Column optimum particle diameter

It should be pointed out that equations (14) and (15) do not give an expression for the minimum column lengths, as the optimum particle diameter has yet to be identified. 

It is seen that there will be a unique value for (dp), the optimum particle diameter, (dp(opt)), that will meet the equality defined in equation (14) and allow the minimum HETP to be realized when operating at a maximum column inlet pressure... 

It follows that knowing the optimum particle diameter, the optimum column length can also be identified. It must be emphasized that this optimizing procedure... 

Thus as (y) will always be greater than unity, the resistance to mass transfer term in the mobile phase will be, at a minimum, about forty times greater than that in the stationary phase. Consequently, the contribution from the resistance to mass transfer in the stationary phase to the overall variance per unit length of the column, relative to that in the mobile phase, can be ignored. It is now possible to obtain a new expression for the optimum particle diameter (dp(opt)) by eliminating the resistance to mass transfer function for the liquid phase from equation (14). 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

Equation (18) allows the optimum particle diameter to be calculated that will allow the separation to be achieved in the minimum time by utilizing the maximum available inlet pressure and operating at the optimum mobile phase velocity. It is one of the most important equations in column design. 

It is seen from figure (1) that the optimum particle diameter ranges from about 2 micron for very simple separations (a=1.l2) carried out at an inlet pressure of 6000 p.s.i. to about 40 micron for difficult separations (ot= 1.01 ) carried out at an inlet pressure of only 2000 p s.i Furthermore, the curves shown in figure (1) appear to be in conflict with popular opinion, in that, the more difficult separations are best achieved with particles of relatively large diameter, whereas, simple separations require particles of small diameter for optimum performance. This apparent paradox will be discussed more fully later in the chapter. Equation (18) also discloses some interesting properties of the optimized column. 

Optimum Column Radius Optimum Column Length Optimum Particle Diameter... 

In the operation of preparative columns, it is necessary to obtain the maximum mass throughput per unit time and, at the same time, achieve the required resolution. Consequently, the column will be operated at the optimum velocity as in the case of analytical columns. Furthermore, the D Arcy equation will still hold and the equation for the optimum particle diameter can be established in exactly the same way as the optimum particle diameter of the analytical column. The equation is fundamentally the same as that given for the optimum particle diameter for a packed analytical column, i.e. (18) In chapter 12, except that (a) and (k ) have different meanings. 

Figure 6 shows the effect of the three limits imposed on the column design, the need to maintain an aspect ratio greater than unity, restricts the column length to a minimum of 5 cm and confines the analysis time to between one minute and one hour, without the restriction, the column with the minimum analysis time would be operated at the maximum pressure available. However, as a result of the limitation on column length, the optimum pressure must be reduced to allow the optimum particle diameter to be ircreased. This, in turn, allows the column length to be increased to... 

It is clear that the major factor controlling the particle diameter will be the separation ratio (a), which reflects the difficulty of the separation. The more difficult the separation, the more theoretical plates are needed, and thus the column must be longer. However, to use a longer column, the particle diameter must be increased to allow the optimum velocity to be realized without exceeding the maximum system pressure. The effect of the capacity ratio of the first solute of the critical pair on the optimum particle diameter is complex. Extracting the function of the capacity ratio (f(k )) from equation (1),... 

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