Column inversion

Pawlisch, C. A. Brie, J. R. Laurence, R. L., "Solute Diffusion in Polymers. 2. Fourier Estimation of Capillary Column Inverse Gas Chromatography Data," Macromolecules, 21, 1685 (1988). 

Solute Diffusion in Polymers by Capillary Column Inverse Gas Chromatography... 

Diffusivity data are available only for a limited number of polymer-solvent systems. This paper describes research that has led to the development of the use of capillary column inverse gas chromatography (IGC) for the measurement of diffusion coefficients of solute molecules in polymers at infinite dilution. The work has resulted in a precise, rapid technique for the diffusion measurements that circumvents the many problems attendant to classical sorption methods and packed column IGC methods. Initial results of the program appeared in two recent publications (1,2)- Some of the material introduced in those papers is discussed here to present background for... 

Following the ideas developed by Guillet and his co-workers, a method using Capillary Column Inverse Gas Chromatography (CCIGC) was developed (1.21 to measure diffusion coefficients in polymer-solvent systems at conditions approaching infinite dilution of the volatile component. 

Column inverse response can be troublesome when boilup is manipulated by bottom level. An extensive analysis of inverse response, including predictive equations, is presented. 

Since frits are relatively cheap the best remedy is to change the old frit for a new one. Alternatively, frits may be cleaned using either ultra-sonication or treatment with strong acids. Most manufacturers supply columns with identical frits at each end and thus, although not usually recommended, column inversion can be a method whereby the top frit is flushed out. This method works well providing that the column is well packed and that no void volume exists at the original top end. 

BAL Baltus, R.E., Alger, M.M., and Stanley, T.J., Solubility and diffusivity of cyclic oligomers in poly(dimethylsiloxane) using capillary column inverse gas chromatography, Macromolecules, 26, 5651, 1993. 

Pawlisch, C.A., Maoris, A., and Laurence, R.L. (1988) Solute diffusion in polymers. 2. Fourier estimation of capillary column inverse gas chromatography data. Macromolecules, 21 (6), 1685-1698. 

Feng, X., and Burns, C.M. (2001) Measurements of partition, diffusion coefficients of solvents in polymer membranes using rectangular thin-channel column inverse gas chromatography (RTCCIGC)./. Membr. Sci., 188,... 

Heat-transfer coefficients —Column approach to flooding and entrainment —Column approach to dumping —Column tray efficiency —Column inverse response —Column-material and energy balances... 

As a final example, let us look at the control of column-base levd by throttling condensate flow fi om the reboiler. We will ignore possible column inverse response but will take swell into account. Column acoustic impedance, seen fi om the base, will be assumed to be resistive only. The basic, open-loop signal flow diagram for the flooded reboiler is given in Figure 15.13. We need in addition the following relationships ... 

In these equations, J and M are quantum numbers associated with the angular momentum operators and J, respectively. The number II = 0, 1 is a parity quantum number that specifies the symmetry or antisymmetry of the column vector with respect to the inversion of the nuclei through G. Note that the same parity quantum number II appears for and Also, the... 

Quantitative Calculations In a quantitative analysis, the height or area of an analyte s chromatographic peak is used to determine its concentration. Although peak height is easy to measure, its utility is limited by the inverse relationship between the height and width of a chromatographic peak. Unless chromatographic conditions are carefully controlled to maintain a constant column efficiency, variations in... 

Ohm s law the statement that the current moving through a circuit is proportional to the applied potential and inversely proportional to the circuit s resistance (E = iR). (p. 463) on-column injection the direct injection of thermally unstable samples onto a capillary column, (p. 568) one-taUed significance test significance test in which the null hypothesis is rejected for values at only one end of the normal distribution, (p. 84)... 

Adjugate Matrix of a Matrix Let Ay denote the cofactor of the element Oy in the determinant of the matrix A. The matrix B where B = (Ay) is called the adjugate matrix of A written adj A = B. The elements by are calculated by taking the matrix A, deleting the ith row and Jth. column, and calculating the determinant of the remaining matrix times (—1) Then A" = adj A/lAl. This definition may be used to calculate A"h However, it is very laborious and the inversion is usually accomplished by numerical techniques shown under Numerical Analysis and Approximate Methods. ... 

If the packing surface is discontinuous in nature, a phase inversion occurs, and gas oubbles through the liquid. The column is not unstable and can be brought back to gas-phase continuous operation by merely reducing the gas rate. Analogously to the flooding condition, the pressure drop rises rapidly as phase inversion occurs. 

Flooding and Loading Since flooding or phase inversion normally represents the maximum capacity condition for a packed column, it is desirable to predict its value for new designs. The first generalized correlation of packed-column flood points was developed by Sherwood, Shipley, and Holloway [Ind. Eng. Chem., 30, 768 (1938)] on the basis of laboratory measurements primarily on the air-water system. 

Thus, the variance of the peak is inversely proportional to the number of theoretical plates in the column. Consequently, the greater the value of (n), the more narrow the peak, and the more efficiently has the column constrained peak dispersion. As a result, the number of theoretical plates in a column has been given the term Column Efficiency. From the above equations, a fairly simple procedure for measuring the efficiency of any column can be derived. 

Equation (33) shows that the maximum capacity ratio of the last eluted solute is inversely proportional to the detector sensitivity or minimum detectable concentration. Consequently, it is the detector sensitivity that determines the maximum peak capacity attainable from the column. Using equation (33), the peak capacity was calculated for three different detector sensitivities for a column having an efficiency of 10,000 theoretical plates, a dead volume of 6.7 ml and a sample concentration of l%v/v. The results are shown in Table 1, and it is seen that the limiting peak capacity is fairly large. 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

As the optimum column radius is inversely proportional to (a-1), and (uopt) is inversely proportional to (ropt)> the simple linear relationship between optimum velocity and the separation ratio is to be expected. The high velocities employed for... 

H type columns must be used at a flow rate and pressure drop below maximum values listed in Tables 4.12-4.16. Standard flow rates are also listed in these tables. They are flow rate range recommendable for long-term usage in tetrahydrofuran at 25°C and vary with temperature. H type columns can be operated at a higher flow rate at elevated temperatures. They also vary with solvent depending on the viscosity. They are approximately inversely proportional to the solvent viscosity. The maximum pressure drop listed in the tables is for one column. When some columns are used in series, the total maximum pressure drop is a summation of values of all columns. 

All packing materials produced at PSS are tested for all relevant properties. This includes physical tests (e.g., pressure stability, temperature stability, permeability, particle size distribution, porosity) as well as chromatographic tests using packed columns (plate count, resolution, peak symmetry, calibration curves). PSS uses inverse SEC methodology (26,27) to determine chromatographic-active sorbent properties such as surface area, pore volume, average pore size, and pore size distribution. Table 9.10 shows details on inverse SEC tests on PSS SDV sorbent as an example. Pig. 9.10 shows the dependence... 

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