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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Linear Rheology of a Series of Second-Generation Dendronized Wedge Polymers Zhiyuan Qian,† Yung P. Koh,† Madhusudhan R. Pallaka,† Alice B. Chang,‡ Tzu-Pin Lin,‡ Pablo E. Guzmań ,§ Robert H. Grubbs,‡ Sindee L. Simon,† and Gregory B. McKenna*,† †

Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States § Energetic Technology Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States Downloaded via WEBSTER UNIV on February 26, 2019 at 17:52:51 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: A series of second-generation dendronized wedge polymers were synthesized by ring-opening metathesis polymerization, and the linear viscoelastic response over a wide range of temperatures was investigated. From 0 to 90 °C the dynamic moduli (G′(ω) and G″(ω)) were determined, and frequency−temperature superposition was used to create master curves that showed behavior from the terminal zone to the glassy regime. An apparent extremely low rubbery plateau of ∼10 kPa was observed in both the dynamic response and in the corresponding van Gurp−Palmen plot. However, further investigation shows that the apparent rubbery plateau is related to the steady-state recoverable compliance, not the onset of entanglements. In addition, these wedge polymers exhibit an extremely low glassy modulus of ∼100 MPa at 0 °C, which is shown to increase at 1 Hz to ∼700 MPa at −80 °C for the wedge polymer 2G-EHW-311. In addition, both small- and wide-angle X-ray scattering patterns were obtained for all of the polymers investigated, and these showed that the polymer molecules adopt an extended cylinder conformation. Furthermore, based on calorimetric measurements, the polymers were found to exhibit two glass transition temperatures, with a 100 K difference between the higher (Tg,hi = 26.8 ± 0.7 °C) and lower glass transition temperatures (Tg,lo = −76.1 ± 1.1 °C) for the 2G-EHW311 material. Hence, an intermediate regime extends to well below the Tg,hi to Tg,lo, providing an explanation for the low glassy modulus of ∼100 MPa at 0 °C and its increase to ∼700 MPa when measured at Tg,hi − 100 °C and approaching the Tg,lo.

1. INTRODUCTION

recoverable compliance rather than entanglement plateau behavior. Another complex side-chain grafted polymer that has been recently reported is the wedge polymer,26−28 also referred to as a dendronized polymer.29−42 Like bottlebrush polymers, wedge polymers feature densely grafted bulky groups; however, bottlebrushes bear polymeric side chains, whereas wedge polymers bear discrete dendronized side groups. In both cases, as the size of the pendant group increases, the persistence length increases, the backbone becomes stiffer, and the distance between entanglements increases.30,43−45 Vlassopoulos and co-workers36,38−40 studied a series of dendronized polymers at different generations with side groups functionalized to promote hydrogen bond formation. It was found that although the entanglement network was absent in the system, because of the strong intermolecular interactions (hydrogen bonding), an elastic plateau was still observed in the dynamic responses.36,39,40 Hu et al.46 performed linear rheological measurements for a series of (unfunctionalized) firstgeneration wedge polymers with backbone DPs varying from

With its long chain nature, the properties of polymers are determined by the monomer structure as well as the degrees of polymerization. Bottlebrush polymers, which feature linear polymeric side chains uniformly and densely grafted to a polymer backbone, have recently drawn significant attention.1−24 Recent studies11,12,22 showed that bottlebrush polymers adopt a sphere-like shape when the backbone length is comparable with the side chain length. As the backbone length increases, the shape of the molecules becomes anisotropic and takes on a cylindrical conformation. The dynamic master curves for these materials show that the molecules undergo hierarchical or sequential relaxation25 processes; i.e., the side chains relax first, and then the backbone relaxes. Furthermore, as the backbone is stiffened by the densely grafted side chains, the persistence length and distance between entanglements increase with grafting density. As a result, the formation of an entanglement network requires higher degrees of backbone polymerization.2−4,13,14,18,19 In fact, Hu et al.10 showed that for a series of bottlebrush systems (having a backbone degree of polymerization (DP) up to 800) a low plateau of 2−5 kPa appears in the dynamic modulus data that is related to the contribution of the steady-state © XXXX American Chemical Society

Received: October 4, 2018 Revised: February 18, 2019

A

DOI: 10.1021/acs.macromol.8b02122 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

Figure 1. Structure of second-generation dendronized wedge-type polymers synthesized by ring-opening metathesis polymerization (ROMP).48

Table 1. Characteristics of Second-Generation Wedge-Type Polymers sample IDa

DPb

Mw (kg/mol)

PDI

2G-EHW-77 2G-EHW-170 2G-EHW-251 2G-EHW-311 2G-EHW-402

77 170 251 311 402

137 303 447 555 717

1.03 1.08 1.18 1.18 1.30

Tgc (°C) 33.4 33.6 33.5 33.4 33.8

± ± ± ± ±

0.15 0.12 0.16 0.15 0.17

C1,gd 10.7 10.5 10.6 10.7 10.4

± ± ± ± ±

0.07 0.07 0.07 0.09 0.05

C2,gd (K) 63.5 61.1 62.5 61.2 59.0

± ± ± ± ±

0.68 0.68 0.60 0.81 0.47

me 52 53 52 53 54

± ± ± ± ±

0.64 0.67 0.60 0.84 0.51

a 2G-EHW stands for second-generation ethylhexyl wedge dendronized macromonomer. bDP is degree of polymerization of backbone. cThe rheological glass transition temperature (Tg) was obtained based on the peak position in the tan δ vs T plot when the relaxation time is 100 s (corresponding to a frequency of 0.01 rad/s). Uncertainties are the standard deviation obtained from 3 points near the peak temperature. dC1,g and C2,g are the fitting parameters from the WLF equation using Tg as the reference temperature. Uncertainties are standard error of estimate from curve fit. eThe dynamic fragilities (m) were estimated from eq 2. Uncertainties are standard errors of estimate propagated from the uncertainties in C1,g and C2,g and Tg.

monomers (as shown in Figure 1) using the third-generation bis(pyridine) initiator, (H2IMes)(pyr)2(Cl)2RuCHPh. The detailed synthesis method has been published elsewhere.48 By controlling the ratio of monomer to initiator, we obtained wedge polymers with various molecular weights. Their characteristics are listed in Table 1. These second-generation 2-ethylhexyl wedge polymers are identified as 2G-EHW-x, where x indicates the backbone degree of polymerization (DP). 2.2. Small- and Wide-Angle X-ray Scattering (SAXS/WAXS). Synchroton SAXS and WAXS measurements were performed at Beamline 12-ID-B at the Advanced Photon Source at Argonne National Laboratory. SAXS and WAXS data were collected for bulk samples. The samples were mounted such that the X-ray beam only passed through the sample and air. Measurements were performed at 25 °C using 13.3 keV X-rays and a sample-to-detector distance of 3.6 m, calibrated using a silver behenate standard. 2.3. Rheological Measurements. The rheological measurements were performed using an Anton Paar MCR 501 rheometer with RheoCompass software. A CTD 600 oven with TC 30 temperature controller is equipped with the instrument for temperature control (stability of ±0.02 °C). Five millimeter aluminum disposable parallel plates were used for the measurements. The sample was directly molded inside of the rheometer between the parallel plates and formed into a disk shape with ∼1 mm height. The dynamic frequency sweep measurements were performed over a temperature range from 100 to 0 °C. The frequency range for dynamic tests was 100 to 0.1 rad/s. Liquid nitrogen was used as the cooling source for the low temperature measurements; nitrogen was used as an inert atmosphere for the high temperature measurements. For the tests performed in the glassy state and in the glass transition regime, the sample was annealed at the temperature of interest for 1.5 h prior to running the test. The dynamic data were corrected for machine compliance by using the method reported by McKenna and co-workers.49,50 Also, because of the observation of a very low glassy value for G′(ω), a set

700 to 5314. The dilution effect of the side groups on the backbone47 led to low entanglement density and low rubbery plateau moduli of ∼10 kPa. Moreover, an extremely low glassy modulus of 100 MPa was observed. In this study, similar findings of low glassy modulus are reported for secondgeneration wedge polymers and are investigated through absolute heat capacity measurements and calorimetric DSC measurements. In the current work, a series of second-generation dendronized wedge polymers having backbone degrees of polymerization ranging from 77 to 402 were synthesized using ring-opening metathesis polymerization (ROMP).48 Compared with the first-generation wedge polymers,27 which bear three dodecyl groups (−C12H25) per backbone unit, the second-generation wedge polymers are even bulkier: each backbone unit bears nine 2-ethylhexyl chains. The structure− property relationship of dendronized wedge polymers is of great interest. The microstructure was investigated using X-ray scattering. The rheological responses from the terminal regime to the glassy regime were investigated. Moreover, absolute heat capacity measurements and low temperature differential scanning calorimetric (DSC) measurements were performed and related to the observation of an extremely low glassy state modulus in the material. These observations provide further insight into the impact of molecular architecture on polymer dynamics.

2. EXPERIMENTAL SECTION 2.1. Polymer. Second-generation dendronized wedge-type polymers were synthesized by ROMP of norbornene-based dendronized B


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Macromolecules of tests were performed at a single frequency of 1 Hz and at temperatures from 0 to −150 °C at a cooling rate of 1 K/min. 2.4. Calorimetric Measurements. The absolute heat capacity of the material was measured using the step-scan method51 using a PerkinElmer Pyris 1 differential scanning calorimeter (DSC) with a Freon intercooler. The methodology consists of sequential isothermal steps using a step size of 2 K and 0.8 min isothermal holds. The heating rate between sequential steps was 10 K/min. Measurements were performed in the temperature range of −30 to 70 °C after cooling at 30 K/min from above Tg. Results are reported based on the average of three separate measurements of different samples each having ∼5 mg in mass. The absolute heat capacity calibration was performed using a sapphire standard. Low temperature DSC measurements were performed on a Mettler Toledo DSC 1 equipped with a liquid nitrogen cooling system. Prior to the measurements, samples with approximately 15−18 mg mass were heated to 80 °C (above Tg) and held for 5 min to erase the thermal history. Heating scans were performed from −130 to 80 °C at 10 K/min after cooling at the same rate. The limiting fictive temperature (Tf′) is obtained using Moynihan’s method52 and is approximately equal to (within 1 K) the calorimetric glass transition temperature (Tg) obtained on cooling at the same rate;53 hence, Tf′ will be referred as Tg in the Results and Discussion section. Isothermal aging measurements were also performed at −75.6 and −78.6 °C for an aging time of 100 min to confirm the presence of a low temperature glass transition. Temperature calibration was performed on heating at 10 K/min with n-octane (Tm = −57 °C) and nhexadecane (Tm = 18 °C), and isothermal calibration for aging experiments was performed at 0.1 K/min.54,55

obtained from the dynamic moduli master curves using the following equations:63 η0 = lim

ω→ 0

Js =

−C1(T − Tref ) C2 + T − Tref

(3)

G′(ω) 1 lim 2 0 ω→ η0 ω2

(4)

3.3. Retardation Spectrum. The effect of bulky side group on the formation of the entanglement network is of interest. One way to study this phenomenon is to calculate the retardation spectrum (L(τ)). As shown by Plazek64 and Plazek and Echeverria,65 L(τ) is very sensitive to the onset of entanglement of the polymer chains. Here, we estimated L(τ) from the dynamic data (G′(ω) and G″(ω) vs ω) using the following first-order approximation:56 For n < 1: L(τ ) = −AJ ′d log J ′/d log ω|1/ ω = τ A=

sin(nπ /2) nπ /2

(5)

(6)

For n > 1: L(τ ) = A′J ′(2 + d log J ′/d log ω)|1/ ω = τ

3. DATA ANALYSIS 3.1. Glass Transition Temperature and Fragility. Dynamic modulus, G′(ω) and G″(ω), master curves were constructed by shifting the dynamic data to a reference temperature of 50 °C based on the time−temperature superposition (TTS) principle.56 The obtained horizontal shift factors (aT) were fitted with the Williams−Landel−Ferry (WLF)57 equation: log aT =

G″(ω) ω

(7)

A′ =

sin(nπ /2) π (1 − n/2)

(8)

J′ =

G′ G′ + G″2

(9)

2

4. RESULTS AND DISCUSSION 4.1. Microstructure from X-ray Scattering. Figure 2 shows the 1-D averaged SAXS and WAXS profiles data for all

(1)

where C1 and C2 are the fitting parameters. Based on the WLF equation, the frequency sweep data (G′(ω) and G″(ω) vs ω) at a reference temperature of 50 °C were converted to temperature sweep data (G′(T) and G″(T) vs T) at the frequency of 0.01 rad/s. The rheological glass transition temperature (Tg) was then estimated from the peak of tan δ. New WLF parameters (Cg1 and Cg2) using Tg as the reference temperature were then calculated, and the dynamic fragility (m),58−60 which characterizes the temperature dependence of dynamics at Tg, was calculated from the following equation:61,62 m=

C1gTg C2g

(2)

The values of rheological Tg and m for the second-generation wedge polymers are listed in Table 1. For calorimetric measurements, Tg is obtained from the halfheight method for absolute Cp measurements from step scan. For dynamic heating scans, Tg is equated to Tf′53 with the latter obtained using Moynihan’s method.52 3.2. Zero Shear-Rate Viscosity and Steady-State Recoverable Compliance. The zero shear-rate viscosity (η0) and steady-state recoverable compliance (Js) can be

Figure 2. X-ray scattering patterns for 2G-EHW wedge polymers at different DP.

polymers studied herein. Two broad peaks are observed, consistent with previous reports of bottlebrush polymers13,23,24,66 and other dendronized polymer systems.39,67−69 The low-q peak (q1 = 0.22 Å−1) corresponds to the average distance between backbones: d1 = 2π/q1 = 29 Å. The high-q peak (q2 = 1.4 Å−1) likely reflects short-range van der Waals C


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Figure 3. van Gurp−Palmen plots for second-generation dendronized wedge polymers investigated. (a) 2G-EHW-77, (b) 2G-EHW-170, (c) 2GEHW-251, (d) 2G-EHW-311,and (e) 2G-EHW-402, (f) Compilation of plots a−e. The insets are the vGP plots for 2G-EHWs at high moduli end or low temperatures which show the lack of superposition.

interactions among the side groups, where d2 = 2π/q2 = 4.5 Å. The values of d1 and d2 remain the same for all samples, regardless of backbone length (77 ≤ DP ≤ 402). The apparent backbone−backbone correlations extracted from the low-q peak positions are consistent with extended chain conformations (i.e., a thick cylindrical conformation), which has been reported for bottlebrush polymers11,13,16,23,24,66,70,71 as well as dendronized polymer systems,39,43,67−69 and the bulky side group presumably adopts a helical conformation67 around the backbone. The low-q peaks suggest the presence of large-scale composition fluctuations, which has also been observed in bottlebrushes.23 It is superficially reminiscent of the low angle scattering found in polyelectrolytes where large scale clustering can arises.72 Moreover, such broad low-q peaks also indicate that liquid crystalline order is absent.39 We note that an average backbone−backbone distance d1 = 29 Å suggests that the average polymer diameter (Dsc) must be between 29 and 58 Å, corresponding to either zero or complete overlap between side groups. In addition, the geometry of one repeat unit was optimized using molecular mechanics (MM2) in Chem3D. The largest distance from the backbone (considered as the methylene next to the bisimide

group) to any terminal methyl group was determined to be 20 Å, corresponding to a polymer diameter (Dsc) of ∼40 Å. The backbone contour length (L) can be estimated as 6.2 Å × DP.73 We recall that recent theory and experiments anticipate a crossover from bottlebrush-like to sphere-like behavior when L/Dsc ≈ 1.11,12,22 In this work, the lowest molecular weight sample (DP = 77) corresponds to L = 480 Å and L/Dsc = 12; the highest molecular weight sample (DP = 402) corresponds to L = 2500 Å and L/Dsc = 62. Even the maximum value Dsc = 58 Å corresponds to L/Dsc ≫ 1. These large L/Dsc values suggest that the polymers should adopt extended cylindrical conformations rather than compact spherical conformations. 4.2. Van Gurp−Palmen Plot. The van Gurp−Palmen (vGP)74 analysis of the dynamic data is a useful tool in the assessment of the validity of time−temperature superposition (TTS). Figures 3a−e present the vGP plots for the 2G-EHW wedge polymers of different DP. We see that the curves obtained at different temperatures create a single curve (except in the high modulus end, where the breakdown of TTS appears, which is discussed subsequently) in the plot of phase angle versus the magnitude of G*(ω), which supports the validity of TTS for the second-generation dendronized wedge D


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Figure 4. Master curves for second-generation dendronized wedge polymers investigated at a reference temperature of 50 °C: (a) 2G-EHW-77, (b) 2G-EHW-170, (c) 2G-EHW-251, (d) 2G-EHW-311, and (e) 2G-EHW-402. (f) Compilation of plots a−e. Vertical shift is only applied for 2GEHW-311 and 2G-EHW-402 in the glassy state, and the value of the vertical shift factor (bT) is no greater than 1.2 and 1.05, respectively. The insets are the loss modulus (G″) master curve for 2G-EHWs at high frequencies which show the lack of superposition.

polymer. For all samples, as |G*(ω)| increases (or temperature decreases), the phase angle (δ) gradually decreases from 90°, i.e., from the terminal (viscous) regime, to a local minimum (δmin,1). δmin,1 decreases with increasing DP, e.g., δmin,1(DP = 77) = 65 °C and δmin,1(DP = 402) = 51 °C. As G*(ω) continues to increase, the system moves toward the glassy regime and a second minimum (δmin,2) occurs. At δmin,2, the

lack of superposition in the single curve appears, which is consistent with a breakdown of TTS in the glassy regime. This phenomenon was also observed for the first-generation wedge polymers 1G-W studied by Hu et al.46 δmin,2 reflects the glassy modulus or α-relaxation and one would typically expect there to be a high frequency β-relaxation at lower temperatures. This aspect of the observed behavior is discussed subsequently. E


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Macromolecules Compilation of the 2G-EHW vGP plots is shown in Figure 3f. It is readily seen that as the backbone DP increases, δmin,1 decreases and the corresponding complex modulus (G δ*min,1) decreases.75 We do not attribute this to the plateau modulus (G0N), since it is well-known that G0N is independent of molecular weight (or DP).56 The data of Figure 3f also show that the glassy moduli of all the 2G-EHW wedge polymer are close to 108 Pa. 4.3. Dynamic Master Curves. By applying TTS, the dynamic modulus responses, G′(ω) and G″(ω), measured at different temperatures were shifted along the frequency axis to form a master curve. Figures 4a−e show the master curves for the different DP wedge polymers at a reference temperature of 50 °C. The responses for all 2G-EHWs are similar: characteristic terminal behavior [where G′(ω) ∼ ω2 and G″(ω) ∼ ω] is reached in the low (reduced) frequency regime, and TTS seems to break down when the temperature is below Tg [as seen by the lack of good superposition of the G″(ω) curves at high (reduced) frequencies]. For a better comparison, the master curves of the wedge polymers are plotted together in Figure 4f. In the glassy regime (high frequency) and transition regime (intermediate frequency), the responses of G′(ω) and G″(ω) for the 2G-EHW systems are independent of DP. However, as the frequency further decreases, the onset of terminal behavior decreases with increasing DP. The DP affects the behavior only at low frequency because at high frequency, or short times, the polymer chains undergo short-range molecular motion, whereas at low frequency, or long time, the properties are determined by the long-range motions of the entire polymer chain.56 In the glassy regime, G′(ω) is greater than G″(ω), indicating solid-like behavior. In the transition and terminal regimes, the samples show a fluid-like behavior since G″(ω) is greater than G′(ω). At the same time, a plateau-like response starts to develop in both G′(ω) and G″(ω) as DP increases. Similar behavior has been observed by Plazek64 in polystyrene with a molecular weight of 16000 g/mol (below the entanglement molecular weight (Me) ∼ 18000 g/mol for polystyrene) and which was attributed to the effect of the steady-state recoverable compliance (Js) on the dynamic data. In addition, Plazek and co-workers64,65,76 clarified that the plateau in the stress relaxation modulus response for polymeric amorphous selenium77−80 should be the consequence of the contribution of Js instead of the rubber-like elasticity, and the contribution of Js also resulted in a plateau in the storage modulus response. A similar result has been reported by Hu et al.10 for their unentangled bottlebrush polymers. Therefore, it is important to examine the origin of the plateau-like behavior for the wedge polymers investigated here, viz., whether it is associated with Js. Recalling the vGP plots (Figures 3a−f), there is insight into be obtained from the behavior in the vicinity of δmin,1. Recently, Qian and McKenna75 re-examined the vGP of polymers with different topologies and defined a new parameter, the reciprocal of the complex modulus at the first minimum moving from the terminal regime (1/G δ*min,1), and compared it with Js. In the case of linear polymers, when wellentangled, the value of G δ*min,1 gives the plateau modulus and is independent of molecular weight. When unentangled, 1/G δ*

Figure 5. Molecular weight dependence of 1/G δ*min,1 and Js for secondgeneration dendronized wedge polymers. Both are proportional to Mw1.

to the dynamic data) for the 2G-EHWs, and it is readily seen that 1/G δ*min,1 and Js have similar values and they both show a near to Mw1 dependence, which is consistent with the dynamics being Rouse-like. 56,81,82 A plateau generally associated with entanglements is not reached even for the largest molecular weight or backbone DP; viz., these large molecules do not entangle even up to a DP a 402 (and total Mw > 700 kg/mol). Furthermore, the results show that nearly quantitatively the values of 1/G δ*min,1 and Js are the same, consistent with the hypothesis that the plateau seen at low frequency in the dynamic data should be attributed to the steady-state recoverable compliance rather than to a rubbery, entanglement plateau. 4.4. Further Evidence for Lack of Entanglements. The molecular weight dependence of the zero shear-rate viscosity (η0) is plotted in Figure 6 at the same reference temperature of

Figure 6. Molecular weight dependence of η0 for second-generation dendronized wedge polymers at the reference temperature of 50 °C. A power law dependence of η0 ∼ Mw1 is observed.

50 °C. It clearly shows that η0 is approximately proportional to Mw1; i.e., the 2G-EHWs do not entangle even up to the largest molecular weight. The same conclusion can be drawn from the retardation spectrum (L(τ)), which is plotted in Figure 7 for 2G-EHW-311 and 2G-EHW-402 materials. In both cases, only one peak is observed. Although the peak intensity increases with molecular weight, the entanglement network is not

min,1

behaves very much like Js. Figure 5 shows the molecular weight dependence of 1/G δ*min,1 and Js (here obtained by applying eq 4 F


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represent the equilibrium behavior. At low temperatures, because the sample is in the glassy state and out of equilibrium, the expected departure from WLF behavior is observed.84 The rheological glass transition temperatures (Tg) for the 2GEHWs were calculated based on the method described in section 3.1 (the Tg for ω = 0.01 rad/s or for a relaxation time of 100 s) and are found to be independent of the molecular weight, as shown in Table 1. Also, the values are close to the Tg for the first-generation wedge polymer 1G-W (37.1 °C) studied by Hu et al.46 This suggests that the effect of the bulkier side group on the rheological Tg is small. The dynamic fragilities (m) for the 2G-EHWs were calculated from eq 2 and are listed in Table 1. The average value of m is ∼53, which is smaller than that for the 1G-W (m = 65).46 The lower value of m for the 2G-EHW is consistent with the lower Tg compared with that for the 1G-W and suggests that the 2G-EHW remains relatively flexible.61 A similar, but stronger, trend has been observed for poly(n-alkyl methacrylates),85 for which both m and Tg decrease as the size of alkyl group increases.86 While the bulky side group in the dendronized wedge polymers stiffens the backbone and delays the onset of entanglement, they also have a major impact on the glassy properties as described in the following sections. 4.6. Low Glassy Modulus. For most amorphous polymers, the glassy modulus is approximately on the order of 109 Pa.56 However, similar to the first-generation wedge polymer (1GW) studied by Hu et al.,46 the glassy modulus for the 2G-EHW is extremely low. As seen in the master curves, at ∼30 °C below Tg, the modulus barely reaches 108 Pa. Considering the general behavior of polymeric materials, it is common to find reduced glassy moduli when there is a very large high frequency or a low temperature β-transition87 or when an additional low temperature glass transition exists. We anticipated that a similar behavior would be observed in the wedge polymers and therefore performed a temperature sweep test from 0 to −150 °C at a cooling rate of 1 °C/min and a frequency of 1 Hz. Figure 9 plots the results (log(G′(T)) and log(G″(T)) vs T) for 2G-EHW-311. The testing was successful only to −80 °C due to sample slip and/or fracture because of the brittleness of the unentangled polymer. From examination of the dynamic moduli down to −80 °C we see that G′(T) and

Figure 7. Retardation spectra for two second-generation dendronized wedge polymers with DP of 311 and 402 at the reference temperature of 50 °C.

developed since there is neither a broadened peak nor a splitting into two peaks in the retardation spectra, as is typically seen in linear polymers and their solutions as entanglement sets in. The steric hindrance resulting from the bulky side group significantly reduces the flexibility of the backbone and yields a thick cylindrical conformation. In addition, the side groups dilute the backbone concentration, which then increases the distance between entanglements. Therefore, polymer chains with much larger DP than those investigated here are required to form an entanglement network. It is worth mentioning here that Costanzo et al.39 suggested that the onset of entanglements requires at least a DP of 1500 (this value was estimated based on the Kavassalis−Noolandi theory83 and consideration of the polymer persistence length) for their dendronized polymers if the intermolecular correlations and bonding interactions are not considered. 4.5. Temperature Shift Factors and Dynamic Fragilities. The temperature shift factors (aT) used to construct master curves for the 2G-EHW wedge polymers are plotted in Figure 8. At temperatures above the glass transition temperature, the shift factors are independent of the molecular weight and can be fitted by the WLF equation. Above Tg the data

Figure 9. Storage modulus and loss modulus as a function of temperature for the wedge polymer 2G-EHW-311 obtained from temperature sweep test at a cooling rate of 1 °C/min and test frequency of 1 Hz.

Figure 8. Temperature dependence of horizontal shift factors (aT) for the second-generation dendronized wedge polymer with different molecular weights. The solid line is the WLF fit to equilibrium data. G


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Figure 10. (a) Comparison of absolute heat capacities of a second-generation dendronized wedge polymer with DPs of 77, 311 and a linear polystyrene with molecular weight of 35 kg/mol at the same temperature distance from the relevant glass transition temperatures. The inset is the DSC trace of 2G-EHW-77 and 2G-EHW-311 versus temperature, and the dashed lines mark the Tgs. (b) Apparent heat capacity for the wedge polymer 2G-EHW-311 with Tg,hi and Tg,lo marked as dashed lines. (c) Baseline subtracted apparent heat capacities of unaged and aged wedge polymer 2G-EHW-311 (aged for 100 min at −75.6 and −78.6 °C, respectively). Apparent heat capacity data in (b) have been relatively shifted to match the absolute heat capacity of 2G-EHW-311.

temperature for the 2G-EHWs (0.076 and 0.093 J g−1 K−1) are much smaller than that for PS (0.276 J g−1 K−1) such that the wedge polymers have higher glassy-state entropies than does the polystyrenean unexpected result. We therefore performed scanning (DSC) measurements over a temperature range beginning at −130 °C, well below the lowest rheological measurement temperature, and the results are shown in Figure 10b for the 2G-EHW-311; the measurements were made on heating at 10 K/min after cooling at the same rate with data shifted to match the absolute heat capacity obtained from the step-scan measurements. Two Tgs are apparent. In addition to the upper Tg at 26.8 ± 0.7 °C (note that this is slightly different than the value of 26.1 °C from the step-scan measurements) with a ΔCp,hi of 0.081 ± 0.004 J g−1 K−1 (consistent with the absolute Cp data in Figure 10a), the data clearly shows a low temperature glass transition at Tg,lo = −76.1 ± 1.1 °C with a ΔCp,lo of 0.13 ± 0.01 J g−1 K−1. The total change in heat capacity over the two glass transitions (ΔCp,lo + ΔCp,hi) is ∼0.21 J g−1 K−1, which is slightly lower than that of most polymer glasses.88,89 To further corroborate the existence of Tg,lo, isothermal aging was performed at −75.6 and −78.6 °C for 100 min. Enthalpy overshoots typically associated with structural relaxation were observed and are shown in Figure 10c, confirming that Tg,lo is in fact a second glass transition. The occurrence of two calorimetric glass transitions has been reported in many polymer systems, including, but not limited to, miscible binary blends, hairy-rod polyimides, poly(nalkyl methacrylates), poly(di-n-alkyl-itaconates), poly(n-alkyl acrylates), diketopyrrolopyrrole-based polymers with non-

G″(T) both increase with decreasing temperature, and G′(T) is ∼700 MPa at −80 °C. This increase is reminiscent of the existence of a low temperature transition, with a second maximum in G″(T) at lower temperature and a concomitant increase in the storage modulus G′(T) to ∼109 Pa. Importantly, as seen in the next section on the calorimetry of the wedge polymers, it appears that the low temperature behavior is related to a second (at a very low temperature) glass transition temperature Tg,lo rather than to a more common β-relaxation. 4.7. Calorimetric Measurements. In preliminary work on the thermal analysis of the 2G-wedge type polymers, we had observed a very weak change in the heat capacity (ΔCp) at the calorimetric glass transition, suggesting either that the equilibrium liquid state had a low heat capacity or that the glassy state had a high heat capacity. To investigate which of these two was the correct interpretation and with the thought that this might be related to the very low glassy modulus observed, we performed absolute heat capacity (Cp) measurements on the 2G-EHW-77 (Tg = 25.2 ± 0.3 °C) and 2GEHW-311 (Tg = 26.1 ± 1.2 °C) samples, and the results were compared with those from a linear polystyrene (Mw of 35 kg/ mol). (Note that the calorimetric Tgs are always lower than the rheological Tgs for the present set of measurements.) The comparison of Cp between the two 2G-EHWs (representative of the 2G-EHWs) and PS plotted versus T − Tg is shown in Figure 10a. In the liquid state, the values of the absolute hear capacity (Cp) for 2G-EHWs and PS are comparable, whereas in the glassy state, the 2G-EHWs have a much larger Cp. As a consequence, the step change (ΔCp) at the glass transition H


Article

Macromolecules conjugated flexible linkers, and linear-dendronized diblock copolymers with a similar dendronized structure as the 2Gwedge polymers studied in this work.42,90−94 In general, the existence of two glass transitions are attributed to a large difference in mobility between rigid backbones and flexible side chains.42,90−92 In addition, Cheng and co-workers93 reported that the stiff backbone and flexible side chain incompatibility leads to a microphase separation where the phases can be either amorphous, liquid crystalline, or crystalline based on structural order. Similarly, Beiner and co-workers reported nanophase separations in the case of poly(n-butyl methacrylates) systems with evidence from NMR and SAXS studies,91 and also additional evidence for nanophase separations was reported by Voit and co-workers using AFM imaging for linear-dendronized diblock copolymers.42 In the case of the present work on the 2G-wedge polymers, the complex chain architecture may induce incompatibility between the rigid backbone and the bulky and flexible dendronized side chain resulting in two glass transitions Tg,hi and Tg,lo with a relatively large glassy heat capacity below Tg,hi; a small ΔCp was associated with both transitions. The presence of a second glass transition, Tg,lo at −76.1 °C is consistent with the low glassy modulus of ∼100 MPa at 0 °C and its increase toward 700 MPa as temperature decreases to −80 °C. It is also worth remarking that the occurrence of two Tgs in miscible binary blends (observed either in DSC 95,96 or in terms of dynamics97−99) has been attributed to large-scale composition fluctuations.94,95,100 These observations are similar to what is seen here in low-q X-ray scattering peaks, though the exact nature of the fluctuations here is limited by the fact that the dendronized side chains are connected to the backbone chains; hence, composition fluctuations may be localized differently.

Time−temperature shift factors were also analyzed and the dynamic fragility index m ≈ 53 for all the DPs examined for these second-generation dendronized wedge polymers.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (G.B.M.). ORCID

Alice B. Chang: 0000-0001-5036-2681 Tzu-Pin Lin: 0000-0001-7041-7213 Robert H. Grubbs: 0000-0002-0057-7817 Sindee L. Simon: 0000-0001-7498-2826 Gregory B. McKenna: 0000-0002-5676-9930 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Z.Q. and G.B.M. thank the Texas Tech University Graduate School and the John R. Bradford endowment at Texas Tech University, each for partial support of the project. S.L.S. and M.R.P. thank the National Science Foundation under Grant DMR-1610614 for partial support for the project.

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REFERENCES

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5. SUMMARY AND CONCLUSIONS The linear rheological properties and structure−property relationships of a series of second-generation dendronized wedge polymers synthesized by ROMP were investigated in the current work. The SAXS/WAXS results suggest an extend cylindrical conformation for the polymer chain. Time− temperature superposition of the rheological data was found to be valid from the terminal regime up to the glass transition regime. At temperatures below Tg, TTS was not applicable. Two minima in the phase angle are observed in the van Gurp− Palmen plot74 for all of the second-generation wedge polymers (2G-EHW) investigated. The minimum at the low modulus regime at 104−105 Pa varies with molecular weight and is related to the contribution of the steady-state recoverable compliance to the dynamic response rather than to an entanglement network. Up to the largest molecular weight, having a backbone DP of 402, no entanglement network exists. The minimum at the high modulus end at 108 Pa is independent of molecular weight and reflects the glassy modulus at 0 °C. The low modulus value is attributed to the presence of a secondary glass transition, occurring for the 2GEHW-311 at Tg,lo = −76.1 ± 1.1 °C in addition to Tg,hi at 26.8 ± 0.7 °C according to low temperature DSC measurements. The presence of two glass transitions is presumably due to a phase separation of the incompatible rigid backbone and the bulky and flexible dendronized side chain and explains the low glassy modulus of ∼100 MPa at 0 °C, its increase toward 700 MPa as temperature decreases to −80 °C, the low value of ΔCp for the higher Tg, and the correspondingly high value of the absolute heat capacity in the glassy state between Tg,lo and Tg,hi. I


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