On the sampling variance of ultra-dilute solutions

Area of Science:

• Analytical Chemistry
• Physical Chemistry
• Nanotechnology

Background:

• Modern analytical techniques enable substance determination in ultra-dilute solutions, reaching picomol per liter (pM) and below.
• Reduced sample volumes and quantification limits allow for the analysis of zeptomol quantities of analytes.

Purpose of the Study:

• To address the challenges in analyzing ultra-dilute samples.
• To investigate the impact of sampling variance on analytical precision.
• To provide a method for calculating expected sampling variance.

Main Methods:

• Utilizing contemporary analytical methodologies for ultra-dilute solution analysis.
• Employing techniques capable of determining zeptomol amounts.
• Applying statistical principles, specifically Poisson distribution, to model sampling variance.

Main Results:

• Analysis of ultra-dilute samples is feasible down to zeptomol levels.
• Intrinsic sampling variance, stemming from the quantized nature of matter, is a significant limitation.
• The expected sampling variance can be calculated using the Poisson distribution for limited analyte molecules per test portion.

Conclusions:

• Despite advancements in analytical techniques, sampling variance remains a critical factor affecting precision in ultra-trace analysis.
• Understanding and quantifying sampling variance through statistical models like the Poisson distribution is essential for accurate ultra-dilute sample analysis.