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Practically, one measures the number of moles adsorbed as a function of equilibrium pressure, i.e. one does not directly measure

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BET surface Area measurements continued Practically, one measures the number of moles adsorbed as a function of equilibrium pressure, i.e. one does not directly measure 2. Algebraic rearrangement of the
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BET surface Area measurements continued Practically, one measures the number of moles adsorbed as a function of equilibrium pressure, i.e. one does not directly measure 2. Algebraic rearrangement of the BET isotherm to produce a linear equation is usually applied to experimental data. Recall: 11-1 This implies that over the range where the BET isotherm is valid a plot of z/n(1-z) vs z will be linear. The slope and intercept of this line will allow the determination of nmono and c. The specific area of the sample is simply: Where F is the molecular area (footprint) of the adsorbed molecule BET plot 11-2 There are several equivalent forms of the BET equation In the book it is given as (see eq., 3.51) p/v(p0 p) = 1/c + c-1/cvm * (p/p0) P: equil vap press P0: vapour pressure of adsorbate Vm: standard volume of gas per gram of adsorbant Vm: Volume of adsorbate gas per monolayer C: constant 11-3 Commercial Instrument 11-4 Mercury Porosimetry Pore dimensions greater than 300nm Sample is evacuated and immersed in mercury Mercury fills pores Pressure is applied Amount of Hg entering is a function of pressure The pressure required to intrude mercury into the sample s pores is inversely proportional to the size of the pores. 11-5 Mercury porosimetry routinely is applied over a capillary diameter range from to 360 µm (five orders of magnitude). This would be equivalent to using the same tool to measure accurately and precisely both the height of a 30-story building and the diameter of a grain of sand. 11-6 Quartz Crystal Nanobalance: page 167 et seq. The Quartz Crystal Microbalance (QCM) is a very sensitive tool to detect changes in weight and thus a helpful method to sense adsorption processes at solid/gas or solid/liquid interfaces. The basis of the QCM is a thin quartz exhibiting the inverse piezoelectric effect. Applying an alternating current excites a mechanical oscillation of the quartz plate. Using the specific resonance frequency of the quartz leads to a direct proportionality of the mass load and the frequency change. This effect was first found by G. Sauerbrey in Sauerbrey equation f 0 Resonant frequency (Hz) Δf Frequency change (Hz) Δm Mass change (g) A Piezoelectrically active crystal area (Area between electrodes, m 2 ) ρ q Density of quartz (ρ q = g/cm 3 ) μ q Shear modulus of quartz for AT-cut crystal (μq = 2.947x1011 g/cm.s 2 ) ν q Transverse wave velocity in quartz (m/s) Fundamental frequency varies from 600kHz to 30 MHz Can be used in gas and liquid phases Roughly: a 1Hz change is about a nanogram!! 11-8 Recall: Densities of atoms/ions on surface Consider Pt{111} : Pt Pt distance is 2.8 D ( accept for now) Area of triangle = ½(5.6 X 5.6 sin 60) 13.6 D 2 = 1.36 X cm 2 Number of atoms in triangle =2 Surface density = 2 atoms/13.6 D 2 Usually expressed at atoms/cm 2 Do the other low index planes 2 atoms per 1.36 X cm 2 So: Gives 1.5 X Pt atoms / cm 2 About a billionth of a mole Which is the densest?? Let s see approximately how much a monolayer weighs Choose a square cm : 1.5 X Pt atoms / cm 2 Lets say each Pt atom adsorbs a Sulfur atom. AW: S = 30 g/mol If each Pt atom adsorbs an S : 2=1 1.5 X S atoms weigh 32 X 1.5 X / 6 X = 8 x 10-8 g 80 ng which is easily detected 11-10 So submonolayer quantities can be detected easily: Most systems use AT cut quartz 5-9 MHz Sensitivity ng / cm Shear mode is used: Piezzo electric effect Crystal is part of oscillator circuit 11-12 Commercial instruments are available; see p 169 For use in liquids One side is kept dry Around 20 - $30K 11-13 Applications and Examples Humidity sensor Surface-adsorbed water and water vapor in gas streams can be important contaminants in the ultraclean gas-handling environments required for semiconductor manufacturing. In applications in which highpurity conditions must be maintained, water is difficult to monitor and control for two reasons: It is ubiquitous in the atmosphere and on surfaces that have been exposed to the atmosphere, and it has physical and chemical properties that make it difficult to eliminate. Small quantities of water vapor (below 1 nmol mol 1) can adversely affect the performance and yield of silicon-based semiconductors and compound semiconductors used in photonic devices Can also be coupled to electrochemical experiments Potential on surface of QCM can be controlled 11-15 Some work from my labs: Reduction and Oxidation of silver on gold 11-16 Silver Zeolite electrochemistry 11-17
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