Tài liệu HPLC for Pharmaceutical Scientists 2007 (Part 17) doc

17 DEVELOPMENT OF F AST HPLC METHODS Anton D. Jerkovich and Richard V. Vivilecchia 17.1 INTRODUCTION Developing fast high-performance liquid chromatography (HPLC) methods can improve work efficiency during research, development, or production of a drug substance or a drug product. HPLC is a key technique in all of these areas. Until recently, analysis times of greater than 30 minutes were common. Modern pharmaceutical R&D, with its high-throughput screening, demands high-throughput methods to deal with the large number of samples.To reduce production cycle time, fast HPLC methods are essential for on-line or at-line process control and for rapid release testing. Consider a GMP laboratory responsible for releasing a single batch of drug substance.Assuming a run time of 30 minutes and a total of 12 injections, a run time of 6 hours would be required to cover system suitability, calibration,and sample analysis. If the run time were 5 minutes, only 1 hour would be required for the analysis. With the advent of commercial chromatographic porous media of less than 5µm and more recently in the 1- to 2-µm range, analyses times of less than 1–2 minutes have been demonstrated. Hundreds of samples which required days can now be analyzed in less than a day. This chapter will focus on how to optimize iso- cratic and gradient methods for speed without sacrificing resolution. In addi- tion, the implication on selection of column dimensions and media particle size on the speed of methods development will also be discussed. Reducing chromatographic media particle size allows the number of theo- retical plates per second to be increased. However, due to the resolution 765 HPLC for Pharmaceutical Scientists, Edited by Yuri Kazakevich and Rosario LoBrutto Copyright © 2007 by John Wiley & Sons, Inc. dependence on N 1/2 , doubling of N will only increase resolution by 2 1/2 . As dis- cussed below, a reduction in particle size can lead to a pressure limitation due to the inverse dependence of pressure drop to the square of the particle diam- eter and the maximum operating pressure of the chromatograph. The key to optimizing speed is to maximize selectivity, α. Maximizing selectivity for the critical separation pairs will allow the shortest column lengths and highest mobile-phase linear velocity. Short columns, 3–10cm packed with particles in the 1- to 3-µm range, provide high-speed analyses while maintaining reason- able pressure drop. Due to the fast analysis time of these short columns, method development time can also be shortened. Multiple columns can be rapidly screened for optimizing selectivity. Short columns are especially useful when the components to be separated are known. However, when dealing with complex samples with unknown components such as forced decomposition or biological samples, using longer columns may be more judicious to achieve optimum separation of critical components. After selectivity optimization, the method can be optimized for speed by reducing column length. The dis- cussion in this chapter will focus on optimizing speed of analysis and not on selectivity. The reader is referred to Chapters 4 and 8 on how to optimize selectivity. 17.2 BASIC THEORY To understand how to optimize a separation for speed, it is worth revisiting some of the theoretical concepts developed earlier in this text. The analysis time, t a , is the time it takes for all sample components to elute off a column at a certain flow rate and is given by (17-1) where L is the column length, u is the linear flow velocity of the mobile phase, and k is the retention factor of the latest-eluting peak. Notice here some obvious ways to increase the speed of analysis: The length of the column can be shortened, mobile phase can be pumped at a faster flow velocity, and one can ensure that the retention of sample components is not prohibitively long. Once any of these approaches are attempted, however, it is quickly seen that other important parameters of the separation are affected, principally the res- olution and the column backpressure. These parameters must be considered when enhancing the speed of analysis. Ideally, the analyst would like to max- imize both resolution and speed of analysis, while remaining within the pres- sure capabilities of the instrument.What is discovered,though, is the inevitable existence of a trade-off between resolution, analysis time, and backpressure. Resolution can be enhanced if more time is allowed; conversely, analysis time can be shortened, but at the expense of resolution. In addition, both t L u k a =+ () 1 766 DEVELOPMENT OF FAST HPLC METHODS resolution and speed are limited by the constraints of the instrumentation. T he interrelationship between these factors will be considered, starting with the most important parameter describing the quality of our separation— resolution. 17.2.1 Resolution and Analysis Time The practical goal of most separations is not to achieve the greatest resolution possible, but rather to obtain sufficient resolution to separate all components in the shortest amount of time. To optimize for speed, the starting condition is that there is a minimum resolution requirement for the separation. Resolu- tion is a function of three parameters: column efficiency, or theoretical plates (N), selectivity (a), and the retention factor (k): (17-2) Selectivity and retention are influenced by the choice of column chemistry and the mobile phase and gradient conditions. Due to the trade-off between resolution and analysis time, any “excess” resolution that can be generated beyond the minimum requirement can theoretically be traded for shorter analysis times. In this regard, the power of selectivity cannot be underesti- mated, especially when a is close to 1. For example, Karger et al. [1] have shown that an increase in a from 1.05 to 1.10 can result in more than a three- fold reduction in analysis time. High selectivity also lessens the required the- oretical plate count necessary to resolve all components, which allows use of a shorter column to speed up the analysis. Consequently, choosing a column or using mobile-phase conditions that produce a high relative selec- tivity between critical peak pairs can be very advantageous for achieving fast methods. In addition, resolution as well as analysis time depends on the reten- tion factor. For isocratic conditions, the optimum k for resolution and speed occurs in the range of 1–10 [1]. For samples containing many components or with analytes of wide-ranging polarity, gradient elution must then be used to achieve reasonable analysis times. Optimizing selectivity and retention so as to maximize resolution and minimize analysis time in gradient separations is discussed further in Section 17.6. Beyond these two parameters, the minimum resolution that must be achieved will require a certain number of theoretical plates, which can be expressed in terms of the column length and plate height, H,as (17-3) From this equation, column efficiency scales directly with column length and is inversely proportional to the plate height. Solving this equation for L and N L H = R Nk k s =       −     +     4 1 1 2 2 a a BASIC THEORY 767 substituting into equation (17-1) results in a useful expression that more clearly relates analysis time to the quality of the separation: (17-4) Note that if the plate height (H) remains constant, an increase in the required plate number (N) will require a proportional increase in the analy- sis time. This is because for a fixed plate height, an increase in plate number must be obtained by an increase in the column length. Here one encounters the trade-off between resolution and speed.While it is desirable to use a short column to limit analysis time, it is also seen that a longer column provides a higher plate count and resolution. However, resolution increases not with N, but with , meaning the gain in resolution from lengthening the column will always be proportionally less than the price paid in time. Consequently, for fast analyses, columns no longer than that which gives the minimum theo- retical plates to adequately resolve all peaks should be used. Note also that t a varies with the ratio H/u. Equation (17-3) shows that reduc- ing the plate height is one way to obtain higher theoretical plates without increasing the column length. Now it is seen that for a fixed plate number (the plates needed to achieve the resolution requirement), decreasing the plate height will shorten analysis times by allowing use of a shorter column. As dis- cussed in the next section, though, plate height is dependent on the linear velocity. Thus, when optimizing for speed, the two must be considered together.The goal, then, is not just to reduce H, but to minimize H/u.This will favor both high resolution and short analysis times. Minimizing H/u, then, encompasses the heart of what is desired in a fast HPLC method—greatest resolution per unit of time. Exploring this concept a little further, knowing that H = L/N and u = L/t 0 , substituting in these relationships results in (17-5) This is known as the “plate time” and has units of seconds. It is equivalent to the amount of time it takes to generate one theoretical plate. Its inverse would be “plates per second,” N/t 0 . Plates per second may also be expressed more generally as N/t for elution times other than the void time [2, 3]. These terms more effectively describe the criteria of resolution per unit time that are desired to be maximized (actually, N/t is proportional to resolution squared per time); unfortunately, they are not widely used in the literature, and for the sake of continuity will not be used in this discussion. The following sections will look at what influences plate height and velocity and how best to mini- mize H/u. H u t N = 0 N t NH u k a =+ () 1 768 DEVELOPMENT OF FAST HPLC METHODS 17.2.2 Plate Height and Band-Broadening Plate height is a measure of peak-broadening and column performance: Reducing or eliminating sources of band-broadening should be a main goal when choosing columns and instrumentation, and otherwise developing methods. Plate height can also be described in terms of its dependence on the linear flow velocity, u, by the van Deemter equation [4]: (17-6) where A, B, and C are the coefficients for “eddy” diffusion, longitudinal dif- fusion, and resistance to mass transfer, respectively. A plot of H versus u is often referred to as a van Deemter plot and is shown in Figure 17-1 along with plots of the individual terms that comprise it. While other, more complex and theoretically correct equations have been derived [5–8], the simplicity of the van Deemter equation makes it useful in understanding sources of band- spreading and how to minimize them. Each of the three terms in the equation represents a contribution to the broadening of a peak and will be examined in more detail. The A term of the van Deemter equation is independent of the mobile- phase linear velocity and describes the broadening that occurs due to the mul- tiple flow paths present within the column. Since these paths are of different lengths, molecules will travel different distances depending on what flow paths they experience. For a column bed of randomly packed particles, the A term is proportional to the particle diameter, d p , and to a factor λ related to the packing structure: HA B u Cu=++ BASIC THEORY 769 Figure 17-1. van Deemter plot showing contribution of individual terms . (17-7) T he B term describes broadening due to axial molecular diffusion and is inversely proportional to the linear velocity. In other words, the faster an analyte zone migrates through the column, the less broadening due to diffu- sion it will experience. The B term coefficient is given by (17-8) where D M is the diffusion coefficient of the analyte in the mobile phase, and γ is the tortuosity or obstruction factor, accounting for the obstruction to diffu- sion presented by the packing material. The C term, or resistance to mass transfer term, is a complex agglomera- tion of all broadening that becomes worse with increasing flow velocity. Multiple contributions to the C term have been described; however, for the purposes of this discussion the focus will only be on the relationships relevant to improving resolution per unit time. In general, C is related to the diffusion coefficient D of the analyte in the medium through which mass transfer is taking place, and it is also related to the square of the distance d over which it occurs. Fast diffusion and short diffusional distances aid mass transfer and reduce band-spreading; hence, the C term takes the form (17-9) For example, for the mass transfer in the bulk mobile phase between stationary-phase particles, D becomes the diffusion of the analyte in the bulk mobile phase, D M , and d becomes the distance between particles, which is roughly proportional to the particle diameter, d p . The mobile-phase C term expression C M can therefore be approximated as (17-10) When looking at the individual plate height equations, some important rela- tionships are noticed. The B term worsens at slower flow velocities and with faster molecular diffusion. In contrast, C-term broadening worsens at faster velocities, but improves with faster molecular diffusion. These opposing phe- nomena are what cause the van Deemter curve to possess a minimum plate height at some intermediate velocity (the optimum velocity, u opt ). It can also be seen from Figure 17-1 that the increase in plate height is more abrupt at the low velocity end of the curve (where broadening is dominated by the B term) than it is at the high velocity side (where the C term is dominant). Since conditions that favor speed are desired, operating at velocities greater than C d D M p M ∝ 2 C d D ∝ 2 BD M = 2g Ad p = l 770 DEVELOPMENT OF FAST HPLC METHODS the optimum velocity without significantly sacrificing efficiency is advanta- geous . Although the B and C terms exhibit opposite relationships with analyte dif- fusion, the C-term relationship is mainly of interest because resistance to mass transfer is the dominant form of band-spreading at the faster velocities that are desired. Equations (17-9) and (17-10) imply that speeding up diffusion will increase mass transfer and help decrease plate height.The Wilke–Chang equa- tion [9] shows that diffusivity is directly proportional to temperature and inversely proportional to viscosity: (17-11) where T is temperature, h is the solvent viscosity, V 1 is the molar volume of the solute, M 2 is the molecular weight of the solvent, and Y 2 is a solvent asso- ciation factor. Since mobile-phase composition largely dictates the selectivity of our separation, varying the viscosity of the mobile phase directly by the selection of solvents may not be an option. Raising the temperature of the mobile phase, then, is the most effective way to speed up diffusion. It also has the added benefit of lowering the mobile-phase viscosity, thereby increasing diffusion indirectly. This all serves to reduce the plate height at faster veloci- ties. As shall be seen in the next section, raising the temperature also speeds up the analysis by lowering the pressure drop across the column. The plate height relationships also show that the A term is dependent on the particle diameter, and the mobile-phase C-term is dependent on the par- ticle diameter squared. Reducing the diameter of the packing material is there- fore a powerful approach for reducing plate height. The minimum attainable plate height for a column, H min —that is, the plate height occurring at the optimum velocity u opt —will be proportional to d p . When operating at veloci- ties greater than u opt , the quadratic dependence of C on d p means that the reduction in plate height is especially significant. This makes sense, since mass transfer will improve as the distances molecules must travel become smaller. That is, smaller particles result in smaller interparticle spaces and thus shorter diffusional distances. By using a smaller particle size, the slope of the C-term side of the van Deemter curve will decrease dramatically, allowing operation at higher velocities without having to sacrifice as much in resolution compared to larger particles. This is illustrated in Figure 17-2, which shows the perfor- mance of columns packed with 1.7-, 3-, and 5-µm particles. Smaller plate heights and higher velocities are made possible, thus considerably reducing H/u. As a result, one should aim to keep the particle diameter as small as possible. Since the goal is to reduce analysis time by minimizing H/u while holding N constant (at the minimum required plate count), the approximation can be made that H ∝ d p , and therefore N ∝ L/d p . This means as the particle diameter is reduced, the column length must also be reduced proportionally. D MT V =× − 74 10 8 22 1 06 . . Ψ h BASIC THEORY 771 Holding L/d p constant while both length and particle size are decreased is therefore one of the most effective means of achieving fast separations . This is the motivation seen in the evolution of chromatography columns over the last few decades. Where once the 25-cm column packed with 5-µm particles was the standard workhorse analytical column, now 10- and 15-cm columns packed with 3-µm particles are used. As column technology continues to improve, even shorter columns packed with particles <3µm are being introduced. To illustrate more clearly the effect of these variables on analysis time, reduced parameters can be used for the plate height and velocity. Reduced parameters effectively normalize the plate height and velocity for the particle diameter and the diffusion coefficient to produce dimensionless parameters that allow comparison of different columns and separation conditions. The reduced plate height and reduced velocity are expressed, respectively, as (17-12) (17-13) Solving these equations for H and u, respectively, and substituting into equation (17-4) yields (17-14) t h v d D Nk a p M =+ () 2 1 v ud D p M = h H d p = 772 DEVELOPMENT OF FAST HPLC METHODS Figure 17-2. Performance of 2.1- × 100-mm columns packed with 1.7-, 3.5-, and 5-µm particles. Stationary phase was bridged-ethyl hybrid C18 prototype material in each case. The benefit of reducing the particle diameter on separation time is most evident here . It is also seen that increasing diffusion will speed up the analysis. Now that the factors affecting plate height have been examined, it is time to turn to the effect of linear velocity and the limitation of pressure on the resolution per unit time. 17.2.3 Flow Velocity and Column Backpressure It is known that increasing the linear flow velocity of the mobile phase will lead to faster separations. But since H is dependent on u, what velocity is needed to maximize the resolution per unit time (minimize H/u)? Using the van Deemter equation, H/u may be expressed as (17-15) From this equation, H/u approaches its minimum value of C as u becomes large. In other words, the separation should be performed at the fastest veloc- ity possible. (Note also that this represents mathematically what was presented in the previous section; that is, in the case of optimizing for speed, the sepa- ration is dominated by the C-term.) This doesn’t mean that the resolution itself will improve—on the contrary, since H generally increases with velocity when u > u opt , resolution will worsen—but that the resolution per unit time is improv- ing.Again, since the quality of the separation must not be sacrificed, the speed of analysis can be improved only to the point where resolution can no longer be sacrificed. Of course, the ability to increase u depends on the pressure capabilities of the instrument, since pressure is directly proportional to velocity: (17-16) where ∆P is the pressure drop across the column, η is viscosity, and φ is the flow resistance factor. Thus the speed of analysis is limited by the maximum pressure capability of the instrument. As a result, the most should be made of the pressure available by reducing the pressure drop across the column as much as possible. Decreasing the column length lowers the pressure requirement propor- tionally, allowing use of the available pressure to gain an advantage in speed. Column efficiency, however, drops with use of a shorter column and at faster velocities. Care must therefore be taken to ensure that resolution between peaks is not lost when decreasing analysis time in this manner. Lowering the viscosity of the mobile phase is another way to lessen the required pressure. This may be accomplished by raising the column tempera- ∆P uL d p = ηφ 2 H u A u B u C=+ + 2 BASIC THEORY 773 ture. Increasing temperature has the double advantage of allowing use of a higher flow velocity and speeding up diffusion, both of which appear in the denominator of equation (17-14).This is a strong motivator for the use of tem- perature above ambient conditions in order to speed up the separation. Of course, sample degradation, the boiling point of our mobile phase, stability of the stationary phase, and the capability of the column heater limit the maximum temperature that can be used. Temperatures up to about 70°C are considered routine; beyond that, columns and heaters specifically designed for high-temperature chromatography are needed. Much research has been done in the area of elevated-temperature chromatography, where interesting possi- bilities arise, such as the use of temperature gradients and purely aqueous mobile phases [10]. Chapter 18 elaborates on the use of temperature in chro- matography for pharmaceutical applications. The velocity we can obtain at a given pressure will also be limited by the resistance to flow presented by the column, known as the specific column permeability. In equation (17-16) the permeability is broken up into its two main components: the flow resistance parameter, φ, and the particle diameter squared, d p 2 , and can be expressed as (17-17) where ε is the interstitial porosity of the column (i.e., the fraction of the total column volume occupied by the interparticle space), usually about 0.4. The flow resistance parameter is given by (17-18) and is purely a function of the porosity of the column—that is, the packing density. Its value is essentially fixed for a given column and out of the analyst’s control. The quantity f/e, represented by the symbol Φ, has a value around 1000 for well-packed columns [11]. Reducing the particle diameter can be a powerful way to gain speed in sep- arations. On the other hand, equation (17-16) shows an inverse quadratic rela- tionship of pressure to the particle diameter. This strong dependence means that an enormous price in pressure is paid for reducing the particle diameter. However, it was stated previously that when reducing the particle diameter the column length can be reduced as well to keep L/d p constant. Since pres- sure scales with column length, this eases the pressure requirement. But even keeping L/d p constant, the pressure will still go up with 1/d p . Eventually, the upper pressure limit of the pump will be reached and it won’t be possible to further reduce d p without either a proportionally greater reduction in L, which reduces the efficiency, or a relatively smaller linear velocity, which cuts back on speed. Because u opt increases in proportion to 1/d p , the maximum pressure f e e = − () 185 1 2 2 B d p 0 2 = ε φ 774 DEVELOPMENT OF FAST HPLC METHODS [...]... steps toward making UHPLC a viable tool for pharmaceutical analysis Two pressure regimes have been described: very-high pressure LC (VHPLC), for the pressure range of about 400–1500 bar, and ultra-high pressure LC (UHPLC), for pressures >1500 bar [20, 21, 34] This naming convention is not strictly adhered to, however, and it is often common to refer to anything above the conventional HPLC pressure limit... 2000 bar for injection volumes of 1–2.5 µL [35] Given the challenges of performing injections under highpressure conditions, it is strongly recommended that the injection performance of a high-pressure instrument is evaluated before developing methods for highly accurate quantitative analyses Doing this during performance qualification (PQ) of the instrument or an initial vendor evaluation before purchasing... spectrometers For fast, highly efficient chromatography, a time-of-flight (TOF) mass analyzer may be the best option for very fast detection Detector requirements for fast LC is covered in more detail in Section 17.7.2 Currently the availability of columns packed with sub-2-µm stationaryphase material is rather limited This situation will likely change as the use of UHPLC proliferates and the demand for such... in pharmaceutical analysis such as protein and peptide separations, where sample volumes are often very small and the slower molecular diffusivities make the absence of pores especially beneficial due to the decreased C-term band-broadening The development of high-quality porous particles 1–2 µm in size for use with elevated pressures has therefore been a necessary and critical advancement for UHPLC... components, such as pumps, valves, and detection schemes, onto the chip is another essential step for future development The reader is referred to the reviews cited in the references for research performed with microchips [46–48] 788 DEVELOPMENT OF FAST HPLC METHODS 17.6 OPTIMIZING GRADIENT SEPARATIONS FOR SPEED 17.6.1 Advantages of Gradient Chromatography Gradient chromatography is a very powerful... (as it is in some modern fast HPLC instruments), equilibration time for the narrow diameter columns is decreased to within the range of the larger bore columns See Section 17.7 for discussion of optimization of instrumental parameters for fast methods Column equilibration time must be determined as part of the method development Equation (17-21) may not apply to all methods For example, more than five... structure of the sample [49] For molecular weights below 500, S ≅ 5 and the equation reduces to k *= 20 tg F ∆% VM (17-23) The retention factor k* is a constant for all solutes eluting in a linear gradient This simple equation provides the basic insight for a starting point for developing or optimizing a method Adjusting the parameters in the above equation such that k* is about 5 for the target analyte... A solvent viscosity of 1.0 cP was used for all calculations a comparison, consider conditions typically encountered in conventional HPLC A 4.6- × 100-mm column packed with 3-µm particles operating at 1 mL/min (corresponding to 1.5 mm/sec) will require 170 bar and generates only 0.19 W of heat Columns larger than 2.1 mm in diameter would therefore be undesirable for pressures and conditions outlined... deaggregation of the proteins 17.4.3 UHPLC Applications Isocratic separation of test compounds is a useful way to demonstrate the performance of a system Basic chromatographic characteristics, such as theoretical plates, are easily measured and can be compared to what is expected from theory and to performance of other chromatographic systems Figure 17-4 is a UHPLC chromatogram obtained under isocratic... 500, with an average peak width of 14.5 seconds This is significantly higher than the peak capacities of conventional HPLC columns packed with 5-µm particles, which tend to be below 200 for similar samples Low flow rates and narrow peak widths make capillary UHPLC particularly suitable for coupling with mass spectrometry via nanoelectrospray ionization [23, 45] Tolley et al [34] have used very-high pressures . However, due to the resolution 765 HPLC for Pharmaceutical Scientists, Edited by Yuri Kazakevich and Rosario LoBrutto Copyright © 2007 by John Wiley & Sons,. toward making UHPLC a viable tool for pharmaceutical analysis. Two pressure regimes have been described: very-high pressure LC (VHPLC), for the pressure