The diameter that is measured in DLS is a value that refers to how a particle diffuses within a fluid so it is referred to as a hydrodynamic diameter
The diameter that is obtained by this technique is the diameter of a sphere that has the same translational diffusion coefficient as the particle
The translational diffusion coefficient will depend not only on the size of the particle “core”, but also on any surface structure, as well as the concentration and type of ions in the medium
Particle core Shell formed by solvent particles, ions etc. Low conductivity medium will produce an extended double layer of ions around the particle, reducing the diffusion speed and resulting in a larger, apparent hydrodynamic diameter. Thus, the measurements are usually done in 10mM NaCl (ISO13321 Part 8 1996)
The dark spaces in the speckle pattern produced by light scattering are where the phase additions of the scattered light are mutually destructive. The bright spots of light in the speckle pattern are where the light scattered from the particles arrives with the same phase and interfere constructively.
The observed signal depends on the phase addition of the scattered light falling on the detector. In example A, two beams interfere and “cancel each other out” resulting in a decreased intensity detected. In example B, two beams interfere and “enhance each other” resulting in an increased intensity detected.
For a system of particles undergoing Brownian motion, a speckle pattern is observed where the position of each speckle is seen to be in constant motion. This is because the phase addition from the moving particles is constantly evolving and forming new patterns.
The rate at which these intensity fluctuations occur will depend on the size of the particles. Figure above schematically illustrates typical intensity fluctuations arising from a dispersion of large particles and a dispersion of small particles.
The small particles cause the intensity to fluctuate more rapidly than the large ones.
It is possible to directly measure the spectrum of frequencies contained in the intensity fluctuations arising from the Brownian motion of particles, but it is inefficient to do so. The best way is to use a device called a digital auto correlator.
If the intensity of a signal is compared with itself at a particular point in time and a time much later, then for a randomly fluctuating signal it is obvious that the intensities are not going to be related in any way, i.e. there will be no correlation between the two signals.
However, if the intensity of signal at time t is compared to the intensity a very small time later (t+δt), there will be a strong relationship or correlation between the intensities of two signals.
Perfect correlation is indicated by unity (1.00) and no correlation is indicated by zero (0.00).
If the signals at t+2δt, t+3δt, t+4δt etc. are compared with the signal at t, the correlation of a signal arriving from a random source will decrease with time until at some time, effectively t = ∞, there will be no correlation.
If the particles are large the signal will be changing slowly and the correlation will persist for a long time. If the particles are small and moving rapidly then correlation will reduce more quickly.
Consider 2 populations of spherical particles of diameter 5nm and 50nm present in equal numbers.
If a number distribution of these 2 particle populations is plotted, a plot consisting of 2 peaks (positioned at 5 and 50nm) of a 1 to 1 ratio would be obtained.
If this number distribution was converted into volume, then the 2 peaks would change to a 1:1000 ratio (because the volume of a sphere is proportional to d 3 ).
If this was further converted into an intensity distribution, a 1:1000000 ratio between the 2 peaks would be obtained (because the intensity of scattering is proportional to d 6 from Rayleigh’s approximation).
In DLS, the distribution obtained from a measurement is based on intensity.
Measurement of Porosity and Specific Surface Area by Gas Adsorption
What are Porous Materials? F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999
Low specific surface area
Low specific pore volume
High specific surface area
High specific pore volume
Porous materials have highly developed internal surface area that can be used to perform specific function. Almost all solids are porous except for ceramics fired at extremely high temperatures
Measure of Porosity Pore size and its distribution Specific Surface Area, m 2 /g = Porosity There are three parameters used as a measure of porosity; specific surface area, specific pore volume or porosity, and pore size and its distribution. Mass of the solid, g Total surface area, m 2 Specific Pore volume, cm 3 /g Mass of the solid, g Total pore volume, cm 3 = Porosity, % = Volume of solid (including pores) Volume of pores X 100
Concept of Porosity: Open vs. Closed Pores Dead end (open) Closed Inter-connected (open) Passing (open) F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999 Open pores are accessible whereas closed pores are inaccessible pores. Open pores can be inter-connected, passing or dead end.
Size of Pores (IUPAC Standard) 2 nm 50 nm Micropores Mesopores Macropores Zeolite, Activated carbon, Metal organic framework Mesoporous silica, Activated carbon Sintered metals and ceramics Porous material are classified according to the size of pores: material with pores less than 2 nm are called micropores, materials with pores between 2 and 50 nm are called mesopores, and material with pores greater than 50 nm are macrospores Sing, K. S. W. et al. Reporting Physisorption Data for Gas/Solid Systems. Pure & Appl. Chem. 57, 603-619 (1985).
Shapes of Pores Conical Interstices F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999 Slits Cylindrical Spherical or Ink Bottle Pore Shapes
Adsorption Process Adsorption is brought by the forces acting between the solid and the molecules of the gas. These forces are of two kinds: physical (physiosorption) and chemical (chemisorption) Adsor bent - the solid where adsorption takes place Adsor bate - the gas adsorbed on the surface of solids Adsor ptive - adsorbate before being adsorbed on the surface
Physisorption vs Chemisorption http://www.soton.ac.uk PHYSISORPTION CHEMISORPTION WEAK, LONG RANGE BONDING Van der Waals interactions STRONG, SHORT RANGE BONDING Chemical bonding involved. NOT SURFACE SPECIFIC Physisorption takes place between all molecules on any surface providing the temperature is low enough. SURFACE SPECIFIC E.g. Chemisorption of hydrogen takes place on transition metals but not on gold or mercury. Δ H ads = 5 ….. 50 kJ mol-1 Δ H ads = 50 ….. 500 kJ mol -1 Non activated with equilibrium achieved relatively quickly. Increasing temperature always reduces surface coverage . Can be activated, in which case equilibrium can be slow and increasing temperature can favour adsorption. No surface reactions. Surface reactions may take place:- Dissociation, reconstruction, catalysis. MULTILAYER ADSORPTION BET Isotherm used to model adsorption equilibrium. MONOLAYER ADSORPTION Langmuir Isotherm is used to model adsorption equilibrium.
Adsorption Process 1 . Diffusion to adsorbent surface 2 . Migration into pores of adsorbent 3 . Monolayer builds up of adsorbate 1
Gas molecules admitted under increasing pressure to a clean, cold surface.
Data treatment techniques find the quantity of gas that forms the first layer.
S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 2 3 1 2 3
Adsorption Process Adsor bent Adsor bate S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 Equation of adsorption isotherm
Pore Size Distribution V a Pore diameter, d Narrow pore size distribution Pore diameter, d Multimodal pore size distribution The distribution of pore volume with respect to pore size is called a pore size distribution. V a Broad pore size distribution Unimodal pore size distribution
Pore Size Distribution G ads = RT(lnP ads - lnP 0 ) G des = RT(lnP des - lnP 0 ) G des < G ads 1 P/P o ( P/P o ) des ( P/P o ) ads
Adsorption or desorption isotherm.
The desorption isotherm is preferred over adsorption isotherm.
Multilayer formation occurs in parallel to capillary condensation.
Capillary condensation is described by the Kelvin equation.
Pore Size: Kelvin Equation Actual radius of the pore Kelvin radius of the pore Thickness of the adsorbed layer Prior to condensation, some adsorption has taken place on the walls of the pore, r k does not represent the actual pore radius. Adsorbed layer
Methods for Calculation of Pore Size Distribution
BJH (Barrett, Joyner and Halenda) method
DH (Dollimore Heal) method
HK (Horvath-Kawazoe) method
Mesoporous solids Microporous solids
NLDFT (Non Local Density Functional Theory) and Monte Carlo simulation method
Microporous and Mesoporous solids
Porosity Analyzer Outgassing station Analysis station Liquid nitrogen bath