10. The van Deemter Equation

Write the short form of the van Deemter equation and define each term (give units where appropriate). For each term, give an indication of its dependence on specific column or analyte properties. (1.1+2.4+3.1)

Formula: H = A + (B/u) + Cu

- H = Height equiv to a theoretical plate (cm) (HETP = L/N)

- A = Mult flow path term (A-term)

- B = Longitudinal diffusion term (B-term)

- C = Mass transfer term (C-term)

- u = linear velocity (cm/s)

A-term: column packing factor; particle diameter (dp)

B-term: analyte diffusion coefficient in m.p.; tortuosity factor (packing)

C-term: Cmp + Csp

- Cmp: analyte retention (f(k’)), square of particle diameter (dp^2), analyte diffusion coefficient in m.p. (Dmp)

- Csp: analyte retention f’(k’), stationary film thickness (df), analyte diffusion coefficient in s.p. (Dsp)

T/F? The A term in the van Deemter equation is not applicable for open tubular columns that are not packed with particles. (1.3d+3.3d+6.2f)

True (A-term)

T/F? In GC, changing to a thicker stationary phase film will increase capacity, but it will decrease efficiency. (1.3j)

True (thick)

T/F? In GC, changing to a thinner stationary phase film will decrease capacity, but it will increase efficiency.

True (thin)

T/F? Nitrogen carrier gas allows GC separations to be pushed to fast flow rates with minimal loss of efficiency. (3.3a)

False; H2

T/F? The height equivalent to a theoretical plate (HETP) depends on the length of the column. (3.3b)

False; H = L/N, invariant with length (Ideally, HETP should remain constant for a given column type and conditions.)

T/F? Doubling the length of a column will cause the number of theoretical plates to increase by a factor of 2. (1.3c+3.3c)

True (TP)

What is one advantage and one disadvantage of using HPLC columns packed with circa 1 um diameter particles (3.4b)

Advantage:

Allows high efficiency separations at faster flow rates. The C-term of the van Deemter is diminished and the curve is flatter than that for larger particles at high flow rates.

Disadvantage:

• High back pressure; need UPHLC pumps to operate at high flow rate

• Column construction - difficult to hold small particles ~ 1um in packed bed using standard fits

• Harder to pack effectively compared to e.g. 5 um dp particles

What processes lead to band broadening and loss of efficiency in packed column HPLC? For each band broadening process, indicate one parameter associated with the packed column or analyte, which has a primary effect on the process, besides flow rate or linear velocity? (4.6+6.5)

These processes are described by the van Deemter equation:

A) Multiple flowpaths exist for analytes through a packed bed. The degree of broadening due to this is controlled by particle diameter and how well the bed is packed. The smaller particle diameter the better. 

B) Longitudinal diffusion occurs the longer analyte resides in the separation system. This is also controlled by quality of column packing via the so-called tortuosity factor. It is also dependent on the analyte diffusion coefficient in m.p.

C) Mass transfer can occur in the m.p. or s.p. Increased residence time in either the m.p. or s.p. will increase mass transfer effects (function of capacity/retention). Particle diameter and stationary phase thickness also affects mass transfer. Mass transfer is reduced when each is minimized.

List the names of the three terms associated with the van Deemter equation. (5.5)

A) Multiple flowpaths/ Eddy diffusion

B) Longitudinal diffusion

C) Mass transfer

T/F? UHPLC refers to a version of HPLC where columns packed with smaller diameter (< 2 um) are operated under higher pressure to achieve higher efficiency and throughput.

True (UHPLC)

T/F? GC is a higher efficiency separation technique than LC. (6.2j)

True (GC)