Statistical copolymers definition

State Correlation Diagram (SCO) approach 27-8 statistical copolymerization see copolymerization statistical copolymers sea also copolymers definition 333... 

While the percentage composition of copolymers (i.e., the ratio of comonomers) is not given, copolymers with architecture other than random or statistical are identified as alternating, block, graft, etc. Random or statistical copolymers are not so identified in the CA index. Oligomers with definite structure are noted as dimer, trimer, tetramer, etc. 

Due to the nonmiscibility between blocks of different chemical nature (see Section 4.4), block copolymers are generally segregated in multiphase systems in which each phase preserves its properties. In that respect, they are definitely different from statistical copolymers having the same overall composition. 

The above-mentioned statistical characteristics of the chemical structure of heteropolymers are easy to calculate, provided they are Markovian. Performing these calculations, one may neglect finiteness of macromolecules equating to zero elements va0 of transition matrix Q. Under such an approach vector X of a copolymer composition whose components are X = P(M,) and X2 = P(M2) coincides with stationary vector n of matrix Q. The latter is, by definition, the left eigenvector of this matrix corresponding to its largest eigenvalue A,i, which equals unity. Components of the stationary vector... 

Eigenvalues of the operator Qr are real while the largest of them, Af, equals unity by definition. As a result, in the limit n-> oo all items in the sum (Eq. 38), excluding the first one, Q Q f = Xr/Xfh will vanish. In this case, chemical correlators will decay exponentially along the chain on the scale n 1/ In AAt values n < n the law of the decay of these correlators differs, however, from the exponential one even for binary copolymers. This obviously testifies to non-Markovian statistics of the sequence distribution in molecules (see expression Eq. 11). The closer is to unity, the greater are the values of n. The situation when n 1 corresponds to proteinlike copolymers. 

A polymer derived from the polycondensation of a single actual monomer, the molecules of which terminate in two different complementary functional groups (e.g. 6-aminohexanoic acid) is, by definition, a (regular) homopolymer. When two different monomers of this type react together, the product is a copolymer that can be named in appropriate fashion. For example, if 6-aminohexanoic acid is copolycondensed with 7-aminoheptanoic acid, leading to a statistical distribution of monomeric units, the product is named poly[(6-aminohexanoic acid)-stoi-(7-aminoheptanoic acid)]. 

The term ionomer was originally introduced in 1964 by Dupont to indicate a thermoplastic polymer containing both covalent and ionic bonds (5-7). By definition, ionomers are statistical thermoplastic copolymers consisting of (8) ... 

Figure 15 Composition profiles shown as a function of reduced monomer number i /Vfor 512-unit MIST-tuned copolymer sequences having 1 1 AB composition. The present definition assumes that the A-type monomers are coded by symbol +1, whereas symbol -1 is assigned to the B-type monomers. For an ideal RCP in which chemically different units follow each other in a statistically random fashion, the probability Pa that monomer A is iocated at the th position in the chain is % for any . (a) Optimization of the transition temperature V at different Ti leads to sequences that have a gradient (or S-iike) distribution of A and B monomers, as schematically depicted In the right panel, (b) Optimization of the characteristic length scale r at different leads to sequences that have a tapered (or bolas-like ) distribution of A and B monomers, as schematically depicted in the right panel.

A—B diblock copolymers adsorb spontaneously at the interface between two immiscible A and B homopolymers. Our objective here is to make quantitative predictions of the nature of the adsorbed layer, fri this case, the phase behavior depends on (Mily one x parameter, that between the A and B homopolymers, and the statistical segment lengths of the A and B chains. The specific example that we will smdy is the adsorption of a SPB(89)-SPB(63) diblock copolymer at the interface between SPB(89) and SPB(63) homopolymers at room temperamre [A = SPB(89) and B = SPB(63)]. For this system, x = 0.0064 (system 33 in Table 19.1), I A = 0.49 nm, and /b = 0.75 nm. We consider the interface between SPB(89) and SPB(63) homopolymers with Na = 4,230 and Nr =3,600. It is straightforward to show that the two homopolymeis are highly immiscible because xAave =6.2 which is much greater than 2 (see Eq. (19.8) for definition of Nave)- We consider the adsorption of a SPB(89)-SPB(63) diblock copolymer with NAb = 790 and Nsb = 730 where the subscript b refers to the chains comprising the block copolymer. We consider two flat homopolymer-rich phases with the diblock copolymer adsorbed at the interface. The z-axis of our coordinate frame is perpendicular to the interface. The results of SCFT predictions for 0 e volume fraction of the A-B... 

The definitions above of statistical and random copolymers are idealized. In reality, significant nonrandomness may exist. Since the physical and mechani-... 

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