Surface Area

Surface AreaSur (French “above”)

Face (French “face”)

Area (Latin “open empty space”)

Surface Area – what is it?Surface Area – what is it?“Surface Area is the means through which a

solid interacts with its surroundings, especially liquids and gases.”

Surface area is created by division of particles (size reduction) and the generation of porosity.

Surface area is destroyed by sintering (exceeding Tg), melting and Ostwald ripening.

How to Create Area

• Size Reduction– Grinding, – milling, – nanoscale preparation

• Make pores– Partial decomposition– Leach– Gel then lyophilize

How to destroy area

• Surface area is destroyed by

– melting – sintering (exceeding Tg), and – Ostwald ripening

Surface Area – Importance?Surface Area – Importance?Remember that surface area is the means through which a solid interacts with its surroundings.

Consider the following three interactions:

Solid-Solid: autohesiveness (cohesiveness) eg flow, compactibility etc.

Solid-Liquid: wetting, non-wetting, adsorption capacity etc.

Solid gas: adsorption, catalysis, etc.

Dynamic a

ngle of re

pose

Dynamic a

ngle of re

pose

Static angle of reposeStatic angle of repose

Solid-Solid Interaction

What happens next?

Liquid-solid interaction

Wicking: adhesive forces exceed cohesive forces… liquid wax is drawn up through fibers of wick to the exterior where it evaporates, mixes with air and burns upon ignition from the hot gases above.

Gas-Solid interaction

Measuring Accessible

Area

Suitable methods of determination

• Gas adsorption allows probing of entire surface including irregularities and pore interiors.

• The amount adsorbed is a function of temperature, pressure and the strength of attraction or interaction potential.

• Physisorption is generally weak and reversible. The solid must be cooled and a method used to estimate the monolayer coverage from which surface area can be calculated.

The gas sorption process - intermolecular forces

Lennard-Jones potential function

The gas sorption process

• Langmuir[i] described the kinetic behavior of the adsorption process. He postulated that at equilibrium, the rate of arrival of adsorptive (adsorption) and the rate of evaporation of adsorbate (desorption) were equal. Furthermore, the heat of adsorption was taken to be constant and unchanging with the degree of coverage, θ.

[i] I. Langmuir, J. Amer. Chem. Soc., 40, 1368 (1918)

Irving Langmuir (1881-1957)

Graduated as a metallurgical engineer from the School of Mines at Columbia University in 1903

1903-1906 M.A. and Ph.D. in 1906 from Göttingen.

1906-1909 Instructor in Chemistry at Stevens Institute of Technology, Hoboken, New Jersey.

1909 –1950 General Electric Company at Schenectady where he eventually became Associate Director

1913 -Invented the gas filled, coiled tungsten filament incandescent lamp.

1919 to 1921, his interest turned to an examination of atomic theory, and he published his "concentric theory of atomic structure" . In it he proposed that all atoms try to complete an outer electron shell of eight electrons

http://public.lanl.gov/alp/plasma/history.html

1927 Coined the use of the term "plasma" for an ionized gas.

1935-1937 With Katherine Blodgett studied thin films.

1948-1953 With Vincent Schaefer discovered that the introduction of dry ice and iodide into a sufficiently moist cloud of low temperature could induce precipitation.

1932 The Nobel Prize in Chemistry "for his discoveries and investigations in surface chemistry"

Confining adsorption to a monolayer, the Langmuir equation can be written

 

 

where V is the volume of gas adsorbed at pressure P, Vm is the monolayer capacity (i.e. θ=1) expressed as

the volume of gas at STP and K is a constant for any given gas-solid pair. Rearranging in the form of a straight line (y=ab+x) gives

 

KPKP

VV

m

1

mm V

P

KVV

P

1

Langmuirian behavior

Adsorption Process

Adsorbent

AdsorbateAdsorptive

The Isotherm

• The amount of gas adsorbed is a function of – The strength of interaction between gas and

solid (intrinsic)– Temperature (fixed)– Pressure (controlled variable)

Physisorption Process

4)

2

Very Low pressure behavior (micropore filling)

Low pressure behavior (monolayer)

The “knee”

Medium pressure behavior (multilayer)

High pressure behavior (capillary condensation)

Choice of gas and temperature

• Gases– Nitrogen– Argon– Krypton– Carbon dioxide– Others

• Temperatures– Liquid Nitrogen– Liquid Argon– Dry ice/acetone– Water/ice– Others

Apparatus

Measurement Method

Classical vacuum, volumetric.

Requires that adsorbate be adsorbed by the sample, at some reduced temperature, as a function of pressure of pure adsorptive.

Vacuum-Volumetric

• P/Po values are achieved by creating conditions of partial vacuum.

• High precision and accurate pressure transducers monitor pressure changes due to the adsorption process.

Vacuum-VolumetricPo, p0, psat

Po value can be

• measured in a dedicated cell– with or – without dedicated transducer

• calculated from atmospheric pressure

• input manually (eg Kr 2.63mmHg at 77.4K)

• measured in cell over sample

Vacuum-Volumetric

Working Equation

PV = nRT

nads = ndosed - nvoid

nads = (PV/RT)man. - (PV/RT)cell

Sample Preparation

Sample preparationThe adsorbate has to “see” the real surface.

• Whilst a little pre-adsorbed moisture wouldn't affect the monolayer capacity, it would affect the strength with which it is adsorbed, so the monolayer would be formed at a different pressure than on a clean surface.

• Pores can be easily blocked by moisture. Water undergoes capillary condensation at humidities well below bulk saturation in the confines of the pore (just as nitrogen does as we will see later).

• Micropores can be completely filled, not just blocked!

• We always quote surface area per unit of dry mass.

Outgassing of SurfaceOutgassing of Surface

Sample is cleaned of adsorbed contaminants, mainly moisture, by the application of vacuum or flow of dry inert gas and preferably some heat.

How much heat?

Outgassing of SurfaceOutgassing of Surface

How much heat?

What is the proper temperature for sample preparation?

•Should be high enough to promote rapid removal of surface adsorbed species without changing the surface texture.

•Obviously not high enough to melt the solid, nor hot enough to exceed the glass transition point, Tg. Estimate Tg as melting pt 0.7 in kelvin (allow safety margin).

•Or no more than melting point 0.5 (kelvin) – Tammann temperature.

•Example:Magnesium Stearate monograph: 40 °C (for 2 hours)

Vacuum or flow

• A flow is good at removing large quantities of weakly bonded “wet” water by displacement of the vapor from external surfaces. However in the depths of a pore, water must diffuse out… and in doing so must battle past a much higher concentration of purge gas. Only when it is out of the pore will it be physically swept away.

Vacuum or flow• Vacuum is not so good at removing large

quantities of weakly bonded “wet” water since once it has left the sample it must diffuse towards the pump. (A “random walk” will make the actual distance needed to travel MUCH further than it looks to us! It will spend

much of its time wandering back towards the sample!). However in the depths of a pore, water must diffuse out… and in doing so does not have to battle past much - certainly not any purge gas.

TrapsTraps are used on vacuum outgassing systems to prevent:

• Oil backstreaming from pump (use foreline trap of activated alumina or cold trap)

(Or use a dry pump system!)

• Evolved species off the sample from migrating to the pump and – reducing pump efficiency,– effectively “pausing” the outgassing at the vapor pressure of

the evolved contaminants.

• Method

• Temperature

• Time

• Test

• Backfill

Sample Preparation

Degassing Parameters

Is it ready?Test (vacuum)

• A sample still outgassing will cause a pressure rise when isolated from the vacuum system

• Hot samples outgas faster than cool ones.

• Generally less than 50 microns/min hot, 20 microns/min cool will indicate readiness.

• (background rise of empty degas station?)

Is it ready?Backfill (vacuum)

• Cell should be backfilled to ambient pressure to allow easy removal and to prevent ingress of atmosphere.

• Avoid inconsistent use of helium as backfill gas – buoyancy errors.

• He buoyancy error approx 1 mg/ml of cell volume.

• Backfilled cells cool much faster.

• An evacuated cell barely warm to the touch can be hot enough to cause burns when backfilled.

Elutriation

Elutriation: The process of separating the lighter particles of a powder from the heavier ones by means of an upward directed stream of fluid (gas or liquid).

IUPAC Compendium of Chemical Terminology 2nd Edition (1997)

Elutriation

Its how a vacuum cleaner works!

Remember, a vacuum doesn’t suck!

Filters, pro’s and cons

The ability of a filter to trap particles depends on its fineness and its tortuosity.

It serves to both sieve out particles and to slow the rate of evacuation, hence to reduce gas flow velocity.

The obstruction to flow can limit effective vacuum.

Filters can become blocked!

Filters, pro’s and cons (continued…)

• What effect might a contaminated filter have on resultant data?

• Isotherms might appear “open”.

• Isotherms may be “shifted” slightly.

• Surface area values might be lower than expected.

Sample Cells

Analysis Hardware

Sample cells

“What are the characteristics of a sample cell?”

• Overall length.

• Volume of “bulb”.

• Diameter of stem.

“How do I select the right one?”

Sample cells• Overall length.

– Sample must be completely immersed under coolant, as should shoulder part of bulb. Cells are long to allow for the evaporation of cryogenic coolant. A coolant which does not evaporate can be used with a “short” cell.

• Volume of “bulb”.– Should be large enough to accommodate sufficient sample for

reasonable accuracy (e.g. at least 1 m2) but never more than 2/3 full. Small sample quantities should be accommodated in small bulbs (see void volume control).

• Diameter of stem.– Large enough to easily accommodate particle size, but small enough to

improve overall sensitivity.

“How do I select the right one?”

Void volume control“What is void volume and why bother?”

• Quantity of gas adsorbed is determined by (i) waiting for minimal/zero pressure change and (ii) subtracting quantity of gas in internal volume of equilibration “zone” from total quantity “dosed” into cell.

• The total volume in which the final equilibrium pressure is monitored is the void volume.

Void volume control“Therefore it should be minimized”

“How?”

• Close off the manifold after the dose.

• Use a small manifold if the valve must stay open.

• Use a sample cell with small internal volume.

• Cool as little of the cell as is absolutely necessary.

• Work at low pressure.

Void volume control“Close off the manifold after the dose”

• A pressure transducer on the analysis station monitors pressure drop due to adsorption (rise due to desorption) in the station volume only.

• For a given quantity of gas being adsorbed, a smaller volume gives rise to a larger (and more easily and accurately measured) pressure change.

n = PV/RTi.e. greater sensitivity

This is the standard configuration for all Autosorb gas sorption analyzers.

Void volume control“Use a small manifold if the valve must stay open”

• Large manifold volumes can deliver large quantities of gas, but are less sensitive.

• Small manifolds can more easily deliver small quantities of gas (for accurately targeting and approaching data point pressures).

The standard configuration for Autosorbs and NOVAs is 18-20 mL, 40mL for a Hydrosorb.

Void volume control“Use a sample cell with small internal volume.”

• Choose narrowest stem reasonable for use with your sample.

• Use a filler rod.

• Use as small a bulb size as reasonably practicable. The bulb is usually at greatly depressed temperature, so volume per volume, the “cold zone”contains many more gas molecules than the “warm zone”.

See “coolant level”

Void volume control“Cool as little of the cell as is absolutely necessary”

• Immersion depth should be limited.

• Additional benefit in that hydrostatic pressure variation in Po is minimized.

Standard condition in Autosorb is to use thermistor coolant level control.

Void volume control“Work at low pressure”

• When adsorption amounts are small, the error associated with subtracting the quantity of gas in the void volume from the quantity dosed can be significant.

• The quantity of gas in the void volume is a function of pressure as well as volume, therefore void volume errors continuously diminish as the pressure decreases.

• So, use krypton gas. Po = 2.63 mmHg at 77.4K. (surface area still uses same P/Po range).

• For P/Po = 0.3, krypton measurement has approximately 1/30 the number of gas molecules in the void volume as for nitrogen analysis.

• Additional benefit: pressure measurements for krypton done using 1 and/or 10 torr full scale transducer (c.f. 100 torr range transducer for nitrogen BET).

Sample cells• Stems, outside diameter: 6mm (1/4”), 9mm,

12mm.

• Corresponding internal diameters: 4mm, 7mm, 10mm (1mm wall thickness).

• Bulbs: none (bulbless – sample space has same diameter as stem), small (jelly-bean shape or “spherical” according to stem diameter and instrument, large (1’/2.5cm) diameter sphere

Filler rods

• Should be long enough to fill most of stem.

• Should be clean!!

• Don’t try to make it exactly same size as I.d. of stem (glass will jam).

• Rods with caps should not close off gas ingress and egress to/from the cell.

How much sample ?

• For all gas sorption equipment – minimum amount in cell required !– > 0.5 m2 total area = minimum– Use 10X to be sure !

• Example : we have an approximately 5 m2/g sample• So, 2g X 5 m2/g = 10 m2 total = OK• 100mg (0.1g) => 0.5 m2 total = Borderline OK• 50mg (0.05g) = 0.25m2 total = TOO LITTLE !

• Upper limit –> volume of cell, time !

Sample Weight

• Recommended procedure :– Weigh Cell empty (9.0g)– Add sample – weight full (9.55g)– Difference = weight before outgassing = 0.55g– Outgass sample– Weigh cell (9.45g)– Difference = .45g (18.2% loss) = weight for

analysis.

• Caution – backfill with N2 to avoid bouyancy errors.

B.E.T.Calculation of Specific Surface Area

Principles of BET Surface Area Measurement and Calculation

Determine the monolayer capacity Vm from which the surface area of the solid can be computed.

Adsorbate most commonly used is nitrogen...

• Readily available in high purity

• Appropriate coolant, liquid nitrogen, also plentiful.

• Gas-solid interaction relatively strong.

• Widely accepted cross sectional area.

BET: Since when?

1938A

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??Quiz

Brunauer, Emmett & Teller

• Model of adsorption extended to multilayers. BET ‘C’ constant varies from solid to solid. Low values represent weak gas adsorption typical of low surface area solids, organics and metals in particular.

00

11

]1)[(

1

P

P

CV

C

CVPPV mm

Measurement

Obtain at least three data points in the relative pressure range

0.025 to 0.30

Plot 1/[VSTP(Po/P)-1] versus P/Po. It should yield a straight line… if the BET model holds true.

On all surfaces the BET model fails to accurately predict the multilayer adsorption behavior above P/Po = 0.5 (the onset of capillary condensation which fills pores with liquid adsorbate)

Calculation

Fit best straight line through BET data set using least squares regression to find:

CV

Csslope

m

1

CVi

m

1intercept

Calculation (continued)

isVm

1

v

mavmt M

ALVS

Solving for Vm

Total surface area, St, is calculated thus

Lav = 6.022 x 1023

Am = 0.162 nm2

Mv = 22 414 mL

nm2 to m2, x 10-18

Why L for Avogadro’s Number?

Loschmidt calculated the number, not Avogadro!

A

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Multi-Point BET Plot (Interpretation)

• Never use data points too low in relative pressure (P/Po).

• Never use data points too high in (P/Po).

Under-equilibrated Data

Under-equilibrated Data

Multi-Point BET Plot (Interpretation)

• Discard under-equilibrated points (at low P/Po)

• Never use less than three, preferably five data points.

• Set intercept to zero, i.e ignore ‘C’ (adsorption strength)

• Monolayer volume is inverse of slope.

• P/Po = 0.3 gives good general agreement with multi-point – the higher the C value, the better the agreement.

(note: monolayer is formed closer to P/Po = 0.2

Single-point BET Method

Approximate values of C

C = 2 to 50 metals, polymers, organics

C = 50 to 200 oxides, silicates

C = >200 activated carbons, zeolites

Flow

• Required P/Po is achieved by diluting nitrogen (adsorbate) with helium (non-adsorbing).

• The sample is cooled with liquid nitrogen, to cause adsorption.

• The adsorption (and subsequent desorption) process is monitored using a thermal conductivity detector.

Dynamic Flow

The signal is calibrated against a known volume of pure nitrogen injected into the gas stream.

• The method is extremely rapid and ideally suited to manufacturing processes using the single point method. • Very dilute concentration of krypton at liquid nitrogen temperature is used for extremely low surface areas.

Other Uses of the Single-point Method

To determine appropriate P/Po range for multi-point BET.

• Acquire minimum seven data points in the P/Po range 0.05 to 0.3.

• Discard objectively from the multipoint surface area calculation those higher P/P0 values that clearly do not lie on a straight BET

line…

• The upper limit of the linear BET range can usually be obtained by calculating the single-point BET area using each datum point in turn. Normally, the calculated single-point area will increase with increasing P/P0 up to some maximum, beyond which the

calculated value will decrease. That maximum indicates the upper limit for the multi-point range.

Limitations of BET Surface Area Method

• In certain cases, the calculated single–point value never goes through a maximum. Evidenced by a gradual decrease in slope in the BET plot.

•This may or may not be accompanied by a short linear region at lower relative pressures, If there is no truly linear region, then it can be said that the BET equation is invalid for that particular sample…

Enhanced Adsorption• Isotherms of such samples appear to have some type III

character at very low pressure, indicative of very weak adsorption, yet demonstrate enhanced adsorption within the normal BET region.

• This behavior can be attributed to a cooperative adsorption process.

• Has been described for slit-shaped pores of critical dimensions; water on carbon (hydrophobic surface) is a typical example.

Questioning BET data

• Caution !

• Clue – adsorbed amounts low. (OK if sample mass sufficient)

• Sample mass = 1.52 g (OK?)

• Resulting BET Plot – looks OK?

• r=0.998, surface area = 0.22m2/g

• Problem : 1.52g * 0.22m2/g = 0.33m2

• Solution => Use more sample to validate result.

Common Problem : Bulk Condensation at top of isotherm

P > P0 ! Bulk condensation.Note point spacing, nearly infinite slope !

Data OK, can be recalculated with P0 from point of pressure rise