Curve molecular mass

FIGURE 2.4 Calibration curve of dextran on Sephacryi S-300 SF. Calibration curves were calculated from one chromatogram of a broad MWD reference sample using data for the molecular mass distribution as obtained by a calibrated gel filtration column ( , upper curve) and on-line MALLS ( ). The calibration curve was found useful for estimating the size of globular proteins. [Reproduced from Hagel et al. (1993), with permission.]... 

Yield strength as determined in tensile tests [53] at ambient temperature was plotted in Fig. 6.1 against M 1, the inverse molecular mass between crosslinks. All the samples of polymer A (the most crosslinked polymer) failed before the polymer started to yield. Therefore, load-extension-curves were extrapolated up to a hypothetical yield strain in this case. The extrapolated tensile is marked by brackets (Table 6.1). 

Fig. 7-10 Kohler curves calculated for the saturation ratio Phjo/PhjO of a water droplet as a function of droplet radius r. The quantity im/M is given as a parameter for each line, where m = mass of dissolved salt, M = molecular mass of the salt, i = number of ions created by each salt molecule in the droplet.

Gel Filtration. The lyophilized protein was redissolved in 50 mM phosphate buffer, pH 7.4 0.15 m NaCl 0.013 % sodium azide and loaded on a Superdex 75HR1030 column equilibrated with the same buffer. Elution was downward flow (0.15 ml/min) and 0.25 ml fi actions were collected. Fractions with pectin lyase activity were combined, dialyzed against distilled water and used in the next step. To estimate the molecular mass of PNL, the column was calibrated with standard proteins (Sigma MW-GF-70 Albumin, 66,000 Da Carbonic Anhidrase, 29,00 Cytochrome, 12,400 and Aprotinin, 6,500). The proteins were eluted in the conditions described above and their volumes (F ) were calculated fi om the peak maximum of the absorbance at 280 nm. The partition coefficient was obtained fi om the relationship where F, represents the bed volmne of column and F the void volume (which was calculated using blue dextran. Sigma). The molecular mass was determined using a standard curve of vs the logarithm of the molecular masses of the standards [28, 29]... 

In Fig. 3.4d the relative molecular mass of the solute, Mr, is plotted on a log scale against the retention volume. The interstitial volume, which represents the volume range within which separations occur, and the size range of solutes that are eluted in this volume range, depend on the sort of material that is used for the stationary phase. Because for a given separation, F0 and V are constant, we can reliably predict the total volume of solvent or the time taken for a particular analysis. The calibration curve is established by determining the retention volume for standards of known Mr. 

Fig. 10a, b. Contributions of the different modes to the relaxation of the dynamic structure factor S(Q,t)/S(Q,0) (see text) for PE of molecular masses, a Mw = 2.0 x 103 g/mol and b Mw = 4.8 x 103 g/mol. The experimental Q-values are indicated by vertical lines curves correspond to mode numbers increasing from bottom to top. (Reprinted with permission from [52]. Copyright 1993 The American Physical Society, Maryland)... 

The obvious definition of the number average, Mn, of the distribution is the position on the M-axis that divides the area under the n (A/)- curve in equal parts (cf. Fig. 1.3). Because of the fact that n M) is normalized to 1, each of the subareas is equal to 0.5. As 50% of all the molecules are shorter than Mn, the other 50% are longer than Mn. Bearing in mind the normalization, the number average molecular mass is... 

Figure 7.1 Separation of proteins by SDS-PAGE. Protein samples are incubated with SDS (as well as reducing agents, which disrupt disulfide linkages). The electric field is applied across the gel after the protein samples to be analysed are loaded into the gel wells. The rate of protein migration towards the anode is dependent upon protein size. After electrophoresis is complete, individual protein bands may be visualized by staining with a protein-binding dye (a). If one well is loaded with a mixture of proteins, each of known molecular mass, a standard curve relating distance migrated to molecular mass can be constructed (b). This allows estimation of the molecular mass of the purified protein...

Levine and Slade [1.16] investigated the mechanics of cryostability by carbohydrates. Figure 1.19.1 shows an idealized phase diagram developed from differential scanning calorimetry (DSC) measurements for hydrolyzed starch (MW > 100) and for polyhydroxy combinations having a small molecular mass. With slow cooling (quasi in equilibrium conditions), no water crystallizes below the Tg curve. 

The elution volume of a solute is determined mainly by its relative molecular mass and it has been shown that the elution volume is approximately a linear function of the logarithm of the relative molecular mass. It is possible to determine the relative molecular mass of a test molecule using a calibration curve prepared from the elution volumes of several reference substances of known relative molecular mass. This should be done using the same column and conditions (Figure 3.37) and in practice it may be possible to calibrate the column and separate the test substance at the same time by incorporating the reference compounds in the sample. Such a method is rapid and inexpensive and does not demand a highly purified sample, provided that there is a specific method for detecting the molecule in the eluate. 

In each gel, a lane of standard proteins of known molecular masses is run in parallel with the test proteins. After staining the gel to make the protein bands visible (Subsection 8.2.8), the migration distances are measured from the top of the resolving gel. The gel is calibrated with a plot of log Mr vs. migration distances for the standards. The migration distances of the test proteins are compared with those of the standards. Interpolation of the migration distances of test proteins into the standard curve gives the approximate molecular masses of the test proteins. 

Once the amounts and molecular weights of the fractions have been determined, the molecular-weight distribution of a polydisperse material can be expressed graphically in the form of a distribution curve. The mass distribution function is written as ... 

Calculation of the molecular mass of an unknown protein follows the same procedure as, for example, quantitative protein determination plotting of the Rf of the calibration proteins against their molecular mass computing of a standard curve and estimation of the MW of the unknown protein and using the regression functions of the standard curve (c.f Fig. 2.1). 

Yield stress values can depend strongly on filler concentration, the size and shape of the particles and the nature of the polymer medium. However, in filled polymer melts yield stress is generally considered to be independent of temperature and polymer molecular mass [1]. The method of determining yield stress from flow curves, for example from dynamic characterization undertaken at low frequency, or extrapolation of shear viscosity measurements to zero shear rate, may lead to differences in the magnitude of yield stress determined [35]. 

A polymer, even in its pure state, corresponds to a distribution of macromolecules with different masses. Exclusion chromatography can determine the distribution in molecular weights and the most probable mass and the mean mass. For this type of application, a calibration curve is made using macromolecules of known masses by plotting the retention times (or volumes) on the abscissa and the logarithms of the molecular masses on the ordinate. As can be seen in Fig. 7.5, a linear relationship is obtained. Using this graph, an approximate mass of the unknown can be determined by use of the retention time (volume). This assumes that the mass and the molecular volumes are directly related. 

Figure 7.5—Determination of molecular mass. The use of a calibration curve made with standards of known molecular masses. It should be noted that the calibration curve is linear over a wide range of masses due to the use of a mixture of stationary phases. (Reproduced by permission of Polymer Lab.) The bottom right figure shows the geometry assumed by a linear polymer in solution (figure from PSS).

Figure 26-38 Calibration curve for protein molecular mass in sodium dodecyl sulfate-capillary gel electrophoresis. The abscissa, fre, Is the migration time of each protein divided by the migration time of a small dye molecule. [Data from j. K, Grady, J. Zang, t. M. Laue, RArosio, and N. D, Chasteen, "Characterization of the H- and L-Subunlt Ratios in Ferritins by Sodium Dodecyl Sulfate-Capillary Gel Electrophoresis," Anal. Biochem. 2002,302.263.)...

Figure 3-10 Estimation of the molecular mass of the polypeptide chain of the nitrogenase Fe-protein using SDS-poly-acrylamide electrophoresis from a set of four standard curves. The marker proteins are (1) catalase, (2) fumarase, (3) aldolase, (4) glyceraldehyde-phosphate dehydrogenase, (5) a-chymotrypsinogen A, and (6) myoglobin, (o) indicates position of azoferredoxin. From Nakos and Mortenson.195...

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