Adsorption and complementary in situ methods for the characterisation of microporous materials philip.llewellyn@univ-provence.fr www.lc-provence.fr Equipe Matériaux Divisés MATDIV (UMR6264) Université de Provence & CNRS Marseille, France
CO + ½ O 2 CO 2 on a Rh catalyst Animation showing how a gas-phase CO molecule adsorbs, interacts with an O neighbour, and finally desorbs as a CO 2 molecule (C in green, O in red, the catalyst in grey) http://www.fhi-berlin.mpg.de/th/highlights/cathy_99.html
What is adsorption a short history where do we find adsorption Methodology Different adsorption apparatus What can we characterise using adsorption different types of isotherm surface area Henry, Langmuir, BET Pore volume and external surface area t-plot, as plot Micropore size HK ideas behind DFT Trouble shooting
So what is adsorption?
Adsorption by solids It is the increase in concentration of a gas or dissolved species in the neighbourhood of a solid A general phenomenon To be useful, needs an extensive surface area Active carbon : 100 to 2600 m 2 of porous surface per gram of carbon.
The discovery of adsorption The ancient Egyptians already used adsorbents in the form of clay, sand or wood charcoal to desalinate water, clarify fat and oil, or treat diseases; the Greeks and Romans continued; the «sorcerer s black stone» known and used for centuries to suck venom from snake bites is a good adsorbent (around 100 m 2 /g) Around 1775 : first quantitative measurements of gas adsorption by charcoals (Scheele, Priestley, Fontana) 1885 : investigation of decolorizing properties of charcoal (Lowitz)
The discovery of adsorption (cont.) 1822: first description of heat of immersion (Pouillet) 1854: first measurement of heat of adsorption (Favre) 1881: introduction of word «adsorption» (Kayser) and first «adsorption isotherms» (Chappuis and Kayser) 1909: «sorption» combines ad- and absorption (McBain) 1916: theory of the monolayer adsorption (Langmuir) 1938:the BET equation (Brunauer, Emmett and Teller)
So what about adsorption in everyday life?
Activated carbons for water treatment
Pressure Swing Adsorption http://www.norit.com/?rubriekid=2138 Gas Mixture A + B Adsorbent bed Pure Gas B
Smaller units for hospital oxygen
Hot topics current and future CO 2 recovery Hydrogen purification Hydrogen storage Alkane/alkene separations Biodiesel Purification Water from ethanol Adsorption of mercaptans Liquid hydrogen filling station at Munich Airport
However, we can use of adsorption to characterise a solid What can we characterise surface area internal surface area (in the porosity) external surface area porosity pore volume pore size pore connectivity b f e c d a
So schematically how can we imagine the phenomenon of adsorption? Fluid (gas, liquid) or Adsorptive Adsorbed phase or Adsorbate Solid or Adsorbent
So why do molecules adsorb on a surface? For surface atoms A s fi 0 i For atoms in the bulk A B fi 0 i The resultant of the forces on the surface atoms As is not zero the internal energy of the surface atoms A s - with a certain interfacial tension - is greater than the atoms in the bulk A B
The smaller the particles, the more surface atoms and the more reactive the surface Variation of the proportion of surface molecules as a function of the particle size (solid with molar volume Vm = 30 cm 3 mol -1 ) Percentage of surface atoms (=%) 25 20 15 10 5 0-2 -1.5-1 -0.5 0 Log (d / µm)
Consequences of the presence of a nonnegligible quantity of atoms at the surface the atoms can attract other species to the surface : adsorption the atoms can release energy : immersion Quantification of the surface atoms by the measurement of the extent of surface : specific surface area (related to 1 gram of product)
Types of Texture found in a Porous Material e f d b c a : Surface roughness b : Bottle-neck shaped pore c : Opening d : Interconnection e : Pores opened at one end f : Closed porosity a
Experimental methods / Pore Width nm 10-1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 0.3nm 1nm 2nm* 10nm 50nm* 100nm 1µm 1mm micropores mesopores macropores. * IUPAC ultra super nanopores adsorption Micropore filling Capillary condensation Adsorption microcalorimetry Thermoporometry micro capillaries / capillaries / macro capillaries e f b c d Mercury porosimetry a Immersion microcalorimetry
Definition and Representation of Adsorption Phenomena The phenomena of adsorption Gibbs representation of adsorption Surface excess concentration
So schematically how can we think of adsorption? Fluid (gas, liquid) or Adsorptive Adsorbed phase or Adsorbate Solid or Adsorbent
Adsorption The phenomenon of adsorption When a fluid is in the region of solid surface, its concentration increases close the interface. Definition The enrichment of one or more components in the region between two bulk phases (gas/solid, liquid/solid) The word "adsorption" is also used to describe the phase change of a fluid which adsorbs.
Adsorption Definitions Adsorption The enrichment of one or more components in the region between two bulk phases (gas/solid, liquid/solid) Gas/Solid Adsorption : The accumulation is due to the solid attractive forces on the gas molecules The solid material on which adsorption occurs is called the adsorbent The gas is called adsorptive and when it s in the adsorbed state, the adsorbate Physisorption or chemisorption Adsorption Liquid/Solid : it always involves a competition between the solvent and solute
Physisorption or Chemisorption Adsorption is brought about by the interactions between the solid and the molecules in the fluid phase Two kinds of forces are involved, which give rise to either physical adsorption or chemisorption Physisorption General phenomenon A physisorbed molecule keeps its identity and on desorption returns to the fluid phase in its original form Gas adsorption is exothermic and the amount adsorbed decreases with the temperature at a given pressure Multi-layer adsorption Chemisorption Specific: depends on the reactivity on the adsorbent and adsorptive A chemisorbed molecule undergoes reaction or dissociation, loses its identity and cannot be recovered by desorption Adsorption can be exothermic, endothermic or athermic Chemisorption occurs only as a monolayer
So schematically how can we think of adsorption? Fluid (gas, liquid) or Adsorptive Adsorbed phase or Adsorbate Solid or Adsorbent
Schematically, What is adsorption? [c] Concentration of the adsorbed phase Concentration of the gas phase z
Surface excess concentration : = n /A n is the surface excess quantity A is the extent of surface a is the specific surface area (= A /m s ) n / m s =. a
Adsorption equilibrium One equilibrium adsorption state, at one temperature T, is characterised by one value of the surface excess concentration which depends on the gas pressure, p : n. a f ( p). g( T m s )
Adsorption isobar : p = cte n / m s Physical Adsorption Chemical Adsorption n. a f ( T m s ) Physisorption Chemisorption T adsorption
Argon isotherm at 77.4 K n s m 5 4 3 2 1 n. a f ( p) m s 0 0 0.2 0.4 0.6 0.8 1 p / p o
Definition of the Adsorption Isotherm An adsorption isotherm is the set of equilibrium states, for one temperature T given, for values of pressure between 0 and p (the saturation vapour pressure of the adsorptive at T). p/p is known as the equilibrium relative pressure".
Physisorption Isotherms n s m T 1 T 2 > T 1 Adsorption is an exothermic phenomena ads Isosteric Enthalpies T T h 1. 2 R.. ln T T 2 1 p p 2 1 n / m s p 1 p 2 p
n s m 5 4 3 2 1 A 0 Argon isotherm at 77.4 K : B C Indicative points F D 0 0.2 0.4 0.6 0.8 1 E n. a f ( p) m s p / p o
Measurement of Adsorption Isotherms Adsorption manometry Adsorption gravimetry Procedure of an adsorption experiment
Commercial Apparatus (Manometry)
Adsorption Volumetry : Brunauer apparatus Gas Manifold Adsorptive Vacuum Mercury manometer Adsorbent Mercury Burette Cf. Adsorption by Powders and Porous Solids, F. Rouquerol, J. Rouquerol & K. Sing Wiley Interscience, 2000.
Adsorption Manometry : Simplified schema Pressure gauge Constriction Manifold Adsorptive Vacuum Stopcock Adsorption Cell Adsorbent
Adsorption Gravimetry : McBain Balance Adsorptive Vacuum Bucket
Adsorption Gravimetry : magnetic compensation symmetrical balance Pressure gauge Adsorptive Vacuum Flag Sample Reference
Magnetic Suspension Balance Electromagnet Permanent magnet Cones to pick up independantly the cell and the sinker Sinker Sample Position 0 Position 1 Position 2 3 different positions position 0 : tare and calibration position 1 : measurement of the mass adsorbed position 2 : measurement of the gas density
Procedure of an adsorption experiment Outgassing under vacuum temperature Pressure gauge Vac. Obtain a well-defined state of the sample prior to adsorption Regulator Elimination of species adsorbed during storage (e.g. H 2 O) without degradation
Procedure of an adsorption experiment Outgassing under vacuum temperature Determination of the dead space volume (v g,0 ) gas that one considers non-adsorbed (He) Gas Pressure gauge p V ref T ref v g,0 Vac. T samp
Procedure of an adsorption experiment Outgassing under vacuum temperature Determination of the dead space volume (v g,0 ) gas that one considers non-adsorbed (He) Adsorption continuous method Dn s = Dn e - Dn r point by point method n i in v + v g,0 ref n f in v ref + v g,0 n s = n i - n f Gas n i Pressure gauge p Pressure gauge p T sample V ref T ref n f Vac.
Calculation of the amount adsorbed Amount of adsorptive gas introduced into the system n i = P ref *V ref /R*T ref Amount adsorbed : n = n i -n f where n f is the amount left in the gas phase n f is determined using a gas that is not adsorbed (e.g. He) or via a prior blank experiment on an empty cell Determination of a reference curve n f =f(p) At equilibrium : n = n i - f(p equilibrium )
Where can the measurement go wrong
Low pressure n /m s x x x xx x x x Problem of equilibrium x x x x x x Log p/p
Hysteresis : the desorption branch does not rejoin the adsorption branch (1) 0.012 0.01 Problems? n a / mmol.g -1 0.008 0.006 0.004 0.002 Simple experimental error Increase in temperature (due to excess loss in liquid nitrogen from the cryostat) 0 0 0.2 0.4 0.6 0.8 1 p / p
Hysteresis : the desorption branch does not rejoin the adsorption branch (2) v a / cm 3 STP g -1 5 4 Problems? Simple experimental error 3 Leaks 2 1 0 0 0.2 0.4 0.6 0.8 1 p / p 0 Equilibrium Adsorbate retained ultramicropores organic chains
Interpretation and Classification of Adsorption Isotherms
Interpretation of Adsorption Isotherms Mechanisms of adsorption localised adsorption micropore filling monomolecular adsorption multimolecular adsorption capillary condensation Classification of physisorption isotherms : BDDT, IUPAC, Sing
IUPAC Classification of physisorption isotherms I II III n /m s B IV V VI B p/p 0 T < Tc
Type II Isotherm : Adsorption on a purely non-porous sample Formation of a statistical monolayer Multimolecular adsorption n / m s B p / p 0
Type IV Isotherm : Adsorption on a purely mesoporous sample : d 2 à 50 nm n / m s Formation of a statistical monolayer Multimolecular adsorption Capillary condensation Hysteresis B d( pore) d( gas) 5 à 125 p / p 0
Type III and V isotherms Type III : n /m s I II III - weak adsorbent-adsorbate interactions Type V : - indicative of weak adsorbentadsorbate interactions - hysteresis loop associated with the mechanism of pore filling and emptying B IV V VI B p/p 0
Type VI Isotherm I II III n /m s Type VI : stepped isotherm B - relatively rare - associated with layerby-layer IV adsorption V on a VI highly uniform surface B p/p 0 T < Tc
Adsorption on a purely microporous sample : d 0.4 à 2 nm d( pore) 1 à 5 d( gas) n / m s Micropore filling ultramicropores supermicropores co-operative mechanism p / p 0
Exploitation of the adsorption isotherm n s /m s Capillary Condensation Localised Adsorption Micropore filling Formation of a monolayer Multimolecular Adsorption p/p
Confrontation results vs. Calculations It is quite possible to get good experimental data outgassing equilibrium enough adsorption points It is more difficult to be really sure of the results from the calculations are the assumptions valid are they general to all pore sizes what about the chemical nature of the solid surface?
Exploitation of the adsorption isotherm n /m s Capillary Condensation Kelvin equation (BJH) Broekhoff de Boer DFT Localised Adsorption Adsorption Energies Micropore filling HK DFT Dubinin, MP. Monte Carlo Monolayer formation BET Multimolecular Adsorption t-plot a S method p/p
Characterisation of solids by adsorption Surface area Methods available : Langmuir (Single layer coverage) BET (Multilayer coverage) t -plot
The Langmuir theory
Irving Langmuir, 1881-1957 Condensation / Evaporation Mechanisms All sites are energetically identical Gas sticks to the surface : 1 layer only possible No lateral interactions Gas bounces off a species already adsorbed 12345678910 11 13 14 15
Langmuir Theory (Chimisorption) - 1 type of adsorption site" - no lateral interactions - 1 adsorption site fixes 1 adsorptive molecule : the adsorption is limited to a single monomolecular layer N s = number of adsorption sites N a = number of molecules adsorbed Degree of coverage a N N s
Langmuir Isotherm Chemisorption Isotherm Often used in Chem. Eng. for adsorption at T amb bp n n m 1 bp b K exp E / RT at low pressure bp << 1, therefore Henry s Law n n m bp at high pressure, bp >> 1, therefore n n m
Langmuir Isotherm : influence of the adsorption co-efficient b 1 0.8 n / n m 0.6 0.4 0.2 b=0.01 b=0.01 b=0.01b = 0.1 0.1 b = 0.1 1 b = 10 0 0 100 200 300 400 500 Pression
1.2 In the linear form : Langmuir isotherm p n 1 n b p m n m 1 0.8 0.6 0.4 0.2 n is the specific amount of gas adsorbed at the equilibrium pressure p n m is the monolayer capacity ( = n/n m ) b the adsorption coefficient, exponentially related to the positive value of the energy of adsorption E 0 Pression Pressure
Calculation of the surface area using the Langmuir equation Ar at 87.28 K on zeolite 13X n / mol g -1 8000 7000 6000 5000 4000 3000 2000 1000 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 p/p 0 p / n 0.03 0.025 0.02 0.015 0.01 0.005 R 2 = 0.9987 a = 637.8 m 2 g -1 0 0 50 100 150 200 250 p
BET theory
BET equation : one of the 10 most significant papers in science S. Brunauer, P.H. Emmett. E. Teller (1938). Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309-319. Stephen Brunauer 1903-1986 Paul H Emmett 1899-1985 Edward Teller 1908-1957
Brunauer Emmett et Teller (BET) Theory Hypotheses 1 type of adsorption site no lateral interactions } E 1 = molar energy of adsorption for the 1 st layer from the second layer E 1 E L molar liquefaction energy of the adsorptive
Basic assumptions used in BET theory s o s 1 s 2 s 3 A surface s o covered by 0 adsorbed layer... s 1... 1............ s i... i total surface A = s o + s 1 + + s i +...
Brunauer Emmett et Teller (BET) Theory Even more equations N=number of layers x = p/p 0 = equilibrium relative pressure If N n a n m C n a n m Cx ( 1 x)[1 x( C 1)] exp Cx 1 x E1 E RT L N 1 ( N 1) x Nx 1 ( C 1) x Cx N 1 N 1 Transformed BET equation x 1 a n(1 x) n mc C n a 1 x mc
Influence of the number of layers N on the shape of a theoretical BET adsorption isotherm 4 3 2 N = 25 à Curve with general shape of type II isotherm N = 7 N = 6 N = 5 N = 4 1 n n a m Cx 1 x N 1 ( N 1) x Nx 1 ( C 1) x Cx N 1 N 1 0 0 0.2 0.4 0.6 0.8 1 p / p o
Influence of the Energetic Constant C on the shape of a theoretical BET adsorption isotherm 5 4.5 n n a a / / n n a a m m 4 3.5 3 2.5 2 1.5 1 0.5 0 C = 0.1 C = 0.1 C = 10.1 C = 1 0.1 C = 10 C = 10 1 C = 100 C = 100 C = 1000 0 0.2 0.4 0.6 0.8 1 p / p C < 10: the shape changes, the point of inflection is lost (type III isotherm) n a n m Cx ( 1 x)[1 x( C 1)]
Treatment of the isotherm by the BET method exempla : alumina NPL / N 2 / 77 K x / / n a a.(1-x) n a / mmol g -1 350.08 200 0.07 180 30 30 160 0.06 25140 0.05 120 20 20 0.04 100 15 15 0.03 80 10 60 10.02 40 0.01 5 5 20 y = 89.95x + 1.31 y = 93.59x + 0.94 Slope : y = 91.52x + 1.16 1 Intercept : n a C m 00 0 00 0.05 0.2 0.1 0.4 0.15 0.2 0.6 0.25 0.80.3 0.35 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 p p / / / p p p 0 C 1 a n C m n a x (1 x) 1 a n C m C 1 x a n C m 1 n a m 0.011 S I S C 1 70 I
Application of the BET equation p / p (1 p / p) Graph = f(p/p 0 ) n a 0.05 < P/P 0 < 0.30 : find a linear variation In this linear part, the slope and the intercept allow to calculate n a m and C With n a m Specific surface area. C~exp {(E 1 -E L )/RT)} energetic parameter which gives information to the interaction between the adsorbate and the adsorbent 1 point method : when C is large n a m=n a (1-p/p )
Checking results obtained using the BET method example : alumina NPL / N 2 / 77 K 0.016 a n m 0.011 0.014 0.012 a n m C 70 n a / mmol g -1 0.01 0.008 0.006 1 ( p / p) a n m C 1 0.107 0.004 0.002 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 p / p 0
Hypothesis of the measurement of specific surface area a n m m = quantity of substance required to cover the surface with a monomolecular layer For N 2 at 77,35 K m = 0,162 nm 2 a 2 m g where m = area occupied by a single molecule in the monolayer a v m a 2 m g 1 n mol a m g 1 mol A 1 Is the volume of adsorbed gas (STP) necessary to cover the surface of one gram of adsorbent with a monolayer N 1 m m 2 0,097 n mol g a m 1 4,35 3 cm g a m 1 v
Cross sectional area of adsorbate molecules m Hypotheses * adsorbed molecules treated as spheres of radius r occupying an area m on the surface of a solid completely covered by a monolayer * monolayer supposed to be - compact (hexagonal compact arrangement ) - liquid (density l at the temperature of adsorption) Calculations 1,091 m M l N A N A Avogadro constant M Molar mass of substance adsorbed Examples : N 2 à 77,35 K m = 0,162 nm 2 H 2 O à 300 K m = 0,105 nm 2 2/3
Assessement of specific surface area by gas adsorption General idea : Determination of n a m Estimation of the amount of adsorbate required to cover the unit mass of solid surface with a complete monomolecular layer. The specific surface area of the adsorbent is : a BET = n a m.n A. m /m with m the adsorbent mass, N A the Avogadro constant and m area occupied by one molecule
Calculating the specific surface area using BET example : alumina NPL / N 2 / 77 K n a / mmol g -1 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 a BET a BET 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 p / p 0 n a m N A 0.01110 2 a BET 1.07 m g a a BET nm 100 3 1 a n m 0.011 C 70 N 2 6.0210 23 0.16210 18
t & a s - methods
Kiselev 1957 t or a S method: background search for the standard isotherm - non-porous = n/a BET n/n m Lippens-de Boer 1965 thickness of the layer, t t = (n/n m )d' d' = M / ( L liq ) = 0.354 t = 0.354 n/n m Sing 1968 n m implies A BET chemical effects of the surface, at low coverage, are not taken into account reference sample of same chemical nature replace n m by n 0.4 (n at p/p 0 = 0.4) a s n n 0.4
"t" method (de Boer) [1] Non-porous solids multimolecular adsorption t (thickness of the adsorbed layer) increases with p/p according to a universal t curve" [= 0,354 n a /n m = f(p/p )] the layer covering the surface (supposed liquid) A occupies a volume V l : V l = A. t
t / nm Fitting the t curve 2.5 2 de Boer de Boer Halsey Harkins-Jura Harkins-Jura Data from «de Boer» Physical and Chemical Aspects of Adsorbents and Catalysts Ed B. G. Linsen, Acad. Press, London (1970) p.33. 1.5 1 Harkins et Jura 0.1399 t 0.034 log( p / p) 1/ 2 0.5 0 0 0.2 0.4 0.6 0.8 1 Halsey 5 t 0.354 ln( p / p) 1/3 p / p
Construction of the t-plot n a /m s Unknown Isotherm n a /m s t t p/p t curve
Isotherms and corresponding t plots p / p 0 a Type II b c Type I B B Type IV n / m s Capillary condensation Micropore filling Non porous adsorbent t
"t " Method (de Boer) [2] Solid under investigation adsorption isotherm which can be transformed using the universal t curve transformed t curve" with co-ordinates : n a /m s, t if there is a linear region, one can calculate a (t ) from the slope s t : for N 2 adsorbed at 77.35 K (v l = 34.61 cm 3 mol -1 ) a (t) = 34.6 x ( s t / mmol g -1 nm -1 ) s t = (n a / m s ) / t where m s = sample mass
Treatment of the isotherm using the t method example : alumina NPL / N 2 / 77 K 0.025 0.08 0.16 0.025 0.07 0.14 0.02 0.02 0.06 0.12 y = 0.0203x + 0.0046 n a / mmol.g -1 n a / mmol.g g -1 0.05 0.1 0.015 0.015 0.04 0.08 0.01 0.01 0.03 0.06 0.02 0.04 0.005 0.005 0.01 0.02 a (t) = 34.6 x ( s t / mmol g -1 nm -1 ) a (t) = 34.6 x 0.0203 m 2 g -1 a (t) = 0.70 m 2 g -1 0 00 0 00 0.2 0.2 0.5 0.2 0.4 0.4 0.4 1 0.6 0.6 1.5 0.6 0.8 0.8 2 1 2.5 1 t / p t nm / p nm 0
Comparison of specific surface areas obtained : alumina NPL / N 2 / 77 K 0.08 0.07 0.06 0.05 a BET = 1.07 m 2.g -1 n a / mmol g -1 0.04 0.03 a t = 0.7 m 2.g -1 0.02 0.01 0 0 0.2 0.4 0.6 0.8 1 p / p 0
Microporous Materials very special isotherms
Adsorption on a purely microporous sample : d 0.4 à 2 nm d( pore) 1 à 5 d( gas) n / m s Micropore filling ultramicropores supermicropores co-operative mechanism p / p 0
(/ k) / K Potential energy in a slit-shaped pore 200 100 0-100 w = 14 w = 8 w = 4 w = 3 w = 2.5 w = 2 r gas -200-300 -400-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 z / nm 9 ( z) 4 gs z z 1 nm / k 124 K 3
Adsorption isotherms with microporous samples : use of semi-log plots 12 3 6 10 2.5 5 2 n / mmol.g -1 n / mmol.g -1 0 0 12 0.2 0.4 0.6 0.8 1 0 0 3 0.2 0.4 0.6 0.8 1 0 0 6 0.2 0.4 0.6 0.8 1 10 2.5 5 8 2 4 n / mmol.g -1 6 n / mmol.g -1 1.5 n / mmol.g -1 n / mmol.g -1 8 4 6 1.5 3 4 1 2 2 DAY / N 2 / 77K 0.5 AlPO 4-11 / N 2 / 77K 1 VPI-5 / Ar / 87K p / p p / p p / p 3 4 1 2 2 0.5 1 0 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 p / p 0 1E-07 1E-06 0.00001 0.0001 0.001 0.01 0.1 1 p / p 0 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 p / p
Microporous Materials what about using the BET method to characterise the surface area?
Effective molecular area adsorbed in micropores Slits Cylinders = 1 = 4 = 2 Ultramicropores a BET under estimated
The concept of Equivalent BET Surface Area In the case of microporous samples, the BET equation can still be applied (for very low equilibrium relative pressures) Here, one talks of an equivalent BET surface area obtained on supposing that the quantity n m (determined via the BET law) is adsorbed in a single monomolecular layer
Nitrogen adsorption at 77 K on a microporous alumina 3 2.5 n a / mmol.g -1 2 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 p / p 0
x / n a (1-x) BET treatment in the case of a microporous solid : microporous alumina / N 2 / 77K n a / mmol.g -1 0.07 0.2 3 0.18 0.06 0.16 2.5 0.14 0.05 2 0.12 0.04 1.5 0.1 0.03 0.08 1 0.06 0.02 0.04 0.5 0.01 0.02 y = 0.476x + 0.0005 n a m 0 0 0.05 0.2 0.10.05 0.4 0.15 0.2 0.6 0.1 0.25 0.8 0.3 0.35 0.15 1 p / / p 0 1 2.10 S I S C 1 953 I a BET a BET a nm N 2.110 A 3 a BET N 2 6.0210 23 205 m 2 0.16210 g 1 18
The concept of Equivalent BET Surface Area In the case of microporous samples, the BET equation can still be applied (for very low equilibrium relative pressures) Here, one talks of an equivalent BET surface area obtained on supposing that the quantity n m (determined via the BET law) is adsorbed in a single monomolecular layer
Characterisation of solids by adsorption Microporosity Methods available : t -plot total pore volume HK method pore size DFT pore size a s -plot surface area and pore volume MP method pore size Dubinin methods???
t & a s methods (cont)
Isotherms and corresponding t plots p / p 0 a Type II b c Type I B B Type IV n / m s Capillary condensation Micropore filling Non porous adsorbent t
Nitrogen adsorption at 77 K on a microporous alumina 3 2.5 n a / mmol.g -1 2 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 p / p 0
n a / mmol.g -1 3.0 2.5 2.0 1.5 1.0 0.5 t and a S calculation : N 2 / 77K / microporous alumina t method 0.0 0.0 0 0.5 0.5 1 1.5 1.5 2 t / nm a S y = 4.3472x R 2 = 0.973 a S calculation with ref. Alumina NPL a a n x BET a 0.4 aa S a BET a n ( ref ( ref BET a 0.4 ) ( ref ) slope ref ( ) ) 1.07m 2. g 1 0.016mmol. g 290 m 2. 205 m g 2. 1 g 1 1 Ultramicropores a BET underestimated
Summary : t / a S methods for the characterisation of microporous solids Need a good expression of the t curve HJ, FHH.. The 't' method does not work for t < 1nm in the programs supplied commercially a S requires a good reference isotherm for each sample type It is then possible to extract ultra- and super- micropore volumes / surfaces Neither method gives any information on pore size distribution MP method HK DFT
HK method
Horwath-Kawazoe Method : background Horwath-Kawazoe - 1983 expression for slit shaped pores (carbons) N-C interactions at 77 K Saito-Foley - 1991 expression for cylindrical pores Ar-O (87 K) Cheng-Yang - 1994 expression for spherical pores correction for isotherm non-linearity
Horwath-Kawazoe method : calculations Pore filling pressure gas-solid interaction Set-up for slit shaped carbon micropores C C C C C C C C C C C C C C H ( z) ( z) ( H z) pore g s gs Interaction of a molecule with the each wall of a slit shaped pore Gas-solid Interactions first plane Gas-solid Interactions second plane
Horvath-Kawazoe Method(HK) Assumptions Pores of width = H Pressure of micropore filling related to the energy of adsorbate-adsorbent interaction Calculations : N 2,77 K / Carbon molecular sieve 3-7 61,23 1,895 10 2,709 10 ln( p / p) 3 9 ( H 0,64) ( H 0,32) ( H 0,32) 0,05014
Horwath-Kawazoe and Saito-Foley : H-K formulas! 10-4 potential function to describe the interactions : ( z) pore k z 10 4 z H z 10 H z 4 S-F 3 p 62.38 1.89510 2.708710 ln 0 0.64 0.323 0.329 p H H H 7 0.05014 ln 3 7 p 28.57 1.58410 1.72910 4.79310 0 3 9 p H 0.612 H 0.306 H 0.306 2
Horwath-Kawazoe (S-F) Method 1.6 «DAY» Diff. pore vol. / cm 3.g -1.nm -1 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 1.2 1.4 1.6 1.8 2 diameter / nm
Differential Pore Volume / cm 3.g -1 Horwath-Kawazoe (S-F) method 0.03 obtained with AlPO 4-11 0.025 0.02 0.015 can be mislead by an unusual two step pore filling process 0.39 0,39 x 0.63nm 0,63 0.01 0.005 0 0 0.5 1 1.5 2 Pore width / nm
Horwath-Kawazoe method : summary Require good points at very low pressure < 10-5 p/p 0 equilibrium pressure gauge stability!!!! H-K aimed for carbons and nitrogen at 77K Saito-Foley aimed at zeolite cylinders and argon at 87K Attention first peak : artefact in calculation
DFT
Type I isotherm : DFT
n a / mmol.g -1 1. Construction of reference isotherms DFT 2.5 2. Reconstruction of the experimental isotherm using the reference isotherms 2 1.5 1 0.5 0 0.000001 0.00001 0.0001 0.001 0.01 0.1 p / p 0
DFT results obtained with carbon fibre s 0.035 Pore Volume / cm 3 g -1 0.03 0.025 A B 0.02 0.015 0.01 0.005 0 0.1 1 10 100 Pore Width / nm
Overall Summary for Microporous Solids Microporous samples usually give rise to Type I isotherms An estimation of the specific surface area of microporous samples can be done using the following approaches : BET method equivalent surface area t method external surface area not adapted for the total surface area Pore size distribution of micropores Horwath-Kawazoe DFT
Exploitation of the adsorption isotherm n /m s Capillary Condensation Kelvin equation (BJH) Broekhoff de Boer DFT Localised Adsorption Adsorption Energies Micropore filling HK DFT. Monte Carlo Monolayer formation BET Multimolecular Adsorption t-plot a S method p/p
Physisorption Isotherms n s m T 1 T 2 > T 1 Adsorption is an exothermic phenomena ads Isosteric Enthalpies T T h 1. 2 R.. ln T T 2 1 p p 2 1 n / m s p 1 p 2 p
p / Torr Calorimetry @ 77K 10 9 8 Hydrogen / MIL91 @ 77K 900 800 700 Calorimetry @ LT - T : 77K (87K) - P max : 1bar - ads h / kj mol -1. 7 6 5 4 3 2 1 600 500 400 300 200 100 - QS : 200-300mg 0 0 1 2 3 4 5 n a / mmol g -1 0
Adsorption coupled with XRPD Synchrotron radiation 0.5 mm Photo : Y. Filinchuk, C. Serre, Th. Devic, SNBL-ESRF 2007
AlPO 4-11 / N 2 / 77K 3 3 2.5 2.5 2 2 n / mmol.g -1 1.5 n / mmol.g -1 1.5 1 1 0.5 0.5 0 0 0.2 0.4 0.6 0.8 1 p / p 0 1E-07 1E-06 0.00001 0.0001 0.001 0.01 0.1 1 p / p
Adsorption Microcalorimetry Methane on AlPO 4-11 24 22 A 1 - ads h / kj.mol -1 20 18 B 0.8. 16 14 12 10 8 vap H CH 4 0.6 0.4 0.2 p / p 0 Neutron diffraction : methane translational mobility increases!! A : D t =0.5 10-6 cm 2 s -1 B : D t =2.0 10-6 cm 2 s -1 6 0 0.5 1 1.5 2 2.5 3 0 n a / mmol.g -1
Adsorptio-desorption isotherm : microporous model Silicalite-1 / N 2 at 77K 40 35 hysteresis cracks 30 25 n a / mol.uc -1 20 15 10 5 Sub-step at low p/p 0!! 0 0 0.2 0.4 0.6 0.8 1 p / p 0
Adsorption Microcalorimetry Methane at 77 K / Silicalite 0.53 x 0.56 nm 20 0.025 0.665 18 16 5 0.02 a b c 0.45 0.51 x 0.55 nm Energetically homogeneous 6 micropore structure - ads h / kj.mol -1. 14 12 10 8. n a / mmol.g -1. 4 3 2 1 0 vap H CH4. 0 0.005 0.01 0.015 0.02 0.025 p / p 0 0 1 2 3 4 5 n a / mmol.g -1 0.015 0.01 0.005 0 p / p 0
17 15 Adsorption Microcalorimetry Argon at 77 K / Silicalite 0.002 0.0016 Neutron scattering - ads h / kj.mol -1 13 5.4 mmol.g -1. 11 9 0.0012 0.0008 p / p 0 3.9 mmol.g -1 2.3 mmol.g -1 7 vap H Ar 0.0004 0 mmol.g -1 5 0 1 2 3 4 5 6 n a / mmol.g -1-1 0 0.5 1 1.5 2 2.5 Q / Å -1 disordered fluid ordered solid
- ads h / kj.mol -1 17 15 Adsorption Microcalorimetry Nitrogen at 77 K / Silicalite 13 0.12. 11 a 0.2 0.16 p / p 0 Neutron scattering 5.4 mmol.g -1 4.1 mmol.g -1 9 0.08 2.5 mmol.g -1 7 vap H N2 0.04 0 mmol.g -1 5 0 1 2 3 4 5 6 n a n a / / mmol.g mol.uc -1-1 0 0.5 1 1.5 2 2.5 Q / Å -1 disordered fluid a ordered fluid ordered solid
Exploitation of the adsorption isotherm n /m s Capillary Condensation Kelvin equation (BJH) Broekhoff de Boer DFT Localised Adsorption Adsorption Energies Micropore filling HK DFT. Monte Carlo Monolayer formation BET Multimolecular Adsorption t-plot a S method p/p
Differences in properties of adsorptive molecules Adsorptive CH 4 Ar Kr O 2 N 2 CO Molecular dimensions / nm 0.42 0.38 0.40 0.39 x 0.28 0.41 x 0.30 0.37 x 0.42 Kinetic diameter / nm 0.38 0.34 0.36 0.35 0.36 0.39 Cross-sectional area / nm 2 0.158 0.138 0.195 0.141 0.162 0.168 Polarizability a 10-3 nm 3 2.60 1.63 2.48 1.59 1.76 1.95 Dipole moment m / 10-30 Cm 0.39 Quadrupole moment Q / 10-40 Cm 2-1.3-5.0-12.3 Enthalpy of Liq. vap H / kj.mol -1 8.18 6.49 10.50 6.92 5.57 6.03 Liquid density at 77 K l / g.cm -3 0.424 1.394 2.415 1.141 0.809 0.789 Solid density at 77 K s / g.cm -3 0.489 1.623 2.826 1.300 0.945 0.924
25 Nitrogen isotherms taken at different points during the calcination of MCM-41 760 C Amount Adsorbed / mmol g -1 20 15 1000 C 300 C Problems? Adsorbate retained inside organic chains 10 5 150 C 100 C 0 0 0,2 0,4 0,6 0,8 1 p / p 0
Getting more points during the vertical regions of the isotherm (for ASAP) I ve added this after our discussions on Friday! To add more points on adsorption at low pressure Analysis Conditions Low Pressure Incremental dose mode Dose amount cm3/g Min (0.3 to 1) hours Max 4 hours To add more points later on adsorption / desorption (eg more MCM type mat Analysis Conditions Maximum volume increment cm3/g
Krypton vs. Nitrogen vs. Argon Krypton is often recommended for the estimation of very low surface areas Why? : The p = 1.8 mmhg : thus error on the estimation of the amount not adsorbed in the sample cell is very low w.r.t. nitrogenpv n But! : Krypton does not wet solids well: thus varies (1.8 to 2.1 RT nm 2 ) Nitrogen is the standard asdorptive for experiments at 77K Why? : Cover the real p/p range up to liquid saturation, good wetting But! : can vary w.r.t. surface chemistry, std 0.162 nm 2 can be 0.13 nm 2 Argon can be a compromise Why? : Good wetting for a non-polar adsorptive, does not seem to vary (0.138 nm 2 ),
Schematics of the Solid Argon Effect 16 n / mmol.g -1 14 12 10 8 6 Nitrogen adsorption Argon adsorption at 77 K if Nitrogen argon remained adsorption liquid Argon adsorption at 77 K p The of NAr argon p 2 liquid solid of adsorption Ar at liquid 77 K at is 77 thus K at (207 truncated 77 K Torr) (223 at Torr) 77 K due to solidification 4 2 0 0 0.2 0.4 0.6 0.8 1 1.2 p / p
Argon can show hysteresis at 77 K when 12 12 Nitrogen does not 11.5 10 11 Argon Closure point : p/p = 0.2 n / mmol.g -1 8 10.5 610 9.5 4 9 Nitrogen Closure point : p/p = 0.4 2 8.5 0 8 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 1 p / / p p Pore diameter of 3.8 nm corresponds to a nitrogen desorption at p/p =0.42 -> catastrophic desorption
To what branch do we apply mesopore size calculations DFT suggests that for pores larger than 6nm both the experimental adsorption and desorption branches follow the theoretical spinoidal condensation and equilibrium evaporation phenomena. For pores smaller than 4 nm, the experimental adsorption and desorption branches follow the same path (no hysteresis). Theory suggests that this occurs at equilibrium evaporation pressures. Intermediate pores (4-6 nm), the desorption is fine (experiment and theoretical equilibrium coincide), the experimental adsorption branch is not able to be described. Theory would suggest that the closing point for hysteresis occurs at lower pressures than those observed experimentally
Adsorption in a nanoporous material
Adsorption coupled with XRPD Synchrotron radiation Christian, Thomas & Patricia @ ESRF 0.5 mm Photo : Y. Filinchuk, C. Serre, Th. Devic, SNBL-ESRF 2007
Desorption Adsorption MIL53 Fe / CO 2 P CO 2 P CO 2 80 10 mbar 1.5 0.4 bar P CO 2 8.8 1.7 bar P CO 2 3.7 8.8 bar P CO 2 0.6 2.1 bar P CO 2 50 400 mbar Vacuum
Pression / bar Understanding the sorption phenomena through collaborative research e.g. CO 2 / MIL53(Cr) 12 G. Férey et al., Inst. Lavoisier, Versailles SNBL, ESRF Grenoble 10 CO 2 CH 4 n a / mmol g -1 8 6 4 2 0 CO 0 10 20 30 40 50 Pression / bar N 2 He Rotation du cycle benzène [200] [110] 1 b Desorption 16 b Adsorption 1 b 1 2 3 4 5 6 7 8 10 16 14 12 10 8 7 6 5 4 3 2 1 0 Se c 50 30 «Rotules» 662 653 (2 bars) P (bar) 1 -adsh / kj mol -1. 40 30 20 10 0 0 2 4 6 8 10 n a / mmol g -1 25 20 15 10 5 0 G. Maurin, Inst. Gerhardt Montpellier 659 0,4 (10 bars) 662 653 (4 bars) 670 650 (cm -1 ) 2,5 10 6 1 O H O Cr Cr A. Vimont, LCS Caen C O 1. S. Bourrelly, P. L. Llewellyn, C. Serre, F. Millange, T. Loiseau, G. Férey, Different Adsorption Behaviors of Methane and Carbon Dioxide in the Isotypic Nanoporous Laboratoire Metal Terephthalates Chimie MIL-53 Provence and MIL-47, J.Amer.Chem.Soc. 127(39), 2005, 13519-13521. 2. C. Serre, S. Bourrelly, A. Vimont, N. A. Ramsahye, G. Maurin, P. Llewellyn, M. Daturi, Y. Filinchuk, O. Leynaud, P. Barnes & G. Férey, An explanation for the very large breathing effect of a metal-organic framework during CO2 adsorption, Advanced Materials, 2007.
What do we define as an Interface? An interface is the separation between two volumic phases. Although one often uses either the terms surface or interface, the word interface is often used when one considers two condensed phases which are often explicitly named. E.g.: solid/liquid interface; solid/gas interface. The term "surface" is used to describe the solids interface whether it be in contact with another phase (gas or liquid) or not (under vacuum).
Several definitions concerning powders Agglomerate : rigid assembly of particles Aggregate : lose assembly of particles External surface area : that excluding the pores, but including any surface roughness Internal surface area : in the pore volume Specific surface area : surface area per gram of solid Roughness : resulting from cavities that are more large than deep
Texture : geometric arrangement of particles and pores in a grain Geometric surface (with respect to 1g of material) External Surface : includes all irregularities (more large than deep) Internal Surface : includes all the accessible pores (to a given probe molecule) Porosity Pore size distribution : surface p (or pore volume ) distribution of the as a function of the pore width. Definitions used for Powders and Porous Materials V V p V s a 2 m g 1 ( / 6 g cm 3 )( d / m) V p = pore volume (accessible?) V s = volume occupied by the non porous bulk material
Geometrical Surface Area of the interface which can be calculated directly from the particle geometry This area is related to a gram of solid supposed to be non-porous and is noted a For spherical particles of diameter d and density : a = 6 / d a in m 2 g -1, in cm 3 g -1, d in µm
Definitions Internal surface area: area of pore walls External surface area: area of surface outside pores Total surface area = Internal surface area + External surface area The properties of a porous solid depend on the pore geometry, the pore size and the pore size distribution Micropore: pore of internal *width less than 2 nm Mesopore: pore of internal width between 2 and 50 nm Macropore: pore of internal width greater than 50 nm * Pore width = pore size: the available distance between the two opposite walls
Porosity is usually defined as the ratio of the volumes of voids and pores (open and closed) to the volume occupied by the solid : porosity V p : volume of voids and pores V S : V total - V p V p V p V s Pore size distribution: the pore distribution according to their width
More definitions for Porous Materials Pore : open or closed cavity ; in the latter case, more deep than wide Pore Width : more general than diameter Micropores : pore width below 2 nm d( pore) d( gas) Mesopores : pore width between 2 and 50 nm 1 to 5 Macropores : pore width above 50 nm d( pore) d( gas) (also : "nanoporous materials", pore width up to 10 nm) 5 to 125
c How can we calculate the quantity adsorbed? (a) Interfacial layer Surface : A Solid : v s Quantity adsorbed : v a Residual gas : v g quantity adsorbed n a n a A. 0 c dz 0 t z
How can we calculate the quantity adsorbed? (b) Representation of GIBBS Gibbs dividing surface GDS : A c dn dv c g c g.v a Solid : v s Excess quantity adsorbed : n Total volume : v g,0 z Surface excess concentration n A Excess quantity adsorbed n n g n n i n a = n s + c g.v a T : n a n g f
Argon adsorption in the nanopores of VPI-5 (d : 1.2 nm)
So schematically how can we think of adsorption? Fluid (gas, liquid) or Adsorptive Adsorbed phase or Adsorbate Solid or Adsorbent