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Aggregational Effect on the Rate of Condensation of Triethoxysilyl-Terminated PolystyrenesKinetic Evidence K. Suzuki,† J. Oku,† H. Okabayashi,*,† and C. J. O’Connor‡ Department of Applied Chemistry, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan, and Department of Chemistry, The University of Auckland, Private Bag 92019, Auckland, New Zealand Received March 7, 2003. In Final Form: June 4, 2003 Five well-defined polymeric silane coupling agents, triethoxysilyl-terminated polystyrene (TESi-PS), substituted with polystyrene moieties of various molecular weights, were condensed in tetrahydrofuran, in the presence of methanesulfonic acid as the catalyst. The effects on the reaction rate of the molecular weight of TESi-PS, of the amount of included polystyrene, and of nonpolar solvents have been examined. The kinetic data provide ample evidence that the formation of aggregates, during the condensation reaction, accelerates the reaction rate. To explain the acceleration effect, an aggregational model is presented in which the ethoxysilyl groups are concentrated in the polar core. This model may be applied to other polymerization processes.
Introduction In composite materials, inorganic materials such as fiberglass, talc, and mica have been extensively used as fillers to enhance their mechanical properties. A number of silane coupling agents (SCAs) have been developed for the modification of the surfaces of these fillers, thereby enhancing the mechanical properties. Most of the SCAs used are of low molecular weight, and details of the condensation reaction have already been reviewed.1-3 Nishio et al.4 have used Fourier transform near-infrared attenuated total reflection spectroscopy to investigate the dehydration process of 3-aminopropyltriethoxysilane on the surface of glass. The results indicated that the reactivity of silane molecules and the characteristics of reinforcement materials may be associated with the molecular structure of the modified silane, which depends strongly upon the conditions for silane treatment. They also investigated the effect of pH, silane concentration, solvent, and method of application of the silane solution, all of which affected the mechanical properties of the treated material. Shimizu et al.5 reported the 13C- and 1 H-NMR and IR spectra of a silane 3-aminopropyltriethoxysilane-toluene system and found that the dependence on silane concentration of these spectra was related to the formation of reversed micelles. Furthermore, Nishio et al.4 showed that there exists an optimum concentration for enhancement of the interfacial strength, thus highlighting the important role of the modified silane that has condensed on the material. When the aggregation of SCAs occurs on a surface, then the subsequent modified structures should be associated * Corresponding author. † Nagoya Institute of Technology. ‡ The University of Auckland. (1) Lasocki, Z. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 1963, 11, 637. (2) Plueddemann, E. P. In Interface in Polymer Matrix in Composites in a Series of Composite Materials; Brautman, L. J., Krock, R. H., Eds.; Academic Press: New York, 1974; Vol. 6, p 1. (3) Lebrun, J. J.; Porte, H. In Comprehensive Polymer Science; Eastmond, G. C., Ledwith, A., Russ, S., Sigwalt, P., Eds.; Pergamon Press: Oxford, 1989; Vol. 5, Chapter 34. (4) Nishio, E.; Ikuta, N.; Okabayashi, H.; Hannah, R. W. Appl. Spectrosc. 1990, 44, 614. (5) Shimizu, I.; Okabayashi, H.; Hattori, N.; Yoshino, A.; O’Connor, C. J. Colloid Polym. Sci. 1997, 275, 293.
with the mechanical properties of the material.4 Thus, further investigation of the aggregated structure of such modified silane molecules is highly desirable. Recently, attractive results were reported for the increased interfacial strength of a surface modified by a polymeric SCA, alkoxysilyl-terminated macromonomers.6-10 However, reaction data for such low-molecularweight SCAs cannot necessarily be applied to those of high-molecular-weight SCAs because, in the latter case, not only is there a very low concentration of the functional group but also the polymeric alkoxy moiety tends to form an aggregate in organic solvents.6-8 We have previously investigated the modification of well-defined polymeric SCAs on the surface of inorganic fillers11-14 and have reported details of the acid-catalyzed4,11,12,14 condensation reaction of triethoxysilylterminated polystyrene (TESi-PS), an example of a polymeric SCA. The products were shown to be oligomers with a very narrow molecular weight distribution, and the use of strong alkaline catalysts brings about dissociation of the polystyrene (PS) moiety. The role of kinetic studies in the elucidation of the interaction between the organosilane layer bound onto the surface of a substrate is very important, particularly with respect to the effect on the stability of the silaneto-surface bonding of curing the organosilane layer. Although extensive research has been carried out on the kinetics of simple organosilanes bound onto a surface, using a variety of experimental techniques,15-25 very little (6) Munir, A.; Goethals, E. J. Makromol. Chem., Rapid Commun. 1981, 2, 693. (7) Lee, K. W.; MacCarthy, T. J. Macromolecules 1988, 21, 3353. (8) Chujo, Y.; Ihara, E.; Ihara, H.; Saegusa, T. Macromolecules 1989, 22, 2040. (9) Mourey, T. H.; Miller, S. M.; Wesson, J. A.; Long, T. E.; Kelts, L. W. Macromolecules 1992, 25, 45. (10) Surivet, F.; Lam, T. M.; Pascault, J. P.; Pham, Q. T. Macromolecules 1992, 25, 4309. (11) Takaki, M.; Suzuki, K.; Mano, T. Kobunshi Ronbunshu 1991, 48, 171. (12) Takaki, M.; Suzuki, K.; Kondo, Y.; Oku, J. Polym. J. 1991, 23, 917. (13) Suzuki, K.; Katsumura, G.; Kondo, Y.; Oku, J.; Takaki, M. Kobunshi Ronbunshu 1992, 49, 825. (14) Suzuki, K.; Esaki, M.; Misawa, A.; Takaki, M. Kobunshi Ronbunshu 1994, 51, 11.
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is known about the kinetics of condensation of polymeric silane-coupling agents. In this present study, the kinetics of the condensation reactions of TESi-PS, substituted with PS moieties of various molecular weights, have been examined using gelpermeation chromatography (GPC). In particular, the effects on the kinetics of the molecular weight of TESi-PS and of the varying PS substituents and differing solvents are discussed with respect to the relationship between the formation of the aggregates and the reaction rate.
Figure 1. Calibration curves (b, PS standards; O, polymerized TESi-PS sample).
Experimental Section Materials. sec-Butyllithium (s-BuLi; Aldrich, 1.3 M in cyclohexane) was used after careful filtration and solvent replacement with benzene. These treatments were carried out under high vacuum (10-5 mmHg) conditions using a vacuum line. Commercially available styrene was purified as previously described.14 Catalysts (methanesulfonic acid) and solvents [tetrahydrofuran (THF), hexane, benzene, ethylbenzene (EB), and methanol] used for the condensation were reagent grade and were used as received. Preparation of PS and TESi-PS. Living PS with various molecular weights was prepared by anionic polymerization of styrene, which was purified immediately prior to polymerization with the initiator s-BuLi. Finally, the end of the living PS was protonated with methanol. TESi-PS with various molecular weights (Mn ) 2000, 3000, 6800, 8600, and 10 400; abbreviations for these samples are TESi-PS(2000), TESi-PS(3000), TESiPS(6800), TESi-PS(8600) and TESi-PS(10 400), respectively) were prepared by the coupling reaction of living PS and chlorotriethoxysilane.14 The PS and TESi-PS samples, thus obtained by recrystallization in methanol, were dried in a vacuum at room temperature and were used for the reaction. Condensation. TESi-PS, catalysts, and solvents were placed into an ampule, sealed under high vacuum (10-3 mmHg) conditions, and the contents were homogenized by shaking. Sample-containing ampules, of a number equal to the number of required aliquots at each temperature, were prepared for the time-dependent experiments. The condensation of the samples thus prepared was carried out in a temperature-controlled bath. The reaction mixture was kept at 293 and 333 K for a prescribed time. The resulting polymer was recovered by pouring the reaction mixture into a large excess of methanol to quench the condensation. The precipitated polymer was filtered through a glass filter and dried at room temperature. The yield of polymerized TESiPS was determined from the GPC curve of the polymer recovered after condensation (the ratio of the peak area of condensed TESiPS to the total response, as obtained using a refractive index detector). The yield [Y (%)] of the condensate was calculated using the equation
Y (%) ) 100 × [GPC peak area of polymerized TESi-PS]/ [total GPC peak area of the reacted products] (1) (15) Ogasawara, T.; Yoshino, A.; Okabayashi, H.; O’Connor, C. J. Colloids Surf. 2001, 180, 317. (16) Waddell, T. G.; Leyden, E. D.; DeBello, M. T. J. Am. Chem. Soc. 1981, 103, 5303. (17) Witten, T. A.; Cates, M. E. Science 1986, 232, 1607. (18) Sander, L. M. Sci. Am. 1987, 256, 94. (19) Schaefer, D. W.; Keefer, K. D. Mater. Res. Soc. Symp. Proc. 1986, 73, 277. (20) Vrancken, K. C.; Van Der Voort, P.; Gillis-D’Hammers, I.; Vansant, E. F.; Grobet, P. J. Chem. Soc., Faraday Trans. 1992, 88, 3197. (21) Vrancken, K. C.; Coster, L. D.; Van Der Voort, P.; Grobet, P.; Vansant, E. F. J. Colloid Interface Sci. 1995, 170, 71. (22) Brinker, C. J.; Keefer, K. D.; Schaefer, D. W.; Ashley, C. S. J. Non-Cryst. Solids 1982, 48, 47.
The area of the band resulting from the trace constituents was subtracted from the apparent GPC peak area of the polymerized TESi-PS. The Y values thus obtained were used to calculate the rate constant. The maximum Y value was regarded as a functionality [f (%)] of TESi-PS. To check the effect of the trace amount of water and also for the presence of a possible side reaction, the condensation of the TESi-PS-solvent systems, prepared in the absence of catalysts, was also carried out. Characterization. For the condensed products with molecular weights higher than 10 000, GPC curves were recorded on a Toso HLC-802A with two GMH columns at a column oven temperature of 313 K. For the condensed products with a lower molecular weight, GPC curves were recorded on a Toso HLC802UR with G2000H and G3000H columns. The nominal flow rate of the eluent was 1 mL/min; actual flow rates were inspected during the recording of a GPC curve, and their constancy was confirmed. Therefore, we have assumed that irreversible adsorption of insoluble polymer on the GPC column, which would have changed the flow rate, did not occur during the GPC measurements. The GPC data were calibrated with PS standards (Figure 1). The amount of the TESi-PS-catalyst-THF solution injected onto the GPC column was controlled so as to provide a linearly increased refractive index and linearly increased UV absorbance (360 nm), measured simultaneously.
Results and Discussion In our previous paper,14 we reported data for the condensation reaction of TESi-PS, with a narrow molecular weight distribution (Mw/Mn ) 1.05) and high functionality (f g 96%) catalyzed by acids in various solvents. The results showed that the rate of reaction depends strongly upon the species of the catalyst and of the solvent used for the condensation. Moreover, it was assumed that the ratedetermining step was the hydrolysis of the ethoxysilyl groups rather than condensation of the silanol groups. Furthermore, we found that the molecular weights of the condensate obtained after a sufficiently long reaction time corresponded to the dimer, trimer, or tetramer of TESiPS, depending upon the species of catalyst and solvent used. The kinetics of the condensation reaction of TESiPS catalyzed by methanesulfonic acid in THF are now discussed in detail. Characterization of Macromonomers. The functionalities [f (%); that is, the maximum Y values] of TESiPS(2000), TESi-PS(3000), TESi-PS(6800), TESi-PS(8600), and TESi-PS(10 400), obtained at 293 K, were 96, 95, 99, 98, and 94%, respectively. These results imply that these macromonomers contained 1-6% unfunctionalized materials (most of which is probably unreacted PS). No attempt was made to remove these unfunctionalized materials. (23) Shimizu, I.; Yoshino, A.; Okabayashi, H.; Nishio, E.; O’Connor, C. J. J. Chem. Soc., Faraday Trans. 1997, 93, 1971. (24) Yoshino, A.; Okabayashi, H.; Shimizu, I.; O’Connor, C. J. Colloid Polym. Sci. 1997, 275, 672. (25) Keefer, K. D.; Schaefer, D. W. Phys. Rev. Lett. 1986, 56, 2376.
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Figure 2. GPC elution profiles of [A] TESi-PS(8600)-THF solution used for the control experiment (Y ) 3.6%, T ) ca. 298 K, t ) 3 h; band a, unreacted monomers, and band b, the trace constituent band) and [B] condensed TESi-PS(8600) catalyzed by methanesulfonic acid in THF (Y ) 97%, T ) 333 K, t ) 760 h; band a, unreacted monomers, and band b, condensed products).
Figure 3. Time course of unreacted TESi-PS (8600) monomers in THF at 293 K (O, observed; b, calculated). Table 2. Mn Effect on the Y Valuea of Condensed TESi-PS (T ) 333 K, t ) 0.5 h)
Table 1. Time-Dependence of the Y and Z Values for the TESi-PS(8600) Condensationa reaction time (h) 2 4 8 24 597
Yb
(%)
42 62 73 90 93
Zc
(%)
58 38 27 10 7
a Catalyzed by methanesulfonic acid in THF at 293 K. b Calculated using eq 1. c Z (%) ) 100 - Y (%).
Kinetics of the Condensation for TESi-PS. It is very difficult to separate the independent contributions to the condensation rate of the trace amount of water from those of unfunctionalized materials or a possible side reaction. However, the total contribution can be evaluated from the control experiments of the sample systems, prepared in the absence of catalyst, which were performed for solutions of all TESi-PS monomers. Figure 2A shows one of the GPC elution profiles for the TESi-PS(8600)-THF solution obtained from the control experiment. The peak, b, appeared at the lower elution side of the macromonomer peak, a, was assigned to the elution band formed as a consequence of the total effect of the three factors mentioned above, which may be regarded as the contribution [Ctc (%)] of the trace constituents. The Ctc values, obtained from the control experiments at 293 K, were 6.6% [TESi-PS(2000)], 11.6% [TESiPS(3000)], 0.3% [TESi-PS(6800)], 3.6% [TESi-PS(8600)], and 2.3% [TESi-PS(10400)]. We have confirmed that these Ctc values remain constant during the control experiments. This contribution (that is, areas of band b) was subtracted from the area of polymerized TESi-PS (band b in Figure 2B) to obtain the Y value used to calculate the rate constant. The rate of the acid-catalyzed condensation was measured by following the time dependence of the yield [Y (%)] of polymerized TESi-PS at 293 or 333 K. The percentages [Z (%) ) 100 - Y (%)] of the TESi-PS(8600) monomers, which remained unreacted, are listed in Table 1. It is assumed that the Z value is equal to 100 at reaction time t ) 0 s and equal to 0 at t ) 1800 s. It is found that Y increases exponentially with time while Z decreases exponentially. Therefore, the time dependence of Y and Z reflects the kinetics of the acid-catalyzed reaction of TESi-PS in THF. To analyze these rate data, we have assumed that the first-order reaction process participates in the condensation of all TESi-PS systems. If we assume that the time course of the TESi-PS monomer can be
TESi-PS Mn × 10-3
[prepolymer] (mmol/kg)
wt %
CH3SO3H (mol/kg)
Y (%)
2.0 3.0 6.8 8.6 10.4
40.1 40.3 40.2 41.1 39.0
8.0 12.1 27.8 34.9 41.0
0.100 0.099 0.099 0.097 0.010
19 23 41 50 56
a
Calculated using eq 1.
expressed by y ) A exp(-kt) + B [A ) 100 and B ) 0, k (s-1) ) rate constant], then the kinetics for the timedependent decrease in Z can be analyzed using only one parameter (k). A representative plot of Z (%) versus t, which provides the best fit of the calculated values and observed data at 293 K, is shown in Figure 3. Effect of the Molecular Weight of TESi-PS Monomer on the Reaction Rate. The effect of the molecular weight (Mn) of the TESi-PS monomer on the yield of its condensed product has been examined. The Y (%) values of polymerized TESi-PS, obtained at 0.5 h at 333 K, are listed in Table 2. It is evident that an increase in Mn for the TESi-PS monomer brings about an increase in yield, implying acceleration of the reaction rate by highermolecular-weight TESi-PS monomers. To confirm this effect of molecular weight on the reaction rate, we have examined the time course of the condensation reaction for two TESi-PS monomers with Mn ) 2000 and 8600 (Figure 4). It is evident that the higher-molecularweight TESi-PS monomer condenses more rapidly. The rate constants for these two reactions are also listed in Table 3, and the results confirm that the TESi-PS with the larger-sized PS moiety provides the faster rate. We offer the following explanation for this observation. During the reaction, formation of TESi-PS aggregates probably occurs. As the molecular weight of a PS moiety increases, the hydrophobicity of this moiety becomes greater, promoting formation of a core in which unhydrolyzed ethoxy groups are concentrated, leading to a faster reaction rate (Figure 5A). For the SiOH groups, which are produced by hydrolysis of TESi-PS in the core, formation of associated SiOH groups may be possible.26 Most of the silanol groups, which belong to the associated SiOH groups, probably form a hydrogen-bonding network with SiOH itself, possibly (26) Ogasawara, T.; Nara, A.; Okabayashi, H.; Nishio, E.; O’Connor, C. J. Colloid Polym. Sci. 2000, 278, 1070.
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Figure 4. Time course of the TESi-PS condensations catalyzed by methanesulfonic acid in THF at 333 K (b, Mn ) 2000; 9, Mn ) 8600). Table 3. Reaction Rate Constants [k (s-1)] for the TESi-PS Condensation (Catalyst, Methanesulfonic Acid; Solvent, THF) molecular weighta (Mn)
k × 106 (s-1)
8600 2000
724.5 110.1
a Condensation catalyzed by methanesulfonic acid catalyst in THF at 333 K. [Prepolymer] ≈ 40 mmol/kg; [Catalyst] ≈ 0.1 mol/ kg.
providing reactive silanol groups that accelerate the TESiPS condensation. Recently, Izawa et al.27,28 used small-angle X-ray scattering (SAXS) spectra to detect the aggregates of alkylalkoxides [perfluorooctyltriethoxysilane (PFOTES) and n-octyltriethoxysilane (OTES)] in ethanol as a polar solvent. The time-resolved SAXS profiles have led to an aggregational model in which condensation between the SiOH groups brings about a particle with a Si-O-Si bonding network structure inside, and this structure expands to become the core of a particle with the hydrophobic chains on the outside. That is, this model is similar to that of a reversed micelle. Izawa et al.29 also confirmed, by time-resolved GPC profiles for polymerization of PFOTES or OTES catalyzed by HCl, that a relatively large number of perfluorooctyl or n-octyl chains remain unhydrolyzed in the reaction mixture. Furthermore, they assumed the presence of a PFOTES- or OTES-ethanol complex in the ethanol solution because such a SCA molecule easily forms the solvated-type complex [R1Si(OEt)3(OHEt)m-3] in ethanol. Two-dimensional correlation GPC was used to confirm successfully the correlation between the SCA monomers-polymeric aggregates, implying the presence of the aggregates.28 Accordingly, because the hydrophobicity of a PS moiety in TESi-PS monomers with Mn ) 2000-1000 is much greater than that of a perfluorooctyl or an n-octyl chain of alkylalkoxides, we may assume the presence of an aggregate of TESi-PS monomers in THF. Indeed, we have confirmed that the condensates of TESi-PS molecules are oligomers (trimer or tetramer). Thus, we may assume the presence of aggregates comprised of an assembly of PS moieties and formation of siloxane linkages in the core, (27) Izawa, K.; Ogasawara, T.; Masuda, H.; Okabayashi, H.; Monkenbnsch, M.; O’Connor, C. J. Colloid Polym. Sci. 2002, 280, 725. (28) Izawa, K.; Ogasawara, T.; Masuda, H.; Okabayashi, H.; Noda, I. Macromolecules 2002, 35, 92. (29) Einaga, H. Inorganic Synthesis in Solution as a Reaction Field; Baifukan: Tokyo, 2000; p 169.
Figure 5. Schematic models of a TESi-PS aggregate.
based on the time-resolved SAXS data27,28 mentioned above. For further identification of this aggregational model, SAXS measurements are highly desirable. Effect of Added PS on the Condensation. To understand the role of the PS moiety of a TESi-PS monomer, PS molecules of various molecular weight were added to the reaction system, and the yield [Y (%)] of condensed products obtained after 0.5 h (333 K) was examined. Figure 6 shows plots of Y versus amounts of added PS for the TESi-PS(2000) reaction system. It is found that the Y value increases with an increase in amounts of added PS, regardless of its molecular weight, indicating that added PS accelerates the rate of condensation. The result implies that the PS moiety plays a critical role in the acceleration of the TESi-PS condensation in THF. This PS effect may be explained as follows. Additional PS molecules probably promote the aggregation of TESiPS monomers, due to incorporation of monomers into the hydrophobic PS moieties (Figure 5B). Consequently, aggregation leads to acceleration of the condensation rate. Therefore, the molecular-weight effect, found in the TESiPS condensation, is likely to be due to the increased number of styrene units in the aggregate, leading to increased stacking between the benzene rings, thereby promoting aggregation. When the concentration of added PS is very high, we may consider that the PS molecules behave as solvents. However, because the molecular weights of the PS
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Langmuir, Vol. 19, No. 18, 2003 7615 Table 4. Effect of Added Nonpolar Solvents and Methanol on the Yield of Condensed TESi-PS(2000)a TESi-PS (mmol/kg)
CH3SO3H (mol/kg)
solvent
conversion (%)
41.8 39.8 40.5 40.1
0.1 0.1 0.1 0.1
benzene THF + n-hexaneb THF + methanolc THF
65 50 11 19
a
T ) 333 K; t ) 0.5 h. b n-Hexane, 31 wt %. c Methanol, 31 wt
%.
Figure 6. Plots of Y versus amounts of added PS (Mn of added PS: O, 2000; ], 24 300; 4, 34 800; 0, 87 100; b, no addition for the TESi-PS(2000) reaction system).
Figure 7. Plots of Y versus amounts of added EB for the TESiPS(2000) condensation catalyzed by methanesulfonic acid in THF (t ) 0.5 h, T ) 333 K; b, no addition).
molecules are much higher than that of THF, it is unlikely that the added PS molecules behave independently as solvents. However, if one were to regard added PS molecules as solvent, then as the percentage of added PS increases, the polarity of the PS-THF mixed solvent would probably decrease, rendering the solvent system more nonpolar. Consequently, the reduced polarity should induce further aggregation of TESi-PS molecules, thereby further accelerating the reaction rate. Effect of Solvents on the Condensation. The effect of the addition of EB, which can be regarded as a modelcompound for a styrene unit, has been examined. Figure 7 shows plots of the yield [Y (%)] of condensed TESi-PS versus the amount of added EB. It is evident that Y increases with increasing amount of EB, implying the existence of an EB effect that accelerates the reaction rate. It should be noted that addition of 72% EB induces a rapid increase in Y. It is possible that EB added in excess of this concentration promotes further an aggregation of TESi-PS monomers, which accelerates the reaction rate. The mechanism of this EB effect should be analagous to that of the PS effect. That is, a benzene ring of an EB
molecule, incorporated into the hydrophobic PS moieties of the TESi-PS monomers, may be stacked with that of a PS moiety of TESi-PS (Figure 5C), promoting formation of an aggregate, which accelerates the TESi-PS condensation. We found that the Y values of condensed TESi-PS, obtained after a 0.5 h reaction time in THF-hexane (31 wt %) and benzene (100%), are 50 and 65%, respectively (Table 4). This fact indicates that the rate of condensation is also accelerated in such a nonpolar medium. That is, the TESi-PS monomers form aggregates analogous to the reversed micelles formed in such nonpolar media,30 in which both the ethoxysilyl groups and methanesulfonic acid catalyst are incorporated into the core and accelerate the reaction rate. Conversely, it has also been found that the yield of condensate obtained in the mixed solvent THF-methanol (31 wt %) fell to 11% (Table 4), implying that the polar medium slows the rate of the TESi-PS condensation, due to inhibition of formation of the aggregate. We further note the complexities that exist in this reaction. In our previous investigation,14 in which we used trifluoroacetic acid as the catalyst for the condensation, we noted that solvents with high polarities such as nitrobenzene apparently accelerated the reaction. The role of the catalyst obviously overrides the smaller effects caused by the polarity or nonpolarity of the solvent. Concluding Remarks For TESi-PS, an increase in Mn of the PS moiety, an increased amount of added PS, and the use of nonpolar solvents accelerate the condensation rate, possibly due to formation of an aggregate in the reaction medium. This aggregation-mediated acceleration of the reaction rate may be applied to other polymerization processes. It is probable that structural studies of these polymeric aggregates, using time-resolved SAXS (or neutron scattering) may lead to a successful explanation of the acceleration of this reaction rate. Furthermore, the novel analytical technique, two-dimensional correlation GPC, may provide information on the time-dependent structural variation of polymeric aggregates, which may well be associated closely with the accelerated reaction rate. When polymeric coupling agents are modified onto the surface of a material, the aggregational effect proposed herein may play a critical role in the enhancement of the material’s interfacial strength. Further investigation of the size and concentration of an aggregate in the reaction medium or on a surface is a major priority. LA030091O (30) Jo¨nsson, B.; Lindman, B.; Holmbelg, K.; Kronbelg, B. Surfactants and Polymers in Aqueous Solution; Wiley: Chichester, U.K., 1998; p 31.
