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**BET Surface Area Analyzer Seminar and Practical Training Short Course**

October 18-19, 2006 Rice University, Houston TX Quantachrome I N S T R U M E N T S © Quantachrome Instruments

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Quantachrome Quantachrome...renowned innovator of ideas for today's particle technology needs. For more than 30 years, Quantachrome's scientists have revolutionized measurement techniques and designed instrumentation to enable the accurate, precise, and reliable characterization of powdered and porous materials. Products designed and manufactured to ISO9000. Quantachrome Instruments Corporate Headquarters, Boynton Beach, Florida

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**Martin Thomas PhD PhD; Birmingham University, U.K.**

Research Investigator, Cookson Group Principal Research Officer, ICI Katalco With Quantachrome since 1991 ASTM Committee Member (D32, D24, D11, C01) Co-Author “Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density” by S. Lowell, J.E Shields, M.A. Thomas & M. Thommes pub.Springer (2004)

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Autosorb-3B Measure surface area and pore size of up to 3 samples simultaneously . Autosorb-3B equipped with three built-in degas ports. Features BatchStart and MaxiDose operating methods. Autosorb®-3B

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**Surface Area & Gas Sorption**

Quantachrome I N S T R U M E N T S Surface Area & Gas Sorption © 2004 Quantachrome Instruments

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**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. 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 creation of porosity.

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**How to Create Area Size Reduction Make pores Grinding, milling,**

nanoscale preparation Make pores Partial decomposition Leach Gel then lyophilize

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**How to Destroy Area Surface area is destroyed by melting**

sintering (exceeding Tg), and Ostwald ripening

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**Surface Area – Importance?**

Remember that surface area is the means through which a solid interacts with its surroundings. Consider the following four interactions: Solid-Solid: adhesion Solid-Solid: autohesiveness (cohesiveness) eg flow, compactibility etc. Solid-Liquid: wetting, non-wetting, adsorption capacity etc. Solid-Gas: adsorption, catalysis, etc. 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 creation of porosity.

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**Adhesion Carbon black is used as a reinforcing agent in rubber.**

Different grades of carbon black are used in tire innerliners, carcasses, sidewalls and treads, as well as in industrial rubber products, like belts, hoses and gaskets. Race compound is formulated with specialized ultra-fine carbon black to yield higher grip. 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 creation of porosity.

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Autohesion

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**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.

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**Gas-Solid Interaction**

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**The gas sorption process**

Langmuir[1] 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. [1] I. Langmuir, J. Amer. Chem. Soc., 40, 1368 (1918)

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Irving Langmuir ( ) Graduated as a metallurgical engineer from the School of Mines at Columbia University in 1903 M.A. and Ph.D. in 1906 from Göttingen. 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

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**Irving Langmuir (1881-1957)… continued**

1927 Coined the use of the term "plasma" for an ionized gas. With Katherine Blodgett studied thin films. 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"

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Langmuirian behavior 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

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**Gas Sorption Isotherms**

Quantachrome I N S T R U M E N T S Gas Sorption Isotherms © 2004 –2006 Quantachrome Instruments

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**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.

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**The gas sorption process - intermolecular forces**

Lennard-Jones potential function

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Adsorption Process Adsorptive Adsorbate Adsorbent

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**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)… expressed as relative pressure P/Po

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**Saturation Pressure Po, 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

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**Physisorption Process**

4) 2

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**Very Low Pressure Behavior (micropore filling)**

Amount Adsorbed Relative Pressure, P/Po

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**Low Pressure Behavior (monolayer)**

The “knee” Amount Adsorbed Relative Pressure, P/Po

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**Medium Pressure Behavior (multilayer)**

Amount Adsorbed Relative Pressure, P/Po

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**High Pressure Behavior (capillary condensation)**

Amount Adsorbed Relative Pressure, P/Po

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**Types of Isotherms Volume adsorbed Type I or pseudo-“Langmuir”**

Relative Pressure (P/Po) Volume adsorbed Steep initial region due to very strong adsorption, for example in micropores. Limiting value (plateau) due to filled pores and essentially zero external area.

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**Types of Isotherms Type II Volume adsorbed Relative Pressure (P/Po)**

Rounded knee indicates approximate location of monolayer formation. Absence of hysteresis indicates adsorption on and desorption from a non-porous surface.. Low slope region in middle of isotherm indicates first few multilayers

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**Types of Isotherms Type III Volume adsorbed Relative Pressure (P/Po)**

Lack of knee represents extremely weak adsorbate-adsorbent interaction BET is not applicable Example: krypton on polymethylmethacrylate

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**Types of Isotherms Type IV Volume adsorbed Relative Pressure (P/Po)**

Rounded knee indicates approximate location of monolayer formation. Low slope region in middle of isotherm indicates first few multilayers Hysteresis indicates capillary condensation in meso and macropores. Closure at P/Po~0.4 indicates presence of small mesopores (hysteresis would stay open longer but for the tensile-strength-failure of the nitrogen meniscus.

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**Types of Isotherms Type V Volume adsorbed Relative Pressure (P/Po)**

Example: water on carbon black Type V Volume adsorbed Lack of knee represents extremely weak adsorbate-adsorbent interaction BET is not applicable Relative Pressure (P/Po)

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**Choice of Gas and Temperature**

Gases Nitrogen Argon Krypton Carbon dioxide Others Temperatures Liquid Nitrogen Liquid Argon Dry ice/acetone Water/ice Others

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**Choice of Gas and Temperature**

Gases Nitrogen Argon Krypton Carbon dioxide Others Temperatures Liquid Nitrogen Liquid Argon Dry ice/acetone Water/ice Others

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**Apparatus & Measurement**

Quantachrome I N S T R U M E N T S Apparatus & Measurement © 2004 Quantachrome Instruments

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**(Classical vacuum, volumetric.)**

Measurement Method Manometric (Classical vacuum, volumetric.) Requires that adsorbate be adsorbed by the sample, at some reduced temperature, as a function of pressure of pure adsorptive.

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Manometric 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.

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Manometric

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

Working Equation PV = nRT nads = ndosed - nvoid nads = (PV/RT)man. - (PV/RT)cell

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

Working Equation nads = (PV/RT)man. - (PV/RT)cell That is, the amount adsorbed is calculated as the difference between a) the amount of gas “dosed” from the manifold to the cell and b) the mount of gas which remains not adsorbed at the end of the “equilibration time”.

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**BET Calculation Quantachrome I N S T R U M E N T S**

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**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.

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**Brunauer, Emmett & Teller**

Model of adsorption extended to multilayers. S. Brunauer, P.H. Emmett and E. Teller, J. Amer. Chem. Soc., 60, 309 (1938)

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**Brunauer, Emmett & Teller**

Or, in its familiar linearized form… 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.

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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)

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**The Gas Adsorption Isotherm**

Amount adsorbed, X negative intercepts are unacceptable Relative pressure, P/Po

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**Calculation of Surface Area by the BET method.**

X[(Po/P)-1] 1 I/slope+intercept = Vm, the amount of gas covering the surface in a monloayer. The number of individual molecules is calculated (Vm/22414)*Lav and the area occupied is that number times the area of one moelcule, Acs. Multiply by to convert from sq.nm to sq.m. negative intercepts are unacceptable relative pressure, P/Po

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

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**Calculation (continued)**

Solving for Vm Total surface area, St, is calculated thus Lav = x 1023 Am = nm2 Mv = mL nm2 to m2, x 10-18

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**Calculation of Surface Area by the BET method.**

X[(Po/P)-1] 1 visual check for linearity negative intercepts are unacceptable relative pressure, P/Po

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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).

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**Multi-Point BET Plot (Interpretation)**

Discard under-equilibrated points (at low P/Po) Never use less than three, preferably five data points.

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**Calculation of Surface Area by the BET method.**

X[(Po/P)-1] 1 I/slope+intercept = Vm, the amount of gas covering the surface in a monloayer. The number of individual molecules is calculated (Vm/22414)*Lav and the area occupied is that number times the area of one moelcule, Acs. Multiply by to convert from sq.nm to sq.m. negative intercepts are unacceptable relative pressure, P/Po

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**Single-point BET Method**

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 Approximate values of C C = 2 to 50 metals, polymers, organics C = 50 to 200 oxides, silicates C = >200 activated carbons, zeolites

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**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.

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**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…

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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.

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**Standard Surface Area Method**

e.g. USP 846 Static Volumetric Apparatus Multi-point BET Correlation coefficient, r >0.9975 Dynamic Flow Apparatus Single-point BET Krypton for very low surface areas (<0.5 m2/g) USP <846>

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**Applying the method to a common pharmaceutical ingredient.**

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**Excipient: Magnesium Stearate**

Imparts certain compaction, hardness, disintegration and dissolution characteristics to solid dosage forms. Primarily added in order to lubricate powder flow and compaction. Specific surface areas from 3.53 to 53.6 m2/g have been reported. Majority of values lie in the range 4 to 10 m2/g.

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**Excipient: Magnesium Stearate**

Variability in measured surface area values can be imparted by different outgassing. The BET C constant for N2 adsorption on magnesium stearate (at 77.4 K) is low (3 – 15). Care must be taken to ensure that sufficient time be allowed for adsorption to come to complete equilibrium at each point.

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**Multi-point BET vs.Single-point Comparison**

Corrected by multiplier C/C-2

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**MgSt Monograph Outgas 40 degC for 2 hours P/Po range 0.05 to 0.15**

“If the plot deviates from linearity for P/Po values of 0.05 to 0.15, then a suitable range of P/Po values should be validated for linearity. In this case, it is necessary to state the range of validated P/Po values, and the outgassing conditions employed.”

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**“On the difficulty of assessing the specific surface area of magnesium stearate”**

Abstract The water content of magnesium stearate modified by ageing in humid air at room temperature or by vacuum treatment. The complete adsorption–desorption isotherms of nitrogen and krypton measured at liquid nitrogen temperature after standardized vacuum degassing. (a) the BET surface area values computed from the adsorption branch vary widely and is increasing with increasing water content; Cyrille Andre`s, Pierre Bracconi, Yvette Pourcelot International Journal of Pharmaceutics 218 (2001) 153–163

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**Mag. Stearate Thermograms**

Mikko Koivisto, Hannu Jalonen and Ensio Laine Outgassed 105 degC Outgassed 60 degC As received Moisture, 6 weeks Temperature (degC)

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**“On the difficulty of assessing the specific surface area of magnesium stearate”**

(b) anomalous hysteresis of varying amplitude is observed in all cases except adsorption of krypton on the material with the lowest water content; (c) the hysteresis loops extend down to very low desorption pressure values and cannot be accounted for by capillary condensation. (d) the surface area value of a given material computed from nitrogen and krypton adsorption may differ by a factor as high as six. Cyrille Andre`s, Pierre Bracconi, Yvette Pourcelot International Journal of Pharmaceutics 218 (2001) 153–163

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**In pursuit of linearity: shortcomings of <846> and monograph.**

Chemical state of MgSt ignored. Neither <846> nor monograph demand consecutive data points be used. Neither <846> nor monograph demand a minimum P/Po spread. ANY three points spaced closely enough could yield sufficient linearity. Reasonable value of “C” not considered.

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**In pursuit of linearity: shortcomings of <846> and monograph.**

“It may be worth reemphasizing that the correctness of the theory* is not proven if a plot of the data according to equation (38)* gives a straight line. It is also necessary that the evaluated constants should have reasonable values” * refers to what we now call the BET equation. Stephen Brunauer “The Adsorption of Gases and Vapors, Volume 1” Princeton Univeristy Press, 1945, page 154.

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**Changing Outgassing in Pursuit of Linearity**

“state… the outgassing conditions employed” suggests that 40 degC for 2 hours is not an absolute requirement! Let’s look at the influence of temperature and time…

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**Surface Area as fn of Degas Temperature (He flow, 24 hours)**

D.S.Phadke and J.L. Coller Drug Dev. Ind. Pharm. 20(5) (1994)

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**Surface Area as fn of Degas Time @ 40 degC**

Private communication, unpublished data (1999)

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**“Let’s make some careful, slow measurements for a more precise result**

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**Non-bovine Magnesium Stearate**

isotherm BET plot

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Zinc Stearate isotherm BET plot NOT the answer!

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What can be done? Outgas well… low temperature and short time need good exposure of surface to vacuum. Use a large bulb cell, spread sample around inside of bulb. Analyze quickly: aim for no more than 5m2 in the cell; don’t waste time measuring Po (use atmos P + 10 torr); don’t use overlong equilibrium settings. Freeze/thaw outgassing technique can give different values than simple evacuation (or flow).

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**Surface Area Summary Why?**

Surface Area affects reaction rates with liquids and gases, e.g. dissolution, catalytic activity

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Bibliography Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density by S. Lowell, J.E Shields, M.A. Thomas & M. Thommes (2004) Springer ISBN: Adsorption, Surface Area and Porosity by S.J. Gregg and K.S.W. Sing 2nd Edition (1982) Academic Press ISBN: Particle Size Measurement Vols 1 & 2 by Terence Allen 5th edition (1997) Springer ISBN: (2 volume set) Particle Characterization: Light Scattering Methods by Ren Xu (2000) Springer ISBN: Particle-Particle Adhesion in Pharmaceutical Powder Handling by Fridrun Podczeck (1999) World Scientific Publishing Company ISBN: Manual on Test Sieving Methods (ASTM Manual Series, Manual 32) by ASTM Committee E-29 on Particle and Spray Characterization(1998) ASTM ISBN: Particle Size Characterization (Recommended Practice Guide) Special Publication 960-1, NIST (2001)

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