Dynamic Heterogeneity in Random Copolymers of Polymethacrylates

Article pubs.acs.org/Macromolecules

Dynamic Heterogeneity in Random Copolymers of Polymethacrylates Bearing Different Polyhedral Oligomeric Silsesquioxane Moieties (POSS) Stelios Alexandris,† Adrian Franczyk,‡,§ George Papamokos,† Bogdan Marciniec,§ Robert Graf,∥ Krzysztof Matyjaszewski,‡ Kaloian Koynov,∥ and George Floudas*,†,∥ †

Department of Physics, University of Ioannina, 45110 Ioannina, Greece Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, Pennsylvania 15213, United States § Center for Advanced Technologies, Adam Mickiewicz University in Poznan, Umultowska 89c, 61-614 Poznan, Poland ∥ Max Planck Institute for Polymer Research, 55128 Mainz, Germany ‡

S Supporting Information *

ABSTRACT: Random copolymersusually considered as dynamically homogeneous with a single glass temperature can show dynamic heterogeneity by appropriate choice of their repeat units. Random copolymers based on polymethacrylates with polyhedral oligomeric silsesquioxane (POSS) moieties as side groups substituted with seven isobutyl ((i-Bu)7POSSOSiMe 2 (CH 2 ) 3 -MA) and 2,4,4-trimethylpentyl ((iC8H17)7POSS-OSiMe2(CH2)3-MA) groups were synthesized and studied by dielectric spectroscopy, density functional theory, differential scanning calorimetry, and rheology. Two distinct relaxation processes were found by dielectric spectroscopy giving rise to two glass temperatures. In addition, rheology revealed significant broadening of the viscoelastic functions leading eventually to the failure of time−temperature superposition for all copolymer compositions. These results provide signatures of dynamic heterogeneity in a random copolymer. calorimetry (DSC),18−31 rheology,18−20,26,30−32 dielectric spectroscopy (DS),24,27,33,34 ellipsometry,35,36 molecular dynamics simulations,33 and theory.37 There is now a vast literature on the composition dependence of glass temperature in such systems. As an example, a single study reported a data set comprising more than 400 glass temperatures of several random copolymers with glass temperature difference of pure components, ΔTg, ranging from 1 to 165 K. The composition dependence of the glass temperatures in random copolymers has been discussed in terms of the Gordon and Taylor40 or the DiMarzio and Gibbs39 equations that assume respectively volume additivity of the repeat units and additivity of “flexible” bonds, thus emphasizing packing vs intermolecular effects. These relations, together with the simpler Fox equation,40 were subsequently extended to account for diad sequence contribution to the glass temperature of the copolymers. In all studies of random copolymers a single glass temperature was found. It was interpreted as suggesting the presence of a single phase with a limited compositional heterogeneity. To the best of our knowledge, only a single study (on emulsion polymerized butyl acrylate−methyl methacrylate copolymer)

I. INTRODUCTION Interest over the conformational properties and the related dynamics of random copolymers stems from the fact that they can provide a deeper understanding of more complex systems, like proteins.1 In addition, in commercially relevant polymer materials, copolymerization is particularly useful in tuning the glass temperature. Random copolymers are distinctly different from block copolymers both structurally and dynamically. Nanophase separated block copolymers exhibit two wellseparated glass temperatures that correspond to the pure components.2 In addition, they are dynamically different from miscible block copolymers and blends. The latter exhibit “dynamic heterogeneity”3−16 which is manifested by (i) broadening of the relaxation spectra with respect to the homopolymers and (ii) the presence of two distinct relaxation processes that reflect the component’s segmental dynamics. The segmental relaxation times and thus the corresponding glass temperatures, however, are modified with respect to the pure components according to the “self-concentration” model introduced by Lodge and McLeish (LM), i.e., the local enrichment of each segment at the Kuhn length scale due to chain connectivity.17 The situation is different in random copolymers where a single glass temperature is commonly anticipated. Indeed, many random copolymers were investigated with differential scanning © XXXX American Chemical Society

Received: March 30, 2017 Revised: May 4, 2017

A

DOI: 10.1021/acs.macromol.7b00660 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 1. Structure and characterization of comonomers (i-Bu)7 and (i-C8H17)7.

reported two glass temperatures, but this finding was reflecting the nonuniform distribution of comonomer sequences along the copolymer chains due to difference in reactivity of the comonomers.31 We mention here parenthetically that two glass temperatures have been reported in homopolymers of a particular “architecture” (with a side group much longer than the backbone length).41,42 In the present work we design the first truly random copolymer that exhibits two glass temperatures. The comonomers are based on the polyhedral oligomeric silsesquioxane methacrylate monomers of ((i-Bu)7POSS-OSiMe2(CH2)3-MA) and ((i-C8H17)7POSS-OSiMe2(CH2)3-MA), with seven isobutyl and 2,4,4-trimethypentyl substituents and a flexible spacer between the POSS cage and the methacrylate group. This molecular design is based on earlier studies that explored the relative influence of intra- and intermolecular correlations on the glass temperature of amorphous polymers and glassforming liquids.43−45 It was shown that the key parameters controlling the dynamics associated with the glass temperature are the monomeric volume and local packing. Our molecular design takes advantage of the unique cubic siloxane cages that are physically large, i.e., the POSS units that can be considered as giant atoms providing with a large repeat unit volume.46−48 They are composed of a robust silicon−oxygen framework that can be easily functionalized at the corners of the cage with different organic substituents. Furthermore, POSS reagents can be incorporated into polymer systems using established polymerization protocols. Polyhedral oligomeric silsesquioxane (POSS) moiety as nanometer-size building block has been successfully incorporated into a range of polymeric materials.49−56 Recently, a new polyhedral oligomeric silsesquioxane methacrylate monomer ((i-Bu)7POSS-OSiMe2(CH2)3-MA) with seven isobutyl substituents and a flexible spacer between the POSS cage and the methacrylate group was polymerized via atom transfer radical polymerization (ATRP).57 A subsequent study58 employed a series of poly(POSS-MA)s and investigated the effect of spacer length and polymer molecular weight on the self-assembly as well as the thermodynamic and dynamic properties of the nanocomposites. It was shown that POSS cages modify interchain correlations and result in multiple dynamic processes that reflect the cooperative relaxations of both the pendant POSS units and ester dipoles as well as the polymer backbone. As a result, the freezing of backbone dynamics was shifted to lower temperatures, and the nanocomposites appeared softer than their linear counterpart (i.e., PMMA) of similar degrees of polymerization. On the basis of these results, it was suggested that POSS cages can be employed as nanometer size blocks that

can impart mobility and control over the mechanical properties of nanocomposites. In this study a combination of differential scanning calorimetry, dielectric spectroscopy, solid state NMR, and rheology techniques is employed to investigate the dynamics of random copolymers of ((i-Bu)7POSS-OSiMe2(CH2)3-MA) and ((i-C8H17)7POSS-OSiMe2(CH2)3-MA) as a function of composition. Density functional theory is employed to calculate the monomer dipole moment in the gas phase in conjunction with the DS study. Two distinct relaxation processes were found by dielectric spectroscopy, giving rise to two glass temperatures. In addition, rheology revealed significant broadening of the viscoelastic functions leading eventually to the failure of time−temperature superposition. These results provide signatures of dynamic heterogeneity in a random copolymer. They are discussed in terms of the LM model that emphasizes the influence of local environment on the segmental dynamics.

II. EXPERIMENTAL SECTION Synthesis and Characterization of Comonomers. In the present study two comonomers with a different type of silsesquioxane moiety (Figure 1, compound (i-Bu)7 and (i-C8H17)7) were chosen for the synthesis of linear homo- and copolymers by ATRP. The synthesis, characterization, and homopolymerization of (i-Bu)7 by ATRP were previously reported.57 On the other hand, (i-C8H17)7 is a new substance which was synthesized following a similar route to the i-Bu derivative. (i-C8H17)7 comonomer was fully characterized by 1H NMR, 13 C NMR, 29Si NMR, and EA (Supporting Information, part I-A-2) analyses and the thermal properties were determined by DSC and TGA (Figure 1). Despite the fact that both compounds contain branched alkyl groups connected with the Si−O cube core, they have distinctly different physical properties, e.g. (Figure 1) (i-C8H17)7 is a highly viscous oil whereas (i-Bu)7 is solid at room temperature. The melting point and crystallization temperatures of (i-C8H17)7 are 100 K lower than for (i-Bu)7 (DSC); for (i-C8H17)7 the 5% of weight loss is observed at 572 K; that is 70 K higher than that of the i-Bu derivative (TGA). The solubility of (i-C8H17)7 is similar to that of (i-Bu)7; both comonomers are very well soluble in hexane, toluene, acetone, diethyl ether, THF, CH2Cl2, and CHCl3, they have limited solubility in MeOH and CH3CN, and they are not soluble in H2O. These facts suggest that homo- or copolymerization of these substances will provide macromolecules with variable physical properties. Moreover, 1H NMR analysis of (i-Bu)7 and (i-C8H17)7 (performed in CDCl3) revealed the presence of characteristic signals derived from −CH3 groups for each comonomer (Figure 2, top). This feature is important for quantitative determination of the composition of (iBu)7/(i-C8H17)7 mixtures. A representative 1H NMR spectrum of an equimolar mixture of (i-Bu)7 and (i-C8H17)7 is shown in Figure 2 (bottom). Homo- and Copolymers with POSS Moieties: Synthesis and Characterization. The synthesis and characterization of homopolymer (i-Bu)7/(i-C8H17)7 (100/0) were described earlier.57,58 The B


Article

Macromolecules

To further confirm that the formed copolymers are random, radical polymerization of the (i-Bu)7 and (C8H17)7 mixture (50/50) with a ratio of 50/50 was performed. The experiment was carried out with AIBN as an initiator, in toluene, at 333 K, in an Ar atmosphere. After termination of the process, the copolymers were isolated from the comonomer residue following the same techniques applied to ATRP and analyzed by 1H NMR and GPC. The analysis of the thus-obtained copolymers revealed that the ratio of incorporated monomers in the chain is 50:50 (Figures S28 and S29). Lastly, the same ratio was found in the residual mixtures of unreacted monomers (Figure 4), thus confirming that the copolymers were truly random. The NMR characterizations of the copolymers (75/25) and (25/75) mixture are given in Figures S16−S18 and S30−S32, respectively. We further checked the possibility for phase separation by 2D wide-line separation (WISE) measurements recorded for the (i-Bu)7/(i-C8H17)7 (50/50) copolymer (at 700 MHz 1H Larmor frequency, at T = 323 K and 5 kHz MAS). The result is shown in Figure S33. There was not a significant difference in the line width of the components (both components were mobile). Hence, a length for the segregation of domains could not be extracted by spin-diffusion measurements.

Figure 2. Top: 1H NMR analysis of comonomers (i-Bu)7 and (iC8H17)7. Bottom: 1H NMR analysis of an equimolar mixture ((i-Bu)7/ (i-C8H17)7 = 50:50). homopolymer (i-Bu)7/(i-C8H17)7 (0/100) and the copolymers (iBu)7/(i-C8H17)7 (75/25), (i-Bu)7/(i-C8H17)7 (50/50), and (i-Bu)7/(iC8H17)7 (25/75) were prepared in a similar way. Homo- and copolymerization results and macromolecular characterization are presented in Table 1. Copolymers (i-Bu)7/(i-C8H17)7 (75/25), (i-Bu)7/(i-C8H17)7 (50/ 50), and (i-Bu)7/(i-C8H17)7 (25/75) were isolated by filtration through alumina and precipitation in acetone, washed with acetone, and dried under vacuum. Subsequently, all samples were characterized by GPC and 1H, 13C, and 29Si NMR. Both methods confirmed the absence of monomer content in all isolated copolymer samples. Moreover, 1H NMR analysis confirmed the presence of comonomers (i-Bu)7 and (i-C8H17)7 in the polymer chains. Applying different ratios of comonomer mixtures during the polymerization resulted in copolymers with different amounts of appropriate units. Indeed, integration of the corresponding comonomer signals in the 1H NMR spectra of the copolymers confirmed the theoretically calculated compositions (Figure 3). To further check the constant relative consumption of comonomers during the whole polymerization process, samples were collected at selected intervals during polymerization, and 1H NMR measurements were made. As an example, during the polymerization of the mixture of (i-Bu)7/(i-C8H17)7 = 50/50, three samples after 3, 8, and 12 h of the process were collected, and each copolymer was isolated from the unreacted comonomers. The 1H NMR of isolated copolymers and mixtures of comonomers confirmed that at every step of polymerization the consumption and incorporation of both comonomers is constant during the whole process (Figures S22−S27 in Supporting Information). Representative 1H NMR analysis of copolymer (i-Bu)7/ (C8H17)7 (50/50) after 8 h is presented in Figure 4.

III. CHARACTERIZATION METHODS Gel Permeation Chromatography (GPC). MW and MWD of the formed polymers were measured by gel permeation chromatography using Polymer Standards Services (PSS) columns (guard, 105, 103, and 102 Å), with THF eluent at 308 K, flow rate 1.00 mL/min, and differential refractive index (RI) detector (Waters, 2410). Diphenyl ether was used as the internal standard to correct for any fluctuation of the THF flow rate. The number-average MW (Mn,GPC) and MWD (Mw/Mn) were determined with a calibration based on linear poly(methyl methacrylate) (PMMA) standards using WinGPC 6.0 software from PSS. Multiangle Laser Light Scattering Gel Chromatography (MALLS). The measurements were performed on an Agilent 1260 Infinity system coupled to a DAWN-EOS laser light scattering detector (Wyatt Technologies) equipped with a He−Ne laser operating at the wavelength of 685 nm and an ERC refractive index detector. Chromatographic separation was performed by using a combination of three PSS SDV columns, 10 μm, 8 × 300 mm, with porosities: 106, 105, and 500 Å. All experiments were performed in THF at a flow rate of 1 mL/min and at temperature of 303 K. The refractive index increment of the samples was determined assuming 100% mass recovery. All data were recorded and evaluated using WinGPC UniChrom software from PSS. Nuclear Magnetic Resonance Spectrometry (NMR). 1H, 13C, and 29Si NMR spectra were recorded on a Varian Gemini 300 VT spectrometer and a Varian Mercury 300 VT in CDCl3. Thermogravimetric Analysis (TGA). TGA was performed using a TGA Q50 V20.13 Build 39, and the data were recorded over a

Scheme 1. Homo- and Copolymerization of (i-Bu)7 and (i-C8H17)7 Methacrylates

C


Article

Macromolecules Table 1. Homo- and Copolymerization Results and Characterization of Polymers with POSS Moieties (co)polymer (i-Bu)7/(i-C8H17)7 (i-Bu)7/(i-C8H17)7 (i-Bu)7/(i-C8H17)7 (i-Bu)7/(i-C8H17)7 (i-Bu)7/(i-C8H17)7 a

(100/0) (0/100) (75/25) (50/50) (25/75)

reagents ratioa

conv (%)

Mn,theor (×103)

Mn,GPC (×103)

Mn,MALLS (×103)

900/0/1/3/3 0/900/1/3/3 600/300/1/3/3 450/450/1/3/3 300/600/1/3/3

92 95 76 50 80

843 1269 1034 1093 1152

195 230 91.3 55.2 101

310 1750 330 190 423

Mw/Mn,GPC(MALLS) 1.40 2.55 1.20 1.20 1.22

(1.20) (2.49) (1.17) (1.40) (1.20)

T5% (T10%) 553 636 506 520 591

(571) (653) (601) (561) (622)

[(i-Bu)7]0/[(C8H17)7]0/[EBiB]0/[CuBr]0/[PMDETA]0, toluene (nPOSS‑MA/Vtoluene = 34.5 mmol/mL), T = 333 K, Ar. corresponding heating rates from 10 to 1 K/min (T = T0 + βt + AT sin ωt; β is the rate, t the time, AT the amplitude, and ω the frequency). Dielectric Spectroscopy (DS). The sample cell consisted of two electrodes, 20 mm in diameter and a thickness of 50 μm maintained by Teflon spacers. Samples were prepared as melts under vacuum by pressing the electrodes to the spacer thickness. Dielectric measurements were made at different temperatures in the range 248.15− 383.15 K, at atmospheric pressure, and for frequencies in the range from 1 × 10−2 to 1 × 106 Hz using a Novocontrol Alpha frequency analyzer with an active sample head. The complex dielectric permittivity ε* = ε′ − iε″, where ε′ is the real and ε″ is the imaginary part, is a function of frequency ω, temperature T, and in general pressure P, ε* = ε*(ω,T,P).59−61 In the analysis of the DS spectra we have used the empirical equation of Havriliak and Negami (HN) * (ω , T ) = ε∞(T ) + εHN

Figure 3. 1H NMR analysis of copolymers (i-Bu)7/(i-C8H17)7 (75/25) (top), (i-Bu)7/(i-C8H17)7 (50/50) (middle), and (i-Bu)7/(i-C8H17)7 (25/75) (bottom).

σ0(T ) Δε(T ) m n + [1 + (iωτHN(T )) ] iεf ω

(1)

where τHN(T,P) is the characteristic relaxation time, Δε(T,P) = ε0(T,P) − ε∞(T,P) is the relaxation strength of the process under investigation, m and n (with limits 0 < m, mn ≤ 1) describe respectively the symmetrical and unsymmetrical broadening of the distribution of relaxation times, σ0 is the dc conductivity, and εf is the permittivity of the free space. In the fitting procedure, we have used the ε″ values at every temperature. The ε′ data were also used as a consistency check. From τHN the relaxation time at maximum loss, τmax, is obtained analytically following

⎛ πm ⎞ 1/ m⎛ πmn ⎞ τmax = τHN sin−1/ m⎜ ⎟ ⎟ sin ⎜ ⎝ 2(1 + n) ⎠ ⎝ 2(1 + n) ⎠

(2)

In the temperature range where two relaxation processes contribute to ε* there are different ways of representing the data. The one followed here is based on a summation of two HN functions and assumes statistical independence in the frequency domain. Viscoelastic Properties. Rheology was performed using an Advanced Rheometric Expansion System (ARES) equipped with a force-rebalanced transducer. Plate−plate geometry with plate diameters of 13 mm was used. The gap between plates was around 1 mm. Experiments were performed under dry nitrogen atmosphere. Oscillatory shear deformation was applied under conditions of controlled deformation amplitude that was kept in the range of the linear viscoelastic response of the studied samples. Frequency dependencies of the storage G′ and the loss G″ moduli of the complex shear modulus were determined from frequency sweeps within the frequency range 10−2−102 rad/s at various temperatures. Master curves for G′ and G″ at a reference temperature were constructed using the time−temperature superposition principle, as discussed in the text. Density Functional Theory (DFT). Calculations of the dipole moment of (i-Bu)7 and (i-C8H17)7 homopolymers were performed at the DFT - B3LYP62,63 level of theory and the 6-31G(d,p) basis set. Normal mode analysis confirmed that the stationary points found correspond to local minima evidenced by the absence of negative frequencies for all modes. Gaussian 09 software package64 was employed in the calculations while the visualization was made by the VMD.65 Cartesian coordinates of the optimized structures are available in the Supporting Information, section III.

Figure 4. 1H NMR spectra for (i-Bu)7/(C8H17)7 (50/50) copolymer together with a mixture of unreacted, isolated comonomers (i-Bu)7 and (C8H17)7 measured after 8 h of the polymerization process. temperature range of 298−873 K under a nitrogen atmosphere at a heating rate of 10 K/min. Differential Scanning Calorimetry (DSC). A Q2000 (TA Instruments) was used for thermal analysis with a cooling/heating rate of 10 K/min at a temperature range from 200 to 320 K. The instrument was calibrated for best performance on the specific temperature range and heating/cooling rate. The calibration sequence included a baseline calibration for the determination of the time constants and capacitances of the sample and reference sensor using a sapphire standard, an enthalpy and temperature calibration for the correction of thermal resistance using indium as standard (ΔH = 28.71 J/g, Tm = 428.8 K), and a heat capacity calibration with sapphire standard. Temperature-modulated DSC (TMDSC) was made with an amplitude of 1 K and for periods in the range from 20 to 200 s with D


Article

Macromolecules

IV. RESULTS AND DISCUSSION Segmental and Local Dynamics. Dielectric spectroscopy is usually employed to reveal the dynamic processes of polymers bearing different dipole moments. Some representative dielectric loss spectra of copolymers with antisymmetric compositions, e.g., (i-Bu)7/(i-C8H17)7 (75/25) and (i-Bu)7/(iC8H17)7 (25/75), at several temperatures are shown in Figure 5. Evidently, the dielectric loss curves of the copolymers are

Figure 6. Temperature dependence of the HN parameters, TΔε (top), m (middle), and mn (bottom), corresponding to the faster process of the copolymers (i-Bu)7/(i-C8H17)7 (75/25) (blue squares) and (iBu)7/(i-C8H17)7 (25/75) (magenta squares) and the slower process of the copolymers (i-Bu)7/(i-C8H17)7 (75/25) (blue circles) and (i-Bu)7/ (i-C8H17)7 (25/75) (magenta circles).

calculations for the molecular charge distribution, and the resulting dipole moments from DFT calculations are shown in Figure 7. By comparing the dipole moment of the ester group of MMA with the (i-Bu)7POSS-OSiMe3 and (i-C8H17)7POSSOSiMe3 groups, it is evident that the former (MMA) dominates the overall contribution to the dipole vectors. Moreover, the (iC8H17)7POSS-OSiMe3 group possesses a somewhat larger

Figure 5. Dielectric loss spectra of copolymers (i-Bu)7/(i-C8H17)7 (75/25) (top) and (i-Bu)7/(i-C8H17)7 (25/75) (bottom) at several temperatures within the range from 248 to 383 K in 5 K steps. Representative fits with a sum of two HN functions are shown at T = 293 K. The red solid and dashed lines represent the “faster” and “slower” segmental processes, respectively. The rise in dielectric loss at higher frequencies/lower temperatures is caused by a faster process (γprocess).

bimodal for several temperatures. At lower temperature this dynamic asymmetry is amplified. Therefore, two mechanisms are necessary to describe the loss spectra, i.e., a “fast” mechanism of higher dielectric strength (referred to as αfast) and a “slow” mechanism of lower dielectric strength (referred to as αslow). Some representative fits with a summation of two HN functions are shown at T = 293 K for both copolymers (Figure 5). To aid in the identification of the processes, we compare the shape parameters (temperature-normalized dielectric strength (TΔε), low- and high-frequency shape parameters) with respect to data shown in Figure 6. The figure depicts the temperature dependence of the HN parameters, TΔε, m, and mn corresponding to the two processes for the (i-Bu)7/(iC8H17)7 (75/25) and (i-Bu)7/(i-C8H17)7 (25/75) copolymers. Clearly, the faster process has approximately 3−5 times higher temperature-normalized dielectric strength than the slower process. Furthermore, TΔε for the faster process scales approximately with (i-Bu)7 content in the copolymers. Knowledge of the dipole moment of the individual comonomer units here is of immense importance in elucidating the origin of the dynamic processes. For this purpose we employ DFT

Figure 7. Calculated dipole moment (μ) of MMA, (i-Bu)7POSSOSiMe3, (i-Bu)7POSS-OSiMe2(CH2)3-MA, (i-C8H17)7POSS-OSiMe3, and (i-C8H17)7POSS-OSiMe2(CH2)3-MA accompanied by pictorial representation of their optimized structures at the B3LYP level of theory. Basis set employed: 6-31G(d,p). Black arrows represent the dipole moment vectors. Color code of the atoms: oxygen is represented in red color, carbon in cyan, and silicon in yellow. Hydrogen atoms are not shown. E


Article

Macromolecules dipole moment as compared to the (i-Bu)7 POSS-OSiMe3 group. Despite this, the dipole moment value for the (iBu)7POSS-OSiMe2(CH2)3-MA comonomer is higher than that of the (i-C8H17)7POSS-OSiMe2(CH2)3-MA. This can be explained by the relative orientation of the MMA group. In (i-Bu)7POSS-OSiMe2(CH2)3-MA, the optimized geometry follows the fully extended conformation (every dihedral angle of the main chain of the spacer possesses a value close to 180°). However, in (i-C8H17)7POSS-OSiMe2(CH2)3-MA, the plane of the MMA group is oriented vertically to the plane of the rest of the spacer, thus decreasing the molecular dipole moment. By combining the DFT and DS results, we conclude that the faster and slower processes associate with the (i-Bu)7 and (i-C8H17)7 segmental dynamics, respectively. This is in agreement with the dielectric strengths of the two processes as presented in Figure 6. Additional information on the dipole−dipole orientation correlations can be extracted by studying the dielectric strength of the α-process, Δε. The static dielectric permittivity of polar liquids with short-range interactions between molecules has been the subject of the Kirkwood−Fröhlich theory.59,60 The theory considers an infinite continuum of dielectric permittivity, ε′S, and within this a spherical region containing N elementary dipoles that are treated explicitly. Then the dielectric permittivity can be expressed as Δε = ε′S − ε∞ =

μ2 N 1 Lg 3ε0 kBT V

Figure 8. Arrhenius relaxation map of the local dynamics for homopolymer (i-C8H17)7 (red) and copolymers (i-Bu)7/(i-C8H17)7 (75/25) (blue), (i-Bu)7/(i-C8H17)7 (50/50) (green), and (i-Bu)7/(iC8H17)7 (25/75) (magenta). The different processes are as follows: (rhombi) γ-process from DS for (i-C8H17)7; (squares) fast α process of the copolymers from DS; (black and red up triangles) α process of homopolymers (i-Bu)7 and (i-C8H17)7, respectively, from TMDSC; (green, blue, and magenta up triangles) faster α process (αfast) of the copolymers from TMDSC; (circles) slower α process (αslow) of copolymers from DS.

⎛ B ⎞ τ = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠

(3)

(4)

where τ0 is the relaxation time in the limit of very high temperatures, B is the activation parameter, and T0 is the “ideal” glass temperature for the two processes, respectively. The corresponding parameters for the (i-C8H17)7 homopolymer and copolymers (i-Bu)7/(i-C8H17)7 (75/25), (i-Bu)7/(i-C8H17)7 (50/50), and (i-Bu)7/(i-C8H17)7 (25/75) are summarized in Table 2. On the other hand, the even faster γ-process with shape parameters m = 0.4 and mn = 0.2 is located in the glassy state and has an Arrhenius temperature dependence according to

Here, L = ε′S(ε∞ + 2)2/(2(ε′S + ε∞)) is the local field, N/V is the number density of dipoles expressed as (ρ/M)NA, where ρ is the mass density (obtained assuming the same rhombohedral unit cell58 as in the monomers for both homopolymers resulting in ρ ∼ 1.12 and 1.55 g/cm3 for (i-Bu)7 and (i-C8H17)7, respectively), M is the molar mass, μ is the dipole moment, and g is the Kirkwood−Fröhlich dipole orientation correlation function. The latter is defined as the ratio of the mean-squared dipole moment measured in a dense system divided by the same quantity obtained in a noninteracting case, i.e., in the gas phase, g = μ2/μgas2. Knowledge of the gas phase dipole moments of (i-Bu)7 and (i-C8H17)7 (DFT) results in a dipole orientation correlation function with g ∼ 0.2. These values are suggestive of a destructive interference of dipoles in the melt state of poly(POSS-MA)s. The relaxation times of the different processes in the homopolymers (i-Bu)7 and (i-C8H17)7 and the copolymers with (i-Bu)7/(i-C8H17)7 ratio (75/25), (50/50), and (25/75) are summarized in the usual Arrhenius representation (Figure 8). The figure depicts three dielectrically active processes (γ, αslow, αfast) with distinctly different temperature dependencies. A single albeit broad process obtained from TMDSC (structural relaxation) is also included and coincides with αfast process of the copolymers, e.g., the process with the higher dielectric strength. Figure S34 provides the TMDSC traces of homopolymers and copolymers. Notably, even the derivative of the heat capacity traces (not shown here) is not capable to distinguish the two glass temperatures, possibly because they are closely spaced (ΔTg ∼ 20 K). The relaxation times at maximum loss of the αslow and αfast processes conform to the Vogel−Fulcher−Tammann (VFT) equation:

⎛ E ⎞ ⎟ τ = τ0 exp⎜ ⎝ RT ⎠

(5)

−10

with τ0 = 2 × 10 s and an activation energy, E, of 36.5 kJ/ mol for the (i-C8H17)7 homopolymer. (For clarity reasons the same process in the copolymers is omitted from Figure 8.) Notice that this process merge with the αfast process at a frequency of ∼105 Hz, suggesting a more cooperative character than typical local relaxations in the glassy state. Evidently, all copolymers possess two segmental processes and hence two glass temperatures. Figure 9 depicts their dependence on composition. The presence of dual segmental processes and their associated Tg’s is reminiscent of miscible blends6−16 and block copolymers but not of random copolymers.18−36 This suggests the presence of dynamic heterogeneity in the copolymers and this despite their random distribution and the proximity of the glass temperatures of the parent homopolymers. It would be of interest to obtain an estimate of the local composition associated with each dynamic process. According to the “self-concentration” model of LM,17 the average composition of the local environment around any chosen segment is enriched by the same species because of chain connectivity effects. The effective local concentration F


Article

Macromolecules

Table 2. VFT Parameters of the Slower and Faster α-Process for the (i-C8H17)7 Homopolymer and Copolymers (i-Bu)7/(iC8H17)7 (75/25), (i-Bu)7/(i-C8H17)7 (50/50), and (i-Bu)7/(i-C8H17)7 (25/75) 75/25 τ0 (s) B (K) T0 (K)

50/50

25/75

(i-C8H17)7

fast

slow

fast

slow

fast

slow

3 × 10−8 980 ± 50 211 ± 2

2 × 10−8 1020 ± 80 219 ± 3

3 × 10−10 2700 ± 100 172 ± 5

2 × 10−8 1070 ± 80 210 ± 3

3 × 10−10 2400 ± 100 180 ± 30

8 × 10−9 1280 ± 90 199 ± 4

3 × 10−10 3300 ± 80 146 ± 3

Viscoelastic Properties. As this is the first example of a random copolymer with dual segmental processes, it is of interest to explore the response to an external oscillating stress. According to the principle of time−temperature superposition (tTs), the frequency (ω) dependence of the complex shear modulus, G*, at any temperature can be obtained from a master curve at a reference temperature (Tr) according to the equation G*(ω , T ) = G*(a Tω; Tr)

(9)

When the tTs is valid, then at each temperature a single frequency scale shift factor, aT, allows superposition of all viscoelastic data at temperature T. Figure 10 depicts the Figure 9. Dependence of the liquid-to-glass temperature obtained from DS on copolymer composition. The red solid line represents the Fox equation. The dashed lines represent fits of the data to the Lodge−McLeish model with the indicated values of self-concentration.14

(φeff) sensed by a polymer segment is calculated by considering the bulk concentration (φ) and the self-concentration (φs) of the considered polymer segment: φeff = φs + (1 − φs)φ

(6)

The self-concentration of a given compound is determined from the volume occupied by monomers in one Kuhn length inside a volume of VK = lK3 as φs =

C∞M 0 kρNAV

(7)

where C∞ is the characteristic ratio, M0 is the repeating unit molar mass, k is the number of backbone bonds per repeat unit, and ρ is the density. According to this model, the monomeric friction factor of one component actually senses a different effective Tg, determined by (8)

Figure 10. Master curves for the storage modulus (G′, squares) and loss modulus (G″, circles) for the homopolymer (i-Bu)7/(i-C8H17)7 (0/100) and the copolymers (i-Bu)7/(i-C8H17)7 (25/75), (i-Bu)7 /(iC8H17)7 (50/50), and (i-Bu)7 /(i-C8H17)7 (75/25) using data in the range 257 < T < 293 K. The reference temperature was T = 263 K in all master curves.

and the corresponding expression for another component. In other words, the effective Tg for one component is determined from the macroscopic Tg(φ) but now evaluated at φeff rather than φ. As for the macroscopic composition dependence of the glass temperature, the model employs the Fox equation. Lastly, modifications of the LM model (that resulted into a selfconsistent definition) as well as deviations from the Fox equation are beyond the scope of this study. Here, we have employed the LM model and extracted φself for each component in the copolymers. For the slow component ((iC8H17)7), a self-concentration value of 0.58 is extracted and for the fast component ((i-Bu)7) a value of 0.47. These results demonstrate that dynamic heterogeneity can be tuned by regulating the size of the repeat unit in random copolymers.

frequency dependence of the master curves for the storage and loss moduli of the homopolymer (i-C 8 H17 ) 7 and the copolymers (i-Bu)7/(i-C8H17)7 (25/75), (i-Bu)7/(i-C8H17)7 (50/50), and (i-Bu)7/(i-C8H17)7 (75/25) at a reference temperature of 263 K. The crossing of the moduli at lower temperatures (higher frequencies) signifies the onset to the glassy region while at higher temperatures, there is a near parallel behavior of the shear moduli (with G′ ∼ G″) over a broad temperature/frequency range. More interesting is the region associated with the glass “transition”. This regime broadens with increasing (i-Bu)7 composition in the copolymers and in the case of (i-Bu)7/(i-C8H17)7 (75/25) extends over several decades.

Tgeff (φ) = Tg(φ = φeff )

G


Article

Macromolecules These features of the shear moduli represent a not-typical behavior for single-component systems (i.e., homopolymers and even random copolymers). The latter are characterized by a single glass temperature, narrow G″ peaks, a broad intermediate zone, and terminal behavior at low frequencies with the characteristic frequency dependence (G′ ∼ ω2 and G″ ∼ ω1). Here a significantly broadened glassy region is observed with a lack of an intermediate zone which is accompanied by a nonterminal behavior. Moreover, the master-curve construction of Figure 10 gives the wrong impression that the systems exhibit thermorheological simplicity (master curves are constructed with a single shift factor, whose temperature dependence is shown in Figure S35). Figure 11 compares master curves of the loss modulus at

Figure 12. Comparison of the master curves for the loss tangent (tan δ) of the homopolymer (i-Bu)7/(i-C8H17)7 (0/100) (red) and the copolymers (i-Bu)7/(i-C8H17)7 (75/25) (blue), (i-Bu)7/(i-C8H17)7 (50/50) (green), and (i-Bu)7/(i-C8H17)7 (75/25) (magenta). In the inset, the temperature dependence of the loss tangent minimum for the homopolymer (i-Bu)7/(i-C8H17)7 (0/100) and the copolymers (iBu)7/(i-C8H17)7 (50/50) (green) and (i-Bu)7/(i-C8H17)7 (25/75) (magenta) are shown. The solid lines represent linear fits, and the corresponding slopes are indicated.

thermorheologically simple. The breakdown of tTs reflects the different shift factors for the segmental and chain relaxations on approaching the glass temperature. This has been experimentally demonstrated under both “isobaric” (i.e., by changing temperature)69−73 and “isothermal” (by changing pressure)74 conditions by DS. To quantify the efficacy of time−temperature superposition (tTs), in the inset to Figure 12 we employ the temperature dependence of the local minimum in loss tangent. The values of the slopes, as can be easily seen, violate the tTs criterion:66−68

Figure 11. Comparison of master curves of the loss modulus for the homopolymer (i-Bu)7/(i-C8H17)7 (0/100) (red) and the copolymers (i-Bu)7/(i-C8H17)7 (75/25) (blue), (i-Bu)7/(i-C8H17)7 (50/50) (green), and (i-Bu)7/(i-C8H17)7 (25/75) (magenta). The reference temperature was T = 263 K in all master curves. In the inset, a comparison is made between the loss modulus master curve and the dielectric loss for the copolymer (i-Bu)7/(i-C8H17)7 (75/25) at temperature T = 293 K.

d tan δmin ≥ 5 × 10−4 K−1 dT

(10)

Thus, the homopolymer (i-C8H17)7 and the copolymers (iBu)7/(i-C8H17)7 (25/75), (i-Bu)7/(i-C8H17)7 (50/50) and (iBu)7/(i-C8H17)7 (75/25) constitute thermorheologically complex systems presumably because of the bulky side groups. This is in accord with the dielectric spectroscopy study. However, DS is more sensitive to the presence of dynamic heterogeneity in the copolymers. Nevertheless, despite the different sensitivity, both rheology and DS provide evidence for dynamic heterogeneity in the random copolymers.

the glassy region for homopolymer (i-C8H17)7 and copolymers (i-Bu)7/(i-C8H17)7 (25/75), (i-Bu)7/(i-C8H17)7 (50/50), and (i-Bu)7/(i-C8H17)7 (75/25). Pronounced broadening of the loss moduli at the rubber-to-glass “transition” is evident. This feature can be attributed to increasing dynamic heterogeneity at the pertinent length scale that is similar to the one described in miscible polymer blends. The same figure (inset to Figure 11) compares the loss moduli of copolymer (i-Bu)7/(i-C8H17)7 (75/25) with the dielectric loss curve all referring to 293 K. Evidently, the loss modulus is very broad and practically embraces both segmental processes as clearly evidenced in the dielectric loss curve. Interestingly, the observed broadening and failure of time−temperature superposition (see below with respect to Figure 12) occurs despite the fact that the pure components exhibit a rather moderate dynamic asymmetry (i.e., ΔTg ≈ 20 K). More informative about the issue of thermorheological simplicity/complexity in the copolymers is a representation of the rheology data that is based on the loss tangent.66−68 The superposition of the loss tangent (tan δ) data (Figure 12) has some distinct features that include the minimum in a region between the segmental and chain relaxations and the deviations from a perfect superposition in the region between the tan δ minimum and maximum. Evidently, and according to this representation none of the copolymers can be considered as

V. CONCLUSION Random copolymers, thought of as dynamically homogeneous exhibiting a single glass temperature, can be engineered to engender dynamic heterogeneity by appropriate choice of the comonomers. In the present study this was made possible by employing comonomers with the POSS cubic siloxane cage as side groups on a polymethacrylate backbone. In effect, POSS units with their large repeat unit volume effectively trigger dynamic heterogeneity. 1H NMR at every step of the polymerization process confirmed the random character of the copolymers. A combination of differential scanning calorimetry, dielectric spectroscopy, and rheology techniques was employed to investigate the dynamics of these random copolymers of ((i-Bu)7POSS-OSiMe2(CH2)3-MA) and ((iC8H17)7POSS-OSiMe2(CH2)3-MA) as a function of composiH


Article

Macromolecules

ordered state in proximity to the ODT and ordered state. Macromolecules 1996, 29, 1326−1336. (6) Colby, R. H. Breakdown of time-temperature superposition in miscible polymer blends. Polymer 1989, 30, 1275−1278. (7) Roland, C. M.; Ngai, K. L. Dynamic heterogeneity in a miscible blend. Macromolecules 1991, 24, 2261−2265. (8) Chin, Y. H.; Zhang, C.; Wang, P.; Inglefield, P. T.; Jones, A. A.; Kambour, R. P.; Bendler, J. T.; White, D. M. Glass transition dynamics in a compatible blend by two-dimensional solid-state NMR. Macromolecules 1992, 25, 3031. (9) Pathak, J.; Colby, R.; Floudas, G.; Jerome, R. Dynamics in miscible blends of polystyrene and poly(vinyl methyl ether). Macromolecules 1999, 32, 2553−2561. (10) He, Y.; Lutz, T.; Ediger, M. Segmental and terminal dynamics in miscible polymer mixtures: tests of the Lodge-Mcleish model. J. Chem. Phys. 2003, 119, 9956−9965. (11) Krygier, E.; Lin, G.; Mendes, J.; Mukandela, G.; Azar, D.; Jones, A.; Pathak, J.; Colby, R. H.; Kumar, S. K.; Floudas, G.; Krishnamoorti, R.; Faust, R. Segmental dynamics of head-to-head polypropylene and polyisobutylene in their blend and pure components. Macromolecules 2005, 38, 7721−7729. (12) Ngai, K. L.; Roland, C. M. Models for the component dynamics in the blends and mixtures. Rubber Chem. Technol. 2004, 77, 579−590. (13) Zetsche, A.; Fischer, E. W. Dielectric studies of the α-relaxation in miscible polymer blends and its relation to concentration fluctuations. Acta Polym. 1994, 45, 168−175. (14) Cangialosi, D.; Alegría, A.; Colmenero, J. Predicting the time scale of the component dynamics of miscible polymer blends: The polyisoprene/poly(vinylethylene) case. Macromolecules 2006, 39, 7149−7156. (15) Schwartz, G. A.; Colmenero, J.; Alegría, A. Single component dynamics in miscible poly(vinyl methyl ether)/polystyrene blends under hydrostatic pressure. Macromolecules 2007, 40, 3246−3255. (16) Harmandaris, V.; Kremer, K.; Floudas, G. Dynamic heterogeneity in fully miscible blends of polystyrene with oligostyrene. Phys. Rev. Lett. 2013, 110, 165701. (17) Lodge, T.; Mcleish, T. Self-concentrations and effective glass transition temperatures in polymer blends. Macromolecules 2000, 33, 5278−5284. (18) Fitzgerald, J. J.; Binga, T. D.; Sorriero, L. J.; O’Reilly, J. M. Dielectric relaxation behavior of styrene butyl acrylate copolymers near Tg. Macromolecules 1995, 28, 7401−7406. (19) Arsac, A.; Zerroukhi, A.; Ainser, A.; Carrot, C. Rheological characterization of styrene methyl methacrylate copolymers. Int. J. Polym. Anal. Charact. 2002, 7, 117−129. (20) Jakubowski, W.; Juhari, A.; Best, A.; Koynov, K.; Pakula, T.; Matyjaszewski, K. Comparison of thermomechanical properties of statistical, gradient and block copolymers of isobornyl acrylate and nbutyl acrylate with various acrylate homopolymers. Polymer 2008, 49, 1567−1578. (21) Schneider, H. The meaning of the glass temperature of random copolymers and miscible polymer blends. J. Therm. Anal. Calorim. 1999, 56, 983−989. (22) Penzel, E.; Rieger, J.; Schneider, H. The glass transition temperature of random copolymers: 1. Experimental data and the Gordon-Taylor equation. Polymer 1997, 38, 325−337. (23) Daimon, H.; Okitsu, H.; Kumanotani, J. Glass transition behaviors of random and block copolymers and polymer blands of styrene and cyclododecyl acrylate. I. Glass transition temperatures. Polym. J. 1975, 7, 460−466. (24) Merenga, A. S.; Papadakis, C. M.; Kremer, F.; Liu, J.; Yee, A. F. Broadband dielectric spectroscopy of the inter- and intramolecular dynamics of a series of random polyester copolymers. Colloid Polym. Sci. 2001, 279, 1064−1072. (25) Penzel, E.; Rieger, J.; Schneider, H. The glass transition temperature of random copolymers: 2. Extension of the GordonTaylor equation for asymmetric Tg vs composition curves. Polymer 1997, 38, 1323−1337.

tion. The effective dipole moment in the melt state was evaluated from dielectric spectroscopy with input from density functional theory calculations performed in the gas phase. Two distinct relaxation processes were found by dielectric spectroscopy giving rise to two glass temperaturesthis despite the fact that the pure components exhibited only moderate dynamic asymmetry (i.e., ΔTg ≈ 20 K). In addition, rheology revealed significant broadening of the viscoelastic functions leading eventually to the failure of time−temperature superposition for all copolymer compositions. Considering all together, results provide signaturesfor the first timeof dynamic heterogeneity in a random copolymer. It shows that dynamic heterogeneity can be tuned by regulating the size of the repeat unit. This finding was discussed in terms of the selfconcentration model of Lodge and McLeish, usually employed for the segmental dynamics in miscible blends or copolymers. Self-concentrations in the range from 0.5−0.6 were estimated for the two components.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00660. Sample characterization methods, 2D WISE NMR, results from temperature-modulated DSC, Cartesian coordinates of optimized structures (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*(G.F.) E-mail gfl[email protected]. ORCID

Krzysztof Matyjaszewski: 0000-0003-1960-3402 George Floudas: 0000-0003-4629-3817 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The current work was supported by the Research unit on Dynamics and Thermodynamics of the UoI cofinanced by the European Union and the Greek state under NSRF 2007-2013 (Region of Epirus, call 18). K.M. acknowledges support from the National Science Foundation (DMR 1501324). B.M. and A.F. acknowledge support from the National Centre for Research and Development in Poland - PBS3/A1/16/2015.

■

REFERENCES

(1) Shakhnovich, E. I. Proteins with selected sequences fold into unique native conformation. Phys. Rev. Lett. 1994, 72, 3907−3910. (2) Stühn, B.; Stickel, F. Dielectric normal mode spectroscopy in the ordered and disordered states of diblock copolymers. Macromolecules 1992, 25, 5306−5312. (3) Floudas, G.; Paraskeva, S.; Hadjichristidis, N.; Fytas, G.; Chu, B.; Semenov, A. N. Dynamics of polyisoprene in star block copolymers confined in microstructures: A dielectric spectroscopy study. J. Chem. Phys. 1997, 107, 5502−5509. (4) Floudas, G.; Hadjichristidis, N.; Iatrou, H.; Pakula, T. Microphase separation in model 3-miktoarm star co- and terpolymers. 2. Dynamics. Macromolecules 1996, 29, 3139−3146. (5) Karatasos, K.; Anastasiadis, S.; Floudas, G.; Fytas, G.; Pispas, S.; Hadjichristidis, N.; Pakula, T. Composition fluctuation effects on dielectric normal-mode relaxation in diblock copolymers. 2. DisI


Article

Macromolecules (26) Morais, V.; Encinar, M.; Prolongo, M. G.; Rubio, R. G. Dynamical mechanical behavior of copolymers made of styrene and methyl methacrylate: random, alternate and diblock copolymers. Polymer 2006, 47, 2349−2356. (27) Kahle, S.; Korus, J.; Hempel, E.; Unger, R.; Horing, R.; Schroter, K.; Donth, E. Glass transition cooperativity onset in a series of random copolymers poly(n-butyl methacrylate-stat-styrene). Macromolecules 1997, 30, 7214−7223. (28) Kim, J.; Mok, M. M.; Sandoval, R. W.; Woo, D. J.; Torkelson, J. M. Uniquely broad glass transition temperatures of gradient copolymers relative to random and block copolymers containing repulsive comonomers. Macromolecules 2006, 39, 6152−6160. (29) Wong, C. L. H.; Kim, J.; Torkelson, J. M. Breadth of glass transition temperature in styrene/acrylic acid block, random and gradient copolymers: unusual sequence distribution effects. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2842−2849. (30) Liu, G.; Zhang, L.; Yao, Y.; Yang, L.; Gao, J. Glass transition temperatures and rheological behavior of methyl methacrylate-styrene random copolymers. J. Appl. Polym. Sci. 2003, 88, 2891−2896. (31) Faghihi, F.; Mohammadi, N.; Hazendonk, P. Effect of restricted phase segregation and resultant nanostructural heterogeneity on glass transition of nonuniform acrylic random copolymers. Macromolecules 2011, 44, 2154−2160. (32) Halary, J. L.; Oultache, A. K.; Louyot, J. F.; Jasse, B.; Sarraf, T.; Muller, R. Viscoelastic properties of styrene-co-methyl methacrylate random copolymers. J. Polym. Sci., Part B: Polym. Phys. 1991, 29, 933− 943. (33) Encinar, M.; Prolongo, M. G.; Rubio, R. G.; Ortega, F.; Ahmadi, A.; Freire, J. J. Dielectric and molecular dynamics study of the secondary relaxations of poly(styrene-co-methylmethacrylate) copolymers: influence of the molecular architecture. Eur. Phys. J. E: Soft Matter Biol. Phys. 2011, 34, 134. (34) Ezquerra, T. A.; Baltá-Calleja, F. J.; Zachmann, H. G. Dielectric relaxation of amorphous random copolymers of poly(ethylene terephthalate) and poly(ethylene-2,6-naphthalene dicarboxylate). Acta Polym. 1993, 44, 18−24. (35) Park, C. H.; Kim, J. H.; Ree, M.; Sohn, B. H.; Jung, J. C.; Zin, W. C. Thickness and composition dependence of the glass transition temperature in thin random copolymer films. Polymer 2004, 45, 4507− 4513. (36) Beevers, R. B.; White, E. F. T. Physical properties of vinyl polymers. Part 2.-The glass transition temperature of block and random acrylonitrile+methyl methacrylate copolymers. Trans. Faraday Soc. 1960, 56, 1529−1534. (37) Moskalenko, A.; Kuznetsov, Y. A.; Dawson, K. A. Glass transition in random copolymers. Phys. A 1998, 249, 358−361. (38) Gordon, M.; Taylor, J. S. Ideal copolymers and the second-order transitions of synthetic rubbers. i. non-crystalline copolymers. J. Appl. Chem. 1952, 2, 493−500. (39) Di Marzio, E. A.; Gibbs, J. H. Glass temperature of copolymers. J. Polym. Sci. 1959, 40, 121−131. (40) Fox, T. G. B. Influence of diluents and of copolymer composition on the glass temperature of a polymer system. Am. Phys. Soc. 1956, 1, 123. (41) Beiner, M.; Huth, H. Nanophase separation and hindered glass transition in side-chain polymers. Nat. Mater. 2003, 2, 595−599. (42) Beiner, M.; Schröter, K.; Hempel, E.; Reissig, S.; Donth, E. Multiple glass transitions and nanophase separation in poly(n-alkyl methacrylates). Macromolecules 1999, 32, 6278−6282. (43) Floudas, G.; Mpoukouvalas, K.; Papadopoulos, P. The role of temperature and density on the glass transition dynamics of glass formers. J. Chem. Phys. 2006, 124, 074905. (44) Roland, C. M.; McGrath, K. J.; Casalini, R. Volume effects on the glass transition dynamics. J. Non-Cryst. Solids 2006, 352, 4910− 4914. (45) Dudowicz, J.; Freed, K. F.; Douglas, J. F. Direct computation of characteristic temperatures and relaxation times for glass-forming polymer liquids. J. Chem. Phys. 2005, 123, 111102.

(46) Wang, Z.; Li, Y.; Dong, X.-H.; Yu, X.; Guo, K.; Su, H.; Yue, K.; Wesdemiotis, C.; Cheng, S. Z. D.; Zhang, W.-B. Giant gemini surfactants based on polystyrene-hydrophilic polyhedral oligomeric silsesquioxane shape amphiphiles: Sequential ‘’click’’ chemistry and solution self-assembly. Chem. Sci. 2013, 4, 1345−1352. (47) Yu, X.; Yue, K.; Hsieh, I. F.; Li, Y.; Dong, X.-H.; Liu, C.; Xin, Y.; Wang, H.-F.; Shi, A.-C.; Newkome, G. R.; Ho, R.-M.; Chen, E.-Q.; Zhang, W.-B.; Cheng, S. Z. D. Giant surfactants provide a versatile platform for sub-10-nm nanostructure engineering. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 10078−10083. (48) Yue, K.; Liu, C.; Guo, K.; Wu, K.; Dong, X.-H.; Liu, H.; Huang, M.; Wesdemiotis, C.; Cheng, S. Z. D.; Zhang, W.-B. Exploring shape amphiphiles beyond giant surfactants: Molecular design and click synthesis. Polym. Chem. 2013, 4, 1056−1067. (49) Li, G.; Wang, L.; Ni, H.; Pittman, C. U., Jr. Polyhedral oligomeric silsesquioxane (POSS) polymers and copolymers: a review. J. Inorg. Organomet. Polym. 2001, 11, 123−154. (50) Kuo, S.-W.; Chang, F.-C. POSS related polymer nanocomposites. Prog. Polym. Sci. 2011, 36, 1649−1696. (51) Schwab, J. J.; Lichtenhan, J. D. Polyhedral Oligomeric Silsesquioxane (POSS)-Based Polymers. Appl. Organomet. Chem. 1998, 12, 707−713. (52) Cordes, D. B.; Lickiss, P. D.; Rataboul, F. Recent developments in the chemistry of cubic polyhedral oligosilsesquioxanes. Chem. Rev. 2010, 110, 2081−2173. (53) Hussain, H.; Shah, S. M. Recent developments in nanostructured polyhedral oligomeric silsesqioxane-based materials via ‘controlled’ radical polymerization. Polym. Int. 2014, 63, 835−847. (54) Pyun, J.; Matyjaszewski, K. Synthesis of hybrid polymers Using atom transfer radical polymerization: Homopolymers and Block Copolymers from polyhedral oligomeric silsesquioxane monomers. Macromolecules 2000, 33, 217−220. (55) Pyun, J.; Matyjaszewski, K.; Kowalewski, T.; Savin, D.; Patterson, G.; Kickelbick, G.; Huesing, N. Synthesis of Well-Defined Block Copolymers Tethered to Polysilsesquioxane Nanoparticles and Their Nanoscale Morphology on Surfaces. J. Am. Chem. Soc. 2001, 123, 9445−9446. (56) Pyun, J.; Matyjaszewski, K.; Wu, J.; Kim, G.-M.; Chun, S. B.; Mather, P. T. ABA triblock copolymers containing polyhedral oligomeric silsesquioxane pendant groups: synthesis and unique properties. Polymer 2003, 44, 2739−2750. (57) Franczyk, A.; He, H.; Burdyńska, J.; Hui, C. M.; Matyjaszewski, K.; Marciniec, B. Synthesis of high molecular weight polymethacrylates. ACS Macro Lett. 2014, 3, 799−802. (58) Alexandris, S.; Franczyk, A.; Papamokos, G.; Marciniec, B.; Matyjaszewski, K.; Koynov, K.; Mezger, M.; Floudas, G. Polymethacrylates with polyhedral oligomeric silsesquioxane (POSS) moieties: influence of spacer length on packing, thermodynamics and dynamics. Macromolecules 2015, 48, 3376−3385. (59) Kremer, F., Schoenhals, A., Eds.; Broadband Dielectric Spectroscopy; Springer: Berlin, 2002. (60) Floudas, G.; Paluch, M.; Grzybowski, A.; Ngai, K. L. In Molecular Dynamics of Glass-Forming Systems; Springer: 2011. (61) Floudas, G. Dielectric Spectroscopy. In Polymer Science: A Comprehensive Reference;Matyjaszewski, K., Möller, M., Eds.; Elsevier BV: Amsterdam, 2012; Vol. 2.32, pp 825−845. (62) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5652. (63) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (64) Gaussian 09, Revision E.01: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; J


Article

Macromolecules Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian, Inc.: Wallingford, CT, 2009. (65) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38. (66) Pathak, J.; Kumar, S.; Colby, R.; Kamath, S.; Stadler, R. Rheology of miscible blends: SAN and PMMA. Macromolecules 1998, 31, 8988−8997. (67) Blochowiak, M.; Pakula, T.; Butt, H.; Floudas, G. Miscibility of binary blends of ethylene/norborene copolymers: comparison to a lattice cluster theory. Polymer 2007, 48, 6010−6017. (68) Blochowiak, M.; Pakula, T.; Butt, H.; Floudas, G.; Bruch, M. Thermodynamics and rheology of cycloolefin copolymers. J. Chem. Phys. 2006, 124, 134903. (69) Plazek, D. J. Temperature dependence of viscoelastic behavior of polystyrene. J. Phys. Chem. 1965, 69, 3480. (70) Plazek, D. J.; Schlosser, E.; Schönhals, A.; Ngai, K. L. Breakdown of the Rouse model for polymers near the glass transition temperature. J. Chem. Phys. 1993, 98, 6488. (71) Ngai, K. L.; Plazek, D. J. Thermo-theological, piezo-rheological and TVgamma-rtheological complexities of viscoelastic mechanisms in polymers. Macromolecules 2014, 47, 8056−8063. (72) Schönhals, A. Relation between main and normal mode relaxations for polyisoprene studied by dielectric spectroscopy. Macromolecules 1993, 26, 1309−1312. (73) Nicolai, T.; Floudas, G. Dynamics of linear and star poly(oxypropylene) studied by dielectric spectroscopy and rheology. Macromolecules 1998, 31, 2578−2585. (74) Floudas, G.; Reisinger, T. Pressure dependence of the local and global dynamics of polyisoprene. J. Chem. Phys. 1999, 111, 5201− 5204.

K


Dynamic Heterogeneity in Random Copolymers of Polymethacrylates

Recommend Documents