Copolymer molar mass averages

The calculation of copolymer molar mass averages and so on, and copolymer polydispersity D is done as in conventional GPC calculations using the copolymer molar mass calculated from Eq. (3). 

Copolymer molar mass averages etc. and copolymer polydispersity... 

The calculation of copolymer molar mass averages and copolymer polydispersity is made as in conventional SEC... 

The number average of the molar masses of the homosequences A or B and the number average of the copolymer molar mass are... 

Figure 10.18 reports the SEC calibration line for the random copolymer (the experimental points are marked as circles), along with the calibration lines for PDA (the butylene-adipate homopolymer) and for PBSe (the buty-lene-sebacate homopolymer). The genuine SEC calibration line for the random copolymer was used to compute molar mass averages, which turned out to be M = 8500, = 12800. It can be noted that the SEC calibration... 

Figure 25 demonstrates the importance of the 2D-LC for separation and molecular characterization of complex polymer system, the block copolymer poly-styrene-block-poly(methyl methacrylate). It is evident that SEC alone could not disclose presence of homopolymers in the block copolymer. On the other hand, LC LCD has well separated both parent homopolymers from the block copolymer within a single step and the online SEC colunm afforded their molar mass averages and dispersities. 

However, traditional chemical thermodynamics is based on mole fractions of discrete components. Thus, when it is applied to polydisperse systems it has been usual to spht the continuous distribution function into an arbitrary number of pseudo-components. In many cases dealing, for example, with a solution of a polydisperse homopolymer in a solvent (the pseudobinary mixture), only two pseudo-components were chosen (reproducing number and mass averages of molar mass of the polymer) which, indeed, are able to describe some main features of the liquid-liquid equilibrium in the polydisperse mixture [1-3]. In systems with random copolymers the mass average of the chemical distribution is usually chosen as an additional parameter for the description of the pseudo-components. However, the pseudo-component method is a crude and arbitrary procedure for polydisperse systems. 

Polymers vary by a number of characterization variables. The molar mass and their distribution function are the most important variables. However, tacticity, sequence distribution, branching, and end groups determine their thermodynamic behavior in solutions too. For copolymers, the chemical distribution and the average chemical composition are also to be given. Unfortunately, much less iirformation is provided with respect to the polymers or copolymers that were applied in most of the thermodynamic investigations in the original hterature. In many cases, the samples are characterized only by one or two molar mass averages and some additional information (e.g., Tg, T, Pb, or how and where they were synthesized). Sometimes even this information is missed. 

Volume fractions imply a temperature dependence and, as they are defined in equation (38), neglect excess volumes of mixing and, very often, the densities of the copolymer in the slate of the solution are not known correctly. However, volume fractions can he calculated without the exact knowledge of the copolymer molar mass (or its averages). Base mole fractions are seldom applied for copolymer systems. The value for A o, the molar mass of a basic unit of the copolymer, has to he determined according to the corresponding average chemical composition. Sometimes it is chosen arbitrarily, however, and has to he specified. 

In this section, we review the properties of a series of PNIPAM-b-PEO copolymers with PEO blocks of varying length, with respect to the PNIPAM block. Key features of their solutions will be compared with those of PNIPAM-g-PEO solutions. PNIPAM-b-PEO copolymers were prepared by free-radical polymerisation of NIPAM initiated by macroazoinitiators having PEO chains linked symmetrically at each end of a 2,2/-azobis(isobutyronitrile) derivative [169,170]. The polydispersities of PEOs were low, enabling calculations of the number-average molar mass for each PNIPAM block from analysis of their H-NMR spectra (Table 2). 

Fig. 10a Average hydrodynamic radii ((Rh)agg) and b weight-average molar mass ((Mw)agg) of the aggregates in aqueous block copolymer solutions at different polymer concentrations (c given in moles of PNIPAM blocks) at 45 °C a NE-A, b NE-B, c NE-C, d NE-1, e NE-2, and/ NE-3. (Reprinted with permission from Ref. [169] copyright 2002 American Chemical Society)... 

Rule 1.8 Specifications about mass fractions (w), mole fractions (x), molar masses (A/), relative molecular masses (M-), degrees of polymerization (DP) or the average values of the latter three quantities, may be expressed by placing the corresponding values in parentheses after the formula of the macromolecule in a manner analogous to that recommended for the naming of copolymers [6]. 

Whereas subscripts placed immediately after the formula of the monomeric unit or the block designate the degree of polymerization or repetition, mass and mole fractions and molar masses - which in most cases are average quantities - may be expressed by placing corresponding figures after the complete name or symbol of the copolymer. The order of citation is the same as for the monomer species in the name or symbol of the copolymer. Unknown quantities can be designated by a, b, etc. 

Fig. 15 Number average molar masses (Mn opc) and PDI values obtained for the first blocks and for the final copolymers of PMA, PnBA, PMMA, or PDMAEMA (25 units) with PEEA (25, 50, 75, and 100 units for 100% conversion). AH Mn pc values are calculated against PMMA standards. SEC eluent CHClsiNEtsii-PrOH. (Reprinted with permission from [87]. Copyright (2005) American Chemical Society)...

Consistent notation is adopted throughout this book. Diblock copolymers are written poly(monomer A) poly (monomer B) or PA-PB, where examples of PA and PB are illustrated in Fig. 1.2. Similarly, triblock copolymers are written poly(monomer A)-poly(monomer B)-poly(monomer C) or PA-PB PC. Deuterated blocks are denoted dpoly(monomer A) or dPA. The molar mass of a copolymer is denoted by M, or Af corresponding to the weight- or number-average respectively, and the composition is specified by the volume fraction of one component,/. In solution, the volume fraction of a copolymer is denoted [Pg.3]

In a solution containing both unimer and micelles, Ma, which is by definition more sensitive to low molar mass particles, is always less than the weight-average molecular weight, Mv. Further details on osmometry can be found in the review by Adams (1989), whilst examples of its application to micellar block copolymer solutions are given in Chapter 3. 

The mass-average molar mass of the block copolymer solute, M , and the second virial coefficient, A2, can be obtained from SLS. These quantities can be determined from the concentration dependence of the scattered light intensity using the relationship (cf. Section 1.4.10)... 

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