Poly(methyl methacrylate-co-ethyl acrylate) Latex Particles with Poly

Mar 3, 2007 - Water-based copolymer dispersions were prepared using methyl methacrylate (MMA), ethyl acrylate (EA) (MMA/EA = 1:2), and a series of non...
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Langmuir 2007, 23, 3590-3602

Poly(methyl methacrylate-co-ethyl acrylate) Latex Particles with Poly(ethylene glycol) Grafts: Structure and Film Formation Staffan Schantz,*,† Hans T. Carlsson,† Thomas Andersson,† Stefan Erkselius,‡ Anders Larsson,§ and Ola J. Karlsson‡,| PAR&D, AstraZeneca R & D, S-43183 Mo¨lndal, Sweden, Polymer Science and Technology, Lund UniVersity, S-22100 Lund, Sweden, and Institute for Surface Chemistry, S-11486 Stockholm, Sweden ReceiVed September 25, 2006. In Final Form: January 10, 2007 Water-based copolymer dispersions were prepared using methyl methacrylate (MMA), ethyl acrylate (EA) (MMA/ EA ) 1:2), and a series of nonionic polymerizable surfactants, i.e., “surfmers” based on poly(ethylene glycol)(meth)acrylates. The latexes were compared with the behavior of a conventionally stabilized (nonionic nonylphenol ethoxylate, NP100 with 84 ethylene oxide units) dispersion with the same MMA-EA composition (PMMAEA). A number of techniques were employed in order to characterize structure, dynamics, and film formation properties: solution/solid-state NMR, dynamic/static light scattering (DLS/SLS), differential scanning calorimetry (DSC), tensile/ shear mode dynamic mechanical thermal analysis (DMTA), and atomic force microscopy (AFM). The surfmers were found to be miscible with the MMA-EA copolymer at room temperature, with 46-85 mol % of the reacted surfmer detected at the particle surfaces, and the remaining part buried in the particle bulk. In contrast, the NP100 surfactant formed a separate interphase between the copolymer particles with no mixing detected at room temperature or at 90 °C. For a 4.0% dry weight concentration, NP100 phase separated and further crystallized at room temperature over a period of several months. Composition fluctuations related to a limited blockiness on a length scale above ∼2 nm were detected for PMMAEA particles, whereas the surfmer particles were found to be homogeneous also below this limit. On a particle-particle level, the dispersions tended to form colloidal crystals unless hindered by a broadened particle size distribution or, in the case of PMMAEA, by the action of NP100. Finally, a surface roughness (Rq) master plot was constructed for data above the glass transition temperature (Tg) from Tg + 11 °C to Tg + 57 °C and compared with the complex shear modulus over 11 frequency decades. Shift factors from the 2 methods obeyed the same Williams-Landel-Ferry (WLF) temperature dependence, thus connecting the long-time surface flattening process to the rheological behavior of the copolymer.

1. Introduction Water-based film formation from polymer dispersion particles is a subject of considerable interest. From an industrial viewpoint, this is mainly driven by the demand for environmentally friendly coatings without the use of organic solvents in the manufacturing/ application processes. In pharmaceutical development, colloidal systems have a widespread use: for example, as latex films that can be used to control the dissolution and release of a drug substance.1 Academically, some fundamental aspects of film formation have been greatly debated recently, such as the exact role of water and even the driving force for particle deformation.2 Traditionally, latex film formation was considered to involve three main stages: evaporation of water until close-packing, deformation of particles to fill all the voids, and finally interdiffusion of polymer molecules across particle interfaces to form a mechanically coherent film.3 The later stages take place at temperatures above the polymer glass transition temperature (Tg) and have been successfully studied using, for example, small * Corresponding author. Telephone: +46 31 7762503. Fax: +46 31 7763729. E-mail: [email protected]. † AstraZeneca R & D. ‡ Lund University. § Institute for Surface Chemistry. | Present address: Physical Chemistry 1, Lund University, SE-22100 Lund, Sweden. (1) Pharmaceutical Coating Technology; Cole, G., Ed.; Taylor & Francis: London, 1995. (2) For a review, see Steward, P. A.; Hearn, J.; Wilkinson, M. C. AdV. Colloid Interface Sci. 2000, 86, 195. (3) For a review, see Keddie, J. L. Mater. Sci. Eng. 1997, 21, 101.

angle neutron scattering (SANS),4-6 atomic force microscopy (AFM),7-10 and nonradiative energy transfer directly probing polymer chain diffusion at interfaces.11-15 All these studies, mainly of surfactant-free model systems, point to the close link between particle coalescence and the viscoelastic properties of the polymer as indicated by Tg. Despite this, several approaches to model the mechanical response have been proposed ranging from purely elastic to viscous flow models.16-19 A few years ago, a unified theoretical model was proposed by Russel and Routh (R-R model) that seems to explain much of (4) Hahn, K.; Ley, G.; Schuller, H.; Oberthur, R. Colloid Polym. Sci. 1986, 264, 1092. (5) Linne´, M. A.; Klein, A.; Miller, G. A.; Sperling, L. H. Macromol. Sci. Phys. 1988, B27, 217. (6) Yoo, J. N.; Sperling, L. H.; Glinka, C. J.; Klein, A. Macromolecules 1990, 23, 3962. (7) Goudy, A.; Gee, M. L.; Biggs, S.; Underwood, S. Langmuir 1995, 11, 4454. (8) Lin, F.; Meier, D. J. Langmuir 1995, 11, 2726. (9) Lin, F.; Meier, D. J. Langmuir 1996, 12, 2774. (10) Pe´rez, E.; Lang, J. Macromolecules 1999, 32, 1626. (11) Zhao, C. L.; Wang, Y.; Hruska, Z.; Winnik, M. A. Macromolecules 1990, 23, 4082. (12) Wang., Y.; Winnik, M. A. Macromolecules 1993, 26, 3147. (13) Farinha, J. P. S.; Martinho, J. M. G.; Kawaguchi, S.; Yekta, A.; Winnik, M. A. J. Phys. Chem. 1996, 100, 12552. (14) Odrobina, E.; Feng, J.; Kawaguchi, S.; Winnik, M. A.; Neag, M.; Meyer, F. Macromolecules 1998, 31, 7239. (15) Wu, J.; Tomba, J. P.; Winnik, M. A.; Farwaha, R.; Rademacher, J. Macromolecules 2004, 37, 2299. (16) Brown, G. L. J. Polym. Sci. 1956, 22, 423. (17) Vanderhoff, J. W.; Tarkowski, H. L.; Jenkins, M. C.; Bradford, E. B. J. Makromol. Chem. 1966, 1, 361. (18) Dillon, R. E.; Matheson, L. A.; Bradford, E. B. J. Colloid Sci. 1951, 6, 108-117. (19) Sheetz, D. P. J. Appl. Polym. Sci. 1965, 9, 3759.

10.1021/la062802z CCC: $37.00 © 2007 American Chemical Society Published on Web 03/03/2007

Latex Copolymers with PEG Grafts

the contradiction in literature regarding driving forces.20,21 The process model for surfactant-free latex predicts different driving forces to be operative depending on the evaporation rate balanced by the particle deformation rate. Typically, well above Tg, deformation is mainly caused by the polymer-water surface tension when compaction is faster than evaporation (wet sintering). At the other extreme, known as dry sintering, water evaporation takes place before deformation. This condition is normally realized by low temperatures (T < Tg) and is driven by the reduction in polymer-air surface tension. Intermediate is the capillary regime where the water-air surface tension causes deformation through the capillary pressure arising from the curvature of the water-air interface between particles. The material response in the R-R approach is taken as a simple viscoelastic model with a single relaxation time, in most cases controlled by the low-shear polymer viscosity (ηo) through a dimensionless parameter λh ) ηoRE/(γH). Here, R is the particle radius, E is the drying rate, γ is the polymer-water interfacial tension, and H is the initial dispersion thickness. The low-shear viscosity is dominating the temperature dependence of film formation through its strong temperature dependence relative to Tg. Also, molecular mass (M) is important, since ηo ∝ M3.4 above the entanglement point for linear polymers. Many experimental results in the literature have been found to correlate well with the model, although accurate measurement of ηo is lacking in most cases.22 It appears that this parameter is not experimentally accessible in all practical situations, e.g., for high molecular mass polymers due to degradation at the high temperatures often required to reach the Newtonian regime. Although significant progress thus has been made in recent years for the understanding of particle-water dispersions, the water-soluble additives commonly used in commercial latex systems cause a complication. For example, as pointed out by Haw et al.,23 the R-R model does not include changing phase behavior during drying. This group studied drying of particles and nonadsorbing polymer in relation to the bulk phase diagram. More commonly, surfactants are important components of the emulsion polymerization process for nucleation and particle stability; however, much is still unknown regarding their influence during drying, coalescence, and aging. Investigations reported in the literature suggest that surfactants can influence the whole film formation process.13,14,24-26 From an application point of view, negative side effects relate to the tendency for surfactants to migrate to the coating interfaces. The surfactants can thus form a separate phase that may affect a range of properties such as adhesion and barrier characteristics.27,28 Zhao et al. proposed that the surfactants tend to migrate so as to minimize the interfacial energy of the system, but also that the water flux during drying can transport nonadsorbed surfactant.29 Surfactant-polymer compatibility has been proposed as yet another important parameter for the final structure.30 A recent model by Gundalaba (20) Routh, A. F.; Russel, W. B. Langmuir 1999, 15, 7762. (21) Routh, A. F.; Russel, W. B. Langmuir 2001, 17, 7446. (22) Routh, A. F.; Russel, W. B. Ind. Eng. Chem. Res. 2001, 40, 4302. (23) Haw, M. D.; Gillie, M.; Poon, W. C. K. Langmuir 2002, 18, 1626. (24) Issacs, P. K. J. Macromol. Chem. 1966, 1, 163. (25) Okubo, M.; Takeya, T.; Tsutsumi, Y.; Kadooka, T.; Matsumoto, T. J. Polym. Sci.: Polym. Chem. 1981, 19, 1. (26) Eckersley, S. T.; Rudin, A. J. Appl. Polym. Sci. 1993, 48, 1369. (27) Zhao, C. L.; Holl, Y.; Pith, T.; Lambla, M. Br. Polym. J. 1989, 21, 155. (28) Mulvihill, J.; Toussaint, A.; De Wilde, M. Prog. Org. Coat. 1997, 30, 127. (29) Zhao, C. L.; Dobler, F.; Pith, T. Holl, Y.; Lambla, M. J. Colloid Interface Sci. 1989, 128, 437. (30) Evanson, K. W.; Thorstenson, T. A.; Urban, M. W. J. Appl. Polym. Sci. 1991, 42, 2297.

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et al. predicts the distribution of surfactants in the film, with the surfactant adsorption isotherm being a critical physical parameter.31 An elegant solution to the migration problems of surfactantparticle systems is to use surfmers, i.e., a surface-active molecule that possesses a reactive group that is active through a free radical mechanism.32 Ideally, after emulsion polymerization, the resulting polymer particles are then stabilized by the grafted, hydrophilic groups of the reacted surfmer. During film formation, the surfactant species are covalently linked to the polymer, so that desorption and further migration is hindered. However, often observed is a lack of stabilization, which has been explained in terms of surfmer burial or formation of large oligomers in the aqueous phase. Particle growth may lead to surfmer burial when very reactive surfmers are used, and hence, they react early in the process. Buried surfmers do not contribute to colloidal stabilization, and coagulation can readily take place. On the other hand, when the surfmer reacts extensively with the substances present in the aqueous phase, water-soluble oligomers may be formed. In addition, these large oligomers can adsorb onto neighboring polymer particles, provoking bridging flocculation.33 One of the most common reactive groups used in polymerizable surfactants for the free radical emulsion polymerization is based on maleate diester surfactants. The maleic functionality cannot react with itself, and therefore, the formation of large watersoluble molecules can be avoided.34 Other types of polymerizable groups have also been reported, e.g., vinyl and allyl.35,36 In comparison with conventional surfactants, a reduction in migration to the film-air interface during film formation has been observed,37 as well as improved film properties, such as reduced water sensitivity38,39 and even enhanced mechanical properties.40,41 However, we have not found in the literature for such systems a detailed characterization of the latex structure or quantitative investigations of the coalescence behavior in relation to recent theories. In this work, we investigate a series of methyl methacrylate (MMA)-ethyl acrylate (EA) copolymer latexes with different types of nonionic surfmer based on PEG (meth)acrylates (see Figure 1). The results are compared with “PMMAEA”, a latex of the same MMA-EA composition but stabilized with a conventional nonylphenol ethoxylate surfactant denoted NP100 (with EO84) (Figure 1). The overall aim is to correlate the particle/ surfactant structure with the film-forming properties. Thus, the latexes are thoroughly characterized, focusing on structure and dynamics of particles/surfactants including glass transition behavior, miscibility, particle homogeneity, and surfactant distribution. The viscoelastic response is then probed, covering a range from the glassy to the molten state to also investigate (31) Gundabala, V. R.; Zimmerman, W. B.; Routh, A. F. Langmuir 2004, 20, 8721. (32) Guyot, A. AdV. Colloid Interface Sci. 2004, 108-109, 3. (33) Guyot, A.; Tauer, K.; Asua, J. M.; Es, S. V.; Gauthier, C.; Hellgren, A.-C.; Sherrington, D.; Montoya-Goni, A.; Sjo¨berg, M.; Sindt, O.; Vidal, F.; Unzue, M.; Schoonbrood, H.; Shipper, E.; Lacroix-Desmazes, P. Acta Polym. 1999, 50, 57. (34) Montoya-Goni, A.; Sherrington, D. C.; Schoonbrood, H. A. S.; Asua, J. M. Polymer 1999, 40, 1359. (35) Guyot, A. AdV. Colloid Interface Sci. 2004, 108-109, 3. (36) Mestach, D. Prog. Colloid Polym. Sci. 2004, 124, 37. (37) Aramendia, E.; Mallegol, J.; Jeynes, C.; Barandiaran, M. J.; Keddie, J. L.; Asua, J. M. Langmuir 2003, 19, 3212. (38) Amalvy, J. I.; Unzue, M. J., Schoonbrood, H. A. S.; Asua, J. M. J. Polym. Sci.: Polym. Chem. 2002, 40, 2994. (39) Aramendia, E.; Barandiaran, M. J.; Grade, J.; Blease, T.; Asua, J. M. Langmuir 2005, 21, 1428. (40) Soula, O.; Guyot, A.; Williams, N.; Grade, J.; Blease, T. J. Polym. Sci.: Polym. Chem. 1999, 37, 4205. (41) Mallegol, J.; Dupont, O.; Keddie, J. L. J. Adhes. Sci. Technol. 2003, 17, 243.

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Figure 1. Definition of the conventional stabilizer NP100 (a) used in the PMMAEA latex and the surfmers (b) used in SD1-SD5.

polymer molecular mass effects. Finally, the results are compared with surface flattening data taken as a measure of coalescence. The main techniques employed are light scattering (SLS/DLS), solid/liquid-state nuclear magnetic resonance (NMR), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), and atomic force microscopy (AFM). 2. Experimental Section 2.1. Materials. Ethyl acrylate (EA) (Aldrich) and methyl methacrylate (MMA) (Aldrich) were purified by passing them through a column filled with aluminum oxide (Merck, active base). The purified monomers were stored at 4 °C before use. Four types of nonionic polymerizable surfactants (surfmer) having either an acrylic reactive group (SD1, SD2, SD4) (noncommercial samples from Cognis Deutschland GmbH, Du¨sseldorf, Germany) or a methacrylic reactive group (SD5) (Polyscience, Inc.) were used as supplied. The surfmers were stored at 4 °C, and 1H/13C NMR before the emulsion polymerization verified the surfmer structures. The surfmer ethylene oxide chain length and hydrophobe varied among the surfmers, and the structures are given in Figure 1. In addition, the surfmer molecular formula, molecular weights, and HLB numbers42 are given in Table 1. Distilled, deionized water (DI) was used. Sodium persulphate (NaPS) (Merck) and sodium dodecyl sulfate (SDS) (BDH) were of analytical grade and used without further treatment. All other chemicals were used as supplied. The PMMAEA dispersion, containing MMA/EA (1:2) copolymer particles and NP100 surfactant, was purchased from Ro¨hm GmbH Pharma Polymers, Germany (Eudragit NE30D). The starting product had 30 wt % solids content and contained 1.5 wt % NP100 according to the supplier. The molecular mass distribution is reported to be monomodal with Mw ) 730.000 g/mol, Mn ) 252.000 g/mol, and thus Mw/Mn ) 2.90.43 2.2. Emulsion Polymerization. The emulsion polymerization experiments (SD1, SD2, SD4, and SD5G-types) were performed in a 2 L pressure calorimetric reactor (ChemiSens RM-2L, Lund, Sweden). The polymerization rate was measured and monitored online, and the data were used to control monomer charging rates and to study the monomer conversion. The latexes were prepared following a general procedure, which resulted in a final total charge weight to the reactor of approximately 1 kg with a solids content close to 30 wt %. The molar ratio between MMA and EA was always 1:2, and the surfactant charge varied between 0.7 and 2.2 wt % based on monomer. To prepare stable dispersions, a mixture of surfmer and SDS was used in the experiments. Emulsions of the monomer and surfactant mixtures were prepared prior to charge through addition of the monomer mixture to a well-stirred solution of water and surfactants (42) Davies, J. T.; Rideal, E. K. Interfacial Phenomena; Academic Press: London, 1963. (43) Adler, M.; Pasch, H.; Meier, C.; Senger, R.; Koban, H.-G.; Augenstein, M.; Reinhold, G. e-Polym. 2004, no. 055.

Schantz et al. and thereafter subjecting the emulsion to high shear for 2 min. In the polymerization experiments, the final particle sizes were controlled by adding a portion of the monomers and surfactants as an emulsion in a nucleation step, and the remaining monomers and surfactants were fed to the reactor as an emulsion. The latex recipes are given in Table 1, and the ratios between the nucleation step and the feeding step are given in Table 2, as well as the distribution of surfactants (surfmers and SDS), given as wt % in the nucleation step and the feeding step, respectively, and as mol % of surfmer and SDS as total charged surfactants in Table 2. The general practical procedure was as follows: In the nucleation step, the emulsion and other chemicals, except the initiator, were charged together with the water. The reactor contents and the initiator solution were repeatedly degassed and purged with nitrogen at room temperature. The reactor was then tempered at 70 °C and the calorimeter calibrated. The reaction was started by adding the initiator solution, preheated to 70 °C, through a valve. When the reaction rate had dropped to zero, the remaining emulsion was fed for 8 h in experiments SD1, SD2, and SD4 and for 4 h in experiments SD5G, SD5G2, and SD5G3. Additional initiator was charged to the reactor (Table 2) in order to maintain the level of radical flux to the particles. When all emulsion had been added to the reactor, the reaction rate declined immediately, but the temperature was kept at 70 °C for 60 min before the reactor was cooled to room temperature in order to minimize the amount of nonreacted monomers. The low molecular weight species such as SDS were removed by dialyzing the ready dispersions using a Spectra/Por Membrane (Spectrum Medical Industries, Inc.) with a molecular weight cutoff (MWCO) of 100.000 g/mol. The dialyses were performed against flowing double-distilled and deionized water for at least 7 days, and the concentration of remaining SDS was below the detection limit of 1H NMR in all samples. The commercial PMMAEA dispersion was dialyzed using the same protocol. 2.3. Latex Characterization. The main latex characteristics are shown in Table 3. Dry weights were determined gravimetrically after drying to constant weight at 75 °C in a vacuum oven. The static light scattering (SLS) experiments were carried out on a DAWN EOS (Wyatt Technology Corp., Santa Barbara, CA) with scattering angles from 23° to 147°. The root-mean-square particle diameter was obtained from Guinier-type plots using angles in the lower region when this was most appropriate. The hydrodynamic particle size was obtained from dynamic light scattering (DLS) using a Brookhaven BI-200SM goniometer (90° scattering angle), a BI9000AT correlator, and an argon ion laser (LEXEL 2W). The CONTIN algorithm included in the software package was used. The method of phase analysis light scattering (PALS) was employed to measure the ζ potential (Brookhaven Instruments ZetaPALS). All light scattering experiments were performed at 25 °C on samples diluted typically 105 times to avoid multiple scattering. For samples in SLS/DLS and PALS, respectively, 1 mM and 10 mM NaCl solutions were used. An exception was PMMAEA, which was diluted with purified water. Solution 1H NMR was used to quantify the total amount of reacted surfmer, the reacted surfactant content on the particle surfaces, as well as the NP100 content in PMMAEA (see Table 4). The 1H NMR spectra of the colloids investigated are completely dominated by surface groups for which the high local mobility averages the dipolar interactions and give sharp isotropic chemical shifts. Resonances from the bulk of particles are not detected due the solidlike dynamics and consequent line-broadening in the absence of strong hydroplasticization. The 1H NMR spectra were recorded on a Varian Inova 600 spectrometer operating at a magnetic field of 14.07 T, equipped with a 5 mm triple-resonance gradient probe or a Varian Inova 500 spectrometer (11.74 T) using a 5 mm inverse detection probe. The FID was recorded with at least 4 scans, and the spectral window was typically between -5 and 14 ppm. A π/2 pulse was used with an acquisition time of 4 s and a delay time of 56 s between each pulse. The acquisition data was zero filled at least 2-fold, and the transformation was made using a line-broadening factor of 0.3. The spectra were carefully phase-corrected prior to integration.

Latex Copolymers with PEG Grafts

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Table 1. Recipes for the Preparation of EA-MMA Copolymer Latexesa surfmer type (see Figure 1) latexn R1 SD1

4

SD2

10

SD4

H

25

SD5G

H

9

SD5G2 SD5G3

b

H

Mw R2 (g/mol) HLBb C13

431

C11

667

C18

1425

CH3 H

9

483

CH3 H

9

composition

483

CH3 H

483

4

nucl. init. feed nucl. init. feed nucl. init. feed nucl. init. feed nucl. init. feed nucl. init. feed

7 9 12 12 12

H2O (g)

EA (g)

330.4 13.3 333.8 330.0 13.8 333.6 329.2 13.8 332.3 538.9 5.8 115.6 539.0 5.8 115.6 539.3 5.8 115.9

53.7

26.9

0.54

0.54

164.0 53.7

82.0 26.9

1.64 0.92

1.64 0.54

164.5 53.7

82.3 26.9

2.83 1.75

1.65 0.54

165.1 91.0

82.6 45.5

5.39 1.02

1.65 0.45

131.5 13.3

65.8 6.7

1.47 1.02

1.34 0.35

209.2 104.6 6.7 3.3

1.47 1.02

1.34 0.05

215.9 107.9

1.47

1.00

MMA surfmer SDS NaHCO3 (g) (g) (g) (g)

NaPS (0.84 mL/L) (g); (hr)

0.27 0.89; (0) 0.22; (0.8) 0.33; (3.4) 0.22; (7.1) 0.27 0.89; (0) 0.22; (1.0) 0.33; (3.2) 0.28; (6.0) 0.27 0.89; (0) 0.22; (0.8) 0.33; (2.9) 0.28; (5.6) 0.31 1.34; (0) 0.48; (0.8) 0.31 1.34; (0) 0.48; (0.8) 0.31 1.34; (0) 0.48; (0.8)

a H2O from initiator injections is summarized as “init.” in the H2O column. The amounts of NaPS are given as weight NaPS; (charge time (hr)). The HLB numbers are calculated according to ref 42.

Table 2. Feed Ratios, i.e., Pre-emulsion, Monomer, and Surfactant Distribution surfactant distribution (% of total surfactant) nucl. (wt. %)

preem (wt. %)

total (mol %)

total init

preem distribution (wt.%)

monomer distribution (wt. %)

latex

surfmer

SDS

surfmer

SDS

surfmer

SDS

(pphm)

nucl.

feed

nucl.

feed

SD1 SD2 SD4 SD5G SD5G2 SD5G3

12 15 19 24 24 29

12 9 6 11 8 1

38 48 58 34 35 42

38 28 18 31 32 28

40 43 40 45 47 59

60 57 60 55 53 41

0.51 0.51 0.51 0.55 0.55 0.55

41 41 41 68 56 55

59 59 59 32 44 45

25 25 25 41 6 3

75 75 75 59 94 97

Table 3. Main Characteristics of the Latexes solids content (% w/w)

particle size (nm)

Tgb (°C) ζ-potentiala

latex

before dialysis

after dialysis

dhc

dgd

(mV)

onset

inflection

SD1 SD2 SD4 SD5G SD5G2 SD5G3 PMMAEA

32 32 31 31 32 32 30

16 19 12 19 21 19 22

136 131 218 130 143 ∼260-600 153

104 100 174 99 109 270 n.d.

-40 -31 -32 -31 -38 -29 -43

10 8 6 7 7 8 -9

14 13 12 12 9 10 3

a From PALS (standard deviation