Optimal Operating Strategies for Emulsion Polymerization with Chain

Article pubs.acs.org/IECR

Optimal Operating Strategies for Emulsion Polymerization with Chain Transfer Agent Cynthia Tjiam and Vincent G. Gomes* School of Chemical and Biomolecular Engineering, The University of Sydney, New South Wales 2006, Australia ABSTRACT: Batch and semibatch emulsion polymerization was investigated with a chain transfer agent (CTA) to optimize key process attributes such as monomer conversion and product properties such as molecular weight and particle size. The test monomer, styrene was polymerized in the presence of the chain transfer agent, n-dodecyl mercaptan, to control the final molecular weight. The process model used for conducting optimization incorporated the nucleation, reaction kinetics, and phase heterogeneity involving the aqueous, monomer droplet and polymer particle phases during the various stages of the reaction. The model developed was able to predict the behavior of emulsion polymerization, while describing the significant effect of CTA on molecular weight distribution (MWD) and polydispersity index (PDI) for both batch and semibatch processes. The optimal operating strategies for the process were developed using reaction temperature and monomer feed rate as process variables to obtain desired process trajectories and product properties.

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INTRODUCTION Emulsion polymerization is widely used to generate products, such as coatings, paints, adhesives, binders, fibers, and tires, among others. The usefulness of emulsion polymerization is derived from its compartmentalized nature, the possibility of preparing polymers with unique properties, controlled chain length distribution, efficient heat removal, and environmental benefits due to its use of water as the reaction medium.1,2 The ultimate polymer properties are largely related to the molecular weight distribution (MWD) and product composition,4 which affect properties such as elasticity, strength, toughness and solvent resistance of films.5 Controlled molecular weights are required to tune products for various applications. Scrub resistance of paint increases with molecular weight, and high molecular weight with a broad MWD is useful in adhesives to impart mechanical resistance. While low molecular weights are required for ensuring adhesion, narrow MWDs with low molecular weights are required for photocopier toners.6 A chain transfer agent (CTA) with optimal operating strategy is able to control the product properties crucial in shaping a number of end-use properties, such as polymer molecular weight and functionality of polymer chains.3 Thus, the use of a CTA to control molecular weight is critical for a wide range of applications. Typical CTAs used in emulsion polymerization are CCl4, CBr4, halomethanes, disulfides, mercaptans, and compounds that have an available H-atom to readily draw on. Among these, mercaptans are by far the most widely preferred.7 A chain transfer agent enters into the propagation step by transferring a proton to the growing radical chain, terminating it while initiating a new chain. The reaction scheme for a chain transfer agent is shown below: Pn• + RX → Pn−X + R•

(R1)

R• + M → R−M•

(R2)

R−M• + Pm → RPm + 1•

(R3) © 2014 American Chemical Society

RX, a chain transfer agent, typically contains a thiol or a halogen group which is transferred during the interactions.8 A propagating radical Pn• reacts with RX, terminates the propagating chain to form an oligomer Pn−X and a new radical R•(1), which reacts with the monomer to form a new propagating chain via steps R2 and R3.3 In a previous work, the chain transfer behavior of mercaptans was studied in terms of the consumption of monomer and chain transfer agent and their effect on the average degree of polymerization (DPn) and polydispersity index.9 The chain transfer coefficient, Cs, typically decreases with increasing carbon chain length due to the lower rate of diffusion through the aqueous phase. The effect of primary mercaptans (C2, n-C4, n-C7, n-C12) on the nucleation and growth of polymer particles were also described.10 The reduction in polymerization rate per particle increases with decrease in molecular weight of CTA as the solubility in water increases. For n-C12 type CTAs the polymerization rate is not significantly affected.10 The two film theory for emulsion polymerization has been used to account for mass transfer of CTA (n-C7 to n-C12) from monomer droplets to polymer particles.11 The consumption rate of high molecular weight mercaptan (C-atom >10) was much lower in emulsion compared to bulk polymerization due to the slow rate of transport of mercaptan molecules arising from diffusion resistance between monomer droplets and polymer particles. Instantaneous and cumulative MWD was estimated from CTA concentration inside the particles when mass transfer limitations exist.12 A kinetic model for emulsion polymerization with n-DDM13 employed model parameters estimated by fitting experimental data. The result showed that CTA had no effect on polymerization Special Issue: John Congalidis Memorial Received: Revised: Accepted: Published: 7526

October 3, 2013 March 22, 2014 March 24, 2014 March 24, 2014 dx.doi.org/10.1021/ie4032956 | Ind. Eng. Chem. Res. 2014, 53, 7526−7537

Industrial & Engineering Chemistry Research

Article

rate but significantly affected molecular weight distribution (MWD). A starved-fed and unseeded emulsion polymerization6 aimed at producing constant MWD with tert-nonyl mercaptan (C9) and tert-dodecyl mercaptan (C12). A mathematical model was used to explain the effect of the CTA chain length. C12 was found to be preferable relative to C9 CTA because of narrower, unimodal MWDs obtained with batch process, while for starved operation C9 was preferable due to lower mass transfer resistance and higher reactivity, ensuring shorter reaction time.6 A comprehensive mathematical model of emulsion polymerization is of substantial value for the polymer industry as noted from the literature21−23 for determining conversion, particle size, and molecular weight. However, limited information is available on these aspects with controlled molar mass. We used model parameters from the literature with no fitting of parameters for our experimental data. Several studies14−17 reported optimization and control of polymerization reactors while others18−20 reported optimization and control of product attributes without CTA. The key objective of this work was to modify the conventional emulsion polymerization by incorporating the transfer agent and investigate its effects on polymerization rate, MWD, and PSD for both batch and semibatch operation. On the basis of validated models, optimal operating strategies were developed to maximize conversion and minimize molecular weight in the presence and absence of CTA.

Table 1 Aqueous Phase kd

initiation

Initiator → 2I•

propagation

I• + M → IM•

k pi

i K p,aq

IM•i + M ⎯⎯⎯⎯⎯→ IM•i + 1 K ei

IM•i + micelle → new particle,

nucleation

i = z , ..., jCrit − 1

K ei

IM•i + latex particle → entry,

radical absorption

i = z , ..., jcrit − 1

Organic/Particle Phase K pi

propagation

IM•i + M → IM•i + 1

termination

IM•i + IM•j → IMi + j

transfer to monomer

IM•i + M ⎯→ ⎯ IMi + M•

transfer to CTA

IM•i + RX ⎯⎯⎯⎯⎯⎯→ IM•i − X + R•

radical desorption and re-entry

E + particle XooooY particle

K ti

K tri

K trCTA

K eE

K dm

model based on zero-one kinetics. The mass balances for the aqueous radical species and monomer in the reactor are given by

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d[I•] = 2fkd[I] dt

GOVERNING EQUATIONS The conventional emulsion polymerization model needs to be modified to accommodate the CTA processes R1−R3 in the aqueous and particle phases.8 The zero-one kinetic model is based on the consideration that the rate of radical−radical termination within a particle is fast relative to the rate of radical entry into particles and is valid for small particles where the radicals terminate instantaneously.13,24 Thus, a particle contains either zero or one free radical. Our model is based on the following main premise: • Particles form via micellar (dominant) and homogeneous (minor) nucleation. • The aqueous phase radical grows to length z prior to entering a latex particle. • The entry of a z-mer, CTA radical and re-entry of exited radical (radical desorption) into a latex particle containing a free radical results in instantaneous termination. • The concentrations of monomers in different phases (monomer-swollen polymer particles, aqueous phase, and monomer droplets) are in thermodynamic equilibrium. • Coagulum formation is negligible as the surfactant (concentration above the critical micellar concentration) stabilizes the system. • Diffusion from droplet−aqueous phase interface to aqueous phase is the rate-determining step for CTA mass transfer. • Three types of particles exist with no radical (type n0), monomeric radical (type n1m), and polymeric radical (type n1p). The polymerization is based on the reactions shown in Table 1. Material Balance. The mathematical model was developed by including the effects of CTA on the emulsion polymerization

(1)

d[IM1•] 1 1 [I•]CwM − k p,aq [IM1•]CwM − kt , aq[IM1•][T•] = k p,aq dt (2)

For i < z, then d[IM•i ] i−1 i [IM•i − 1]CwM − k p,aq [IM•i ]CwM = k p,aq dt • CTA − k trCTA − kt , aq[IM•i ][T•] ,aq[IM i ]Cw

For i = z, ..., j d[IM•i ]

crit−1,

(3)

then

i−1 i = k p,aq [IM•i − 1]CwM − k p,aq [IM•i ]CwM

dt

• CTA − k trCTA − k t,aq[IM•i ][T•] ,aq[IM i ]Cw

− kei[IM•i ] d[IM•J ] Crit

dt

Ntot i Cmicelle[IM•i ] − ke,micelle NA

JCrit − 1 [IM•J = k p,aq

Crit

M − 1]Cw

− k t,aq[IM•J

Crit

− 1][T

(4) •

] (5)

d[E•] = dt

jCrit − 1

∑

k trCTA[IM•i ]CwCTA − keE[E•]

n=1 R Cmicelle[E•] + kdE − ke,micelle

Ntot NA

N1R − k t,aq[E•][T•] NA (6)

Total radical concentration in the aqueous phase [T•] is given by the sum of the exited and aqueous phase oligomeric radicals: [T•] =

jCrit − 1

∑ i=1

7527

[IM•] + [E•] (7)

dx.doi.org/10.1021/ie4032956 | Ind. Eng. Chem. Res. 2014, 53, 7526−7537


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the propagational growth rate for a particle containing a single free radical K = kpMwMCp/NAdp, Cp is monomer concentration in particle, dp is polymer density, MM w is monomer molar mass. An n1p type particle forms when an oligomeric radical enters an n0 particle, and the monomeric radical propagates in an n1r type particle to form a polymeric radical. The n0 particle forms when a radical (oligomeric or exited) enters n1r or n1p particles and when monomeric radicals exit an n1r type particle. An n1r type particle forms by chain transfer within particles containing a polymeric radical and via entry of exited monomeric radicals into n0 type particles. These particles are consumed through propagation of radicals in existing particles, by desorption of monomeric radicals from existing n1m particles, and by entry of a radical into existing n1r type particles. An n1p type particle is affected by growth of particles as radicals propagate without changing particle identity. The total number of particle in system is n = n0 + np1 + nr1, and the average number of radicals in a particle is

The moles of monomer and CTA fed to the reactor are dNM,Feed dt

dNct,Feed dt

= Fm ,

NM,Feed(t = 0) = NM,o

= FCTA ,

(8)

NCTA,Feed(t = 0) = NCTA,o

(9)

The mass balances for monomer and CTA are dNm = Fm − R pMVr dt

(10)

dNct = FCTA − R pCTAVr dt

(11)

The volumes of droplets (Vd), water (Vw), and particle (Vp) phases are M wM M CTA (NM − CpMVp − CwMVw ) + w ρM ρCTA

Vd =

(NCTA − CpCTAVp − CwCTAVw )

Vw =

dVp dt

(12)

n̅ =

Vwo 1 − [(M wMCwM /ρM ) + (M wCTA CwCTA /ρCTA )]

=

(14)

⎡ [S ] − [Sads] − [cmc] ⎤ ⎥ Cmicelle = max⎢0, added nagg ⎥⎦ ⎢⎣

The total volume (Vr) of the reactor contents is ⎛ ⎞ ⎛ ⎞ dVr 1 1 1 1 ⎟ = M wMR pMVr ⎜⎜ − ⎟⎟ + M wCTA R pCTAVr ⎜⎜ − ρm ⎠ ρCTA ⎟⎠ dt ⎝ ρp ⎝ ρp

Sads =

(15)

Population Balance Equations. The population balance or evolution equations expressed in terms of the unswollen volume (V) and total number of particles in the systems are given as follows:18,24,28 1. Particles containing a single polymeric radical (n1p).

JCrit − 1

∑

i ke,micelle Cmicelle[IM•i ]] + k pCpMn1r

i=1

− k trMCpMn1p + ρi n0 − ρn1P −

∂(Kn1P) ∂V

(16)

2. Particles containing no free radical (n0). ∂n0(V , t ) = ρ(n1P + n1r − n0) + kdEn1r ∂t

∂P ̅(M ) = P(M ) = n ̅ (k trCp + ρavg ) ∂t ⎛ −(ρ + k trCp) M ⎞ ⎟ exp⎜⎜ k pCp M w ⎟⎠ ⎝

(17)

3. Particles containing a monomeric or a CTA-derived radical (n1r). ∂n1r(V , t ) CTA = ke,micelle Cmicelle[E•] + keE[E•]n0 − ρn1r ∂t − kdEn1r − k pCpMn1r + k trMCpMn1P

4πrs 2Ntot NAas

(20)

(21)

where cmc is the critical micellar concentration; nagg is the mean aggregation number for the surfactant; Stot is the total concentration of the added surfactant; Sads represents the amount of surfactant per unit volume adsorbed onto the polymer surface; and as is area occupied by an adsorbed surfactant molecule. From this equation one may conclude that micellar nucleation (particle formation via micelles) stops when the surfactant concentration falls below its critical value. Molecular Weight Distribution and Polydispersity. The physical and mechanical properties of polymers depend on their molecular weight and molecular weight distribution (MWD). The molecular weight distribution in the absence of CTA is estimated from8,22

∂n1P(V , t ) JCrit − 1 M = δ(V − V0)[k p,aq Cw [IM•J − 1] Crit ∂t +

(19)

The latex particle and monomer droplets are dispersed in the aqueous phase and stabilized by the adsorption of surfactant molecules onto their surface. The micelle concentration can be determined by total concentration of surfactant added minus the rate of surfactant consumption:

(13)

M wMR pMVr ρp

n1P(V , t ) + n1r(V , t ) n(V , t )

(22)

and in the presence of CTA is ∂P ̅(M ) = P(M ) = n ̅ (k trCp + ρavg + C trk pCpCTA ) ∂t ⎡ −(k C + ρ + C k C CTA ) ⎤ tr p tr p p M ⎥ avg exp⎢ ⎢ k pCp MW ⎥⎦ ⎣

(18)

The above set of coupled partial integro-differential equations describes volume-based dynamic distributions for latex particles in emulsion polymerization with CTA, where K is 7528

(23)



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slowly than the particle volume. A finite difference method was used to transform the partial differential equations into a set of ordinary differential equations. A number of discrete groups of particles, G, with constant radius was used, and an ordinary differential equation represented the particle population in that group. Discretization allowed the integro-differential components of the equations to be expressed as finite difference approximations in equally spaced radial increments (Δr).18 The backward finite difference approximation was adopted for imparting stability. The model parameters employed are given in the Appendix.

As there is transfer to monomeric radicals, the chain transfer constant is defined as the ratio of the transfer rate coefficient and the propagation rate coefficient:29,30 k trCTA kp

C tr =

(24)

The rate coefficient for desorption of small radicalsis (E*) a function of radical diffusion both in water and inside the particle, the aqueous and particle concentrations of the desorbed radical and the particle volume:27

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EXPERIMENTAL SECTION Water of Milli-Q standard was used, and styrene monomer, initiator (potassium persulfate, KPS), surfactant (sodium dodecylsulfate, SDS), buffer (sodium bicarbonate, NaHCO3), and chain transfer agent (normal dodecyl mercaptan, n-DDM, CH3(CH2)10CH2SH) were obtained from Sigma Aldrich. Styrene monomer was purified by passing it through an inhibitor removal column. All other chemicals were used as received. Both batch and semibatch polymerizations were carried out at 70 °C under slight nitrogen pressure in a 1 L laboratory reactor with an agitation speed of 350 rpm (Figure 1). A temperature

3Dw Dmon

kdE(V ) =

(qDmon + Dw )rs

2

(25)

where q is the partitioning coefficient of the exited monomeric species and equal to CP/Cw; Dmon is the diffusion rate coefficient for the monomer inside the particle and is given by the following experimentally determined expressions:18 Dmon

⎧ 0.417Φ− 29.51Φ+ 53.14Φ2 − 36.03Φ3 ⎪10 Φ < 0.8 =⎨ ⎪ −8 Φ ≥ 0.8 ⎩ 9 × 10 exp( −19.16Φ)

(26)

where Φ is the polymer volume fraction inside the particle and is estimated as a function of time from the monomer concentration inside the particle ⎛ CpMo ⎞ Φ=1−⎜ ⎟ ⎝ dm ⎠

(27)

At high Φ the particle becomes glassy, resulting in a reduced entry rate of z-mer into particles. The propagation rate coefficient as a function of reaction temperature8 is given by 1/k p = 1/k po + 1/kdiff

(28)

where

Figure 1. Schematic diagram of experimental setup.

k po = 1.259 × 107e(−29000/ RT ) (L/(mol · s))

controlled heater/circulator (Julabo, Germany) provided heating/cooling flows through the external jacket to maintain reaction temperatures at desired values. For batch and semibatch processes, a mixture of styrene and CTA were pre-emulsified with water and surfactant in the presence of nitrogen gas to reduce mass transfer limitation of CTA in aqueous phase. Meanwhile, the initiator and buffer solution was heated to 70 °C. Once the temperature stabilized at 70 °C, the initiator mixture was poured into the reactor to start the reaction. Residual water was used to flush any residual styrene and initiator from beakers and poured into the reactor. Table 2 notes the procedural aspects of our experiments with the inclusion of CTA.

and kdiff is diffusion controlled rate coefficient given by kdiff = 4πσNA(Dmon + Drd )

(29)

where Drd is the diffusion coefficient arising from reaction− diffusion: Drd = k pCpα 2/6

(30)

The number and weight average molecular weights are given by the first and second moments of the distribution:22 α

Mn =

∫0 MP(M ) dM α

∫0 P(M ) dM α

Mw =

=

2

∫0 M P(M ) dM α

∫0 P(M ) dM

=

∑ MP(M ) ∑ P(M ) ∑ M2P(M ) ∑ MP(M )

(31)

Table 2. Procedures for Batch and Semi-Batch Operation with and without CTA at 70 °C

(32)

The molecular weight polydispersity index is MWPI = Mw/Mn. Numerical Solution. The above model contains differential and nonlinear algebraic equations in addition to population balances consisting of coupled integro-partial differential equations in radius and time [eqs 16−18]. To overcome the challenge of solving them, the population balances were discretized first with respect to radius, since the particle radius increases much more

styrene (g)

water (mL)

KPS (g)

buffer (g)

SDS (g)

CTA (g)

Fm (g/min)

75 75 75 75

500 500 500 500

0.2 0.2 0.2 0.2

0.05 0.05 0.05 0.05

1.2 1.2 1.2 1.2

1.46 1.46

0.44 0.44

For semibatch operation, the initial charges of monomer (30% of the total amount along with water), CTA, and 7529



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consumption at the beginning. However, the final monomer conversions attained were not significantly affected by the CTA. Figure 3 presents the number average molecular weight with variable concentration of CTA. We note approximate agreement between experimental and simulation values. The result shows that an increase in CTA concentration leads to decrease in average molecular weight, Mn. Molecular weight increases at the beginning and then decreases until it reaches a steady state at 32 570 g/mol. Mn increases at the beginning due to low concentration of CTA in particles. This is because of slow diffusion rate of CTA to latex particle.9 At about 7200 s, the number of transfer chains provided by CTA increases, and propagation rate decreases at about 4500 and 2100 s for 1 mol % CTA and 2 mol % CTA, respectively. In contrast, without CTA, Mn increases with conversion until about 240 000 g/mol (Figure 3). Transfer to monomer is the dominant chain stoppage event in a zero-one system as transfer to mercaptan gradually becomes less in this process. Thus, for a batch process, CTA is able to control the product Mn, lowering it by a factor of 7, compared to a process without CTA. Figure 4 shows that the CTA concentration has an effect on PDI and molecular weight, shifting the distribution to the left. Relatively lower MWPI and narrower MWD are observed for emulsion polymerization of styrene with CTA. Figure 5 shows good agreement between experimental data and model predictions for polymer average diameter and PDI. Changes in CTA concentration at the levels (1−2 mol %) tested do not appear to significantly affect overall particle size. However, some retardation in particle growth is observed. This is due to the presence of the CTA which affects transport processes related to monomer droplet and the CTA to the particles through the aqueous phase.9,11 For reactive chain transfer agents with low water solubility, transport of the chain transfer agent from the monomer droplets to the polymer particles can become diffusion limited. Thiols are extremely reactive toward styrenic radicals, and the reactivity of monomer toward the mercaptan CTA is also an important factor in the process. In the absence of CTA, monomers enter into the particles for continuing the polymerization and increasing particle size until all monomers are consumed. Figure 5B shows that with the modest changes in CTA concentration there is no significant effect of CTA on PDI. Semi-Batch Process. Model predictions and experimental data for the semibatch process are given in Figure 6. The monomer conversion increases until monomer is introduced in semibatch mode. The sudden decrease in conversion is due to monomer accumulation in reactor at the feed point. The polymerization rate is lower at the early stages due to the barrier between monomer droplets and particles in the presence of CTA.9 During the batch preperiod, the CTA and monomer diffuse to latex particle, promoting propagation and transfer rate both to monomer and CTA. Thus, conversion with CTA is slightly higher before the monomer feed was introduced. However, there is no significant difference in final conversion on operating with and without CTA. In the absence of CTA, the polymer Mn increases with conversion until 177 400 g/mol as observed in Figure 7. Poly(styrene) Mn for the semibatch process is lower compared to that for the batch process. This is due to starved monomer feed rate and limiting amount of monomer molecules in the reactor. The rate of monomer feed is greater than the polymerization rate, thus giving rise to accumulation of

surfactant (SDS) were brought to the desired reaction temperature with nitrogen bubbled to eliminate oxygen. Finally, the initiator and buffer solution at reaction temperature was added to the reactor contents to initiate the reaction. The remaining monomer was fed continuously to the reactor at 0.44 g/min (with syringe dosing pump), 90 min after the batch period. Monomer conversion was gravimetrically determined offline using samples taken at regular intervals from the reactor. The samples were dried, solid contents were determined, and conversion was estimated. Molecular weight analyses were carried out using a high temperature chromatography system (PL-GPC 120) at 40 °C with tetrahydrofuran eluent at 1 mL min−1. Calibration was conducted using polystyrene standards. A PL data stream was used for data acquisition and processed using Cirrus GPC software. Particle size was determined with a zetasizer (Malvern, U.K.).

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RESULTS AND DISCUSSION Batch Process. Figure 2 shows that the experimental data for overall conversion with variable CTA concentration are in

Figure 2. Effect of CTA on monomer conversion for batch process at 70 °C. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●).

good agreement with model simulations. The amount of CTA concentration was varied from 0 to 2 mol % (2.9 g) relative to monomer amounts with constant initiator and surfactant concentrations at 70 °C. As monomer molecules propagate (interval I), conversion increases with time through to intervals II and III. The polymerization rate mostly depends on the entry, exit, and bimolecular termination. CTA does not significantly affect the rate of exit of free radicals from latex particles; rather, the propagation rate is faster compared to particle exit.10,26 With addition of chain transfer agent there is an initial change in rate of polymerization; subsequently, the final conversion for both with and without the transfer agent reaches similar values. With the modest typical changes in CTA concentration (1−2 mol %), the overall polymerization rate was not found to be significantly affected. Such a situation was also noted for styrene/butyl acrylate emulsion polymerization with CTA.4 However, the effect becomes more pronounced as the number of carbon atoms in the mercaptan is decreased. The retardation of polymerization is observed at the early stages when CTA is introduced into the reactor since CTA molecules create barriers between the monomer droplets and particles;9,11 as a result, the monomer molecules experience slower diffusion through the aqueous phase, thereby lowering monomer 7530



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Figure 3. Effect of CTA for batch process at 70 °C on (A) Mn and (B) MWPI. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●).

Figure 4. Effect of CTA on MWD for batch process at 70 °C. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●).

Figure 6. Effect of CTA on monomer conversion for the semibatch process at 70 °C. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line).

monomer in the reactor. This may shift the nucleation mechanism from a micellar to a homogeneous one. Figure 7 shows that Mn increases with time until it reaches 19 543 g/mol in the presence of CTA. This is due to the increase in the molar ratio of monomer to CTA when monomer is fed to the reactor. Thus, the rates of propagation and of chain transfer also increase. The reaction time to reach steady state is longer for semibatch compared to batch operation. This longer

period of agitation increases droplet dispersion and reduces mass transfer limitations due to increase in interfacial area. Apart from greater molar effectiveness of CTA, this also leads to lower molecular weight for the semibatch process. Overall, Mn for the semibatch process was reduced by a factor of 9 with CTA compared to that without CTA. A slight narrowing effect of the CTA on distribution is noted in Figure 7B.

Figure 5. Effect of CTA for batch process at 70 °C on (A) particle size and (B) PSPI. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●). 7531



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Figure 7. Effect of CTA for semibatch process at 70 °C on (A) Mn, number average molecular weight; (B) MWPI, molecular weight polydispersity index. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●).

requires an additional constraint in terms of the total moles of monomer fed to the reactor (Nm,T). Case 1a (without CTA): Maximize monomer conversion by manipulating monomer flow rate and temperature as functions of time: max J = [xmon(Nm , t )]; ∀ Fm_in ∈ [0.0, 0.001] g/s; Nm,T ∈ [1.05, 1.55] mol T ∈ [326, 356]K; t ∈ [0, t f ]; xmon ∈ [0, 1] (33)

Case 1b (with CTA): Maximize monomer conversion (eq 33) using a constant CTA flow rate, FCTA of 0.000135 g/ s. The CTA feed rate provides for an overall amount of 1 mol % typically used in practice. Case 2a (without CTA): Minimize polymer molecular weight by manipulating monomer flow rate and temperature as functions of time:

Figure 8. Effect of CTA on MWD for semibatch process at 70 °C. Legend: 0 mol % CTA (Model, dashed-dotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●).

Figure 8 shows that the presence of CTA reduces Mn and causes a shift in MWD to the left. Thus, lower molar mass and polydispersity is observed for styrene polymerization with CTA compared to that without CTA. Figure 9 shows good agreement between model predictions and experimental data with respect to average diameter and polydispersity index. The particle characteristics are not significantly affected by batch or semibatch styrene polymerization with and without CTA.

min J = [M n(M , t )]; ∀ Fm_in ∈ [0.0, 0.001] g/s; Nm,T ∈ [1.05, 1.55] mol T ∈ [326, 356]K ; t ∈ [0, tf ]; M n ∈ [104 , 3 × 104] g/mol (34)

Case 2b (with CTA): Minimize polymer molecular weight (eq 34) using a constant CTA flow rate, FCTA, of 0.00135 g/s. In the expressions above, tf is the total processing time, T is the reaction temperature, and Fm_in is the monomer feed rate. An initial time of 1500 s is specified for the first stage set for seeding. The overall time horizon is bound between 5000 and 20 000 s. The actual feed rates begin after 1500 s, and the dynamic model includes a 1500 s time delay for all feed rates. The mathematical solver for optimization is based on a CVP approach which is based on the consideration that the timevarying control variables are piecewise constant or linear functions of time over a specified number of control intervals. For computation, the differential algebraic equation solver (DASOLV) and the successive reduced quadratic programming (SRQPD) programming algorithms were implemented. The DASOLV code solves the underlying differential equations and computes sensitivities, while the SRQPD solver employs a

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OPTIMAL OPERATING STRATEGY On the basis of the dynamic model, two main optimal control objectives were formulated with and without CTA. The control objectives were to produce desired molecular weight and conversion within a specified operating time. The key variables that influence the process are reaction temperature and monomer flow rate, while the CTA concentration is maintained at a low level. The validated mathematical model was used to calculate the optimal process trajectories. Two optimization cases were considered: (1) maximize monomer conversion and (2) minimize polymer molecular weight within a set range. Both cases were designed for semibatch operation (a) in the absence of CTA and (b) in the presence of CTA. The optimization for semibatch operation 7532



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Figure 9. Effect of CTA for semibatch process at 70 °C on (A) particle diameter and (B) PSPI for styrene. Legend: 0 mol % CTA (Model, dasheddotted line; Expt, ■); 1 mol % CTA (Model, solid line; Expt, ▲); 2 mol % CTA (Model, dashed line; Expt, ●).

Figure 10. Optimal profiles for maximizing conversion (case 1a) and minimizing Mn (case 2a) without CTA: (a) Monomer conversion; (b) molecular weight (solid lines) and MWPI (dashed lines); (c) temperature; (d) monomer flow rate.

nonlinear programming method to determine the optimum values.27 The results for case 1 (to maximize monomer conversion) and for case 2 (to minimize molecular weight) are shown in Figures 10 and 11. Cases (a) and (b) investigated relate to the absence or presence of chain transfer agent in the reactor. In the absence of CTA, the corresponding monomer feed rate profiles to ensure starved fed condition for 1a and 2a are given

in Figure 10D. The dynamic optimization suggests that relatively high monomer feed rates are required to increase the amount of monomer in the particles. As a result, reaction rate increases and monomer conversion attains a higher value. As the temperature increases, the coefficients of transfer and termination processes increase, leading to a decrease in the degree of polymerization and a broadening of MWD with a low average molecular weight. Figure 10C shows that the operating 7533



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Figure 11. Optimal profiles for maximizing conversion (case 1b) and minimizing Mn (case 2b) with CTA: (a) Monomer conversion; (b) molecular weight (solid line) and MWPI (dashed line); (c) temperature; (d) monomer flow rate.

for cases 1b and 2b, which agree approximately with the experimental data of 15 to 20 kDa for average molar mass in the presence of CTA. With the reaction temperature at 355 K to ensure low molar mass, the monomer feed rate is increased in order to obtain high fractional conversion value at termination.

temperature for 2a is higher in order to obtain an increase in transfer rate coefficients relative to polymerization rates at around 15 000 s in comparison with case 1a. The main objective for case 2a was to minimize molecular weight with a conversion constraint (≥80%). After 15 000 s, the reactor temperature is increased from 328 to about 342 K, while the monomer feed rate is maintained relatively constant. Thereby, the molecular weight is reduced while the fractional conversion reached a steady state. On applying the suggested conditions, conversion profiles obtained were similar to those indicated by simulation, and the measured final product molar masses were in the 110 to 150 kDa. On testing cases 1 and 2 in the presence of CTA, the corresponding results are shown in Figure 11. For maximizing conversion (1b), the optimization profile suggests the use of low monomer feed rates to ensure starved feed conditions in the absence of monomer droplets as shown in Figure 11D. Figure 11A shows the monomer conversion obtained for case 1b and 2b with reasonable agreement with experimental data. For case 2b, due to high monomer feed rate, the conversion drops to a low value of about 70% and then increases again until it reaches about 95% at termination of reaction. The drop in conversion is due to the sudden increase in monomer flow rate. However, the decrease in monomer conversion is shortlived as the concentration inside the particles begins to increase with monomer diffusion from the aqueous phase. As a result, the reaction rate increases and monomer conversion increases. Figure 11B shows the corresponding molecular weight obtained

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CONCLUSIONS A mathematical model was developed to understand the effect of CTA on emulsion polymerization for batch and semibatch operation. The model predictions show reasonable agreement with experimental data. The effect of CTA (n-dodecyl mercaptan) on conversion, MWD, PSD, and PDI for both batch and semibatch were investigated. There is no significant difference for overall monomer conversion by increasing the concentration of CTA. In the semibatch process, 1 mol % CTA was effective in reducing the polymer Mn by a factor of 9 with a higher MWPI compared to operation without CTA. However, for a batch process, 1 mol % CTA reduced the Mn by a factor of 7 with lower MWPI compared to batch operation without CTA. Thus, semibatch operation is an effective way to control molecular weight in comparison with batch operation. Due to longer reaction time and longer duration of agitation, starved monomer feed to the reactor results in decrease in mass transfer resistance and possibly increase in both the interfacial area and mass transfer coefficient. CTA does not significantly affect particle size and PDI for both batch and semibatch processes. We found that the model is capable of adequately predicting important polymer attributes, such as, PSD, MWD, 7534



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CM p CRad p Ctr CM p_sat

and conversion for different operating modes (batch and semibatch processes). The optimal strategies for emulsion polymerization of styrene with and without CTA were determined in a semibatch reactor by adjusting monomer flow rate and temperature of the reactor. The results identified the conditions required to obtain maximum conversion and minimum molecular weight under process constraints.

CCTA w

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CCTA w_sat

APPENDIX Model parameters for emulsion polymerization of styrene with CTA are shown in Table 3.

CM w CM w_sat dCTA dm dp Drd

Table 3

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parameter

value

ref

as Ctr CMC CM p,sat CM w,sat ρp ρm Dw Jcrit ktr kt,aq = kt,o kd KCTA d,w KCTA w,p KX,wtAd k1p,aq k2p,aq k3p,aq nagg z σ alpha

42 × 10−18 (dm2) 15.6 (−) 0.003 (mol/L) 5.5 (mol/L) e(−1.514−1259/T) (mol/L) 1050.1 − 0.621T (g/L) 923.6 − 0.887T (g/L) 1.55 × 10−7 (dm2/s) 5 (−) 7.5 × 10−5e(25289/RT) (L/(mol·s)) 1.703 × 109e(−9464/RT) (L/(mol·s)) 8 × 1015e(−13500/RT) (L/s) 4.9 × 107 3.14 × 10−8 5 × 104 10kp (L/(mol·s)) 6kp (L/(mol·s)) 2kp (L/(mol·s)) 60 3 6.02 × 10−9 7.4 × 10−9 (dm)

8 12 8 8 8 8 18 8 8, 24 25 11 8, 18 11 11 6 18 18 18 8, 18 8, 24 18 18

Dw DwX Dmon ΔH [E•] f FI Fm FCTA G i I2 I• [I] [I•] [IM•i ] jcrit

AUTHOR INFORMATION

K KM w,p KM d,p

Corresponding Author

*E-mail: [email protected] (V.G.G.). Notes

The authors declare no competing financial interest.

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KM d,w KCTA w,p KCTA d,p KCTA d,w kd

ACKNOWLEDGMENTS We thank our colleagues, Mr. R Techasuwana and Dr. Altarawneh, for assistance with experiments and gratefully acknowledge research support from the Australian Research Council, Canberra.

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kdiff

NOMENCLATURE as Minimum area occupied by a single surfactant molecule on a particle surface, dm2 α, alpha Root mean square end-to-end distance per square root of number of monomer units in a polymer chain, dm CTA0 Initial CTA agent concentration, mol/L cmc Critical micellar concentration, mol/L Cmicelle Micellar concentration, mol/L CCTA Initial CTA concentration in latex particles, mol/L p CCTA Saturated initial CTA concentration in latex p_sat particles, mol/L

kdE kie kEe kie,micelle kp kp,ij kip,aq 7535

Monomer concentration in latex particles, mol/L Concentration of all radicals inside particle, mol/L Chain transfer coefficient of CTA Saturated monomer concentration in latex particles, mol/L Initial CTA concentration in aqueous phase, mol/L Saturated initial CTA concentration in aqueous phase, mol/L Monomer concentration in aqueous phase, mol/L Saturated monomer concentration in aqueous phase, mol/L Density of CTA, g/L Density of monomer, g/L Density of polymer, g/L Diffusion coefficient arising from reaction−diffusion, dm2/s Diffusion coefficient for monomer radical in water phase, dm2/s Diffusion coefficient for CTA radical in water phase, dm2/s Diffusion coefficient of monomer in particle phase, dm2/s Heat of reaction, J/mol Aqueous phase concentration of desorbed radicals, mol/L Initiator efficiency Feed rate of initiator, g/s Feed rate of monomer, g/s Feed rate of chain transfer agent, g/s The number of radius increments Number average degree of polymerization Undecomposed initiator molecule Decomposed initiator fragment Initiator concentration, mol/L Initiator fragment concentration mol/L The oligomeric initiator-derived radical concentration with degree of polymerization i, mol/L Critical degree of polymerization for homogeneous nucleation Rate of propagation growth per particle, L/s Water−particle partitioning coefficient of monomer Droplet−particle partitioning coefficient of monomer Droplet−water partitioning coefficient of monomer Water−particle partitioning coefficient of CTA Droplet−particle partitioning coefficient of CTA Droplet−water partitioning coefficient of CTA First-order rate coefficient for the dissociation of initiator, L/s Diffusion controlled rate coefficient of monomeric radicals, L/s Rate coefficient for desorption of monomeric and CTA radicals from particles, L/s Entry rate coefficient for oligomeric radical, L/(mol·s) Re-entry rate coefficient of desorbed radical, L/(mol·s) Rate coefficient for entry of an oligomeric radical into a micelle, L/(mol·s) Propagation rate constant, L/(mol·s) Propagation rate coefficient of polymeric radical i with monomer j, L/(mol·s) Aqueous phase propagation rate coefficient for oligomeric radicals of degree “i”, L/(mol·s) dx.doi.org/10.1021/ie4032956 | Ind. Eng. Chem. Res. 2014, 53, 7526−7537


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kt,aq

Aqueous phase termination rate coefficient, L/(mol·s) Termination rate coefficient between oligomeric kt,aqij radicals of degree “i” and “j” in aqueous phase, L/(mol·s) ktr,CTA Rate coefficient for chain transfer to CTA, L/(mol·s) ktr = ktr,M Rate coefficient for chain transfer to monomer, L/(mol·s) Modifier mass transfer coefficient, dm/s kX,wt M Molecular weight of polymer chain, g/mol Average molecular weight, g/mol Mavg Chain transfer agent molecular weight, g/mol MCTA w MM Monomer molecular weight, g/mol w M̅ n,ins Instantaneous molecular weight of polymer, g/mol Mn Number average molecular weight, g/mol Mw Weight average molecular weight, g/mol [M]p Concentration of monomer in particle, mol/L NA Avogadro’s number NM Number of moles of monomer, mol NCTA Number of moles of CTA, mol Nm,TNi,Feed Total amount of monomer fed into the reactor, mol Np Total number of polymer particles n̅ Average number of radicals per particle, mol/(L·dm) nagg Micelle aggregation number Molar concentration density of particles containing n0 no radicals, mol/(L·dm) nr1 Molar concentration density of particles containing one monomeric-radicals, mol/(L·dm) nP1 Molar concentration density of particles containing one polymeric-radicals, mol/(L·dm) P(M) Instantaneous molecular weight distribution P̅(M) Cumulative molecular weight distribution Pm Molecular weight of repeating unit, g/mol Qi ith moment of the number chain length distribution, mol/L RM Rate of polymerization in emulsion polymerization, p mol/(L·s) RCTA Rate of consumption of initial CTA, mol/(L·s) p rs Swollen radius of latex particle, dm Sads Amount of surfactant per unit volume adsorbed onto the polymer surface, mol/L Stot Total concentration of added surfactant, mol/L T Temperature, K [T•] Total radical concentration in aqueous phase, mol/L Vwo Volume of water in reactor, L Vd Volume of the monomer in system, L Vp Volume of the polymer in system, L Vr Total reaction volume, L Vw Volume of water phase, L XCTA Fractional conversion of CTA XMon Fractional conversion of monomer Xi Instantaneous molar conversion monomer i δ(V − V0) Dirac delta function ρ First order pseudo-rate coefficient for all entry events, L/s ρs First order pseudo-entry-rate coefficient, L/s Density of monomer, g/L ρi z Critical degree of polymerization for entry Φ Polymer volume fraction δ Ratio of water-side resistance to overall mass transfer resistance for CTA radical

Article

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Optimal Operating Strategies for Emulsion Polymerization with Chain

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