Homopolymer calibration curves

In such cases, the copolymer molar mass M can be determined from the interpolation of homopolymer calibration curves M V) and the weight fractions w. of the comonomers k according to [1]... 

From a SEC point of view, an AB block copolymer, where a sequence of comonomer A is followed by a block of B units, is a simple copolymer. The only hetero-contact in this chain is the A-B link, the A and B segments of the block copolymer will hydrodynamicaUy behave like a pure homopolymer of the same chain length. In the case of long A and B segments, the A-B link acts as a defect position and will not change the overall hydrodynamic behavior. Consequently, the molar mass of the copolymer chain can be approximated by the molar masses of the respective segments. Similar considerations are true for ABA, ABC, and other types of block stmctnres and for comb-shaped copolymers with low side-chain densities. In snch cases, the copolymer molar mass can be determined from the interpolation of the two homopolymer calibration curves M V) and the weight fractions of the comonomers k [26] ... 

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. 

The GPC analysis of block copolymers is handicapped by the difficulty in obtaining a calibration curve. A method has recently been suggested to circumvent this difficulty by using the calibration curves of homopolymers. This method has been extended so that the calibration curves of block copolymers of various compositions can be constructed from the calibration curve of one-component homopolymers and Mark-Houwink parameters. The intrinsic viscosity data on styrene-butadiene and styrene-methyl methacrylate block polymers were used for verification. The average molecular weight determined by this method is in excellent agreement with osmometry data while the molecular weight distribution is considerably narrower than what is implied by the polydispersity index calculated from the GPC curve in the customary manner. 

This is the case of parallel calibration curves discussed in the previous paper. Equation 4 shows that when the calibration curves are parallel, the equivalence ratio, r, is constant to the elution volume V. It varies with the latter when aA aB—i.e., the calibration curves are not parallel. For that case Equation 3 would have to be used. Equation 4 also shows that the equivalence ratio can be calculated from the Mark-Houwink parameters K and a. It offers a way to determine r in addition to obtaining it from the GPC calibration curves of homopolymers. 

Figure 7. Calibration curve relating experimentally measured C-ls/O-ls intensity ratios to the known carbon-to-oxygen stoichiometries of a series of oxygen-containing homopolymers POM, PVAc, PEO, and PMMA.

A calibration curve for a copolymer consisting of components A and B can be constructed from those for the two homopolymers A and B, if the relationships of the molecular weights and the molecular sizes of the two homopolymers are the same as their copolymer and if the size of the copolymer molecules in the solution is the sum of the sizes of the two homopolymers times the corresponding weight fractions. The molecular weight of the copolymer at retention volume I, Mq i, is calculated using... 

Although Dj varies with the polymer-solvent system, it is independent of molecular weight in a given system, at least for random coil homopolymers. The separation of differing molecular-weight components is therefore based solely on differences in D, which means that the principles of universal calibration that are relevant to SEC are also applicable to thermal FFF. Thus, a calibration curve made with one polymer-solvent system can be applied to other systems, provided the two Dj values associated with each polymer-solvent system are available. Fortunately, accurate values... 

When calibration curves for two homopolymers A and B are linear, another attempt at constructing a caUbration curve for a block copolymer has been reported [5]. When two calibration curves for homopolymers are parallel to each other, the following relation can be assumed ... 

When the linear calibration curves of two homopolymers are not parallel with each other. 

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... 

A calibration curve for diblock copolymers of PS and poly(ethylene oxide) was constructed by assuming that the size of diblock copolymer in solution was linearly related to the sizes of the corresponding homopolymers, and by observing that the two calibration curves for the homopolymers in DMF were parallel [28]. Then eqn (5.33) was obtained for a diblock copolymer and a PS... 

What one needs to interpret self-quenching data properly is a calibration curve relating mean decay time to local concentrations. More specifically one should be able to fit l(t) curves to the form predicted by Inokuti and Hirayama to obtain a measure of the actual distribution of dye/dye separations. Model studies are needed to demonstrate that simple chrcMBophores in homopolymer matrices show the appropriate behavior. Once Ro values are determined here, the way will be open to more quantitative interpretation of swelling and contraction in complex polyphasic polymer systems. 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

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