Hyperbranched Polymers. Synthesis, Modeling, Experimental

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Hyperbranched Polymers. Synthesis, Modeling, Experimental Validation, and Rheology of Hyperbranched Poly(methyl methacrylate) Derived from a Multifunctional Monomer (MFM) Route Simon P. Gretton-Watson,† Esat Alpay,*,† Joachim H. G. Steinke,*,‡ and Julia S. Higgins† Department of Chemical Engineering and Chemical Technology and Department of Chemistry, Imperial College London, London, SW7 2AZ, United Kingdom

The synthesis of hyperbranched PMMA has been achieved using a facile one-step batch solution polymerization reaction. The reaction is essentially a linear polymerization doped with appropriate amounts of a multifunctional monomer (MFM) and chain transfer agent (CTA). On this basis, a theoretical model for the MFM reaction has been developed and experimentally validated for the number-average molecular weight and degree of branching data, by assuming isothermal batch conditions and employing key reaction parameters from established linear PMMA kinetics. A first comparison of the melt rheology of the hyperbranched polymer with that of the linear one revealed a significant reduction in melt viscosity and shear thinning. It is expected that the generic model developed here will guide the manufacture of other free-radical hyperbranched polymers, of desired architecture or physical properties, using modeling and optimization methods. 1. Introduction In many ways triggered by the advent of dendrimers, the synthesis of hyperbranched polymers has received widespread attention as a means of producing architecturally complex molecules that exhibit, albeit to a lesser extent but more economically, some of the unique bulk and solution properties associated with dendrimers, such as lower solution and melt viscosities, increased solubility, and higher functional group density.1-3 Possible uses of these polymers range from rheology modifiers and bulk phase additives to applications in nanotechnology and in the biomaterials area.4 Owing to the laborious and time-consuming multistep synthesis required to obtain the highly ordered and perfectly branched dendrimer architectures, these polymers are currently interesting for high-added-value applications only. As a result, a plethora of synthetic methodologies have been developed for the synthesis of hyperbranched polymers, many of which are industrially attractive onepot reaction schemes.4 There has been much greater activity in developing polycondensation approaches to hyperbranched polymers than has been the case for chain growth processes. Theoretically, hyperbranched polymers were first described by Flory in 1952,5 setting out a polycondensation reaction scheme involving ABn type monomers, where A and B are different functional groups that can react with each other but not with themselves. Kricheldorf and co-workers, in 1982,6 produced highly branched polyesters in the first experimental demonstration of hyperbranched polymer syn* To whom correspondence should be addressed. Tel: +44 20 7594 5852. Fax: +44 20 7594 5804. E-mail: j.steinke@ imperial.ac.uk. † Department of Chemical Engineering and Chemical Technology. ‡ Department of Chemistry.

thesis via the copolymerization of AB- and AB2-type monomers. This was followed by Kim and Webster in 1988,7 where the first homopolymerization of an AB2type monomer was reported. This seminal work acted as a seed, inspiring many other research groups to apply the basic concept to translate most linear polycondensation chemistries into a hyperbranched version.1,8,9 A step change occurred when self-condensing vinyl polymerization was introduced by Frećhet et al.,10 extending hyperbranched methodologies to vinyl monomers with end group control and living polymerization features. Hyperbranched polymer synthesis based on vinyl monomers11 was developed further by several research groups and includes living free radical polymerization chemistries,12-21 self-condensing vinyl polymerizations,22-27 catalytic chain transfer processes,28 and ionic29-31 and coordination methodologies.32 Self-condensing ring-opening polymerization33 and protontransfer polymerization34 represent imaginative ways of translating other types of commercially important linear polymerization chemistries into their hyperbranched versions. An inherent limitation with many of these methodologies is the need for designed functional monomers, which are costly to manufacture and would, therefore, render many cases economically nonviable for large-scale production. Crucially, Sherrington and co-workers (Costello et al.,35 O’Brien et al.,36 Isaure et al.,37,39,40 and Slark et al.38) have recently demonstrated a new facile route for the synthesis of branched polymers based on commercially available vinyl monomers and the addition of chain transfer agents (CTAs). The stoichiometric balance between the cross-linker [multifunctional monomer (MFM)] and the CTA is the most important parameter that determines whether the polymer remains soluble throughout the reaction or gels and forms a cross-linked network. The introduction of appropriate amounts of

10.1021/ie0488041 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/17/2005

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CTA has the effect of reducing the average polymer chain length and, thus, the statistical likelihood of polymer-polymer termination reactions. This inventive step has allowed highly branched polymers to be synthesized at high conversions. The ability to form branched polymer architectures from easily accessible starting material, in which the fundamental reaction process remains essentially that for a linear free radical polymerization, turns the MFM methodology into the obvious front runner for producing bulk quantities of hyperbranched polymers on an industrial scale.41,42 These considerations prompted us to investigate the MFM kinetic and reaction model, which ultimately would develop a generic tool allowing the production and scale up of hyperbranched polymers with tailored structural properties. We can assume isothermal batch conditions and that key reaction parameters from established linear PMMA kinetics43 can be used to describe the hyperbranched system with sufficient accuracy. The linear polymerization kinetic model had to be modified, of course, to account for the contribution of MFM and CTA. We opted for a PMMA-based model reaction system, as the vast amount of reaction, structure, and property data for linear PMMA would be beneficial when comparing and optimizing the reaction model, as well as in highlighting differences in bulk and solution properties for the final polymer material. Our distant goal is to develop a generic model in which modeling and optimization methods can be applied to other free-radical polymerization reactions, and furthermore, where experimental design and optimization methods can be used to predict desired polymer properties. 2. Experimental Section The reagents used were methyl methacrylate (MMA, 99%, Lancaster Ltd U. K.), xylene (99%, Fisher Scientific U. K.), AIBN (2,2′-azobisisobutyronitrile, 97%, Fisher Scientific U. K.), TPGDA (tri-propyl glycol diacrylate, 98%, Aldrich Ltd.), 1-dodecanethiol (97%, Aldrich Ltd.), 2,6-di-tert-buyl-4-methylphenol (99%, Lancaster Ltd. U. K.), dichloromethane (99% GPR, BDH), and hexane (95%, BDH). The MMA was stabilized with 60-100 ppm 4-methoxyphenol as an inhibitor. All the materials were used without further purification, which conforms to typical industrial practices. Bench-scale batch experiments were carried out in 250 mL three-necked round-bottom flasks, each fitted with a condenser and supplied with an argon purge. The reaction vessel was charged with xylene (2.01 mol, 247 mL) and MMA (0.935 mol, 100 mL) at room temperature. The vessel was cooled with a liquid nitrogen bath for 5 min and then charged with AIBN (5.69 mmol, 935 mg) and TPGDA (16 mmol, 5.0 mL). An argon atmosphere was introduced by passing a stream of argon through the solution. After 30 min, the solution was cooled until frozen using a liquid nitrogen bath. The frozen solution was then allowed to thaw, and once completed, the argon degassing was resumed for another 20 min. A freeze-thaw cycle was repeated twice, before the flask was introduced into a thermostatically controlled water bath preheated to 80 °C (( 0.1 °C). 1-Dodecanethiol (9.22 mmol, 2.21 mL) was added between the second and third freeze-thaw cycles, and agitation of the solution was started (515 rpm) using a mechanical stirrer (Janke & Kunkel RW20 DZM). The reaction temperature was kept constant throughout the

Table 1. Initial Molar Ratio Amount of AIBN, CTA, MFM, MMA, and Xylene Used under Batch Conditions at 80 °C molar ratios reaction code

AIBN

CTA

MFM

MMA

xylene

MFM-1 MFM-2 Linear-1 Linear-2

1.0 1.0 1.0 1.0

1.6 0.4 1.6 0.4

2.7 2.7 0.0 0.0

164 164 164 164

360 360 360 360

polymerization process, which lasted up to 7 h. Aliquots were taken from the reaction mixture every 20 min via an airtight PTFE-lined syringe, with approximately 2 mL of sample solution being taken each time, and subsequently mixed with a preweighed solution of xylene (2 mL) and 2,6-di-tert-buyl-4-methyphenol (0.064 mmol, 14 mg) at ambient temperature. The sample vial was then reweighed, placed into a liquid nitrogen bath for 30-40 s, and stored at 4 °C until the time when the polymer was precipitated from the reactant solution. Upon completion of the polymerization, the remaining solution was diluted with an equal volume of a 0.064 mmol solution of 2,6-di-tert-buyl-4-methyphenol in xylene, placed in a liquid nitrogen bath for 5 min, and finally stored at 4 °C. In subsequent experiments, the same reaction conditions were employed; however, different reagent compositions were used (see Table 1). Experiments “Linear-1” and “Linear-2” are reaction analogous to “MFM-1” and “MFM-2”, respectively, in the absence of a MFM agent to determine the degree of branching. Precipitation of the hyperbranched polymer (MFM experiments) was achieved through the dropwise addition of the stored polymer solutions to a stirred solution of 10 times its volume of hexane. The precipitate was filtered (Whatman, Grade 1) and finally dried in a vacuum oven at 50 °C until a constant weight was acheived. From the weight of the dry polymer, the conversion was determined gravimetrically. 2.1. Triple Detection Gel Permeating Chromatography (TD-GPC). Hyperbranched polymer GPC samples were prepared using 2 mL screw top vials, with accurate concentrations of ∼2 mg/mL being prepared. The sample concentrations were determined by weighing the polymer sample and tetrahydrofuran (THF) used (using a five-digit weighing scale). The samples were then filtered after 24 h using a 5 mL gastight glass syringe with a 0.2 µm pore filter (Whatman Puradisk 13 mm syringe filters, PTFE membrane). The molecular weight distribution was determined by double injection of the sample using 2 × 5 µm mixed-bed TSK gel columns (7.5 mm × 300 mm, Tosoh Corporation) in THF (Chromatography GPC grade, Fisher Scientific U. K.) at a 1 mL/min flow rate at 30 °C using a triple-detector Viscotek GPC (TDA 302 detector - refractive index, differential pressure and 90° light scattering), in combination with TriSEC Version 3 software. The dn/dc value used for the hyperbranched PMMA was 0.087 mL/g [determined by S. Holding (UK GPC service; Rapra Technology Limited; TriSEC calculation)]. A different procedure was performed for Linear-1 and Linear-2 experiments, where 1 µl of the sample solution was dissolved into ∼2 mL of THF. In this case, the THF used was weighed, whereas the sample solution was measured accurately using a clean 10 µl airtight glass syringe. The samples were then filtered after 24 h using a clean 5 mL airtight glass syringe with a 0.2 µm pore filter. The molecular weight distribution was deter-

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Ind. Eng. Chem. Res., Vol. 44, No. 23, 2005 Table 2. Elemental Kinetic Processes of the Free Radical MFM-Derived Hyperbranched Polymerization Process Initiator Dissociation kI

2

I2 98 I* + I* Initiation kI*A

I* + A 98 A* kI*M

I* + M 98 M* Propagation kA*A

A* + A 98 A* kM*A

M* + A 98 A* kA*M

A* + M 98 M* kM*M

M* + M 98 M* Termination kI*I*

I* + I* 98 i - i kA*I*

A* + I* 98 a - i kA*A*

A* + A* 98 a - a kA*M*

A* + M* 98 a - m kM*I*

M* + I* 98 m - i kM*M*

M* + M* 98 m - m Figure 1. Reaction scheme for free-radical MFM-based hyperbranched polymer synthesis. Capital letters indicate unreacted initiator (I2), monomer (M), MFM (A), and CTA (C), with the active center prefixed with “*” (i.e., I*, A*, M*, and C*). Lower case letters indicate reacted groups (i, a, m, and c, respectively).

mined using both conventional and universal calibration methods (calibrated using linear PMMA standards). 2.2. Melt Viscosity Studies. The melt viscosity work was performed using a Rosand capillary rheometer using Flowmaster software. Viscosity measurements were performed by allowing the rheometer to reach steady-state processing temperatures, which were 180 °C, 190 °C, 200 °C, and 210 °C for the hyperbranched sample and 230 °C, 240 °C, and 250 °C for the linear PMMA analogue. Approximately 50-60 g of polymer was placed into the capillary rheometer barrel and allowed to reach the selected steady-state temperature (i.e., for ∼30 min). The cycle of piston compression of the polymer sample was then programmed into the Flowmaster software, and the experiment was performed. The samples investigated were synthesized hyperbranched samples MFM-1 (Mn ) 28 kDa, Mw ) 141 kDa) and a linear PMMA analogue (Mn ) 40 kDa, Mw ) 85 kDa)striple detection data. 3. Theory 3.1. Reaction Scheme. The applied reaction scheme for the MFM-derived hyperbranching of poly(methyl methacrylate) is shown in Figure 1. The polymerization starts with the formation of an initiator (I*), and

propagation proceeds linearly, incorporating vinyl groups along the polymer backbone. These vinyl groups take the form of monomers (M) and MFMs (A-A). The inclusion of a difunctional monomer along the polymer backbone leads to the formation of a pendent “a-A” group, and it is this latent “A” group that is subject to attack by other independently growing radical chains, subsequently forming a “branch” (a-a). In essence, the hyperbranched polymer is a complex array of linear chains, which are linked together via a number of “aa” groups. The reaction can be controlled using a CTA, which reduces the average linear chain length and, as a result, allows control over the macromolecular size. The MFM polymerization, shown in Figure 1, is composed of a number of distinct kinetic steps, shown in Table 2. The series of reactions require 13 unknown kinetic rate constants. However, even though the MFM reaction scheme is different from that of a linear polymerization reaction scheme, it is assumed to possess similar kinetic parameters, since essentially a linear reaction is being performed, with little perturbation arising from the relatively small amounts of MFM and CTA dosage. Consequently, a well-documented linear kinetic scheme can be employed. The kinetic scheme described by Fan et al.43 was employed as a first approximation in this investigation, prior to further kinetic evaluation (see section 3.3). Also, within the reaction scheme, CTAs are used to control the propagating polymer chain radical. The


kinetics steps of the chain transfer process can be described by the set of equations listed in Table 3. Note that chain transfer to the monomer and solvent were included in this work, though they were found to have a negligible effect on the conversion and numberaverage molecular weight trends. Therefore, details of this aspect of the modeling are not included here. 3.2. Reaction Model. Given the reaction schemes shown in Tables 2 and 3 and assuming an isothermal and well-mixed batch reactor, material balances for the different reaction species can be written as

NLin ) [IDiss] + [CTAactive] - [a - a]disp - [xtcTerm] (9) NHyp ) [IDiss] + [CTAactive] - [a - a]disp [xtcTerm] - [a - a] (10) The first term on the right-hand side of eqs 9 and 10 represents the total number of dissociated initiator molecules (IDiss), which have initiated the growth of linear polymer chains, and is given by

d[IDiss] ) 2fkI[I2] dt

Initiator Dissociation d[I2] ) -2fkI2[I2] dt

(1)

Monomer (M) and MFM (A) d[M] ) -kA*M[A*][M] - kI*M[I*][M] dt kM*M[M*][M] - kCTA*M[CTA*][M] (2) d[A] ) -kA*A[A*][A] - kI*A[I*][A] - kM*A[M*][A] dt kCTA*A[CTA*] [A] (3) CTA d[CTA] ) -kA*CTA[A*][CTA] - kI*CTA[I*][CTA] dt kM*CTA[M*][CTA] - kCTA*CTA[CTA*][CTA] (4) Active Centers dI* ) -[I*](kI*M[M] + kI*A[A] + kI*CTA[CTA] + dt kI*M*[M*] + kI*A*[A*] + kI*CTA*[CTA*]) + 2fkI2[I2] (5) dA* ) [A](kI*A[I*] + kM*A[M*] + kCTA*A[CTA*]) dt [A*](kA*M[M] + kA*CTA[CTA] + kA*I*[I*] + kA*M*[M*] + kA*CTA*[CTA*] + 2{kA*A*[A*]}) (6) d[M*] ) [M](kI*M[I*] + kA*M[A*] + kCTA*M[CTA*]) dt [M*](kM*A[A] + kM*CTA[CTA] + kM*I*[I*] + kM*A*[A*] +kM*CTA*[CTA*] + 2{kM*M*[M*]}) (7) d[CTA*] ) [CTA](kI*CTA[I*] + kA*CTA[A*] + dt kM*CTA[M*]) - [CTA*](kI*CTA*[I*] + kM*CTA*[M*] + kA*CTA*[A*] + 2kCTA*CTA*[CTA*]) (8) 3.2.1. Number of Macromolecules. The number of macromolecules within a linear polymerization reaction can be calculated by performing a balance of radicals, where the summation of the dissociated initiator (IDiss) and activated CTA (CTAactive) gives the total number of polymer chains in the reaction. For a hyperbranched polymerization, the same balance of radicals is also applicable; however, coupling of the linear chains takes place since the MFM acts as a branching agent. Accordingly, the number of macromolecules within the linear (NLin) and hyperbranched (NHyp) reactions can be written as

(11)

The second term represents the total number of activated CTA and is given by

d[CTAactive] ) kCTA[CTA]([I*] + [A*] + [M*]) dt

(12)

The third term represents the number of terminal vinyl groups formed when disproportionation-based termination occurs. These groups act as further branching points on the macromolecule and can be calculated using the following material balances:

[

]

d[a - A]disp xtd ) Term - [a - A]disp(kI*A[I*] + dt 2 kA*A[A*] + kM*A[M*] + kCTA*A[CTA*]) (13)

∑

d[a - a]disp ) [a - A]disp(kI*A[I*] + kA*A[A*] + dt kM*A[M*] + kCTA*A[CTA*]) (14) d[Term] ) 2(kI*A*[I*][A*] + kI*M*[I*][M*] + dt kI*CTA*[I*][CTA*] + kA*A*[A*][A*] + kA*M*[A*][M*] + kM*M*[M*][M*] + kCTA*CTA*[CTA*][CTA*] + kCTA*A*[CTA*][A*] + kCTA*M*[CTA*][M*]) (15) The fourth term represents the total number of coupled macromolecules arising through combinationbased termination. The coupling term leads to a reduction in the number of macromolecules and is calculated by summing all the termination reactions and multiplying by the fraction of combination termination (xtc). Regarding disproportionation-based termination, it is neglected from the radical balance (eqs 9 and 10), since this termination pathway does not lead to a change in the number of macromolecules. The fifth term on the right-hand side of eq 10, [a-a], represents the total number of branching points formed in the hyperbranched architecture. This term will reduce the number of macromolecules because, for each [a-a] formed, it will combine two independent macromolecules, that is, assuming cyclization is negligible. At any time, the number of branched points, [a-a], can be determined through the simultaneous solution of the following material balances:

d[A - A] ) -2[A - A](kI*A[I*] + kA*A[A*] + dt kM*A[M*] + kCTA*A[CTA*]) (16)

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d[a - A] ) 2[A - A](kI*A[I*] + kA*A[A*] + dt kM*A[M*] + kCTA*A[CTA*]) - [a - A](kI*A[I*] + kA*A[A*] + kM*A[M*] + kCTA*A[CTA*]) (17) d[a - a] ) [a - A](kI*A[I*] + kA*A[A*] + kM*A[M*] + dt kCTA*A[CTA*]) (18) 3.2.2. Conversion, Number-Average Molecular Weight, and Number of Branches. By using eqs 1-18, it is possible to calculate the monomer conversion (xM) and both linear (MnLin) and hyperbranched (MnHyp) number-average molecular weights, that is

Table 3. Effect of the CTA on the Hyperbranched Polymerization Mechanism Chain Transfer Initiation kCTA*CTA

CTA* + CTA 98 cta + CTA* kI*CTA

I* + CTA 98 i + CTA* kA*CTA

A* + CTA 98a + CTA* kM*CTA

M* + CTA 98 m + CTA* Chain Transfer Propagation kCTA*A

CTA* + A 98 cta - A* kCTA*M

xm )

Amount of monomer reacted ) Total initial amount of monomer

MnLin )

∑ niMi ∑ ni

∑ niMi MnHyp ) ∑ ni

)

[M]0 - [M] [M]0 (19)

([M]0 - [M])MWM NLin

([M]0 - [M])MWM ) NHyp

NB )

MnLin

[a-a] -1) NHyp

Chain Transfer Termination kCTA*CTA

CTA* + CTA* 98 cta - cta kCTA*I*

(20)

CTA* + I* 98 cta - i kCTA*A*

CTA* + A* 98 cta - a kCTA*M*

CTA* + M* 98 cta - m

(21) Table 4. Kinetic Rate Constants for MMA Polymerization

These simulated profiles can subsequently be compared to experimental data. It is noted that the incorporation of initiator, MFM, and CTA has been neglected from the number-averaged molecular weight calculation, since their concentrations are negligible. Finally, the average number of branches (NB) per hyperbranched molecule can be calculated from the ratio of hyperbranched and linear number-average molecular weights, that is

MnHyp

CTA* + M 98 cta - M*

parameter

reference

kI2 ) 1.58 × 1015 exp(-1.2874 × 105/RT) f) 0.58 kp0 ) 7.0 × 106 exp(-2.6334 × 104/RT) kt0 ) 1.76 × 109 exp(-1.1704 × 104/RT) kCTA ) 0.7kp xtc ) 0.21 xtd ) 1 - xtc R ) 8.314

Pinto and Ray48 Kumar and Gupta49 Pinto and Ray48 Pinto and Ray48 Hutchinson et al.45 Moad and Solomon50 Moad and Solomon50 Perry and Green51

equal to the termination of MMA (kt), such that

(22)

3.3. Kinetic Parameters and Initial Conditions. 3.3.1. Kinetic Assumptions. In section 3.2, the initiator dissociation, propagation, chain transfer, and termination rate constants can be written as kI2 ) kAIBN, kM*M ) kp, kM*CTA ) kCTA, and kM*M* ) kt, respectively, where kAIBN is the dissociation rate constant for AIBN, kp is the propagation rate constant for methyl methacrylate (MMA), kCTAis the chain transfer rate constant for CTA, and kt is the termination rate constant for a MMA radical. Consequently, it is possible to derive the reactivity kinetics of the other propagating species (Brandrup et al.44) by comparison to the propagation rate constant for MMA (kp). Accordingly, kM*A ) kp/2, kA*M ) kp/0.5, kA*A ) kp/0.25, kCTA*M ) kp, kCTA*A ) kp, kI*A ) kp/2, and kI*M ) kp have been used in the model. The kinetics for the chain transfer of other radical species to CTA have been assumed to be the same as the rate of chain transfer from 1-dodecanethiol to MMA (Hutchinson et al.45), since this is essentially the dominant reaction and other interactions will be insignificant in comparison; therefore, one can write kM*CTA ) kA*CTA ) kI*CTA ) kCTA*CTA ) kCTA. The termination kinetics for all the radical species were assumed to be

kM*M* ) kM*A* ) kM*CTA* ) kA*A* ) kA*CTA* ) kCTA*CTA* ) kI*M* ) kI*A* ) kI*CTA* ) kI*I* ) kt 3.3.2. Kinetic Parameters. As previously discussed (see section 3.1), it has been assumed that a linear kinetic model is applicable to the hyperbranched reaction; consequently, a linear kinetic model for MMA polymerization by Fan et al.43 has been adopted. This assumption strongly depends on the hyperbranched architecture not interfering with the propagating and terminating polymer radicals. Nevertheless, the hyperbranched reactions demonstrated in this paper use only ∼1% (molar) of the MFM and CTA agents; therefore, this assumption should hold, though when larger amounts of MFM are being used, this assumption will have to be re-examined. The kinetic rate constants and physical property parameters are summarized in Tables 4-6, with the propagation (kp) and termination (kt) rate constant expressions given at the initial onset of polymerization. The onset of gel and glass effects have been included in the kinetics via a semiempirical relationship (see Table 5) developed by Baillagou and Soong46 and Soroush and Kravaris.47 This has been chosen as it provides a convenient means of adjusting the rate constants as the polymer fraction increases. All

Ind. Eng. Chem. Res., Vol. 44, No. 23, 2005 8687 Table 5. Gel and Glass Effect Constitutive Equations (Baillagou and Soong,46 Soroush and Kravaris47) kp ) kp0/(1 + kp0ξ0/Dkθp) kt ) kt0/(1 + kt0ξ0/Dkθt) D ) exp{2.303(1 - φp)/ [0.168 - (8.21 × 10-6)(T - 387)2 + 0.03(1 - φp)]} kθp ) 3.0233 × 1013 exp(-1.1700 × 105/RT) kθt ) 1.4540 × 1020 × Cif exp(-1.4584 × 105/RT) φm ) M × MWm/Fm φp ) (M0 - M)MWm/Fp φ s ) 1 - φm - φ s dξ0/dt ) 2fkI2[I2] - ktξ02 Table 6. Physical Property Parameters physical parameter

reference

Fm ) 915 Fs ) 886 Fp ) 1200 Fi ) 915 MWm ) 100 MWs ) 106 MWi ) 164

Brandrup et al.44 Perry and Green51 Brandrup et al.44 Baillagou and Soong46 Brandrup et al.44 Brandrup et al.44 Brandrup et al.44

other constants were assumed to remain constant throughout the polymerization. 3.3.3. gPROMS Simulation and Initial Conditions. The gPROMS modeling environment was used to solve eqs 1-22, in which a standard solver, SRADAU, was employed.52 The kinetic assumptions and parameters used have been outlined, and the initial conditions used were

[I2]|t)0 ) [I2]0, [A]|t)0 ) 2[A - A]0, [M]|t)0 ) [M]0, [CTA]|t)0 ) [CTA]0, [A - A]|t)0 ) [A - A]0 with

[M*]|t)0 ) I*|t)0 ) A*|t)0 ) [CTA*]|t)0 ) [Term]| ) [CTAactive]|t)0 ) [IDiss]|t)0 ) [a - A]|t)0 ) [a - A]disp|t)0 ) [a - a]|t)0 ) [a - a]disp|t)0 ) 0 4. Results and Discussion With the kinetic model implemented, we then carried out a series of polymerizations in which the concentration of monomers totalled 30% w/v at a 100 g scale in xylene. The concentration was kept at a modest level to minimize the risk of macrogelation. The choice of scale was guided by the amounts required to study the rheology and mechanical properties of the hyperbranched polymer sample. The vital stoichiometry of CTA to MFM to MMA (1.6:2.7:164) was based on experimental data by Costello et al.35 At this initial stage of the model validation, a standard three-necked round-bottom flask with mechanical stirring was employed (using a four-blade stainless steel mixer). Freezepump-thaw cycles were included to minimize the presence of oxygen in order to avoid any undesirable inhibition and, thus, induction period from which we otherwise would have to modify our kinetic model. During the polymerization, aliquots were removed from the reaction vessel, quenched, and subsequently precipitated following a standard protocol to minimize fractionation effects. Conversion was calculated from the weight balance of the precipitated polymer aliquots. Determination of the molecular weight and molecular weight distribution (MWD) of each sample was achieved with a standard triple detection system using the 90° signal as input from the light scattering detector in THF

as an eluent. All samples were filtered through a 0.2 µm membrane filter prior to injection. 4.1. Development of the Molecular Weight Distribution. The development of the MWD with time for our first set stoichiometry (MFM-1) is shown in Figure 2a. As one would have expected, the number- and weight-average molecular weights increase with conversion and so does the polydispersity index (PDI). The first molecular weight distribution was obtained at 24.6% conversion and shows a maximum and a shoulder to lower molecular weight. With increasing conversion, the shoulder becomes more pronounced and simultaneously migrates to higher molecular weight. The original maximum also shifts to higher molecular weight while the polymerization is progressing. At ∼50% conversion, a second shoulder becomes visible in the MWD curve, located at high molecular weight; it develops with time into a distribution maximum and shifts to higher molecular weight with conversion. The final molecular weight distribution at ∼89% conversion is characterized by a broad, (at least) trimodal pattern extending into the 106 Da region. A very similar evolution of molecular weight was observed by Costello et al.35 under very similar conditions but has also been observed for a variety of quite unrelated branching methodologies.12-14,22,23,26,53-56 We consider the monotonic development of the MWD curve as an indicator for reliable and consistent chromatography throughout the sample series. The development of the MWD curve with conversion is intriguing as it suggests that, at low conversion, we have to consider at least two distinct MWDs that, with time, move to higher molecular weight; however, concurrently, at least a third higher molecular weight species is being formed. At the early stage of polymerization, incorporation of the MFM agent produces mostly linear chains with a higher proportion of dangling vinyl groups than compared to the feed. This originates from the MFM agent being an acrylate and, thus, more reactive than a methacrylate moiety, consequently producing a bias toward MFM incorporation. The emergence of “shoulders” in the MWD is commonly observed in branched polymers35 and can be rationalized by the presence of multiple MWDs in the complex reaction scheme (i.e., caused by branched polymers), which cannot be differentiated by chromatography. The presence of a shoulder or maxima at the early stages of polymerization suggests the preferential formation of branched species. As the data presented here is calculated from light scattering triple detection data, they represent accurate molar mass values. Thus, we can at least qualitatively correlate the maxima and shoulders present in the MWD graph if we know the Mn value for the polymer formed under identical conditions in the absence of MFM. For MFM-1, this value is 6 kDa (vide supra; Linear-1). At low conversion (24.6%), we can now estimate that the maximum centers around a threebranch structure, and the shoulder corresponds to a singly branched polymer chain. However, we cannot explain why there should be a particular preference at all. In fact, this preference is retained throughout the polymerization, though with raising conversion, the shoulders and maxima become less pronounced and the MWD broadens significantly. This evolution of the MWD is consistent with a statistical grafting process of polymer radicals onto dangling vinyl group side chains. Why we form, in this process, a new highmolecular-weight maximum at ∼ 100 kDa remains

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Figure 2. (a) Development of MFM-1 molecular weight distribution, with the dotted line indicating increasing time. Sampling times and conversion (%) are as indicated, with the AIBN/CTA/MFM/MMA/xylene ratio ) 1:1.6:2.7:164:360. Molecular weight distributions from TD-GPC data. (b) Development of MFM-2 molecular weight distribution, with the dotted line indicating increasing time. Sampling times and conversion (%) are as indicated, with the AIBN/CTA/MFM/MMA/xylene ratio ) 1:0.4:2.7:164:360. Molecular weight distributions from TD-GPC data.

unexplained and requires further investigations. What we can say, though, is that at 89.2% conversion, the shoulder corresponds to two branches per polymer chain on average and the two maxima correspond to approximately 6 and 16 branches per macromolecule. Whether we produce branched species or hyperbranched ones in this polymerization process remains an open question. Given the evolution of the MWD for MFM-1, we would expect the formation of branched polymer structures to be dominant at the early stages of the polymerization reaction, but with increasing levels of branching, the proportion of hyperbranched polymer entities increases and the final product contains a proportion of both architectures.57 The monotonic increase in the molecular weight of these three main features of the distribution curve could be explained with the continuous depletion of MFM and MMA, thereby constantly increasing the likelihood to which the second MFM vinyl group is being incorporated into the evolving hyperbranched polymer architecture. By definition, this reduces the number of macromolecules within the reaction and, hence, causes movement toward higher molecular weight. Polymerization MFM-2 was, in all aspects, identical to MFM-1, with the exception of a reduced level of CTA. Employing only a quarter of the CTA used in MFM-1 is

expected to move the polymerization closer to gelation, which should produce higher number- and weightaverage molecular weights. Indeed, this has been found to be the case, as can be seen from Figure 2b. The trends and patterns of the MWD curve for MFM-2 are intriguingly similar to those discussed earlier for MFM-1. This time, a more pronounced lower molecular weight shoulder is found next to the distribution maximum at low conversion. With time, both features move to higher molecular weights while a third (and higher modality) distribution emerges with increasing conversion, and this moves well into the 106 Da range. At ∼75% conversion (i.e., ∼10 000 s), the polymerization mixture turned into a gel at which stage the polymerization was stopped.58 At this point, there was insufficient CTA present to support the formation of shorter branched chains and minimize the chances of polymer-polymer termination. For this reason, one has to be cautious to what degree we can compare MFM-1 and MFM-2 at higher degrees of conversion. However, looking at the data for 13.6% conversion, we can attribute the shoulder to molecular species containing a single branch (24 kDa) and the maximum to polymer chains with two branches (36 kDa) (vide supra; Linear-2). Again, with increasing conversion, the MWD broadens, with both the shoulder and maxima moving


Figure 3. Change in weight-average molecular weight (Mw) with time for MFM-1 and MFM-2. TD-GPC data.

Figure 4. Change in polydispersity (PDI) with time for MFM-1 and MFM-2. TD-GPC data.

Figure 5. (a) Change in number-average molecular weight (Mn) with time for MFM-1. TD-GPC data. (b) Change in numberaverage molecular weight (Mn) with time for MFM-2. TD-GPC data.

toward higher molecular weights. The maximum beyond 106 Da develops into an increasingly distinct feature quite separate from the majority of the molecular weight distribution, which may be an indication of the formation of internally cross-linked species (microgels).58,59 4.2. Weight- and Number-Average Molecular Weight Trends. The temporal change in MWD for MFM-1 (Figure 2a) and MFM-2 (Figure 2b) can be summarized by the number- and weight-average molecular weight trends. The weight-average molecular weight for MFM-1 increases almost linearly with conversion, whereas Mw for MFM-2 shows an exponential behavior (Figure 3). Regarding the PDI, all the reactions show an initial PDI of ∼1.8, with MFM-1 exhibiting an almost linear increase in PDI up to ∼5 (i.e., ∼25 000 seconds), whereas MFM-2 demonstrates exponential characteristics with a maximum PDI of ∼15 (see Figure 4). Interestingly, MFM-2 shows a peak and dip in the PDI at ∼8000 seconds, which may have been caused by the formation of small gel fractions before macrogelation was observed at ∼10 000 s. In Figure 5a and b, measured and calculated profiles of the temporal change of Mn are shown. Both the model and the experimental results demonstrate an increase in the number-average molecular weight (Mn) with time, which is not observed in linear polymerizations. In Figure 5a, the MFM-1 reaction shows a steady increase in Mn, with a plateau occurring after ∼20 000 s at Mn ∼ 28 kDa. The simulation indicates a reasonable level of fit with the experimental results, though the plateau seen in the experimental data is not so apparent. Error bars of 10% have been included for all the molecular weight data, since repeated GPCs of various hyperbranched samples have shown this range of error. In contrast, MFM-2, shown in Figure 5b, shows an exponential increase in the molecular weight, and the simulation fits well with the experimental data, with

the highest Mn achieved being 90 kDa. Interestingly, for MFM-2 at a time > 11 000 s, the Mn f ∞, and this corresponds to the Mw f ∞ in Figure 3, which indicates the formation of percolation. As a result, the model appears to forecast the onset of networked related gelation. The accurate model prediction for the numberaverage molecular weight trends validates the employment of a linear kinetic model (Fan et al.43) in place for describing the hyperbranched reaction (this may be different for higher degrees of branching, which is a work in progress). Moreover, key assumptions such as neglecting the effect of the hyperbranched architecture on the kinetic parameters and neglecting cyclization (i.e., polymer backbiting) appear to be valid. Since the kinetic and reaction models have been validated using number-average molecular weight data, the next advance would be to predict the average number of branches per hyperbranched molecule (NB). This can be performed by recognizing that the hyperbranched molecule is an amalgamation of linear chains. As a result, it is important to validate the reaction model using molecular weight data from linear polymerization reactions. Subsequently, reactions MFM-1 and MFM-2 were repeated without MFM, giving samples Linear-1 and Linear-2. The calculated and experimentally determined number-average molecular weight trends for Linear-1 and Linear-2 are shown in Figure 6a and b, respectively. The linear Mn profiles are approximately constant with time, which is unlike the hyperbranched case. Linear-1 shows a good data fit, whereas Linear-2 displays minor disparity with the calculated profile, slightly overestimating the experimental Mn profile. Stoichiometrically, Linear-1 uses 4 times more CTA than Linear-2, which translates into halving Mn, with Mn ∼ 6 and 12 kDa, respectively. It is for this reason that we observe substantial differences between reactions MFM-1 and MFM-2, where MFM-2 gels after

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Figure 8. Shear (melt) viscosity of MFM-1 (Mn ) 28 kDa, Mw ) 141 kDa) at 180, 190, 200, and 210 °C using a capillary rheometer.

Figure 6. (a) Comparison of calculated and experimental values for the change in number-average molecular weight (Mn) with time for Linear-1, using conventional and universal calibration (PMMA standards). (b) Comparison of calculated and experimental values for the change in number-average molecular weight (Mn) with time for Linear-2, using conventional and universal calibration (PMMA standards). Figure 9. Comparison of shear (melt) viscosities of MFM-1 (Mn ) 28 kDa and Mw ) 141 kDa) at 180 and 190 °C and linear PMMA (Mn ) 40 kDa and Mw ) 85 kDa) at 230, 240, and 250 °C, using a capillary rheometer.

Figure 7. Comparison of calculated and experimental values for the change in average number of branches per molecule for MFM-1 and MFM-2.

∼10 000 s but MFM-1 remains soluble throughout the experiment (i.e., ∼25 000 s). In effect, the longer average polymer chain (and branch) in MFM-2 contains more latent MFM groups, which essentially increases the statistical likelihood of percolation. Figure 7 complements the modeling work further by showing the simulated and experimentally determined average number of branches per molecules, which is determined by comparing the number-average molecular weight for the corresponding hyperbranched and linear cases. The simulated profiles fit the experimental data reasonably, with MFM-1 exhibiting a steady increase in branching with time, whereas MFM-2 exhibits an exponential increase, which reaffirms the onset of gelation. Consequently, the model has been validated using linear polymerization molecular weight data, which adds further confidence to the reaction model and has allowed an analysis of the degree of branching. 4.3. Melt Viscosity. Figure 8 illustrates the effect of shear rate on the melt viscosity of MFM-1 at different processing temperatures. We find typical polymer melt

shear thinning behavior for MFM-1; however, the viscosity becoming more Newtonian at higher temperatures (i.e., at ∼230 °C), which is similar to melt viscosity behavior reported for dendrimers60 and hyperbranched polymers.61 Figure 9 compares the hyperbranched MFM-1 sample (i.e., Mn ) 28 kDa, Mw ) 141 kDa) with a linear PMMA analogue with a comparable Mn but, unavoidably, a lower Mw value (i.e., Mn ) 40 kDa, Mw ) 85 kDa). Strikingly, the melt viscosity of our hyperbranched MFM-1 sample at 180 °C is similar to that of the linear PMMA one at ∼240-250 °C. We attribute the reduction in temperature by ∼60 °C to the reduced levels of chain entanglement62 present in MFM-1 (on the basis of Linear-1, the average branch length has a Mn of ∼6 kDa). The dropoff in viscosity with increasing shear rate (shear thinning) also reflects reduced levels of chain entanglement. Figure 10 displays the MWD for MFM-1 before and after melt viscosity measurements, and the insignificant change to the distribution rules out polymer chain degradation as a contributing factor to the reduction in melt viscosity. For the small but significant increase in the distribution profile around 106 Da found in the processed sample, we have yet to find an explanation; however, given that it is an increase, it does not affect our overall conclusions regarding the changes in melt rheology. 5. Conclusions The theoretical MFM reaction model has been experimentally validated using number-averaged molecular weight and branching data, while assuming a linear


Figure 10. Comparison of molecular weight distribution for MFM-1, before (solid line) and after (dashed line) melt viscometry measurement.

kinetic model to be applicable for the hyperbranched reaction and isothermal batch conditions. The combination of kinetic modeling and conversion-dependent molecular weight distribution data allowed us to comment on the evolution of branching in some detail. Moreover, the melt viscosity data obtained for one of the hyperbranched polymers has shown a significant reduction in the temperature (by ∼60 °C) required for processing when compared to a linear analogue of similar Mn, hinting at the potential of branched and hyperbranched polymers as rheology modifiers and processing aids. The prime significance of this work lies in the development of a generic branched/hyperbranched model, which can be used to guide the production of other free-radical hyperbranched polymers. By using modeling, optimization, or experimental design methods, the manufacture of hyperbranched polymers of desired architecture or physical properties can be expedited, which is economically advantageous and of particular interest to the large-scale production of new polymer architectures. In conjunction with the facile and inexpensive methodology by Costello et al.,35 this combination should provide a powerful incentive for the development of new but costeffective polymeric materials. Acknowledgment The authors thank members of RAPRA and Viscotek UK Ltd. for all their help regarding polymer GPC analysis, with special thanks going to Dr. Steve Holding (RAPRA) and Paul Clarke (Viscotek UK Ltd.). Nomenclature A ) multifunctional monomer (MFM) concentration, mol/L A* ) multifunctional monomer (MFM) radical concentration, mol/L a ) reacted multifunctional monomer (MFM) molecule, dimensionless A - A ) number of unreacted multifunctional monomer (MFM) molecules, mol/L a - A ) number of latent reacted multifunctional monomer (MFM) molecules, mol/L a - a ) number of branched multifunctional monomer (MFM) molecules, mol/L [a - A]disp ) number of latent branches formed via disproportionation termination, mol/L [a - a]disp ) number of branches formed via disproportionation termination, mol/L CTA ) chain transfer agent (CTA) concentration, mol/L CTA* ) chain transfer agent (CTA) radical concentration, mol/L

CTAactive ) number of used chain transfer agent (CTA) molecules, mol/L cta ) reacted chain transfer agent (CTA) molecule, dimensionless D ) parameter in the gel effect constitutive equation, dimensionless f ) initiator efficiency, dimensionless I2 ) initiator concentration, mol/L I* ) initiator radical concentration, mol/L IDiss ) number of dissociated initiator molecules, mol/L i ) reacted initiator molecule, dimensionless M ) monomer concentration, mol/L M* ) monomer radical concentration, mol/L m ) reacted monomer molecule, dimensionless MnLin ) number-average molecular weight for linear polymer, kg/kmol MnHyp ) number-average molecular weight for hyperbranched polymer, kg/kmol MWm ) molecular weight of monomer, kg/kmol MWs ) molecular weight of solvent, kg/kmol MWi ) molecular weight of initiator, kg/kmol NB ) average number of branches in hyperbranched polymer, dimensionless NLin ) number of macromolecules in linear reaction, mol/L NHyp ) number of macromolecules in hyperbranched reaction, mol/L R ) universal gas constant, kJ/kmol K T ) temperature, K Term ) number of termination reactions, mol/L xm ) monomer conversion, dimensionless xtc ) fraction of combination termination, dimensionless xtd ) fraction of disproportionation termination, dimensionless kAIBN ) kinetic constant for initiator decomposition, 1/s kA*A ) kinetic constant for propagation of A* with A, m3/ kmol s kA*M ) kinetic constant for propagation of A* with M, m3/ kmol s kA*CTA ) kinetic constant for propagation of A* with CTA, m3/kmol s kA*A* ) kinetic constant for termination of A* with A*, m3/ kmol s kA*M* ) kinetic constant for termination of A* with M*, m3/ kmol s kA*CTA* ) kinetic constant for termination of A* with CTA*, m3/kmol s kA*I* ) kinetic constant for termination of A* with I*, m3/ kmol s kCTA ) kinetic constant for chain transfer of CTA agent, m3/kmol s kCTA*A ) kinetic constant for propagation of CTA* with A, m3/kmol s kCTA*M ) kinetic constant for propagation of CTA* with M, m3/kmol s kCTA*CTA ) kinetic constant for propagation of CTA* with CTA, m3/kmol s kCTA*A* ) kinetic constant for termination of CTA* with A*, m3/kmol s kCTA*M* ) kinetic constant for termination of CTA* with M*, m3/kmol s kCTA*CTA* ) kinetic constant for termination of CTA* with CTA*, m3/kmol s kCTA*I* ) kinetic constant for termination of CTA* with I*, m3/kmol s kI2 ) kinetic constant for initiator decomposition, 1/s kI*A ) kinetic constant for propagation of I* with A, m3/ kmol s kI*M ) kinetic constant for propagation of I* with M, m3/ kmol s

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kI*CTA ) kinetic constant for propagation of I* with CTA, m3/kmol s kI*A* ) kinetic constant for termination of I* with A*, m3/ kmol s kI*M* ) kinetic constant for termination of I* with M*, m3/ kmol s kI*CTA* ) kinetic constant for termination of I* with CTA*, m3/kmol s kM*A ) kinetic constant for propagation of M* with A, m3/ kmol s kM*M ) kinetic constant for propagation of M* with M, m3/ kmol s kM*CTA ) kinetic constant for propagation of M* with CTA, m3/kmol s kM*A* ) kinetic constant for termination of M* with A*, m3/ kmol s kM*M* ) kinetic constant for termination of M* with M*, m3/kmol s kM*CTA* ) kinetic constant for termination of M* with CTA*, m3/kmol s kM*I* ) kinetic constant for termination of M* with I*, m3/ kmol s kp ) kinetic constant for propagation, m3/kmol s kp0 ) initial kinetic constant for propagation, m3/kmol s kt ) kinetic constant for termination, m3/kmol s kt0 ) initial kinetic constant for termination, m3/kmol s kθp ) parameter in the gel effect constitutive equation, 1/s kθt ) parameter in the gel effect constitutive equation, 1/s Greek Letters φm ) volume fraction of monomer, dimensionless φp ) volume fraction of polymer, dimensionless φs ) volume fraction of solvent, dimensionless ξ0 ) zeroth moment of “living” polymer chains, kmol/m3 Fm ) density of monomer, kg/m3 Fs ) density of solvent, kg/m3 Fp ) density of polymer, kg/m3 Fi ) density of initiator, kg/m3 Subscripts/Superscripts 0 ) initial value * ) radical molecule

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Received for review December 10, 2004 Revised manuscript received May 30, 2005 Accepted June 6, 2005 IE0488041

Hyperbranched Polymers. Synthesis, Modeling, Experimental

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