Calculated elution volumes

Casassa and Tagami (50) have given a theory for the partition of macromolecules, linear and branched, between a solution and cavities (such as the pores of a GPC gel). They have calculated elution volumes from their results, which agree closely with those derived from the hydrodynamic volume assumption this gives theoretical support to the use of hydrodynamic volume as a correlating parameter for branched polymers. This parameter has been used in studies of branching in polyethylene (Section 10). 

Now that we have our system set up and the column equilibrated and standardized, we are ready to carry out an HPLC separation on a real sample. We might add an internal standard (if necessary, to correct for injection variations), dilute our sample to a usable concentration, and prepare it for injection. After injection, we will record the chromatogram making sure that it stays on scale. Then, from the trace we obtain, we will calculate elution volumes either by measuring peak heights or by calculating peak areas by triangulation. 

The elution volume of sodium nitrate [ Ve (NaN03)] allows one to calculate the volume of solid matrix (V ,) in the column according to... 

With these facts in mind, it seems reasonable to calculate the pore volume from the calibration curve that is accessible for a certain molar mass interval of the calibration polymer. A diagram of these differences in elution volume for constant M or AM intervals looks like a pore size distribution, but it is not [see the excellent review of Hagel et al. (5)]. Absolute measurements of pore volume (e.g., by mercury porosimetry) show that there is a difference on principle. Contrary to the absolute pore size distribution, the distribution calcu-... 

Therefore by combining equations (9) and (10) and assuming some appropriate value for e, the number average number of LCB points per molecule can be calculated as a function of elution volume. The corresponding whole polymer number average number of LCB points per molecule is given by... 

The organic solvent used to elute the compound must be adequately strong (polar for the adsorbent silica gel) and a good solvent for the component. Absolute methanol should be avoided as a siugle solvent because silica gel itself and some of its common impurities (Fe, Na, SO4) are soluble iu this solvent and will contaminate the isolated material. Solvent containing less than 30% methanol is recommended, or ethanol, acetone, chloroform, dichloromethane, or the mobile phase originally used for PLC are other frequently nsed choices for solnte recovery. Water is not recommended because it is so difficult to remove by evaporation during the concentration step (removal by lyophilization is necessary). A formula that has been used to calculate the volume of solvent needed when the PLC mobile phase is chosen for elution is ... 

The calibration function calculation uses multiple linear regression to obtain hydrodynamic volume as a polynomial function of elution volume for a given column set. 

We find that baseline drift is small if careful attention is paid to the chromatographic conditions. Under these circumstances we need only define the initial and final elution volumes to be included in the calculation of the molecular weight distribution. 

Abstract A preconcentration method using Amberlite XAD-16 column for the enrichment of aluminum was proposed. The optimization process was carried out using fractional factorial design. The factors involved were pH, resin amount, reagent/metal mole ratio, elution volume and samphng flow rate. The absorbance was used as analytical response. Using the optimised experimental conditions, the proposed procedure allowed determination of aluminum with a detection limit (3o/s) of 6.1 ig L and a quantification limit (lOa/s) of 20.2 pg L, and a precision which was calculated as relative standard deviation (RSD) of 2.4% for aluminum concentration of 30 pg L . The preconcentration factor of 100 was obtained. These results demonstrated that this procedure could be applied for separation and preconcentration of aluminum in the presence of several matrix. 

Y = Log (Mol. Weight) X = Elution volume (nils) Calculated Actual... 

Dextran polymers were used to evaluate the utility of the linear, polydisperse calibration method for water-soluble polymer characterization. A blend of T-40 and T-70 dextran standards was used as a polydisperse calibration standard. Table VIII displays the report from the linear calibration method using this standard. Nine Iterations of the search algorithm were required for convergence to the true and Mn values of the standard. As can be seen in the report, the elution volume profile of the standard contained 72 area/time slices upon which calibration calculations were based. The slice width was set at 10 seconds/siIce. Figure 5 shows a plot of the calibration curve generated from the linear calibration method utilizing the dextran standard,... 

Vith the procedure outlined above, simple programs of programmable calculator (TI 59) and microprocessor (ZoO) for finding M(Vh) and <>o(%) were vrritten. The mean elution volume and total variance of the experimental chromatograms of well characterized polymer samples are first calculated according to... 

The mean elution volume and total variance calculated from the e qperimental chromatograms of polystyrene and 1,2-polybutadiene on the ARL 9 0 GPC instrument are so listed in Table I. The coefficients of the effective relation, coordinates of the cross-point, paranrater % and spreading factor were computed by the schema outlined above. The results obtained are listed in Table II and III, The effective relations and calibration... 

First, we estimated the parameters a to be 0.01 and 8 to be 0.05. For the estimation of the standard deviation of the DP values, twenty chromatograms of NBS 706 polystyrene were measured and elution volumes at the distinguished per cent points of the integral curve of each chromatogram were calculated. Then, the value a was obtained to be 0.042 mL. The value 6 was estimated to be 0.1 mL, which corresponds to 0.3 % of the elution volume at the center of the calibration curve of this SEC system and 5 % difference of molecular weight. 

The chain lengths of different molecules were then compared with the chain lengths of hydrocarbons to calculate the carbon number which relates the elution volume of the compound to the elution volume of a real or imaginary n-hydrocarbon. The "effective" carbon number for benzene based on its elution volume was experimentally found to be 2.85 - i.e. it eluted near the elution volume for propane which has a carbon number of 3.0 while the calculations based on bond angles and radii of atoms indicated that benzene would have a carbon number of 3.55. Thus corrections to the calculations for carbon number were required. These were derived from the experimentally observed elution behavior of various molecules. 

The elution volumes for n-hydrocarbons show a straight line relationship vs the logarithms of their molar volumes. Molar volumes, calculated from the densities of compounds other than n-hydrocarbons, must be modified to have the elution volumes of these compounds conform to the same calibration line (elution volume vs log molar volume) as that for the n-hydrocarbons. W. W. Schulz (1 ) related the elution behavior of branched alkanes in the range of Cy-C] ] to the average numbers of gauche arrangements (Zg) which the molecule can assume. 

We have recently reported (1 )) the use of this technique for characterization of various compounds. Experimental data obtained for a number of compounds are shown in Figure 2. We calculated the "size factors" for a number of small molecules and oligomers. This factor is a measure of the deviation of the elution volume of a given species from the calibration curve for n-alkanes which is assigned a size factor of 1. This size factor, F, is defined to be equal to A/M, where M is the molecular weight of the compound and A is the molecular weight of a real or hypothetical n-alkane which will elute at the same retention volume as the compound. Size factors for a number of... 

Pore distribution curves can be obtained plotting the change in the sum of residuals, which can be calculated by experimental elution volumes of all standards against the mean diameter of the PS standards [119]. 

However, the calculation requires different algorithms for each specific case. Hence, an explicit mathematical solution providing basing retention data (elution volumes or times, bandwidths, and resolution) is much more frequently used in analytical gradient chromatography, even at a cost of some simplifications [9-11]. 

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