Linear mobile phase

In (1976) Horvath and Lin [8,9] introduced yet another equation to describe the value of(H) as a function of the linear mobile phase velocity (u). Again, it would appear... 

Figure 8. Graph of Variance per Unit Length against Linear Mobile Phase Velocity...

Thus, from equation (13) a value for (2X,dn) can obtained by plotting (H) against (1/Dm) for data that has been obtained at a constant linear mobile phase velocity... 

FIGURE 16.8 HPLC chromatogram of cytochrome c and myoglobin digest, using a 250 cm x 4.6 mm ODS C18 Vydac column and a linear mobile-phase gradient, 5-50% B, in 50 min. Buffer A was 0.1% TFA in water and buffer B was 0.1 TFA in acetonitrile. UV detection was carried out at 214 nm, at room temperature (reprinted with permission from Electrophoresis). 

Permeability is further influenced by the linear mobile phase velocity u (cm/s), mobile phase viscosity g (g/cms) and the length of the HPLC column (cm) ... 

Micro-HPLC operation sets special demands on the gradient instrumentation. As the internal column diameter, d, decreases, lower flow rates should be used at comparable mean linear mobile phase velocities, u = 0.2-0.3 mm/s. At a constant operating pressure, the flow rate decreases proportionally to the second power of the column inner diameter, so that narrow-bore LC columns with 1mm i.d. require flow rates in the range of 30-100pL/min, micro-columns with i.d. 0.3-0.5mm, flow rates in between 1 and lOpL/min, and columns with 0.075-0.1 mm i.d. flow rates in the range of hundreds nL/min. Special miniaturized pump systems are required to deliver accurately mobile phase at very low flow rates in isocratic LC. 

The lumped kinetic model can be obtained with further simplifications from the lumped pore model. We now ignore the presence of the intraparticle pores in which the mobile phase is stagnant. Thus, p = 0 and the external porosity becomes identical to the total bed porosity e. The mobile phase velocity in this model is the linear mobile phase velocity rather than the interstitial velocity u = L/Iq. There is now a single mass balance equation that is written in the same form as Equation 10.8. 

Equation (5) is a hyperbolic function which indicates that there will be a minimum value of (H) for a particular value of (u). That is a maximum efficiency will obtained at a particular linear mobile phase velocity. An example of an HETP curve obtained in practice is shown in figure 1. 

Thus, the approximate value of Hmin, for a well retained solute eluted from a well packed column and operated at the optimum linear mobile phase velocity, can be expected to be about 2.48dp, Furthermore, to the first approximation, this value will be independent of the nature of the solute, mobile phase or stationary phase. For the accurate design of the optimum columns lor a particular separation however, this approximation can not be made, nevertheless, the value of 2.48 for Hmin is a useful guide for assessing the quality of a column. 

The Van Deemter equation remained the established equation for describing the peak dispersion that took place in a packed column until about 1961. However, when experimental data that was measured at high linear mobile phase velocities was fitted to the Van Deemter equation it was found that there was often very poor agreement. In retrospect, this poor agreement between theory and experiment was probably due more to the presence of experimental artifacts, such as those caused by extra column dispersion, large detector sensor and detector electronic time constants etc. than the inadequacies of th Van Deemter equation. Nevertheless, it was this poor agreement between theory and experiment, that provoked a number of workers in the field to develop alternative HETP equations in the hope that a more exact relationship between HETP and linear mobile phase velocity could be obtained that would be compatible with experimental data. 

It is seen that the Golay equation produces a curve identical to the Van Deemter equation but with no contribution from a multipath term. It is also seen that, the value of (H) is solely dependent on the diffusivity of the solute in the mobile phase and the linear mobile phase velocity, It is clear that the capillary column can, therefore, provide a simple means of determining the diffusivity of a solute in any given liquid. 

Values for k were obtained using the retention time of hexamethyl benzene as to. Values for k e were obtained employing tne retention time of the completely excluded solute polystyrene (t(e)o) (Mol. Wt.83,000). t(e)o was also employed for the measurement of the linear mobile phase velocity. 

Comparing equations (1) and (2) it is seen that there is a significant difference between them, in that, only the Van Deemter equations should provide an (A) term that is independent of both the linear mobile phase velocity and the solute diffusivity. The fit of the Van Deemter equation to the experimental data confirms the former condition and the plot of the (A) term against the solute diffusivity, data taken from tables (1) and (2) and shown in figure 2 confirms the latter. 

It can be seen from equation (8) that, at the higher linear mobile phase velocities, the value of (H) depends on (Dm) taken to the power of 0.14 and inversely dependent on the coil aspect ratio and the linear velocity. According to equations (7) and (8) at low velocities the band dispersion increases with (u), whereas at high velocities the band dispersion decreases with (u). It follows that a plot of (H) against (u) should exhibit a maximum at a certain value of (H). By combining equations (7) and (8), an equation can be obtained (5), that predicts the value of (u) at which (H) is a maximum, and is given by,... 

The sample extracts that show either toxicity or no dose response on initial testing should be fractionated. An aliquot of the extract is solvent exchanged to acetonitrile, and an initial analytical scale separation is made to assess the distribution of constituents in the sample. This separation is accomplished by using a Qg reversed-phase system eluted for 45 min with a linear gradient of 0-100% acetonitrile in water. If >75% of the sample elutes after the solvent composition of 80% and 20% acetonitrile, then the fractions are isolated by preparative reversed-phase HPLC. Fraction A is eluted with 100% water fraction B is eluted with a linear mobile-phase gradient from 100% to 75% water and 25% acetonitrile fractions C, D, and E are eluted with gradients with final compositions of 50%, 75%, and 100% acetonitrile. 

Microcapillary (0.200 -s- 0.300 mm diameter) and nanocapiUary (0.075 -t- 0.100 mm diameter) columns limit solvent consumption and interface more easily with mass spectrometer detectors. They can assay only small amounts of sample and are superior for managing Joule heating due to their enhanced surface area to volume ratio and lower volumetric flow rate (uL/min) for a given linear mobile phase velocity (mm/sec). 

Fig. 5.11. Double logarithmic plot of the reduced plate height (h) versus the linear mobile phase velocity (u) in the chromatography of D,L-PA (100 nmol) on an L-PA MIP prepared using benzene as diluent at two different column temperatures. At 20°C k l a 6, k o 2.5. At 45°C k i 2.1, Ic d LO. Mobile phase MeCN/potassium phosphate buffer 0.05 M, pH 7 70/30 (v/v). From Sellergren and Shea [59].

Chromatographers have always used a velocity that is straightforward to calculate from chromatographic data, the linear mobile phase velocity or chromatographic velocity... 

Morbidelli et al. [41] discussed a numerical procedure for the calculation of numerical solutions of the GRM model in the case of an isothermal, fixed-bed chromatographic column with a multicomponent isotherm. These authors considered two different models for the inter- and intra-particle mass transfers. These models can either take into account the internal porosity of the particles or neglect it. They include the effects of axial dispersion, the inter- and intra-particle mass transfer resistances, and a variable linear mobile phase velocity. A generalized multicomponent isotherm, initially proposed by Fritz and Schliider [34] was also used ... 

The linear mobile phase velocity, u, is related to the column design and operating parameters by the following equation (Chapter 5, Section 5.3) ... 

Thicker columns require a pump that ensures a high flow rate, an identical linear mobile phase throughput and hence comparative retention times, being dependent on the flow rate, increasing with the square of the column diameter 1 ml min for a 4 mm i.d. column rising to 6.25 mlmin for a 10 mm i.d. column ... 

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