Separation Science

All separations go against the 2nd Law of Thermodynamics: entropy increases during any natural process

Ancient Separations

1. Metallurgy

2. Distillation

3. Isolation of Dyes

Modern Separations

1. Medical Technology

2. Petroleum & Polymers

3. Environmental Analysis

Phase Distributions

Bring about most separations

1. gas-gas → 235UF6, 238UF6

2. gas-liquid → distillation

3. gas-solid → molecular sieves

4. liquid-liquid → extractions

5. liquid-solid → precipitation, SPE

6. solid-solid → sieving

Liquid-liquid extraction of an analyte based on its partitioning between two different liquid phases.

Solid Phase Extraction of an analyte in a liquid phase using a bed of packing material

Solid Phase Extraction using a filter disk or membrane

Separation of 2 analytes A and B on a bed of packing material using a flowing liquid phase

2 Categories of Separations

1. Phase Equilibira: One of the phases is the analyte

2. Distribution Equilibria: The two phases are composed of compounds other than the analyte.

Distribution Equilibira

Given the complexity of many real samples, interferences between the analyte and concomitants are common.

A logical approach is to reduce the possibility of interference by removing the concomitants.

Distribution Equilibira

This is often achieved by placing the sample in a 2-phase system, and allowing the species to partition between the 2 phases.

From this point of view, separation science may be considered a sample preparation technique.

Partition Coefficient

(or Distribution Coefficient or Ratio)

KD = [S]org / [S]aq = X/Y

[S] is the concentration of the solute (or analyte) in the given phase at equilibrium

X is the fraction of analyte in the organic phase

Y is the fraction in the aqueous phase

Suppose we have a volume of clean organic solvent in a separatory funnel.

Organic Phase

Aqueous Phase

If we add an equal volume of water containing our analyte

(C moles), what will happen?

[S]org = XC

X+Y=1

[S]aq = YC

Organic Phase

Aqueous Phase

The analyte will “partition” between the two phases depending upon its partition coefficient K.

In a successful separation, the analyte (A) and the concomitant (B) have very different partition coefficients:

KA ≠ KB

Organic Phase

Aqueous Phase

In practice, this is seldom the case, or:

KA ≈ KB

So we may need to perform a series of extractions.

Organic Phase

Aqueous Phase

XC: Fraction in Organic Phase

YC: Fraction in Aqueous Phase

Perform a Series of identical extractions:

After we allow the first extraction step to reach equilibrium, but before we remove the water layer…

XC

Fresh water

Fresh water

YC

Now, we shift the aqueous phase: remove the lower layer and add fresh water to funnel #1…

Fresh Organic

YC

YC

And then add the lower “aqueous” phase to a fresh organic layer in funnel #2.

Organic Phase

Aqueous Phase

Organic Phase

Aqueous Phase

Organic Phase

Aqueous Phase

Fresh water

YC

YC

Shift 1 with a series of funnels

Organic Phase

Aqueous Phase

Organic Phase

Aqueous Phase

Organic Phase

Aqueous Phase

XC

Total moles of analyte in each funnel at the end of shift #1

YC 0

Allow each funnel to equilibrate, and shift aqueous phases again (shift #2)…

Organic Phase

Aqueous Phase

Organic Phase

Aqueous Phase

Organic Phase

Aqueous Phase

XC YC 0

(Total Amount in each column)

X(XC)

Y(XC)

X(YC)

Y(YC)

0

0

Fresh water

Y(XC)

Y(XC)

Y(YC)

Y(YC)

0

Amount remaining in organic layer after equilibration

Amount shifted with aqueous layer in next step

Total moles of analyte in each sep. funnel at the end of shift 2. Amounts in each layer are allowed to combine…

X(XC)

0

X(YC)

Y(XC)

0

Y(YC)

X2C 2XYC Y2C

Funnel 1 Funnel 2 Funnel 3

And so on…

After step 3: X3 3X2Y 3XY2 Y3

After 4: X4 4X3Y 6X2Y2 4XY3 Y4

After 5: X5 5X4Y 10X3Y2 10X2Y3 …

Let the funnel number be “n”

And the shift number be “r”

Then the fraction in funnel n after shift # r is given by:

fn = r! Xr-n+1 Yn-1

(r-n+1)! (n-1)!

If we observe what comes out of the last funnel (N = n+1)

fN = r! Xr-N YN

(r-N)! (N)!

So we could predict how an analyte will emerge from the system by plotting fN vs. r.

Or we could predict the time, r, when the maximum amount of an analyte reaches the end by finding the derivative of the fraction with respect to r:

dfN/dr = 0

Both problems are very hard to solve!

Luckily, this formula has already been solved by Bernoulli.

A random experiment with 2 possible outcomes (X and Y) obeys this same formula.

For example:

X is the probability of heads

Y is the probability of tails

r is the number of tosses

N is a particular number of observed heads

fN is the probability that exactly N heads will be observed

This is known to be a binomial distribution

and the mean is given by: n = rY

and the variance is given by: σ = (rXY)1/2

So to get the maximum amount of analyte at the end requires rmax shifts where:

rmax = N/Y

And he spread of the analyte among the funnels is described by σ, where:

σ = (rmax XY)1/2 = (NX)1/2

So this theory predicts that we should observe Gaussian shaped analyte distributions that elute in narrow tall peaks if the aqueous phase is preferred, or short broad peaks if the organic phase is preferred.

We may consider a chromatographic system as a “continuous” array of separatory funnels, or tiny plates. The total number of these plates in the system will be N, and they will be arranged in some real length L. So each individual plate will have some height H=L/N.

This theory is known as “plate theory” and it won a Nobel Prize for Martin and Synge in 1952.

In a real chromatography system, a volume of solution is flowing at a known rate, so the number of shifts, r, is related to time.

Therefore, we can measure a retention time, tr, defined as the time required between injection of an analyte, and the appearance of its maximum concentration at a detector (plate # N).

And it should have a measurable width that depends upon KD.

One of the phases is mobile, or moves through the system, while the other is stationary.

In our separatory funnel example, the mobile phase is aqueous, and the stationary phase is organic.

By convention, a “normal” mode of separation is one where the mobile phase is organic, and the stationary phase is polar.

A “reversed phase” has a polar or aqueous mobile phase, and a non-polar stationary phase.

Plate Theory defines terms measurable based on Gaussian shaped curves:

N = 16 (tr / W)2 = 5.54 (tr / W1/2)2

H = L/N

A large number of plates, or a short plate height characterize more efficient separations.

Shortcomings of Plate Theory

1. Assumes equilibrium is established quickly

2. Ignores diffusion

3. Ignores relative volumes of the two phases