no crystallisation is observed but the bend in the curves signifies a glass transition. Obviously the phase behaviour is determined by the combination of l.c. and polymer properties. 

At low temperatures the bend in the V(T) curves indicates a glass transition. It is of interest, whether this transition can be described in analogy to amorphous polymers on the basis of the concept of using one internal order parameter and whether the liquid crystalline structure is maintained in the glassy state. This will be discussed in Chap. 2.3.4. 

As already mentioned in Chap. 2.2. one of the most obvious features of the l.c. side chain polymers is their ability to become glassy. The glass transition can be observed by cooling nematic, cholesteric and smectic polymers depending on the chemical constitution of the system and is indicated e.g. by a bend in the V(T) curves as schematically shown in Fig. 8. Two questions are of interest which will be discussed in this chapter ... 

Fig. 4 (a) Applied voltage vs. transmission (V-T) curves of in twisted cells at 100 Hz and 25°C. a) Pure 5CB, b) 5CB-capped Pd, c) 5CB-capped Ag-Pd (1/9), d) 5CB-capped Ag-Pd (1/4), e) 5CB-capped Ag-Pd (1/1), f) 5CB-capped Ag-Pd (4/1), g) 5CB-capped Ag-Pd (9/1), and h) 5CB-capped Ag. (b) Cartoon of a liquid crystal cell filled with 5CB-sol containing metal nanoparticles. A self-assembly property of liquid crystal is speculatively perturbed by nanoparticles in the liquid crystal medium [301], (Copyright 2008, American Chemical Society)... 

Typical curves are shown in Fig. 22 a and b for current and potential steps respectively. For the short times (trate determining step is due to a concentration polarization [78], The variation of the transient current versus ]fi is linear, described satisfactorily by the classical Cottrel-type relation (see Fig. 23). After a certain time which depends on the experimental conditions, mainly the oxygen partial pressure in the surrounding atmosphere, a depolarization effect is observed the V (t) curve shows an overshoot while the I(t) curve shows a net enhancement of current. 

V, T curves respectively. The variation of the specific heat with volume, or with pressure is therefore greater the more the substance differs in its behaviour from the perfect gas. It is interesting to note that Cp varies with the pressure for gases which obey van der Waals equation. 

Volumetric and manometric efficiency curves could be plotted, but the usefulness of such curves is limited. Volumetric efficiency is a direct function of the V/T-curve and may be represented by the product oiV/T and a constant, the latter depending on the design of the fan. As the volume delivered at a given revolution per minute varies as the volume per revolution — KiLW/T, and since the overall cubical content of the wheel is the volumetric efficiency = KYjT, where K equals... 

Figure 1.11 I-t curves [34] in (a) EXP. 1 and (b) EXP. 2 (c) V-t curve in EXP. 3. Reproduced from Y. Ke, R.P. Devaty and W.J. Choyke, Self-ordered nanocolumnar pore formation in the photoelectrochemical etching of 6H SiC, Electrochem. Solid-State Lett., 10(7), K24-K27 (2007). Copyright 2007, with permission from The Electrochemical Society...

For V-T curves, Wendlandt (115) found that the heating rate had little effect on the 7] values for KHC03 but it did change the 7f values to some extent. The Tt value found was aboul 165 0 for which the 7 values were 205°C (5°C min - ), 215°C (10°Cmin-1), and 240CC(20°C min-1). There was, naturally, an increase in the Tf— values with an increase in heating rate. 

In the formula, F, and t is the measured value of each measuring point, and F(, is the undetermined coefficient. Through putting n groups of measured values which are getting from the V-t curve after data processing into formula(3), determined equations are obtained as follows ... 

The V-t curves drawn according to the results measured at 150605 face convey gateway, return air mechanized excavation Lane and 121, 102 face convey gateway, return air mechanized excavation lane are shown in Figure 2, 3,4 and 5. 

ZB Specific voluine versus temperature for semictystalline linear polyethylene showing the effect of heating a specimen from 20°C to above the melting point T . The specific volume of the spcumen at 2(rc is v. The specific volume of the amorphous fraction v, is obtained by extrapolating the v-T curve for the liquid down to 20 D. The specific volume of the crystalline fraction is obtained from the lattice constants of the unit cell (see Problem 2.1). The crystal fraction can be obtained using these quantities in eqn 2.2. 

Cake Growth Phase. Here the experimental V, t) curve exhibits a parabolic shape, as e5g)ected from theory. The specific resistance-pressure relationship for newly conditioned sludge takes a value of unity, for the con ressibility coeflhcient. This suggests that is directly proportional to pressure. If this phase is conducted at constant pressure, elementary theory leads to the following relationsh for filtration volume. 

Exponential Compression Phase. Here fiuther increases in the solids concentration inside the filter chambers are attained by compresaon of the contents. The rate of filtration now deviates fi om classical filtration theory with the (V, t) curve taking on an e qponoidal sh e, rather than a parabolic one. 

Fig. 21 Representative force versus extension (x = v t) curves for the tetra-loop system for the pull mode (red) and the relax mode (black). The upper curves are for v = 1 nm/ns (v = -1 nm/ns in the relax mode) and are shifted by 600 pN for clarity. The lower curves are for v = 0.1 nm/ns (v = —0.1 nm/ns). Reprinted with permission from [98]. Copyright (2011) American Chemical Society...

The microporous volume is obtained from a straight line extrapolated to a positive intercept on the ordinate. The estimation of t should be based on the reference isotherm, which yields the same BET constant (Cbet) as that of the material tested (40). The choice of the standard t function and the part of the V-t curve used for linear fitting drastically affect the values of the external surface and micropore volume. To avoid the foregoing complications. Sing (41) introduced and developed the method, in which the normalized adsorption, (= nlno.4), is derived from the isotherm of a reference material by using the amount adsorbed at a relative pressure of 0.4 (uo.a) as the normalization factor. Lecloux... 

Fig. 2.36 Tilt angle effect on applied voltage-transmittance (V-T) curve calculated V-T curves for 2°, 4°, and 6° pretilt angles.

Fig. 2.39 Actual twist angle effect on V-T curve calculated V-T curves of 86°, 88°, and 90° actual twist angles.

The correlation between the behaviour of U, U and v, t-curves found in Ref. [52] may be the basis for developing quantitative methods controlHng the hydrodynamic flux structure near the electrode surfaces, as well as methods for influencing the velocity of the heterogeneous processes by means of controlled changing of the hydrodynamic conditions of interfacial mass exchange. 

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