Field flow fractionation

Field-flow fractionation, abbreviated FFF, is a separation technique invented by J. Calvin Giddings. The technique is based on separation of colloidal or high molecular weight substances in liquid solutions, flowing through the separation platform, which does not have a stationary phase. It is similar to liquid chromatography, as it works on dilute solutions or suspensions of the solute, carried by a flowing eluent. Separation is achieved by applying a field or cross-flow, perpendicular to the direction of transport of the sample, which is pumped through a long and narrow laminar channel. The field exerts a force on the sample components, concentrating them towards one of the channel walls, which is called accumulation wall. The force interacts with a property of the sample, thereby the separation occurs, in other words, the components show differing "mobilities" under the force exerted by the crossing field. As an example, for the hydraulic, or cross-flow FFF method, the property driving separation is the translational diffusion coefficient or the hydrodynamic size. For a thermal field, it is the ratio of the thermal and the translational diffusion coefficient.

Applications and detection methods

FFF is applicable in the sub-micron range in the "normal" mode or up to 50 microns in the so-called steric mode. The transition from normal to steric mode takes place when diffusion becomes negligible at sizes above a micron. FFF is unique in its wide dynamic range of sizes covering both soluble macromolecules and particles or colloids which can be separated in one analysis.
Typical applications are high molar mass polymers and polymer composites, nanoparticles, both industrial and environmental, viruses and virus like particles, lipid nanoparticles, extracellular vesicles and other types of biological samples.
FFF can be coupled to all types of detectors known, from high-performance liquid chromatography to size-exclusion chromatography. Due to FFF's similarity to liquid chromatography, a liquid mobile phase passing through the channel, the most common detectors are those that are also used for liquid chromatography. The most frequently used is an ultraviolet-visible spectroscopy detector, because of its non-destructive nature. Coupling with multi angle light scattering which allows the calculation of the size of eluting fractions and comparison to values obtained via FFF theory. Another popular detector is inductively coupled plasma mass spectrometry to characterize metallic nanoparticles with high specificity and sensitivity.

Advantages

FFF offers a physical separation of complex and inhomogeneous samples, which potentially cannot be characterized by other separation methods, such as size-exclusion chromatography. Because there is no stationary phase, there is less interaction with surfaces or column packing materials. The separation is tunable by modulating the strength of the separation field. FFF is a gentle method and does not exert physical stress on fragile samples, and the carrier solution can be tailored in view of best sample stability. FFF has a well worked-out theory, which can be used to find separation conditions to reach the optimal result, without a series of trial-and-error experiments. It is also possible to extract information of physical parameters of sample fractions from the FFF theory, although almost all users depend mostly on light scattering detectors to measure the size of eluting sample fractions.

Limitations

FFF does not work for small molecules, because of their fast diffusion. For an effective separation, the sample has to be concentrated very close to the accumulation wall, which requires the drift velocity caused by the force field to be two orders of magnitude higher compared to the diffusion coefficient. The maximum field strength which can be generated in an FFF channel determines the lower size range of separation. For current instrumentation this is approximately 1 nm.
Although FFF is an extremely versatile technique, there is no "one size fits all" method for all applications. Different FFF methods need specialized instrumentation. Currently only the so called asymmetric flow field-flow fractionation has gained wide-spread use. Other methods like centrifugal, thermal or electrical FFF still have a niche existence.
FFF behaves differently from column chromatography and can be counter-intuitive for HPLC or SEC users. Understanding of the working principle of FFF is vital for a successful application of the method.

Discovery and general principles

FFF was devised and first published by J. Calvin Giddings in 1966 and in 1976. Giddings had published many articles on flow-FFF which is the most important FFF technique today. Giddings, credited for the invention of FFF, was professor of chemistry and specialist of chromatography and separation techniques at the University of Utah.
As mentioned above, in field-flow fractionation the field can be hydraulic, gravitational, centrifugal, thermal, electrical, or magnetic. In all cases, the separation mechanism is produced by differences in particle mobility under the forces of the field, in a stationary equilibrium with the forces of diffusion: The field induces a downward drift velocity and concentration towards the accumulation wall, the diffusion works against this concentration gradient. After a certain time the two forces equilibrate in a stationary equilibrium. This is best visualized as a particle cloud, with all components in constant motion, but with an exponential decrease of the average concentration going away from the accumulation wall up into the channel. The decrease of air pressure going up from sea level has the same exponential decrease which is described in the barometric formula. After relaxation has been achieved, elution starts as the channel flow is activated. In the thin channel a parabolic laminar-flow-velocity profile exists, which is characterized by a strong increase of the flow velocity with increasing distance from the accumulation wall. This determines the velocity of a particular particle, based on its equilibrium position from the wall of the channel. Particles closer to the accumulation wall will migrate slower compared to others being higher up. The ratio of the velocity of a species of particle to the average velocity of the fluid is called the retention ratio R. In FFF for efficient separation, R needs to be below 0.2, typical values are in the range of 0.02 to 0.1.

Theory and method

Separation in field flow fractionation takes place in a laminar channel. It is composed of a top and bottom block which are separated by a spacer. The spacer has a cut-out void, which creates the channel volume as the spacer is sealed between the blocks. Alternatively, the channel can be milled into the top block as a cavity. The channel is engineered in a way to allow the application of the force field, which means that for each FFF method a dedicated channel is needed. The sample is injected in a dilute solution or suspension into the channel and is separated during migration from inlet to outlet as the carrier solution is pumped through the channel. Downstream of the channel outlet one or several detectors are placed which analyze the eluting fractions.
Giddings and co-workers have developed a theory describing the general retention equation which is common to all FFF methods.

Relating force (F) to retention time (t_r)

The relationship between the separative force field and retention time can be derived from first principles. Consider two particle populations within the FFF channel. The cross field drives both particle clouds towards the bottom "accumulation" wall. Opposing this force field is the particles' natural diffusion, or Brownian motion, which produces a counter acting motion. When these two transport processes reach equilibrium the particle concentration c approaches the exponential function of elevation x above the accumulation wall as illustrated in equation.
represents the characteristic elevation of the particle cloud. This relates to the average height that the particle cloud reaches within the channel and only when the value for is different for the particle populations separation will occur. The of each component can be related to the force applied on each individual particle or to the ratio of the diffusion coefficient D and the drift velocity U.
k is the Boltzmann constant, T is absolute temperature and F is the force exerted on a single particle by the force field. This shows how the characteristic elevation value is inversely dependent to the force applied. Therefore, F governs the separation process. Hence, by varying the field strength the separation can be controlled to achieve optimal levels.
The velocity V of a cloud of molecules is simply the average velocity of an exponential distribution embedded in a parabolic flow profile.
Retention time, t_r can be written as:
Where L is the channel length.
In FFF the retention is usually expressed in terms of the retention ratio, which is the void time t₀ divided by the retention time t_r. The retention equation then becomes:
where is divided by w, the channel thickness or height. Substituting kT/F in place of illustrates the retention ratio with respect to the cross force applied.
For an efficient operation the channel thickness value w far exceeds. When this is the case the term in the brackets approaches unity. Therefore, equation 5 can be approximated as:
Thus t_r is roughly proportional to F. The separation of particle bands X and Y, represented by the finite increment ∆t_r in their retention times, is achieved only if the force increment ∆F between them is sufficient. A differential in force of only 10⁻¹⁶ N is required for this to be the case.
The magnitude of F and ∆F depend on particle properties, field strength and the type of field. This allows for variations and adaptations of the technique. From this basic principle many forms of FFF have evolved varying by the nature of the separative force applied and the range in molecule size to which they are targeted.