Thermal FFF

THERMAL FFF Various synthetic polymers Crude oils and asphaltenes 

FFF Rolgl ren latex beads Viruses Prgejns SDS-protein complex Sulfonated polystyrenes N oj crylic acids 

Thermal field-flow fractionation (TFFF) belongs to the historically oldest subtechniques of FFF. It is based on the principle of thermal diffusion. In early works 

The subsequent study was oriented at the theoretical explanation of the factors that cause and affect zone spreading in TFFF [31]. Contributions of non-equilibrium and polydispersity of polymer samples under study to the total peak width were studied, as was the possibility of determining the precise polydispersity of the polymer by measuring peak width at various linear velocities of the solvent, and by extrapolating to zero velocity, i.e., by eliminating the contribution of non-equilibrium processes [32]. An improved separation in TFFF can be obtained by using 

Thermal FFF (ThFFF) is obtained by placing the channel between two heat conductive blocks that are temperature controlled. One block usually contains a heating element and the other a circulating coolant. A temperature difference of 100 K on a 100 pm wide channel is equal to 10 Kmm .  

This equation, combined with Equation 8.1, tells us that the retention of the smaller particles is less than that of the larger ones and that the field strength is a function of the temperature difference. However, retention times are difficult to calculate because Dx values are not easily available. 

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The most common, and commercially available, FFF variants are flow FFF (FIFFF), sedimentation FFF (SdFFF), and thermal FFF (ThFFF). These techniques are described in greater detail... 

Clearly, sedimentation FFF is a separation technique. It is an important member of the field-flow fractionation (FFF) family of techniques. Although other members of the FFF family (especially thermal FFF) are more effective for polymer analysis, sedimentation FFF is advantageous for the separation of a wide assortment of colloidal particles. Sedimentation FFF not only yields higher resolution than nearly all other particle separation techniques, but its simple theoretical basis allows a straightforward connection between observed particle migration rates and particle size. Thus size distribution curves are readily obtained on the basis of theoretical analysis without the need for (and uncertainties of) calibration. 

Excluded from this list is sieving, to which the concept of selectivity is not applicable. For completeness, we have subdivided the FFF family into sedimentation FFF, thermal FFF, flow FFF, and steric FFF to show how the selectivity of each of these subtechniques compares to that of the other fractionation methods. The values reported here differ from S values reported elsewhere (12), which refer to mass rather than size selectivity. 

This review will introduce the basic principles, theory, and experimental arrangements of the various FFF techniques focusing on the most relevant for praxis Sedimentation-FFF (S-FFF),Thermal-FFF (Th-FFF) and Flow-FFF (Fl-FFF). In a second part,selected applications of these techniques both to synthetic and biological samples will illustrate applications under a variety of conditions, where problems and potential pitfalls as well as recent developments are also considered. 

FFF techniques were pioneered by Giddings in 1966 [1]. Starting from this point, a remarkable development has taken place resulting in a diversity of different FFF methods. Figure 1 gives an overview of the different techniques with their time of invention. The number of different methods is directly related to the variety of force fields which can be applied for the separation of the samples. Practically, only three of those FFF methods are commonly used and commercially available at the present time namely sedimentation-FFF (S-FFF), flow-FFF (Fl-FFF) and thermal-FFF (Th-FFF). The range of possible techniques was established in the early years whereas the main development of the last years is seen in a continuous optimization of the methodology and the instrumentation. This becomes most evident for the case of flow-FFF, where an asymmetrical channel with better separation characteristics has been developed. 

Thermal-FFF. The retention rate directly yields the Soret coefficient DT/D. If D is known (for example from flow-FFF), the thermal diffusion coefficient DT can be obtained which can give information about the chemical sample composition. Unfortunately, no context is known which analytically relates DT with the sample composition [84]. On the other hand, for known DT values (material constant), the diffusion coefficient distribution is directly obtained. 

Flow FFF and Thermal FFF have been used as complementary techniques in a study of core shell latex particles. Flow and sedimentation FFF have been used to determine the size and density of core shell particles and the shell thickness and particle density as a function of pH... 

In addition to molecular weight, thermal FFF is used to measure transport coefficients. For example, the measurement of thermodiffusion coefficients is important for obtaining compositional information on polymer blends and copolymers (see the entry Thermal FFF of Polymers and Particles). Thermal FFF is also used in fundamental studies of thermodiffusion because it is a relatively fast and accurate method for obtaining the Soret coefficient, which is used to quantify the concentration of material in a temperature gradient. However, the accuracy of Soret and thermodiffusion coefficients obtained from thermal FFF experiments depends on properly accounting for several factors that involve temperature. In order to understand the effect of temperature on transport coefficients, as well as the effect on thermal FFF calibration equations, a brief outline of retention theory is given next. 

In all FFF subtechniques, retention depends on a balance of two opposing motions. The first motion is induced by the applied field and results in the concentration of material at the accumulation wall (typically, the cold wall in thermal FFF). The buildup in concentration induces the opposing motion of diffusion. Both motions are accounted for in the retention parameter A, which is defined for all FFF subtechniques as... 

Here, D is the (mass) diffusion coefficient, U is the field-induced velocity of the sample, and w is the channel thickness. In thermal FFF, U is governed by the thermal diffusion coefficient i r) and the temperature gradient (dT/dx), which is applied in the same dimension (x) as the channel thickness (x varies in value from 0 at the cold wall to w at the hot wall). Using the dependence of U on Dj and dT/dx, the retention parameter in thermal FFF can be expressed as... 

Here, V° is the volume of fluid required to flush a sample that is not affected by the field (U = 0). In most FFF subtechniques, the parameters in Eq. (1) are, in fact, constant throughout the channel. In thermal FFF, however, these parameters vary across the channel because they depend on temperature, which varies between the hot and cold walls. As a result, Eq. (3) is only an approximation in thermal FFF. Fortunately, the approximations associated with Eq. (3) are inconsequential for the determination of molecular-weight distributions, so that the only concern is variations in T, as outlined earlier. For measuring transport coefficients, on the other hand, the approximations can lead to significant errors. 

The consequences of the temperature dependence of 7j, K, D, and have been discussed in several articles [3-6], Ko et al. [3] demonstrated that the temperature dependence of the Soret coefficient actually increases the resolution of different molecular-weight components. In a theoretical study by van Asten et al. [4], it was shown that the consequence of ignoring the temperature dependence of k has a nearly negligible effect on the accuracy of D/D values calculated using Eqs. (2) and (3). Ignoring the temperature dependence of 7] and D/Dt, on the other hand, can lead to errors of up to 8% when DIDj values are calculated from retention data. Several refinements to Eq. (3) have been made over the years [2,5,6], When these refinements are used, they yield accurate values for the transport coefficients. Although the resulting equations are quite complex, they are not required for the routine analysis of polymers by thermal FFF. 

The understanding of the effects of sample concentration (sample mass) in field-flow fractionation (FFF) has being obtained gradually with the improvement of the sensitivity (detection limit) of high-performance liquid chromatography (HPLC) detectors. Overloading, which was used in earlier publications, emphasizes that there is an upper limit of sample amount (or concentration) below which sample retention will not be dependent on sample mass injected into the FFF channels [1]. Recent studies show that such limits may not exist for thermal FFF (may be true for all the FFF techniques in polymer separation), although some of the most sensitive detectors on the market were used [2]. 

A continuous-viscosity detector has been shown to be a good detection tool for thermal FFF analysis of polymer solutions [8]. Due to the high sample dilution in FFF, the viscosity detector response above the solvent baseline, AS, is only dependent on the intrinsic viscosity of every sample point, [17], multiplied by the concentration, c, at the corresponding points ... 

Thermal FFF was the first experimentally implemented method [9]. It is used mostly for the fractionation of macromolecules. The temperature difference between two metallic bars, forming the channel walls with highly polished surfaces and separated by a spacer in which the channel proper is cut, produces the flux of the sample components, usually toward the cold wall. The channel for thermal FFF is shown in Fig. 2b. The relation between A and the operational variables is given by... 

Molecular Weight and Molecular-Weight Distributions by Thermal FFF... 

In thermal FFF, the applied held is a temperature drop (AT) across the channel, and the physicochemical parameter that governs retention is the Soret coefficient, which is the ratio of the thermodiffusion coefficient Dj) to the ordinary (mass) diffusion coefficient D). Because AT is set by the user, retention in a thermal FFF channel can be used to calculate the Soret coeffident of a polymer-solvent system. 

In order to calculate the molecular weight M) or molecular-weight distribution (MWD) of the polymer, the dependence of the Soret coefficient on M must be known. Because is virtually independent of M, at least for random coil polymers, the dependence of retention on M reduces to the dependence of D on M. The separation of molecular-weight components by D (or hydrodynamic volume, which scales directly with D) is a feature that thermal FFF shares with size-exclusion chromatography (SEC). In the latter technique, the dependence of retention on D forms the basis for universal calibration, as D scales directly with the product [rjjM, where [17] is the intrinsic viscosity. Thus, a single calibration plot prepared in terms of log([i7]M) versus retention volume (F,) can be used to measure M for different polymer compositions, provided an independent measure of [17] is available. In thermal FFF, a single calibration plot can only be used for multiple polymers when the values of for each polymer-solvent system of interest are known. However, a single calibration plot can be used with multiple channels. In... 

The difference between and b can be explained by the fact that components of different M experience different temperatures as they separate in the thermal FFF channel [1]. 

Once the calibration constants and n have been determined for a given polymer-solvent system, Eq. (4) can be used for all thermal FFF channels, provided the temperature of the cold wall (T ) is held constant. The cold-wall temperature affects the calibration plot because the Soret coefficient DjID) and, therefore, varies with T. For a detailed discussion of temperature effects see the entry Cold-Wall Effects in Thermal FFF. In a thorough study of temperature effects, Myers and co-workers [3] demonstrated that the dependence of the Soret coefficient on can be accurately modeled by... 

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