Field flow fractionation

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 (1).

${\displaystyle c=c_{0}e^{\frac {-x}{\ell }}}$

(1)

${\displaystyle \ell }$ 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 ${\displaystyle \ell }$ is different for the particle populations separation will occur. The ${\displaystyle \ell }$ 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.[13]

${\displaystyle \ell ={\frac {kT}{F}}={\frac {D}{U}}}$

(2)

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:

${\displaystyle t_{r}={\frac {L}{V}}}$

(3)

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 (emergence of a non retained tracer) divided by the retention time t_r. The retention equation then becomes:

${\displaystyle R={\frac {t_{0}}{t_{r}}}=6\lambda [\operatorname {coth} ({\frac {1}{2\lambda }})-2\lambda ]}$

(4)

where ${\displaystyle \lambda }$ is ${\displaystyle \ell }$ divided by w, the channel thickness or height. Substituting kT/F in place of ${\displaystyle \ell }$ illustrates the retention ratio with respect to the cross force applied.

${\displaystyle R=6{\frac {kT}{Fw}}[\coth({\frac {Fw}{2kT}})-2{\frac {kT}{Fw}}]}$

(5)

For an efficient operation the channel thickness value w far exceeds ${\displaystyle \ell }$. When this is the case the term in the brackets approaches unity. Therefore, equation 5 can be approximated as:

${\displaystyle R=6\lambda =6{\frac {kT}{Fw}}}$

(6)

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.

Of these techniques flow FFF was the first to be offered commercially. Flow FFF separates particles based on size, independent of density and can measure macromolecules in the range of 1 nm to 1 μm. In this respect it is the most versatile FFF sub-technique available. The cross flow in Flow FFF enters through a porous frit at the top of the channel, exiting through a semi-permeable membrane outlet frit on the accumulation wall (i.e. the bottom wall). Symmetrical flow has been replaced by asymmetrical flow in the last two decades.

Hollow fiber flow FFF (HF5) was developed by Lee et al. (1974).[14] HF5 has been applied towards the analysis of proteins and other macromolecules. HF5 was the first form of flow FFF to be developed in 1974. The advantage is that HF5 offers a disposable channel unit which can be readily replaced in routine applications. One of the drawbacks of HF5 is the limited choice of membrane materials; only polyether sulfone (PES) membranes are available. Currently, HF5 is not widely used, because of the lack of flexibility and limitations in sample load.

Asymmetric flow FFF (AF4), on the other hand, has only one semi-permeable membrane on the bottom wall of the channel. The cross flow is, therefore, created by the carrier liquid exiting the bottom of the channel. This offers an extremely gentle separation and an “ultra-broad” separation range. The majority of FFF instruments in use are AF4 systems. Main applications are in pharmaceutical research and development for proteins, virus and virus-like particles, and liposomes. AF4 can be applied in aqueous and organic solvents, therefore also organic polymers can be separated by this technique.

High Temperature Asymmetric Flow Field-Flow Fractionation is available for the separation of high and ultra-high molar mass polymers soluble at temperatures above 150 C.

Thermal FFF, as the name suggests, establishes a separation force by applying a temperature gradient to the channel. The top channel wall is heated and the bottom wall is cooled driving polymers and particles towards the cold wall by thermal diffusion. Thermal FFF was developed as a technique for separating synthetic polymers in organic solvents. Thermal FFF is unique amongst FFF techniques in that it can separate macromolecules by both molar mass and chemical composition, allowing for the separation of polymer fractions with the same molecular weight. Today this technique is ideally suited for the characterization of polymers, gels and nanoparticles.

One of the major advantage of Thermal FFF is the simple and very well defined dimensions of the separation channel, which makes the inter-lab or inter-instrument Universal Calibration possible because the Thermal FFF calibration constants closely describe the ratio of ordinary (molecular) diffusion coefficient D to thermal diffusion coefficient (or, thermophoretic mobility) D_T which are only polymer dependent. The ThFFF Universal Calibration is, therefore, instrument and lab transferable, while the well-known size exclusion chromatography Universal Calibration is polymer-transferable on the same instrument only.[15]

Split flow thin-cell fractionation (SPLITT)[16] is a special preparative FFF technique, using gravity[17] or electric,[18] or diffusion differences for separation of over μm-sized particles on a continuous basis. SPLITT system has two inlets and two outlets. It is performed by pumping the sample immerse in a liquid into one inlet at the start of the channel at low flow-rate, whilst simultaneously pumping a carrier liquid into the second inlet at much higher flow-rate. By controlling the flow rate ratios of the two inlet streams and two outlet streams, the separation can be controlled, and the sample components are separated into two distinct sized fractions. The use of gravity alone as the separating force makes SPLITT the least sensitive FFF technique, limited to particles above 1 μm.

In centrifugal FFF, the separation field is generated via a centrifugal force. The channel takes the form of a ring, which spins at rotation speeds which can be programmed during the run. The flow and sample are pumped into the channel and centrifuged, allowing the operator to resolve the particles by mass (size and density). The advantage of centrifugal FFF lies in the high size resolution that can be achieved by varying the force applied, since particle size is proportional to particle mass to the third power.

The unique advantage presented by centrifugal FFF comes from the techniques capability for high resolution given sufficient buoyant density. This allows for the separation of particles with only a 5% difference in size.

Centrifugal FFF has the advantage that particles and macromolecules can be separated by particle density, rather than just particle size. In this instance, two identically sized gold and silver nanoparticles can be separated into two peaks, according to differences in density in the gold and silver nanoparticles,

In AF4 separations, the ratio of mass to time is 1:1. With the addition of the third parameter of density to centrifugal FFF, this produces a ratio more akin to mass:time to the power of three. This results in a significantly larger distinction between peaks and result in a greatly improved resolution. This can be particularly useful for novel products, such as composite materials and coated polymers containing nanoparticles, i.e. particles which may not vary in size but which do vary in density. In this way two identically sized particles can still be separated into two peaks, providing that the density is different.

The limitation of the method lies in the lower limit of size which depends on the density of the sample. Specifically for biological samples, the limit is in the order of 20 to 50 nm in diameter.

In electrical FFF a transverse electrical current (DC) is applied which creates an electric field. Depending on the charge of sample components, an electrophoretic drift velocity is induced, counteracted by the diffusion from Brownian motion, so the separation depends on the ratio of electrophoretic mobility and size. Application of electrical FFF has been limited and is currently rarely used. Other modifications have been developed, namely cyclical electrical FFF where a special alternating current is applied. It allows to separate according to electrophoretic mobility. Another variation is electrical asymmetrical flow FFF (EAF4), where an electrical field is applied in addition to a cross flow field. EAF4 overcomes the limitation of pure electrical FFF which has poor resolution and suffers from electrolysis products and bubbles contaminating the channel outflow and compromising the detector signals.[19]