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Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions
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Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions Chun-Ta Lin a, Chorng-Shyan Chern a,∗ a
Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan
a r t i c l e
i n f o
Article history: Received 19 January 2015 Revised 27 March 2015 Accepted 16 April 2015 Available online xxx Keywords: Miniemulsion Polymeric costabilizer Ostwald ripening Modified Kabal’nov equation Regular solution Intermolecular interactions
a b s t r a c t A thermodynamic approach dealing with a regular solution of monomer (styrene (ST) herein) and different polymeric costabilizers as the disperse phase of miniemulsion were used to develop a model that describes the Ostwald ripening behavior involved in such a colloidal system. The validity of this model was verified by the Ostwald ripening rate data obtained from ST miniemulsions stabilized by living polystyrene costabilizer (PSlc ) or polystyrene costabilizer (PSc ) upon aging at 25 ◦ C. PSlc is more effective in retarding the Ostwald ripening process than PSc , though PSlc and PSc have comparable number-average molecular weights. The model can be also used to study the mutual interaction between monomer and polymeric costabilizer. Satisfactory modeling results achieved for ST miniemulsions using polymethyl methacrylate as the costabilizer further verify the general validity of the present model. Finally, the values of heat of mixing and interaction parameter between ST and different polymeric costabilizers were also determined. © 2015 Published by Elsevier B.V. on behalf of Taiwan Institute of Chemical Engineers.
1. Introduction Emulsions undergo colloidal degradation upon aging primarily via two ways, that is, coalescence and Ostwald ripening. Coalescence among interactive emulsion droplets can be prohibited effectively by an adequate level of surfactant. By contrast, Ostwald ripening is a diffusional degradation process occurring in emulsion with a relatively broad droplet size distribution. It involves the growth of larger droplets with lower excess chemical potential at the expense of smaller ones with higher excess chemical potential via the molecular diffusion of oil molecules from smaller droplets to larger ones [1–3]. Ostwald ripening can be greatly retarded by the incorporation of a low molecular weight, water-insoluble species (e.g., long chain alkanes and alcohols, termed as costabilizers) into oil droplets [4–6], and the kinetically stable colloidal product termed the miniemulsion. Reimer and Schork [7,8] used polymer as costabilizer to prepare relatively stable miniemulsions. Recently, we illustrated the effect of polymeric costabilizer molecular weight on the Ostwald ripening behavior of monomer miniemulsions, and established an approach to determine the critical chain length of polymer costabilizer, consistent with those reported in the literature [9]. In our previous work [10], we developed a model based on the thermodynamics approach to quantitatively describe the Ostwald
∗
Corresponding author. Tel.: +886 27376649; fax: +886 27376644. E-mail address: [email protected] (C.-S. Chern).
ripening behavior in a wide range of volume fraction of costabilizer (ϕ c ) for the two-component disperse phase miniemulsions, in which the disperse phase was a regular solution of monomer and costabilizer (i.e., the enthalpy change of mixining (Hmix ) not equal to zero). A modified Kabal’nov equation was then developed to adequately predict the Ostwald ripening rate (RO ) data and the model is shown below.
1 ϕm = + RO RO,m
ϕc 1 + C ϕc
RO,c
(1)
where RO,i (i = monomer (m) or costabilizer (c)) is the Ostwald ripening rate corresponding to the single component species i, ϕ i the volume fraction of the component i, and C a parameter closely related to the intermolecular interactions in the disperse phase. The model is capable of predicting the Ostwald ripening rate data in a wide ϕ c range for styrene (ST) miniemulsions stabilized by a homolog of n-alkane costabilizers (Cn H2n+2 ) upon aging at 25 ◦ C. The objective of this work was to develop a model via the thermodynamics approach in combination with the Morton equation [11] to quantitatively describe the Ostwald ripening behavior in a wide ϕ c range for the two-component disperse phase miniemulsion stabilized by polymeric costabilizer. The validity of this model was then verified by experimental data for various polymeric costabilizers. Furthermore, thermodynamic parameters such as the Flory–Huggins interaction parameter (χ mp ) and Hmix between monomer and polymeric costabilizer were determined.
http://dx.doi.org/10.1016/j.jtice.2015.04.021 1876-1070/© 2015 Published by Elsevier B.V. on behalf of Taiwan Institute of Chemical Engineers.
Please cite this article as: C.-T. Lin, C.-S. Chern, Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions, Journal of the Taiwan Institute of Chemical Engineers (2015), http://dx.doi.org/10.1016/j.jtice.2015.04.021
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2. Model development 2.1. Partial molar free energy of monomer in the presence of polymer in a two-component disperse phase system Morton et al. [11] considered the equilibrium swelling of emulsion polymer droplets by solvents (e.g., ST) exhibiting a rather limited solubility in the continuous aqueous phase. They derived an expression for partial molar Gibbs free energy of monomer (Gm ) as follows:
Gm = Gmix + Ginterf
(2)
where Gmix represents the contribution from the Gibbs free energy of mixing of monomer and polymer, and Ginterf the contribution from the droplet-water interfacial energy. Furthermore, Gm was expressed in terms of the classical Flory–Huggins theory [11–13]:
1 ΔGmix = ln 1 − ϕp + ϕp 1 − + χmp ϕp2 RT n
(3)
where ϕ p is the volume fraction of polymer in latex droplets, n the number-average degree of polymerization, R the gas constant, T the temperature, and χ mp the Flory–Huggins interaction parameter. As to ΔGinterf , it was given in terms of the Gibbs–Thomson equation [14].
2σ Vm,m ΔGinterf α = = RT aRT a
pressure is effectively compensated by the osmotic pressure. Based on this scenario, Kabal’nov and coworkers [1] then established the equilibrium condition for Gm . Similarly, we derived the following expressions for the equilibrium condition for ΔGm .
1 ΔGm ΔGme α 2 = = ln 1 − ϕpe + 1 − ϕpe + χmp ϕpe + RT RT n ae 2 ϕpe 1 α 2 + 1− ≈ −ϕpe − ϕpe + χmp ϕpe + 2 n ae 1 1 α 2 − χmp ϕpe = − ϕpe − + = constant n 2 ae
(6)
where the subscript e represents a certain parameter at equilibrium. For example, ae is the equilibrium droplet radius. Note that, in the above derivation, the terms of third order and higher were neglected in expanding the function ln(1–ϕ pe ) in a Taylor series. The term α /ae on the right hand side of Eq. (6) represents the Laplace pressure effect [15], and the remaining terms the competitive osmotic pressure effect. In addition, similar to the Kabal’nov approach [1], Eq. (6) can be expressed equivalently as follows:
ϕ pe − ϕ pe +
1 + n
1 1 1 − χmp ϕ pe + ϕ pe = α − 2 a e a e
(4)
(7)
where σ is the droplet-water interfacial tension, Vm,m is the molar volume of monomer, a is the radius of monomer droplet, and α is defined as 2σ Vm,m /RT. Finally, substituting Eqs. (3) and (4) into Eq. (2) gives the so-called Morton equation:
where .ϕ pe ’ and ϕ pe ’’, and ae ’ and ae ’’ are the volume fractions of polymeric costabilizer and the radii of two arbitrary droplets with different sizes brought into equilibrium, respectively. Fig. 1 shows the influence of polymeric costabilizer molecular weight (= n×molecular weight of repeating unit) on Gm . To
1 ΔGm α = ln 1 − ϕp + ϕp 1 − + χmp ϕp2 + RT n a
(5)
ΔGm is also termed as the excess chemical potential that determines the internal energy change for a change in composition arising from the addition of a small amount of monomer into the regular solution. 2.2. Excess chemical potential of monomer in the two-component disperse phase system for the case of zero solubility of polymeric costabilizer in water Formation of a two-component disperse phase system (e.g., miniemulsion) comprising a large population of submicron droplets suspended in the continuous aqueous phase generates an extremely large total oil–water interfacial area. Therefore, interfacial phenomenon naturally comes into play in the stability of colloidal products upon aging. These droplets consist of the major component (monomer) and polymeric costabilizer that is completely insoluble in water (C,p = 0), which form a regular solution therein. This colloidal system is the focus of this work. Kabal’nov et al. [1] considered a two-component disperse phase system with an ideal solution (Hmix = 0) of monomer and costabilizer as the disperse phase to be very similar to a semipermeable membrane since costabilizer was essentially insoluble in water. At equilibrium, the excess chemical potential of solvent (a permeating component) is the same on both sides of the membrane, whereas that of solute (a nonpermeating component) exhibits different values when crossing the membrane. In a similar manner, for a two-component disperse phase system with a relatively narrow droplet size distribution initially, mass transfer of monomer from a smaller droplet to a larger one occurs in consequence of the difference in the capillary pressures. This will then result in a concentration gradient for polymeric costabilizer between the shrinking droplet and the expanding one, thereby leading to the suppression of the Ostwald ripening process. This is simply because insoluble polymeric costabilizer is not allowed to transport between two droplets of different sizes. Eventually, Ostwald ripening is terminated and, therefore, equilibrium is achieved when the capillary
Fig. 1. (a) Profiles of dimensionless excess chemical potential as a function of droplet radius calculated by Eq. (5) with n = 10, 100 and 500 and (b) a representative example of thermodynamic colloidal instability (Gm /RT > 0 and d(Gm /RT)/da < 0), stability (Gm /RT 0) and metastability (Gm /RT > 0 and d(Gm /RT)/da 0).
Please cite this article as: C.-T. Lin, C.-S. Chern, Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions, Journal of the Taiwan Institute of Chemical Engineers (2015), http://dx.doi.org/10.1016/j.jtice.2015.04.021
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construct Fig. 1a, first, the relationship xp = xpi (ai /a)3 (i.e., ϕ p = Kϕ pi (ai /a)3 , where K is a proportional constant between molar fraction and volume fraction) was substituted into Eq. (5) to result in Eq. (8).
G m RT
=−
a 3 1 a 3 2 α 1 i i − + Kϕpi − χmp Kϕpi n a 2 a a
(8)
3
The pioneering Kabal’nov approach was then adopted in this work to give the following expressions for the two-component disperse phase system, in which the disperse phase behaves just like a regular solution and polymeric costabilizer is used to retard Ostwald ripening. In brief, Jm and Jp can be expressed as follws:
Jm = 4π Dm a [Cm − Cs,m ]
(10)
Jp = 4π Dp a [Cp − Cs,p ]
(11)
With values of K = 8.6 (n =10), 85.7 (n = 100) and 428.5 (n = 500), respectively, ϕ pi = 10−2 , ai = 0.5 μm, χ mp = 0. 37 (for toluene/PS) [16] and α = 10−3 μm [17], the value of Gm /RT can be calculated for a given value of a. Based on this algorithm, the Gm /RT-vs.-a profile is thus established. The Gm /RT-vs.-a profile shows that the maximal Gm /RT becomes more prominent as n is increased. Furthermore, Gm /RT becomes positive regardless of the value of a when n 500. According to Ref. [18], the conditions Gm /RT > 0 and d(Gm /RT)/da < 0, Gm /RT 0, and Gm /RT > 0 and d(Gm /RT)/da 0 (representing an energy barrier against Ostwald ripening) are considered as those of thermodynamic colloidal instability, stability and metastability, respectively. In unstable regime, the colloidal system is unstable toward decay into two populations, one being large droplets enriched with monomer, and the other being small ones enriched with polymeric costabilizer. Ultimately, the diffusional degradation process ends up in equilibrium of a macroscopic phase of monomer with Gm 0. In metastable regime, the system is kinetically stable, but not thermodynamically stable. Gm over this regime is positive and from the thermodynamic point of view, the system is unstable (in a similar manner to the unstable regime discussed above). However, the diffusional degradation is very difficult to achieve simply because of the kinetic factor (i.e., the energy barrier identified by an arrow in Fig. 1 is too high). Still, if the polydispersity of droplet size distribution is large enough, metastability will become invalid. This is the reason why polymeric costabilizers with a relatively high molecular weight (n is very large) were considered ‘poor’ costbilizers [8,9].
where Jp is the volume flux for polymeric costabilizer from a droplet to the continuous aqueous phase, Dm (m2 s−1 ) and Dp (m2 s−1 ) are the diffusion coefficients of monomer and polymeric costabilizer, respectively, a (m) is the droplet radius, Cm (g g−1 ) and Cp (g g−1 ) are the solubilities of monomer and polymeric costabilizer in water, respectively, and Vm,p is the molar volume of polymeric costabilizer. Jp governs the Ostwald ripening process because C,m > > C,p . At every instant, droplets of some critical droplet radius (ac ) exist in a polydisperse system for which Jp = 0 (Eq. (14)).
2.3. Ostwald ripening rate in the two-component disperse phase system for the case of nonzero solubility of polymeric costabilizer in water
< 1, both exp(α p /ac ) Taking into account α p /ac (or α p /a) < 1 + α p /ac and exp(α p /a) 1 + α p /a can be approximated to be unity. Thus, Eq. (15) can be further simplified to become
In the scenario that polymeric costabilizer is characterized by a very low but nonzero value of C,p , diffusion of polymeric costabilizer from a droplet into the continuous aqueous phase controls RO . Kabal’nov et al. [1] developed the following equation for the case of ideal solution in the disperse phase and nonzero solubility of costabilizer in water (C,c ).
1 ϕm ϕc = + RO RO,m RO,c
α m Cs,m = C∞,m 1 − ϕp (a) exp , a Cs,p = C∞,p ϕp (a) exp
ac =
ln
αp Cp C∞,p ϕp (ac )
α p
a
(i) water solubility of monomer (C,m ) is much higher than C,c and, therefore, fast distribution of the major component, monomer, among droplets greatly retards the mass transfer of monomer, (ii) xc and a are quite close to their equilibrium values determined by the relationship Gm = Gme = (2σ Vm,m /ae )–RTxci (ai /ae )3 = constant, where xc is the molar fraction of costabilizer and xci and ai are the initial molar fraction of costabilizer and droplet radius, respectively, > α m /aavg,i , where α m is defined as 2σ Vm,m /RT and aavg,i is (iii) xc > the initial average droplet radius, (iv) changes in xc (xc ), determined by the relationship xce ’–xce ’’ = (2σ Vm,m /RT) (1/ae ’–1/ae ’’) = constant, are of the order of xc α m /aavg,i and xc /xc << 1 (i.e., small recondensation rate) and (v) Jm /Jc ϕ m /ϕ c , where Ji (i = m, c; m3 s−1 ) is the volume flux for component i from a droplet to the continuous aqueous phase.
(13)
(14)
Substituting Eq. (14) into Eq. (11) result in the following expression for Jp
Jp = 4π Dp aC∞,p
ϕp (ac ) exp
αp
ac
− ϕp (a) exp
α p
(15)
a
Jp ≈ 4π Dp aC∞,p [ϕp (ac ) − ϕp (a)]
(16)
According to Eq. (7), ϕ p (ac )–ϕ p (a) can be expressed as α (1/ac –1/a) [1/n+(1/2–χ mp ) (ϕ p (ac )+ϕ p (a))] and substituting this relationship into Eq. (16) gives
Jp = 4π Dp aC∞,p α
1 1 − ac a
(9)
It is noteworthy that derivation of Eq. (9) is based on the following assumptions:
(12)
2σ Vm,p RT
αp =
,
2σ Vm,m RT
αm =
1 n
+
1 2
− χmp
1
ϕp (ac ) + ϕp (a)
(17) Furthermore, the term ϕ p (ac )+ϕ p (a) can be approximated to > α m /aavg,i and ϕ p /ϕ p < < 1 (i.e., small reconden2ϕ p (a) because ϕ p > sation rate) for polymeric costabilizer with an extremely low C,p . Thus, Eq. (17) is readily reduced to
Jp = 4π Dp aC∞,p α
1 1 − ac a
1 n
1 + 1 − 2χmp ϕp (a)
(18)
Assuming that Jm /Jp ϕ m /ϕ p, then
J = Jm + Jp =
Jp
ϕp (a)
= 4π Dp aC∞,p α
=
d
1 1 − ac a
4 3
π a3
dt
ϕp (a)
1 n
1
+ 1 − 2χmp
(19)
ϕp (a)
Finally, Kabal’nov and coworkers [17,19] illustrated that the Lifshitz–Slozov theory [20] was applicable to the case considered herein. In brief, the Lifshitz–Slozov theory showed that, after an initial
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nonstationary period, the Ostwald ripening process was characterized by (i) the time independent distribution function for the ratio of a droplet radius to the current mean droplet radius and (ii) the linear growth of the cube of the mean droplet radius with time (referred to RO ). In this manner, RO can be written as
RO =
9RT ϕp
8C∞,p Dp σ Vm,m
1 + 1 − 2χmp ϕp n
(20)
Moreover, the following two limiting cases can be established. Limiting case 1: ϕ p → 1 and (1–2χ mp ) → 0 ( disperse phase → ideal solution)
8C∞,p Dp σ Vm,p n 9RT
RO ≈ RO,p =
(21)
Limiting case 2: ϕ p → 0
RO ≈ RO,m =
8C∞,m Dm σ Vm,m 9RT
(22)
For limiting case 1 (i.e., polymer particles), χ mp approaches 1/2, which defines the Flory θ -temperature, and at which point “polymer chains mix without recognizing each other’s presence” [16]. On the other hand, limiting case 2 corresponds to pure monomer droplets and their stability is dependent on the average droplet size and size distribution. If the difference in the molar volumes of pure components and their interfacial tensions at the oil–water interface is negligible as > compared to the difference between their water solubilities (C,m > C,p ), Eqs. (21) and (22) can be joined into the following modified Kabal’nov equation.
1 ϕm = + RO RO,m =
1 RO,m
ϕp
1 n
+ 1 − 2χmp ϕp RO,p
+
1 1 − nRO,p RO,m
ϕp +
1 − 2χmp RO,p
ϕp 2
(23)
The last term involving ϕ p 2 on the right hand side of Eq. (23) can be neglected provided that ϕ p is small enough. Furthermore, Eq. (23) can be readily reduced to Kabal’nov equation when ϕ p is small enough and n is equal to one (i.e., a low molecular weight species).
reactor equipped with a mechanical agitator and a thermometer. The mixture was then stirred over a period of 1 h. The reaction mixture turned to bright red immediately after sodium trithiocarbonate was produced. Subsequently, 100.8 g of benzyl chloride was added to the reactor over a period of 15 min. The mixture was stirred at 50 °C for 3 h and then at 70 °C for additional 30 min. To complete the reaction, 1.5 g of tributylmethylammonium chloride was added to the reaction mixture without heating overnight. A yellow semi-solid product containing DBTTC (bottom layer) was separated from the aqueous phase (upper layer) using a funnel separator. The crude DBTTC product was washed repeatedly by excessive ethanol. The crystalline product was then filtered and dried at 50 °C. The product was characterized by 1 H NMR and 13 C NMR techniques (Bruker Avance, 500 MHz). Living polystyrene costabilizer (PSlc ) was prepared by an isothermal bulk RAFT polymerization process. First, 100.0 g of ST and 2.70 g of DBTTC (RAFT reagent) were charged to a 500 mL reactor equipped with a mechanical agitator, a reflux condenser and a thermometer immersed in a thermostatic oil bath. The reaction mixture was then purged by nitrogen for 10 min to remove dissolved oxygen, followed by raising the reactor temperature to 100 °C. Thermal polymerization of ST in the presence of DBTTC then proceeded for 16 h. Polystyrene costabilizer (PSc ) was prepared by an isothermal solution polymerization process. First, 79.50 g of ST, 0.48 g of dodecyl mercaptan, 0.08 g of AIBN and 19.94 g of toluene were charged to a 500 mL reactor equipped with a mechanical agitator, a reflux condenser and a thermometer immersed in a thermostatic oil bath. The reaction mixture was then purged by nitrogen for 10 min to remove dissolved oxygen, followed by raising the reactor temperature to 70 °C. Thermal polymerization of ST in the presence of dodecyl mercaptan then proceeded for 5 h. The resultant PSlc (or PSc ) was precipitated by excessive methanol and allowed to stand overnight. This was followed by filtration and then thorough rinse of PSlc (or PSc ) by excessive methanol and water. PSlc (or PSc ) sample thus collected was dried in a vacuum oven at 60 °C over a period of 24 h. The number-average molecular weight (Mn ) and polydispersity index (PDI = Mw /Mn , where Mw is the weight-average molecular weight) data for PSlc and PSc were determined by GPC (Waters, 2410) in combination with a calibration curve established by a series of PS standards. 3.3. Preparation and characterization of miniemulsions
3. Experimental 3.1. Materials The chemicals used include styrene (Taiwan Styrene), sodium dodecyl sulfate (SDS, J. T. Baker, 99 percent), sodium bicarbonate (Riedel de Haen), 2,2 -azobisisobutyronitrile (AIBN, Sigma-Aldrich), benzyl chloride (Acros), carbon disulfide (Panreac), sodium sulfide hydrate (Acros), tributylmethylammonium chloride solution (75 percent, Acros), dodecyl mercaptan (Fluka, > 97 percent), toluene (99.8 percent, Aldrich), methanol (Union Chemical Ind.), ethanol (Union Chemical Ind.), a series of polystyrene (PS) standards for gel permeation chromatography (GPC) calibration (Shodex), tetrahydrofuran (THF, Acros), nitrogen (Ching-Feng-Harng) and deionized water (Barnsted, Nanopure Ultrapure Water System, specific conductance < 0.057 μS cm−1 ). ST was purified at 40 °C under reduced pressure and stored at 4 °C before use. Other chemicals were reagent grade and used as received. 3.2. Preparation and characterization of living polystyrene costabilizer Dibenzyltrithiocarbonate (DBTTC) was synthesized according to the literature [21]. First, 58.5 g of sodium sulfide hydrate, 3.0 g of 75 percent aqueous solution of tributylmethylammonium chloride, 35.4 g of carbon disulfide and 150 mL water were charged to a 500 mL
Miniemulsion was prepared by dissolving SDS and sodium bicarbonate in water and polymeric costabilizer in ST, respectively. This was followed by mixing the oily and aqueous solutions with a mechanical agitator at 400 rpm for 10 min. The resultant emulsion immersed in an ice–water bath was then homogenized with an ultrasonic homogenizer (Misonic sonicator 3000, 30 W) for 30 cycles of 100 s in length with 40 s off-time, and the output power set at 80 percent. For Ostwald ripening experiments, a typical miniemulsion recipe comprises the continuous aqueous phase (40 g water and 3.37 × 10−3 M sodium bicarbonate and 6.24 × 10−3 M SDS based on total water) and the monomer charge (a prescribed concentration of polymeric costabilizer dissolved in ST with a total weight of 10 g). The concentrations of sodium bicarbonate and SDS were kept constant throughout this study. The average monomer droplet size data were obtained from the dynamic light scattering technique (DLS; Otsuka Electronics, Photal LPA-3000/3100). The cumulant method was chosen for measuring the z-average hydrodynamic diameter of colloidal droplets. The sample was diluted with water to adjust the number of photons counted per second (cps) to the range 8000–12000 to eliminate the multiple light scattering effects. The dilution water was saturated with SDS (critical micelle concentration = 8.2 × 10−3 M [22]) and ST (water solubility = 1.92 × 10−3 M [23]). In this manner, diffusion of SDS and ST molecules from miniemulsion droplets into the continuous aqueous phase was prohibited.
Please cite this article as: C.-T. Lin, C.-S. Chern, Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions, Journal of the Taiwan Institute of Chemical Engineers (2015), http://dx.doi.org/10.1016/j.jtice.2015.04.021
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Fig. 2.
1
5
H NMR spectrum of DBTTC.
4. Results and discussion 4.1. Characterization of living polystyrene costabilizer and polystyrene costabilizer Fig. 2 shows the 1 H NMR spectrum of DBTTC, in which the ratio of the integral area of the characteristic peak at chemical shift (δ ) = 4.684 ppm (a) to that of the characteristic peak at δ = 7.3–7.4 ppm (b) is 1:2.45, which is reasonably consistent with the theoretical ratio (1:2.50). The characteristic peaks of DBTTC obtained from 13 C NMR spectrum further confirm the molecular structure of DBTTC (Fig. 3). Mn and PDI of PSlc are 1.11 × 104 g mol−1 and 1.01, respectively. The very narrow molecular weight distribution (PDI = 1.01) reflects the major characteristics of bulk RAFT polymerization used in this work. By contrast, Mn and PDI of PSc are 9.78 × 103 g mol−1 and 3.05, respectively. 4.2. Ostwald ripening behavior of ST miniemulsions The RO of ST miniemulsion with a particular φ p upon aging at 25 ◦ C was determined by the least-squares best-fitted slope of the plot of a3 (a is the average radius of monomer droplets) as a function
of time (t) according to the extended Lifshitz–Slyozov–Wagner theory [1] (data not shown here). For those who are interested in the detail of this issue, refer to Refs. [24,25]. The polymeric costabilizer density necessary for calculating φ p is 1.06 g cm−3 for PSlc and PSc [26]. The data of 1/RO vs. φ p for ST miniemulsions stabilized by PSlc (or PSc ) with φ p in the range 0.02–0.16 are shown in Fig. 4. It is noteworthy that polymeric costabilizers are generally considered less effective in retarding Ostwald ripening as compared to conventional low molecular weight costabilizers. Thus, for ST miniemulsions investigated in this study, a polymeric costabilizer volume fraction range of 0.02–0.16 was used and such polymeric costabilizer levels are much higher than those of low molecular weight costabilizers. Considering such medium to high polymeric costabilizer concentrations (up to 16 percent of total droplet volume), applicability of the Flory–Huggins theory to ST miniemulsions containing polymeric costabilizers may thus be confirmed provided that strong density fluctuations do not occur. As expected, RO decreases (or 1/RO increases) with increasing φ p regardless of the type of polymeric costabilizers used. The 1/RO vs. ϕ p data can be adequately described by Eq. (23), as evidenced by the relatively high values of coefficient of determination (R2 ). The quadratic equation obtained from the lest-squares best-fitted curve passing through the point (0, 1/RO,m ) was used to obtain RO,p according
Please cite this article as: C.-T. Lin, C.-S. Chern, Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions, Journal of the Taiwan Institute of Chemical Engineers (2015), http://dx.doi.org/10.1016/j.jtice.2015.04.021
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Fig. 3.
13
C NMR spectrum of DBTTC.
Table 1 Key Ostwald ripening parameters and some physicochemical properties for ST miniemulsions stabilized by polymeric costabilizer upon aging at 25 ◦ C. Costabilizer
Mn ×10−3 (g mol−1 )
PDI.
n
RO,p ×1023 (cm3 s−1 )
χ mp
Hmix a (J)
PSc PSlc PMMAc
9.78 11.14 5.91
3.05 1.01 1.71
93.9 106.9 59
15.2 8.43 3.13
0.30 0.34 0.39
0.13–0.87 0.14–0.99 0.17–1.13
a
Fig. 4. 1/RO vs. ϕ p data for ST miniemulsions stabilized by PSc upon aging at 25 ◦ C. The continuous curve represents the least-squares best-fitted curve of the 1/RO vs. ϕ p data (1/RO = 2.67×1021 ϕ p 2 +7.00×1019 ϕ p +2.00×1015 with the coefficient of determination (R2 ) = 0.9910) based on the modified Kabal’nov equation (Eq. (23)).
to Eq. (23). The value of RO,m (5×10−16 cm3 s−1 ) was taken from the literature [27]. The values of RO,p and other key parameters for ST miniemulsions stabilized by PSlc (or PSc ) obtained from this work are listed in Table 1. For ST miniemulsions, PSlc is more effective in retarding the Ostwald ripening process than PSc (see Fig. 4 and RO,p data in Table 1), though PSlc and PSc have comparable values of Mn (around 1 × 104 g mol−1 ). This is most likely due to the very narrow molecular weight distribution of PSlc (PDI = 1.01) associated with PSlc in
Hmix = kTNm ϕ p χ mp [16], determined in the φ p range 0.02–0.16.
comparison with the PSc counterpart (PDI = 3.05). In other words, a significant fraction of PSc with a relatively broad molecular weight distribution exhibits higher molecular weight than its Mn and, therefore, this part of PSc does not effectively stabilize ST miniemulsion against Ostwald ripening. It is noteworthy that the faster the Ostwald ripening rate, the higher the probability for particle nucleation to take place in the continuous aqueous phase during subsequent miniemulsion polymerization initiated by a water-soluble initiator such as sodium persulfate [9]. This is because Ostwald ripening occurring primarily in the first half of polymerization (e.g., in the interval of 0–80 min for PSc with Mw = 2×105 g mol−1 and φ p = 0.08) results in a larger average monomer droplet size with a smaller total droplet surface area with the progress of polymerization. As a result, surfactant species originally adsorbed on droplet surfaces tend to desorb back to the continuous aqueous phase and promote the formation of particle nuclei therein, thereby leading to deviation from the ideal one-to-one copy from monomer droplets to polymer particles. For those who are interested in this subject, refer to Ref. [9].
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7
In addition, some Ostwald ripening parameters are summarized in Table 1. PMMAc has a larger value (0.39) of χ mp as compared to the PSc counterpart. This implies that the compatibility between PMMAc (even with a lower Mn (5.91×103 g mol−1 )) and ST is inferior to that between PSc and ST. Again, the χ mp value is smaller than that (0.45) of the solution of PMMA in toluene reported in the literature [29]. These results further verify the general validity of the present model that is capable of predicting the Ostwald ripening behavior involved in ST miniemulsions stabilized by polymeric costabilizers Fig. 6. 5. Conclusion
Fig. 5. 1/RO vs. ϕ p data for ST miniemulsions stabilized by PSlc upon aging at 25 ◦ C. The continuous curve represents the least-squares best-fitted curve of the 1/RO vs. ϕ p data (1/RO = 3.85×1021 ϕ p 2 +1.11×1020 ϕ p +2.00×1015 with R2 = 0.9930) based on the modified Kabal’nov equation (Eq. (23)).
With the knowledge of RO,m, RO,p and n, we can calculate χ mp based on Eq. (23). The χ mp data thus obtained are 0.30 and 0.34 for PSc and PSlc , respectively. All the data of χ mp (= Hmix /kTNm ϕ p , where Nm is the number of monomer in the droplet [16]) are positive, implying that mixing of either PS costabilizer prepared in this work with ST is endothermic in nature and, therefore, the mixing process is thermodynamically unfavorable [28]. For the solution of PS in toluene at 25 ◦ C, the value of χ mp was reported to be 0.37 [16], which is quite close to our experiment data. This result provides supporting evidence for the validity of the Ostwald ripening model developed in this work. Interestingly enough, the χ mp value of PSc is smaller than that of PSlc . This is most likely due to the presence of DBTTC unit in the molecular structure of PSlc . The larger the χ mp (i.e., the larger the difference between the solubility parameter of monomer (δ m ) and that of polymeric costabilizer (δ p )), the less compatibility between polymeric costabilizer and monomer, as predicted by Eq. (24) [16].
χmp = βm +
Vm,m
δm − δp RT
2 (24)
where β m : is the lattice constant of entropic origin. Moreover, the values of Hmix determined in the φ p range 0.02–0.16 can be calculated from the relationship χ mp = Hmix /kTNm ϕ p . The Hmix data thus attained were also included in Table 1. Finally, the RO data for ST miniemulsions using polymethyl methacrylate (PMMAc ) as the costabilizer (in the φ p range 0.02–0.16) taken from our previous work [9] were used to evaluate the general validity of Eq. (23). The modeling results are shown in Fig. 5.
Fig. 6. 1/RO vs. ϕ p data for ST miniemulsions stabilized by PMMAc upon aging at 25 ◦ C. The continuous curve represents the least-squares best-fitted curve of the 1/RO vs. ϕ p data (1/RO = 7.32×1021 ϕ p 2 +5.42×1020 ϕ p +2.00×1015 with R2 = 0.9960) based on the modified Kabal’nov equation (Eq. (23)).
A thermodynamic approach dealing with a regular solution of monomer (ST used in this work) and different polymeric costabilizers as the disperse phase of miniemulsion was used to develop the modified Kabal’nov equation: 1/RO = ϕ m /RO,m +ϕ p [1/n+(1–2χ mp )ϕ p ]/RO,p . The validity of this model was verified by the RO data obtained from ST miniemulsions stabilized by PSlc (or PSc ) upon aging at 25 ◦ C. It was shown that RO decreases (or 1/RO increases) with increasing φ p regardless of the type of polymeric costabilizers used. Interestingly enough, PSlc is more effective in retarding the Ostwald ripening process than PSc , though PSlc and PSc have comparable values of Mn . This is primarily attributed to the very narrow molecular weight distribution of PSlc arising from the RAFT polymerization process. The proposed Ostwald ripening model can be used to study the mutual interaction between monomer and polymeric costabilizer. The positive values of χ mp are 0.30 and 0.34 for PSc and PSlc , respectively, implying that mixing of either PS costabilizer with ST is endothermic in nature and, therefore, the mixing process is thermodynamically unfavorable. Furthermore, the larger value of χ mp for the pair of ST and PSlc indicates the poorer compatibility between PSlc and ST as compared to the pair of ST and PSc . Finally, satisfactory modeling results achieved for the Ostwald ripening behavior involved in ST miniemulsions using PMMAc as the costabilizer further verify the general validity of the present model. Furthermore, PMMAc (even with a lower Mn ) exhibits a larger value (0.39) of χ mp (i.e., the worse compatibility with ST) as compared to the PSc counterpart. References [1] Kabal’nov AS, Shikubin ED. Ostwald ripening theory: applications to fluorocarbon emulsion stability. Adv Colloid Interface Sci 1992;38:69–97. [2] Taylor P. Ostwald ripening in emulsions. Colloid Surf A-Physicochem Eng Asp 1995;99:175–85. [3] Taylor P. Ostwald ripening in emulsions. Adv Colloid Interface Sci 1998;75:107– 63. [4] Higuchi WJ, Misra J. Physical degradation of emulsions via the molecular diffusion route and the possible prevention thereof. J Pharm Sci 1962;51:459–66. [5] Ugelstad J, Mórk PC, Kaggerud KH, Ellingsen T, Berge A. Swelling of oligomerpolymer droplets. New methods of preparation. Adv Colloid Interface Sci 1980;13:101–40. [6] Barnette DT, Schork FJ. Continuous miniemulsion polymerization. Chem Eng Prog 1987;83:25–30. [7] Reimers J, Schork FJ. Robust nucleation in polymer-stabilized miniemulsion polymerization. J Appl Polym Sci 1996;59:1833–41. [8] Reimers J, Schork FJ. Predominant droplet nucleation in emulsion polymerization. J Appl Polym Sci 1996;60:251–62. [9] Lin CT, Wu JM, Chern CS. Effects of the molecular weight of polymeric costabilizers on the Ostwald ripening behavior and the polymerization kinetics of styrene miniemulsions. Colloid Surf A-Physicochem Eng Asp 2013;434:178–84. [10] Lin CT, Chern CS. Modeling Ostwald ripening rate of styrene miniemulsions stabilized by a homolog of n-alkane costabilizers. J Taiwan Inst Chem Eng 2014 Available online 26 December. [11] Morton M, Kaizerman S, Altier MW. Swelling of latex particles. J Colloid Sci 1954;9:300–12. [12] Flory PJ. Principles of Polymer Science. Ithaca, New York: Cornell University Press; 1953. [13] Noel LFJ, Maxwell IA, German AL. Partial swelling of latex particles by two monomers. Macromolecules 1993;26:2911–18. [14] Johnson CA. Generalization of the Gibbs-Thomson equation. Surf Sci 1965;3:429– 44. [15] Skinner LM, Sambles JR. The Kelvin equation—a review. J Aerosol Sci 1972;3:199– 210. [16] Sperling LH. Introduction to Physical Polymer Science. 4th ed. United States of Americ a: John Wiley & Sons, Inc; 2006.
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[17] Kabal’nov AS, Pertzov AV, Shikubin ED. Ostwald ripening in two-component disperse phase systems: application to emulsion stability. Colloid Surf 1987;24:19– 32. [18] Kabalnov A. Ostwald ripening and related phenomena. J Disper Sci Technol 2001;22:1–12. [19] Pertzov AV, Kabal’nov AS, Shchukin ED. Recondensation of particles of a twocomponent disperse phase in the case of a large difference in the solubility of the components in the dispersion medium. Colloid J USSR 1984;46:1015–18. [20] Lifshitz IM, Slozov VV. The kinetics of precipitation from supersaturated solid solution. J Phys Chem Solids 1961;19:35–50. [21] Senyek ML, Kulig JJ, Paker DK. The Goodyer Tire and Rubber Co. US Patent 6, 369, 158; 2002. [22] Rehfeld SJ. Adsorption of sodium dodecyl sulfate at various hydrocarbon–water interfaces. J Phys Chem A 1967;71:738–45.
[23] Sutterlin N. In: Fitch RM, editor. Polymer Colloids II. New York: Plenum Press; 1980. p. 583. [24] Chern CS, Chen TJ. Effect of Ostwald ripening on styrene miniemulsion stabilized by reactive cosurfactants. Colloid Surf A-Physicochem Eng Asp 1998;138:65–74. [25] Meliana Y, Cala NA, Lin CT, Chern CS. Ostwald ripening of two-component disperse phase miniemulsions containing monomer and reactive costabilizer. J Disper Sci Technol 2010;31:1568–73. [26] Brandrup J, Immergut EH, Grulke EA. Polymer Handbook. 4th ed. New York: WileyInterscience; 1999. [27] Tauer K. Stability of monomer emulsion droplets and implications for polymerizations therein. Polymer 2005;46:1385–94. [28] Porter DA, Easterling KE. Phase Transformations in Metals and Alloys. 2nd ed. London: Chapman & Hall; 1992. [29] Mark JE. Physical Properties of Polymers Handbook. New York: AIP Press; 1996.
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Modeling the role of polymeric costabilizers in retarding Ostwald ripening involved in styrene miniemulsions Chun-Ta Lin a, Chorng-Shyan Chern a,∗ a
Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan
a r t i c l e
i n f o
Article history: Received 19 January 2015 Revised 27 March 2015 Accepted 16 April 2015 Available online xxx Keywords: Miniemulsion Polymeric costabilizer Ostwald ripening Modified Kabal’nov equation Regular solution Intermolecular interactions
a b s t r a c t A thermodynamic approach dealing with a regular solution of monomer (styrene (ST) herein) and different polymeric costabilizers as the disperse phase of miniemulsion were used to develop a model that describes the Ostwald ripening behavior involved in such a colloidal system. The validity of this model was verified by the Ostwald ripening rate data obtained from ST miniemulsions stabilized by living polystyrene costabilizer (PSlc ) or polystyrene costabilizer (PSc ) upon aging at 25 ◦ C. PSlc is more effective in retarding the Ostwald ripening process than PSc , though PSlc and PSc have comparable number-average molecular weights. The model can be also used to study the mutual interaction between monomer and polymeric costabilizer. Satisfactory modeling results achieved for ST miniemulsions using polymethyl methacrylate as the costabilizer further verify the general validity of the present model. Finally, the values of heat of mixing and interaction parameter between ST and different polymeric costabilizers were also determined. © 2015 Published by Elsevier B.V. on behalf of Taiwan Institute of Chemical Engineers.
1. Introduction Emulsions undergo colloidal degradation upon aging primarily via two ways, that is, coalescence and Ostwald ripening. Coalescence among interactive emulsion droplets can be prohibited effectively by an adequate level of surfactant. By contrast, Ostwald ripening is a diffusional degradation process occurring in emulsion with a relatively broad droplet size distribution. It involves the growth of larger droplets with lower excess chemical potential at the expense of smaller ones with higher excess chemical potential via the molecular diffusion of oil molecules from smaller droplets to larger ones [1–3]. Ostwald ripening can be greatly retarded by the incorporation of a low molecular weight, water-insoluble species (e.g., long chain alkanes and alcohols, termed as costabilizers) into oil droplets [4–6], and the kinetically stable colloidal product termed the miniemulsion. Reimer and Schork [7,8] used polymer as costabilizer to prepare relatively stable miniemulsions. Recently, we illustrated the effect of polymeric costabilizer molecular weight on the Ostwald ripening behavior of monomer miniemulsions, and established an approach to determine the critical chain length of polymer costabilizer, consistent with those reported in the literature [9]. In our previous work [10], we developed a model based on the thermodynamics approach to quantitatively describe the Ostwald
∗
Corresponding author. Tel.: +886 27376649; fax: +886 27376644. E-mail address: [email protected] (C.-S. Chern).
ripening behavior in a wide range of volume fraction of costabilizer (ϕ c ) for the two-component disperse phase miniemulsions, in which the disperse phase was a regular solution of monomer and costabilizer (i.e., the enthalpy change of mixining (Hmix ) not equal to zero). A modified Kabal’nov equation was then developed to adequately predict the Ostwald ripening rate (RO ) data and the model is shown below.
1 ϕm = + RO RO,m
ϕc 1 + C ϕc
RO,c
(1)
where RO,i (i = monomer (m) or costabilizer (c)) is the Ostwald ripening rate corresponding to the single component species i, ϕ i the volume fraction of the component i, and C a parameter closely related to the intermolecular interactions in the disperse phase. The model is capable of predicting the Ostwald ripening rate data in a wide ϕ c range for styrene (ST) miniemulsions stabilized by a homolog of n-alkane costabilizers (Cn H2n+2 ) upon aging at 25 ◦ C. The objective of this work was to develop a model via the thermodynamics approach in combination with the Morton equation [11] to quantitatively describe the Ostwald ripening behavior in a wide ϕ c range for the two-component disperse phase miniemulsion stabilized by polymeric costabilizer. The validity of this model was then verified by experimental data for various polymeric costabilizers. Furthermore, thermodynamic parameters such as the Flory–Huggins interaction parameter (χ mp ) and Hmix between monomer and polymeric costabilizer were determined.
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2. Model development 2.1. Partial molar free energy of monomer in the presence of polymer in a two-component disperse phase system Morton et al. [11] considered the equilibrium swelling of emulsion polymer droplets by solvents (e.g., ST) exhibiting a rather limited solubility in the continuous aqueous phase. They derived an expression for partial molar Gibbs free energy of monomer (Gm ) as follows:
Gm = Gmix + Ginterf
(2)
where Gmix represents the contribution from the Gibbs free energy of mixing of monomer and polymer, and Ginterf the contribution from the droplet-water interfacial energy. Furthermore, Gm was expressed in terms of the classical Flory–Huggins theory [11–13]:
1 ΔGmix = ln 1 − ϕp + ϕp 1 − + χmp ϕp2 RT n
(3)
where ϕ p is the volume fraction of polymer in latex droplets, n the number-average degree of polymerization, R the gas constant, T the temperature, and χ mp the Flory–Huggins interaction parameter. As to ΔGinterf , it was given in terms of the Gibbs–Thomson equation [14].
2σ Vm,m ΔGinterf α = = RT aRT a
pressure is effectively compensated by the osmotic pressure. Based on this scenario, Kabal’nov and coworkers [1] then established the equilibrium condition for Gm . Similarly, we derived the following expressions for the equilibrium condition for ΔGm .
1 ΔGm ΔGme α 2 = = ln 1 − ϕpe + 1 − ϕpe + χmp ϕpe + RT RT n ae 2 ϕpe 1 α 2 + 1− ≈ −ϕpe − ϕpe + χmp ϕpe + 2 n ae 1 1 α 2 − χmp ϕpe = − ϕpe − + = constant n 2 ae
(6)
where the subscript e represents a certain parameter at equilibrium. For example, ae is the equilibrium droplet radius. Note that, in the above derivation, the terms of third order and higher were neglected in expanding the function ln(1–ϕ pe ) in a Taylor series. The term α /ae on the right hand side of Eq. (6) represents the Laplace pressure effect [15], and the remaining terms the competitive osmotic pressure effect. In addition, similar to the Kabal’nov approach [1], Eq. (6) can be expressed equivalently as follows:
ϕ pe − ϕ pe +
1 + n
1 1 1 − χmp ϕ pe + ϕ pe = α − 2 a e a e
(4)
(7)
where σ is the droplet-water interfacial tension, Vm,m is the molar volume of monomer, a is the radius of monomer droplet, and α is defined as 2σ Vm,m /RT. Finally, substituting Eqs. (3) and (4) into Eq. (2) gives the so-called Morton equation:
where .ϕ pe ’ and ϕ pe ’’, and ae ’ and ae ’’ are the volume fractions of polymeric costabilizer and the radii of two arbitrary droplets with different sizes brought into equilibrium, respectively. Fig. 1 shows the influence of polymeric costabilizer molecular weight (= n×molecular weight of repeating unit) on Gm . To
1 ΔGm α = ln 1 − ϕp + ϕp 1 − + χmp ϕp2 + RT n a
(5)
ΔGm is also termed as the excess chemical potential that determines the internal energy change for a change in composition arising from the addition of a small amount of monomer into the regular solution. 2.2. Excess chemical potential of monomer in the two-component disperse phase system for the case of zero solubility of polymeric costabilizer in water Formation of a two-component disperse phase system (e.g., miniemulsion) comprising a large population of submicron droplets suspended in the continuous aqueous phase generates an extremely large total oil–water interfacial area. Therefore, interfacial phenomenon naturally comes into play in the stability of colloidal products upon aging. These droplets consist of the major component (monomer) and polymeric costabilizer that is completely insoluble in water (C,p = 0), which form a regular solution therein. This colloidal system is the focus of this work. Kabal’nov et al. [1] considered a two-component disperse phase system with an ideal solution (Hmix = 0) of monomer and costabilizer as the disperse phase to be very similar to a semipermeable membrane since costabilizer was essentially insoluble in water. At equilibrium, the excess chemical potential of solvent (a permeating component) is the same on both sides of the membrane, whereas that of solute (a nonpermeating component) exhibits different values when crossing the membrane. In a similar manner, for a two-component disperse phase system with a relatively narrow droplet size distribution initially, mass transfer of monomer from a smaller droplet to a larger one occurs in consequence of the difference in the capillary pressures. This will then result in a concentration gradient for polymeric costabilizer between the shrinking droplet and the expanding one, thereby leading to the suppression of the Ostwald ripening process. This is simply because insoluble polymeric costabilizer is not allowed to transport between two droplets of different sizes. Eventually, Ostwald ripening is terminated and, therefore, equilibrium is achieved when the capillary
Fig. 1. (a) Profiles of dimensionless excess chemical potential as a function of droplet radius calculated by Eq. (5) with n = 10, 100 and 500 and (b) a representative example of thermodynamic colloidal instability (Gm /RT > 0 and d(Gm /RT)/da < 0), stability (Gm /RT 0) and metastability (Gm /RT > 0 and d(Gm /RT)/da 0).
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construct Fig. 1a, first, the relationship xp = xpi (ai /a)3 (i.e., ϕ p = Kϕ pi (ai /a)3 , where K is a proportional constant between molar fraction and volume fraction) was substituted into Eq. (5) to result in Eq. (8).
G m RT
=−
a 3 1 a 3 2 α 1 i i − + Kϕpi − χmp Kϕpi n a 2 a a
(8)
3
The pioneering Kabal’nov approach was then adopted in this work to give the following expressions for the two-component disperse phase system, in which the disperse phase behaves just like a regular solution and polymeric costabilizer is used to retard Ostwald ripening. In brief, Jm and Jp can be expressed as follws:
Jm = 4π Dm a [Cm − Cs,m ]
(10)
Jp = 4π Dp a [Cp − Cs,p ]
(11)
With values of K = 8.6 (n =10), 85.7 (n = 100) and 428.5 (n = 500), respectively, ϕ pi = 10−2 , ai = 0.5 μm, χ mp = 0. 37 (for toluene/PS) [16] and α = 10−3 μm [17], the value of Gm /RT can be calculated for a given value of a. Based on this algorithm, the Gm /RT-vs.-a profile is thus established. The Gm /RT-vs.-a profile shows that the maximal Gm /RT becomes more prominent as n is increased. Furthermore, Gm /RT becomes positive regardless of the value of a when n 500. According to Ref. [18], the conditions Gm /RT > 0 and d(Gm /RT)/da < 0, Gm /RT 0, and Gm /RT > 0 and d(Gm /RT)/da 0 (representing an energy barrier against Ostwald ripening) are considered as those of thermodynamic colloidal instability, stability and metastability, respectively. In unstable regime, the colloidal system is unstable toward decay into two populations, one being large droplets enriched with monomer, and the other being small ones enriched with polymeric costabilizer. Ultimately, the diffusional degradation process ends up in equilibrium of a macroscopic phase of monomer with Gm 0. In metastable regime, the system is kinetically stable, but not thermodynamically stable. Gm over this regime is positive and from the thermodynamic point of view, the system is unstable (in a similar manner to the unstable regime discussed above). However, the diffusional degradation is very difficult to achieve simply because of the kinetic factor (i.e., the energy barrier identified by an arrow in Fig. 1 is too high). Still, if the polydispersity of droplet size distribution is large enough, metastability will become invalid. This is the reason why polymeric costabilizers with a relatively high molecular weight (n is very large) were considered ‘poor’ costbilizers [8,9].
where Jp is the volume flux for polymeric costabilizer from a droplet to the continuous aqueous phase, Dm (m2 s−1 ) and Dp (m2 s−1 ) are the diffusion coefficients of monomer and polymeric costabilizer, respectively, a (m) is the droplet radius, Cm (g g−1 ) and Cp (g g−1 ) are the solubilities of monomer and polymeric costabilizer in water, respectively, and Vm,p is the molar volume of polymeric costabilizer. Jp governs the Ostwald ripening process because C,m > > C,p . At every instant, droplets of some critical droplet radius (ac ) exist in a polydisperse system for which Jp = 0 (Eq. (14)).
2.3. Ostwald ripening rate in the two-component disperse phase system for the case of nonzero solubility of polymeric costabilizer in water
< 1, both exp(α p /ac ) Taking into account α p /ac (or α p /a) < 1 + α p /ac and exp(α p /a) 1 + α p /a can be approximated to be unity. Thus, Eq. (15) can be further simplified to become
In the scenario that polymeric costabilizer is characterized by a very low but nonzero value of C,p , diffusion of polymeric costabilizer from a droplet into the continuous aqueous phase controls RO . Kabal’nov et al. [1] developed the following equation for the case of ideal solution in the disperse phase and nonzero solubility of costabilizer in water (C,c ).
1 ϕm ϕc = + RO RO,m RO,c
α m Cs,m = C∞,m 1 − ϕp (a) exp , a Cs,p = C∞,p ϕp (a) exp
ac =
ln
αp Cp C∞,p ϕp (ac )
α p
a
(i) water solubility of monomer (C,m ) is much higher than C,c and, therefore, fast distribution of the major component, monomer, among droplets greatly retards the mass transfer of monomer, (ii) xc and a are quite close to their equilibrium values determined by the relationship Gm = Gme = (2σ Vm,m /ae )–RTxci (ai /ae )3 = constant, where xc is the molar fraction of costabilizer and xci and ai are the initial molar fraction of costabilizer and droplet radius, respectively, > α m /aavg,i , where α m is defined as 2σ Vm,m /RT and aavg,i is (iii) xc > the initial average droplet radius, (iv) changes in xc (xc ), determined by the relationship xce ’–xce ’’ = (2σ Vm,m /RT) (1/ae ’–1/ae ’’) = constant, are of the order of xc α m /aavg,i and xc /xc << 1 (i.e., small recondensation rate) and (v) Jm /Jc ϕ m /ϕ c , where Ji (i = m, c; m3 s−1 ) is the volume flux for component i from a droplet to the continuous aqueous phase.
(13)
(14)
Substituting Eq. (14) into Eq. (11) result in the following expression for Jp
Jp = 4π Dp aC∞,p
ϕp (ac ) exp
αp
ac
− ϕp (a) exp
α p
(15)
a
Jp ≈ 4π Dp aC∞,p [ϕp (ac ) − ϕp (a)]
(16)
According to Eq. (7), ϕ p (ac )–ϕ p (a) can be expressed as α (1/ac –1/a) [1/n+(1/2–χ mp ) (ϕ p (ac )+ϕ p (a))] and substituting this relationship into Eq. (16) gives
Jp = 4π Dp aC∞,p α
1 1 − ac a
(9)
It is noteworthy that derivation of Eq. (9) is based on the following assumptions:
(12)
2σ Vm,p RT
αp =
,
2σ Vm,m RT
αm =
1 n
+
1 2
− χmp
1
ϕp (ac ) + ϕp (a)
(17) Furthermore, the term ϕ p (ac )+ϕ p (a) can be approximated to > α m /aavg,i and ϕ p /ϕ p < < 1 (i.e., small reconden2ϕ p (a) because ϕ p > sation rate) for polymeric costabilizer with an extremely low C,p . Thus, Eq. (17) is readily reduced to
Jp = 4π Dp aC∞,p α
1 1 − ac a
1 n
1 + 1 − 2χmp ϕp (a)
(18)
Assuming that Jm /Jp ϕ m /ϕ p, then
J = Jm + Jp =
Jp
ϕp (a)
= 4π Dp aC∞,p α
=
d
1 1 − ac a
4 3
π a3
dt
ϕp (a)
1 n
1
+ 1 − 2χmp
(19)
ϕp (a)
Finally, Kabal’nov and coworkers [17,19] illustrated that the Lifshitz–Slozov theory [20] was applicable to the case considered herein. In brief, the Lifshitz–Slozov theory showed that, after an initial
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nonstationary period, the Ostwald ripening process was characterized by (i) the time independent distribution function for the ratio of a droplet radius to the current mean droplet radius and (ii) the linear growth of the cube of the mean droplet radius with time (referred to RO ). In this manner, RO can be written as
RO =
9RT ϕp
8C∞,p Dp σ Vm,m
1 + 1 − 2χmp ϕp n
(20)
Moreover, the following two limiting cases can be established. Limiting case 1: ϕ p → 1 and (1–2χ mp ) → 0 ( disperse phase → ideal solution)
8C∞,p Dp σ Vm,p n 9RT
RO ≈ RO,p =
(21)
Limiting case 2: ϕ p → 0
RO ≈ RO,m =
8C∞,m Dm σ Vm,m 9RT
(22)
For limiting case 1 (i.e., polymer particles), χ mp approaches 1/2, which defines the Flory θ -temperature, and at which point “polymer chains mix without recognizing each other’s presence” [16]. On the other hand, limiting case 2 corresponds to pure monomer droplets and their stability is dependent on the average droplet size and size distribution. If the difference in the molar volumes of pure components and their interfacial tensions at the oil–water interface is negligible as > compared to the difference between their water solubilities (C,m > C,p ), Eqs. (21) and (22) can be joined into the following modified Kabal’nov equation.
1 ϕm = + RO RO,m =
1 RO,m
ϕp
1 n
+ 1 − 2χmp ϕp RO,p
+
1 1 − nRO,p RO,m
ϕp +
1 − 2χmp RO,p
ϕp 2
(23)
The last term involving ϕ p 2 on the right hand side of Eq. (23) can be neglected provided that ϕ p is small enough. Furthermore, Eq. (23) can be readily reduced to Kabal’nov equation when ϕ p is small enough and n is equal to one (i.e., a low molecular weight species).
reactor equipped with a mechanical agitator and a thermometer. The mixture was then stirred over a period of 1 h. The reaction mixture turned to bright red immediately after sodium trithiocarbonate was produced. Subsequently, 100.8 g of benzyl chloride was added to the reactor over a period of 15 min. The mixture was stirred at 50 °C for 3 h and then at 70 °C for additional 30 min. To complete the reaction, 1.5 g of tributylmethylammonium chloride was added to the reaction mixture without heating overnight. A yellow semi-solid product containing DBTTC (bottom layer) was separated from the aqueous phase (upper layer) using a funnel separator. The crude DBTTC product was washed repeatedly by excessive ethanol. The crystalline product was then filtered and dried at 50 °C. The product was characterized by 1 H NMR and 13 C NMR techniques (Bruker Avance, 500 MHz). Living polystyrene costabilizer (PSlc ) was prepared by an isothermal bulk RAFT polymerization process. First, 100.0 g of ST and 2.70 g of DBTTC (RAFT reagent) were charged to a 500 mL reactor equipped with a mechanical agitator, a reflux condenser and a thermometer immersed in a thermostatic oil bath. The reaction mixture was then purged by nitrogen for 10 min to remove dissolved oxygen, followed by raising the reactor temperature to 100 °C. Thermal polymerization of ST in the presence of DBTTC then proceeded for 16 h. Polystyrene costabilizer (PSc ) was prepared by an isothermal solution polymerization process. First, 79.50 g of ST, 0.48 g of dodecyl mercaptan, 0.08 g of AIBN and 19.94 g of toluene were charged to a 500 mL reactor equipped with a mechanical agitator, a reflux condenser and a thermometer immersed in a thermostatic oil bath. The reaction mixture was then purged by nitrogen for 10 min to remove dissolved oxygen, followed by raising the reactor temperature to 70 °C. Thermal polymerization of ST in the presence of dodecyl mercaptan then proceeded for 5 h. The resultant PSlc (or PSc ) was precipitated by excessive methanol and allowed to stand overnight. This was followed by filtration and then thorough rinse of PSlc (or PSc ) by excessive methanol and water. PSlc (or PSc ) sample thus collected was dried in a vacuum oven at 60 °C over a period of 24 h. The number-average molecular weight (Mn ) and polydispersity index (PDI = Mw /Mn , where Mw is the weight-average molecular weight) data for PSlc and PSc were determined by GPC (Waters, 2410) in combination with a calibration curve established by a series of PS standards. 3.3. Preparation and characterization of miniemulsions
3. Experimental 3.1. Materials The chemicals used include styrene (Taiwan Styrene), sodium dodecyl sulfate (SDS, J. T. Baker, 99 percent), sodium bicarbonate (Riedel de Haen), 2,2 -azobisisobutyronitrile (AIBN, Sigma-Aldrich), benzyl chloride (Acros), carbon disulfide (Panreac), sodium sulfide hydrate (Acros), tributylmethylammonium chloride solution (75 percent, Acros), dodecyl mercaptan (Fluka, > 97 percent), toluene (99.8 percent, Aldrich), methanol (Union Chemical Ind.), ethanol (Union Chemical Ind.), a series of polystyrene (PS) standards for gel permeation chromatography (GPC) calibration (Shodex), tetrahydrofuran (THF, Acros), nitrogen (Ching-Feng-Harng) and deionized water (Barnsted, Nanopure Ultrapure Water System, specific conductance < 0.057 μS cm−1 ). ST was purified at 40 °C under reduced pressure and stored at 4 °C before use. Other chemicals were reagent grade and used as received. 3.2. Preparation and characterization of living polystyrene costabilizer Dibenzyltrithiocarbonate (DBTTC) was synthesized according to the literature [21]. First, 58.5 g of sodium sulfide hydrate, 3.0 g of 75 percent aqueous solution of tributylmethylammonium chloride, 35.4 g of carbon disulfide and 150 mL water were charged to a 500 mL
Miniemulsion was prepared by dissolving SDS and sodium bicarbonate in water and polymeric costabilizer in ST, respectively. This was followed by mixing the oily and aqueous solutions with a mechanical agitator at 400 rpm for 10 min. The resultant emulsion immersed in an ice–water bath was then homogenized with an ultrasonic homogenizer (Misonic sonicator 3000, 30 W) for 30 cycles of 100 s in length with 40 s off-time, and the output power set at 80 percent. For Ostwald ripening experiments, a typical miniemulsion recipe comprises the continuous aqueous phase (40 g water and 3.37 × 10−3 M sodium bicarbonate and 6.24 × 10−3 M SDS based on total water) and the monomer charge (a prescribed concentration of polymeric costabilizer dissolved in ST with a total weight of 10 g). The concentrations of sodium bicarbonate and SDS were kept constant throughout this study. The average monomer droplet size data were obtained from the dynamic light scattering technique (DLS; Otsuka Electronics, Photal LPA-3000/3100). The cumulant method was chosen for measuring the z-average hydrodynamic diameter of colloidal droplets. The sample was diluted with water to adjust the number of photons counted per second (cps) to the range 8000–12000 to eliminate the multiple light scattering effects. The dilution water was saturated with SDS (critical micelle concentration = 8.2 × 10−3 M [22]) and ST (water solubility = 1.92 × 10−3 M [23]). In this manner, diffusion of SDS and ST molecules from miniemulsion droplets into the continuous aqueous phase was prohibited.
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Fig. 2.
1
5
H NMR spectrum of DBTTC.
4. Results and discussion 4.1. Characterization of living polystyrene costabilizer and polystyrene costabilizer Fig. 2 shows the 1 H NMR spectrum of DBTTC, in which the ratio of the integral area of the characteristic peak at chemical shift (δ ) = 4.684 ppm (a) to that of the characteristic peak at δ = 7.3–7.4 ppm (b) is 1:2.45, which is reasonably consistent with the theoretical ratio (1:2.50). The characteristic peaks of DBTTC obtained from 13 C NMR spectrum further confirm the molecular structure of DBTTC (Fig. 3). Mn and PDI of PSlc are 1.11 × 104 g mol−1 and 1.01, respectively. The very narrow molecular weight distribution (PDI = 1.01) reflects the major characteristics of bulk RAFT polymerization used in this work. By contrast, Mn and PDI of PSc are 9.78 × 103 g mol−1 and 3.05, respectively. 4.2. Ostwald ripening behavior of ST miniemulsions The RO of ST miniemulsion with a particular φ p upon aging at 25 ◦ C was determined by the least-squares best-fitted slope of the plot of a3 (a is the average radius of monomer droplets) as a function
of time (t) according to the extended Lifshitz–Slyozov–Wagner theory [1] (data not shown here). For those who are interested in the detail of this issue, refer to Refs. [24,25]. The polymeric costabilizer density necessary for calculating φ p is 1.06 g cm−3 for PSlc and PSc [26]. The data of 1/RO vs. φ p for ST miniemulsions stabilized by PSlc (or PSc ) with φ p in the range 0.02–0.16 are shown in Fig. 4. It is noteworthy that polymeric costabilizers are generally considered less effective in retarding Ostwald ripening as compared to conventional low molecular weight costabilizers. Thus, for ST miniemulsions investigated in this study, a polymeric costabilizer volume fraction range of 0.02–0.16 was used and such polymeric costabilizer levels are much higher than those of low molecular weight costabilizers. Considering such medium to high polymeric costabilizer concentrations (up to 16 percent of total droplet volume), applicability of the Flory–Huggins theory to ST miniemulsions containing polymeric costabilizers may thus be confirmed provided that strong density fluctuations do not occur. As expected, RO decreases (or 1/RO increases) with increasing φ p regardless of the type of polymeric costabilizers used. The 1/RO vs. ϕ p data can be adequately described by Eq. (23), as evidenced by the relatively high values of coefficient of determination (R2 ). The quadratic equation obtained from the lest-squares best-fitted curve passing through the point (0, 1/RO,m ) was used to obtain RO,p according
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Fig. 3.
13
C NMR spectrum of DBTTC.
Table 1 Key Ostwald ripening parameters and some physicochemical properties for ST miniemulsions stabilized by polymeric costabilizer upon aging at 25 ◦ C. Costabilizer
Mn ×10−3 (g mol−1 )
PDI.
n
RO,p ×1023 (cm3 s−1 )
χ mp
Hmix a (J)
PSc PSlc PMMAc
9.78 11.14 5.91
3.05 1.01 1.71
93.9 106.9 59
15.2 8.43 3.13
0.30 0.34 0.39
0.13–0.87 0.14–0.99 0.17–1.13
a
Fig. 4. 1/RO vs. ϕ p data for ST miniemulsions stabilized by PSc upon aging at 25 ◦ C. The continuous curve represents the least-squares best-fitted curve of the 1/RO vs. ϕ p data (1/RO = 2.67×1021 ϕ p 2 +7.00×1019 ϕ p +2.00×1015 with the coefficient of determination (R2 ) = 0.9910) based on the modified Kabal’nov equation (Eq. (23)).
to Eq. (23). The value of RO,m (5×10−16 cm3 s−1 ) was taken from the literature [27]. The values of RO,p and other key parameters for ST miniemulsions stabilized by PSlc (or PSc ) obtained from this work are listed in Table 1. For ST miniemulsions, PSlc is more effective in retarding the Ostwald ripening process than PSc (see Fig. 4 and RO,p data in Table 1), though PSlc and PSc have comparable values of Mn (around 1 × 104 g mol−1 ). This is most likely due to the very narrow molecular weight distribution of PSlc (PDI = 1.01) associated with PSlc in
Hmix = kTNm ϕ p χ mp [16], determined in the φ p range 0.02–0.16.
comparison with the PSc counterpart (PDI = 3.05). In other words, a significant fraction of PSc with a relatively broad molecular weight distribution exhibits higher molecular weight than its Mn and, therefore, this part of PSc does not effectively stabilize ST miniemulsion against Ostwald ripening. It is noteworthy that the faster the Ostwald ripening rate, the higher the probability for particle nucleation to take place in the continuous aqueous phase during subsequent miniemulsion polymerization initiated by a water-soluble initiator such as sodium persulfate [9]. This is because Ostwald ripening occurring primarily in the first half of polymerization (e.g., in the interval of 0–80 min for PSc with Mw = 2×105 g mol−1 and φ p = 0.08) results in a larger average monomer droplet size with a smaller total droplet surface area with the progress of polymerization. As a result, surfactant species originally adsorbed on droplet surfaces tend to desorb back to the continuous aqueous phase and promote the formation of particle nuclei therein, thereby leading to deviation from the ideal one-to-one copy from monomer droplets to polymer particles. For those who are interested in this subject, refer to Ref. [9].
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7
In addition, some Ostwald ripening parameters are summarized in Table 1. PMMAc has a larger value (0.39) of χ mp as compared to the PSc counterpart. This implies that the compatibility between PMMAc (even with a lower Mn (5.91×103 g mol−1 )) and ST is inferior to that between PSc and ST. Again, the χ mp value is smaller than that (0.45) of the solution of PMMA in toluene reported in the literature [29]. These results further verify the general validity of the present model that is capable of predicting the Ostwald ripening behavior involved in ST miniemulsions stabilized by polymeric costabilizers Fig. 6. 5. Conclusion
Fig. 5. 1/RO vs. ϕ p data for ST miniemulsions stabilized by PSlc upon aging at 25 ◦ C. The continuous curve represents the least-squares best-fitted curve of the 1/RO vs. ϕ p data (1/RO = 3.85×1021 ϕ p 2 +1.11×1020 ϕ p +2.00×1015 with R2 = 0.9930) based on the modified Kabal’nov equation (Eq. (23)).
With the knowledge of RO,m, RO,p and n, we can calculate χ mp based on Eq. (23). The χ mp data thus obtained are 0.30 and 0.34 for PSc and PSlc , respectively. All the data of χ mp (= Hmix /kTNm ϕ p , where Nm is the number of monomer in the droplet [16]) are positive, implying that mixing of either PS costabilizer prepared in this work with ST is endothermic in nature and, therefore, the mixing process is thermodynamically unfavorable [28]. For the solution of PS in toluene at 25 ◦ C, the value of χ mp was reported to be 0.37 [16], which is quite close to our experiment data. This result provides supporting evidence for the validity of the Ostwald ripening model developed in this work. Interestingly enough, the χ mp value of PSc is smaller than that of PSlc . This is most likely due to the presence of DBTTC unit in the molecular structure of PSlc . The larger the χ mp (i.e., the larger the difference between the solubility parameter of monomer (δ m ) and that of polymeric costabilizer (δ p )), the less compatibility between polymeric costabilizer and monomer, as predicted by Eq. (24) [16].
χmp = βm +
Vm,m
δm − δp RT
2 (24)
where β m : is the lattice constant of entropic origin. Moreover, the values of Hmix determined in the φ p range 0.02–0.16 can be calculated from the relationship χ mp = Hmix /kTNm ϕ p . The Hmix data thus attained were also included in Table 1. Finally, the RO data for ST miniemulsions using polymethyl methacrylate (PMMAc ) as the costabilizer (in the φ p range 0.02–0.16) taken from our previous work [9] were used to evaluate the general validity of Eq. (23). The modeling results are shown in Fig. 5.
Fig. 6. 1/RO vs. ϕ p data for ST miniemulsions stabilized by PMMAc upon aging at 25 ◦ C. The continuous curve represents the least-squares best-fitted curve of the 1/RO vs. ϕ p data (1/RO = 7.32×1021 ϕ p 2 +5.42×1020 ϕ p +2.00×1015 with R2 = 0.9960) based on the modified Kabal’nov equation (Eq. (23)).
A thermodynamic approach dealing with a regular solution of monomer (ST used in this work) and different polymeric costabilizers as the disperse phase of miniemulsion was used to develop the modified Kabal’nov equation: 1/RO = ϕ m /RO,m +ϕ p [1/n+(1–2χ mp )ϕ p ]/RO,p . The validity of this model was verified by the RO data obtained from ST miniemulsions stabilized by PSlc (or PSc ) upon aging at 25 ◦ C. It was shown that RO decreases (or 1/RO increases) with increasing φ p regardless of the type of polymeric costabilizers used. Interestingly enough, PSlc is more effective in retarding the Ostwald ripening process than PSc , though PSlc and PSc have comparable values of Mn . This is primarily attributed to the very narrow molecular weight distribution of PSlc arising from the RAFT polymerization process. The proposed Ostwald ripening model can be used to study the mutual interaction between monomer and polymeric costabilizer. The positive values of χ mp are 0.30 and 0.34 for PSc and PSlc , respectively, implying that mixing of either PS costabilizer with ST is endothermic in nature and, therefore, the mixing process is thermodynamically unfavorable. Furthermore, the larger value of χ mp for the pair of ST and PSlc indicates the poorer compatibility between PSlc and ST as compared to the pair of ST and PSc . Finally, satisfactory modeling results achieved for the Ostwald ripening behavior involved in ST miniemulsions using PMMAc as the costabilizer further verify the general validity of the present model. Furthermore, PMMAc (even with a lower Mn ) exhibits a larger value (0.39) of χ mp (i.e., the worse compatibility with ST) as compared to the PSc counterpart. References [1] Kabal’nov AS, Shikubin ED. Ostwald ripening theory: applications to fluorocarbon emulsion stability. Adv Colloid Interface Sci 1992;38:69–97. [2] Taylor P. Ostwald ripening in emulsions. Colloid Surf A-Physicochem Eng Asp 1995;99:175–85. [3] Taylor P. Ostwald ripening in emulsions. Adv Colloid Interface Sci 1998;75:107– 63. [4] Higuchi WJ, Misra J. Physical degradation of emulsions via the molecular diffusion route and the possible prevention thereof. J Pharm Sci 1962;51:459–66. [5] Ugelstad J, Mórk PC, Kaggerud KH, Ellingsen T, Berge A. Swelling of oligomerpolymer droplets. New methods of preparation. Adv Colloid Interface Sci 1980;13:101–40. [6] Barnette DT, Schork FJ. Continuous miniemulsion polymerization. Chem Eng Prog 1987;83:25–30. [7] Reimers J, Schork FJ. Robust nucleation in polymer-stabilized miniemulsion polymerization. J Appl Polym Sci 1996;59:1833–41. [8] Reimers J, Schork FJ. Predominant droplet nucleation in emulsion polymerization. J Appl Polym Sci 1996;60:251–62. [9] Lin CT, Wu JM, Chern CS. Effects of the molecular weight of polymeric costabilizers on the Ostwald ripening behavior and the polymerization kinetics of styrene miniemulsions. Colloid Surf A-Physicochem Eng Asp 2013;434:178–84. [10] Lin CT, Chern CS. Modeling Ostwald ripening rate of styrene miniemulsions stabilized by a homolog of n-alkane costabilizers. J Taiwan Inst Chem Eng 2014 Available online 26 December. [11] Morton M, Kaizerman S, Altier MW. Swelling of latex particles. J Colloid Sci 1954;9:300–12. [12] Flory PJ. Principles of Polymer Science. Ithaca, New York: Cornell University Press; 1953. [13] Noel LFJ, Maxwell IA, German AL. Partial swelling of latex particles by two monomers. Macromolecules 1993;26:2911–18. [14] Johnson CA. Generalization of the Gibbs-Thomson equation. Surf Sci 1965;3:429– 44. [15] Skinner LM, Sambles JR. The Kelvin equation—a review. J Aerosol Sci 1972;3:199– 210. [16] Sperling LH. Introduction to Physical Polymer Science. 4th ed. United States of Americ a: John Wiley & Sons, Inc; 2006.
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