Kinetics of Self-Condensing Vinyl Hyperbranched Polymerization in Three-Dimensional Space

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1 Kinetics of Self-Condensing Vinyl Hyperbranched Polymerization in Three-Dimensional Space XUEHAO HE, JING TANG Department of Polymer Science and Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin, China Received 21 February 2008; accepted 27 March 2008 DOI: /pola Published online in Wiley InterScience ( ABSTRACT: Self-condensing vinyl hyperbranched polymerization (SCVP) with A-B* type monomer is simulated applying Monte Carlo method using 3d bond fluctuation lattice model in three-dimensional space. The kinetics of SCVP with zero active energy of reaction is studied in detail. It is found that the maximal number average and weight average polymerization degrees and the maximal molecular weight distribution, at varying the initial monomer concentration and double bond conversion, are about 52, 190, and 3.93, respectively, which are much lower than theoretical values. The maximal average fraction of branching points is about 0.27, obtained at full conversion at the initial monomer concentration of The simulation demonstrated the importance of steric effects and intramolecular cyclization in self-condensing vinyl hyperbranched polymerization. The results are also compared with experiments qualitatively and a good agreement is achieved. VC 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: , 2008 Keywords: bond fluctuation model; hyperbranched; Monte Carlo; self-condensing vinyl hyperbranched polymerization; simulations; theory INTRODUCTION Hyperbranched polymers have attracted much attention in past decades due to their unique properties, such as low viscosity and multiple terminal groups, in the fields of physics and chemistry. 1 Another reason is that in contrast to dendrimer synthesized by the tedious, stepwise reaction, hyperbranched polymer can be easily prepared by one pot polymerization. Usually, hyperbranched polymerization uses AB n type monomers or mixing A n and B nþ1 type monomers (A and B are the reactive groups in condensation This article includes Supplementary Material available from the authors upon request or via the Internet at www. interscience.wiley.com/jpages/ x /suppmat. Correspondence to: X. He ( xhhe@tju.edu.cn), Vol. 46, (2008) VC 2008 Wiley Periodicals, Inc reaction and when n 2 hyperbranched polymer forms). This class of polycondensation dominated the past synthesis of hyperbranched polymer till Fréchet et al. in 1995 proposed self-condensing vinyl hyperbranched polymerization (SCVP) using self-initiated vinyl monomer (A-B* type monomer). 2 This novel route directs a series of polymerization skills for the preparation of vinyl hyperbranched polymer, e.g., cationic, anionic or nitroxide-mediated radical polymerization, atom transfer radical polymerization (ATRP), group transfer polymerization (GTP), and open-ring polymerization. 2 8 In general, SCVP uses self-initiated vinyl monomer A-B*, which has a vinyl group A and an active center B*. Two inimers react to create a dimer A-B-A*-B* in which the new active center A* comes from the initiate reaction of vinyl group A. Further, the two active centers A* and

2 KINETICS OF VINYL POLYMERIZATION 4487 (PI) including residual monomers in ideal SCVP read: P n ¼ 1 1 x ¼ es P w ¼ 1 ð1 xþ 2 ¼ e2s PI ¼ 1 1 x ¼ es ð1þ Scheme 1. The mechanism of SCVP with the inimer A-B*, A and B* are double bond and active center, respectively. The A* is the new active center after the initiation of double bond A and becomes into A 0 after the further reaction. B* in dimer react with other monomers or polymers to form hyperbranched polymer (Scheme 1). The diversity of reactions among polymers with various polymerization degrees and branching degrees, lead to the complicated dependences of molecular weight and branching degree of polymer on the double bond conversion. Up to now, the realistic kinetics of self-condensing vinyl polymerization is not known due to the embarrassment of the characterization to the molecular weight and branching degree of highly branched polymer. In theory, Müller and Yan et al. first studied SCVP in ideal condition by solving kinetic master equation, 9,10 and discovered the dependences of the average molecular weight, the molecular weight distribution, and the average degree of branching on the double bond conversion. Theoretical study showed that the molecular weight and molecular weight distribution increase exponentially with the increase of reduced reaction time s. The number- and weight average degrees of polymerization (P n and P w ), and the polydispersity index Although eq 1 presents a general character of the kinetics of self-condensing vinyl hyperbranched polymerization, it exists large deviation with the experimental results especially at high double bond conversion. 7 From eq 1, it is shown that the molecular weigh distribution of SCVP is extremely broad at high double bond conversion x: the polydispersity index (PI) is equal to the number average degree of polymerization: P w /P n ¼ P n. While P n reaches the infinity at full double bond conversion x ¼ 1. However, the P n or PI in reality is not very high even the errors of experiment and characterization are considered. A lower P n or PI less than a definite value is often measured. The deviation chiefly comes from the neglect of steric effects in system, such as the steric hindrance of molecules, the diffusion difference of reactants (polymer and inimer), and the intramolecular cyclization. The introduction of steric elements is a critical point in understanding the realistic kinetics of SCVP and the hyperbranched structure of polymer. In this article, it is the first time to simulate self-condensing vinyl polymerization applying Monte Carlo method using 3d bond fluctuation lattice model (3d-BFLM) which has been widely used to study the static and dynamic properties of linear polymer chain in the past. 11 Using such model, basically steric effects, such as the steric hindrance of macromolecules, molecular diffusion, intramolecular cyclization, and the entanglement of polymer chains, are encompassed on a coarse-grained scale. In this work, the kinetics of SCVP with zero active energy of reaction is explored in detail. The simulation result is compared with that of theory and experiments. In contrast to the theoretical result, the simulation data achieved in threedimensional space shows better agreements with experimental data. The possible deviation of our simulation from real experiments is also discussed.

3 4488 HE AND TANG monomer concentration c 0, are randomly put into lattice space. c 0 ¼ the total number of monomers 3 8 the total number of lattice sites ð2þ Scheme 2. The movements of polymer chain unit and inimer. (1) branching point unit; (2) end unit; (3) linear unit; (4) monomer; bold and thin lines are the conformations of polymer before and after movement, respectively. BOND FLUCTUATION LATTICE MODEL AND ALGORITHM FOR SCVP In 3d bond fluctuation lattice model of SCVP, a bead used as a monomer or a unit of polymer chain occupies a whole cell (with eight sites in three-dimensional lattices) on a simple cubic lattice. The bond length of neighboring units in a chain was controlled in a set of values 2, H5, H6, 3, H10 corresponding to 108 bond vectors in the sets {[2, 0, 0], [2, 1, 0], [2, 1, 1], [2, 2, 1], [3, 0, 0], [3, 1, 0]}. 11 The chain relaxation and monomer diffusion is implemented by random move of randomly selected bead to nearest neighbor lattice site (Scheme 2). Acceptance of a move is subject to the excluded volume and bond length restriction. The prominent merit of 3d-BFLM is that the movement of branched point unit of polymer is available and the steric effects, e.g., excluded volume and entanglements of chain, are both kept. Detail description of 3d-BFLM refers to refs. 11 and 12. To add the reaction process, a simple reaction rule is introduced such that every bead reacts only with one bead at the second nearest neighbor lattice sites [For clarity, Scheme 1(a) shows the case in 2d]. 13 After a reaction, a bond is created and the groups involved in the reaction change the states (see Schemes 1 and 3, A?A*, B*?B 0, A*?A 0 ; A 0 or B 0 is the group without double bond or active center). Before formal simulation, a certain mount of monomers (beads) corresponding to the initial c 0 is less than 1.0 to keep a certain number of vacancy sites as solvent and free volume. Then, the beads move randomly without any reaction about 10,000 Monte Carlo Steps (MCS) for equilibrium. The formal simulation is carried out as follows: at first, randomly select a bead, which may be an inimer or a unit of hyperbranched polymer, and tempt to move a lattice position in one of 6 directions randomly (Scheme 2). Again, randomly select another bead which attempts to react with one bead randomly selected at the nearest 54 positions, to build a new bond if the reaction condition is satisfied, i.e., one bead contains active center and another bead possess a double bonds [Scheme 3(b)]. Every monomer attempting one move and one reaction on average accounts one Monte Carlo Step. In this work, the reaction is assumed to be fast as it happens immediately after two beads meet. It corresponds to the reaction with zero active energy. 14 The self reaction of inimer (A- B*) and double connections between two inimers (cyclization of two beads) are not permitted. All data are analyzed under excluding unreacted monomers to compare with the experiments. A testing simulation using random algorithm with no consideration of steric elements was carried out, and compared with theory to test the correction of program codes. It is operated by randomly selecting two beads for reaction with no consideration of the distance. This algorithm is same with that in the refs. 15 and 16, and the result is in excellent agreement with theory. 9 The intramolecular cyclization is estimated applying searching algorithm of the topology of hyperbranched polymer for every attempted reaction. In this way, a switch, i.e., the intramolecular reaction is permitted or not, can be installed to show the influence of the intramolecular cyclization on SCVP. All simulations are carried out in a large size of sample lattice space (L x ¼ L y ¼ L z ¼ 250) to eliminate the influence of periodic boundary. Final simulation results are calculated on a simple average with repeating simulations 100 times, starting with different initial distribution of monomers and random seeds, to ensure statistical precision.

4 KINETICS OF VINYL POLYMERIZATION 4489 Scheme 3. The reaction rule: a bead only reacts with another bead in the second nearest neighbor site [There are totally 54 positions in 3d and 12 positions in 2d (a)]. After the reaction, the bonds are formed and the states in beads changed accordingly (b). The various reactions are shown between monomers (1), polymer unit and monomer (2 and 3), and polymer and polymer (4). RESULTS AND DISCUSSION Figure 1 shows the dependence of double bond conversion on the reaction time at the various initial monomer concentrations. Generally, the polymerization reveals two stages in reaction rate. At the initial stage, the double bond conversion increases quickly with the increase of time. After the double bond conversion reaches about 0.95, the increase of x becomes slow. The reaction rate, i.e., the slope of curve, decreases with the decrease of the initial monomers concentration c 0. For example, in the case of c 0 ¼ 0.95, the double bond conversion x reaches 0.95 at 18 Monte Carlo Steps (MCS). While in the case of c 0 ¼ 0.6, the same conversion needs 24 MCS. In the case of low initial concentration c 0 < 0.3, the slopes of curves at initial stage show a relation with kc 0 (k is a reaction constant). The strong dependence of reaction rate on c 0 is resulted from the various diffusion distance of reaction monomers at various concentrations. The dependences of the number average and weight average polymerization degrees on the time present the similar fashion in Figure 2. By experiencing a relatively slow increase at the early stage (t < 10 MCS), the molecular weight quickly increases and slows down at the later stage. They correspond to the domination of different reactions, i.e., the reactions between monomers or monomer and oligomer at early stage and the reactions between hyperbranched polymers at middle stage. At later stage, the reactions become slow due to the influence of molecular diffusion and steric hindrance of hyperbranched polymer. With the decrease of initial monomer concentration c 0, such trend in the whole polymerization becomes smoother and smoother because the reactions between hyperbranched polymers decrease with the decrease of initial monomer concentration.

5 4490 HE AND TANG Figure 1. Dependences of the double bond conversion on Monte Carlo steps (MCS) at the various initial monomer concentration c 0. At later stage, P n and P w gradually approach a limiting value with the increase of reaction time. The limiting values of P n and P w equal about 49.3 and 180.8, respectively, after enough long time in the case of the initial monomer concentration c 0 ¼ When c 0 ¼ 0.6, P n and P w reach 35.3 and at 60 MCS and do not change again with the increase of double bond conversion. Corresponding polydispersity index, PI (PI ¼ P w /P n ), also appears a maximal value but at a certain reaction time at the various initial monomer concentration. For example, at c 0 ¼ 0.95, the PI reaches the largest value 3.92 at 24 MCS (corresponding to the double bond conversion x ¼ 0.98) and then decrease to 3.67 at full double bond conversion. With the decrease of initial monomer concentration, the peak in PI curve becomes unconspicuous. Figure 2. Dependences of the number average polymerization degree P n, the weight average polymerization degree P w, and the polydispersity index PI on Monte Carlo steps (MCS) at the various initial monomer concentration c 0.

6 KINETICS OF VINYL POLYMERIZATION 4491 Figure 3. Dependences of the number average polymerization degree P n, the weight average polymerization degree P w, and the polydispersity index PI on the double bond conversion x at the various initial monomer concentration c 0. Inset figures show the dependences of P n, P w, and PI on the initial monomer concentration c 0 at x ¼ 1.0. When the reaction time is long enough, the double bond groups are exhausted and the full double bond conversion x ¼ 1.0 is reached. Figure 3 shows the dependences of P n, P w, and PI on the double conversion x at the various initial monomer concentration. Inset ones give the data at full double bond conversion. Theoretical P n, P w, and PI excluding residual monomers are estimated from ref. 9 (eqs 21 0,22 0, and 23 0 ). It is found that although the P n and P w in simulation increase exponentially with the increase of double bond conversion and show similar fashion with theoretical results, the values of P n and P w at the same conversion are much lower than theoretical ones. Meanwhile, at the same double bond conversion, the SCVP at the lower initial monomer concentration shows lower molecular weight and molecular weight distribution. It is worthy to note that the past theory is incapable of describing the dependence of SCVP on the initial monomer concentration. At the highest monomer concentration, c 0 ¼ 1.0, P n, P w, and PI are discovered to equal about 52, 190, and 3.7, respectively, by fitting method. When varying the initial monomer concentration c 0 and the double bond conversion x, the largest PI equals about 3.93 in Figure 4. The main difference between simulation and theory is the introduction of steric elements and intramolecular cyclization in our simulation. Three sets of data from theory, simulation considering steric elements with intramolecular cyclization, and simulation considering the steric elements without intramolecular cyclization, are compared together to illustrate the influences of steric elements and intramolecular cyclization.

7 4492 HE AND TANG Figure 5 shows that the molecular weight distribution of SCVP, considering all steric effects and intramolecular cyclization, is lowest among all values. When we screen the cyclization reaction, PI becomes higher than that of SCVP containing the intramolecular cyclization but it is still much lower than theoretical value. It means that steric elements even without intramolecular cyclization also have strong influence on hyperbranched polymerization. The steric hindrance and the intramolecular cyclization make the intermolecular reaction difficult and play similar roles in decreasing the molecular weight distribution of SCVP like adding multifunctional initiator. 17 Through topological analysis of hyperbranched polymers, the ratio of intramolecular cyclization at various double bond conversions and the various initial monomer concentrations is calculated as: C R ¼ the number of intramolecular cyclization all monomers residual monomers ð3þ Figure 4. Dependence of the maximal polydispersity index, PI MAX, on the initial monomer concentration c 0. The unreacted monomer is excluded in the analysis. It is found that the content of intramolecular reaction in SCVP strongly depends on the initial monomer concentration c 0. With the decrease of initial monomer concentration c 0, the cyclization ratio, C R increases in Figure 6. When the double bond conversion approaches 100%, i.e., x ¼ 1, a simple relation P n ¼ 1/C R is found. The more the intramolecular cyclizations the lower the molecular weight, and the narrower the polydispersity. The average fraction of branching points in simulation is used to characterize the branching properties of polymer to avoid the bifurcation of the various definitions of branching degree. Here, the average fraction of branching points reads: FB ¼ branching point units all monomers residual monomers ð4þ Theoretical FB is calculated using the expression of FB in Yan et al. s work. 10 Figure 7 Figure 5. Dependences of the polydispersity index, PI and the weight average polymerization degree, P w (inset figure) on the double bond conversion x at the initial monomer concentration, c 0 ¼ The residual monomers are excluded in analysis. ( ) Theory prediction; (*) Simulation without the steric elements; (~) Simulation of screening intramolecular cyclization in 3d; (!) Simulation with steric elements including intramolecular cyclization in 3d. Figure 6. Dependences of the intramolecular ratio, C R on the double bond conversion x at the various initial monomer concentration c 0.

8 KINETICS OF VINYL POLYMERIZATION 4493 Figure 7. Dependences of the average branching fraction of hyperbranched polymer FB on the time and the double bond conversion at the various initial monomer concentration c 0. shows the dependence of FB on the time or double bond conversion at the various initial monomer concentrations. With respect to the reaction time, the increase of branching degree at the higher initial monomer concentration c 0 is faster than that at the lower c 0 (Fig. 7, left). The dependence of FB on the double bond conversion shows that FB increases monotonously with increase of the double bond conversion (Fig. 7, right). Corresponding to the same double bond conversion x, the FB only varied slightly with the increase of the initial monomer concentration but obviously larger than theoretical value. It is shown that the largest value appears at the full conversion, FB x ¼ 1.0 equals 0.27 at c 0 ¼ 0.75, larger than theoretical FB x ¼ 1.0 which equals (see Fig. 8). Because of rare systematic data from experiment, we qualitatively compared our simulation results with the data of some experiments (SCVP by atom transfer radical polymerization, group transfer living polymerization, and other living polymerization). It is discovered that the molecular weight distributions PIs obtained in simulation locate at the same region of the experimental ones. For example, Gaynor et al. 5 obtained hyperbranched polymer with the largest PI ¼ 2.5 characterized by GPC at x ¼ Hong and Pan 18 gained largest PI ¼ 2.92 by SEC/RI. Simon et al. 7 reported the larger PI ¼ 5.48 at x ¼ For two special cases, Fréchet et al. 2 reported SCVP with PI ¼ 9.8 characterized by GPC by cationic living polymerization; Baskaran 3 obtained the relative higher PI ¼ 17.8 by living anionic SCVP but adding another monomer, styrene, as chain growth promoter. Except for Simon s and Frechet s results, all experimental values PIs are in the range of the simulation data and lower than the largest value, Matyjaszewski et al. 19 applied monomer ((2-(2-Bromopropionyloxy) Ethyl Methyl Acrylate, BPEA) as inimer for SCVP, which processes similar molecular structure for A* and B* groups with near equal activity. They obtained the hyperbranched polymer with P n ¼ 48.5 at x ¼ 0.95 by SEC in the bulk polymerization much closer our simulation results, P nx;c0 ¼ 52. It is worthy to note that, in our simulation, the specificity of SCVP, such as living po-!1:0 lymerization type, activity difference of two active Figure 8. Dependences of the average fraction of branching point at the full double bond conversion, FB x ¼ 1.0, on the initial monomer concentration c 0. Theoretical FB x ¼ 1.0 equals

9 4494 HE AND TANG centers, and the rigidity of polymer chain, are not considered. The rigidity of polymer chain possibly baffles intramolecular cyclization and leads to the increase of PI. On the other hand, chemical side reactions, such as the deactivation of active centers, uncommon coupling reactions of hyperbranched polymers, and system errors in characterization possibly lead to some deviations of the simulation with the experiment. It is known that the branching degree in SCVP with near equal reactivity is difficult to characterize by NMR because the chemical shifts of branching unit and linear unit are much closer. However, open ring hyperbranched polymerization of 4-(2-Hydroxyethyl)-e-caprolactone, in which A* and B* have same reactivities, can provide the information about branching degree by NMR. It is found that the average branching degree DB in experiment equals about This value is much closer to the simulation results DB ¼ at 0.1 < c 0 < 0.95 based on the relation DB ¼ 2FB (Fig. 8). It indicates that the simulation result is consistent with the experiment in branching degree. CONCLUSIONS Self-condensing vinyl hyperbranched polymerization is studied by means of Monte Carlo simulation applying 3d bond fluctuating model. The results show that steric hindrance, molecular diffusion, and intramolecular cyclization play important roles in SCVP. It is found that selfcondensing vinyl hyperbranched polymerization by one pot polymerization does not lead to very high molecular weight and molecular weight distribution as the prediction of theory. The maximal number- and weight average polymerization degrees of SCVP are about 52 and 190, respectively, and the maximal polydispersity index is about The largest average fraction of branching points is about 0.27, which is obtained at full double conversion and the initial monomer concentration c 0 ¼ The dependence of the molecular weight, the molecular weight distribution, and the average fraction of branching points on the initial monomer concentration, reaction time, and double bond conversion is also described in detail. Simulation results show good agreements with experimental data. The project is supported by the National Natural Science Foundation of China and SRF for ROCS, SEM. REFERENCES AND NOTES 1. Gao, C.; Yan, D. Y. Prog Polym Sci 2004, 29, Fréchet, J. M. J.; Henmi, M.; Gitsov, I.; Aoshima, S.; Leduc, M.; Grubbs, R. B. Science 1995, 269, Baskaran, D. Polymer 2003, 44, Hawker, C. J.; Fréchet, J. M. J.; Gubbs, R. B.; Dao, J. J Am Chem Soc 1995, 117, Gaynor, S. G.; Edelman, S.; Matyjaszewski, K. Macromolecules 1996, 29, Sakamoto, K.; Aimiya, T.; Kira, M. Chem Lett 1997, Simon, P. F. W.; Müller, A. H. E. Macromolecules 2004, 37, Sunder, A.; Hanselmann, R.; Frey, H.; Mulhaupt, R. Macromolecules 1999, 32, Müller, A. H. E.; Yan, D.; Wulkow, M. Macromolecules 1997, 30, Yan, D.; Müller, A. H. E.; Matyjaszewski, K. Macromolecules 1997, 30, Deutsch, H.; Dickman, R. J Chem Phys 1990, 93, Carmesin, I.; Kremer, K. Macromolecules 1988, 21, He, X. H.; Nagel, J.; Lehmann, D.; Heinrich, G. Macromol Theory Simul 2005, 14, The non zero active energy can be introduced and the results concerned will be reported in future. 15. He, X. H.; Liang, H. J.; Pan, C. Y. Polymer 2003, 44, He, X. H.; Liang, H. J.; Pan, C. Y. Macromol Theory Simul 2001, 10, Yan, D.; Zhou, Z.; Müller, A. H. E. Macromolecules 1999, 32, Hong, C. Y.; Pan, C. Y. Polymer 2001, 42, Matyjaszewski, K.; Gaynor, S. G.; Kulfan, A.; Podwika, M. Macromolecules 1997, 30, Liu, M.; Vladimirov, N.; Fréchet, J. M. J. Macromolecules 1999, 32,