Number of monomer units

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

Povodyrev et aJ [30] have applied crossover theory to the Flory equation ( section A2.5.4.1) for polymer solutions for various values of N, the number of monomer units in the polymer chain, obtaining the coexistence curve and values of the coefficient p jj-from the slope of that curve. Figure A2.5.27 shows their comparison between classical and crossover values of p j-j for A = 1, which is of course just the simple mixture. As seen in this figure, the crossover to classical behaviour is not complete until far below the critical temperature. 

Since PY ) x V, we have x V It is important to note that Xj should be independent of the length of the Rouse unit given by <3j. Since rj is proportional to the number of monomer units between two beads, should scale... 

Chain Length. The total number of monomer units (which approximately equals x - - y - - z. in the above formula) in PE chains is called the degree of polymerization. It can vary from small (about 10—20 in PE waxes) to very large (over 100,000 for PE of ultrahigh molecular weight (UHMW)). Consequentiy, the molecular weights of PE resins can range from several hundred to several million. 

Fig. 22.1. (a) The ethylene molecule or monomer (b) the monomer in the activated state, ready to polymerise with others (<)-(f) the ethylene polymer ("polyethylene") the chain length is limited by the addition of terminators like —OH. The DP is the number of monomer units in the chain. 

The average kinetic chain length r is defined as the number of monomer units consumed per active centre formed and is given by R fV (or R tV ). 

The number average degree of polymerisation x is defined as the average number of monomer units per polymer chain. Therefore if termination is by disproportionation r = jc, but if by combination r = x. 

They further suggest that the thickness is related to the interfacial tension, y, and the mean density in terms of number of monomer units per unit volume, po, thus ... 

A chain reaction polymerization of vinyl monomer, which is usually carried out by a photoinitiator to produce a primary radical (R ), which can interact with a monomer molecule (M) in a propagating process to form a polymer chain composed of a large number of monomer units (see Eq. [2] and reaction Scheme [3]. 

Relate the molar mass of a polymer to the number of monomer units. 

Consider the polymers referred to in Table 23.1. If each one contains the same number of monomer units, which one has the largest molar mass ... 

The degree of polymerization of a polymer (X) is equal to the chain length i (the number of monomer units in the chain). If wc neglect end groups, the number molecular weight (Afn) is given by eq. 10 ... 

All polymers are giant molecules made up of repeating units called monomers or mers. These units may be the same or different. The number of monomers that join to form a polymer or macromolecule is called the degree of polymerization and is theoretically infinite, but, in practice, the number of monomer units is commonly in the range of 1000 to 20,000 if no crosslinks are present. 

The subscript n in the above formulae is a whole number indicating the number of monomer units in the polymer chain. This is called the polymer s degree of polymerization. 

For a polymer molecule, its molecular weight is the number of monomer units that it consists of multiplied by the molecular weight of the monomer unit (minus the molecular weight of any by-products of the polymerization). A molecular weight of at least 5000 is normally required before the polymer displays useful mechanical properties. 

X indicates a small substituent, which may be an atom such as hydrogen (H) or chlorine (Cl) or it may he a group such as methyl (CH3), cyano (CN), carhoxyl (COOH), carbomethoxy (COOCH3), etc. The growing chain is terminated by collision with another chain or other radical source or by one of several other mechanisms. The number of monomer units in the polymer chain is the degree of polymerization, abbreviated DP. If the degree of polymerization is very low, the product is sometimes referred to as an oligomer. 

Polyalphaolefin Hydraulic Fluids. Polyalphaolefms are made by oligomerizing alphaolefins such as 1-decene in the presence of a catalyst (Newton 1989 Shubkin 1993 Wills 1980). The crude reaction mixture is quenched with water, hydrogenated, and distilled. The number of monomer units present in the product polyalphaolefin oil depends on a number of reaction parameters including the type of catalyst, reaction temperature, reaction time, and pressure (Shubkin 1993). The exact combination of reaction parameters used by a manufacturer is tailored to fit the end-use of the resulting polyalphaolefin oil. A typical polyalphaolefin oil prepared from 1-decene and BF3- -C4H9OH catalyst at 30 °C contains predominantly trimer (C30 hydrocarbons) with much smaller amounts of dimer, tetramer, pentamer, and hexamer. While 1-decene is the most common starting material, other alphaolefins can be used, depending on the needs of the product oil. 

Fig. 17 FT-IR spectra of crystalline (upper) and amorphous (lower) iPS in the region 500-1400 cm-1 [13] m indicates the minimum number of monomer units included in the 3/1 helix parts of the polymer chains...

Average number of monomer units between crosslinks. 

Clearly there are two sets of absorptions, as shown in Table 3.7, which were attributed to polarons and bipolarons by the authors. All the IRAV bands are relatively narrow and so suggest that the carriers occupy a well-defined number of monomer units. The highest frequency IRAV has been attributed to a combination of the intra-ring OC vibration and the inter-ring C-C stretch which increases in frequency as the conjugation length decreases, consistent with the bipolaron being somewhat shorter than the polaron. 

Data from Yamashita et al., 1980 b Number of monomer units in cyclic oligomers... 

For step-change polymerization at steady-state in a CSTR represented by the kinetics model in Section 7.3.2, derive equations giving the weight fraction of r-mer, wr, on a monomer-free basis, as a function of r, the number of monomer units in polymer Pr at the reactor outlet. This is a measure of the distribution of polymers in the product leaving the reactor. 

The absolute number of monomer units of the polystyrene (m) and polybutadiene (n) blocks were determined by combined H-NMR and GPC measurements. The triblock copolymer is a commercially available polystyrene-b-polybutadiene-i-polystyrene polymer and was purchased from Aldrich (M = 100,000 28 wt% polystyrene). 

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