Blaine value vs position parameter

The Rosin Rammler distribution has nothing to do with surface area. It is determined by converting two sieve residues into the Rosin-Rammler particle size distribution. This involves plotting the natural logarithm of the sieve grain size (45μ, 90μ, 150μ) etc, against the double natural logarithm of 100/Residue at that sieve size. The slope “m” of the Rosin Rammler distribution is the first way to characterise the fineness of a powder. The second way to characterise the fineness of a powder is the “position parameter” of the Rosin Rammler distribution, which corresponds to the intercept on the x axis of the distribution, i.e. when ln(ln(100/Residue)) = 0.

snowmen:

Respected Dr. Michal Clarke Please let me brief about relation between Blaine value (surface area) vs Position parameter(PP) & n value(slope) which get from RRSB distribution - Particle size Analyser. AKT

There was an early 80's article presented in ZKG where such relation was reported by authors (Sorry, I dont have exact referance now) here is that equation the accuracy of reported equation is +/- 5%

Specific surface area =41048 x (PP^-0.394) x (n^-0.198) x (density^-1.078)

Where PP is position parameter on RRSB Graph for given sample

n = RRSB Number or RRSB Slope

density = density of sample in g/cm3 (typically for cement = 3.15 g/cm3)

Ex: For a typical cement sample which i have measured for a client was as follows

PP= 30.03   ; n   =  1.16 ; density = 3.15 g/cm3

Calculated surface area was = 3028 Blain (measured value was 3152 blain) which is well is stipulaed limit of +/- 5%

There is another DIN 66145 (german standard for representation of particle size distributions; RRSB-grid ) which also gives Blaine along with slope and PP which has just to be interpolated

You can also see PP 182 and 183 in cement Engineers' Handbook By Labahn/Kohlhaas 

 

Most often, today, particle size distributions (PSD) are measured by laser diffraction.
All suppliers also calculate a specific surface from this PSD.
This calculation includes a "shape factor" to take the shape of the particles into account.
Note that the evaluation of the PSD from the scattered light distribution (SLD) also involves model hypothesis concerning transparency or shape.

The blaine is based on measuring a friction between an air flow and a cement sample.
The Kozeny–Carman equation establishes a link between the pressure drop (friction) and the size of the particles (also assumed to be spherical in this theory).

It is no surprise that there is, usually, a good correlation between blaine measurements and the calculated specific surfaces. At least the correlations are as good as they could be, given the errors in both methods. As you can guess, the errors are mainly experimental but they are also partly fundamental since none of the methods really measure the surface directly, unlike surface adsorption methods.

However, what really matters is the value of such measurements for predicting the strength development and other quality aspects (water demand e.g.). It is clear that the PSD contains more information than the blaine and it is therefore more valuable. The correlation between the PSD or various PSD parameters and strength development is proven. The correlation is higher for short term strengths than for long term, as one would expect. Multiple components (slag, flyash, sulfates) can blur this picture.

If you (really) want to evaluate the Blaine from the Rosin-Rammler parameters, you can do that with a bit of algebra. Here the formula:

[1]  Blaine = Shape  *  6/ro/xo  *  
                   Gamma( (n-1)/n  ,  (x1/xo)^n )

where:
   Blaine: is the specific surface in ad-hoc units
   Shape: a shape factor
   ro : the density
   xo: the Rosin-Rammler diameter
   n:  the exponent of the Rosin-Rammler curve 
   Gamma: is the Euler (incomplete) Gamma function 
                (see mathworld link below)
   x1: the diameter of the smallest particles you want to take into account

To the first order, the impact of x1 is proportional to Log[x1/xo] .
This "smallest diameter" should then be related to the purpose we have: correlating with the strength devilment, specially the 1 to 7 days strengths. For this reason, the sub-micron particles can for sure be discarded as they will react very quickly and will not significantly influence the 1d-7d strengths. Therefore, the cut diameter x1 is something in the micrometer range.

Finally, the fit of the PSD to the Rosin-Rammler curve is rarely perfect. The misfit can cause big differences between the RR calculations above and the results calculated from the detailed PSD, especially if the discrepancies occur for the fine particles. The best advice is to use the full PSD and do the full calculation. This is normally done automatically by the laser systems. This note from Sympatec explains how the surface can be calculated from the PSD: http://www.sympatec.com/LaserDiffraction/publications/LD_1997_cementquality.pdf .

 http://mathworld.wolfram.com/IncompleteGammaFunction.html