Functional copolymers, compositional

The copolymer composition equation relates the r s to either the ratio [Eq. (7.15)] or the mole fraction [Eq. (7.18)] of the monomers in the feedstock and repeat units in the copolymer. To use this equation to evaluate rj and V2, the composition of a copolymer resulting from a feedstock of known composition must be measured. The composition of the feedstock itself must be known also, but we assume this poses no problems. The copolymer specimen must be obtained by proper sampling procedures, and purified of extraneous materials. Remember that monomers, initiators, and possibly solvents are involved in these reactions also, even though we have been focusing attention on the copolymer alone. The proportions of the two kinds of repeat unit in the copolymer is then determined by either chemical or physical methods. Elemental analysis has been the chemical method most widely used, although analysis for functional groups is also employed. 

Figure 7.8 Mole fractions styrene (Mj) and methyl methacrylate (M2) in feedstock (f) and copolymers (F) as a function of the extent of polymerization. Average copolymer compositions are also shown. [From V. E. Meyer and R. K. S. Chan, Polym. Prepr. 8 209(1967), used with permission.]...

Fig. 1. Copolymer composition as a function of monomer feed ratio for various reactivity ratio combiaations, designated I—V and explained ia the text...

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

One final point should be made. The observation of significant solvent effects on kp in homopolymerization and on reactivity ratios in copolymerization (Section 8.3.1) calls into question the methods for reactivity ratio measurement which rely on evaluation of the polymer composition for various monomer feed ratios (Section 7.3.2). If solvent effects arc significant, it would seem to follow that reactivity ratios in bulk copolymerization should be a function of the feed composition.138 Moreover, since the reaction medium alters with conversion, the reactivity ratios may also vary with conversion. Thus the two most common sources of data used in reactivity ratio determination (i.e. low conversion composition measurements and composition conversion measurements) are potentially flawed. A corollary of this statement also provides one explanation for any failure of reactivity ratios to predict copolymer composition at high conversion. The effect of solvents on radical copolymerization remains an area in need of further research. 

Chain compositional heterogeneity is of particular relevance to functional copolymers which find widespread use in the coalings and adhesives industries.13,240,246 In these applications, the functional copolymer and a crosslinking agent are applied together and are cured to form a network polymer. The functional copolymers are based on functional monomers with reactive groups (e.g. OH), it is desirable that all copolymer molecules have a functionality of at least two. Nonfunctional polymer will not be incorporated and could plasticize the network or be exuded from the polymer. Monofunctional polymers are not involved in crosslink formation and will produce dangling ends. 

FIGURE 5.12 Change in the morphology of an A-B-A block copolymer as a function of composition. (From Walker, M. and Rader, C.P. (eds.). Handbook of Thermoplastic Elastomers, Van Nostrand Reinhold, New York, 1988.)... 

The rate of release of levonorgestrel from films of block copolymers of e-caprolactone and dl-lactic acid (drug load 30%) was shown to be a function of the copolymer composition. The rate was unchanged for compositions of 100% and 88% e-capirolactone, but decreased thereafter as the e-caprolactone content decreased (42). 

The limit of detection for this instrument is about 10 pg/ ml for polystyrene in 2-butanone,163 which is close to two orders of magnitude higher than that of the deflection-type DRI. Moreover, the response of the ELSD is linear over only two decades in concentration.163 The ELSD is a useful backup detector when the DRI or UV detectors are not appropriate, e.g., when the UV absorbance or RI change is a function of copolymer composition as well as concentration or in gradient elution systems where changes in solvent composition cause drift in baselines of the UV and DRI detectors. Compounds about as volatile as the solvent are poorly detected by ELSD. 

More recently, the same author [41] has described polymer analysis (polymer microstructure, copolymer composition, molecular weight distribution, functional groups, fractionation) together with polymer/additive analysis (separation of polymer and additives, identification of additives, volatiles and catalyst residues) the monograph provides a single source of information on polymer/additive analysis techniques up to 1980. Crompton described practical analytical methods for the determination of classes of additives (by functionality antioxidants, stabilisers, antiozonants, plasticisers, pigments, flame retardants, accelerators, etc.). Mitchell... 

In a first part of this paper, we will discuss results of a 27A1 NMR study of the binding of Al ions on acrylamide-acrylic acid copolymers as a function of pH, at the light of a simple electrostatic model. The second part deals with the phase diagrams, physical gelation and precipitation phenomenon, for different copolymer compositions and under various conditions of concentrations, pH and salinity. 

Figure 31 Copolymer composition as a function of monomer mixture composition in the case of styrene methyl methacrylate mixtures. Reproduced from Mercier and Marechal [15], Reproduit avec I autorisation de I editeur. Tous droits reserves.

The dynamic mechanical behavior indicates that the glass transition of the rubbery block is basically independent of the butadiene content. Moreover, the melting temperature of the semicrystalline HB block does not show any dependence on composition or architecture of the block copolymer. The above findings combined with the observation of the linear additivity of density and heat of fusion of the block copolymers as a function of composition support the fact that there is a good phase separation of the HI and HB amorphous phases in the solid state of these block copolymers. Future investigations will focus attention on characterizing the melt state of these systems to note if homogeneity exists above Tm. 

The best-known and simplest class of block copolymers are linear diblock copolymers (AB). Being composed of two immiscible blocks, A and B, they can adopt the following equilibrium microphase morphologies, basically as a function of composition spheres (S), cylinders (C or Hex), double gyroid (G or Gyr), lamellae (L or Lam), cf. Fig. 1 and the inverse structures. With the exception of the double gyroid, all morphologies are ideally characterized by a constant mean curvature of the interface between the different microdomains. 

The change in melting point and glass transition of the copolymers as a function of copolymer composition are also of particular interest because this reveals information about the copolymer microstructure. This is discussed along with the crystallinity characterization in the following section. 

Fig. 4. Crystallinity of several polyanhydride copolymers as a function of composition. From Mathiowitz et al. (1990b). Reprinted with permission.

When deriving this expression for the average composition distribution, authors of paper [74] entirely neglected its instantaneous constituent, having taken (as is customary in the quantitative theory of radical copolymerization [3,84]) the Dirac delta-function < ( -X) as the instantaneous composition distribution. Its averaging over conversions, denoted hereinafter by angular brackets, leads to formula (Eq. 101). Note, this formula describes the composition distribution only provided copolymer composition falls in the interval between X(0) and X(p). Otherwise, this distribution function vanishes at all values of composition lying outside the above-mentioned interval. 

Figure 1. Molar kerr constant values (x 10 ucm7SC 2mot ) calculatedforpolyfstyrene-co-p-bromostyrene) copolymers as a function of composition Cand tact icily pr Black squares are experimental results. (Reproduced from Ref 3. Copyright 1981, American...

The copolymer composition produced by these two catalysts can be estimated using the Mayo-Lewis equation [38] and these values of i and r2. Figure 10 depicts the hypothetical comonomer content in the polymer (F2) as a function of the mole fraction of comonomer in the reactor (f2). The good incorporator produces a material with higher F2 as f2 increases. In contrast, the composition from the poor incorporator is relatively flat across a broad range and increases only at very high values of/2. The F2 required to render the copolymer amorphous is comonomer-dependent for 1-octene, this value is near 0.19. In this hypothetical system, the good incorporator produces that composition at f2 = 0.57, at which the poor incorporator incorporates very little comonomer (F2 = 0.01). 

Even though the works of Bailey et al. [120,127] and Epps et al. [121] present very comprehensive studies about the variation of the morphology as a function of composition and topology, they did not study in detail the relationship microphase separation-crystallization . Several contributions have been made in this area, when the triblock copolymers have only one crystal-lizable block [101,118,119,122,126,128-130]. Some relevant aspects of these references have already been mentioned. 

Figure 2. G-value for radical production for poly(methacrylic acid-co-styrene) as a function of copolymer composition.

Multiplication by [M2] gives what are generally referred to as the copolymerization equations, Equations 7.17 and 7.19, which gives the copolymer composition without the need to know any free radical concentration, and which gives the composition of the growing polymer as a function of monomer feed (Equation 7.19). 

Fig. 16 Representative data from the surface wrinkling metrology, demonstrating the unprecedented range of moduli and the precision that the methodology unlocks a modulus of a thickness gradient library of PS (reproduced with permission from [72]) b modulus as a function of composition for P(S-I-S) triblock copolymer blends c modulus as a function of thickness for ultrathin PS films (reproduced with permission from [74]). The lines are meant to guide the eye and the error bars represent one standard deviation of the data, which is taken as the experimental uncertainty of the measurement...

Figure 6-1 shows the variation in the copolymer composition as a function of the comonomer feed composition for different values of r Mayo and Walling, 1950]. The term ideal... 

A useful method for analyzing copolymer composition as a function of conversion is that developed by Skeist [1946], Consider a system initially containing a total of M moles of the two monomers and in which the copolymer formed is richer in monomer Mi that is the feed (i.e., F >/i). When dM moles of monomers have been copolymerized, the polymer will contain F dM moles of monomer 1 and the feed will contain (M — dM)(f — df ) moles of monomer 1. A material balance for monomer 1 requires that the moles of Mi copolymerized equal the difference in the moles of Mi in the feed before and after reaction, or... 

Data for the feed and copolymer compositions for each experiment with a given feed are substituted into Eq. 6-36 and r2 is plotted as a function of various assumed values of r. Each experiment yields a straight line and the intersection of the lines for different feeds gives the best values of r and r2. Any variations observed in the points of intersection of various lines are a measure of the experimental errors in the composition data and the limitations of the mathematical treatment (see below). The composition data can also be treated by linear least-squares regression analysis instead of the graphical analysis. 

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