Of monomeric units

The most effective and widely used dispersants are low molecular weight anionic polymers. Dispersion technology has advanced to the point at which polymers are designed for specific classes of foulants or for a broad spectmm of materials. Acrylate-based polymers are widely used as dispersants. They have advanced from simple homopolymers of acryflc acid to more advanced copolymers and terpolymers. The performance characteristics of the acrylate polymers are a function of their molecular weight and stmcture, along with the types of monomeric units incorporated into the polymer backbone. 

Biopolymers are the naturally occurring macromolecular materials that are the components of all living systems. There are three principal categories of biopolymers, each of which is the topic of a separate article in the Eniyclopedia proteins (qv) nucleic acids (qv) and polysaccharides (see Carbohydrates Microbial polysaccharides). Biopolymers are formed through condensation of monomeric units ie, the corresponding monomers are amino acids (qv), nucleotides, and monosaccharides, for proteins, nucleic acids, and polysaccharides, respectively. The term biopolymers is also used to describe synthetic polymers prepared from the same or similar monomer units as are the natural molecules. 

FIGURE 1.10 The sequence of monomeric units in a biological polymer has the potential to contain information if the diversity and order of the units are not overly simple or repetitive. Nucleic acids and proteins are information-rich molecules polysaccharides are not. 

The propagation step of polymerization involves an addition of monomeric units to the growing centers followed by regeneration of these centers. A series of consecutive propagation steps yields eventually a long polymeric molecule. 

Since 1 is a monomer with low activity, copolymers 2 obtained at any stage of the copolymerization process, irrespective of the monomer ratio in the initial mixture, always contain a smaller amount of monomeric units of 1 than that in the corresponding monomer mixture. 1 being prone to enter the chain-transfer reaction, the increase of its content in the initial monomer mixture reduces substantially the reaction rate and decreases the molecular mass of the copolymers. It was found that copolymers 2 which contain 2—8% of monomeric units of 1 and are suitable for obtaining fibres must have a molecular mass between 45 000 and 50000. Such copolymers can be obtained with a AN 1 ratio in the initial mixture between 95 5 and 85 15. Concentrated solutions of copolymers, especially those with a molecular mass smaller than the above limit, are characterized by a very low stability which is a substantial shortcoming of these copolymers. 

It was established that for the further modification of copolymers, as well as that of finished fibres, using the aromatic amino group, and, in particular, to achieve deep staining, a content up to 2% of monomeric units of 7 in the copolymer is sufficient. 

The optimum molecular mass (Mw) of these copolymers containing 1,5-2% of monomeric units of 7, amounts to 47000—55 000 which makes it possible to obtain concentrated (15—17%) solutions with sufficiently high stability and to spin fibres with high physicomechanical properties (P = 36—40 gf/tex, (4—4,4 g/denie),... 

Copolymers of AN with diene monomers and, in particular, with butadiene and isoprene, deserve special attention. These copolymers with a predominating content of monomeric units of dienes are known to have been produced in the form of rubbers for a long time and are finding a broad application in various branches of technology. 

During the investigation of the principles governing the process of copolymerization of AN with ISP in DMSO at 30 °C in the presence of ammonium persulfate, it was established that the anisotropic type of copolymerization is characteristic for this pair of monomers. The azeotropic point, as it is seen from Fig. 1 corresponds to a content of 60% of monomeric units of ISP in the monomer mixture. 

As it can be seen from the above data, by introducing 4—15% of monomeric units of ISP into the macromolecules of the AN copolymer, the elastic properties of PAN fibres and, especially, their resistance to abrasion and double bends can considerably be improved. 

Copolymers of AN with ISP, containing more than 25% of monomeric units of ISP with a molecular mass of 50000 to 60000, obtained in emulsion at pH 3, in distinction to PAN, are capable of passing into the state of viscous flow without destruction and cyclization and are processed into fibres at 180—220 °C. When copolymers of higher molecular mass are used it is necessary to raise the temperature of processing. This leads to an intensive crosslinking and to cyclization, due to which it becomes impossible to obtain fibres from them. 

Insertion of monomeric units of 10 into macromolecules of PAN results in the lowering of the glass-transition and softening temperature and also reduces the cyclization intensity of the nitrile groups. 

Fibres based on AN copolymers containing 4—10% of monomeric units of JO42 and obtained by wet spinning from solutions in DMF have a much better (2-8 times) resistance to multiple deformations than PAN fibres and have a higher light-fastness than PAN fibres. They are, however, inferior to the latter with respect to abrasive resistance and thermal stability. 

Reactivity ratios for the copolymerization of AN and DM WS in DMSO were found to be rj =0,53 and r2=0,036, and in water r1=0,56 and r2=0,25. The higher reactivity of DM VPS in the copolymerization with AN in aqueous medium, as compared with its reactivity in DMSO, can be explained by a higher degree of dissociation of DMVPS in aqueous medium. This fact also produces a considerable effect on the character of the distribution of monomeric units within the copolymers, which manifests itself in the change of their solubility in water. Copolymers containing 30% of monomeric units AN obtained from a 90 10 mixture of AN and DMVPS in DMSO, irrespective of the level of conversion, are completely soluble in water, whereas copolymers of the same composition, but obtained in aqueous medium with a yield 40%, are insoluble in water. 

Polysaccharides composed of only one kind of monosaccharide are described as homopolysaccharides (homoglycans). Similarly, if two or more different kinds of monomeric unit are present, the class name heteropolysaccharide (heteroglycan) may be used. (See 2-Carb-39.)... 

Chain length is another factor closely related to the structural characterization of conducting polymers. The importance of this parameter lies in its considerable influence on the electric as well as the electrochemical properties of conducting polymers. However, the molecular weight techniques normally used in polymer chemistry cannot be employed on account of the extreme insolubility of the materials. A comparison between spectroscopic findings (XPS, UPS, EES) for PPy and model calculations has led some researchers to conclude that 10 is the minimum number of monomeric units in a PPy chain, with the maximum within one order of magnitude n9- 27,i28) mechanical qualities of the electropolymerized films,... 

Polymer products synthesized in laboratories and in industry represent a set of individual chemical compounds whose number is practically infinite. Macro-molecules of such products can differ in their degree of polymerization, tactici-ty, number of branchings and the lengths that connect their polymer chains, as well as in other characteristics which describe the configuration of the macromolecule. In the case of copolymers their macromolecules are known to also vary in composition and the character of the alternation of monomeric units of different types. As a rule, it is impossible to provide an exhaustive quantitative description of such a polymer system, i.e. to indicate concentrations of all individual compounds with a particular chemical (primary) structure. However, for many practical purposes it is often enough to define a polymer specimen only in terms of partial distributions of molecules for some of their main characteristics (such as, for instance, molecular weight or composition) avoiding completely a... 

The simplest, from the viewpoint of topological structure, are the linear polymers. Depending on the number m of the types of monomeric units they differentiate homopolymers (m=1) and copolymers (m>2). In the most trivial case molecules in a homopolymer are merely identified by the number l of monomeric units involved, whereas the composition of a copolymer macromolecule is defined by vector 1 with components equal to the numbers of mono-... 

For example, the enthalpy of mixing of copolymer specimen AH per mole of monomeric units can be expressed... 

Statistical characteristics of the second type define the microstructure of copolymer chains. The best known characteristics in this category are the fractions P [/k) (probabilities) of sequences Uk involving k monomeric units. The simplest among them are the dyads U2, the complete set of which, for example, for a binary copolymer is composed of four pairs of monomeric units M2M, M2M2. The number of the types of k-ad in chains of m-component copolymers grows exponentially as mk so that with practical purposes in mind it is generally enough to restrict the consideration to sequences Uk] with moderate values of k. Their calculation turns out to be rather useful... 

Another kind of situation arises when it is necessary to take into account the long-range effects. Here, as a rule, attempts to obtain analytical results have not met with success. Unlike the case of the ideal model the equations for statistical moments of distribution of polymers for size and composition as well as for the fractions of the fragments of macromolecules turn out normally to be unclosed. Consequently, to determine the above statistical characteristics, the necessity arises for a numerical solution to the material balance equations for the concentration of molecules with a fixed number of monomeric units and reactive centers. The difficulties in solving the infinite set of ordinary differential equations emerging here can be obviated by switching from discrete variables, characterizing macromolecule size and composition, to continuous ones. In this case the mathematical problem may be reduced to the solution of one or several partial differential equations. 

For a number of copolymers, whose kinetics of formation is described by nonideal models, the statistics of alternation of monomeric units in macromolecules cannot be characterized by a Markov chain however, it may be reduced to the extended Markov chain provided that units apart from their chemical nature... 

When calculating the average copolymer composition and the probabilities P Uk] of the sequences of monomeric units it is possible to set Ta=0 in the expressions in (7), that is to neglect the finiteness of the size of the macromolecules. In this case the absorbing Markov chain (7) is replaced by the ergodic Markov chain with transition matrix Q whose elements ... 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

Knowing the functions (26) and(27) it is possible by means of the formalism of the theory of Markovian processes [53] to find any statistical characteristic in an ensemble of macromolecules with labeled units. A subsequent label erasing procedure is carried out by integration of the obtained expressions over time of the formation of monomeric units. Examples of the application of this algorithm are reported elsewhere [25]. 

As the result of theoretical consideration of polycondensation of an arbitrary mixture of such monomers it was proved [55,56] that the alternation of monomeric units along polymer molecules obey the Markovian statistics. If all initial monomers are symmetric, i.e. they resemble AaScrAa, units Sa(a=l,...,m) will correspond to the transient states of the Markov chain. The probability vap of transition from state Sa to is the ratio Q /v of two quantities Qa/9 and va which represent, respectively, the number of dyads (SaSp) and monads (Sa) per one monomeric unit. Clearly, Qa(S is merely a ratio of the concentration of chemical bonds of the u/i-ih type, formed as a result of the reaction between group Aa and Ap, to the overall concentration of monomeric units. The probability va0 of a transition from the transient state Sa to an absorbing state S0 equals l-pa where pa represents the conversion of groups Aa. 

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