Surface area circle

Figure 5.17 Reversible amount of hydrogen (electrochemical measurement at 298 K) versus the BET surface area (circles) of a few carbon nanotube samples including two measurements on high surface area graphite (HSAC) samples...

Fig. 3.5 Effect of calcination on crystallite size (squares) and BET surface area (circles) of HyCOM Ti02.

Variation of BET surface area (circles) and hydroxyl coverage (boxes) for multi-component borosiiicate samples during healing at 2°C/min (filled symbols no isothermal hold open symbols l8-hour isothermal hold) (57). 

Specific surface area, sq ft/cu ft Acceleration due to gravity, 32.2 ft/s or 9.8 m/s Area of segment of a circle, sq ft Cro.ss-sectional flow area, sq ft Cross-sectional area at bottom of vessel occupied by continuous aqueous phase, sq ft Cyclone inlet area = WjH,- for cyclone wdtb rectangular inlet, sq ft... 

Using ASME flanged and disbed heads (F D) from Appendix Tables of Blanks, the circle size is 152 in. for a 12-ft diameter tank. Then add 3-in. straight flange which becomes 158 in. which is 158/12 = 13.166 ft diameter. Area of this diam,eter for surface area of head = 136.14 sq ft equivalent surface area of one head. For a horizontal vessel there are two heads possibly exposed to fire. 

Time traces OH light intensity I, flame surface area A, pressure fluctuahons p, and computed pressure fluctuations kdA/dt. Circles indicate extracted flame surface areas A in cm (S and A are used indifferently to designate the flame surface). Black circles marked a, b, c, d correspond to flame patterns presented in images from Figure 5.2.3. 

Surface roughness is also expected to result in depression of the capacitance semi-circle. This phenomenon, which is indeed apparent in both Figures 1 and 2, is, however, unrelated to surface area. Rather, it is attributable to surface heterogeneity, i.e. the surface is characterized by a distribution of properties. Macdonald (16) recently reviewed techniques for representing distributed processes. A transmission line model containing an array of parallel R/C units with a distribution of values is physically attractive, but not practical. An alternative solution is introduction of an element which by its very nature is distributed. The Constant Phase Element (CPE) meets such a requirement. It has the form P = Y0 wn... 

Fig. 12.4. Vapor-to-water transfer data for saturated hydrocarbons as a function of accessible surface area, from [131]. Standard states are 1M ideal gas and solution phases. Linear alkanes (small dots) are labeled by the number of carbons. Cyclic compounds (large dots) are a = cyclooctane, b = cycloheptane, c = cyclopentane, d = cyclohexane, e = methylcyclopentane, f = methylcyclohexane, g = cA-l,2-dimethylcyclohexane. Branched compounds (circles) are h = isobutane, i = neopentane, j = isopentane, k = neohexane, 1 = isohexane, m = 3-methylpentane, n = 2,4-dimethylpentane, o = isooctane, p = 2,2,5-tri-metbylhexane. Adapted with permission from [74], Copyright 1994, American Chemical Society...

To size particles, graticule circles of known area on the graticule are superimposed until one is found that best fits the particle the surface area is then used to calculate particle size. 

Fig. 6.16 The normalized integrated absorbance of SiH and SiH2 species (filled symbols), the PL intensity (open circles) and the specific surface area (open diamonds) as a...

Fig. 14.16 ECA evolution (inset normalized ECA) for Pt supported on nitrogen-doped MC (square) and Pt supported on high surface area carbon black (circle). Operating conditions voltage cycling between 0.5 to 1.0 V vs. RHE, 50 mVs"1 scan rate, room temperature, 0.1 M HC104 (Reprinted with permission from [151] - 2012 Wiley).

Figure 7. Comparison between H-Beta zeolites (open circles and dashed lines) and HY zeolites (continuous lines) for gas-oil cracking (a) First-order activity constant by specific surface area vs, Si/Al ratio (b) and (c) Average total conversion vs. gas-oil ratio for a H-Beta with Si/Al=27 and a HY Si/Al=35, and for a H-Beta with Si/Al=10 and a Hy with Si/Al=7.7 respectively. Solid circles correspond to the H-Beta steamed at 750 C and 1 atmosphere of water pressure.

In a circle of unit surface area on the charged plane A-A, the negative charges acquired by the adsorbed organic ions (amphiphiles) within this area represent the surface charge density o ... 

Notice that the surface-area-to-volume ratio for a given spatial extent increases as one goes from the third dimension to the fourth. We see this easily in the second and third dimensions by using familiar formulas for area and volume for circles and spheres ... 

Fig. 4.40 Procedures used in measuring the dipole moment of adatoms by an FIM-FEM combination experiment, (a) A clean W surface is prepared by low temperature field evaporation and characterized by the FIM image. (b) The (110) plane is lined up with a Faraday cap using an external gimbal, the image gas is pumped out and the polarity of the tip is changed. A FN plot is then taken, (c) Adatoms are deposited on the (110) surface and their number found by the field ion image, in this case 9 adatoms. (d) A FN plot is taken again from the same surface area but now with the presence of 9 adatoms on the surface, (e) Two sets of data collected from two different (110) planes are shown (circles are for clean W (110), and squares are with 10 adatoms). The solid lines are for W adatoms and the broken lines are for Ta adatoms.

To derive the equation of Young and Laplace we consider a small part of a liquid surface. First, we pick a point X and draw a line around it which is characterized by the fact that all points on that line are the same distance d away from X (Fig. 2.6). If the liquid surface is planar, this would be a flat circle. On this line we take two cuts that are perpendicular to each other (AXB and CXD). Consider in B a small segment on the line of length dl. The surface tension pulls with a force 7 dl. The vertical force on that segment is 7 dl sin a. For small surface areas (and small a) we have sin a d/R where R is the radius of curvature along AXB. The vertical force component is... 

Fig. 9. Correlation between specific surface area and A1 content of the samples. Upstream Gironde data are circled.

Fig. 17 Dependence of the average PEO brush height ((Jj)brush) on the surface area per grafted chain (s), where (/i)brush was calculated by two different methods. The squares represent (h)brush from the difference between the average radii of the PNIPAM microgels with and without the grafted PEO chains and the circles from the ratio of / [70]...

Thus we see that the net force acts in the negative y direction, and is proportional to viscosity, journal surface area, and tangential speed, and inversely proportional and very sensitive to the displacement a. Indeed, as a approaches zero, the force grows and approaches infinity, so clearly, this force prevents the journal from contacting the harrel with the tight clearance circling the hearing. 

Fig. 10 Rate constant app as function of the surface area S of metal nanoparticles normalized to the unit volume of the system squares SPB-Ag composite particles, circles microgel-Ag composite particles, triangles microgel-Pd composite particles, and diamonds SPB-Pt composite particles [72]. T = 20°C, [4-nitrophenol] = O.lmmolL-1, [NaBPLj] = lOmmolL-1 [24]...

Fig. 12. Dependence of the ln(ifads) as a function of (1/7) for H2 molecularly adsorbed at the surface of high-surface-area MgO on different cationic sites MgjJ (triangles), Mg J (squares), and (circles). In the top part the adsorption enthalpies obtained for the various sites are given in kJmoD. (Adapted with permission from Gribov et al. (124))...

Figure 2.9 Hydrogen adsorption isotherm of MOF-5 with low specific surface area (triangles) [88], of MOF-5 prepared by BASF (circles) [13] and of MOF-5 prepared avoiding exposure to air (square) [91] (data corrected to give the wt% storage capacity as defined in Eq. (2.2)).

Figure 1. Dependence of surface area upon temperature of heat treatment (open circles) and of steam treatment (solid circles).

Figure 2 A cross section of a part of a macromolecule in space (atoms are shown as black circles) rolling probe, van der Waais, and accessible surface areas are indicated in the figure.

FIGURE 23.10 (A) Cerebrospinal fluid (CSF) methotrexate N(MtX) concentrations after an intrathecal dose of 12 mg/m. Children designated as open squares and adolescents designated as closed circles had lower concentrations than did adults represented as open circles, and lower concentrations were associated with a higher risk of treatment failure. (B) Growth rate of central nervous system volume relative to whole body growth represented by body surface area. (Reproduced with permission from Bleyer WA. Cancer Treat Rep 1977 61 1419-25.)... 

---