Molar mass elution volume

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-... 

PMMA). Under these conditions, some inevitable peaks are observed in the low molar mass range. This area starts for an elution volume of Mpmma of about 600. Enclosing a further column for this low molecular size range generally improves the separation, but the elution sequence of oligomer and disturbing peaks remains constant. 

The effect is that the polymer molecules are separated into fractions. These are measured by an appropriate detector located at the end of the column, and the detector records the response as a peak on a chart. The chromatogram thus consists of a series of peaks corresponding to different elution volumes, the shortest elution volume being due to the largest molar mass polymer molecules within the sample. Details of the molar mass distribution can be determined from the size and number of the individual peaks in the chromatogram. An example of a gel permeation chromatogram is shown as Figure 6.4. 

Gel permeation chromatograms actually give information about molecular size. For any polymer, size is determined hy a number of factors. These include not only molar mass but also temperature and thermodynamic quality of the solvent. Hence the relationship between size and molar mass is unique for each particular polymer-solvent combination, and we caimot assume that because two peaks of different polymers, even in the same solvent at the same temperature, have the same elution volume their molecules have the same molar mass. 

In practice, therefore, gel permeation chromatographs are usually cahbrated by running monodisperse specimens of known molar mass, and determining their elution volume. From the results, a graph is plotted of log M against... 

An example can best explain the procedure. A poly(bisphenolA carbonate) sample characterized by a broad-MMD was injected in an SEC apparatus, about 100 fractions were collected, and 24 of them were analyzed by MALDI [7]. Figure 15.2 reports the SEC trace of the PC sample. The trace covers a quite broad range of elution volumes and it is centered at about 30 ml. The polymer starts eluting at about 26 ml and ends at about 38 ml. The MALDI spectra yielded MP values (see above). Using this information, the SEC trace in Fig. 15.2 is calibrated and the average molar masses turn out to be Mw = 55,800, Mn = 23,600. 

The first curve is a histogram of the mass fraction detected in each slice. It is not yet the correct molar mass distribution w(M), because a hnear spacing with respect of the elution volume corresponds to a logarithmic spacing in the molar... 

The significant intrinsic limitation of SEC is the dependence of retention volumes of polymer species on their molecular sizes in solution and thus only indirectly on their molar masses. As known (Sections 16.2.2 and 16.3.2), the size of macromolecnles dissolved in certain solvent depends not only on their molar masses but also on their chemical structure and physical architecture. Consequently, the Vr values of polymer species directly reflect their molar masses only for linear homopolymers and this holds only in absence of side effects within SEC column (Sections 16.4.1 and 16.4.2). In other words, macromolecnles of different molar masses, compositions and architectures may co-elute and in that case the molar mass values directly calculated from the SEC chromatograms would be wrong. This is schematically depicted in Figure 16.10. The problem of simultaneous effects of two or more molecular characteristics on the retention volumes of complex polymer systems is further amplifled by the detection problems (Section 16.9.1) the detector response may not reflect the actual sample concentration. This is the reason why the molar masses of complex polymers directly determined by SEC are only semi-quantitative, reflecting the tendencies rather than the absolute values. To obtain the quantitative molar mass data of complex polymer systems, the coupled (Section 16.5) and two (or multi-) dimensional (Section 16.7) polymer HPLC techniques must be engaged. 

In this case, enthalpic interactions within the HPLC system exceed the exclusion effects (Eigure 16.3b). The retention volumes of polymer species as a rule exponentially increase with their molar masses. The limitations of the resulting procedures were elucidated in Section 16.3 the retention of (high)polymers is usually so large that these do not elute from the column (Section 16.6). Therefore, the majority of enthalpy controlled HPLC procedures is applicable only to oligomers—up to... 

The principle of enthalpy-assisted SEC (ENA SEC) is evident from Figure 16.3c and d (Section 16.3.3). The exclusion mechanism governs the order of elution that is the retention volumes decrease with the rising molar mass of sample. The presence of the controlled enthalpic interactions, however, raises the separation selectivity. 

FIGURE 16.13 Schematic representation of separation of a block copolymer poly(A)-block-poly(B) from its parent homopolymers poly(A) and poly(B). The elnent promotes free SEC elntion of all distinct constitnents of mixtnre. The LC LCD procednre with two local barriers is applied. Poly(A) is not adsorptive and it is not retained within colnmn by any component of mobile phase and barrier(s). At least one component of barrier(s) promotes adsorption of both the homopolymer poly(B) and the block copolymer that contains poly(B) blocks, (a) Sitnation in the moment of sample introdnction Barrier 1 has been injected as first. It is more efficient and decelerates elntion of block copolymer. After certain time delay, barrier 2 has been introdnced. It exhibits decreased blocking (adsorption promoting) efficacy. Barrier 2 allows the breakthrongh and the SEC elution of block copolymer but it hinders fast elution of more adsorptive homopolymer poly(B). The time delay 1 between sample and barrier 1 determines retention volume of block copolymer while the time delay 2 between sample and barrier 2 controls retention volume of homopolymer poly(B). (b) Situation after about 20 percent of total elution time. The non retained polymer poly(X) elutes as first. It is followed with the block copolymer, later with the adsorptive homopolymer poly(B), and finally with the non retained low-molar-mass or oligomeric admixture. Notice that the peak position has an opposite sign compared to retention time or retention volume Tr. 

It should be noted that the relationships between molar mass and retention volume for lignin sulfonates shown in Figures 3 and 4 are strictly only valid for the samples studied in these experiments because lignin sulfonates are polyelectrolytes and thus interact with each other and with the gel matrix of the column. The shape of the calibration curve is thus affected by, among other things, the size and concentration of the sample (2). Interactions between molecular species can be eliminated by eluting with a suitable electrolyte. 

The column is calibrated using proteins of known molar mass. The relative retention volumes 0.0 and 1.0 are defined by the elution of Blue Dextran (molecular weight 2 000 000) and sulfosalicylic acid (molecular weight 218), respectively. 

Fractionation on Sephadex G-25 using 0.5M sodium hydroxide as eluent causes the low molar mass lignin components in black liquor to elute in the relative retention volume range 0.3-1.3 with partial separation from each other, as shown in Figure 11. 

Fraction I, which consists mainly of low molar mass compounds, also contains a small amount of high molar mass lignin derivatives eluting with relative retention volumes of 0-0.1. These derivatives are polar and some may be bound to carbohydrates, or otherwise they would have been eluted by RPC along with the hydrophobic fractions II-IV. 

Polyfmethyl methacrylate), initiated and polymerized at 250 by t-butylmagnesium bromide in toluene-THF solution (—). Mole fraction of monomer, X.VJM = 0.1 OM. XTHF is indicated in each case. A mixture of standard polystyrene samples of indicated molar mass (------). All traces are aligned so that the elution volumes correspond. 

The investigations mentioned so far aimed at objectives of rather low molar mass. Reversed-phase chromatography of polystyrenes with 17,500 and 50,000 g/mol was performed on C 18 columns with water/tetrahydrofuran gradients or mixtures3). The latter sample was isocratically eluted from 30 nm-pore packing with 85 % THF as a broad band, 87 % THF let the polymer elute in the void volume, whereas 83 % did not produce an observable band at all. 

The static laser light scattering apparatus used as an on-line GPC detector has been popular for a while. Here, we illustrate another but less known method of combining the results from (gel permeation chromatography) and DLS. The basic principle is as follows There is a similarity between these two tools in that the translational diffusion coefficient D obtained by DLS and the elution volume V in GPC are related to the hydrodynamic size of a given macromolecule. In a first approximation, if the hydrodynamic size is proportional to the molar mass, we have... 

Sample molecules that are too large to enter the pores of the support material, which is commercially available in various pore dimensions, are not retained and leave the column first. The required elution volume Ve is correspondingly small. Small molecules are retained most strongly because they can enter all the pores of the support material. Sample molecules of medium size can partly penetrate into the stationary phase and elute according to their depth of penetration into the pores (Fig. 7.3). No specific interactions should take place between the molecules of the dendrimer sample and the stationary phase in GPC since this can impair the efficiency of separation by the exclusion principal. After separation the eluate flows through a concentration-dependent detector (e.g. a UV/VIS detector) interfaced with a computer. One obtains a chromatogram which, to a first approximation, reflects the relative contents of molecules of molar mass M. If macromolecules of suitable molar mass and narrow molar mass distribution are available for calibration of the column, the relative GPC molar mass of the investigated dendrimer can be determined via the calibration function log(M) =f( Vc). 

This procedure results in a concentration - volume curve, from which, after previous calibration, the molar mass distribution can be derived. Calibration can be carried out with known monodisperse polymers, and is needed only once for a certain type of polymer on a certain column. The measurement takes only a few hours. From the measured MMD the various averages can be computed easily. It is also possible to characterise the eluted polymer solution not only on concentration, but also on molar mass, e.g. by laser light scattering. In this way the calibration can be avoided. 

The distribution coefficient Kj (Equation 2) is defined as the volume fraction of pores, in a stationary phase, which is effectively permeated by a solute of a given size. V0 is the interstitial volume of the porous medium, measured by the elution volume of a high molar mass solute that is totally excluded from the matrix pores. Ve is the elution volume of the product of interest. Vs represents the total solvent volume within the pores, available for small solutes. 

For determining the molar mass of branched polymers gel permeation chromatography can be used. An important quantity in this connection is the hydrodynamic volume of the polymer coil, which, as shown before in Eq. (9.27), is proportional to the product [rj M. According to Benoit and co-workers (1966) the hydrodynamic volume is the key size parameter in the establishment of a universal calibration curve for gel permeation chromatography columns (see Chap. 2) if log (h/]M) is plotted versus the elution volume for a variety of polymers, the data fit a single curve. 

---