Molar-mass dependent chemical composition

Composition drift, that is, variations in the polymer composition with variations in the molar mass, can be observed by combining SEC (separation according to molar mass) with methods that yield information on the chemical composition. Online combinations are denoted with a hyphen (e.g. SEC-IR, SEC-NMR, SEC-MS) and are hence known as 

The easiest hyphenated system consists of an LC instrument with a multi-wavelength (e.g. diode-array) UV detector. Such a system is excellent for characterizing copolymers consisting of two or more types of monomeric units, all of which exhibit (different) UV activity. Unfortunately, this is hardly ever the case. A combination of a UV detector and a refractive-index (RI) detector connected in series does in principle provide sufficient information for copolymers (two different monomeric units). However, the interdetector volumes and band broadening are a complicating factor, as are the different background and blank signals (solvent peaks) provided by the two instruments. 

LC and SEC can be coupled with other spectroscopic techniques, such as FTIR or NMR spectroscopy, or with MS. 

The offline (Adrian et al., 2000) and online (Kok, 2004) coupling of FTIR spectroscopy with comprehensive two-dimensional LC (LC x SEC, see Section 7.4.4.) has already been demonstrated. 

The combination of LC and NMR is arguably the most attractive hyphenated system for polymer analysis, as well as in many other fields. NMR may yield a wealth of information on molecular composition and structure (e.g. chain regularity, branching, comonomer sequence see Section 7.4.1). Also, as mentioned in Section 7.4.1, NMR provides excellent opportunities for quantitative analysis. Thus, LC-NMR is a highly desirable proposition for polymer analysis. 

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The phase behaviour of such a system strongly depends on details in the interaction and may change completely upon variations in pressure, temperature, molar mass and chemical composition of the polymer(s). As in polymer solutions, blends may show upper critical, lower critical, or hourglass type demixing behavior. 

We have carried out a wide range of studies concerned with the dextran concentration dependence of the transport of the linear flexible polymers and have varied both molecular mass and chemical composition of this component. Moreover, we have studied the effect of the variation of the molar mass of the dextran on the transport of the flexible polymers 51). In general, the transport of these polymers in dextran solutions may be described on common ground. At low dextran concentrations the transport coefficients of the polymers are close to their values in the absence of the dextran and may even exhibit a lower value. This concentration range has been discussed in terms of normal time-independent diffusional processes in which frictional interactions predominate. We have been able to identify critical dextran concentrations associated with the onset of rapid transport of the flexible polymers. These critical concentrations, defined as C, are summarized in Table 1. They are... 

All potentially molar-mass-dependent quantities have been labelled with a summation index k in Eq. (30), which, in this form, also holds for dilute solutions of mixtures of chemically different species or copolymers with heterogeneity of both chemical composition and degree of polymerization. 

Equation (33) can be further simplified in the case of homopolymers or copolymers with constant chemical composition. It is well known from the literature that Dtis independent of molar mass [11,21,36,37], and the same holds for (dnldck)p>T>Cl kif M is sufficiently high to neglect end-group effects. Under these preliminaries, the molar mass dependence of ak reduces to the concentration of the respective species ak c0>k. 

The HPLC-SEC analysis of a 16-component star block St-Bd copolymer showed very good selectivity. The gradient HPLC could be optimized to fractionate by chemical composition subsequent SEC automatically characterized the fractions for their molar mass dependence. All 16 components could be isolated and could be quantified. 

Since most recent polymers are complex mixtures, in which the composition and molar mass depend in multiple ways on the polymerization kinetics, the polymerization technique, and the process conditions, the polymer processing parameters must be carefully controlled and monitored to obtain polymeric materials with the desired properties. It is essential to understand the influence of molecular parameters on polymer properties and end-use performance. Molar mass distribution and average chemical composition may no longer provide sufficient information for process and quality control nor define stmcture-property relationships. Modern characterization methods now require multidimensional analytical approaches rather than average properties of the whole sample [5]. 

As expected, a small molar mass dependence of the H PLC separation is indicated by a drift of the peaks for components of similar chemical composition (e.g., with peaks nos. 1, 5, 9, and 13). This kind of behavior is normal for polymers, because pores in the HPLC stationary phase lead to size-exclusion effects, and these overlap tvith the enthalpic interactions at the surface of the stationary phase. The 2D experiment is sufficiently sensitive to reveal influences of this type. The amount of butadiene in each peak could be qmntitatively determined through an appropriate calibration with samples of known composition. The molar masses could be calculated based on a conventional molar mass calibration of the second dimension. 

FIGURE 5.2 Molar mass dependences of elution volume for polystyrene on Eurogel-P-RP-100 column at different eluent compositions of THF-hexane. Source Reprinted with permission from H. Pasch, A. Deffieux, I. Henze, M. Schappacher, L. Rique-Lurbet, Analysis of Macrocyclic Polystyrenes. 1. Liquid Chromatographic Investigations., Macromolecules, 29 (1996) 8776. (1996) American Chemical Society (Ref. [9]). 

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. 

Fast high-pressure fractionation of tails in the molar-mass-distribution and/or the chemical-composition-distribution of a (co)polymer [47] during the polymerisation process will indicate eventual drifts in (co)polymer composition. Several important polymer properties depend strongly on such tails in the (co)polymer distribution. On--line fractionation data are strongly needed. 

Molar mass determination requires the knowledge of the specific refractive index increment Ant Ac which in the case of complex polymers depends on chemical composition. Copolymer refractive index increments (dn/dc)copo can be accurately calculated for chemically monodisperse fractions, if comonomer weight fractions and homopolymer values are known ... 

The classical approach is based on the dependence of copolymer solubility on composition and chain length. A solvent/nonsolvent combination fractionating solely by molar mass would be appropriate for the evaluation of MMD, another one separating with respect to chemical composition would be suited for determining CCD or FTD. However, in reality, precipitation fractionation yields fractions which vary both in chemical composition and molar mass. Even high resolution fractionation would not improve the result. Narrower fractions can be obtained by cross-fractionation separating in two different directions. However, even in this case, it is almost impossible to obtain perfectly homogeneous fractions. 

One of the unique characteristics of Th-FFF is that retention depends not only on the molar mass but also on the chemical composition of the polymer. This chemical differentiation is due to the dependence of the underlining thermal diffusion process on polymer (and solvent) composition [84]. This effect can likely be used to determine compositional distributions in copolymers and blends [111]. Figure 10 compares the resolving power of Th-FFF and SEC on two polymers of similar molecular weight but varying chemical composition. The polymers coelute in SEC because their sizes are similar whereas Th-FFF resolves the polymers because they differ in chemical composition. 

Recent studies [111,214] indicate that Th-FFF can even be used to determine the relative chemical composition of two components in random copolymer and linear block copolymers whose monomers do not segregate due to solvent effects. However, this application is limited by the unpredictable nature of thermal diffusion. Nevertheless, combining information from Th-FFF with those derived on fractions by independent detectors selective to composition (such as an IR spectrometer) can yield further insight into the dependence of DT on the chemical composition. Even more powerful is the combination of Th-FFF with SEC as, here, the chemical composition (from Th-FFF) can be studied as a function of the molar mass (from SEC). This was demonstrated by van Asten et al. by cross fractionating copolymers and polymer blends with SEC and Th-FFF [358]. 

Using the value of a determined above, the results of the standard assay made initially to check the enzyme activity, the assay in part C, and the given concentration of the enzyme stock solution in g L , calculate the specific activity of the enzyme— that is, the number of micromoles of sucrose hydrolyzed per minute per gram of enzyme present. (The specific activity of an enzyme preparation is of course a function of the purity of the enzyme. As inactive protein is removed from the preparation, the specific activity will rise. When the specific activity can no longer be increased by any purification method, a homogeneous enzyme preparation may have been achieved but proof of this depends on other criteria.) The exact chemical composition of invertase is still unknown, but its molar mass has been estimated at 100,000 g mol Combining this datum with your calculated specific activity, estimate the turnover number for the enzyme. 

However, HPLC sorbents also show SEC behavior to some extent dependent on the pore size of the stationary phase relative to the molar size of the solute. Copolymers with the same composition but diflFerent molar masses will in general have somewhat diflFerent retention characteristics. This may lead to copolymer HPLC fractions with heterogeneous chemical compositions and may contain some chains with different molar mass and comonomer content. 

Block copolymers are an important class of polymers used in many applications from thermoplastic elastomers to polymer-blend stabilizers. Their synthesis is most often done by ionic polymerization, which is both costly and sometimes difficult to control. However, block copolymer properties strongly depend, for example, on the exact chemical composition, block molar mass, and block yield. These parameters can be evaluated in a single experiment using copolymer GPC with multiple detection. 

In analytical practice, the logarithm of sample molar masses, or molar volumes, is plotted versus retention volumes in calibration dependences of low molecular substances while values or effective hydrodynamic volumes, are used as size parameters in gel chromatography of macromolecules [12,13]. is often called universal calibration parameter because in ideal gel chromatography of randomly coiled macromolecules, it enables the transfer of data from one polymer to another regardless of both the physical (linearity, branching, tacticity, etc.) and the chemical (composition) structure of macromolecules [12]. The hydrodynamic volume of a particular polymer is proportional to the product of its molar mass and limiting viscosity number [ij], in the solvent that is used as mobile phase [ij]Mm. 

Liquid-liquid demixing in solutions of polymers in low molar mass solvents is not a rare phenomenon. Dembcing depends on concentration, temperature, pressure, molar mass and molar mass distribution function of the polymer, chain branching and end groups of the polymer, the chemical nature of the solvent, isotope substitution in solvents or polymers, chemical composition of copolymers and its distributions, and other variables. Phase diagrams of polymer solutions can therefore show a quite complicated behavior when they have to be considered in detail (see Ref la). 

Experimental techniques such as small-angle x-ray scattering and electron microscopy have been instrumental for the characterization of the ordered structures formed by block copolymers and their dependence on molecular parameters such as molar mass, chemical structure, and composition. 

All latex samples prepared by emulsion polymerization are characterized by a broad distribution of molar masses, and in the case of copolymer latexes, a distribution of copolymer composition. Since the diffusion coefficient for a polymer depends upon both the chain length and the chemical structure, the polymers in any one film sample will be characterized by a rather broad distribution of Dcm values. Experiments to detormine in such systems actually yield a value averaged over the distribution, Dts. As will be seen below, since different components of the system contribute to the measured signal at different times, and the fastest diffusing species dominate the diffusion at early times, experi-mental values of Detr decrease with the ext t of interdiffiision. For such sanqiles, one is normally less int sted in the absoluie values of than in how extonal... 

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