nanosurface 2007-01-11 22:16
BET测量方法
[size=3][color=darkgreen]BET方法是测量比表面积的主要方法之一,可能有许多网友没有机会在课堂上学习(我自己也没有系统的学习过).这里我想把这方面的资料汇集一下.特别是测量原理和实验部分.与大家一起分享.[URL=http://imageshack.us][IMG]http://img293.imageshack.us/img293/7427/schemeya8.jpg[/IMG][/URL][/color][/size]
[size=3][color=darkgreen][/color][/size]
[b][size=3][color=darkgreen]一. 分子吸附的过程[/color][/size][/b]
[size=3][color=darkgreen][b]Physical Concept of Adsorption
[/b]
To illustrate the concept of adsorption consider a closed system consisting of a small number of gas phase molecules in contact with a solid surface.
[b]1. Effect of Temperature[/b]
[/color][/size]
[size=3][color=darkgreen]
[font=Arial][size=3][color=darkgreen] [font=Tahoma]T1 < T2[/font]
[/color][/size][table][tr][td][font=Arial][size=3][color=darkgreen]T1: [/color][/size][/font]
[font=Arial][size=3][color=darkgreen][/color][/size][/font]
[font=Arial][size=3][color=darkgreen][img]http://img62.imageshack.us/img62/6112/temp1compme5.gif[/img] [/color][/size][/font]
[/td][td=1,1,20%][/td][td][font=Arial][size=3][color=darkgreen]T2:
[/color][/size][/font]
[font=Arial][size=3][color=darkgreen][img]http://img62.imageshack.us/img62/8391/temp2compom8.gif[/img][/color][/size][/font]
[font=Arial][size=3][color=darkgreen][/color][/size][/font]
[/td][/tr][/table][/font]
[size=3][color=darkgreen]Note that:
* Adsorption is a dynamic equilibrium
* At higher temperature (T2):
o Greater ratio of gas phase molecules
o Average time spent by a molecule on the surface (residence time) is lower (see red molecule).
_______________________________________________________________________
[/color][/size]
[size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen][b]2. Effect of Pressure[/b][/color][/size]
[size=3][color=darkgreen][/color][/size]
[font=Arial][size=3][color=darkgreen] P1 < P2[/color][/size][/font]
[font=Arial][size=3][color=darkgreen] [/color][/size][table][tr][td][font=Arial][size=3][color=darkgreen]P1:
[img]http://www.jhu.edu/%7Echem/fairbr/pres2comp.gif[/img] [/color][/size][/font][/td][td=1,1,20%][size=3][color=darkgreen][/color][/size][/td][td][font=Arial][size=3][color=darkgreen]P2:
[img]http://www.jhu.edu/%7Echem/fairbr/pres1comp.gif[/img] [/color][/size][/font][/td][/tr][/table][/font][/color][/size]
[[i] 本帖最后由 nanosurface 于 2007-01-11 11:37 编辑 [/i]]
nanosurface 2007-01-12 00:38
[align=center][font=Arial][size=3][color=darkgreen][/color][/size][/font][size=4][color=darkgreen]Derivation of the Langmuir isotherm[/color][/size][/align]
[size=3][color=darkgreen]For molecules in contact with a solid surface at a fixed temperature, the Langmuir Isotherm, developed by Irving Langmuir in 1916, describes the partitioning between gas phase and adsorbed species as a function of applied pressure. [/color][/size][size=3][color=darkgreen][/color][/size][size=3][color=darkgreen]Derivation of the Langmuir Isotherm[/color][/size][size=3][color=darkgreen]
[url=http://imageshack.us/][img]http://img406.imageshack.us/img406/4583/surface4mr7.gif[/img][/url]
The adsorption process between gas phase molecules, A, vacant surface sites, S, and occupied surface sites, SA, can be represented by the equation, [/color][/size][size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_1.gif[/img] [/color][/size][size=3][color=darkgreen]assuming that there are a fixed number of surface sites present on the surface. [/color][/size]
[size=3][color=#006400][/color][/size]
[size=3][color=darkgreen][/color][/size][size=3][color=darkgreen]Thermodynamic Derivation[/color][/size]
[size=3][color=darkgreen]An equilibrium constant, K, can be written: [/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_9.gif[/img] [/color][/size][size=3][color=darkgreen][font=symbol]q[/font] = Fraction of surface sites occupied (0 <[font=symbol]q[/font]< 1) [/color][/size]
[size=3][color=darkgreen]Note that [/color][/size]
[list][*][size=3][color=darkgreen][b][SA][/b] is proportional to the surface coverage of adsorbed molecules, or proportional to [font=symbol]q[/font] [/color][/size][*][size=3][color=darkgreen][b][S][/b] is proportional to the number of vacant sites, (1 - [font=symbol]q[/font]) [/color][/size][*][size=3][color=darkgreen][b][A][/b] is proportional to the pressure of gas, P [/color][/size][/list][size=3][color=darkgreen]Thus it is possible to define the equilibrium constant, b: [/color][/size][size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_7.GIF[/img] [/color][/size]
[size=3][color=darkgreen]Rearranging gives the expression for surface coverage: [/color][/size][size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_8.GIF[/img][/color][/size]
[size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen]Kinetic Derivation[/color][/size]
[size=3][color=#006400][/color][/size]
[size=3][color=darkgreen]The rate of adsorption will be proportional to the pressure of the gas and the number of vacant sites for adsorption. If the total number of sites on the surface is N, then the rate of change of the surface coverage due to [/color][/size][size=3][color=darkgreen]adsorption is:[/color][/size]
[size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_3.gif[/img] [/color][/size]
[size=3][color=darkgreen]The rate of change of the coverage due to the adsorbate leaving the surface (desorption) is proportional to the number of adsorbed species: [/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_4.gif[/img] [/color][/size]
[size=3][color=darkgreen]In these equations, ka and kd are the rate constants for adsorption and desorption repectively, and p is the pressure of the adsorbate gas. At equilibrium, the coverage is independent of time and thus the adorption and desorption rates are equal. The solution to this condition gives us a relation for [font=symbol]q[/font]: [/color][/size]
[size=3][color=#006400][/color][/size]
[size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/eq_8.GIF[/img] [/color][/size]
[size=3][color=darkgreen]where b=ka/kd. [/color][/size][size=3][color=darkgreen]Note b is only a constant if the enthalpy of adsorption is independent of coverage. [/color][/size][size=3][color=darkgreen]As with all chemical equilibria, the position of equilibrium will depend upon a number of factors: [/color][/size]
[list=1][*][size=3][color=darkgreen]The relative stabilities of the adsorbed and gas phase species involved. [/color][/size][*][size=3][color=darkgreen]The temperature of the system (both the gas and surface, although these are normally the same). [/color][/size][*][size=3][color=darkgreen]The pressure of the gas above the surface. [/color][/size][/list]
[size=3][color=darkgreen]In general, factors (2) and (3) exert opposite effects on the concentration of adsorbed species - that is to say that the surface coverage may be increased by raising the gas pressure but will be reduced if the surface temperature is raised. [/color][/size][size=3][color=darkgreen][url=http://imageshack.us/][img]http://img366.imageshack.us/img366/4826/isotherm1ts2.gif[/img][/url][/color][/size]
[size=3][color=darkgreen]where b3 > b2 > b1 [/color][/size]
[[i] 本帖最后由 sally208 于 2007-12-13 20:30 编辑 [/i]]
nanosurface 2007-01-12 00:44
[align=center][font=Arial][size=3][color=darkgreen][/color][/size][/font][size=4][b][color=darkgreen]BET Derivation[/color][color=darkgreen]Consider a surface: [/color][/b][/size][/align][size=3][color=#006400][/color][/size]
[size=3][color=#006400][/color][/size]
[size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][url=http://imageshack.us/][img]http://img366.imageshack.us/img366/1705/layerscs1.gif[/img][/url][/color][/size]
[size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/ads.gif[/img] [/color][/size]
[size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen][b]Definition:[/b] [/color][/size]
[table][tr][td=1,1,5%][size=3][color=darkgreen][/color][/size][/td][td][font=Arial][size=3][color=darkgreen][font=symbol]q[/font]0, [font=symbol]q[/font]1, ..., [font=symbol]q[/font]n = Surface area (cm-2) covered by 0, 1, ..., n layers of adsorbed molecules. [/color][/size][/font][/td][/tr][/table][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen][b]At Equilibrium:[/b] [/color][/size]
[table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td=1,1,90%][font=Arial][size=3][color=darkgreen][font=symbol]q[/font]0 must remain constant. [/color][/size][/font][/td][/tr][/table][size=3][color=darkgreen][/color][/size][b][size=3][color=darkgreen] . [/color][/size][/b]
[b][size=3][color=darkgreen] Rate of Evaporation Rate of Condensation [/color][/size][/b]
[b][size=3][color=darkgreen] . . =from First Layer onto Bare Surface[/color][/size][/b]
[size=3][color=darkgreen] [img]http://www.jhu.edu/~chem/fairbr/equal_13.GIF[/img] [/color][/size]
[size=3][color=darkgreen]Similarly, at equilibrium [font=symbol]q[/font]1 must remain constant. [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][b][size=3][color=darkgreen] . Rate of Condensation Rate of Condensation . . on the Bare Surface on the 1st Layer + = + Rate of Evaporation Rate of Evaporation from the second layer from the second layer[/color][/size][/b][/td][/tr][/table][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][b][size=3][color=darkgreen] . . .[/color][/size][/b][/td][td][size=3][color=darkgreen]k1P[font=symbol]q[/font]0 + k-2[font=symbol]q[/font]2 = k2P[font=symbol]q[/font]1 + k-1[font=symbol]q[/font]1 [/color][/size][/td][/tr][/table][size=3][color=darkgreen]Substituting into (I) gives [/color][/size][size=3][color=darkgreen]k-2[font=symbol]q[/font]2 = k2P[font=symbol]q[/font]1 [/color][/size]
[size=3][color=darkgreen]Extending this argument to other layers, [/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_14.GIF[/img] [/color][/size]
[size=3][color=darkgreen][b]Definitions:[/b] [/color][/size][size=3][color=darkgreen]Total surface area of the catalyst, [/color][/size]
[table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_1.gif[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen]Total volume of gas adsorbed on surface [/color][/size]
[table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_2.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen]where v0 is the volume of gas adsorbed on one square centimeter of surface when it is covered with a complete layer. [/color][/size]
[table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][b][size=3][color=darkgreen] . . .[/color][/size][/b][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_3.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]where vm is the volume of gas adsorbed when the entire surface is covered with a complete monolayer. [/color][/size][size=3][color=darkgreen]From (I), [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_5.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]If we assume that the properties of the 1st, 2nd, ... layers are equivalent, then, [/color][/size][table][tr][td][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_4.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]Similarly, [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_6.GIF[/img] [/color][/size][/td][/tr][/table][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][font=Arial][size=3][color=darkgreen][font=symbol]q[/font]3 =x[font=symbol]q[/font]2 =x2[font=symbol]q[/font]1 [/color][/size][/font][/td][/tr][/table][size=3][color=darkgreen]Generally, [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][font=Arial][size=3][color=darkgreen][font=symbol]q[/font]i =x[font=symbol]q[/font]i-1 =xi-1[font=symbol]q[/font]1 =xi-1y[font=symbol]q[/font]0 =cxi[font=symbol]q[/font]0 {c=x/y} [/color][/size][/font][/td][/tr][/table][size=3][color=darkgreen]Substituting into (V), [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_7.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]Now, [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_8.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]Also, [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_9.GIF[/img] [/color][/size][/td][/tr][/table][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][b][size=3][color=darkgreen] . . .[/color][/size][/b][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_10.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]At saturation pressure of gas P0, an infinite number of adsorbate layers must build up on the surface. From equation VII, for this to be possible, [/color][/size][table][tr][td=1,1,10%][size=3][color=darkgreen][/color][/size][/td][td][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_12.GIF[/img] [/color][/size][/td][/tr][/table][size=3][color=darkgreen]must be infinite. This means that at P0, x must equal 1. [/color][/size][table][tr][td][b][size=3][color=darkgreen] . . .[/color][/size][/b][/td][td][font=Arial][size=3][color=darkgreen]g = P0 [/color][/size][/font][/td][td][font=Arial][size=3][color=darkgreen](From definition of x) [/color][/size][/font][/td][/tr][/table][table][tr][td][b][size=3][color=darkgreen] . . .[/color][/size][/b][/td][td][font=Arial][size=3][color=darkgreen]x = P/P0 [/color][/size][/font][/td][/tr][/table][size=3][color=darkgreen]Substituting into VII, we arrive at the recognized form of the BET isotherm, [/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_17.gif[/img] [/color][/size]
[size=3][color=darkgreen]This can be rearranged to give, [/color][/size][size=3][color=darkgreen][img]http://www.jhu.edu/~chem/fairbr/equal_18.gif[/img] [/color][/size]
[size=3][color=#006400][/color][/size][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen][/color][/size][size=3][color=darkgreen][b]Graphical form of the BET isotherm[/b][/color][/size]
[size=3][color=darkgreen] [/color][/size]
[size=3][color=darkgreen][URL=http://imageshack.us][IMG]http://img362.imageshack.us/img362/1976/betgraphpf1.gif[/IMG][/URL][/color][/size]
[[i] 本帖最后由 nanosurface 于 2007-01-11 11:51 编辑 [/i]]
nanosurface 2007-01-12 00:54
Experimental Procedure
[color=darkgreen][size=4]BET ISOTHERM:[/size][/color]
[size=4][color=#006400][/color][/size]
[size=3][color=darkgreen]This experiment is designed to measure the adsorption characteristics of nitrogen molecules on activated charcoal particles maintained at liquid nitrogen temperature. The basic outline and theory of this experiment can be found in [b]Experiment 26[/b] of [i]Garland and Shoemaker[/i]. [/color][/size]
[size=3][color=#006400][/color][/size]
[size=3][color=darkgreen]This experiment also incorporates a specific web-based module designed to help students come to grips with the underlying physical nature of adsorption. The web-site can found at [/color][/size][url=http://www.jhu.edu/~chem/fairbr/isot.html][size=3][color=darkgreen]http://www.jhu.edu/~chem/fairbr/isot.html[/color][/size][/url][b][size=3][color=darkgreen]. [/color][/size][/b]
[b][size=3][color=#006400][/color][/size][/b]
[color=darkgreen][size=3]The essence of this experiment involves a series of volume expansions, ultimately to determine the adsorption properties of nitrogen on activated charcoal. A pictorial representation of the experimental set-up can also be found at [/size][/color][color=darkgreen][size=3][b][url=http://www.jhu.edu/~chem/fairbr/betexptl.pdf]http://www.jhu.edu/~chem/fairbr/betexptl.pdf[/url][/b][/size][/color]
[color=darkgreen][size=3][/size][/color][size=3][color=darkgreen]The pre-lab is constructed as a series of questions – answers to these questions should constitute a working knowledge of adsorption and enable you to carry out the experiment.[/color][/size]
[size=3][color=#006400][/color][/size]
[b][size=3][color=red]Basis for Pre-Lab:[/color][/size]
[/b][list=a][*][size=3][color=darkgreen]What is the pressure-to-volume relationship for an ideal gas expansion between two vessels with volumes V1, V2 and initial pressures P1 and P2? After expansion the pressures can be written P1` and P2`. [/color][/size][*][size=3][color=darkgreen]What is the fundamental chemical concept underlying the pressure-to-volume relationship; conservation of mass, energy, number of moles or volume? Show how this leads to the relationship used in (a) [/color][/size][*][size=3][color=darkgreen]Answer the following question: If gas at 500 Torr is expanded into another container, initially under high vacuum (i.e. P2 = O Torr) having four times the volume of the initial container what will the final pressure of the overall system be? Show your working clearly and carefully. [/color][/size][*][size=3][color=darkgreen]How would the volume expansion relationship be modified in the case of adsorption? Explain either in words or using an equation how volume expansions be used to determine adsorption characteristics? [/color][/size][*][size=3][color=darkgreen]Why do we out gas the carbon prior to adsorption experiments? [/color][/size][*][size=3][color=darkgreen]What the liquid nitrogen is used for (2 reasons)? [/color][/size][*][size=3][color=darkgreen]The Langmuir adsorption isotherm ([b]see web page[/b]) is a simplified version of the BET isotherm that gives the same qualitative form of the variation in adsorption as function of external pressure at low gas pressures. Using the Langmuir isotherm explain in words how the number of moles adsorbed on the activated charcoal should vary as a function of the external pressure. (e.g. number of moles of gas adsorbed is constant as a function of the applied pressure) [/color][/size][*][size=3][color=darkgreen]Also from the animated [i]gifs[/i] provided on the webpage explain at a molecular level how adsorption is effected by external parameters such as temperature and pressure? [/color][/size][*][size=3][color=darkgreen]Give some examples of practical everyday situations where adsorption is important. [/color][/size][*][size=3][color=darkgreen]Identify likely sources of error in the experiment?[/color][/size][/list][size=3][color=#006400][/color][/size]
[b][i][u][size=3][color=red]Experimental Procedure:[/color][/size][/u][/i][/b]
[b][i][u][size=3][color=#ff0000][/color][/size]
[/b][/i][/u][b][size=3][color=darkgreen](A) Preparation of "activated" charcoal: [/color][/size]
[/b][list=1][*][size=3][color=darkgreen]Carefully remove the sidearm flask from the glass line [/color][/size][*][size=3][color=darkgreen]Measure approximately 2 grams of activated carbon and transfer into the sidearm flask without contaminating the glass wool filter inside the sidearm flask [/color][/size][*][size=3][color=darkgreen]Reattach the sidearm flask to the glass line, and begin pumping through the sidearm valve to reestablish the vacuum [/color][/size][*][size=3][color=darkgreen]Attach the heating tape to the flask so that as much of the carbon is covered without overlaying the heating tape on itself. Power the heating tape at 100/140 on the Variac (Heat for 30 minutes) [/color][/size][*][size=3][color=darkgreen]Remove heating tape from flask and allow to cool for 15 minutes [/color][/size][*][size=3][color=darkgreen]Once cool, slowly open the valve connecting the sidearm flask to the glass line making sure that the vacuum in the glass line does not disturb the carbon in the flask[/color][/size][/list][size=3][color=darkgreen]Close the valve and repeat the helium expansion from above, making sure that when you evacuate the side arm flask the you do it through the sidearm or else you may lose some of your now activated carbon[/color][/size]
[size=3][color=#006400][/color][/size]
[b][size=3][color=darkgreen](B) Helium Expansion into glassware to determine the volume of the line and the volume of the sidearm vessel containing the charcoal:[/color][/size]
[/b][list=1][*][size=3][color=darkgreen]check to make sure that all relevant stop cocks are open for initial pumping [/color][/size][*][size=3][color=darkgreen]start the Alcatel mech. pump and pump the glass line and both gas line to the regulators, (both the Helium and Nitrogen) – [b]MAKE SURE THAT THE NEEDLE VALVES ON BOTH NITROGEN AND HELIUM TANKS ARE CLOSED.[/b] [/color][/size][*][color=darkgreen][size=3]fill the 1025 mL round bottom flask with a known pressure of He ([b][i]200-800 Torr in [font=Symbol]»[/font] 100 Torr increments[/b][/size][/color][/i][size=3][color=darkgreen]). Throughout all experiments pressure should be read off the Baratron Digital Pressure Gauge. [/color][/size][*][size=3][color=darkgreen]Pump the line and side arm flask back to base pressure (< 5 Torr) [/color][/size][*][size=3][color=darkgreen](a) Expand the gas from the round bottom flask into the line, recording the pressure drop.[/color][/size][/list][list=a][*][size=3][color=darkgreen]Then expand the round bottom and line pressure in the sidearm flask containing the characoal, again recording the pressure drop.[/color][/size][/list][list=1][*][size=3][color=darkgreen]Fill the round bottom to another known pressure, evacuate the line and sidearm flask and repeat 5(a) and (b) until a total of 7 data points have been acquired.[/color][/size][/list][size=3][color=darkgreen]Once all helium expansions are complete, evacuate the helium line and open the nitrogen line.[/color][/size]
[b][size=3][color=darkgreen](C) Determine the adsorption characteristics of nitrogen in contact with the activated charcoal: [/color][/size]
[/b][list=1][*][size=3][color=darkgreen]Immerse the activated carbon in liquid nitrogen. [/color][/size][*][size=3][color=darkgreen]Fill the round bottom flask and the line with a known pressure of nitrogen (starting low, [font=Symbol]»[/font] 10-20 Torr and going to higher pressures [font=Symbol]»[/font] 700-800 Torr), open the sidearm flask and watch pressure drop stabilize. It will typically take 5-10 minutes for the pressure to stabilize as the system comes to equilibrium. [/color][/size][b][*][size=3][color=darkgreen]Close the stopcock between the sidearm flask and the main glass line [/color][/size][/b][*][size=3][color=darkgreen]Refill the glass line and round bottom to next higher pressure as in 2) and carry our successive expansions into the sidearm.[/color][/size][/list]
[size=3][color=darkgreen]Make sure to watch the liquid nitrogen level does not fall below the level of charcoal in the sidearm vessel as the experiment continues.[/color][/size]
[size=3][color=darkgreen]Once done bring line back to atmosphere before removing the liquid nitrogen for the charcoal, ensuring that the gas has a place to escape.[/color][/size]
[[i] 本帖最后由 sally208 于 2007-12-13 20:32 编辑 [/i]]
nanosurface 2007-01-12 00:55
[b][/b][size=4][color=darkgreen][b]BET Data Analysis:[/b][/color][/size]
[size=3][color=#006400][/color][/size]
[size=3][color=darkgreen]Analysis of the data relies on the fact that the number of moles (n) before and after any expansion must be constant (conservation of mass).[/color][/size]
[align=center][size=3][color=darkgreen][font=Symbol]\[/font] nbulb + nline = n`bulb + n`line[/align][/color][/size][color=darkgreen][/color]
[size=3][color=darkgreen]( ` - denotes after expansion)[/color][/size]
[size=3][color=darkgreen]Assuming ideal gas behavior (good approximation for nitrogen and helium)[/color][/size]
[list][*][size=3][color=darkgreen]PV = nRT[/color][/size][/list][size=3][color=darkgreen]Throughout RTrt. is constant (T- room temperature)[/color][/size]
[size=3][color=darkgreen]Applying this to the bulb and the line:[/color][/size]
[align=center][size=3][color=darkgreen]PbulbVbulb + PlineVline = P`bulbVbulb + P`lineVline[/align][/color][/size][size=3][color=darkgreen]Vbulb is known, Vline is unknown.[/color][/size]
[size=3][color=darkgreen]After expansion the bulb and line are connected;[/color][/size]
[align=center][size=3][color=darkgreen][font=Symbol]\[/font] P`bulb = P`line[/align][/color][/size][align=center][size=3][color=darkgreen]Vline = (P`bulbVbulb – PbulbVbulb)(Pline-P`line)[/color][/size][/align][align=center][size=3][color=darkgreen][/color][/size][/align][size=3][color=darkgreen]Hence Vline can be determined.[/color][/size]
[size=3][color=darkgreen]A knowledge of Vline in turn enables V1 to be calaculated.[/color][/size]
[align=center][size=3][color=darkgreen]V1 = Vbulb + V[/color][/size][size=3][color=darkgreen]line[/color][/size][/align][align=center][size=3][color=darkgreen][/color][/size][/align][size=3][color=darkgreen]A knowledge of V1 can then be used to determine the volume of the charcoal containing bulb (V2) in a similar manner, using volume expansions.[/color][/size]
[size=3][color=darkgreen]Now when we switch to nitrogen this approach can be modified to determine the adsorption characteristics of nitrogen on "activated" charcoal.[/color][/size]
[size=3][color=darkgreen]If the pressure in the bulb and line is P1 and inside the charcoal container is P2 then upon opening the valve between the line and the charcoal container:[/color][/size]
[align=center][size=3][color=darkgreen]nline + nbulb = n`line + n`bulb + nadsorbed on charcoal[/align][/color][/size][size=3][color=darkgreen]Applying the fact that PV = nRT for an ideal gas[/color][/size]
[size=3][color=darkgreen][/color][/size]
[align=center][size=3][color=darkgreen]P1V1 + P2V2 = P1`V1 + P2`V2 + RT x Number of Moles Adsorbed on Charcoal[/color][/size][/align][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen]Since P1, P2, P1`, P2` can be measured and V1 and V2 have been previously determined this enables the number of moles adsorbed on the charcoal to be determined.[/color][/size]
[size=3][color=darkgreen]Remember:[/color][/size]
[list][list][*][size=3][color=darkgreen]P1` = P2` (Once the bulb and line are connected) [/color][/size][*][size=3][color=darkgreen]the number of molecules adsorbed on the charcoal must be added for successively higher expansion pressures. [/color][/size][/list][/list][size=3][color=darkgreen]By convention it is customary to represent the number of moles adsorbed by its ideal gas equivalent at 1atm.[/color][/size]
[size=3][color=darkgreen]v = Number of moles adsorbed x RT/ 760[/color][/size]
[size=3][color=darkgreen](1 atm = 760 Torr)[/color][/size]
[size=3][color=darkgreen]From your data calculate and plot v as a function of x ( x = P1`/P0)[/color][/size]
[size=3][color=darkgreen]P0 is the vapor pressure of the liquid at the temperature of the charcoal (77K for liquid nitrogen) = 760 Torr. [/color][/size]
[size=3][color=darkgreen]This plot should look like Figure 1 on Pg. 301 of Garland and Shoemaker.[/color][/size]
[size=3][color=darkgreen][img=318,78]http://www.jhu.edu/~chem/fairbr/Image12.gif[/img]The usual form of the BET isotherm is given by;[/color][/size]
[size=3][color=darkgreen]Where vm is the volume of nitrogen required to cover the surface with one monolayer (what is a monolayer?)[/color][/size]
[size=3][color=darkgreen][img=88,69]http://www.jhu.edu/~chem/fairbr/Image13.gif[/img][/color][/size]
[size=3][color=darkgreen]Plot[/color][/size]
[size=3][color=darkgreen]vs. x[/color][/size]
[size=3][color=darkgreen]for x = 0.05 –0.3 and [b]determine the slope and gradient both graphically and using linear least squares fitting[/b].[/color][/size]
[b][size=3][color=darkgreen]Use this information to calculate vm and c[/color][/size][/b][size=3][color=darkgreen]. [/color][/size]
[size=3][color=darkgreen]vm can be related to the number of moles of gas adsorbed on the surface (at STP) of the activated charcoal by the relationship;[/color][/size]
[align=center][size=3][color=darkgreen]Pvm = nads R T0 (T0 = 273.15K)[/color][/size][/align][size=3][color=darkgreen][/color][/size]
[size=3][color=darkgreen]Remember that P = 1 atm. by definition. Consequently:[/color][/size]
[align=center][size=3][color=darkgreen][/color][/size][/align][align=center][size=3][color=darkgreen]vm/RT0 = nads[/align][/color][/size][b][size=3][color=darkgreen]Thus calculate nads.[/color][/size]
[/b][size=3][color=darkgreen]Also since:[/color][/size]
[size=3][color=darkgreen]A = N0 nads [font=Symbol]s[/font] [/color][/size]
[size=3][color=darkgreen][font=Symbol]s[/font] (area of N2 molecule – 15.8Å2)[/color][/size]
[size=3][color=darkgreen]A – area of solid [/color][/size]
[size=3][color=darkgreen]N0 – Avadagro’s number[/color][/size]
[b][size=3][color=darkgreen]Hence determine A[/color][/size][/b][size=3][color=darkgreen] and from a knowledge of A and the mass of the charcoal [b]determine the active surface area of the charcoal in cm2/g[/b].[/color][/size]
nanosurface 2007-01-12 00:59
BET - Measuring Areas Using Molecules
[font=Trebuchet MS][size=2][/size][/font][size=3][color=darkgreen]BET comes from the initials Brunauer, Emmett and Teller[/color][/size][url=http://www.bbc.co.uk/dna/h2g2/A845723#footnote1][font=Trebuchet MS, arial, helvetica, sans-serif][size=3][color=darkgreen]1[/color][/size][/font][/url][size=3][color=darkgreen], the men who invented a straight-forward method, and a complicated-looking accompanying theory, to determine the effective surface of solid materials with complicated shapes, such as porous powders, by using adsorbed gas molecules as rulers. The observation of the so-called adsorption and desorption isotherms is used to determine the amount of gas molecules adsorbed to a surface. Knowing the [/color][/size][url=http://www.bbc.co.uk/dna/h2g2/A791246][size=3][color=darkgreen]size of a molecule[/color][/size][/url][size=3][color=darkgreen], one can then calculate the entire effective surface. In scientific literature one will commonly bump into the terms 'BET-isotherm' or 'BET-method' when this approach has been used.[/color][/size]
[font=Trebuchet MS, arial, helvetica, sans-serif][size=4][color=#cc3300][b]OK, But... Why?[/b][/color][/size][/font]
[b][font=Trebuchet MS][size=4][color=#cc3300][/color][/size][/font][/b]
[size=3][color=darkgreen]Why would one need a new way of measuring areas, if one can do that using primitive [/color][/size][url=http://www.bbc.co.uk/dna/h2g2/A476606][size=3][color=darkgreen]trigonometry[/color][/size][/url][size=3][color=darkgreen] and a pocket calculator? Simple areas, like the area of a tennis-court or the surface of a [/color][/size][url=http://www.bbc.co.uk/dna/h2g2/A378010][size=3][color=darkgreen]doughnut[/color][/size][/url][size=3][color=darkgreen], are indeed relatively easy to determine using plain geometry (cf [/color][/size][url=http://www.bbc.co.uk/dna/h2g2/A533189][size=3][color=darkgreen]Calculating the Volume and Surface Area of Various Solid Objects[/color][/size][/url][size=3][color=darkgreen]). More complicated surfaces, however, like the entire surface of a powder, or the entire surface of a grinding-stone, that is, the surface around every little bump it is made of, are a lot more difficult, if not impossible, to measure or calculate using geometry.[/color][/size]
[font=Trebuchet MS, arial, helvetica, sans-serif][size=3][color=#cc3300][b]An Analogy - The Area of a Tennis Court[/b][/color][/size][/font]
[b][font=Trebuchet MS][size=3][color=#cc3300][/color][/size][/font][/b]
[size=3]Before delving into questionably important scientific abracadabra, it is worthwhile taking a look at the following analogy. It is intended for those readers that are not so familiar with scientific formalism. It will demonstrate how to determine the surface area of a [/size][url=http://www.bbc.co.uk/dna/h2g2/A663022][size=3][color=#0066ff]tennis[/color][/size][/url][size=3] court covered with clay.
One could imagine a tennis court covered with a thin film of glue. Now, after unloading a truck of clay onto that surface and shaking it a bit, the surface will be covered with clay corns. The excess of clay, namely the corns that are not glued to the surface, can be easily removed. The next step is to dissolve the glue, and pour the remaining clay, that is, the clay that was once glued to the surface, into a recipient. From the weight of one corn one can deduce how many corns are in the recipient altogether by weighing it. One should now carefully measure the width of one individual corn of clay, and calculate its effective area: that is, the area it will cover on the surface. Multiplying that number with the number of clay corns will yield the surface of the tennis court. If the tennis court is not perfect, that is, if it has tiny bumps, eg, along the demarcation lines, the surface will be slightly larger than the area calculated using traditional geometry. Replacing 'corns of clay' for 'gas molecules' and 'tennis-court surface' by 'solid material surface' will result in the mechanism used in the BET-Method.[/size]
[font=Trebuchet MS, arial, helvetica, sans-serif][size=4][color=#cc3300][b]The BET-Method in Principle[/b][/color][/size][/font]
[b][font=Trebuchet MS][size=4][color=#cc3300][/color][/size][/font][/b]
[size=3]The problem Brunauer, Emmett and Teller were facing in the early 1930s was not so connected to surfaces of tennis-courts but to the surfaces of more complicated-looking solids. Like: how big is the surface of a powder - and what if each corn of that powder has an indeterminate number of holes and pores and cracks? The method they developed is, in principle, quite straight-forward. Namely to use the surface of gas molecules as a ruler, as described in the analogy above.[/size]
[font=Trebuchet MS, arial, helvetica, sans-serif][size=3][color=#cc3300][b]Normal Behaviour[/b][/color][/size][/font]
[b][font=Trebuchet MS][size=3][color=#cc3300][/color][/size][/font][/b]
[size=3]One of the basic properties of gas molecules is that they like to stick to surfaces[/size][url=http://www.bbc.co.uk/dna/h2g2/A845723#footnote2][font=Trebuchet MS, arial, helvetica, sans-serif][size=3][color=#0066ff]2[/color][/size][/font][/url][size=3], all one has to do is to find out how many gas molecules are stuck to the surface of the solid material in question. From the effective area of each molecule one can then obtain the whole area with good accuracy. To determine that amount of molecules, one can look at their adsorption/desorption isotherms. Isotherms are volume and pressure relations at a constant temperature. According to the [/size][url=http://www.bbc.co.uk/dna/h2g2/A673580][size=3][color=#0066ff]gas state equations[/color][/size][/url][size=3], pressure ([i]p[/i]) is (in a first approximation) directly proportional to the number ([i]n[/i]) of molecules a gas is made of:[/size]
[size=3]
V·[i]p[/i] = RT·[i]n[/i]
In this relation, V is the volume where the gas is in - it stays constant if one uses a closed rigid recipient, like a pot of marmalade. R is the gas-constant, which is nothing but a conversion factor, so that the [/size][url=http://www.bbc.co.uk/dna/h2g2/A471476][size=3][color=#0066ff]units[/color][/size][/url][size=3] match. T is the absolute temperature (in K), which in the case of isotherms is also a constant. Hence, if one pumps more and more gas molecules into the pot the pressure will rise linearly. Conversely, if molecules are pumped out of the pot the pressure will decrease linearly. So far, this all sounds incredibly reasonable.[/size]
[font=Trebuchet MS, arial, helvetica, sans-serif][size=3][color=#cc3300][b]Adsorption and Desorption[/b][/color][/size][/font]
[b][font=Trebuchet MS][size=3][color=#cc3300][/color][/size][/font][/b]
[size=3]Experiments showed that when pumping molecules out of a recipient, all goes linearly well and as expected normal until a certain level of 'emptiness' is reached. After that point the curve starts to deviate from the 'normal' behaviour. The pressure does not decrease at the same pace as before. Instead, it decreases a lot slower. The same happens in the other way round, when an empty pot is slowly filled with some gas molecules: in the beginning the pressure seems to increase only very slowly. After a certain point it increases a lot faster, and the pressure then shows again its 'normal' linear behaviour. [/size]
[size=3]
The explanation for this deviation is the following: a gas molecule can only contribute to increase the pressure if it is diffusing around freely. If it sticks to some surface it will not be 'available' to increase the pressure. And that is exactly what happens. The very first molecules that are pumped into the recipient will stick to its surface. One observes a phenomenon called adsorption. All molecules adsorb or stick to surfaces, the question is only how strongly they will do that. After the whole surface is covered with one layer of molecules a second layer will build up. This layer, however, will not be bound as strongly to the first one, because the nature of the interaction is more similar to the one present in the gas - that is, the new molecules will not be interacting with the surface, but with other similar molecules, since the surface is one layer away. In principle this layering might go on forever: a third layer would build up, and a fourth one and so on. Normally after the first two layers the interactions responsible for the adsorption become so small that any new atom added will more likely contribute to increase the pressure than sticking to some layer. At that point the increase in pressure starts to become 'normal'.[/size]
[table][tr][td=1,4,5][/td][td][/td][td=1,4,5][/td][/tr][tr][td][img]http://www.bbc.co.uk/dna/h2g2/B2589921white[/img][/td][/tr][tr][td][font=verdana, helvetica, sans-serif][size=1][color=#ffffff][/color][/size][/font][/td][/tr][tr][td][/td][/tr][/table][size=3]In the schematic representation above this process is illustrated. In the first frame a schematical zoomed-in view of the fresh unloaded surface is depicted. In the second frame the molecules (marked by an X) start adsorbing to the surface. Note that of the eight added molecules only two will contribute to an increase of pressure. In the third frame the first layer is complete and a second layer starts to build up upon the first one. In this example 24 molecules have been added to the recipient and only four contribute to the pressure. In the fourth frame both layers are complete. If one assumes that the formation of a third layer of molecules is improbable, then any new added molecule will contribute to an increase of pressure. That's the point where the behaviour becomes normal: one molecule, one addition to the pressure.[/size]
[size=3]Using this behaviour, one can determine the point where the curve starts deviating from the normal behaviour. When starting with an unloaded surface, the first nick of the curve will indicate the point where the first layer has just finished building-up. A second nick would indicate the building-up of a second layer, and so forth. When going the other way round, ie, unloading the surface, the last nick will indicate the point where the first layer just starts unloading. Normally it is easier to go from the unloaded surface to the loaded surface, because it's easier to identify the first nick than identifying the last since one will never be sure if the observed nick is actually the last.[/size]
[font=Trebuchet MS, arial, helvetica, sans-serif][size=4][color=#cc3300][b]Details, Types of Isotherms, Hysteresis and Surface Textures[/b][/color][/size][/font]
[b][font=Trebuchet MS][size=4][color=#cc3300][/color][/size][/font][/b]
[size=3]As easy as it might seem, it is the deviation from the normal adsorption behaviour that will allow the observer to draw conclusions on the texture or porosity of the surface. And this is also the point where the theory starts to become complicated. This will not be discussed at full detail in this Entry.
In general there are six types of adsorption/desorption isotherms[/size][url=http://www.bbc.co.uk/dna/h2g2/A845723#footnote3][font=Trebuchet MS, arial, helvetica, sans-serif][size=3][color=#0066ff]3[/color][/size][/font][/url][size=3]. The conventional adsorption/desorption isotherm plot shows the volume of adsorbed molecules against pressure, instead of plain volume against pressure. The reason for this is that the point where the layers build up is visualised better, and because this form is apparently easier to connect to the BET-equation. Normally a scientist doing BET-measurements will not calculate that curve using complicated equations over and over again. Instead he or she will check the pattern of the curves with standard pictures.
Since there is no way to add graphics to h2g2 in an easy way, some imagination will be required to follow the next description of the curves. All six curve types start from zero and rise steeply. All of them bend to the 'right' at some point, become shallower and have a characteristic plateau, which is the point where no more molecules can be adsorbed by the material. Four of them have an additional first plateau right at the beginning, which is where the first layer builds up. The remaining two are very atypical and only restricted to some special exceptional cases. To measure the surface area of the material in question all one has to do is to identify the first nick in the curve and take note of the volume, which is the volume of gas molecules used to form the first layer.
Sometimes one might observe hysteresis. Hysteresis occurs when loading a surface is easier than unloading it (for example if there is a pore or a tight crack), the curve for the loading will be steeper than the curve for the unloading. This makes things a bit more complicated, and that's where details start to become important. These details allow conclusions on the texture of the surface - for example about the porosity of the surface, and even about the shape of the pores. Further interpretations can be made but are usually difficult.
There are commercially available BET-measuring devices. In principle they are made of a sample chamber, where one can put the powder to be measured, and which is connected to a gas inlet, a vacuum pump and a (electronic) barometer. The first step is to evacuate the chamber, so that all surfaces get cleaned from adsorbed molecules. Then a small volume of gas is added in a controlled manner, normally automatically, and the pressure measured. This step is repeated several times. For desorption measurements gas is pumped out and the pressure measured. It is important to note that every time gas is added or removed from the chamber one will have to wait some time until equilibrium is reached, only then the measured pressure yields a reliable value.
There are more advanced models for adsorption and desorption isotherms, however, they didn't find as broad application as the BET method. BET is employed as a standard measurement for technical powders, as used in catalysis for example. Normally BET-measurements are carried out with different gas molecules (CO2, N2, and Ar). The values can differ slightly for each gas employed, since their geometry and adsorption characteristics vary. For thit reason the gas used is often given in parenthesis along with the area measured (and other features like the porosity).
[/size]
[indent][font=Trebuchet MS, arial, helvetica, sans-serif][size=1][color=#ffffff][url=http://www.bbc.co.uk/dna/h2g2/A845723#back1][font=Trebuchet MS, arial, helvetica, sans-serif][size=2][color=#0066ff]1[/color][/size][/font][font=Trebuchet MS, arial, helvetica, sans-serif][size=2][color=#ffffff][color=#000000] Stephen Brunauer (1903 -), Paul Hugh Emmett (1900 - 1985) and Edward Teller (1908 -) - Yes, that's right, the 'father' of the H-bomb, a key figure in [/color][url=http://www.bbc.co.uk/dna/h2g2/A685109][color=#0066ff]Project Plowshare[/color][/url][color=#000000]).[/color][/color][/size][/font][/url]
[url=http://www.bbc.co.uk/dna/h2g2/A845723#back2][font=Trebuchet MS, arial, helvetica, sans-serif][size=2][color=#0066ff]2[/color][/size][/font][color=#000000][font=Trebuchet MS, arial, helvetica, sans-serif][size=2] This phenomenon is called 'adhesion'. Note that some molecules are stickier than others.[/size][/font][/url]
[/color][url=http://www.bbc.co.uk/dna/h2g2/A845723#back3][font=Trebuchet MS, arial, helvetica, sans-serif][size=2][color=#0066ff]3[/color][/size][/font][font=Trebuchet MS, arial, helvetica, sans-serif][size=2][color=#000000] Just in case someone asked, the BET equation looks like this:
Vm/(p-p0)·1/V = 1/c[1/p+(c-1)/cp0]
Here, V is the total volume of molecules added, Vm is the volume of gas molecules corresponding to the monolayer, p the pressure and p0 the saturation vapour pressure, c is a constant related to the adsorption heat and it has something to do with probability of adsorbing or desorbing. This equation is indeed a bit complicated and was just included for the sake of completeness.[/color][/size][/font][/url]
[/color][/size][/font][/indent]
[[i] 本帖最后由 nanosurface 于 2007-01-11 12:03 编辑 [/i]]