GPC Retention Volume

With the exception of the report by Pannell (45), published data on the behaviour of branched polymers in GPC support the generalisation (46,47) that the so-called hydrodynamic volume, M[ ], is a valid parameter for the correlation of GPC retention volumes, for polymers differing in either chemical nature or branching or both. The question of the most suitable correlation parameter for linear polymers has been studied in some detail by Dawkins and co-workers (48), who compared M[rj] with the unperturbed dimensions, e.g. Sq , but experimental accuracy was insufficient to distinguish between them (49). 

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). 

The status of current theories of the low shear-rate viscosities (rj0) of polymer melts (and concentrated solutions) was reviewed by Berry and Fox in 1968 (52), since when there has been little development. The viscosity of linear polymers of low MW at constant temperature (or more precisely constant free volume is proportional to Mw, but at high MW it is proportional to a higher power M, where x is empirically about 3.4-3.5 the change of slope of a ogt]0/logMw plot is fairly abrupt The high exponent 3.4—3.5 is attributed to the effects of chain 

Bueche extended his theory of melt viscosity, as affected by chain entanglements, to branched polymers, and obtained (55) the result  

Bueche s results apply to monodisperse polymers. Ajroldi and co-workers (62) have calculated the melt viscosity of polydisperse polymers such as would be produced by random trifunctional and tetrafunctional branching, as a function of Mw, assuming Eq. (5.1) to hold and making specific assumptions about the additivity of melt viscosity in polydisperse polymers. Because of these assumptions their results must be regarded as illustrative only but they show that large effects may be expected, the calculated melt viscosity of the branched polymer being lowered by more than two orders of magnitude in some cases. 

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Studies of polystyrene standards in THF solvent are not uncommon. however, bothersome discrepancies still exist in the literature and in practice. For example, the published Mar 1<-Houw i nk parameters are in wide disagreement il. The purpose of this work is to examine a large number of PS standards from multiple suppliers, covering a wide range of molecular weights. T -,e intrinsic viscosities and GPC retention volumes have been measured and used independently to correlate and crosscheck the molecular weights provided by the suppliers. 

It is now generally accepted that the GPC retention volume is a function of the product M tf, independent of the nature or structure of the polymer 46, 47) though Pannell 45) found that it failed to correlate the elution behaviour of his highly branched polystyrenes, it may be accepted that M rf will be determinable from GPC retention volumes for moderately branched polymers. To estimate branching, it is necessary to separate this product so that M and [rf are both known and the relation between them can then be used, subject to the uncertainties mentioned in Subsection 9.2.2, for this purpose. It is usual to measure rf rather than M in order to make the separation, as it is easier. The combination of GPC and intrinsic viscosity measurements is now the most usual method for studying long branching. 

To use GPC for molecular weight determination, we must measure the volume of solvent that passes through the column before a polymer of particular molecular weight is eluted. This quantity is called the retention volume Vj. Figure 9.14 shows schematically the relationship between M and Vj it is an... 

Figure 9.14 Calibration curve for GPC as log M versus the retention volume Vj, showing how the location of the detector signal can be used to evaluate M. Also shown are the void volume Vy and the internal volume Vj in relation to Vj, and KVj as a fraction of Vj.

One of the most important properties of a chromatographic column is the separation efficiency. A measure of this parameter could be the difference of the retention volume for two different compounds. The result of a GPC analysis is usually, however, only one large peak, and a separation into consecutive molar mass species is not possible. Additionally there is no standard for higher molar masses consisting only of a species that is truly monodisperse. Therefore, the application of the equation to the chromatographic resolution of low... 

Normally a calibration curve—molar mass against the total retention volume—exists for every GPC column or column combination. As a measure of the separation efficiency of a given column (set) the difference in the retention of two molar masses can be determined from this calibration curve. The same eluent and the same type of calibration standards have to be used for the comparison of different columns or sets. However, this volume difference is not in itself sufficient. In a first approximation the cross section area does not contribute to the separation. Dividing the retention difference by the cross section area normalizes the retention volume for different diameters of columns. The ISO standard method (3) contains such an equation... 

Fig. T A shows the GPC traces obtained at wavelength 2 k and 3U0 nm for a 312 nm Dow latex sample. Note the response at 3 0 nm is at twenty-five times the sensitivity of the response at 25 nm and hence considerably exaggerated in comparison. At 25 nm two peaks are clearly noted, a polymer peak and a secondary peak whose retention volume corresponds to that of styrene monomer. At 3 0 nm, since neither monomer nor polymer absorb, the observed peak is attributable to the presence of additives such as emulsifier.

CHROMATOGRAM (F(v)) F(v) conventional raw chromatogram heights as a function of retention volume " MODEL MODEL r CUm(S)TJ where - (j W dX)/X PROPORTIONAL TO WEIGHT OF POLYMER INJECTED INTO THE GPC... 

Figure 12 were superimposable on those for detector 2. Therefore, when the plot shown in Figure 14 is linear over the range of compositions involved in the sample, then (according to equations (1-4) ) the composition of the sample is the same at each retention volume. If the variation with retention volume is negligible the copolymer can then possibly be treated as is a homopolymer in GPC interpretation. In particular, intrinsic viscosity measurements could then lead to estimates of molecular weight via the universal calibration curve. 

To study the bulk copolymerization of styrene n-butyl methacrylate both conventional and unconventional GPC analyses were used. The normally obtained chromatograms, (from dual U.V. detectors) primarily provided area ratios intficative of composition as a function of retention volume. However, even this information was only obtainable after average compositions had been otherwise determined. Furthermore, in general, since the GPC normally separates on the basis of hydrodynamic volume, the polydispersity of aU polymer molecular properties at e h retention time is of serious concern. 

GPC 1 retention time at which chromatogram slice was obtained for GPC 2 Retention volume... 

It was then possible to screen some possible candidates and come up with the probable presence of a chlorinated paraffin. This material was found to elute at the same retention volume as di-2-ethylhexyl-phtha-late and showed no response at 254 nm (Figure 6). For quantitation UV/RI response ratio provided all the data required. However, in order to confirm the presence of this additional component, the sample was hydrolyzed and the acid converted to its dimethyl ester. The products were then examined by GPC. The UV response for the peak of interest was completely... 

The GPC of a local crude (Bryan, Texas) sample spiked with a known mixture of n-alkanes and aromatics is shown in Figure 5 and the GPC of the crude is shown in Figure 6. The hydrocarbon mixture is used to calibrate the length of the species which separates as a function of retention volume. Ttie molecular length is expressed as n-alkane carboa units although n-alkanes represent only a fraction of the hydrocarbons in the crude. In addition to n-alkanes, petroleum crude is composed of major classes of hydrocarbons such as branched and cyclic alkanes, branched and cyclic olefins and various aromatics and nonvolatiles namely asphaltenes. Almost all of the known aromatics without side chains elute after n-hexane (Cg). If the aromatics have long side chains, the linear molecular size increases and the retention volume is reduced. Cyclic alkanes have retention volumes similar to those of aromatics. GPC separates crude on the basis of linear molecular size and the species are spread over 10 to 20 ml retention volume range and almost all of the species are smaller than the polystyrene standard (37A). In other words, the crude has very little asphaltenes. The linear... 

Details of the data analysis for the GPC/Viscometer system have been reviewed by Ouano.(T ) The data reduction scheme is summarized in Figure 2 and briefly will be discussed here. The intrinsic viscosity of the effluent at a given retention volume [n](v) is determined from the DRI and continuous viscosity detector responses according to the following equation... 

A universal calibration curve was developed, using the retention volume vm corresponding to the DRl detector peak maximum of eluting polystyrene calibrants. Data were fitted with the GPC-II program to an equation of the form ... 

The kinetics of the different condensation steps till (7) (and equivalent structures in the TBA system) are similar for TPA and TBA. This is illustrated using GPC data in Fig.2. The GP chromatograms of extracts after 5, 10, 15 and 45 minutes of hydrolysis illustrate the consecutive formation of species identified as dimers of tetracyclic undecamer (4) and (4 ), precursor (5), dimers of precursors (6) and trimer of precursors (7). The assignment is based on the retention volumes and previous identification with 29Si liquid NMR for the TPA system [2]. The GPC traces show that the transformation of species of type (4), (4 ) and (5) into (6) and (7) is slower with TBA than with TPA. This coupling of precursors seems to be hindered by the long butyl chains of occluded TBA. 

The largest silicate species in the extracts of the concentrated TEA system after 45 min, detected with GPC as a shoulder on the main peak, has a retention volume characteristic for dimer of tetracyclic undecamer (Fig.2). This indicates that the first steps of the TEOS polycondensation processes till the formation of (4) and (4 ) occur with TEA as well. This is in agreement with the proposed model in which TEOS hydrolyses at the TEOS-aqueous interfaces in the vicinity of the alkyl groups of the tetraalkylammonium cations (Fig.l). These alkyl groups favor the formation of the hydrophobic silica surfaces encountered already in the smallest species (l)-(3). The absence of trimers... 

Evaluation and Preparative GPC Fractionation of PMMA. The baseline-adjusted retention volume curves of the preparative GPC fractions are shown in Figure 3. The characterization data are shown in Table III. 

Values of Re can be calculated from Equation 6 for narrow fractions of known molecular weights and plotted as a function of Vr, the retention volume. n and w can then be calculated from the GPC molecular-size distribution curve for unknown whole polymers. To obtain /W from Equation 8 requires a value for q. 

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [7/] M) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydro-dynamic volume since [77] M is proportional to the hydrodynamic volume of the molecule in solution. Hence, molecular weights of the two polymers (calibration standard polymer and sample) which have identical retention volume under identical GPC analytical conditions can be expressed in terms of each other by combining the Grubisic relationship ... 

Figure 1. Disagreement between viscometric and GPC viscosity-average molecular weight vs. weight percent of the sample component with retention volume less than the highest molecular weight calibration standard...

The effect of limited penetration of the pores by the largest molecules may also be applied beneficially for the separation of very large molecules. Depending on the size of the molecules (in solution), they will be more ore less excluded from the pores, and hence the retention times will be affected. This effect is used in size exclusion chromatography (SEC) or gel permeation chromatography (GPC). In this technique, any interactions between the solute molecules and the stationary phase are purposefully avoided. The solute molecules remain exclusively in the mobile phase, but the accessible mobile phase volume, and hence the retention volume, may vary between the total volume of the mobile phase and the so-called exclusion volume, which is the total volume of mobile phase outside the pores. The latter elution volume applies to very large solute molecules (excluded solutes),... 

It is also necessary to monitor the volume of solvent which has passed through the GPC column set from the time of injection of the sample (this is called the elution volume or the retention volume). Solvent flow is conveniently measured by means of elapsed time since sample injection, relying implicitly on a con.stant solvent pumping rate. As an added check on this assumption, flow times may be ratioed to those of a low-molecular-weight marker that provides a sharp elution peak at long flow times. 

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