Universal calibration curve for

PMMA, on the unmodified porous glass and silica gel, and the universal calibration curves for polystyrenes and poly(methyl methacrylates) did not coincide (10,12,19). 

FIGURE 20.3 Universal calibration curve for TSK-PW columns with an aqueous mobile phase of 0.10 N sodium nitrate. 

Figure 19. Universal calibration curves for GPC 1 and GPC 2 based on hydrodynamic volume in GPC 1 (Vthf) (J) 100% THF (B3, Table I) obtained by sampling narrow standards infected into GPC 1 (A3, Table I) (2) 57% n-heptane in THF (B4, Table 1) (obtained as in 1 above) (3) 57% n-heptane in THF (B4, Table 1), obtained by direct injection into GPC 2 (4) 62% n-heptane in THF (B5, Table 1) (obtained as in 3 above) (5) 100% THF (A3, Table I), obtained by sampling GPC 1 (NBS706, 0.375 and 0.750 mg into GPC 1 and...

Consequently, a relatively low molecular weight polymer (MM=1.39x 10 ) has an intrinsic viscosity (25.6 dl/g) equivalent to a PS or PDMS more than lOx higher in MW. (Earlier GPC work on PBIC (9) and PHIC (7) had shown no deviations from the universal calibration curve for GPC at high molecular weights). The primary role of chain flexibility in GPC degradation rather than simple molecular hydrodynamic volume is conclusively shown by these results. 

FIG. 2.4 Example of a universal calibration curve for GPC. From Billmeyer (1984) Courtesy John Wiley Sons. 

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. 

Universal calibration curve for size exclusion chromatography. Data points are polybutadienes in tetrahydrofuran at 25 °C in crosslinked polystyrene columns. There is a reasonably linear region of the calibration curve spanning the data (solid line) but the linear region has its limits (dotted curves). 

Figure 4.28 A universal calibration curve for several polymers in tetrahydrofu-ran. (Drawn with data from Ref. 19.)...

FIGURE 9.10 A universal calibration curve for several polymers in tetrahydrofuran. (Reproduced from data by Grubisic, Z., Rempp, R, and Benoit, H., A Polym. Sci. Polym. Lett., 5, 753, 1967. With permission. Copyright John Wiley Sons, New York.)... 

This method was applied to styrene-isoprene block copolymers of AB and ABA types having relatively narrow molecular mass distributions [11]. Universal calibration curves for PS, polyisoprenes, and their block copolymers fell on the same line. Conversion to log M v. Fr was accomplished by obtaining intrinsic viscosities of these copolymers, which were closely related to those of the corresponding homopolymers of equal molecular mass by... 

The Mark-Houwink constants influence the accuracy of the universal calibration curve. The discrepancy between universal calibration curves for PS and P(VC-VAc) copolymers observed by Chen and Blanchard [15] may be due to misuse of the Mark-Houwink constants for polystyrene. These authors obtained the Mark-Houwink equation for P(VC-VAc) copolymers as... 

Since [ /] is known from the viscosity measurement, Wi from SEC curves, and Ji from the universal calibration curves for PS, the value of K corresponds to the value of a and may be determined. Application of this method resulted in lower molecular mass averages than with the use of the eqns (5.18) and (5.19). 

The data are then plotted as log [>>]M versus Vg, as shown In Figure 2. When the test sample is examined in the same column, the product [ i]M can be read directly from the calibration curve. For calculation of the molecular weight, either of two approaches me(y be followed. If the project is of limited scope, one can determine the intrinsic viscosity of the sample, and calculate M from the product [ ]H obtained directly from the universal calibration curve. For projects with a broader scope, it would be desirable to fractionate a preparation with a broad distribution of molecular weights into fractions with narrow distributions by either preparative SEC or established chemical methods (e.g. selective precipitation with organic solvents). The molecular weights and intrinsic viscosities of these samples would then be determined experimentally, followed by the calculation of the Mark-Houwink constants. Finally, the molecular weight of any sample can be calculated from the [>i]M value read from the curve, by the equation [ i]M =... 

The most practical parameter for the size of random coil molecules would be the radius of a hydrodynamically equivalent sphere (Stokes radius). This quantity can be directly determined through the measurements of viscosity, diffusivity or sedimentation velocity, and abundant data have been accumulated. The results of SE measurement can be conveniently expressed in terms of this quantity. This way of presentation at the same time serves as the "universal calibration curve" for SEC columns. 

The raw Crystaf profile provides information about the distribution of crys-tallizabilities of the polymer sample that can be correlated to molecular structure with the use of a proper calibration curve. Contrary to SEC, there is no universal calibration curve for Crystaf for quantitative analysis, calibration curves should be prepared with narrow standards that have microstructures as similar as possible to the sample being analyzed. 

Fig. 26. Universal calibration curve for SEC. Polystsrrene (linear) O polystyrene ( comb ) + polystyrene ( star ) A polystyrene-poly(methylmethacrylate) copolymer (heterograft) x poly(methylmethacrylate) (linear) poly(vinylchloride) V polystyrene-poly(methylmethacrylate) copolymer (graft-comb) Bpolylphenyl siloxane) A polystyrene-poly(methylmethacrylate) copolymer (statistical-linear) n polybutadiene. From Ref 31.

Figure 3.23 The universal calibration curves for polystyrene and poly(vinyl acetate) (94), The number 5 in the x-axis units means that the scale is in siphon counts of 5 cm so that the x-ordinate 30 corres 3onds to an elution volume of 150cm (R. Dietz, private communication, November 1984,) Mr is the peak GPC molecular weight, usually the unknown, Rvalues are close to the geometric mean of M and M .

The method commonly involves the use of the universal calibration curve for GPC and the expression... 

FIGURE 9.15 Universal calibration curve for different polymer types and structures established using an onbne viscometer and an RI detector [18]. 

Fig. 3.26 Universal calibration curve for crosslinked polystyrene gels with tetrahydrofuran as solvent %y linear polystyrene 0 branched polystyrene (comb type) +, branched polystyrene (star type) A, branched block copolymer of styrene methyl methacrylate x, poly (methyl methacrylate) poly (vinyl chloride) V, graft copolymer of styrene methyl methacrylate , polybutadiene (reprinted with permission from Comprehensive Polymer Science, copyright 1989, Pergammon Press pic).

The calibration curve, strictly speaking, applies only to the particular polymer, solvent, temperature, flow rate, and column for which it was established. Change any one, and the calibration is no longer valid. Most SEC calibrations are obtained with polystyrene, because the necessary monodisperse standards are readily available at reasonable cost. What do you do when you want to analyze another polymer One approach was suggested by Grubisic et al. When they plotted log([ /]M) (the product MM is proportional to the hydrodynamic volume of the molecules) vs. v, they obtained a single, universal calibration curve for a variety of different polymers. Thus, if you measure intrinsic viscosity along with SEC elution volume for your polystyrene stand-... 

Figure 8.14 Examples of the universal calibration curve for GPC. (a) Universal calibration for tetrahydrofuran solution at ambient temperature , linear polystyrene , polybutadiene O, branched polystyrene x, polymethyl methacrylate A, styrene/ methyl methacrylate copolymer , poly(phenyl siloxane). (b) Universal calibration for various types of polyethylene. Solvent, o-dichlorobenzene at 130°C. , linear polyethylene fractions open symbols, branched polyethylene fractions. (From Ref 6.)...

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