Signatures of Nonergodicity Transition in a Soft Colloidal System

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Signatures of Nonergodicity Transition in a Soft Colloidal System Florian Ozon,† George Petekidis,† and Dimitris Vlassopoulos*,†,‡ Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas (FO.R.T.H.), Heraklion, Crete, Greece, and Department of Materials Science and Technology, UniVersity of Crete, Heraklion, Crete, Greece

We have investigated the dynamics of an ultrasoft colloidal star suspension over a wide concentration range with the aim at exploring its liquid-to-solid transition. Whereas dynamic light scattering reveals a nonergodic plateau in the intermediate scattering function when the suspension solidifies macroscopically, qualitatively similar to the hard-sphere analogue, the rheological response seems richer; although, in the ergodic regime, the star suspension relaxes via a fast cooperative and a slow self-diffusion process, its corresponding rheological response is characterized by an almost self-similar behavior resembling that of a weak gel, and eventually, at higher volume fractions, it conforms to the glassy rheological response with a strong, frequency-independent storage modulus and a weakly frequency-dependent loss modulus. The implication is that the liquid-to-glass transition in these ultrasoft colloids occurs via an extended intermediate self-similar structural star rearrangement with a frequency-independent loss angle, accompanied by the emergence of a weak slow mode in the intermediate scattering function. The significant polymeric layer of these systems should be responsible for this behavior. I. Introduction In the past decade, the field of colloidal glasses and gels has received much attention, because of the scientific challenges related to the glass-transition phenomenon as well as the potential technological applications emerging from the ability to control the flow of suspensions.1,2 In an attempt to classify the behavior of soft systems exhibiting a phenomenologically similar behavior with respect to the loss of their ability to flow, the so-called “jamming phase diagram” was proposed;3 although this term includes systems that become arrested with and without an imposed flow field, it underlines the need to understand fundamentals of the liquid-to-solid transition in soft systems and, in particular (for the present contribution), colloids. A specific problem that is quite generic in colloidal systems (but is not limited to colloids) is that of the transition from a liquid state to a solid state in a system at rest, when the volume fraction of particles increases. Whereas this is usually associated with a glass transition, it could well be a gelation transition, because their phenomenology is very similar, with their main differences being the volume fraction (much higher in the former case) and, at a more microscopic level, the nature of the particle-particle interactions (repulsive and attractive, respectively).4-6 To this end, significant progress has been made in the last 15 years on the experimental front, primarily with regard to hard-sphere colloids and the use of model colloidpolymer mixtures for tuning the particle-particle interactions, as well as on the theoretical side, using the mode coupling approximation.7 The key finding is that the liquid-to-solid transition is accompanied by a nonrelaxing intermediate scattering function in dynamic light scattering (DLS) measurements, often called the “long-time nonergodic plateau”,7,8 and a similarly nonrelaxing mechanical spectrum, characterized by an almost-plateau storage modulus (G′) and a weakly frequencydependent loss modulus (G′′) in small amplitude oscillatory * To whom correspondence should be addressed. Tel.: +30 2810 391469. Fax: +30 2810 391305. E-mail: [email protected]. † FO.R.T.H., Institute of Electronic Structure and Laser. ‡ University of Crete.

shear measurements.9 Extensive dynamic and steady rheological measurements have been reported for hard-sphere or almosthard-sphere systems,9-13 as well as, more recently, softer coreshell or microgel particles,14,15 diblock micelles,16 and attractive colloids.17 Despite all this progress, however, the effects of interactions on the rheological behavior of soft colloids have not been fully explored and understood yet. Therefore, it is interesting to investigate the effects of softness (polymeric coat of significant size) on such liquid-solid transitions and, in particular, to examine the respective nonergodic behavior measured by DLS and, at the same time, its reflection on the rheological properties of the soft colloidal suspension. Furthermore, fragmental experimental information on model ultrasoft colloids (see below) vitrified upon heating via increase of their effective volume fraction18 suggests a great sensitivity of rheology to the approach of the glass transition and renders such a study timely and useful. A limiting case of soft colloids are the so-called colloidal star or multiarm star polymers, i.e., stars with large number of arms f (functionality), which have emerged in the past decade as a novel class of model soft materials that interpolate between linear polymeric chains and hard colloids;19-23 the former case corresponds to f ) 1 or 2 and the latter case corresponds to high functionalities (f f ∞). They are characterized by a nonuniform monomer density profile (see below) and can be thought of as ultrasoft colloidal spheres with a very small deformable core and a corona consisting of grafted chains (arms).23-25 The interplay of polymeric (arms) and colloidal (overall sphere) features in these systems reflects the wide range of alternatives for designing and controlling soft materials with desired properties. A wide-range effective weak repulsive potential U(r) was proposed for describing the interaction between two stars:23-25 U(r) ) kT

{

(for r e σ) (σr ) + (1 + x2f) ] xf(r - σ) xf σ (for r > σ) 1 + ) ( ) exp[2 r 2σ ]

[ (

-1

/18f 3/2 -ln

5

5

/18f 3/2

-1

10.1021/ie051373h CCC: $33.50 © 2006 American Chemical Society Published on Web 04/08/2006

(1)

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where σ is the corona diameter (e.g., σ ∝ f1/5Na3/5 for good solvents, Na being the arm degree of polymerization). The key concept is that, for high functionality, these systems are virtually spherical objects exhibiting a Yukawa type of interaction at long distances, typical for sterically stabilized colloids, whereas, at short distances, they feel a strong logarithmic repulsion. The interactions are tuned by the number and size of the arms. In the limit of low functionality, the stars resemble polymer coils, whereas for high functionality, they behave almost as hard spheres. Two important properties of these systems that relate to their inherent softness have been identified recently: (i) their already mentioned reversible thermal vitrification,18 where heating the star suspension yields swelling, thus enhancement of the effective volume fraction and, eventually, a liquid-to-solid transition; and (ii) the depletion effect of added linear polymer on soft star glasses, where the osmotic forces induce melting.26 Therefore, it seems possible to tune the response of these model systems at will, from liquid to solid. Consequently, a natural question relates to the signature of the various kinetic states and the possibility of using them to characterize these kinetic transitions. This is the scope of this paper; in particular, we focus on one soft colloidal suspension in an athermal solvent, and we examine its rheological and DLS response with increasing volume fraction toward and within the kinetically frustrated state regime. The paper is organized as follows: after this introduction, the materials and techniques used are briefly presented in section II. The experimental results then are shown and discussed in section III, and the main conclusions are summarized in section IV. Before proceeding, however, we summarize below some experimental results that constitute the background of this work. The dynamics of interacting star polymers was explored using DLS, and three relaxation modes were probed in the semidilute regime:19 (i) the fast cooperative diffusion, which is characteristic of the polymeric nature of the stars (partly interpenetrating arms); (ii) the self-diffusion of the stars detected through the refractive index contrast induced by the small size polydispersity of the stars, and confirmed by independent pulsed-field gradient NMR measurements; and (iii) the structural relaxation, which corresponds to rearrangements of the ordered stars (this particular mode is barely observed in this work however, because of the small size of the stars used, as explained below). These observations were rationalized by a mean field theoretical approach.19 The fast cooperative diffusion exhibited a stronger concentration dependence, compared to the linear chains, the deviation being sharper for the intensity. The slow self-diffusion mode was significantly slowed and its intensity weakened with concentration. Finally, the intermediate structural mode showed an intensity and time that increased with the scattering wave vector, q, bringing analogies to the structure factor S(q) of hardsphere colloids at high volume fractions4,27 and dense micelles.28 All these measurements were performed on ergodic samples, and thus the behavior at higher concentrations, where the suspensions become nonergodic, remains an open question. Rheological measurements were conducted on crowded solutions of colloidal star polymers; temperature-induced and concentration-induced glasslike transitions were observed for an effective volume fraction, respectively below and above a critical “soft sphere close packing” volume fraction.18,26,29 The phenomenon of reversible liquid-to-solid transition upon heating was attributed to the slow formation of clusters (scattering

entities with large correlation length) causing a kinetic arrest of the swollen interpenetrating stars at high temperature, and could be described in a coarse-grained fashion by accounting for the effect of temperature-induced swelling of the star on the star-star pair potential.30 The reported dramatic change of both the transition temperature and the respective plateau storage modulus for a 128-arm star over a very small concentration range for different solvents indicated that, with increasing concentration, the ability to form glassy states is enhanced, and also there is a transition from softer to stronger glasses. Here, we focus on the concentration-induced glasslike transition and we present both DLS and rheological measurements from semidilute to more-concentrated colloidal star polymer suspensions. II. Experimental Section A. Materials. A multiarm star 1,4-polybutadiene (267 arms) with an arm molecular weight of Ma ) 4490 g/mol, coded as LS2, was used. Its synthesis is based on the hydrosilylation of a short 1,2-polybutadiene backbone chain with HS(CH3)Cl2, yielding two coupling sites per monomer unit; the latter were substituted with 1,4-polybutadiene via the addition of poly(butadienyl)lithium.21 On average, four out of five monomer segments are substituted, and the other segments give some flexibility to the backbone. Although star polymers of this type are irregular, because of the absence of a truly spherical dendritic core, small-angle neutron scattering (SANS) studies have showed that these systems can be considered to have a virtually spherical shape.31 For the DLS experiments, the stars were mixed with cyclohexane (chosen because of its high refractive index contrast to polybutadiene and very good solvent quality19) and, for rheological measurements, with toluene (which is nearly as good as cyclohexane,19,28,31 but is less volatile; thus, it better suited for rheological work). The solutions were, in both cases, gently stirred at 20 °C for at least 8 h and left still for 2 days before use. A small amount (up to 0.1 wt %) of antioxidant (4-methyl2,6-di-tert-butylphenol) was added, to prevent degradation. Using the aforementioned considerations, the dilute solution DLS studies (see below) yield a translational diffusion of D0 ) 1.5 × 10-7 cm2/s and an estimated hydrodynamic radius from the Stokes-Einstein relation,

Rh )

kT ) 16 nm 6πηsD0

where k is the Boltzmann constant, T the temperature, and ηs the viscosity of the solvent. The resulting overlapping concentration (c*) is then obtained from

c* )

Mw (4/3)πRh3NA

) 0.12 g/mL

(where NA is Avogadro’s number); the same value is used for both good solvents cyclohexane and toluene. At this point, it should be noted that, throughout this work, the weight concentration (c) is used to quantify the stars content in suspensions; when needed, the effective volume fraction is used, which is defined as the ratio c/c*. B. Dynamic Light Scattering. The field autocorrelation function g1(q,t) ) [(g2(q,t) - 1)/f*]1/2 is obtained from the experimental intensity autocorrelation function g2(q,t) )

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Figure 1. Field autocorrelation functions of LS2 stars in cyclohexane for a scattering angle θ ) 120°. The concentrations of the different solutions are the following: (b) c ) 0.11c*, (0) c ) 0.51c*, (2) c ) 0.84c*, (]) c ) 1.11c*, (1) c ) 1.49c*, and (4) c ) 2.7c*.

〈I(q,t)I(q,0)〉/〈I(q)〉2 (where f* is the instrumental coherence factor), measured by photon correlation spectroscopy over a broad time range (10-7-102 s).32,33 The scattering wave vector

q)

(4πnλ ) sin(θ2)

(where λ is the laser wavelength in a vacuum, n the solvent refractive index, and θ the scattering angle) ranges from 8.7 × 10-3 nm-1 to 3.3 × 10-2 nm-1. An ALV-5000 full digital correlator was used in conjunction with a Nd:YAG laser at λ ) 532 nm. All measurements were performed at 20 °C. The analysis of g1(q,t) proceeds via the inverse Laplace transformation (ILT), assuming a superposition of exponentials: 33

g1(q,t) )

∫L(ln τ) exp(- τt ) d ln τ

which determines a continuous spectrum of relaxation times L(ln τ). The characteristic relaxation times (τ) correspond to the maximum values of L(ln τ). The ILT, which was realized using the program CONTIN,34 allowed the determination of the relaxation time and intensity of the different modes, as revealed by the distribution of relaxation times L(ln τ). C. Linear Rheology. A strain-controlled Rheometric Scientific Model ARES-HR rheometer was utilized with a force rebalance transducer (Model 100FRTN1) in the parallel plate geometry (with diameters of 25 or 8 mm, and a sample gap of ∼0.5 mm). All experiments were performed at 20 °C and temperature control within (0.1 °C was achieved via a recirculating ethylene glycol/water mixture. Measurements included dynamic frequency sweeps, dynamic strain sweeps (to determine the limits of linear viscoelastic response), and dynamic time sweeps (to establish steady-state measurement conditions). III. Results and Discussion A. Dynamic Light Scattering Measurements. Figure 1 depicts the behavior of the field autocorrelation function of LS2 stars for a specific scattering angle (θ ) 120°) and for several concentrations. In the more dilute solution, c ) 0.11c*, one

Figure 2. Reduced diffusive coefficients of the LS2 stars in cyclohexane versus reduced concentration: (9) cooperative diffusion and (b) star selfdiffusion. Dashed line with slope ) 0.77 represents the scaling prediction for linear chains. Inset shows the intensity of the cooperative diffusion of the LS2 stars in cyclohexane versus reduced concentration (denoted with solid square symbols, 9); the solid line in the inset with slope ) -0.3 represents the scaling prediction for linear chains. The inset also shows the intensity of the star self-diffusion of the LS2 stars in cyclohexane versus reduced concentration (denoted by open circle symbols, O); the dashed line with slope ) -1.6 represents the scaling prediction for star polymers (see text).

diffusion process is detected and D0 is recovered. At c ) 0.51c*, a second, slower process appears, and as the concentration increases, this process slows down substantially, with the correlation function still relaxing fully within the experimental time window. Finally, at the highest concentration (c ) 2.7c*), the system exhibits nonergodic behavior (for times smaller than ∼1 s), as shown by the nonzero value plateau reached by the correlation function. In such a situation, to obtain a meaningful intensity autocorrelation function, one must take an ensemble average (i.e., averaging the dynamics at different speckles). For the present purposes and this concentrated star sample, it is sufficient to recognize that the plateau exhibited by g1(t) expresses the arrest of the dynamics: the stars are trapped in cages formed by their neighbors and cannot move freely anymore through the suspension. The reduced diffusive coefficients of the two processes, versus the reduced concentration, are presented in Figure 2. In the range of concentrations plotted in the figure, both processes are determined to be purely diffusive, the rates being q2-dependent. The fast process, which is called the cooperative one, scales with concentration with a power law very similar to that of the semidilute linear chains (0.77).19,35 The deviation predicted (due to the stretching of chains in the near-core region, yielding a slightly stronger dependence)19 is not easily distinguished, apparently because of the small core size of the stars. Furthermore, to detect, with light scattering, the structural mode, which corresponds to the local rearrangements of the densely arranged stars, it is necessary to approach the regime qR ≈ O(1).19 In regard to the LS2 samples of this work where the maximum qR is 0.56, it is evident that the structural mode is not visible here. The other process can be identified with the star selfdiffusion; it shows a strong decrease as the concentration increases, which is linked to the strong increase of the viscosity. The inset of Figure 2 depicts the intensities of the two processes for the ergodic samples. Compared to the good-solvent scaling, (c/c*)-0.3, the cooperative process has a stronger decrease with concentration; this is explained by the star architecture effects.

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Figure 4. Intensity of the self-diffusion versus q for different reduced concentrations of LS2 star polymers in cyclohexane: (9) c ) 0.51c*, (0) c ) 1.11c*, (O ) c ) 1.1c*, (b) c ) 1.49c*,(2) c ) 2.7c*. Inset: The intensity of the star self-diffusion of the LS2 stars in cyclohexane versus q2 for the nonergodic sample. The linear fit of (Is/Itot)-1/2 vs q2 yields ξ.

Figure 3. Field autocorrelation functions of LS2 stars in cyclohexane for two concentrations and for scattering angles θ ) (0) 60°, (b) 90°, (4) 120° and ([) 150°. The inset shows the q-dependence of the plateau value at t ) 0.1 s.

For the star self-diffusion intensity, the scaling is consistent with theoretical predictions:19

Is ≈

(c*c )

-1.6

The field autocorrelation functions at different angles (ranging from 60° to 150°) are plotted in Figure 3 for a semidilute solution (c ) 0.84c*) and for a concentrated one (c ) 2.7c*). In the semidilute case, the sample is ergodic and all the functions g1(t) decay to zero during the experiment duration (100 s), whereas, for the concentrated and nonergodic case, they saturate to a value that can be related to the nonergodicity parameter f(q,∞) of the system.6 The link between the hard and soft suspensions is not straightforward, whereas, in the former case, the two relaxations, called β and R, are associated with the selfdiffusion of the particles, inside and outside the cage; in the latter case, the fast relaxation is affected strongly by the mobility of the polymeric arms in such a way that the two processes may be identified as the faster cooperative diffusion of the star arms and the slower center of mass self-diffusion. Nevertheless, an interesting analogy exists. The scattering intensity of the various processes can be analyzed by examining its dependence on q. For all concentrations, a q-independent cooperative intensity was measured, as anticipated.19,31 The self-diffusion intensity (Is) shown in Figure 4 is also q-independent for the ergodic samples; however, for the nonergodic case, it exhibits a strong increase for low q, apparently implying the presence of large structures (bringing analogies to long-range density fluctuations, resulting in very slow cluster modes11,29,31,36). The typical size of such correlations (ξ) can be estimated to a first approximation from a Debye-

Figure 5. Intensity of the star self-diffusion of the LS2 stars in cyclohexane at q ) 0 versus reduced concentration; the dashed line with slope ) -1.6 represents the scaling prediction for star polymers (see text).

Bueche fit:33

Is(q) )

I0 (1 + q2ξ2)2

for low qξ values (see inset of Figure 4). The value ξ ≈ 66 nm corresponds to ∼4 times the hydrodynamic radius of the LS2 stars. The q-dependence of the nonergodicity plateau is shown in the inset of Figure 3b. Although, in absolute values, it must be affected by the existence of the fast cooperative mode of the polymer arms, its q-dependence should be unaffected because the cooperative mode has a q-independent intensity. Note that similar structures on the order of a few particle radii were also observed in other systems, such as dense attractive colloids;17 on the other hand, even larger structures (tens to hundreds of particle radii) were reported in polyelectrolyte copolymer micelles, although these structures were probably existing under nonequilibrium conditions.37 The intensity in the limit q f 0 (I0) is plotted in Figure 5 for all concentrations investigated. A sharp increase of the intensity of the nonergodic sample is observed, originating from an increase of the intensity of the slow mode, especially at low q values, for which the theory does not hold. This change, which is unambiguous, despite the fact that only one nonergodic sample

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Figure 6. Dynamic frequency sweeps of LS2 stars in toluene: c ) 0.7c* (square symbols), c ) 0.8c* (circles), c ) c* (triangles), and c ) 1.37c* (diamonds). Filled symbols represent data for G′ and the open symbols represent data for G′′.

was available, is both qualitative and quantitative and serves as a means to identify the nonergodic state of a particular sample. B. Rheological Measurements. It is now interesting to examine the rheological signatures of the nonergodicity transition for these soft colloids. Figure 6 depicts the dynamic frequency sweeps of different LS2 stars in toluene. It can be observed that, in the entire concentration range studied (c ) 0.7c*-1.4c*), the storage modulus G′ always exceeds the loss modulus G′′, and, moreover, both exhibit almost identical frequency dependence. This type of behavior is very typical of critical gels38,39 and clearly suggests a self-similar behavior in the sense of a large-scale organization within the sample. From G′ ≈ G′′ ≈ ωn, one can extract the exponent n ) 0.35 for the two lowest concentrations and associate it with some type of fractal dimension in the sample. This type of behavior has not been reported for hard-sphere glasses, to the best of the authors’ knowledge, although a gradual enhancement of moduli (but never with the same slope) was observed as the volume fraction increased toward the glass transition.9 We attribute this selfsimilar behavior to the polymeric nature of the colloidal stars, namely the strong contribution of the interacting, partially interpenetrating arms; the DLS analogue of this seems to be the emergence of a weak slow mode (see Figure 1 and refs 18, 29, and 31), which grows with the volume fraction and eventually results in the nonergodic response. Such a self-similar rheological response has been reported for other soft colloids with a significant corona consisting of grafted polymeric chains, such as block copolymer micelles.39,40 Note that arm relaxation is known to be responsible for such types of self-similar-like behavior in branched polymeric structures, although in the latter case, this does not relate to glass or gelation phenomena.41 As the concentration increases, G′ and G′′ become more separated (reaching about half a decade for the more-concentrated sample studied), and, more importantly, the phenomenology of a colloidal glass is recovered:7,17 G′ is virtually frequencyindependent and G′′ exhibits a weak but unambiguous frequency dependence with a tendency for a weak increase at lower frequencies, reminiscent of the high-frequency tail of a Maxwell model. Such a behavior, which could be described in the framework of the mode coupling approach,7,9,14 has been observed for other colloidal star systems but at larger volume fractions (i.e., stronger glasses) as well as a variety of other

Figure 7. Plateau value of G′ versus reduced concentration of LS2 stars in toluene; the dashed line represents a fit by a power law. Inset shows the typical size (δ) of the cage versus reduced concentration.

soft colloids but not as soft as the stars.11-14 Therefore, glasslike rheological behavior is observed, which is in agreement with the literature. What is interesting, in our opinion, is the rather gradual transition toward the glassy state, via a self-similar type of behavior, and its association with the enhancement of the slow mode in DLS and eventually the transition to nonergodicity. The reason for the occurrence of liquid-like dynamics in a system that behaves rheologicaly as a weak solid is probably related to the unrestricted diffusion of a significant fraction of the stars that do not participate in the interconnected network of clusters at concentrations near c*, as well as to the local dynamics of the star arms. These would be characteristic of the star system (possibly also of other ultrasoft polymerically stabilized particles11-13,15,16) because of interpenetration of the arms, resulting in transient clustering and network formation, which is absent in hard-sphere systems. At even higher concentrations, the number of clusters increase, finally filling the entire space, whereas the low-concentration regions, which allow higher particle mobility between the clusters, disappear, creating a system that resembles a homogeneous glass. To elucidate this gradual rheological transition, the highfrequency plateau value of G′ in Figure 6, hereafter called the plateau modulus (G′plateau) is plotted against the effective volume fraction (φeff) in Figure 7.42 A power-law fit, G′plateau ≈ φeffm, yields an exponent of m ) 5.7. This result compares very favorably with the respective scaling exponents obtained with thermosensitive core-shell microgel particles14 and polymercoated particle suspensions.12 In these works, rheological measurements indicate that the soft particles studied behave much like Brownian hard spheres at low effective volume fractions, exhibiting a solidlike behavior at higher volume fractions, with the value of m ranging between 4 and 8, depending on the cross-link density (of the microgel core). Note that, for less soft hairy particles (with smaller polymeric coat), the behavior of which is more similar to that of hard spheres, the same type of fit gives much larger exponents, depending on the particle softness.11,43 On the other hand, for fractal colloidal gels, G′ scales with a much lower exponent of m ) 3.9.44 Neglecting hydrodynamic interactions,45 the relation between the plateau value of G′ and the particle-pair potential43,46-48 clearly shows the soft behavior of the star polymers, as the close-packing concentration is approached (the same applies to polymer-coated particles12). Furthermore, generally, the power-law exponent m was suggested to correlate to the pair interaction potential of the form U(r) ≈ 1/rn via m )

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1 + n/3.43,48 For the present star system, this yields U(r) ≈ 1/r14.1, which is consistent with the strong logarithmic repulsions of colloidal stars at short distances.25 The inset in Figure 7 illustrates the estimated maximum free excursion δ of a star, before it is caged by neighbors. For this estimation, we used the expression proposed by Cloitre et al.:49

G′plateau )

kT Rhδ2

As the concentration increases, this size decreases from a value close to the hydrodynamic radius, indicating that the typical size scale of the system (mesh in a gel-like system initially and cage size in the glass eventually) becomes smaller and then the gel becomes stronger. The values of δ deduced from G′ were used to obtain an estimate of the nonergodicity parameter f(q,t ) ∞), because 〈∆r2(t ) ∞)〉 ) δ2 and then f(q,t ) ∞) ) exp(-q2δ2/6); in this way, we get values of f(q,t ) ∞) between 0.998 and 0.99 within the q-range of our experiment for the sample with c ) 1.4c*. Such high values were not detected by DLS in the present systems, because of the effect of the cooperative arm diffusion, which causes a decay of the correlation function at short times. As a final note, by comparing Figures 6 and 3, it is clear that, although the DLS data suggest an ergodic system with a slow mode, the rheological data already indicate some type of rearrangements in the system, causing a weak solidlike response. Despite the fact that it was not possible to extend the rheological measurements (because of extremely limited sample availability), it is beyond doubt that a clearly nonergodic sample (e.g., 2.7c*) would exhibit an even stronger glasslike response. However, it is interesting that rheology is extremely sensitive, at least quantitatively, and concerning the sensitive issue of liquid-to-solid transition in this colloidal star system, it seems more sensitive than DLS. IV. Concluding Remarks In this work, we examined the dynamics of an ultrasoft colloidal star suspension over a wide concentration range. The dynamic light scattering (DLS) study demonstrated a clear liquid-solid transition, relative to concentration, which is reflected as a change from an ergodic response to a nonergodic response in the intermediate scattering function. On the other hand, the rheological study seems to suggest that the transition from the Newtonian liquid to the glassy solid behavior occurs gradually, via an extended intermediate self-similar rearrangement of the stars, characterized by a frequency-independent loss angle. This intermediate range seems to be correlated with an emerging weak slow mode in the intermediate scattering function. The softer the particles, the more pronounced the observed behavior, and this behavior should be related to the polymeric nature of the polymer-coated corona. As such, it could serve as an identifying signature of the particle softness; however, more systematic work clearly is needed in this particular direction, before definite conclusions are drawn. At the highest volume fractions, the classical picture of colloidal glass behavior is recovered. Acknowledgment This paper is respectfully dedicated to Professor W. B. Russel, on the occasion of his 60th birthday. We are grateful to J. Roovers for providing the star polymers and for helpful discussions. This work was partly supported by the EU (HUSC

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ReceiVed for reView December 9, 2005 ReVised manuscript receiVed March 2, 2006 Accepted March 9, 2006 IE051373H