Autodilution

The Single Particle Optical Sizing (SPOS) method requires that concentrated suspensions be diluted in order to eliminate particle coincidences in the sensing photozone. A particle coincidence is when more than one particle is in the detection zone at once. Since many colloidal systems manufactured industrially have a high solids loading, often massive dilutions are required, sometimes on the order of 50,000X. Such large dilutions can be difficult to perform accurately and precisely on the lab bench. Particle Sizing Systems has developed the AccuSizer 780 , an SPOS system that uses an automatic dilution scheme called Autodilution. Autodilution quickly and accurately can dilute a small aliquot of concentrated sample by a factor of 100,000 in 5 minutes.

A schematic of the Autodilution fluidics is shown above. The Autodilution system consists of a source of clean diluent, a pump, a dilution chamber, a light obscuration sensor, and a waste container. The system starts with the dilution chamber, under mixing, containing volume v of clean diluent. The user injects a small aliquot of concentrated sample into the dilution chamber. The pump is turned on, adding clean diluent to the dilution chamber at a flow rate of F. The dilution chamber is closed which means that liquid leaves the vessel at flow rate F. The volume v will not change as the flow rate into and out of the dilution chamber is the same. The liquid leaving the dilution chamber goes through the sensor where the particle counts can be monitored. Under these conditions, the concentration of particles will decrease with time, falling exponentially. The concentration vs time relationship can be expressed as:

 

    \[C(t) = C_oe^-t/\tau\]

Where: C_o initial concentration of particles in the dilution chamber

t is the time

\tau is the time constant, equal to V/F

Here is that it looks like graphically:

 

With a typical values of V = 60 ml and F = 60 ml/min, the Autodilutor will reduce the concentration of particles in the dilution chamber by a factor of 3 in 1 minute and a factor of 8 in three minutes. The above graph also contains details of how a typical measurement is made. A small aliquot of concentrated sample is injected into the Autodilutor. The pump begins operation, flowing clean diluent into the dilution chamber at flow rate F. Usually the data collection will begin only when the concentration drops below a certain threshold, C_s_p (when coincidences are deemed statistically insignificant). The exponential dilution continues for a user settable collection time after which the measurement ends. This curve can be used to develop the basis of converting the particle counts obtained in a measurement (between t_sand t_e) to a particle concentration for the entire sample. First we must introduce the concept of Dilution Factor or DF. Defining DF as the ratio of particles introduced into the system over the particles counted between tsand te, the following equation can be developed:

    \[DF = (e^{-ts/\tau}- e^{-te/\tau})^{-1}\]

Where: t_s is the data collection start time

t_e is the data collection end time

The inverse of DF then is the fraction of the total particles in the dilution chamber at the start of the measurement that actually get counted by the light obscuration sensor.

An example of an Autodilution measurement can be seen:

The particle size distribution above is from a commercial dispersion of 1 micron polystyrene latex spheres. These particles are very narrowly dispersed. The expected particle concentration of this dispersion is 1.9 +/- 0.2 x 10^{10}particles/ml. The measurement was performed by injecting 2 microliters of the dispersion into the 780 Autodilution system. The number of particles counted in a 60 second collection time was 145,333 and the DF determined to be 278.31. The concentration of particles as measured by the Accusizer is (145,333 x 278.31)/0.002 or 2.02 x 10^{10}particles/ml, a result within the expected range. Furthermore, the known solids loading of this dispersion is 1%. Since all the particles in the dispersion are countable, the solids volume recovery should be 100%. The 780 recovered 99.5% of the solids volume. Both the particle concentration and % volume recovery numbers confirm the accuracy the Autodilution approach.

The actual results from the printout can be seen below.

 

In conclusion, Autodilution is the enabling technology for SPOS. It provides a quick and accurate way to perform massive dilutions on concentrated colloidal dispersions. It allows SPOS to be used to characterize the tails of colloidal systems allowing the stability to be determined.