Effects of Core Microstructure on Structure and Dynamics of Star

Jul 16, 2014 - Institute of Electronic Structure & Laser, FORTH, Heraklion 70013, ... and Technology, University of Crete, Heraklion 71302, Crete, Gre...
0 downloads 0 Views 483KB Size
Download PDF
Article pubs.acs.org/Macromolecules

Effects of Core Microstructure on Structure and Dynamics of Star Polymer Melts: From Polymeric to Colloidal Response Frank Snijkers,†,‡ Hong Y. Cho,§ Alper Nese,§ Krzysztof Matyjaszewski,§ Wim Pyckhout-Hintzen,∥ and Dimitris Vlassopoulos*,†,⊥ †

Institute of Electronic Structure & Laser, FORTH, Heraklion 70013, Crete, Greece Department of Engineering for Innovation, University of Salento, Lecce 73100, Italy § Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States ∥ Jülich Centre for Neutron Science and Institute for Complex Systems, Forschungszentrum Jülich GmbH, Jülich 52428, Germany ⊥ Department of Materials Science and Technology, University of Crete, Heraklion 71302, Crete, Greece ‡

S Supporting Information *

ABSTRACT: The structure and linear viscoelastic behavior of four different model star polymer melts were investigated experimentally. The star polymers were prepared via different synthetic routes based on atom transfer radical polymerization (ATRP). Stars with small elongated (linear backbone) cores exhibited slight differences in the asymmetry of the core, which however did not affect the rheological properties significantly. The relaxation behavior of these stars with an asymmetric core was well-described by available tube models. On the other hand, stars with large cross-linked cores exhibited a core−shell morphology and their stress relaxation was dominated by a power-law decay over about 8 decades, akin to gel-like soft systems. This behavior reflected their liquid-like ordering and small intercore distances, and bares analogueies to that of interpenetrating soft colloids and microgels. number of arms increases.1,11,12 Furthermore, the stars can be either symmetric with an equal length for each arm or asymmetric with arms of different length.10 Note that stars with equal length of arms but nonspherical cores (which are often termed asymmetric cores) on which the arms are grafted, also exist3,12−14 and will be in fact discussed in this work. Finally, their arms can be flexible or rod-like and hydrophilic or hydrophobic.15 Herein, we prepared symmetric and flexible homoarm stars of poly(butyl acrylate) (PBA) using two different synthetic approaches: “core-first” and “arm-first”. Star polymers with a linear backbone (LB) and with a cross-linked core (CC) were synthesized using “core-first” method with linear ATRP initiators and “arm-first” method with divinylbenzene as a cross-linker, respectively. Even for such flexible homoarm stars, the physical properties (e.g., the spatial organization or the manner in which stress relaxes) can vary dramatically as functions of arm molar mass Ma and arm functionality f (i.e., the number of arms per star).16 Flexible stars with a low functionality (typically f < 30) are well-studied and understood both experimentally and theoretically. They have a Gaussian

I. INTRODUCTION One of the ultimate goals of polymer science is understanding the relation between molecular structure, as determined by the chemical composition and topology, and macroscopic physical properties. The ability to tune rheology by manipulating the molecular structure has been repeatedly shown in the past. One possibility to manipulate the physical properties, and hence design new materials with improved performance, is by modifying the topology of the polymers. Among the various polymeric architectures, star polymers are one of the simplest structures, consisting of multiple linear chains (arms) connected to a central core.1 Star polymers have a wide range of potential application areas from thermoplastic elastomers2 to drug or gene delivery carriers.1 They can be synthesized by various controlled polymerization techniques from anionic1,3 to radical polymerizations such as reversible addition−fragmentation chain transfer (RAFT) polymerization4,5 and atom transfer radical polymerization (ATRP).6−9 In general, there are two synthetic approaches to prepare star polymers: “core-first” and “arm-first”.8 Depending on the polymer arm composition, star polymers can comprise of homoarm with identical arm composition and miktoarm with two or more different arm species.8,10 These various synthetic methods result in different local microstructures,1−4,6−8 which may affect their macroscopic properties, especially when the © XXXX American Chemical Society

Received: April 21, 2014 Revised: July 1, 2014

A

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

Scheme 1. Synthesis of Star Polymers with Two Different Core Types: (A) Stars with a Linear Backbone (LB) Prepared by a “Core-First” Method and (B) Stars with a Cross-Linked Core (CC) Prepared by an “Arm-First” Method

Table 1. Star Copolymers with either a Linear Backbone (LB) or a Cross-linked Core (CC) labela

star composition

Mn,arme (×10−3)

Mn,starf (×10−3)

Mw/Mng

Mn,absol,starh (×10−3)

Mn,absol,star/Mn,star

DParm

fi

LB10b LB20b CC27c CC46d

(PBA240)10-PBiBEA10 (PBA230)20-PBiBEA20 (PBA165)27-P(BA29-co-DVB19) (PBA98)46-P(BA8-co-DVB10)

30.8j 29.5j 21.1 12.5

183.0 251.0 198.5 164.4

1.14 1.15 1.27 1.39

308.0j 590.0j 605.0l 598.0l

1.68 2.35 3.05 3.64

240 230 165 98

10k 20k 27m 46m

a Experimental conditions. b[PBiBEA10 or 20]0/[BA]0/[CuBr]0/[CuBr2]0/[PMDETA]0 = 1/700/0.475/0.025/0.5, 70 °C in anisole (6%). c[EBrP]0/ [BA]0/[DVB]0/[CuBr2]0/[TPMA]0/[Sn(EH)2]0= l/200/24/0.02/0.1/0.4, [BA]0 = 2.33 M, 80 °C in anisole (66%). The temperature was elevated to 100 °C after addition of DVB (at 12 h, 80% BA conversion). d[EBrP]0/[BA]0/[DVB]0/[CuBr]0/[PMDETA]0 = l/120/12/2/2, [BA]0 = 3.25 M, 80 °C in anisole (50%). The temperature was elevated to 100 °C after addition of DVB (at 5 h, 85% BA conversion). eNumber-average molar mass of arm (PBA). fNumber-average molar mass of star, measured with RI detector based on polystyrene standards. gObtained by GPC with RI detector, calibrated with PS standards. hAbsolute molar mass, measured with multiangle laser light scattering (MALLS) detector. iNumber-average value of the number of arms per star. jMolar mass based on 1H NMR. kDP of PBiBEA. lMolar mass obtained by THF GPC with MALLS detector. m Number-average value of the number of arms per star molecule ( f = Mn,absol,star × Armwt %/Mn,arm). Armwt % is the weight fraction of PBA arm in the star polymer.

anisotropic cores on which the arms are grafted. Fragmental evidence in the literature suggests that this does not affect their nearly spherical shape or rheology.12 In this paper, we address these delicate issues. We report on the properties of four different star polymers synthesized with different approaches, albeit always within the ATRP framework. In particular, the cores of these stars differ from those of most other stars reported in the literature. In two cases, the cores are elongated and based on a small linear backbone. In the other two cases, the cores are relatively large and loosely cross-linked, hence the stars can be considered as effective core−shell systems even at intermediate functionalities. We present an experimental investigation of the form factors of the stars in dilute solution in a good solvent, from which models for their bulk behavior may be distilled and the importance of different molecular constitutions can be checked, and their rheological behavior in the melt, thereby highlighting the large effect on (and consequently high tunability of) the rheological properties of the samples due to differences in the internal microstructure.

coil conformation, and in the molten state their stress relaxes independent of functionality, via a combination of arm retraction and thermal constraint release.17,18 These mechanisms are included in contemporary tube models, such as the branch-on-branch (BOB) model, which can accurately describe their linear viscoelasticity.19,20 Inherent in this approach is the theoretical consideration of the core as an effective branch point that does not interfere with the relaxation of the arm. However, upon increasing f, the core cannot be neglected anymore21 and the stars become effectively spherical polymer brushes, i.e., core−shell hybrids16,22 comprising both features of polymer chains and soft colloids. They relax stress via the classic arm response and have slower center-of-mass motion because their neighbors essentially cage them. The caging is an excluded volume effect at the macromolecular size scale and the colloidal aspect of the slow relaxation in the melt is a cooperative process which can resemble a cage escape.23 At the same time, these stars exhibit liquid-like order in the melt.23 There are therefore two reasons why the effective core of a star polymer can be non-negligible and influence its dynamics: (i) bulky core prepared by cross-linking (in our case by divinyl compounds), and (ii) high arm functionality. A general issue of significance of identifying the role of core on the dynamics of stars or grafted particles in general, and more specifically, distinguishing star-like from (block copolymer) micelle-like response.24−28 Related to this point and concerning star polymers, between low-f stars with long arms (e.g., 16 arms, each being at least eight entanglements in size) and high-f “colloidal stars” (i.e., 64 arms or more), there is an intermediate regime where quantifying the interplay of polymeric and colloidal response remains a subtle issue.23,29 Moreover, even for low-f stars, it remains unclear whether the shape of the core (spherical or anisotropic) may affect the star’s structure and dynamics. On the other hand, high-f stars often have

II. MATERIALS AND METHODS II.1. Star Polymer Synthesis. The synthesis of the star polymers is described below and additional details are provided in the Supporting Information. Four types of poly(n-butyl acrylate) (PBA) star polymers were prepared with different core structures, as shown in Scheme 1 (which is drawn out of scale). PBA star polymers with a linear backbone and with a cross-linked core are labeled as LB and CC, respectively. Synthesis of LBs. LBs were prepared by grafting PBA from multifunctional ATRP macroinitiators (poly(2-bromoisobutyryloxyethyl acrylate) (PBiBEA)) according to the previously reported procedure.14 Briefly, PBiBEAs with degree of polymerization (DP) 10 and 20 were prepared by ATRP of trimethylsilyloxyethyl acrylate (HEATMA) and subsequent esterification with 2-bromoisobutyryl bromide to incorporate ATRP initiating groups to each monomeric B

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

unit. LB10 and LB20 star polymers were prepared using the same reaction conditions but different DP of PBiBEA. PBA side chains were grown from the PBiBEA macroinitiators using PMDETA/CuBr catalyst system in anisole at 70 °C. Monomer/initiator ratio of 700/ 1 was used for the synthesis of both LB10 and LB20. LB10 with DP of side chains 240 was prepared by stopping the reaction after 21 h at 33% monomer conversion. LB20 was obtained by stopping the reaction after 26 h at 34% monomer conversion giving DP of side chains 230. Molecular weight and molecular weight distribution analysis results are given in Table 1 and GPC traces for the LB10 and LB20 in Supporting Information, Figure S1. DP values of side chains for each star polymer are theoretical values calculated by monomer conversion from NMR assuming 100% initiation efficiency. PBiBEA is a very good initiator for n-butyl acrylate polymerization which should provide nearly quantitative initiation efficiency even at low conversion values. The initiation efficiency exceeded 87% at as low as 12.3% monomer conversion during a much more sterically congested molecular bottlebrush synthesis previously.30 LBs contained short linear backbones with long side chains. The side chains (PBAs) are much longer (DP ≥ 230) than backbone (DP=10 or 20), resembling stars rather than bottlebrushes (Scheme 1A). As shown in Table 1, LB10 and 20 have roughly equal arm lengths, i.e., nearly same DP, but a different number of arms because of the different length of the star core. With a few exceptions in the case of multiarm stars,3,13 commonly the core of the stars reported in the literature is spherical. Here, the cores are elongated, and an increase in the number of arms implies a slight increase in the length of the core as shown in Scheme 1A. The contraction factor of branched polymer (i.e., star polymer) (g = ⟨Rg,br2⟩/⟨Rg,lin2⟩) has a value less than 1 because the radius of gyration of star polymer is smaller than that of linear polymer with the same molecular weight.31 However, for star-shaped copolymer, it is difficult to prepare a linear analogue of the star copolymer with precisely the same chemical composition. Therefore, the ratio Mn,absol,star/Mn,star (the absolute molecular weight Mn,absol,star is measured with multiangle light scattering and is sensitive to the weight averaging of the stars, whereas the apparent Mn,star is based on linear polystyrene standards; see also Supporting Information) reflects the relative compactness of star polymers.32 A star polymer with a higher Mn,absol,star/Mn,star value should have a more compact structure and correspondingly smaller radius of gyration. Mn,absol,star/Mn,star values for LB10 and LB20 were 1.68 and 2.35, respectively. Thus, LB20 has a more compact structure than LB10. Synthesis of CCs. CCs were prepared via an “arm-f irst” method using either classical ATRP33,34 (Table 1, CC46) or activator regenerated by electron transfer ATRP35,36 (ARGET ATRP) (Table 1, CC27). Both CCs were synthesized in a one-pot process. Instead of the isolation and purification of macroinitiators, the addition of crosslinker at high conversion of monomer produced directly star polymers with a cross-linked core.32 During the polymerization of BA, the monomer conversion was carefully monitored. At the conversion ∼80%, X equimolar amount of N2-bubbled DVB (i.e., X = [DVB]0/ [EBrP]0) was injected to the system. Subsequent copolymerization of injected DVB with remaining BA (∼20%) produced cross-linked core (i.e., poly(BA-co-DVB)). Using this process CC46 with PBA (DP=98) was prepared by classical ATRP (50% anisole solution). The results of BA polymerization are shown in Supporting Information, Figure S2. First-order kinetic plot during the BA polymerization was almost linear until the addition of DVB at 85% BA conversion after 5 h (Figure S2A). The molecular weights increased along with theoretical values preserving narrow molecular weight distributions (Figure S2B). Molecular weights evolution followed by GPC showed smooth molecular weight shifts from linear to star structures (Figure S2C). After the injection of DVB to the system, higher molecular weight was observed, confirming the copolymerization of DVB with remaining BA and formation of cross-linked core of star polymers. The final star polymers were purified by fractionational precipitation using acetone/ hexanes mixture, confirmed by GPC. To prepare star polymers with longer DP of PBA, 50% solution polymerization was used. The high solution viscosity using longer PBA

arms prevented successful star formation (Figure S3). At certain point during the star formation (between 13 and 22.5 h), the gelation was observed by GPC. This might be caused by star−star coupling reaction under the concentrated conditions. To reduce the solution viscosity, the reaction system was diluted from 50% to 66% anisole solution. However, the polymerization was slow (80% BA conversion after 48.5 h) and both the reactivity of macroinitiator and the yield of star were low (Figure S4). To overcome the limitations of star synthesis in diluted system by normal ATRP, the ARGET ATRP-technique was utilized. Stars with longer PBA arms (DP = 165), CC27, were successfully prepared in 66% anisole solution by ARGET ATRP with Sn(EH)2 as a reducing agent. After 12 h, BA conversion reached to 80% and, then N2-bubbled DVB was injected to the system. The results of PBA arm synthesis and star formation are shown in Supporting Information, Figure S5. As shown in Table 1, both CCs have approximately the same total molar mass but different number of arms and hence arm lengths. Concerning cross-linking density, the core of the CC46 is smaller but more densely cross-linked than the core of the CC27. Comparison of Mn,absol,star/Mn,star values indicates that CC46 has a more compact structure than CC27. Dynamic light scattering (DLS) analysis of CC27 and CC46 yields different hydrodynamic diameters Dh = 28.5 and 24.3 nm, respectively, which is consistent with the static measurements from small-angle X-ray scattering (SAXS) discussed below. Recently, similar approach was used to synthesize stars with short, unentangled arms.11 II.2. Small-Angle X-ray Scattering (SAXS). SAXS experiments were carried out on dilute star solutions to assess their form factor. To this end, solutions of 1 wt % of star polymer in the good solvent tetrahydrofuran (THF) were prepared and measured on the NANOSTAR U (Bruker AXS, Germany) equipped with a rotating anode source and operated at 40 kV and 40 mA. The wavelength was monochromatized to the Cu Kα line of 1.54 Å, and the sample− detector distance was 1.06 m. Data were recorded two-dimensionally with a 2D Vantec 2000 detector (xenon gas filled) with a 2048 × 2048 resolution. The transmissions of the samples were determined from absorbance measurements using a glassy carbon sample placed in the optical path in-between sample and detector. The scattering vector q, defined as q = 4π/λ sin(θ/2), ranges from 0.09 nm−1 up to 3.0 nm−1. THF was chosen as solvent for contrast reasons and complies to good solvent and sufficiently differing electron density differences with the solute. Solutions were glass-sealed in 1 mm diameter borosilicate capillaries (Hilgenberg, Germany). The temperature in the vacuum chamber of the SAXS instrument was 29 ± 1 °C. All measurements were corrected for empty capillary scattering and dark current. A flat solvent scattering was taken care of in the fitting procedures. The data were absolutely calibrated in [cm−1] by means of a secondary standard, which was calibrated before with water and Lupolene using the SAXS beamline, ID02 (ESRF, France) and SANS at KWS1 (Forschungszentrum Jülich, Germany). In view of the chemical preknowledge about the asymmetry and cross-linking effects, two models were adopted for the description of the stars. For the LB-series a star-like approach was assumed, taking into account a spacer parameter.37−39 The spacer is 0 in case of a real starburst configuration but is assumed to be of the order of the size of an end-to-end distance of the center chain in the case under consideration. Without further discussion here and referring to the appropriate literature,37−40 the absolute scattered intensity [cm−1] is described by I(q) = φVW,total

Δn2 NA

2((v − 1 + exp(−v) + (f − 1)/2(1 − exp(−v 2)2 exp(− (qS)2 )) fv 2

Here, v = (qRg,arm)2, φ is the volume fraction (φ = c/ρ with c being the mass concentration and ρ the polymer density), Vw,total = Mw,total/ρ (with Mw,total the weight-average molar mass of the polymer, which is denoted as Mn,absol,star in Table 1), f the number of arms, Rg the radius of gyration, and S the spacer parameter. The number of monomers per C

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

Figure 1. Absolute scattered intensity I as a function of scattering wavevector q for the four different stars at a concentration of 1 wt % in THF. Both the experimental data (symbols) and the model fits (lines) are shown in each subfigure, in (a) for the LB20, (b) for the LB10, (c) for the CC27, and (d) for the CC46 samples. arm is considered in Rg. The contrast factor Δn2 is determined by the difference in scattering length densities “n” of solvent and star polymers (see below). In the case of the CC-series the core of a star-based polymer is randomly chemically cross-linked. An appropriate scattering model is that of a core−shell particle in which core and shell scatter differently in contributions with the solvent. To allow for internal anisometry in the core, a general oblate shape which is controlled by an asymmetry parameter α, was used which can also be applied to isotropic particles (for α = 1). The experimental intensity is then compared with the theoretical one:41,42

I(q) =

φ Vshell

∫0

the oven to reduce the risk of degradation. The samples were simply positioned on the bottom plate using a spatula and then compressed with the rheometer. After a stabilization time, the samples were trimmed with a spatula and slightly further compressed. The final height was always between 0.8 and 1.3 mm. Subsequently, to ensure that all residual stresses from the loading are relaxed, the samples were kept under steady conditions for some time (several hours for the CC27) and checked with dynamic time sweeps at constant frequency and low strain amplitude. Dynamic rheological measurements were carried out in the temperature range −50 to +100 °C. The thermal expansion of the plates was always taken into account when changing temperature by making the appropriate changes in gap spacing. The measurements at high temperatures were performed as fast as possible and sample stability was always checked by testing the reproducibility of the measurements at an intermediate temperature. At each temperature, dynamic time sweep and strain sweep experiments were conducted to ensure thermal equilibrium of the sample and to determine the linear viscoelastic region. Finally, the time−temperature superposition principle was used in order to combine frequency sweep experiments at different temperatures and to create master curves.

1

(3(nc − nshell)Vcorej1 (ucore)/ucore

+ 3(nshell − nsolvent)Vshellj1 (ushell)/ushell)2 dα with the definitions: u = q(rmax2(1 − α2) + rmin2α2)1/2, j1(x) = (sin(x) − x cos(x))/x2. In addition, SAXS measurements were performed in the melt for the CC stars. The experimental protocol was the same as discussed above for solutions, except for the fact that the samples were sandwiched between Kapton foils since they could not be filled into capillaries. Therefore, their thickness was defined with some ambiguity and the reported absolute intensities after correction for the containing Kapton windows are prone to errors of about 10−20%. The data were corrected in the same way as the data of the solutions, and this is discussed in detail in section III.1 below. Note that it was not possible to measure melts of LB stars as the contrast was judged to be too low. II.3. Rheometry. After overnight drying and annealing of the samples, the linear viscoelastic responses were probed by small-strainamplitude oscillatory shear measurements with an ARES-2KFRTN1 strain-controlled rheometer equipped with a force rebalance transducer (TA Instruments, USA). As flow geometry, invar (copper−iron alloy with low thermal expansion coefficient) parallel plates with a diameter of 8 mm were used. Temperature control was achieved with an accuracy of ±0.1 °C by use of an air/nitrogen convection oven. A liquid nitrogen Dewar was used for measurements at temperatures below ambient. For the higher temperatures, nitrogen gas was fed into

III. EXPERIMENTAL RESULTS AND DISCUSSION III.1. Form Factor of the Single Stars in Dilute Solution. Figure 1 shows the absolute scattered intensity I as a function of the scattering vector q for the four different dilute samples in THF. For LBs, the form factor of a star polymer in Θ-state or melt as defined above is applied. We corrected in an approximate way43 for the good solvent quality, as well as for the presence of unlinked single arms from the synthesis: the quality of the solvent was taken into account by replacing v = (qRg arm)2 by vε = (qRg arm)2ε with ε = 1/(2ν) and ν the Flory exponent (≈0.6 for good solvents, 0.5 for Θ solvent) following Hammouda.44 It was impossible to fit the SAXS data without the consideration of free unbound arms. The intensity is thus a weighted sum of star-linked polymer scattering following the above scattering law and a single-chain Debye-like contribution D

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

Figure 2. (a) Master curves for the time−temperature superimposed elastic G′ and loss G″ moduli as a function of angular frequency ω for the four different samples at a reference temperature of 20 °C. Legend: (red ○) G′, (red △) G″ for the LB10; (green ○) G′, (green △)G″ for the LB20; (blue −) G′, (blue --) G″ for the CC46; (−) G′, (--) G″ for the CC27. The dark gray line has a slope of 0.5 and serves to guide the eye. (b) Horizontal aT and vertical bT shift factors as a function of temperature T. Legend: (red ○) aT, (red △) bT for the LB10; (green ○) aT, (green △) bT for the LB20; (blue ○) aT, (blue △) bT CC46; (○) aT, (△) bT for the CC27. The dark gray line is the WLF-fit for both the LB10 and the LB20; the blue and black lines are the WLF-fits for the CC46 and CC27, respectively.

of which the length is fixed to the arm size. As the data were calibrated absolutely, the number of parameters to be fitted was as low as three (i.e., Rg arm, the fraction of free arms and the additional background due to the solvent). All other parameters were constrained directly from the chemical composition and characterization: the arm number f, the number of monomers in the arms, the computed scattering length densities (SLD, abbreviated with “n” in the equations) for the center, arms and solvent respectively determined as n(PHEA)=9.79 × 1010 cm−2, n(PBA)=9.99 × 1010 cm−2, and n(THF)=8.39 × 1010 cm−2, and finally the length of the center backbone which acts effectively as a spacer. The size of this spacer S, i.e., the end-to-end distance was estimated to be 1.8 nm for the LB10 and 2.5 nm for the LB20 star sample using the ⟨Ree2⟩/M relations of Fetters et al.45 for acrylate polymers with M the particular molar mass of the central backbone and ⟨Ree2⟩ the mean-squared end-toend distance of the backbone. For the LB10, the fit led to a radius of gyration of the arms Rg arm of 7.6 ± 0.1 nm. For the LB20, the fit yielded a Rg arm of 7.7 ± 0.2 nm. The model fits are shown as red lines in Figures 1a and 1b. The computed curve with fixed intensity parameters (i.e., contrasts) is further proof of consistency and of the composition and only the qdependence needed to be fitted. To assess the sensitivity to the spacer (S), a proper consideration of the correlations is needed, and this has to be done: it is clear that the size of the arm in the star is highly correlated with the size of the central backbone. This can be easily visually understood. If the spacer is set to 0, thereby turning the model into a theoretical star with a spherical core of negligible size, the size of the arms increases to about 8.6 ± 0.3 nm to accommodate the scattering data. However, the overall fit quality is slightly worse (results not shown). On the other hand, if the spacer S is made larger than assumed via the endto-end distance, the low q-scattering part (0.1 < q < 0.5 nm−1) which reflects the overall size, is considerably shifted to lower scattering vectors and sensitively reacts to S. Here, we aim at being as consistent as possible: for an arm length of 240 monomers, the expected size of a chain in the unperturbed state can be calculated from Rg = 0.24M0.5 ≈ 4.2 nm. A very rough calculation for the excluded volume effects can be made: taking the dilute arm naively expanded as Rg(good solvent)/Rg(Θ solvent) ∼ N0.6−0.5= 2400.1 ≈ 1.7 leads to an equivalent unperturbed Rg of about 7.7/1.7 ≈ 4.5 nm. Despite this very

crude approximation and assuming the relation for a free chain to a tethered linear chain to apply,46 considering the qdependence yields a molar mass of arms of about 35000 g/mol, which corresponds very well to the value from chemical characterization. We also note that the same information can be obtained immediately from the forward scattering at q = 0. The intensity I(q = 0) = φMw,totalΔn2/ρ, with ρ the bulk density and the total molar mass Mw,total = Mcore + f Marms (as also mentioned above). As a general remark, the sensitivity for the spacer is clearly present through the arm size, but cannot be simply quantified. As discussed above, the CC-series was fitted using a particle scattering factor (i.e. form factor) which takes into account the specific chemical details. As an example it was already questioned whether the cross-link density leads to visually different core dimensions. Model-independent Guinier evaluations are ideally suited for this and from ln(I) = ln(I0) − (qRg)2/3, limited to the lowest q-regions, an overall radius of gyration Rg of 8.7 ± 0.1 nm for the CC27 and 7.87 ± 0.06 nm for the CC46 could be extracted. Rg can be converted into an equivalent compact sphere radius R by multiplying by (5/3)1/2. This leads to core radii of R = 11.0 and 10.1 nm for CC27 and CC46, respectively. More detailed parameters can be obtained from fits to the spherical core−shell model defined before, thereby exploiting the full range of the scattering vector. With these the core−shell nature of the particles can be confirmed without doubt. We note that the thickness of the PBA shell t is comparable in both samples despite the difference in un-crosslinked PBA arms, which is reflected in the molar mass ratio 165/98 (see Table 1). The fit resulted in values R = 7.6 nm and t = 3.6 nm for the CC27 (total radius 11.2 nm) and R = 6.8 nm and t = 3.2 nm for the CC46 (total radius 10 nm), respectively. They are in excellent agreement with the sizes that were determined from the former Guinier approximation. The so determined comparable values of the shell thickness are therefore real and must be the synergetic result of chain conformation and different polydispersity effects around the core. Indeed, the integral volume that f-arms (27 and 46) of PBA of different lengths (degrees of polymerization 165 and 98) make, is virtually identical for both samples and therefore the comparable shell is rationalized. The amplitude of scattering further depends on the different contrast factors. The scattering length density n of the shell in both particles comes out E

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

a true plateau modulus can only be extracted from data on polymers with Me = (4/5)((ρRT)/(GN0)) a number of entanglements roughly above 20.48 On the other hand, the relaxation behavior of CCs is clearly different from the relaxation behavior of both entangled flexible stars and high-f multiarm star melts.23 Their response appears to be gel-like, exhibiting a remarkable power-law relaxation over almost 8 decades in frequency with G′−ω and G″−ω-slopes of about 0.38 for the CC27 and 0.5 for the CC46. This is in qualitative agreement with the findings in ref 11 for similar systems, but over a shorter frequency range (about 6 decades). The dark gray line in Figure 2a has a slope of 0.5 (following the critical gel scaling49 G′ ∼ G″ ∼ ω0.5) and serves to guide the eye. Note that the difference in terminal relaxation times from Figure 2 is at least 4 decades and cannot be rationalized by the difference in arm molar mass, corroborrating the fact the arm relaxation is not primarily responsible for the observed behavior. Despite the small number of entanglements per arm and the respective significant core, as well as the fact that in ref 11 the arms are practically unentangled, it is tempting to compare the behavior that leads to very slow terminal relaxation to that of high functionality star polymers (with many entangled arms). The star’s center-of-mass motion follows the arm relaxation and controls flow.27 In this picture, a disengaged star hops through a crowded environment of other stars in the melt. However, the experimental times and molecular characteristics of the present systems do not compare quantitatively with the scaling predictions, which suggest much faster relaxation: considering the data of Table 1, the predictions of the ratio τslow/τs (with τs the segmental time) amount to about 106 for both stars (with identical product of number of arms and arm molar mass), whereas the respective experimental values are about 107 for CC46 and 1010 for CC27. The reason is that, unlike ref 27, the arms of CC46 are unentangled and those of CC27 barely entangled (1.5 entanglement), and in addition the present cores are too large. Nevertheless, this picture, i.e., the fact that in these hybrid stars in the melt interact via excluded volume repulsions at their entire size scale and effectively act as solvent-free colloids,50 provides inspiration for investigating their structure with SAXS and suggesting a similar connection of structure and dynamics in order to explain the data of Figure 2. Figure 3 depicts SAXS measurements of the star melts with the DVB-based cores, CC27 and CC46 in the same setup as described before in the Experimental Section. The experimental data reflect the non-negligible contrast between the DVB-based cross-linked cores and the PBA shell. Therefore, from the scattering perspective these stars can be viewed as mixtures of core−shell particles densely arranged, with interdigitating arms, as typically known from TEM pictures.51 The CC46 data indicate a clear evidence for a structure factor peak at an intermediate scattering wavevector q ≈ 0.055 Å−1. At high q values, the signature of the form factor of the DVBcross-linked cores of the interacting particles can still be recognized. For a quantitative description of the effective particle interactions, the classic Percus−Yevick model for hardsphere interactions was used, along with a spherical form factor for the cores.52 Indeed, the model appears to fit the data well, as shown in Figure 3. From the fitting we extract the following parameters: The radius of the cross-linked core is 1.88 ± 0.02 nm, which is quite smaller than that in dilute solution (see section III.1), as expected since in the latter case cores take-up solvent and swell. The distance between the centers of mass of

virtually identical to the calculation for PBA (theoretically: 9.99 × 1010 cm−2; fitted: 9.7 × 1010 cm−2). The linearly combined nvalues for the DVB-cross-linked cores (using n(DVB) = 8.46 × 1010 cm−2) leads to n(mixed core)=9.38 × 1010 cm−2 for CC27 (with 0.60PBA/0.40DVB) and 9.15 × 1010 cm−2 for CC46 (with 0.45PBA/0.55DVB)). They overestimate by about 20% the fitted values (7.3 × 1010 cm−2 and 7.7 × 1010 cm−2, for the CC27 and CC46, respectively), which are likely due to factors such as THF uptake inside the core and incorrect assumptions about the mixed contributions and bulk densities. The form factors of both CC-stars are described satisfactorily by the assumption of monodisperse core−shell particles and the resulting fits are shown in Figure 1, parts c and d, although the data look more smeared due to a distribution of core-sizes and probably also arm-number distribution. We note that our present analysis is meant to provide support for the interpretation of the stars structure and rheology rather than detailed structural investigation. Clearly, smearing of the above-mentioned theoretical model functions with the appropriate distributions would enhance the quality of fitting. However, this requires an exact knowledge of various parameters such as (1) scattering instrument details (collimation, detector resolution, beam divergence, wavelength distribution), functional form of distribution, (2) polydispersity in arm length and number, and (3) details of random crosslinking, some of which are unknown. Hence, we restrict the discussion at the level of analysis presented without loss of the main message. We find that both characterizations of the LB and CC series in dilute solution should form a firm basis with which bulk properties should at least be compatible. The dilute scattering experiments highlight the structural characteristics, which cannot be studied in the bulk microscopically, i.e., core and shell. The key conclusion is that LB series are like conventional stars whereas CC series are like core−shell colloidal particles. III.2. Viscoelasticity and Structure of the Stars in the Molten State. The master curves for the storage G′ and loss G″ moduli as a function of angular frequency ω at a reference temperature TREF = 20 °C are shown in Figure 2a for the four samples. The master curves were obtained by time−temperature superposition (see section II.3). The master curves of LBs are qualitatively similar to those of moderately entangled conventional (i.e., with spherical cores of negligible size), flexible star polymers.19,20,47 Further, note that taking into account small uncertainties in the rheological experiments (associated with loading), slight differences in the molar masses of the arms of the two stars and the dispersity of the samples, the rheological data of the two LBs overlaps within accuracy. Hence, to a first order approximation, there are no pronounced effects of the slight differences in the shape of the core (as star LB20 is slightly more elongated than the core of LB10) on the rheological data. In this case, the viscoelastic response is governed by arm relaxation (see also section III.3) and from the minimum in tan(δ) = G″/G′ at intermediate frequencies a plateau modulus of 1.4 × 105 Pa is extracted (Figure 2a), suggesting an entanglement molar mass of 14500 g/mol for PBA following, i.e. 115 monomer units, in reasonable agreement with the recently reported Me value when compared at the same temperature.11 Note however that these stars are only moderately entangled and hence the extracted value for the plateau modulus is undoubtedly different (or equivalently, the molar mass between entanglements different). For example, extended data on linear polyisoprenes in literature suggest that F

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

entanglements long, and no transient rubbery region and entanglement plateau is expected. Hence, the larger moduli, more extended power-law region with smaller slope and slower relaxation of CC27 are rationalized primarily by the shorter interparticle distances and stronger correlations. We can further estimate the moduli of the shell and core of the CC stars from rubber elasticity theory,46 according to which G0N = ((ρRT)/(Mx)) with Mx being the molar mass of an arm (for the shell) or a segment between cross-links (for the core). Given the numbers in Table 1, we find that for both stars the shell moduli are on the order of 105 Pa and the core moduli are on the order of 107 Pa. These reasonable estimates, especially for the core, are based on the rough assumption of each BA site being cross-linked and neglects the DVB in the spacer length, yielding Mx values of 100 and 200 g/mol for CC46 and CC27, respectively. On the basis of this, the rheological spectra of Figure 2 suggest that at lower frequencies right above the crossover to terminal flow we probe the shell response (plateau modulus of PBA); at the highest frequencies we probe the core response; and at intermediate frequencies (and length scales) we probe the self-similar cooperative structural rearrangements. It is worth pointing out that complex viscoelastic response in melts with power-law relaxation and low-frequency plateau storage modulus reminiscent of soft gels, has been reported in the literature. We mention in particular the earlier works of Antonietti and co-workers with polystyrene microgels of varying size and cross-link density.54,55 Gel-like power-law response was observed with slope of about 0.3, extending for about 6 decades,54 as well as low-frequency plateau.55 At that time, these data were interpreted as nonreptative relaxation in bulk polymers. It is clear, however, that microgels are colloidal particles with few dangling ends (if at all), hence the excluded volume effects mentioned above are important. Moreover, as already discussed, in the present work the values of the moduli just before the terminal relaxation are well above the plateau modulus of the PBA arms (see comparison of CC and LB stars in Figure 2a), whereas in the respective situation for microgels the moduli are at the level of the plateau modulus.54,55 More importantly, the cores of CC stars are much more densely cross-linked that the microgels (with near 1 cross-link per monomer vs the microgels having up to 1 cross-link per 10 styrene monomers) and as a result they exhibit higher moduli. The stronger interdigitation of the present stars, which is coupled to the liquid-like arrangement, represents another difference from the microgels. We also note for completion, that power-law stress relaxation has been also observed in other systems are well. For example, nanocomposites often exhibit such response, which is attributed to the formation of fractal networks.56−58 Pressure sensitive adhesives may also exhibit similar response, however not necessarily over so extended frequency range, whereas terminal behavior is usually not reached.59−63 Finally, the class of supersoft elastomers, also exhibit a very extended power-low relaxation without the classic entanglement plateau but at the lowest frequencies a gel-like low plateau modulus is observed, to which their name is attributed as well.62,64 Therefore, the present systems are rather unique, despite the mentioned similarities. We now examine the horizontal aT and vertical bT shift factors used for obtaining the viscoelastic master curves of Figure 2a. They are plotted as a function of temperature T (at TREF = 20 °C) in Figure 2b. The vertical shift factors were calculated from the change of the density of PBA with

Figure 3. Experimental SAXS data, showing the contribution of an apparent structure factor on top of the form factor in the star melts CC27 (squares) and CC46 (triangles). The lines are fits to the data (see text).

these cores (or stars) is 10.0 ± 0.09 nm, which corresponds to a hard sphere interaction radius of 5.0 ± 0.05 nm. The respective hard-sphere volume fraction φCC46,HS amounts to 0.12 ± 0.01. Note that, especially for the fit curve, a weak high-q shoulder is seen at a q value which is almost double the peak value, suggesting liquid-like order, apparently due to the excluded volume interactions of the stars. The form factor of the core is virtually constant in this range which encompasses the Guinier regime of the core. For the CC27 star, the data are more noisy and the intensity clearly lower by about a factor of 5. This factor is too high to be due to a calibration error of the scattering volume alone (e.g., related to the thickness ambiguity), since this would not affect the relative intensity. Instead, it should reflect the reduced contrast as compared to CC46 stars. Apparently the core−shell character is less pronounced, interfaces less defined and both phases (core and shell) to a certain extent intermixed which reduces the contrast between both. Still, a peak in I(q) is clearly resolved but it is quite broad (Figure 3). It is shifted to a higher q value (about 0.7 nm−1) compared to the smaller CC46, consistent with the expectation of smaller interstar spacings. The analysis reveals a core radius of 2.18 ± 0.03 nm (again smaller than its size in dilute solution), which is slightly larger than that of CC46, and a mean distance between the centers of mass, 7.98 ± 0.13 nm, i.e., a hard sphere interaction radius of 4.0 ± 0.1 nm. The volume fraction φCC27,HS amounts to 0.12 ± 0.01, i.e., it is the same as for CC46. These numbers conform well to the smaller number of (larger) arms and weaker crosslinking density of the core of CC27 as compared to CC46 (see section II.1.). Hence, the above SAXS data conform to the linear viscoelastic data of Figure 2a. Indeed, both stars behave like core−shell particles in the melt. They have the same effective fraction of cores, alternatively identical total arm molar mass. Their liquid-like order is congruent with a viscoelastic response reflecting correlations over distances larger than their sizes.23,53 This can explain the power-law like stress relaxation observed in Figure 2a, typical of soft gels;23,49,53 here the power-law exponent varies from about 0.5 for CC46 to about 0.38 for CC27, as already discussed. In addition, larger particles with the same core fraction in this dense regime (melt) are closer together and also interpenetrate more. Indeed, CC27 have higher entanglement density compared to CC46. However, as already mentioned, even for CC27 the arms are only about 1.5 G

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

temperature;65 bT = ((ρ(TREF)(TREF + 273.2))/(ρ(T)(T + 273.2))) with the density of PBA ρ (in g/cm3) as a function of temperature T (in °C) given by ρ(T) = 1.059 − 6.679 × 10−4 T − 1.507 × 10−7 T2 as fitted to the data for PBA in ref 66. However, especially for the CC stars, the change of density with temperature is in fact unknown due to the cross-linked cores. The vertical shift factors are nevertheless close to one. The horizontal shift factors resulted from the least-squares fit as done by the standard Orchestrator software. Fits of the horizontal shift factors with the Williams− Landel−Ferry (WLF) equation65 log(aT) = ((−C1(T − TREF))/ (C2 + T − TREF)) are also shown in Figure 2b. At TREF = 20 °C, the WLF-coefficients are C1 = 4.86 and C2 = 116 °C for LBs, C1 = 8.28 and C2 = 134 °C for the CC46, and C1 = 12.6 and C2 = 154 °C for the CC27. Also the shift factors reflect the fact that the stars do not behave as simple flexible polymers of the same chemistry, in which case the horizontal shift factors of different stars would overlap. Finally, we need to remark that, in contrast to LB stars, the CC stars are not thermo-rheologically simple as the master curves in Figure 2a seem to suggest, mainly due to the large scale of the y-axis (8 decades). To justify this statement, Figure 4 depicts the damping factors tan(δ) = G″/G′ for the two CC

The thermo-rheological complexity of the CC stars, as shown in Figure 4, is much more severe than the complexity found for the star polymers of the literature68,69 and is in fact comparable to that found in microgels54,71 and nanocomposites.72,73 We tentatively attribute it to the different temperature dependence of the microscopic friction and related local motions of the PBA arms and the PBA-co-DVB segments in the core. This is likely in systems with substantial density heterogeneity such as the CC stars with core−shell morphology and large core, as opposed to the LB stars with small core. III.3. Modeling of the Viscoelastic Behavior of LBs. From Figure 2 we concluded that qualitatively, LBs behave as regular low-functionality entangled stars with essentially the same glass transition temperature. In this section, we report on the modeling of the data with the so-called branch-on-branch (BOB) model19 as implemented in Reptate74 to confirm or refute that the stars behave (also quantitatively) just like regular flexible low-functionality entangled stars. The stars were modeled with an arm molar mass, Mn,arm = 31 kg/mol, a molar mass of the BA monomer, M0 = 128.17 g/mol, a density of PBA ρ (at 20 °C) of 1.05 g/cm3. The stars were set to have 10 arms but the results from the model are independent of the number of arms.17−20 The two remaining model parameters are the relaxation time of an entanglement τe and the number of monomers between entanglements Ne. The model was fitted to the data using values for τe (at 20°C) of 1.5 × 10−4 s and Ne of 70. The number of monomers between entanglements was optimized to yield an identical value for G′ at the minimum of tan(δ) as the experimental data. Note however that the necessary value of Ne corresponds to a molar mass between entanglements Me of 9000 g/mol, which is low as already mentioned,11,75 and clearly differs from the value extracted using Me = (4/5)((ρRT)/(G0N)), with GN0 being the value of G′ at minimum tan(δ). The reason for the discrepancy was explained in section III.3 and relates to the fact that the arms of the stars are only moderately entangled with no more than 3 entanglements per arm, rendering the method to estimate GN0 from minimum tan(δ) inaccurate. Figure 5 shows the comparison between the experimental data and two model predictions using the above parameters, one assuming

Figure 4. Master curves for the time−temperature superimposed damping factors tan(δ) as a function of angular frequency ω for the two CC-samples at a reference temperature of 20 °C. Legend: blue and black dots for the CC46 and CC27, respectively.

star samples. In this plot one can appreciate the non-negligible thermo-rheological complexity. In fact, usually homopolymers of different molecular architecture but very similar tacticity and microstructure are thermo-rheologically simple.67 Only in a few cases conventional flexible stars with few long arms or other polymers with long-chain branching have been reported to exhibit thermo-rheological complexity.17,68−70 For these simple stars, the occurrence of the complexity seems to depend mainly on chemistry and seems to correlate with the coefficient of thermal expansion of the polymer chain.17,68−70 The present situation with the stars having PBA arms is to the best of our knowledge unknown. Although we do not observe any thermorheological complexity for the LB stars, we note that they have relatively short arms, and thermo-rheological complexity would presumably not be apparent for these samples, even if they would display complexity when arms would be longer. We also note that the horizontal shift factors for the two LB stars are identical (pointing also to the same glass transition temperature) whereas those of the two CC stars are clearly different.

Figure 5. Master curves for the elastic G′, loss G″ moduli, and tan(δ) = G″/G′ as a function of angular frequency for both LBs are compared with tube-model predictions from the BOB-model. Legend: (red ○) G′, (red △)G″, (red □) tan(δ) for the LB10; (green ○) G′, (green △) G″, (green □) tan(δ) for the LB20; (−) G′, (--) G″, (-·-) tan(δ) for the BOB-model assuming monodisperse stars (model parameters see text); (−) G′, (--) G″, (-·-) tan(δ) for the BOB-model with identical parameters, but a Gaussian polydispersity of 1.15. H

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

■

ACKNOWLEDGMENTS We thank Michael Rubinstein and Costantino Creton for inspiring discussions and comments. F.S. and D.V. acknowledge financial support from the EU (ITN-COMPLOIDS, FP7234810 and FP7 Infrastructure ESMI, GA-262348). K.M. acknowledges support from the NSF (DMR 0969301). NMR instrumentation at CMU was partially supported by NSF (CHE-1039870).

monodisperse stars (black lines) and one assuming stars with a Gaussian arm polydispersity of 1.15 (blue lines). Figure 5 shows that the comparison between the experimental data and the model is good, thereby confirming that LBs behave like regular low-functionality entangled stars. In closing, we note that the viscoelastic response of the CC stars with core−shell structure and unentangled or barely entangled arms cannot be described by a tube-base model. Instead, coarse grained models accounting by the thermodynamic (due to structure factor) and transient (due to interdigitation) forces appear promising.76,77

■

ASSOCIATED CONTENT

* Supporting Information S

Synthesis of the stars, including characterization and kinetic data. This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

(1) Hadjichristidis, N.; Pitsikalis, M.; Pispas, S.; Iatrou, H. Chem. Rev. 2001, 101, 3747−3792. (2) Quirk, R. P.; Kim, J. Rubber Chem. Technol. 1991, 64, 450−468. (3) Roovers, J.; Toporowski, P.; Martin, J. Macromolecules 1989, 22, 1897−1903. (4) Quinn, J. F.; Chaplin, R. P.; Davis, T. P. J. Polym. Sci., A: Polym. Chem. 2002, 40, 2956−2966. (5) Blencowe, A.; Tan, J. F.; Goh, T. K.; Qiao, G. G. Polymer 2009, 50, 5−32. (6) Matyjaszewski, K.; Xia, J. H. Chem. Rev. 2001, 101, 2921−2990. (7) Matyjaszewski, K. Polym. Int. 2003, 52, 1559−1565. (8) Matyjaszewski, K.; Tsarevsky, N. V. Nat. Chem. 2009, 1, 276− 288. (9) Gao, H.; Matyjaszewski, K. Prog. Polym. Sci. 2009, 34, 317−350. (10) Roovers, J. Macromolecules 1994, 27, 5359−5364. (11) van Ruymbeke, E.; Muliawan, E. B.; Vlassopoulos, D.; Gao, H.; Matyjaszewski, K. Eur. Polym. J. 2011, 47, 746−751. (12) Loppinet, B.; Stiakakis, E.; Vlassopoulos, D.; Fytas, G.; Roovers, J. Macromolecules 2001, 34, 8216−8223. (13) Gauthier, M.; Munam, A. Macromolecules 2010, 43, 3672−3681. (14) Nese, A.; Mosnacek, J.; Juhari, A.; Yoon, J. A.; Koynov, K.; Kowalewski, T.; Matyjaszewski, K. Macromolecules 2010, 43, 1227− 1235. (15) Heuer, D. M.; Saha, S.; Archer, L. A. Biopolymers 2003, 70, 471− 481. (16) Grest, G. S.; Fetters, L. J.; Huang, J. S.; Richter, D. Adv. Chem. Phys. 1996, 94, 67−163. (17) McLeish, T. C. B. Adv. Phys. 2002, 51, 1379−1527. (18) Milner, S. T.; McLeish, T. C. B. Macromolecules 1997, 30, 2159−2166. (19) Das, C.; Inkson, N. J.; Read, D. J.; Kelmanson, M. A.; McLeish, T. C. B. J. Rheol. 2006, 50, 207−235. (20) Snijkers, F.; Ratkanthwar, K.; Vlassopoulos, D.; Hadjichristidis, N. Macromolecules 2013, 46, 5702−5713. (21) Daoud, M.; Cotton, J. P. J. Phys. (Paris) 1982, 43, 531−538. (22) Forster, S.; Wenz, E.; Lindner, P. Phys. Rev. Lett. 1996, 77, 95− 98. (23) Vlassopoulos, D.; Pakula, T.; Fytas, G.; Roovers, J.; Karatasos, K.; Hadjichristidis, N. Europhys. Lett. 1997, 39, 617−622. (24) Watanabe, H. Acta Polym. 1997, 48, 215. (25) Watanabe, H.; Matsumija, Y.; Ishida, S.; Takigawa, T.; Yamamoto, T.; Vlassopoulos, D.; Roovers, J. Macromolecules 2005, 38, 7404−7415. (26) Watanabe, H.; Matsumija, Y. Macromolecules 2005, 38, 3808. (27) Kapnistos, M.; Semenov, A. N.; Vlassopoulos, D.; Roovers, J. J. Chem. Phys. 1999, 111, 1753−1759. (28) Laurati, M.; Stellbrink, J.; Lund, R.; Willner, L.; Ricther, D.; Zaccarelli, E. Phys. Rev. Lett. 2005, 94, 995504. (29) Vlassopoulos, D.; Fytas, G. Adv. Polym. Sci. 2010, 236, 1. (30) Sumerlin, B. S.; Neugebauer, D.; Matyjaszewski, K. Macromolecules 2005, 38, 702−708. (31) Burchard, W. Adv. Polym. Sci. 1999, 143, 113. (32) Gao, H.; Matyjaszewski, K. Macromolecules 2006, 39, 3154− 3160. (33) Gao, H.; Matyjaszewski, K. Macromolecules 2007, 40, 399−401. (34) Gao, H.; Ohno, S.; Matyjaszewski, K. J. Am. Chem. Soc. 2006, 128, 15111−15113.

IV. CONCLUSIONS In this work, we have considered the viscoelastic response of star polymers with small asymmetric or large heavily crosslinked cores and with a moderate number of moderately or marginally entangled arms, in relation to their internal microstructure. We find that the cores in particular may affect the stars response and hence we argue that the stars internal microstructure controls their viscoelastic properties, hence providing an important tunability parameter. Our results can be summarized as follows: 1. As long as the cores as very small compared to the overall star size, they do not affect the stars properties significantly. This is true even when the core shape is asymmetric. In such a case the stars retain their polymeric character. LB stars have smaller and slightly elongated cores as expected from the chemistry and confirmed by the analysis of the SAXS data. The effects of the elongated core on the rheological behavior are nevertheless negligible and they behave like regular lowfunctionality entangled stars. It was shown that their relaxation can be well-described by the BOB tube-based model. 2. Large cores affect the star properties and character. The form factors of CC stars with large, rubbery cores (as expected from the chemistry due to their cross-linked nature) have a colloidal nature, exhibiting a clear core− shell behavior. Their rheological behavior is very unusual and strongly opposed to the behavior of other stars. They display an extended power-law relaxation over a very wide frequency range, reflecting the core response at higher frequencies, shell response and eventual terminal flow at lower frequencies, and a self-similar cooperative rearrangement of the dense structure resulting from their interdigitation and excluded volume interactions. This interpretation is supported by estimates of the core and shell moduli and SAXS measurements in the melt, which reveal a liquid-like order and small intercore distances.

■

Article

AUTHOR INFORMATION

Corresponding Author

*(D.V.) E-mail: [email protected]. Notes

The authors declare no competing financial interest. I

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

(35) Jakubowski, W.; Min, K.; Matyjaszewski, K. Macromolecules 2006, 39, 39−45. (36) Burdynska, J.; Cho, H. Y.; Mueller, L.; Matyjaszewski, K. Macromolecules 2010, 43, 9227−9229. (37) Jeng, U. S.; Lin, T.-L.; Wang, L. Y.; Chang, L. Y.; Ho, D. I.; Han, C. C. Appl. Phys. 2002, A74, 487−489. (38) Pedersen, J. S.; Gerstenberg, M. Macromolecules 1996, 29, 1363−1365. (39) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171−210. (40) Higgins, J. S.; Benoît, H. C. Polymers and Neutron Scattering; Oxford University Press: Oxford, U.K., 1994. (41) Kotlarchyk, M.; Chen, H. S. J. Chem. Phys. 1983, 79, 2461− 2469. (42) Berr, S. S. J. Phys. Chem. 1987, 91, 4760−4765. (43) Picot, C.; Audouin, F.; Mathis, C. Macromolecules 2007, 40, 1643−1656. (44) Hammouda, B. Adv. Polym. Sci. 1993, 106, 87−133. (45) Fetters, L. J.; Lohse, D. J.; Colby, R. H. In Physical Properties of Polymers Handbook, 2nd ed.; Mark, J. E., Ed.; Springer: New York, 2007. (46) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: Oxford, U.K., 2003. (47) Fetters, L. J.; Kiss, A. D.; Pearson, D. S.; Quack, G. F.; Vitus, F. J. Macromolecules 1993, 26, 647−654. (48) Auhl, D.; Ramirez, J.; Likhtman, A. E.; Chambon, P.; Fernyhough, C. J. Rheol. 2008, 52, 801−835. (49) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367−382. (50) Chremos, A.; Panagiotopoulos, A. Z.; Koch, D. L. J. Chem. Phys. 2012, 136, 044902. (51) Jones, C. D.; Lyon, L. A. Macromolecules 2000, 33, 8301−8306. (52) Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 2nd ed., Academic Press: London, 1986. (53) Ozon, F.; Petekidis, G.; Vlassopoulos, D. Ind. Eng. Chem. Res. 2006, 45, 6946−6952. (54) Antonietti, M. Angew. Chem., Int. Ed. 1988, 27, 1743−1747. (55) Antonietti, M.; Pakula, T.; Bremser, W. Macromolecules 1995, 28, 4227−4233. (56) Chevigny, C.; Dalmas, F.; Di Cola, E.; Gigmes, D.; Bertin, D.; Boué, F.; Jestin, J. Macromolecules 2010, 44, 122−133. (57) Oberdisse, J. Soft Matter 2006, 2, 29−36. (58) Moll, J. F.; Akcora, P.; Rungta, A.; Gong, S.; Colby, R. H.; Benicewicz, B. V.; Kumar, S. K. Macromolecules 2011, 44, 7473−7477. (59) Do Amaral, M.; Roos, A.; Asuaa, J. M.; Creton, C. J. Colloid Interface Sci. 2005, 281, 325−338. (60) Jensen, M. K.; Bach, A.; Hassager, O.; Skov, A. L. Int. J. Adhesion Adhesives 2009, 29, 687. (61) Padding, J. T.; Mohite, L. V.; Auhl, D.; Briels, W. J.; Bailly, C. Soft Matter 2011, 7, 5036−5046. (62) Neugebauer, D.; Zhang, Y.; Pakula, T.; Sheiko, S. S.; Matyjaszewski, K. Macromolecules 2003, 36, 6746−6755. (63) Deplace, F.; Rabjohns, M. A.; Yamaguchi, T.; Foster, A. B.; Carelli, C.; Lei, C.-H.; Ouzineb, K.; Keddie, J. L.; Lovellb, P. A.; Creton, C. Soft Matter 2009, 5, 1440−1447. (64) Pakula, T.; Zhang, Y.; Matyjaszewski, K.; Lee, H.; Boerner, H.; Qin, S.; Berry, G. C. Polymer 2006, 47, 7198−7206. (65) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley: New York, 1980. (66) Walsh, D.; Zoller, P. Standard Pressure Volume Temperature Data for Polymers; Taylor & Francis: New York, 1995. (67) Kapnistos, M.; Vlassopoulos, D.; Roovers, J.; Leal, L. G. Macromolecules 2005, 38, 7852−7862. (68) Carella, J. M.; Gotro, J. T.; Graessley, W. W. Macromolecules 1986, 19, 659−667. (69) Fetters, L. J.; Graessley, W. W.; Krishnamoorti, R.; Lohse, D. J. Macromolecules 1997, 30, 4973−4977. (70) Levine, A. J.; Milner, S. T. Macromolecules 1998, 31, 8623−8637. (71) Roland, C. M.; Santangelo, P. G.; Antonietti, M.; Neese, M. Macromolecules 1999, 32, 2283−2287.

(72) Baeza, G. P.; Genix, A.-C.; Degrandcourt, C.; Petitjean, L.; Gummel, J.; Couty, M.; Oberdisse, J. Macromolecules 2013, 46, 317− 329. (73) Berriot, J.; Montes, H.; Lequeux, F.; Long, D.; Sotta, P. Macromolecules 2002, 35, 9756−9762. (74) Ramirez, J.; Likhtman, A. E. Rheology of Entangled Polymers: Toolbox for the Analysis of Theory and Experiments. Reptate, http:// www.reptate.com 2007. (75) Jullian, N.; Leonardi, F.; Grassil, B.; Peyrelasse, J.; Derail, C. Appl. Rheol. 2010, 20, 33685. (76) Briels, W. J. Soft Matter 2009, 5, 4401−4411. (77) Padding, J. T.; van Ruymbeke, E.; Vlassopoulos, D.; Briels, W. J. Rheol. Acta 2010, 49, 473−484.

J

dx.doi.org/10.1021/ma5008336 | Macromolecules XXXX, XXX, XXX−XXX