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Molecular Parameters of Hyperbranched Polymers Made by Self-Condensing Vinyl Polymerization

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Molecular Parameters of Hyperbranched Polymers Made by Self-Condensing Vinyl Polymerization 7024 Macromolecules 1997, 30, 7024-7033 Molecular Parameters of Hyperbranched Polymers Made by Self-Condensing Vinyl Polymerization. 2. Degree of Branching† Deyue Yan‡ and Axel H. E. Mu1 ller* Institut fu¨ r Physikalische Chemie, Universita¨t Mainz, D-55099 Mainz, Germany Krzysztof Matyjaszewski Department of Chemistry, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213-3890 Received December 30, 1996; Revised Manuscript Received July 30, 1997X ABSTRACT: Using a modified definition, the average degree of branching, DB, the fraction of branchpoints, FB, as well as the fractions of various structural units are calculated as a function of conversion of double bonds for hyperbranched polymers formed by self-condensing vinyl polymerization (SCVP) of monomers (or “inimers”) with the general structure AB*, where A is a vinyl group and B* is an initiating group. The results are compared to those for the polycondensation of AB2-type monomers. At full conversion, DB is somewhat smaller for SCVP (DB∞ 0.465) than for AB2 systems (DB∞ ) 0.5). ≈ There are two kinds of linear groups in SCVP whereas there is only one kind in AB2 systems. Since there are two different active centers in SCVP, i.e., initiating B* and propagating A* centers, the effect of nonequal reactivities on DB is also discussed. At a reactivity ratio of the two kinds of active centers, r ) kA/kB 2.59, a maximum value of DB∞ ) 0.5 is reached. For the limiting case r << 1, a linear polymer resembling≈ a polycondensate will be formed whereas for r >> 1 a weakly branched vinyl polymer is expected. NMR experiments allow for the determination of reactivity ratio r. Introduction Scheme 1 together with a schematic representation of The degree of branching, DB, is one of the most the further steps up to the formation of tetramers. In important molecular parameters of hyperbranched poly- order to find a short representation for the various mers since it determines many physical properties of groups in the hyperbranched polymers, we use capital the polymers, such as viscosity in melt or solution. letters for unreacted active centers (A*, B*) and lower- Hawker et al.1 proposed a definition for the degree of case letters for reacted ones (a, b). “A” always denotes branching of hyperbranched polymers formed in the the vinyl group. It is seen that beside the unit carrying polycondensation of AB -type monomers, the vinyl group (A-b) there can be four different 2 monomeric units in a polymer: terminal (T ) DA*- DB ) B*), branched (B ) Da-b<), and two different linear (number of dendritic units) + (number of terminal units) ones: one resembles a repeat unit of a polycondensate total number of units (Lc ) DA*-bD) and one a monomer unit of a vinyl polymer (Lv ) Da(B*)D). The chemical nature of these where “units” mean reacted monomer units and the units is shown in Scheme 2 using one possible hexamer “dendritic units” are the branchpoints. The “focal point” of p-(chloromethyl)styrene as an example. or “core” of the molecule is not taken into account; i.e., Interestingly, only one out of the five tetrameric it is not counted as a unit at all. This definition has been isomers (4d) is branched. A further extension of frequently used in order to determine DB from NMR Scheme 1 shows that there are four (out of 12) branched spectra of hyperbranched polymers made by polycon- pentamers and 16 (out of 32) branched hexamers, one densation of AB2-type monomers. Here, the monomer hexamer having two branchpoints. In further poly- unit carrying the unreacted A function is regarded as merization steps the fraction of branched structures the “core”. increases and finally hyperbranched polymers are gen- 2 4 Recently, Fre´chet and co-workers - reported a new erated. Ideally, all molecules possess exactly one double way of forming hyperbranched polymers and named it bond, and the number of active centers (and thus of self-condensing vinyl polymerization (SCVP). This re- groups which can be functionalized) is equal to the action involves a monomer of AB* type, in which B* is degree of polymerization. Thus, SCVP presents an a group capable of initiating the polymerization of vinyl attractive alternative to dendrimers, combining many groups, A (“inimer”). The chain initiation is the addition functional groups in a very compact molecule with a of an initiating B* group to the vinyl group of another convenient one-pot synthesis. monomer forming a dimer with two active sites and one From Scheme 3 the following important rules of SCVP double bond. Both the initiating center, B*, and the can be deduced: newly created propagating center, A*, can react with the vinyl group of another molecule (monomer or 1. Addition of a vinyl group to a terminal group, T ) polymer) in the same way with rate constants kB and (A*B*), leads to one of the two linear units. If a B* kA, respectively. The initiation step for a simple AB* center adds, it will lead to a condensation-type unit, Lc monomer, i.e. p-(chloromethyl)styrene is shown in ) (A*b) (reactions 1 and 1a); if an A* center adds, it will result a vinyl-type unit, Lv ) (aB*) (reactions 2 and 2a). † Part 1. Preceding paper in this issue. ‡ Permanent address: Shanghai Jiao Tong University, Depart- 2. Addition of a vinyl group to any linear unit ment of Applied Chemistry, 1954 Hua Shan Road, Shanghai (reactions 3 and 4) leads to a branch point, B ) (ab). 200030, The People’s Republic of China. X Abstract published in Advance ACS Abstracts, October 15, 3. Upon addition to any active center, the vinyl group 1997. of a polymer is always converted to an Lc ) (A*b) group S0024-9297(96)01919-5 CCC: $14.00 © 1997 American Chemical Society Macromolecules, Vol. 30, No. 23, 1997 Self-Condensing Vinyl Polymerization 7025 Scheme 1. Initial Steps in Self-Condensing Vinyl Polymerization (reactions 1-4), whereas addition of a monomer, AB*, there are two different active centers in SCVP, i.e. A* always leads to a terminal group, T ) (A*B*) (reactions and B*, the effect of nonequal reactivities on the degree 1a-4a). of branching will be also discussed. 4. Vinyl addition converts an initiating B* center into a propagating A* center (reactions 1 and 3) whereas Definitions of the Degree of Branching. The propagating A* centers remain unchanged (reactions 2 definition of the degree of branching given by Hawker and 4). at al.1 does not take into account that for a linear 5 In Part 1 of this series, we analyzed the general polymer DB should be zero (it is unity for a perfect features of SCVP, especially the kinetics and the mo- dendrimer). According to that equation all linear oli- lecular weight distribution (MWD) and its moments of gomers in Scheme 1 would have DB > 0. For example, the polymers formed and we compared it to Flory’s6 and the linear dimer 2 would have DB ) 1 and the linear our own results for the polycondensation of monomers 1 trimers 3 would have DB ) /2. Since a linear polymer of AB2 structure. It was found that both processes lead to different kinetics and MWD’s. In this publication, has one initial group (or “core”; not counted) and one we calculate DB and the fractions of various structural terminal group, this error can be avoided by subtracting units of the polymers generated by both SCVP and AB2 one terminal group from both the numerator and the polycondensation as a function of conversion. Since denominator12 7026 Yan et al. Macromolecules, Vol. 30, No. 23, 1997 Scheme 2. Example of a Branched Hexamer of p-(Chloromethyl)styrene Scheme 3. Reactions Leading to Linear (1 and 2) and Branched (3 and 4) Structures DB ) (number of branched units) ) (number of branched units) + (number of terminal units) - 1 (number of terminal units) - 1 (total number of units) - 1 This follows from the fact that a linear chain has one For a polymer with an f-functional core, f terminal initial group (not counted) and one terminal group and groups should be subtracted. This equation which is addition of a new branch always adds one branchpoint valid for single molecules can be easily checked with and one terminal group. Again, f terminal groups have the trimers and tetramers shown in Scheme 1. All to be subtracted if the polymer has an f-functional core. oligomers have DB ) 0, except the branched oligomer Thus, eq 1 can be further simplified to 4d which has DB ) 1. The hexamer in Scheme 2 has DB ) 3/5. 2(number of branched units) DB ) (1) From the topology of branched systems with trifunc- (total number of units) - 1 tional branchpoints, for any given molecule the number of branched units is equal to the number of terminal Thus, DB can be regarded as the ratio of branched unit minus one7 units in a hyperbranched polymer to those in a perfect Macromolecules, Vol. 30, No. 23, 1997 Self-Condensing Vinyl Polymerization 7027 dendrimer. Since we are interested in the average value where x is the conversion of vinyl groups (not of of DB for an ensemble of N molecules, N terminal monomer molecules!). groups have to be taken into account. In order to A′ ) A - M, is the fraction of vinyl groups of polymers investigate the dependence of DB on conversion, it is (i.e. excluding monomer). This is identical to the important to exclude the residual monomer from the fraction of polymer molecules in the system. calculation, since we are only interested in the polymer A*, B*, and (B*)′ ) B* - M symbolize the fractions molecules.
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