CHROMATOGRAPHYCHROMATOGRAPHY

A sample that requires analysis is often a mixture of many components in a complex matrix.

For samples containing unknown compounds, the components must be separated from each other so that each individual component can be identified by other analytical methods.

The separation properties of the components in a mixture are constant under constant conditions, and therefore once determined they can be used to identify and quantify each of the components.

Such procedures are typical in chromatographic and electrophoretic analytical separations.

A mixture can be separated using the the differences in physical or chemical properties of the individual components.

An example is the filtering of a solid precipitate to separate it from a solution.

These separations are based on the states of matter of the two components, other physical properties that are useful for separations are density and size.

Some useful chemical properties by which compounds can be separated are solubility, boiling point, and vapor pressure.

Objective of SeparationObjective of Separation

Proteins are extracted from animals and humans as

a mxture in a serum of body fluids.

When immunologists want to study a specific

protein, like an antibody, hormone, or enzyme, they

need to separate it from the mix.

One method of separating proteins, gel filtration,

relies on the fact that proteins differ in molecular

weights.

Examples of Separative Techniques

1. Solvent extraction

2. Chromatography

3. Precipitation

4. Recrystallisation

5. Electrophoresis

An Introduction to Chromatography

What is chromatography?

From Greek words:

Chroma: color

Graphein: writeDetector

Column

Sample M obile phase

Time

Chromatography is a separations method that relies on differences in partitioning behavior between a flowing mobile phase and a stationary phase to separate the the components in a mixture

Sample components that partition strongly into the stationary phase spend a greater amount of time in the column and are separated from components that stay predominantly in the mobile phase and pass through the column faster.

ChromatographyChromatography

As the components elute from the column they can be quantified by a detector and/or collected for further analysis.

An analytical instrument can be combined with a separation method for on-line analysis.

Examples of such "hyphenated techniques" include gas and liquid chromatography with mass spectrometry (GC-MS and LC-MS), Fourier-transform infrared spectroscopy (GC-FTIR), and diode-array UV-VIS absorption spectroscopy (HPLC-UV-VIS).

Mechanisms of chromatographic interactions Adsorption – solid stationary phase Partition – liquid stationary phase Ion-exchange – covalently attached anions or cations on a resin Molecular (Size) exclusion -gel Affinity – anti-bodies attached to a solid support

Chromatography

Chromatogram - Detector signal vs. retention time or volume

time or volume

Det

ecto

r S

igna

l1 2

Purpose of Chromatography

• AnalyticalAnalytical - determine chemical composition of a sample

• PreparativePreparative - purify and collect one or more components of a sample

Mechanisms of Partition to Stationary Phase

Stationary Phase

• The stationary phase consists of semi-permeable, porous

beads with a well-defined range of pore sizes.

• The semi-permeable porous beads are crosslinked

polymers

– Degree of crosslinking is controlled carefully to yield

different pore sizes

– The stationary phase is said to have a fractionation

range (due to the different pore sizes), meaning that

molecules within that molecular weight range can be

separated.

Nature of Porous Material(stationary phase)

• Porous material must swell up and imbibe/absorb the liquid phase

• The created solvent-filled ‘sponge’ allows diffusion of molecules

Therefore, stationary phase may be hydrophilic to imbibe aqueous media, or lipophilic to imbibe non-polar organic solvents.

Mobile Phase

• The mobile phase contains a mixture of

solutes.

• Small solutes will diffuse in and out of the

pores (obeying Fick’s law)

– Their path through the column is longer

–The elution time will be longer

Equilibrium reactionEquilibrium reaction• Can be represented by the equilibrium reaction:

• The equilibrium constant:

• Consider:i. The reaction in completely reversible, and the chemical’s interaction with

the adsorption site cause no alteration in its solution properties or solution state

ii. Chemicals bind to sites in a one-to-one fashion, and the bind only to site.iii. Only one mode of binding to the site; all binding is equal and is described

by a single value Keq

• In many cases, ([S]>>[C]), and the equilibrium becomes:

• Known as linear equilibrium

or

(1)

(4)(3)

(2)

C: dissolved chemical species, S: adsorption site, CS: chemical bound to the site, Keq: equilibrium constant

• Linear chromatography is suitable for analytical chromatography but less useful for preparative or industrial scale adsorption and chromatography

• The most efficient operation uses all the adsorption sites available. So, the concentration of the empty adsorption sites available cannot be ignored. The total number of sites is:

• From (2):

• Known as Langmuir isotherm

• Keq[C]<1: the form of linear adsorption equation is recovered [Equation (4)], Keq[C]>1: [CS]=Stot – the adsorption sites are saturated

• Often used to correlate equilibrium adsorption data for proteins

Equilibrium reactionEquilibrium reaction

(5) Stot:total site concentration

(6)

• Another equilibrium constant:

• Known as Freundlich isotherm• Used to describe the adsorption of a wide range of antibiotics,

steroids, and hormones.

Equilibrium reactionEquilibrium reaction

(7)

Figure 1.Shapes of different equilibrium adsorption isotherms.

Chromatography Column Chromatography Column DynamicsDynamics

Plate models

Figure 2 Properties of a Gaussian peak cmax, maximum peak height; σ, standard deviation; wi, peak width at inflection points; wh, peak width at half-height; w, peak width at base (base intercept); tR, average retention time. (Data from C. Horvath and W. R. Melander, “Theory of chromatography,” Fundamentals and Applications of Chromatographic and Electrophoretic Methods, Part A, E. Heftmann, ed., p. A4l, Elsevier Scientific Amsterdam, Netherlands, 1983.)

• Height of the equivalent theoretical plate (HETP), H:

• From Gaussian peaks: the plate count (N) can be expressed as the squared average retention time divided by the variance of the peak

• Peak width is used in the definition of resolution, Rs, which is measure of the extent of separation of two peaks in a chromatography

Plate modelsPlate models

(8) L: length of the column, N: number of plates

(9) w: peak width at the base

(10) tR1,tR2 = average retention time for separands 1 and 2w1,w2 = peak width (time) for separands 1 and 2

Chromatography Column Mass Chromatography Column Mass Balance with Negligible DispersionBalance with Negligible Dispersion

• Mass balance for chromatography:

• Using an equilibrium isotherm relationship in the form qi =f(ci)(Figure 1), Equation (11) becomes:

• Where qi’(ci) is the slope of the equilibrium isotherm at concentration ci.

(11)

ci = concentration of separand i in the mobile phase = [C]i, qi = concentration of separand i in the stationary phase averaged over an adsorbent particle = [CS]i, ε = void fraction (mobile phase volume/total column volume), commonly 0.3 to 0.4 in fixed beds, v = mobile phase superficial velocity (flow rate divided by the empty column cross-sectional area, Q/A), Deff = effective dispersivity of the separand in the column, t = time, x = longitudinal distance in the column; x = 0 at column inlet

(12)

•If we let:

•Then Equation (12) becomes:

•Thus, the expression for ui given by Equation (13) is the effective velocity of component i through the packed column

Chromatography Column Mass Chromatography Column Mass Balance with Negligible DispersionBalance with Negligible Dispersion

(13)

(14)

• For preparative and industrial scale chromatography processes, the equilibrium is non linear and generally Langmuir isotherm is applicable

• For the non linear Langmuir equilibrium isotherm [Equation (6)], we obtain for the first derivative of qi with the respect to ci.

• From Equation (13), the equation becomes:

• The resulting ui,sh of the solute front is called shock wave velocity

• The leading edge of a solute from a Langmuir isotherm is a self-sharpening shock wave while trailing edge is a continuous diffuse wave

• To predict the elution profile of a peak, both the lading shock wave and the trailing diffuse wave must be calculated

Chromatography Column Mass Chromatography Column Mass Balance with Negligible DispersionBalance with Negligible Dispersion

(15)

(16)

Example 1Example 1 Chromatographic Separation of Two Solutes

Two solutes have linear equilibrium constants of Keq,1 = 7.5 and Keq,2 = 7.8, respectively. For a flow rate of 1.5 liter/mm, in a column 63cm in diameter, with a void fraction of 0.33, and local equilibrium, what column length is required to separate the two solutes by 5 min?

Solution

The effective velocity of solute i for negligible dispersion is given by Equation (13) as

For linear equilibrium,

The superficial velocity is

For solute 1, the effective velocity is therefore

Example 1Example 1

This same equation gives 0.08657 cm/mm for solute 2. Translating solute velocities into

elution times for a constant distance traveled (L),

Solving for L gives

Note that four significant figures are used to calculate u1 and u2 to avoid error in

calculating L.

Example 2Example 2Calculation of the Shock Wave Velocity for a Nonlinear Isotherm Solute I has a Langmuir isotherm characterized by an Stot of 120 µg/ml, and a Keq of

7.5 ml/mg. Calculate the shock wave velocity for an injection of 1 mg/ml, and

column conditions identical to those of Example 1

Solution

To use Equation 16 for the shock wave velocity, we need to know Δq. For the

Langmuir isotherm [Equation 6], the resin concentration q = [CS] in equilibrium

with concentration [C] = 1 mg/ml in the mobile phase is

Since the column initially has no solute,

From Equation (16), we obtain

This is over 10 times the solute velocity for the linear isotherm case given in Example 7.2. This

is because the concentration of the solute is limited to 0.120 mg/ml on the stationary phase.

For the linear case, a 1 mg/mi injection would lead to a 7.5 mg/mi concentration in the

stationary phase.

Example 3Example 3Calculation of the Elution Profile

For an injection volume of 5 liters, and other conditions as stated in Examples 1 and

2, calculate the elution profile for solute 1.

Solution

As determined in Example 2, the velocity of the shock front is 1.20 cm/min. The

diffuse wave velocity is determined by selecting concentrations between 0 and

the injection concentration of 1 mg/ml, and determining the velocity of each of

these concentrations trailing the shock front. For example, at a solute concentration

of 0.4 mg/mi, we can calculate dq1/dc1 from Equation 15:

We can use Equation 13 to calculate the solute velocity:

For a flow rate of 1.5 liters/min, and an injection volume of 5 liters, the

diffuse wave trails the shock by 3 min and 20 s [5 liters/(1.5 liters/min).

Table 1 gives the solute velocities for various concentrations.

Example 3Example 3TABLE 1Diffuse Wave Concentrations Following the Shock Wave for Example 2

Figure The elution profile calculated for a Langmuir isotherm. Conditions are given in the examples in the text.

Example 3Example 3As can be seen, concentrations above 0.23 mg/ml run faster than the shock front. Since nothing can pass the shock front, these concentrations do not appear in the thermodynamic diffuse wave. They do, however, represent concentrations on the isotherm where the derivative is less than the slope of the chord that connects the shock concentrations. Concentrations of 0.23 mg/ml and less run behind the shock front, and thus constitute the diffuse wave. The shock front elutes from the 12.0cm bed in 10.0 min. The diffuse wave is delayed by 3.33 min, as mentioned earlier, and then starts at approximately 0.23 mg/mI. The diffuse wave decreases in concentration to 0.1 mg/ml at 16.5 min, to 0.01 mg/ml at 24.8 min, to 0.005 mg/mI at 25.6 min, and to 0.001 mg/mI at 26.4 min. A representative graph is shown in Figure 1.The Langmuir isotherm and other concave downward equilibrium conditions are very common for large-scale liquid chromatography. Analytical chromatography does not generally deal with concentrations large enough to generate a Langmuir isotherm. Ion exchange binding is related to, but not exactly the same as, the Langmuir isotherm. Concave upwards isotherms result in peaks that have self-sharpening trailing edges and diffuse leading fronts. Most concave upwards isotherms results from multilayer binding in which the binding becomes more energetically favorable as the layers build up. This is most typical in gas/adsorption/ applications and is rarely, if ever, found in liquid chromatography of bioactive molecules

Dispersion Effects in Dispersion Effects in ChromatographyChromatography

• Mass transfer and diffusion play an important role in the mobile scaleup of these techniques.

• Diffusion takes place longitudinally in the mobile phase, and also within the pores of the stationary phase.

• Mass transfer takes place between the mobile and stationary phases.

• The effective dispersity Deff is a combination of the molecular or binary diffusivity in the mobile phase Dm and a dispersion coefficient E

• The mass balance has been solved by Lapidus and Amundson, assuming s linear isotherm, local equilibrium, and a semi-infinite column to give an analytical solution:

(17)

(18)

• Where the dispersion function is:

Dispersion Effects in Dispersion Effects in ChromatographyChromatography

u: velocity of fluid through the interstices of the bed (=v/ε), γ=Keq(1- ε)/ε, erf and erfc: error and complementary error functions

(19)

Figure 3 Prediction of chromatographic peaks from an analytical solution of the mass balance assuming a linear isotherm, local equilibrium, and a semi-infinite column. In this case, initial adsor- bate concentration is zero, and feed solution has a pulse in concentration of ci0 of duration equivalent to 300 ml of feed. (Data from L. Lapidus and N. R. Amundson, “Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns,” J. Phys. Chem., vol. 56, p. 984, 1952.)

• Intraparticle diffusion:

• Fluid phase mass transfer:

• with the matching condition of flux continuity at the particle surface

Dispersion Effects in Dispersion Effects in ChromatographyChromatography

(20)

(21)

(22)

r = distance from center of spherical resin particle, wi,p = concentration of separand i in the pore fluid based on a unit volume of stationary phase (i.e., the solid matrix and the pore space), wi,s = concentration of separand i adsorbed on the internal surfaces of the stationary phase based on a unit volume of stationary phase, ci = concentration of solute i in the mobile phase, Dp = effective separand diffusivity in the pore fluid, ka = forward rate constant of adsorption, kc = fluid mass transfer coefficient, ε* = effective volume fraction of the stationary phase that is accessible to the separand

Dispersion Effects in ChromatographyDispersion Effects in Chromatography• For the case of isocratic solution, where the concentration of elution solvent is

constant, their solution relied on using empirical correlations to predict the height equivalent of a theoretical plate (HETP) for the column.

• Approached by van Deemter et. al. – the bandwidth [(measured as the height equivalent of a theoretical plate, or HETP - see Equation 8 and 9] can be related to the linear velocity in the column by the following expression:

• HETP (H) : length, usually reported in centimeters; A: dead volume and othesources of mechanical mixing and is thought to be proportional to resin particle size; B

(cm2 s-1): molecular diffusion in the mobile phase- of the flow rate is on the order of the liquid phase diffusivity of the solute, the peak broadens; C (s) : mass transfer and intraparticle diffusion – thought to be proportional to the square of the effective liquid film thickness at the surface of the resin particle, divided by the effective diffusivity within the particle.

• Important to show the efficiency of the separation• Van Deemter equation can be normalized as

• H* = H/dp and u* = udp/Dm; dp : stationary phase particle diameter; Dm : diffusivity of the solute of interest; u* : reduced velocity – Péclet number for chromatography; H* : plate height, rarely <2 – two particle diameters in a chromatography bed constitute a mixing zone. Shown in Figure 4.

(23)

(24)

Dispersion Effects in Dispersion Effects in ChromatographyChromatography

Figure 4: Typical van Deemter plot for three particle diameters: 50 µm ( ), 25 µm (■), 10 µm(▲).

•Most efficient separation is achieved with the lowest possible plate height. •Efficient separation – the separation with the least energy lost to entropy (or thermodynamically speaking, most reversible) •In liquid chromatography, u* is a typically large numbers – diffusivities = 10 -5 – 10-7 cm2/s and linear velocities = 10-4 cm/s; the smallest resin diameter = 10-4 cm ( not smaller than 1 µm) is desirable for efficient separations

Dispersion Effects in Dispersion Effects in ChromatographyChromatography

Peg = dispersion Péclet number = dpu/Deff, x = ε/[ε+(1-ε)ε*(1+Keq)]; or the fraction of separand in the mobile phase at long times; ReSc = (Reynolds number)(Schmidt number) = (dpuερ/µ)(µ/ρDm) = dpuε/Dm, reduced velocity or diffusion Péclet number; Nu = Nusselt number = dpkc/DmDm = separand diffusivity in unbounded solution; m = Dm/ε*Dp; m’ = 3/2 m([Keq/(1+Keq)])2; Da = Damköhler number = dp

2ka/4Dp .The physical significance of each term in Equation () is as follows:Peg term: convective axial dispersion, Nu term: fluid phase mass transfer resistance, m term : intraparticle diffusion resistance, m’ term; sorption kinetics resistance

(25)

•The Van Deemter equation has been recast to dimensionless transport parameters by Athalye et. al as follows:

•Equation 25 is valuable because it enables the quantification of each contribution to the plate height, hence a conceptually useful sensivity analysis

Adsorbent TypesAdsorbent Types• Two basic resin materials : polymer and resin

• Silica resin – have hydrophobic coating and are used for reversed phase chromatography

• Polymer resin – used in aqueous applications and are conjugated with ion exchange, hydrophobic interaction, or affinity-type ligands

• Surface area is generally to 100 – 1500 m2/g

• Surface area on the outer surface of a 10 µm diameter solid sphere is 1.7 m2/g - it follows that most of the surface area is in the internal porosity of the particle

• The path length for the diffusion is also must be considered

• The path length is the radius of the resin, which is the maximum length a molecule will diffuse to gain access to the internal surface area of the resin.

• Silica-Based Resins Uncoated silica – compatible with water or organic solvent and serves as a good reversible adsorbent for hydrophilic compounds-organic solvent used as mobile phase, and water is added as the chromatography progresses-not typically stable at extremes of pH-available with high surface area and small particle size; being very rigid; does not collapse under high pressures-denature some proteins and irreversibly bind others-used for purification of many commercial biotechnology products

Coated silica - particles coated with long-chain alkanes

- Has a high affinity for hydrophobic molecules, which increases as the chain length

of the bonded alkane increases.

-Many varieties of the same chain length phase – polymerized, simple monolayer,

and end-capped

Polymer-Based Resins

Adsorbent TypesAdsorbent Types

-frequently used in industrial applications because of their high

stability and low cost

-manufactured by suspension polymerization :

i. emulsion of the polymer is made in an immiscible solvent

ii. cross-linking agent is added.

iii. The reaction is allowed to proceed to completion

iv. The particles are isolated from the suspension, washed and

frequently derivatized

v. Surfactants are added to control the particle size

-larger (10-100 µm) than silica-based resins (1-25 µm), less rigid,

not generally suitable for high pressure applications (>4 bar)

- Two synthetic polymer that are commonly used: styrene divinylbenzene

and polyacrylamide

- Styrene divinylbenzene – very stable at pH extremes, support for ion exchange chromatography because of its stability and rigidity

- Polyacylamide- used less often, not used as a polymer solid but as hydrogel and used as a sixe exclusion gel

- The crosslinking in polyacrylamide can be controleed by the amount of bisacrylamide added in suspension mixture

- Natural polymers such as agarose and dextran are also used in hydrogel for a low pressure chromatography resins.

- Naturally hydrophillic and compatible with protein and other biomaterials

- Agarose – can be crosslinked tp fprm a reasonably rigid bead that is capable of tolerating pressures up to 4 bar.

- Dextran- less rigid and used in size excluseion, can be formed with very large pores, capable of including antibody molecules and virus particles

- Both polymers have been derivatized with ion exchange groups, phenol groups, antibodies, dyes, heavy metals, and other biological epitopes that are allow very specific binding behavior for the target molecule

Adsorbent TypesAdsorbent Types

Ion Exchange ResinsAdsorbent TypesAdsorbent Types

- Resins that have been derivatized with an ionic group- most commonly used ionic groups ( listed in order of increasing pK): sulfoxyl (SO3

-) ( most acidic), caboxyl (COO-), diethylaminoethyl (DEAE) (2C2H5N+HC2H5), and quaternary ethylamine (QAE) (4C2H5N+)( most basic)- Acidic acid exchangers carry a negative charge and attract positive counterions – called cation exchangers- conversely the basic ion exchangers and known as anion exchangers- sulfoxyl and QAE – strong acid and strong base – pK values are close to 1 and 14 – for all practical purposes, they are fully ionized at all pH values-carboxyl and DEAE – weak acid and base – pK values closer to 4 and 10 – used in a pH gradient to ionize more or fewer of the ionic groups on the resin, thus can effecting the separation -almost used in aqueous mobile phases, almost always polymer resins.

- Water is universal solvents for salts, which dissociate poorly in most organic solvents

- To generate ion exchange resins, extreme pH values are used

- Used to separate small amount – used in separation of proteins, peptides, nucleic acids, small polynucleotides, other small molecules such as antibiotics

- Proteins – have distinct isoelectric points based on the content and conformation of their charged

- Have multiples charges and can be separated based on their number of charges, as well as the sign of the charge and sometimes charge heterogeneity

- Nucleic acids – have a charge at each base, bind very well to anion exchangersn and not to all to cation exchangers

- Once bound to anion exchange column, nucleic acids are very difficult to elute in an aqueous solution that does not simultaneously degrade them

- Selection of the buffer – not interact with the adsorbent, which means that the charged from of the buffer should have the same sign as the charge on the adsorbent

- Preferably only simple anions used in anion exchange ( e.g., Cl-, acetate-) and only simple cations (e.g., Na+, K+) in cation exchange

Adsorbent TypesAdsorbent Types

Ion Exchange Chromatography

• In this type of chromatography, the use of a resin (the stationary solid phase) is used to covalently attach anions or cations onto it.

• Solute ions of the opposite charge in the mobile liquid phase are attracted to the resin by electrostatic forces.

Reverse-Phase Chromatography

- Employs a hydrophobic phase bonded to the surface of the resin – typically silica based

- The partitioning of solutes between the mobile phase and stationary phase opposite to bare silica – hydrophobic solutes bind in higher proportion in reversed phased, and hydrophillic solutes bind in higher proportion in normal phase

- Solutes : water, or with minimal amounts of organic solvent – most solutes partition to stationary phase

- Hydrophobic phases that are bonded to silica are typically actyil (C8), actyldecyl (C18), phenyl, and methyl (C1)

- the different chain lengths and densities of the different bonded phases lead to more or less hydrophobicity

- Bare silica participate in separation by interacting with hydrophilic molecules, or hydrophilic domains of large molecules

- Ion did not partition well in hydrophobic phases – a counterion must be choose

Adsorbent TypesAdsorbent Types

Reversed- Phase Reversed- Phase ChromatographyChromatography

• This form of chromatography is based on a thin film formed on the surface of a solid support by a liquid stationary phase.

• Solute equilibrates between the mobile phase and the stationary liquid.

Hydrophobic Interaction ChromatographyAdsorbent TypesAdsorbent Types

-typically used for protein separations-Employs derivatized polymer resins, with phenyl, butyl, or octyl ligand groups-Protein adhere to the hydrophobic surface under high salt conditions and redissolve into the mobile phase as the salt concentration is reduced-differs from reversed phase in that the mobile phase is kept aqueous (polar), and the salt concentration is used to effect the partitioning to the surface

-sensitive to pH, salt used, buffer type, and temperature – must be carefully controlled to achieved reproducible separation but also represent an opportunity for increased selectivity

Affinity Chromatography-effect binding of specific solutes-Antibodies, antigens, or dyes are conjugated to polymer resin for the purpose of binding specific from a mixture-for example, the antibody conjugated to a resin, usually via cyanogen bromide activation, captures the solutes out of the mixture, impurities flow through the column, solute recovered by changing the pH, increasing the salt concentration, or adding a displacer-used from small scale research to large scale production

Affinity Chromatography

• This is the most selective type of chromatography employed. It utilizes the specific interaction between one kind of solute molecule and a second molecule that is immobilized on a stationary phase.

• For example, the immobilized molecule may be an antibody to some specific protein.

• When solute containing a mixture of proteins are passed by this molecule, only the specific protein is reacted to this antibody, binding it to the stationary phase.

• This protein is later extracted by changing the ionic strength or pH.

Immobilized Metal Affinity Chromatography (IMAC)Adsorbent TypesAdsorbent Types

-Some proteins have high affinities for specific metals - may either be structural, or based on the content of specific amino residues -to immobilize metal ions with spacer arms onto polymer resins (IMAC resins)-Used to purify proteins that have one of two characteristics mentioned above-apply in genetic engineering

Size Exclusion Chromatography (SEC)-also called gel filtration chromatography – separates solutes on the basis of their size-no derivatization of the polymer gel, no binding between the solutes and the resin-molecules larger than the largest pores in the gel cannot enter the gel and are eluted first, smaller molecules enter the gel to varying extents, depending on their size and shape, and retarded on their passage through the bed- resins are hydrophilic polymer gels with a broad distribution of pore sizes-used for changing buffers, or for removing small molecules from protein solution

Size Exclusion ChromatographySize Exclusion Chromatography

• Also known as gel permeation or gel filtration, this type of chromatography lacks an attractive interaction between the stationary phase and solute.

• The liquid or gaseous phase passes through a porous gel which separates the molecules according to its size.

• The pores are normally small and exclude the larger solute molecules, but allows smaller molecules to enter the gel, causing them to flow through a larger volume.

• This causes the larger molecules to pass through the column at a faster rate than the smaller ones.

Oven

Detector

Injection port

Nitrogen cylinder

Column

Recorder

Particle Size and Pressure Drop Particle Size and Pressure Drop in Fixed Bedsin Fixed Beds

• Pressure drop is given by the Darcy equation:

• Δp = pressure drop over column length L; µ = viscosity of the mobile phase; v = superficial velocity; k = constant

• From Blake-Kozeny equation, k gives a function of resin particles size and void friction

• Darcy equation applies for rigid particles, such as silicas• When the stationary phase particle size is decreased, the pressure drop in the column

increases as the inverse square• These increases requires pressure additional power in pumping, as well as more specialized

requirements for the construction of the columns and its seals• The smallest particle sizes creates inlet pressures of several hundred bars of pressure • Seals and columns that contains these pressures are typically narrow bore, since a small radius

of curvature is more effective for holding pressure that a large radius• The column end pieces must contain the particles without plugging that can be caused by

caused by resin particles or fragments of particles generated through attrition• To retain binding capacity, the same resin volume must be used.• The smaller particle may be packed in short, flat beds, resembling pancakes, while larger

particles can be accommodates in long tubes

(26)

(27)

EquipmentEquipmentColumns

-cylindrical, vertical vessels design to contain resin particles between 2 and 10 µm in diameter-fluid is pumped downflow through chromatography columns, since air trapped beneath a column can cause voids that are ruinous for resolution -frit of netting, is critical for design of the columns-held in place by the end fittings on the column, often between gaskets, or incorporated into gaskets

-Critical at both the inlet and outlet of the column and serves as a filter of last resort on the column inlet and holds the resin in place in the event the column is back-flushed-the columns comes in three basic types: fixed bed height, variable bed height, axial compression

Fixed bed : used when a process is mature and the columns can be dedicated-fixed bed is a tube that is fixed directly to end fitting-threaded fitting are used on the analytical and preparative scales (up to 10 cm diameter); flanged connection are used for larger diameters-also used for analytical high performance liquid chromatography

Variable or adjustable beds : commons in pilot plants and development settings-typically a tube that fits outside diameter of the end fittings-the end fitting consist of two flat plates sandwiching a gasket-when the end pieces are in place, the flat plates are compressed together, squeezing the gasket out against the tube

-axial compression columns : principally used for large-scale HPLC

-using hydraulic pistons as the inlets piece that compress the resin along

the length of the column

-not only causes the column to achieve the highest possible packing density,

but also holds the resin in place as the action of the pump causes pressure

pulse to wash through the column

EquipmentEquipment

Chromatography Column Packing Procedures- Three objectives in packing the column:i. To have the resin particles fully wetted- Resin is slurry packed – allows the resin to be in full contact with a solvent for an indefinite time prior to packing- At small scale, the resin is actively degassed, by sonication, vacuum or heat.- On large scales, solvents such as ethanol that have high oxygen solubilities can be used to wet the particlesii. To have the particles fully disassociated from one another- Ensure the particles do not clump or form aggregates that can cause segregation during packing- Solvent such as isopropanol are often added to the slurry – decreases the surface tension sufficiently to allow particles to deaggregate- Other agents, such as buffer salts, are sometimes used to effect particle-particle repulsive forcesiii. To achieve the highest possible packing density- chemically, particles should be in their least swollen state- High ionic strength is used to contract the particles- Mechanically, the particles should be packed quickly to deprive the slurry of the opportunity to settle and segregate according to particle size – packed at or above the highest pressure conditions expected for column during normal processing

- The inlet fitting should be placed as quickly and as evenly as possible – no biases in bed

height and the pressure developed in the bed is captured mechanically in the seals

Detectors

EquipmentEquipment

- to match the molecules in the application- almost any detection method can be adapted to chromatography, from Fourier transform infrared spectroscopy to antibody conjugation techniques to mass spectroscopy with the most common are pH, conductivity and light absorbance- conductivity and pH : to check the performance of the gradient, the loading of the column, the regeneration, reequilibration- Light absorbance (280, 254, 229, 214 nm, depending on the application) : used to monitor the effluent for evidence of the target molecules- Other common detection methods in use in large-scale chromatography: refractive index, electrochemical detection, light scattering

Chromatography system fluidics-For column efficiency and reproducibility. Pumps and tubing are the most important-Pumps: typically positive displacement pumps – have a low shear, so do not pose a problem for sensitive biomolecules-comes in two varieties: peristaltic and rotary lobe-Gradient makers: the gradient formed by the pump(s) selecting more or less volume from each reservoir as time progresses

ScaleupScaleup• Chromatography scaleup algorithms accounts for changes in bed height and

diameter, linear and volumetric flow rate and particle size.

• Yamamoto et al. have developed the following proportionality for resolution, Rs, of proteins in linear gradient elution ion exchange chromatography and hydrophobic interaction chromatography:

Dm = diffusion coefficient of the protein in solution; L = column length; g = slope of the gradient (change in concentration of gradient per volume of gradient); V = column volume; V0 = column void volume; u = interstitial fluid velocity; dp = particle diameter

• To remove the volume terms from the expression for resolution, the definitions can be made:

Q = inlet flow rate; ε = column void friction; A = column cross-sectional area

• These substitutions lead to:

(28)

(29)

(30)

(31)

• Thus, for scaleup with constant resolution from scale 1 to scale 2 for the same product and the same column void fraction, the scaleup equation is:

• Thus, as the particle size increases on scaleup, the flow rate relative to the column volume must decrease and/or the gradient slope must decrease to maintain constant resolution, which seems correct intuitively.

• In practice only the ration between column volume and flow rate need be addressed because easy to develop lab scale processes that use the same resin and same gradient that can be used at the commercial process scale

• When the bed height can be maintained on scaleup, the mobile phase linear velocity remains the same, and the column is simply scaled by diameter.

ScaleupScaleup

(32)

(33)

Example 4Example 4Scaleup of a Protein Chromatography

A column 20 cm long, with an internal diameter of 5 cm, gives sufficient purification

to merit scaleup. The column produces 3.2 g of purified protein per cycle, and a

cycle takes 6 h, from equilibration through regeneration. You want a throughput of

10 g/h. What are the new column’s dimensions if linear velocity is held constant?

Solution

As just discussed, for scaleup when the linear velocity is held constant, the

column diameter is increased, and the column height is maintained the same. If

the linear flow rate is held constant, then the cycle time cannot be altered. Thus,

the scaled up column must produce 6 h/cycle x 10g/h = 60g/cycle. Since the flow rate

is proportional to the throughput of protein,

From Equation (33), the scaleup relationship when the gradient and the particle size

are not changed upon scaleup, and since L1= L2,

where D1 and D2 are the column diameters for columns 2 and 1, respectively. Since

D1 = 5.0 cm, we obtain

Note that:

• it is not always necessary to scale according to bed diameter.

• The flow rate may be normalized against the volume of the empty column, to give units of time.

• column bed height may be increased or decreased, depending on the requirements of pressure drop and mechanical seals. A shaIlower bed gives a lower linear velocity and a wider diameter. A deeper bed gives a higher linear velocity (and higher pressure drop) and a proportionally narrower bed diameter.

Example 4Example 4

Example 5Example 5Scaleup of Protein Chromatography Using Standard Column Sizes

Consider the case given in Example 4. Available standard column diameters are

20 and 25 cm. What flow rates and bed depths would apply to each of these columns?

Solution

The column volumes for both columns are still 18.75 times that used in the laboratory

column. Thus,

For a column 20 cm in diameter,

and for column the 25 cm in diameter,

Note that:

• the gradient is also expressed in column volumes.

• The total gradient volume, that is, the total volume of eluent used to go from the

leanest mobile phase condition to the richest, is expressed in terms of column volumes, and this is held constant on scaleup.

Example 6Example 6Scaleup of Elution Buffer Volumes in Protein Chromatography An NaCl gradient is used to elute the product in Example 4. The gradient increases from 100 mM NaCl to 250 mM in 3 h. To form this gradient a 100 mM NaCl solution is combined with a 250 mM NaCl solution in a gradient mixer, in which the 100 mM NaCl solution is mixed (see Figure). The flow rate is 40 ml/min. What volumes of low salt and high salt eluent should be made for the scaleup column with an internal diameter of 20 cm?SolutionThe small-scale volume of each gradient buffer is 3.6 liters (40 ml/min x 180 min/2). The scaleup factor of 18.75 still applies, so that

Volume of each buffer at large scale (18.75) (3.6 liters) = 67.5 liters

Suppose that in development, the product elutes in 60% of the gradient volume. Thegradient may be truncated to save time and buffer volume. From Equation (33), thegradient can be adjusted according to:

chi and clow = concentrations of the high strength and low strength buffers; Vg = total gradient volume

(35)

Example 7Example 7Consideration of Pressure Drop in Column

Scaling Determine the minimum diameter possible for the columns analyzed in

Example 5 and subject to the flow rate given in Example 6, when the column

pressure should not exceed 300 kPa (28.8 psig), the maximum solution viscosity is

1.1 cp, and the void fraction in the column is 0.35. The resin particle size is 100 µm.

Solution

Pressure drop can be calculated using Darcy’s law [Equation 26] by knowing µ, v, k

and L. We can calculate k from the Blake—Kozeny equation (27):

The column volume must be 7359 ml (from Example 5), and the flow rate is 40 ml/min

(from Example 6) times the scaleup factor of 18.75 (= 750 ml/min). We calculate

the pressure drop for the column 20 cm in diameter and 23.4 cm in length, which

would give the higher pressure drop of the two standard column sizes (20 and 25 cm):

From Equation (26) the pressure drop is

Thus, the standard 20 cm diameter column would operate at well below the

maximum allowable pressure.

Example 7Example 7