Langmuir 2003, 19, 6645-6649
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Thermal Jamming in Colloidal Star-Linear Polymer Mixtures Emmanuel Stiakakis,†,‡ Dimitris Vlassopoulos,*,†,§ and Jacques Roovers| FO.R.T.H., Institute of Electronic Structure & Laser, Heraklion, Crete, Greece, Department of Chemistry, University of Crete, Heraklion, Crete, Greece, Department of Materials Science & Technology, University of Crete, Heraklion, Crete, Greece, and NRC, Institute for Chemical Process & Environmental Technology, Ottawa, Ontario, Canada Received February 10, 2003. In Final Form: March 31, 2003 We probe the reversible thermal solidification of crowded solutions of colloidal star polymers in a marginal solvent upon addition of linear homopolymer chains consisting of the same monomers, and for two different linear polymer molecular weights we find that they have a dramatic impact on this phenomenon. If the linear chain molecular weight is much smaller than the star arm molecular weight, penetration is favored, the stars swell (the linear polymer solution acts as a good solvent for the stars), and the jamming temperature drops for a given star concentration. On the other hand, if the linear chain molecular weight exceeds that of the star arm, the stars shrink and the mixture exhibits liquidlike behavior over a wide range of star concentrations and temperatures. These results offer new possibilities for molecular control of the flow properties of soft colloids.
I. Introduction A wide range of materials including colloids, emulsions, and foams undergo a jamming transition at low temperatures and/or high volume fractions, which is characterized by a solidlike rheological response.1,2 The universal features of the jammed systems can be represented by a proposed ‘jamming phase diagram’ involving temperature, number density, and stress, which indicates the ways by which the ability of a system to flow is lost. Of particular interest is the effect of cooling and/or increasing density, which yields vitrification. In recent years, multiarm star polymers (or colloidal stars) and block copolymer micelles have emerged as a class of soft materials encompassing quantifiable polymeric and colloidal characteristics, tunable at the chemical level, and consequently possessing intermediate properties that bridge the gap between polymers and colloids.3,4 In particular, these fluids, usually termed as ultrasoft polymeric spheres because of the nature of their interaction potential (which is proportional to the logarithm of the interparticle distance at short distances and exhibits a Yukawa tail at long distances),5 serve as models for †
Institute of Electronic Structure & Laser. Department of Chemistry, University of Crete. § Department of Materials Science & Technology, University of Crete. | Institute for Chemical Process & Environmental Technology. ‡
(1) Liu, A. J.; Nagel, S. R. Nature 1998, 396, 21. Trappe, V. et al. Nature 2001, 411, 772. Jamming and rheology: Constrained dynamics on microscopic and macroscopic scales; Liu, A. J., Nagel, S. R., Eds.; Taylor and Francis: New York, 2001. (2) Cates, M. E. et al. Phys. Rev. Lett. 1998, 81, 1841. Cates, M. E. In Soft and Fragile Matter. Nonequilibrium dynamics, metastability and flow; Cates, M. E., Evans, M. R., Eds.; Institute of Physics Publishing: Bristol, 2000. Cloitre, M. et al. Phys. Rev. Lett. 2000, 85, 4819. (3) (a) Roovers, J. et al. Macromolecules 1993, 26, 4324. (b) Grest, G. S. et al. Adv. Chem. Phys. 1996, XCIV, 67. (c) Vlassopoulos, D. et al. J. Phys.: C,. Condens. Matter 2001, 13, R855. (d) Likos, C. N. Phys. Rep. 2001, 348, 267. (4) Buitenhuis, J.; Foerster, S. J. Chem. Phys. 1997, 107, 262. Pham, Q. T. et al. J. Rheol. 1999, 43, 1599. Watanabe, H. Acta Polym. 1997, 48, 215. Watanabe, H. et al. Macromolecules 2001, 34, 6742. Gast, A. P. Langmuir 1996, 12, 4060. Hamley, I. A. et al. Langmuir 2000, 16, 2508. Mortensen, K. Europhys. Lett. 1992, 19, 599.
exploring the dynamic arrest in soft systems.6 Lately, we have focused on a special type of kinetic frustration exhibited by colloidal stars, the counterintuitive reversible thermal jamming (gelation) transition.7,8 These materials were suspended in solvents of intermediate quality (between athermal and theta) at concentrations above their overlapping concentration (c*), and upon heating they exhibited a reversible glasslike gelation (in general, considered as a manifestation of the jamming transition). This phenomenon was attributed to the formation of clusters of swollen interpenetrating spheres at high temperatures, which caused a kinetic frustration of the sample, and the resulting solid was classified as a weak glasslike gel (it was recognized that no sharp distinction between soft gels and soft glasses could be made).7-9 From this experimental evidence, a kinetic phase diagram was constructed, depicting Tgel as a function of the effective volume fraction of the soft spheres (φeff), which is basically the reduced concentration c/c*, and illustrating the solidification upon heating. Very recently, we demonstrated that the choice of solvent is crucial for this transition, because it relates to the different amount of star swelling (at the same temperature), and proposed a critical soft sphere close packing volume fraction (φc) separating temperature-induced from concentrationinduced glasslike gelation.8 In addition, we showed that the effective solvent quality can be manipulated by using an athermal solvent and adding, for example, linear homopolymers (same chemical species as the stars) of varying molecular weight and/or concentration.10 In that case, it was found that up to a certain molecular weight the addition of linear chains reduces the modulus of a soft colloidal star gel and eventually leads to melting, a manifestation of polymer-mediated star depletion; this (5) Likos, C. N. et al. Phys. Rev. Lett. 1998, 80, 4450. (6) Dawson, K. A. Curr. Opin. Colloid Interface Sci. 2002, 7, 218. (7) Kapnistos, M. et al. Phys. Rev. Lett. 2000, 85, 4072. Loppinet, B. et al. Macromolecules 2001, 34, 8216. (8) Stiakakis, E. et al. Phys. Rev. E 2002, 66, 051804. (9) Puertas, A. M. et al. Phys. Rev. Lett. 2002, 88, 098301. Bonn, D. et al. Langmuir 1999, 15, 7534. Segre et al. Phys. Rev. Lett. 2001, 86, 6042. Foffi, G. et al. Phys. Rev. Lett. 2003, 90, 238301. (10) Stiakakis, E. et al. Phys. Rev. Lett. 2002, 89, 208302.
10.1021/la034223p CCC: $25.00 © 2003 American Chemical Society Published on Web 07/11/2003
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shows analogies to similar phenomena observed recently with hard colloid-polymer mixtures11a and hard microgel spheres.11b,c Eventually, at very high molecular weights, bridging flocculation phenomena12 give rise to re-entrant jamming. To summarize, two demonstrated promising avenues for manipulating the kinetic arrest of ultrasoft spherical colloids are the temperature and the addition of (linear) polymer, both influencing effectively the quality of the solvent. In this paper we combine, in fact, these two routes and examine the reversible thermal jamming of crowded solutions of colloidal stars in a linear polymer solution in decane. We show that the choice of the linear polymer molecular weight has a huge impact on this transition, as low molecular weight polymers can penetrate the stars and swell them (effective good solvents) whereas high molecular weight polymers effectively reduce the quality of the solvent. We present the experimental details in section II and the results along with a relevant interpretation and discussion in section III. Finally, the main conclusions are summarized in section IV. II. Experimental Section Materials. The synthesis of well-defined multiarm star 1,4-polybutadienes based on chlorosilane coupling chemistry is described in detail elsewhere.3a In this work we used regular stars with nominal functionality f ) 128 and nominal arm molecular weights 80 000 g/mol (actual values are 122 and 72 100 g/mol, respectively), coded as 12 880.3a We used mixtures of this star with monodisperse (Mw/Mn 0 which increased with temperature) for 1,4-polybutadiene, followed by gentle stirring at 20 °C for at least 8 h. A small amount (0.1 wt %) of antioxidant (4-methyl-2,6-di-tert-butylphenol) was added to reduce the risk of degradation. Methods. A Rheometric Scientific ARES-HR sensitive controlled strain rheometer was utilized with a force rebalance transducer 100FRTN1 in the parallel plate geometry (diameter 25 mm, sample gap about 1 mm). A homemade solvent trap fixture was used to reduce decane evaporation at higher temperatures. Temperature control (11) (a) Pham, K. N. et al. Science 2002, 296, 104. (b) Bartsch, E. et al. J. Non-Cryst. Solids 2002, 307-310, 802. (c) Eckert, T.; Bartsch, E. Phys. Rev. Lett. 2002, 89, 125701. (12) Hiemenz, P. C.; Rajagopalan, R. Principles of colloid and surface chemistry, 3rd ed.; Marcel Dekker: New York, 1997. Otsubo, Y.; Umeya, K. J. Rheol. 1984, 28, 95. Swenson, J. et al. Phys. Rev. Lett. 1998, 81, 5840. (13) Roovers, J. Polym. J. 1986, 18, 153. (14) Daoud, M.; Cotton, J. P. J. Phys. (Paris) 1982, 43, 531. (15) Willner, L. et al. Macromolecules 1994, 27, 3821. Likos, C. N. et al. Phys. Rev. E. 1998, 58, 6299. (16) Witten, T. A. et al. Europhys. Lett. 1986, 2, 137. Richter, D. et al. J. Phys. IV 1993, C8, 3. (17) Watzlawek, M. et al. Phys. Rev. Lett. 1999, 82, 5289. (18) Seghrouchni, R. et al. Europhys. Lett. 1998, 42, 271. Semenov, A. N. et al. Langmuir 1999, 15, 358. Fleischer, G. et al. Physica A 2000, 280, 266.
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Figure 1. Dynamic frequency sweeps of G′ (closed symbols) and G′′ (open symbols) for 12 880 at 25 °C and constant concentration c12 880 ) 5.2 wt % in three different solvents: decane, 12 880 (2), decane/linear 1,4-polybutadiene 1000 g/mol, 12 880/1K ([), and decane/linear 1,4-polybutadiene 165 000 g/mol, 12 880/165K (b). The linear concentration was 1.4 wt %.
in the range of (0.1 °C was achieved via a recirculating ethylene glycol/water mixture. Measurements included dynamic frequency sweeps and temperature ramps in the linear viscoelastic regime (to determine the gelation temperature), dynamic strain sweeps (to establish the limits of the linear viscoelastic response), and dynamic time sweeps (to ensure the time stability of the gels). The effective hydrodynamic radii of the star polymer (in dilute solution) in different solvents and temperatures were measured with dynamic light scattering by utilizing an ALV goniometer setup and an ADLAS Nd:YAG laser operating at λ ) 532 nm. The time autocorrelation function of the scattered intensity G(q,t) was determined with the aid of an ALV-5000/E fast multi-τ correlator in the time range 10-7-103 s. The measurement consisted of obtaining the intermediate scattering (field) function C(q,t) ) [(G(q,t) - 1)/f*]1/2 in the polarized (VV) geometry (concentration fluctuations), where f* is an instrumental factor relating to the coherence area and q ) (4πn/λ)sin(θ/2) is the scattering wavevector, with n being the refractive index of the solvent and θ the scattering angle.19 The equivalent hydrodynamic radius was extracted from the measured diffusion coefficient assuming validity of the StokesEinstein relation, Rh ) kT/6πηD (k being Boltzmann’s constant and η the solvent viscosity), for spherical objects; here, D ) Γ/q2 is the diffusion coefficient which is found to be q-independent (Γ is the measured relaxation rate). III. Results and Discussion Figure 1 depicts the effects of added linear chains on the linear viscoelastic spectra of 12 880 solutions in decane at 25 °C and constant star concentration (c12 880 ) 5.2 wt %). In fact, at this temperature the pure star exhibits a gellike behavior with both the storage (G′) and loss (G′′) moduli exhibiting a very weak frequency dependence and G′ > G′′ over more than 3 decades in frequency.7,8,20 Upon adding small linear chains (1K), the gel persists and actually becomes slightly stronger at the same temperature and star concentration. However, the addition of larger linear chains (165K) has a striking effect of breaking (19) Berne, B. J.; Pecora, R. Dynamic light scattering; Wiley: New York, 1976. (20) Sato, T. et al. Macromolecules 2000, 33, 1686. Winter, H. H.; Mours, M. Adv. Polym. Sci. 1997, 134, 165. Shay, J. S. et al. J. Rheol. 2001, 45, 913. Zhao, Y. et al. Macromolecules 2003, 36, 855.
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Figure 2. Dynamic frequency sweeps of G′ (closed symbols) and G′′ (open symbols) for 3.9 wt % 12 880 in the mixture decane/ linear 1,4-polybutadiene 1000 g/mol, C10/1K (linear polymer concentration was clinear ) 1.4 wt %), at different temperatures: 7 °C (right-pointing-triangle), 10 °C (b), 15 °C (1), 20 °C (9), 30 °C ([), and 40 °C (2). (Inset) For the same system, the temperature evolution of zero-shear viscosity (0) in the liquid regime and plateau modulus (O) in the solid regime are shown. The vertical line indicates the gelation temperature. The dotted lines are drawn to guide the eye.
the gel and yielding a Newtonian liquid, again under otherwise unchanged conditions. Bearing in mind the recently studied behavior of linear chains in star polymer gels in athermal solvents,10 we propose here a mechanism that has the same origin, i.e., the osmotic pressure due to the additive polymer. Actually, the small chains can penetrate the stars and swell them (provided that the linear chain (Nlinear) and star arm (Na) degrees of polymerizations satisfy the relation Nlinear , Na1/2),21 thus in effect enhancing the solvent quality for the star (lineardecane versus decane); the swollen stars exhibit very soft interaction potential.22 On the other hand, the large linear chains cannot penetrate the stars of comparable or smaller arm length, due to the huge entropic penalty23 and due to osmotic pressure they yield shrinking of the stars (in other words, they effectively reduce the solvent quality for the stars and thus the interaction potential), eventually causing a melting of the gel. In that case, the shrunk stars exhibit an interaction potential approaching hard-sphere behavior.23 These soft-sphere-linear polymer interactions have been discussed in the melt state as well.24 The limit of very high linear chain molecular weight (with bridging flocculation effects) has not been considered in this work. The effects of temperature on a star-linear polymer mixture are evidenced in Figure 2, which depicts dynamic frequency sweeps of the mixture 12 880/1K (linear polymer concentration was clinear ) 1.4 wt %) in decane at constant star concentration (c12 880 ) 3.9 wt %) and different temperatures. It is observed that at low temperatures the system is liquid and from 7 to 10 °C there is virtually no change in its rheological behavior. Then, at 15 °C the sample still exhibits a liquidlike response but with a slight (21) deGennes, P. G. Scaling concepts in polymer physics; Cornell University Press: New York, 1979. (22) Note that the case of star-linear polymer mixtures in athermal solvent considered recently (ref 10), where the addition of small linear chains yielded a reduction of the modulus of the gel, is quite different as Nlinear was comparable to Na1/2 and in addition the effective volume fraction of the star was higher. (23) Leibler, L.; Pincus, P. A. Macromolecules 1984, 17, 2922. Leibler, L. et al. J. Chem. Phys. 1983, 79, 3550. Gay, C.; Raphael, E. J. Phys. II Fr. 1996, 6, 587. (24) Gohr, K.; Schaertl, W. Macromolecules 2000, 33, 2129. Gohr, K. et al. Macromolecules 1999, 32, 7156. Miros, A. et al. J. Rheol. 2003, 47, 163.
Figure 3. (a) Kinetic phase diagram of colloidal star polymer 12880 depicting the gelation temperature, Tgel, as a function of the star concentration, c12 880, in three different solvent environments: tetradecane, C14 (0), decane, C10 (2), and a mixture of decane and linear 1,4-polybutadiene of molecular weight 1000 g/mol, C10/1K (O) at constant concentration clinear ) 1.4 wt %. (b) Tgel as a function of the total polymer (star and linear) concentration, cpolymer, in decane (2) and decane/linear 1000 g/mol mixture, C10/1K (O). Lines are drawn to guide the eye. (c) Tgel as a function of the effective volume fraction (φeff) for 12 880 in the three solvents, C10, C14, and C10/1K; same symbols as in part a. Lines are drawn to guide the eye. Vertical arrow indicates the critical volume fraction, φc (see text).
enhancement of the loss modulus (viscosity) and a weaker increase of the elastic modulus. As the temperature increases to 20 °C, the sample solidifies and exhibits the rheological signature of a reversible soft solid (we call it gel, but it is essentially a kinetically arrested state that could be termed soft glass as well).7,8,10 Further increase of temperature (up to 40 °C here) yields a stronger gel. This behavior also can be observed in the temperature dependencies of the zero shear viscosity (η0) of the liquid and plateau modulus of the gel (G′), which are depicted in the inset of Figure 2. By using the combination of dynamic frequency sweeps at different temperatures and dynamic temperature ramps at different frequencies, one can unambiguously determine the jamming transition temperature of different mixtures (thereafter called gelation temperature, Tgel), as already established in the literature.7,8 In Figure 3a we present the Tgel of different 12 880/1K mixtures in decane for different concentrations of 12 880, while keeping a constant linear polymer concentration clinear ) 1.4 wt % (thus the solvent C10/1K is exactly the same for all star solutions
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considered).25 For comparison, this figure includes also the Tgel data for 12 880 in neat decane7 and tetradecane.8 The data strongly indicate that the addition of the small linear chains reduces the Tgel; this reduction is smaller as c12 880 increases, but this may relate to the fact that eventually at high c12 880 the Tgel should be independent of c12 880 (as it has been observed for 12 880 in tetradecane).8 This result is a manifestation of the improvement of solvent quality upon addition of small linear chains which can penetrate the stars and consequently swell them. In fact, looking at a concentration of c12 880 = 4.5 wt % in Figure 3a, the effect of solvent quality on Tgel is remarkable: the highest Tgel is exhibited by the poorest solvent, tetradecane, and as the solvent quality improves, Tgel drops substantially (about 30 °C in decane and another 20 °C in the decane/linear polymer mixture). If we consider the total polymer (star and linear chains) concentration in decane, cpolymer instead of the star c12 880 only, we obtain the phase diagram of Figure 3b. It suggests that the linear chains are not as efficient in jamming as the colloidal stars alone; this observation, which is actually true at higher concentrations, is not surprising given the explanation of the phenomenon, which is based on the excluded volume interactions on the star scale.7,8 It is further noted that the apparent coincidence of the star and star-linear mixture data at concentrations cpolymer < 5% reflects the effects of the added linear chains in improving the solvent quality for the stars; for example, virtually the same Tgel ≈ 34 °C is exhibited by a star solution 12 880 in C10 (c12 880 ) 4.5 wt %) and a star-linear mixture 12 880 in C10/1K with the same total polymer concentration cpolymer ) 4.5 wt %, which however corresponds to lower actual star concentration (c12 880 ) 3.4 wt %). An attempt to obtain a master kinetic phase diagram is represented in Figure 3c, which depicts Tgel as a function of the effective volume fraction, φeff. This quantity is the volume fraction of the stars considered as hard spheres of radius Rh, the latter referring to 20 °C, in the temperature-independent region;26 it was determined as the reduced concentration c/c*, where c* ) 3fMa/(4πNARh3) and NA is Avogadro’s number.27,28 The very limited data available (due to limited availability of the particular sample studied) seem to follow a general trend, where Tgel decreases with φeff; then at a critical value of the volume fraction, φc (a possibly universal value of about 1.05), Tgel exhibits a sharp drop, and eventually at higher φeff values it levels off. The high-φeff values of Tgel differ in C14 and the other solvents for reasons attributed to solvent quality and packing of these soft spheres. Whereas we recognize that only the C14 data are truly unambiguous and we cannot draw definite conclusions at this point, the message from this plot might have significant implications: It provides a hint that this kind of data reduction might be meaningful for distinguishing different classes of soft solids, for instance, soft glasses and soft gels. Testing the validity of this idea requires a systematic study with different systems, which is beyond the scope of the present work.29 (25) It is noted that in the determination of Tgel we considered steadystate conditions, but the details of the gelation kinetics and the related hysteresis upon cooling were not considered in detail in this work. These issues are discussed in ref 7. (26) This is done in order to account, in this plot, for the effect of swelling with increasing temperature. If, alternatively, the Rh was taken at Tgel, the swelling effect is absorbed in the parameter φeff(Tgel), and thus the ratio Tgel/φeff(Tgel) is a constant number. These issues are discussed in ref 8. (27) Roovers, J. Macromolecules 1994, 27, 5359. (28) Note that in this consideration the small change of Rh at high star concentrations (ref 15), which slightly affects the value of φeff, was not taken into account.
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Figure 4. Temperature dependence of the hydrodynamic radius, Rh, of 12 880 star in solutions of linear 1,4-polybutadienes in decane at different molecular weights: 1000 g/mol (b) and 165 000 g/mol (2). The star concentrations are 0.015 and 0.010 wt %, whereas the linear polymer concentrations are 1.4 and 1.1 wt %, respectively. Also shown in this plot are the Rh(T) data for 12 880 in net decane (0) and tetradecane (O) as well as the limiting values for athermal solvent cyclohexane (4, measured at 25 °C), and theta-solvent dioxane (], measured at 26.5 °C).
To independently check the suggestion of solvent-quality enhancement upon addition of linear homopolymer chains, we measured the hydrodynamic radius (Rh) of 12 880 in a mixture of decane and linear homopolymer of 1000 g/mol (clinear ) 1.4 wt %) at concentration c12 880 ) 0.015 wt % as function of temperature. The results are depicted in Figure 4 along with the Rh(T) data of 12 880 in the other two solvents considered, namely, decane and tetradecane (the case of 12 880/165K illustrated in this figure is discussed below). Also in this figure two limiting cases are shown, the upper Rh limit for a nearly athermal solvent, cyclohexane (here measured at 25 °C), and the lower one for a theta solvent for polybutadiene, dioxane (at 26.5 °C). It is clear that the C10/1K mixture is a better solvent for the polybutadiene stars compared to neat tetradecane and decane, as implied by the larger Rh. At the same time, this mixture is still an intermediate quality solvent, as judged from the swelling of the stars with increasing temperature; yet beyond 35 °C, Rh seems to approach the athermal limit (plateau). A natural question that arises at this point relates to the effect of linear polymer molecular weight. To address it, we replaced the small linear chains of 1000 g/mol with chains having molecular weight of 165 000 g/mol, about the span molecular weight of the star. As already mentioned, in such a case we expect impenetrability in the star, shrinking of the star, and eventually depletion.10,23 Figure 5 depicts a systematic evolution of the linear viscoelastic spectra of the 12 880/165K mixture (clinear ) 1.4 wt %, c12 880 ) 5.2 wt %) in decane with increasing temperature. We see that whereas increasing the temperature has an appreciable effect on the star-linear mixture, it does not yield a gel within the temperature range investigated; nevertheless, it is evident that for the same frequency, say 10 rad/s in Figure 5, heating the mixture from 25 to 40 °C yields a dramatic enhancement of the moduli (about 4 decades for G′ and over 2 decades for G′′). Moreover, whereas at 25 °C the mixture behaves like a Newtonian liquid, at 40 °C its rheological signature (29) Ozon, F. et al. Unpublished data.
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Figure 5. Dynamic frequency sweeps of G′ (closed symbols) and G′′ (open symbols) for 5.2 wt % 12880 in the mixture decane/ linear 1,4-polybutadiene 165 000 g/mol, C10/165K (the linear polymer concentration was 1.4 wt %), at different temperatures: 25 (b), 30 (2), 35 ([), and 40 °C (1).
indicates a viscoelastic liquid system with entanglements (network forming interactions). Worth noting is the lowfrequency response at this temperature (below 2 rad/s), which is characterized by nearly parallel G′ and G′′, implying that the system approaches a critical gel behavior.20 It is thus very likely that this mixture would gel at higher temperatures. However, compared to the other solution (12 880 in C10/1K) under the same conditions, the moduli in the present system are lower by orders of magnitude (as already discussed above with respect to Figure 1). Moreover, the point made here should be clear, i.e., in the presence of the high molecular weight linear polymers, the stars tend to shrink and/or loose their starstar connectivity, meaning that a lot of thermal energy is needed to swell them sufficiently in order to (re)connect and form gels. This scenario is in fact supported by the Rh(T) data of 12 880 (clinear ) 0.01 wt %) in C10/165K (clinear ) 1.1 wt %) shown in Figure 4, which indicates that C10/165K is the lowest quality solvent here, even below the neat tetradecane. Therefore, the C10/165K mixture is a much worse solvent than C10/1K, yielding reduced moduli and shifting the Tgel to much higher values, above the Tgel values of 12 880 in C14 (e.g., above 60 °C for 5.2 wt % 12880).8 The latter statement, i.e., the fact that increasing the molecular weight of the added linear polymer yields star shrinkage, needs some further elaboration, especially in view of ref 10, where it was argued that the addition of linear polymers to star gels yields melting via a depletion mechanism. First, the star-linear polymer mixture investigated here exhibits sharp differences from that of ref 10, in particular: (i) The present work involves solvent of reduced quality compared to the athermal solvent (toluene) of ref 10. It is noted that solvent quality is crucial as it affects not only the conformations of the stars (collapsed vs swollen), but also all three types of interactions (star-star, star-chain, and chain-chain). Depletion interactions are very sensitive to all three of them, with the important parameter being the so-called “non-additivity” of the interactions.30 (ii) The size ratio star-linear Rh’s is different as the present star has Rh ) 57.6 nm and that of ref 10 Rh ) 63 nm (both measured in the same athermal solvent);22 yet different size ratios have different (30) In fact, depending on the sign of the nonadditivity parameter, depletion interactions can turn from attractive to repulsive,3d bringing about a host of diverse phenomenology that can sensitively depend on solvent conditions.
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effects on the depletion interactions. As a matter of fact, the latter are negligible for very small size ratios and grow for larger ones. (iii) Different star concentrations and thus c/c* were used. (iv) In ref 10 we used the irregular 267-arm star, whereas in the current work we used a regular 128-arm star. Second and most importantly, we emphasize that whereas shrinkage (invoked in this work) and depletion (discussed in ref 10) are two different mechanisms, they do possess the same origin (osmotic pressure from the additive, i.e., the linear polymer). Thus, depletion and shrinkage might have a common origin from which they emanate, but they still remain distinct. In fact, depletion is unavoidable in mixtures of small and large objects (such as the current mixture considered),31 whereas, on the other hand, shrinkage is not necessary. Therefore, both mechanisms can be operative in mixtures of colloidal stars and linear chains, and in this respect the present work complements ref 10 and together they provide a complete picture of the osmotic pressure-induced phenomena in such systems and the implications in their properties.32 In fact, the shrinkage is important as it is the manifestation of the difference between hard spheres (no shrinkage) and soft spheres. IV. Concluding Remarks We have demonstrated that the addition of linear homopolymer chains to dense solutions of colloidal star polymers in a marginal solvent dramatically influences their kinetic arrest upon heating. The nature of this influence depends on the molecular weight of the added polymer and, in particular, its relation with respect to that of the star arm. More specifically, for the thermal jamming phenomenon investigated, if the linear chain molecular weight is much smaller than the star arm molecular weight, penetration of the linear polymers into the stars takes place and consequently the stars swell (the linear polymer solution acts effectively as a solvent of enhanced quality for the stars) and the jamming is facilitated. Tgel drops for a given star concentration. On the other hand, if the linear chain molecular weight exceeds that of the star arm, the polymers cannot penetrate the stars. Instead, due to the osmotic pressure (from the linear polymers), the stars shrink and the mixture exhibits liquidlike behavior over a wide range of star concentrations and temperatures. In that case, the linear polymer solution acts effectively as a reduced quality solvent for the stars. These results could be used as alternative possibilities for controlling the rheology of ultrasoft colloids. Acknowledgment. J.R. acknowledges the hospitality and support of FO.R.T.H. We thank C. N. Likos for helpful discussions. Partial support from the EU (grant HPRNCT-2000-00017) and the Greek Ministry of Education (grant 1090-Applied Molecular Spectroscopy) is gratefully acknowledged. LA034223P (31) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. Hunter, R. J. Foundations of colloid science, 2nd ed.; Oxford: New York, 2001. Poon, W. C. K. et al. Philos. Trans. R. Soc. London A 2001, 359, 897. (32) Actually, in athermal solvent conditions the self-avoidance of the crowded chains in the colloidal stars is strong enough that the addition of linear chains and the osmotic pressure they exert yields a rather small shrinkage of the stars, which may not be as significant as in solvents of intermediate quality where the excluded volume interactions between the chains are not so strong. A dynamic light scattering study underway (Stiakakis, E. et al. Manuscript in preparation, 2003) indicates that both effects are present: the shrikange is present at lower linear polymer concentrations, and at higher ones it is overtaken by the inevitable depletion mechanism.
