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Macromolecules 2008, 41, 4220-4225
Synthesis of Branched Poly(butyl methacrylate) via Semicontinuous Emulsion Polymerization Yuanqin Liu,† Jeffrey C. Haley,†,‡ Kangqing Deng,†,§ Willie Lau,| and Mitchell A. Winnik*,† Department of Chemistry, UniVersity of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Rohm and Haas Company, 727 Norristown Road, Spring House, PennsylVania 19477 ReceiVed January 29, 2008; ReVised Manuscript ReceiVed March 27, 2008
ABSTRACT: Latex particles comprised of branched poly(butyl methacrylate) (PBMA) were prepared via semicontinuous emulsion polymerization. The extent of branching was controlled by adding various amounts of bisphenol A dimethacrylate (BPDM) as a branching agent, and 1-dodecanethiol (C12SH) was used as a chain transfer agent to prevent cross-linking and to control molecular weight. All PBMA samples have relatively high molecular weights with molecular weight distributions similar to that of the polymers synthesized by regular free radical polymerization in the presence of a chain transfer agent. The degrees of branching were determined using 1H NMR. G′ and G′′ measurements indicated no significant entanglement contributions to the rheological properties. The latex particles containing branched PBMAs are monodisperse, and the particle sizes are well controlled.
Introduction Many polymers used in latex coatings are inherently branched. Examples include butyl acrylate (BA) copolymers and vinyl acetate (VAc) copolymers. These polymers are produced by emulsion polymerization, and they are often accompanied by gel formation. With the addition of a chain transfer reagent to the reaction mixture, gelation can be suppressed and some control is possible over the number average molecular weight (Mn). Even with our current understanding of the factors that affect the formation1–3 and properties4,5 of latex films, we have a little knowledge of the influence of chain branching on these properties. When grafting competes with polymerization, as in the reactions described above, even characterizing the polymer and distinguishing long-chain from short-chain branches becomes a challenge.6–10 Long chain branches, particularly if they participate in entanglements, would be expected to have a significant influence on polymer diffusion in latex films and in the polymer rheology. Extensive branching should lead to structures resembling hyperbranched polymers, which have some properties similar to dendrimers. This paper is based on the hypothesis that we can begin to learn about the importance of branching in latex polymers through the study of polymers in which there is greater control over the molecular weight and extent of branching. Many methods have been developed for the synthesis of branched polymers. Gauthier used successive steps of anionic polymerization and chloromethylation to synthesize a series of hyperbranched polystyrenes.11–14 Knauss developed a convergent living anionic polymerization method to produce polystyrene (PS) with dendritic branching.15 A series of long-branched PS of various architectures were prepared by anionic polymerization using a multifunctional initiator.16 Fre´chet and his coworkers synthesized hyperbranched polymers using selfcondensing vinyl polymerization (SCVP).17–19 Others have used group transfer polymerization20 and controlled radical polymerization (e.g., atom transfer radical polymerization (ATRP))21,22 for the preparation of hyperbranched polymers. For example, * Corresponding author. † Department of Chemistry, University of Toronto. ‡ Current address: Lyondell Chemical Company, Cincinnati, OH. § Current address: Department of Applied Chemistry, University of Harbin Institute, Harbin, China. | Rohm and Haas Company.
Armes prepared branched polymers via ATRP and reversible addition fragmentation chain transfer (RAFT) polymerization.23,24 Even though well-defined hyperbranched structures could be produced, none of these methods can be applied generally. Recently Sherrington’s group reported a facile and broadly applicable method for producing branched polymers from vinyl monomers. In this approach, they carried out conventional free radical polymerization of the vinyl monomer in the presence of both a cross-linking agent (to generate branches) and a chain transfer agent (to prevent gel formation). With the correct balance of these two reagents, a soluble branched polymer can be obtained. For example, they polymerized methyl methacrylate (MMA) in the presence of but-2-ene-1,4-diacrylate (BDA, a bifunctional comonomer). To inhibit gelation, they added 1-dodecanethiol (C12SH) as a chain transfer agent. They found that a high yield (77-97%) of soluble polymer was produced when relatively low levels ( 10). Despite these limitations, this new strategy provides a facile one-step method for making highly branched polymers confined to colloidal nanoparticles. We are interested in exploring Sherrington’s emulsion polymerization approach. In this article we describe experiments in which we apply this method to the polymerization of butyl methacrylate (BMA). Instead of batch emulsion polymerization, where problems can arise because of unfavorable reactivity ratios or chain transfer constants, we used semicontinuous emulsion polymerization, which normally provides better control over molecular weight and molecular weight distribution. Our
10.1021/ma800215m CCC: $40.75 2008 American Chemical Society Published on Web 05/22/2008
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Semicontinuous Emulsion Polymerization 4221
Table 1. Typical Recipe for the Synthesis of Branched PBMA
Latex amount (g) ingredient
first stage
H2 O SDS Me-β-CD Na2CO3 KPS monomer pre-emulsion H2O SDS BMA BPDM C12SH
3.0 0.030 0.02 0.05 0.06 0.44 10.0 0.045 4.60 1.18 1.31
second stage
0.01 14.28
primary goal in this first set of experiments was to see if semicontinuous emulsion polymerization extended the range of accessible molecular weights, and offered better control over molecular weight and its distribution. Then we were interested in how polymer properties (such as the glass transition temperature, and linear rheological properties) varied with the extent of branching. We found that the molecular weights of the branched PBMA that we obtained were dramatically higher than the PMMAs made in batch emulsion by the Sherrington group, while the molecular weight distributions were much narrower. Experimental Section Materials. Potassium persulfate (KPS), bisphenol A dimethacrylate (BPDM), sodium carbonate (Na2CO3), sodium dodecyl sulfate (SDS), 1-dodecanethiol (C12SH), hexadecane and 2,2′-azobis(2methylbutyronitrile) were used as received from Aldrich. Butyl methacrylate (BMA, Aldrich) was distilled at reduced pressure, and the purified monomers were stored at 4 °C until use. Methyl-βcyclodextrin (Me-β-CD) was kindly supplied by Rohm and Haas Co. and used as received. Water was purified by a Milli-Q ionexchange filtration system. Latex Preparation. Latex samples were synthesized by semicontinuous emulsion polymerization reactions. A typical recipe for the synthesis of branched PBMA is shown in Table 1. A monomer pre-emulsion was prepared by shaking a mixture of monomer, branching agent, surfactant, chain transfer agent, and water for 30 min. In the first stage, a dispersion of seed particles was prepared by batch emulsion polymerization. Water (3.0 g), Me-β-CD (0.02 g), and SDS (0.03 g) were added into a 100 mL 3-neck flask equipped with a mechanical stirrer, nitrogen inlet and condenser. The flask was immersed in an oil bath. The system was thoroughly purged with nitrogen while the reaction mixture was heated to 80 °C. After the reactor temperature stabilized at 80 °C, the KPS solution (0.06 g in water 0.5 g) as an initiator and the Na2CO3 solution (0.05 g in water 0.5 g) as a pH buffer were added into the reactor followed by the addition of 3 wt % of the monomer preemulsion. The mixture was stirred for 20 min at 80 °C. In the second stage of polymerization, the remaining monomer pre-emulsion was fed into the seed latex dispersion together with an initiator aqueous solution (0.01 g in water 2.0 g) over 5 h. The feed rates were kept identical, controlled by Fluid Metering QG50 pumps. After the addition was completed, the system was maintained at 80 °C for 0.5 h. Then the reaction was cooled to room temperature. Synthesis of High Molecular Weight Linear PBMA. High molecular weight linear PBMA was synthesized by miniemulsion polymerization using SDS/hexadecane as surfactant/costabilizer and 2,2′-azobis(2-methylbutyronitrile) (AMBN) as initiator. A mixture of BMA, SDS, hexadecane, AMBN, and water was emulsified using a Branson Model 250 digital sonifier (40% amplitude) at 0 °C for 30 min. The reaction was carried out at 80 °C for 5 h. Water was evaporated and the polymer was dried in a vacuum oven for 24 h at 40 °C. The dry polymer was fractionated using hexane/ethanol. Then the high molecular weight fraction was collected. GPC and rheological measurement were carried out on this sample. See the Supporting Information for the GPC result.
Characterization of Latex Particles. Particle sizes and size distributions were measured by dynamic light scattering at a fixed scattering angle of 90° at 23 °C with a Brookhaven Instruments model BI-90 particle sizer equipped with a 10 mW He-Ne laser. The solids content was determined by gravimetry. Characterization of Latex Polymers. Differential Refractometer (dn/dc). The refractive index increment (dn/dc) was measured using a Brookhaven Instruments model BI-DNDC differential refractometer at 35 °C. For each polymer sample, five concentrations were used. ∆n was plotted against concentration to give dn/ dc. The obtained dn/dc values are listed in Table 2. Triple Detector Array Gel Permeation Chromatography (TDA/ GPC). Polymer molecular weight and molecular weight distribution were measured by gel permeation chromatography (GPC) using a Viscotek liquid chromatograph equipped with a Viscotek model 2501 UV detector and a Viscotek TDA302 triple detector array (TDA). Two Viscotek GMHHR mixed bed columns were used with tetrahydrofuran (THF) as the elution solvent at a flow rate of 0.6 mL/min. The GPC column oven temperature was 35 °C, and the injection volume was 0.1 mL. The absolute molecular weight was calculated using the dn/dc value. All molecular weight data are listed in Table 2. Differential Scanning Calorimeter. The glass transition temperature (Tg) of copolymers was measured with a TA Instruments DSC Q100 V7.3 Build 249 differential scanning calorimeter over a temperature range of -50 to +150 °C at a heating rate of 10 °C/ min. Each sample was taken through two runs. Tg values were calculated from the second run and the values determined are shown in Table 2. NMR Spectroscopy. 1H NMR spectra were recorded on a Varian Mercury 300 MHz NMR spectrometer using CD2Cl2 as the solvent in 5 mm NMR tubes. The residual 1H signal in CD2Cl2 was used as a reference in all the spectra. Rheological Measurements. The linear viscoelastic response of the PBMA samples was studied at several temperatures above Tg with a Rheometrics RAA instrument in the oscillatory shear mode. We employed a pair of parallel plates (25 mm diameter). The frequency was scanned between 0.01 and 100 rad/s at a constant temperature. Strain sweeps were employed to ensure that all measurements were made in the linear viscoelastic regime. The following procedure was used to prepare the samples for the measurements of viscoelastic properties. First, the samples were dried under vacuum at 80 °C for 12 h to eliminate any trace of volatiles. Then, the samples were pressed between cleaned polytetrafluoroethylene (PTFE) sheets in a Carver Press at 120 °C to eliminate air bubbles. The thickness of the samples was controlled using separators between the plates of the press. In this way, samples free of bubbles, approximately 25 mm in diameter and 1 mm thick, were obtained.
Results Synthesis of Branched PBMAs. There are three objectives in this work. First, we want to prepare “high molecular weight” branched polymers, which here refers to a number-average molecular weight (Mn) of at least several tens of thousands of grams per mole. Second, we wished to control the extent of branching in these high Mn branched polymers, which means the extent of branching in the final product could be tuned by adjusting the recipe for latex synthesis. Finally, we hoped to achieve the above two objectives in a straightforward one-pot reaction. With the three goals in mind, we carried out the synthesis of butyl methacrylate (BMA) copolymers by semicontinuous emulsion polymerization using bisphenol A dimethacrylate (BPDM) as the branching agent and 1-dodecanethiol (C12SH) as the chain transfer agent. A typical recipe is presented in Table 1. While the reactivity ratios for the reaction with BMA are not known, and these will be influenced by the relative solubility of the two monomers in the aqueous medium, we assume that
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Macromolecules, Vol. 41, No. 12, 2008 Table 2. Characteristics of Unlabeled Latex Polymers and Particles
latex samples
mole feed ratio mole ratio by 1H BMA/BPDM/C12SH NMR BMA/BPDM dn/dc
molecular weighta (g/mol) Mn
Mw
particle sizer solids Mw/Mn Rh(nm) Tg(°C) d (nm) Poly.b content (%)
L1: linear-PBMA1 100/0/1 100/0 0.067 56 000 150 000 2.7 6.2 26 152 0.038 20.5 L2: linear-PBMA2 100/0/1.2 100/0 28 000 62 000 2.2 107 0.022 19.8 B1: branched-PBMA1 100/1/1.5 100/1.1 160 000 240 000 1.6 92 0.011 22.3 B2: branched-PBMA2 100/1/2 100/1.0 0.079 58 000 200 000 3.5 6.1 21 147 0.039 20.2 B3: branched-PBMA3 100/5/8 100/6.0 51 000 270 000 5.3 175 0.032 20.5 B4: branched-PBMA4 100/5/9 100/5.9 68 000 190 000 2.8 105 0.048 19.6 B5: branched-PBMA5 100/5/10 100/6.8 0.080 66 000 140 000 2.1 3.3 8 158 0.019 19.4 B6: branched-PBMA6 100/10/15 100/9.8 65 000 130 000 2.0 102 0.025 21.1 B7: branched-PBMA7 100/10/20 100/10.0 0.084 61 000 130 000 2.1 2.1 2 93 0.035 24.0 B8: branched-PBMA8 100/10/22 100/9.6 40 000 78 000 1.9 90 0.112 21.0 a Molecular weights were measured using a Viscotek GPC equipped with TDA302 triple detector array. b Polydispersity (poly) is a measure of the width of the particle size distribution, taking values close to zero (0.000-0.020) for nearly monodisperse samples, and small (0.020-0.080) for narrow size distributions.
Figure 1. 1H NMR spectra of PBMAs with different branching levels. CD2Cl2 was used as solvent. Peaks a and b correspond to protons of BPDM and BMA, respectively.
Figure 2. UV and RI traces in the GPC analysis of branched-PBMA2.
we can overcome any problems with the reactivity ratio differences by running the reactions under monomer-starved conditions. The aromatic rings of BPDM provide UV and NMR signatures for analyzing its incorporation into the polymer. C12SH is an efficient chain transfer agent to suppress gel formation in semicontinuous emulsion polymerizations of acrylate and methacrylate monomers.31 To ensure good transport of these reactants, particularly C12SH, through the aqueous phase during the synthesis, methyl-β-cyclodextrin (Me-β-CD) was included in the reaction mixture.32 While many semicontinuous emulsion polymerization reactions are carried out in the presence of preformed seed particles, we wished to avoid the contribution of even small amounts of high molecular weight linear polymer typical of PBMA seed particles. Therefore, we generated seed particles in situ using a small fraction (typically 3 wt %) of the total feed of monomer pre-emulsion in a batch reaction. The pre-emulsion contained the monomer mixture, water and additional surfactant. The remaining pre-emulsion was then fed continuously into the reaction over 5 h. All of the potassium persulfate (KPS) initiator was added in the first stage.33 Samples of latex produced from the above process were dried in an oven overnight. The dry polymers were then used for molecular weight measurements using a TDA/GPC. Values of dn/dc were determined independently using a differential refractometer. As shown in Table 2, the dn/dc values increase as the fraction of BPDM in the polymer increases. Without BPDM, linear-PBMA1 has a dn/dc value of 0.067. The dn/dc value becomes 0.079 for branched-PBMA2 which contains 1 mol % of BPDM (relative to BMA). However, there is only a small increase of dn/dc when the BPDM fraction was increased to 10 mol % (for branched-PBMA7, dn/dc ) 0.084). The calculated molecular weights are presented in Table 2. For most samples shown in Table 2, Mn is greater than 40 000 g/mol, and Mw is greater than 100 000 g/mol. Among all the branched polymers, there is one sample with a much larger Mn than all the others (for branched-PBMA1, Mn ) 160 000 g/mol). Thus the first goal, synthesis of “high molecular weight” branched
polymers, was achieved. Moreover Mw/Mn is less than 2.8 for most cases, which indicates that the molecular weight distribution is relatively narrow. Another feature can also be observed from the molecular weight data, which is that the molecular weights are comparable for the linear PBMA1 sample and the branched-PBMA2-8 samples. This feature demonstrates the feasibility of controlling the molecular weight of branched polymers by tuning the ratio of branching agent and chain transfer agent. In addition to obtaining “high molecular weight” branched polymers, controlling the extent of branching and preventing gel formation at the same time was also a challenge. Branching control was realized by adjusting the feed ratio of BMA/BPDM, while gel formation was avoided by feeding appropriate amount of C12SH. As presented in Table 2, four molar feed ratios of BMA/BPDM were investigated, in which the BPDM content ranged from 0 to 10 mol % (relative to BMA). After polymerization, the BPDM content in each polymer was determined from the 1H NMR spectrum (Figure 1), and the results are listed in Table 2. One can observe that all experimental ratios are similar to the corresponding feed ratios, even for samples with the highest BPDM concentration (branched-PBMA6-8). Thus the extent of branching could be varied by modifying the feed ratio of BMA/BPDM. No gelation was detected in any of the latex. Gelation could be suppressed when an appropriate amount of C12SH was fed together with the branching agent. Architectures of Branched PBMAs. We deduced the architectures of the branched PBMA chains from a combination of TDA/GPC traces and 1H NMR spectra. From the TDA/GPC data and dn/dc values, we calculated Mn values and polydispersities of the samples. A GPC trace for branched-PBMA2 is shown in Figure 2. Here one sees that the RI trace and UV trace (due to BPDM groups) overlap very well. This result suggests that the BPDM groups are relatively uniformly distributed over the polymer chains of different molecular weight. The absence of a UV peak at low mass indicates that all of the BPDM monomer was incorporated into the polymer.
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Semicontinuous Emulsion Polymerization 4223
Table 3. Estimate of Branching latex samples
NBMAa
NBPDMb
Xc
nBMAd
Tg (°C)
L1, linear-PBMA1 392 0 1 392 26 B2, branched-PBMA2 401 4 13 31 21 B5, branched-PBMA5 393 27 82 5 8 B7, branched-PBMA7 344 34 103 3 2 a The average number of BMA units per chain. b The average number of BPDM units per chain. c The average number of “parts” divided by BPDM per chain. d The average number of BMA units between two branching points.
Figure 3. Polymer architecture for (A) linear-PBMA1, (B) branchedPBMA2, (C) branched-PBMA5, and (D) branched-PBMA7. These drawings assume a uniform distribution of branch points in the polymer molecules.
We used the Mn values and the BMA/BPDM ratios to calculate the average number of BMA units (NBMA) and BPDM units (NBPDM) per polymer chain. The BPDM units divide the polymer chain into a number of “parts”. The network functionality (f) of BPDM is 4; thus (f - 1) ) 3 “parts” are added to the chain for each BPDM unit. The average number of “parts” per chain (X) was calculated with the equation X ) 1 + 3 × NBPDM
(1)
and the average number of BMA units per “part” (nBMA) is given by nBMA ) NBMA/X
(2)
The calculated results of four representative samples containing different BMA/BPDM ratios are shown in Table 3. All samples have a similar average number of BMA units per chain, whereas X values increase significantly with NBPDM. As a consequence, nBMA drops as X increases. For example, the most highly branched sample branched-PBMA7 contains an average of only three µBA units between branch points. In contrast, linear-PBMA1 has no branch points. The information in Table 3 was used to generate the graphical depiction of the chain architectures shown in Figure 3. As a linear chain, linearPBMA1 adopts a random coil structure (Figure 3A). Containing only four branch points per chain, branched-PBMA2 maintains a loose random-coil-like as depicted in Figure 3B. This description of the polymer shape in solution is consistent with the hydrodynamic Rh values acquired by dynamic light scattering (see Table 2). For the more branched PBMAs of similar molecular weight, the chain dimensions in solution become more compact. Branched-PBMA7, the most highly branched polymer chain, is divided by an average of 34 branch points per chain into more than 100 parts, which makes the chain in solution act like a dense sphere (Rh ) 2.1 nm; see Table 2 and Figure 3D). The decreasing Rh with increasing degree of branching was also consistent the GPC elution sequence, which can be
observed from the GPC traces, and a plot of log Mn versus retention volume of the four PBMAs presented in Figure 4. Branched PBMA Latex Particles. The synthesis methodology reported here offers control over branching without loss of control over particle size and size distribution. Particle size was measured by dynamic light scattering using a BI-90 particle sizer, and the results are shown in Table 2. The average diameters for all samples were in the range 100-150 nm. These are typical values for semicontinuous emulsion polymerization. Rheology Measurements. Viscoelastic measurements were carried out on the four representative samples listed in Table 3. The storage modulus (G′) and loss modulus (G′′) were measured as a function of frequency (ω) at a series of temperatures ranging from 40 to 140 °C. In previous experiments, we showed that the time-temperature superposition (TTS) principle could be used to construct master curves for poly(butyl acrylate-co-methyl methacrylate) polymers with various degrees of branching.31 Here we used the TTS principle to obtain shift factors (aT) of the temperature dependence of individual log G′ and log G′′ vs log ω plots. The G′ and G′′ master curves obtained, for T0 ) 40 °C as the reference temperature, are shown in Figure 5. The rheological response of the four samples shows that G′′ > G′ over the entire frequency range. These plots do not show any crossovers of the G′ and G′′ curves in the interval between the high frequency end of the rubbery zone and the terminal zone. For comparison, we examined the corresponding behavior of a high molecular weight linear PBMA sample (Mn ) 790 000, Mw/Mn ) 1.2). These data are presented below in the Discussion. Discussion Control of Molecular Weight. Controlling molecular weight and polydispersity are essential objectives in polymer synthesis. In recent years, there have been many reports describing the synthesis of branched polyacrylates and polyacetates by radical polymerization using the combination of a branching agent and a chain transfer agent. To date, none of them showed the ability to control the molecular weight of branched polymers. In most cases, the branched polymers have low Mn and very broad molecular weight distributions.25–30 Our study shows that in semicontinuous emulsion polymerization, one can achieve reasonable control over Mn and narrower polydispersities than reported previously. The key factors that provide molecular weight control in the synthesis of branched PBMA are summarized in the following paragraph. Literature results indicate that if the chain transfer agent fraction is less than a critical level, gel formation will occur.25–30 It is also well-known that too much CTA will result in oligomers as well as broad polydispersities. Thus it is necessary to determine the appropriate concentration of CTA. Because each BPDM will add two more chain ends to the backbone, at most two C12SH molecules are needed to cap the chain ends to prevent cross-linking. Hence, the C12SH concentrations used here are in the range 1.5-2.2 equiv relative to BPDM, and these compositions gave fairly high molecular weight products without any detectable gel. Maintaining the monomer-starved condition in the second stage of all semicontinuous emulsion polymerizations is the second consideration. The key feature of monomer-starved condition is that almost all of the monomers are consumed within a short time after being added into the reactor. In our reactions, the result is that monomer and branching agent always polymerized at the feed ratio. It was impossible for BPDM to accumulate. The presence of a suitable amount of C12SH, which was fed with the monomers, prevented cross-linking. The resulting polymer chains had a similar composition and length. The last point is the presence of the phase transfer agent, Me-β-CD, which guaranteed transport of monomers and C12SH
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Figure 4. GPC traces (A) RI signal and (B) log Mn vs retention volume for linear-PBMA1 (L1), branched-PBMA2 (B2), branched-PBMA5 (B5), and branched-PBMA7 (B7). The vertical line in part B indicates that the polymer with Mn ) 34 000 has a retention volume of 17.3 mL. The vertical line in part A indicates that ca. 30% of the L1 sample has Mn lower than 34 000.
Figure 5. Plots of master curves of G′ and G′′ for (A) linear-PBMA1, (B) branched-PBMA2, (C) branched-PBMA5, and (D) branched-PBMA7.
from the monomer droplets to reaction loci despite the difference in their water solubility. In fact, effective transport of reactants is a prerequisite to maintaining monomer-starved conditions, since monomers with poor water solubility will become concentrated in the monomer droplets as the reaction proceeds instead of reaching the growing polymer particles. Entanglement Considerations in Branched PBMA. In this section, we consider the potential role of entanglements in the rheology behavior of the linear and branched PBMA samples. The G′ and G′′ master curves shown in Figure 5A for the linear PBMA sample do not indicate the influence of entanglements. To understand this result, we begin by estimating the critical molecular weight for entanglement, Me, of PBMA. We synthesized a high molecular weight sample of linear PBMA by miniemulsion polymerization. As a form of bulk polymerization, miniemulsion polymerization commonly leads to high molecular weight polymer. We then fractionated the polymer to obtain a sample with Mn ) 790 000, Mw/Mn ) 1.2. Master curves (Figure 6) were constructed from obtained G′ and G′′ values measured as a function of frequency at a series of temperatures. These have the properties expected for entangled chains: G′ is greater than G′′ in the rubbery zone, and we expect that the two curves will cross over in the terminal zone if we were to extend the measurement time and temperature. Since there is not a clear plateau on the G′ master curve, we estimated the plateau
modulus GNo as the value of G′ corresponding to the frequency (log ω) of the minimum in G′′. From the expression Me )
FRT GN
(3)
where F is the polymer density, T is the absolute temperature, and R is the gas constant, we calculate that Me for PBMA is approximately 34 000 g/mol. Using this value, we can begin to understand the extent to which entanglements play a role in the rheology of the samples. Taking linear-PBMA1 as an example, the TDA/GPC curve in Figure 4, parts A and B, indicates that ca. 30% of the linearPBMA1 sample by mass has a molecular weight that is less than 34 000 g/mol. This 30% value represents a lower bound of the amount of material in the sample that is below 34 000 g/mol, as the TDA/GPC analysis is known to underestimate the polydispersity by undercounting the lower molecular weight components of a sample. Given that 30% of the sample is unentangled, we can treat this 30% as a viscous Θ solvent for the remaining 70% of the sample that has a molecular weight greater than 34 000 g/mol. Now, we need to consider how this “solvent” dilutes the entanglement network of the remaining high molecular weight polymer. The spacing between polymer entanglements in
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Semicontinuous Emulsion Polymerization 4225 research. Y.L. thanks Materials and Manufacturing Ontario (MMO) for a scholarship.
Supporting Information Available: Figures showing GPC traces for linear PBMA1 and PBMA2 and branched PBMA1 to branched PBMA8, as well as for the fractionated high molecular weight linear PBMA sample. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 6. Plots of master curves of G′ and G′′ for the high molecular weight linear PBMA sample. The vertical dotted line corresponds to the minimum value of G′′.
polymer melts and solutions follows a well established scaling relation34 a2 ∼ φ-R (4) where a is the entanglement spacing (tube diameter), φ is the volume fraction of polymer with a molecular weight greater than Mc, and R is a scaling exponent that ranges between 1.0 and 1.3.34 If we assume that the number of entanglement lengths required to produce an entangled polymer is fixed for PBMA (i.e., it is not a function of φ), then we can derive a scaling law for the effective critical molecular weight for entanglement in a polydisperse melt, Mc,eff. This scaling law is Mc,eff ∼ φ-R
(5)
From this relation, we estimate Mc,eff = 100 000 g/mol by assuming R ) 1. In other words, we believe that only polymers that are above 100 000 g/mol in the polydisperse sample are fully entangled with each other. Only about 15% by weight of the linear-PBMA1 sample has a molecular weight greater than 100 000 g/mol. This relatively small fraction of the sample is probably very hard to detect in our G′ measurements. For such a loosely entangled network, the terminal relaxation time of the entangled fraction may not be well enough separated from the terminal relaxation time of the unentangled fraction to show up in the experiment. For the same reason, the branched PBMA samples are unentangled as well. Summary We reported the synthesis of latex particles comprised of high molecular weight PBMA with various degree of branching using semicontinuous emulsion polymerization method. The most important contribution of this work is the successful control of molecular weight and molecular weight distribution. Also, all branched polymers are free of gel. Latex particles composed of the branched PBMAs are monodisperse in size. Polymer chain structures were estimated based on the molecular weight and the 1H NMR data. Rheological measurements showed that the polymers were unentangled despite the fact that they are linear or branched. Acknowledgment. The authors thank Rohm & Haas, Rohm and Haas Canada, and NSERC Canada for their support of this
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