Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Segmental Dynamics in Multicyclic Polystyrenes Achilleas Pipertzis,† Md. D. Hossain,‡ Michael J. Monteiro,‡,§ and George Floudas*,† †
Department of Physics, University of Ioannina, 45110 Ioannina, Greece Australian Institute for Bioengineering and Nanotechnology and §School of Chemical and Molecular Biosciences, The University of Queensland, Brisbane, QLD 4072, Australia
‡
S Supporting Information *
ABSTRACT: The segmental dynamics and the corresponding glass temperature, Tg, were investigated in a monocyclic and in the corresponding linear polystyrene as well as in a series of multicyclic polystyrenes, all with the same total molecular weight, with dielectric spectroscopy and DSC. There is a strong reduction of Tg with decreasing molecular weight for linear chains but only a moderate reduction for cyclic chains and this below a certain critical molecular weight (Mn ∼ 18 000 g/mol). These data contradict the Gibbs−Di Marzio lattice model predicting an increasing glass temperature with decreasing molecular weight of cyclic polymers. In multicyclic polystyrenes the results emphasize the role of constrained segments at the coupling sites (linkers) on determining practically all features of segmental dynamics: the exact temperature dependence of relaxation times and associated Tg, the dielectric strength, the distribution of relaxation times, and fragility. A nearly linear increase of Tg was found with increasing number of intramolecular constraints. Furthermore, the total molecular weight is an irrelevant parameter in discussing the dynamics of multicyclic polymers. An alternative approach that is based on the concept of free volume emphasizes intermolecular contributions and predicts the same amount of fractional free volume for multicyclic polystyrenes at their respective glass temperature (3.3%) but differences in the respective thermal expansion coefficient of free volume.
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INTRODUCTION
crystallization behavior of cyclic polymers that are based on semicrystalline backbones. It was shown that cyclic polymers attain more easily their extended chain configuration and show a higher melting point.11 The static and dynamic properties above are influencedat least to some extentby the local segmental motions and the associated freezing of the dynamics at the liquid-to-glass temperature (Tg). However, little is known on how the cyclic topology affects Tg.12−15 This is mainly because of the lack of cyclic polymers of high purity. In a first such investigation,12 the segmental dynamics of low molecular weight (4.6 kg/mol) cyclic polystyrene (PS) was investigated by rheology and differential scanning calorimetry (DSC). The temperature dependence of segmental relaxation times and associated Tg for cyclic PS were equivalent to linear PS of very high molecular weight. Similarly, a DSC study of a cyclic PS (nominal
Cyclic polymers have been synthesized by both chemists and biochemists. In the biological world well-known examples are circular DNA and cyclic peptides.1−3 Natural DNA has a simple unknotted circular configuration, but with the introduction of proper enzymes it can produce complex topologies that include duplex knots and catenates.1 Cyclic peptides, on the other hand, have advantages over their linear counterparts that include improved stability and biological activity.2 As such they have been used in pharmaceutical applications. Central to these properties of cyclic polymers is their unique topology that is lacking free ends. This topology affects several structural and dynamical properties: (i) the polymer coil conformations (more compact with a mean radius of gyration, ⟨Rg2⟩ ∼ N2ν, ν ∼ 2/5 to ν ∼ 1/3 with increasing molecular weight),4−7 (ii) the diffusion (faster for cyclic), and (iii) the zero-shear viscosity and Rouse dynamics (η0 ∼ N1.4±0.2; i.e., much weaker dependence as compared to the N3.4 found in entangled linear chains).8−10 In addition, the absence of entanglements, the more compact structure, and the faster diffusion affect the © XXXX American Chemical Society
Received: December 5, 2017 Revised: January 30, 2018
A
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 1. Molecular Weight, Purity, and Coupling Efficiency Data of Complex Cyclic Topologies RI detectionb
purity by LND (%) sample
crude
prep
8d 9d 31 32 33 34 35 36
79.8 92.2 91.4 83.8 77.75 70.53 40.0
>99.0 98.5 99.0 91.23 97.02 84.15 75.3
a
triple detectionc
coupling efficiency (%) LND
Mn
Mp
PDI
Mn
Mp
PDI
Mn by NMR
92.2 91.4 86.6 80.9 74.25 42.0
17300 13430 13320 12850 14050 12890 13920 14920
17970 13760 13590 12940 14280 13130 13980 15020
1.06 1.04 1.04 1.04 1.06 1.04 1.05 1.13
18300 18330 19140 19700 19080 18900 19680 19440
18660 18580 19440 20400 19330 19400 19800 202440
1.004 1.003 1.003 1.017 1.001 1.005 1.002 1.05
17770 17770 18580 19250 19030 18400 18450
a CuAAC coupling efficiency was determined from the RI traces of SEC. Coupling efficiency calculated as follows: purity (LND)/maximum purity by theory × 100. bThe data were acquired using SEC (RI detector) and are based on PSTY calibration curve. cThe data were acquired using DMAc triple detection SEC with 0.03 wt % of LiCl as eluent.
prepared according to literature procedures: methyl 3,5-bis(propargyloxyl)benzoate16 and 1,3,5-tris(prop-2-ynyloxy)benzene.17 All other chemicals used were of at least analytical grade and used as received. The following solvents were used as received: acetone (ChemSupply, AR), chloroform (CHCl3: Univar, AR grade), dichloromethane (DCM: Labscan, AR grade), diethyl ether (Univar, AR grade), dimethyl sulfoxide (DMSO: Labscan, AR grade), ethanol (EtOH: ChemSupply, AR), ethyl acetate (EtOAc: Univar, AR grade), hexane (Wacol, technical grade, distilled), hydrochloric acid (HCl, Univar, 32%), anhydrous methanol (MeOH: Mallinckrodt, 99.9%, HPLC grade), Milli-Q water (Biolab, 18.2 MΩ·m), N,N-dimethylformamide (DMF: Labscan, AR grade), tetrahydrofuran (THF: Labscan, HPLC grade), and toluene (HPLC, LABSCAN, 99.8%). Synthesis of Cyclic Structures. The synthesis and characterization of the multicyclic PS structures are reported in a previous publication.18 As there were some subtle changes in the procedure and the additional synthesis of a new multicyclic structure, full details for the synthesis and characterization of these structures are given elsewhere.19 Analytical Methodologies. Size Exclusion Chromatography (SEC). The molecular weight distributions of the polymers was determined using a Waters 2695 separations module, fitted with a Waters 410 refractive index detector maintained at 35 °C, a Waters 996 photodiode array detector, and two Ultrastyragel linear columns (7.8 × 300 mm) arranged in series. These columns were maintained at 40 °C for all analyses and are capable of separating polymers in the molecular weight range of 500−4 million g/mol with high resolution. All samples were eluted at a flow rate of 1.0 mL min−1. Calibration was performed using narrow molecular weight PSTY standards (PDISEC ≤ 1.1) ranging from 500 to 2 million g/mol. Data acquisition was performed using Empower software, and molecular weights were calculated relative to polystyrene standards. Absolute Molecular Weight Determination by Triple Detection SEC. Absolute molecular weights of polymers were determined using a Polymer Laboratories GPC50 Plus equipped with dual angle laser light scattering detector, viscometer, and differential refractive index detector. HPLC grade N,N-dimethylacetamide (DMAc, containing 0.03 wt % LiCl) was used as the eluent at a flow rate of 1.0 mL min−1. Separations were achieved using two PLGel Mixed B (7.8 × 300 mm) SEC columns connected in series and held at a constant temperature of 50 °C. The triple detection system was calibrated using a 2 mg mL−1 PSTY standard (Polymer Laboratories: Mwt = 110 K, dn/dc = 0.16 mL g−1, and IV = 0.5809). Samples of known concentration were freshly prepared in DMAc + 0.03 wt % LiCl and passed through a 0.45 μm PTFE syringe filter prior to injection. The absolute molecular weights and dn/dc values were determined using Polymer Laboratories Multi Cirrus software based on the quantitative mass recovery technique. Preparative Size Exclusion Chromatography (Prep SEC). Crude polymers were purified using a Varian Pro-Star preparative SEC system equipped with a manual injector, differential refractive index detector, and single wavelength ultraviolet visible detector. The flow
molecular weight of 4 kg/mol) has shown a much higher Tg for the cyclic as compared to a linear PS as well as differences in specific volume and thermal expansion coefficients between cyclic and linear PS (lower for cyclic).13 Here we investigate the segmental dynamics in several cyclic PS structures composed of multicyclic topologies fused together by linkers. The multiple linkers allow us to investigate, for the first time, the effect of a very special topology, namely of multistar or multibranch type structures bearing no chain ends. In the first part the segmental dynamics are compared in a monocyclic and the corresponding linear PS as well as with other cyclic and linear polystyrenes from literature. A complete set of data for the dependence of Tg on molecular weight is presented for cyclic and compared to linear polystyrenes. The results delineate the importance of cyclic topologies in determining Tg. In the second part we investigate multicyclic polystyrenes, all with the same molecular weight, with respect to their segmental dynamics. To this end we explore the effect of constraint segments located in the vicinity of linkers on the mean relaxation time, the distribution of relaxation times, the dielectric strength, and fragility of the segmental process. The results suggest the importance of coupling agents (linkers) in determining the segmental dynamics of cyclic polymers. A nearly linear increase of Tg was found with increasing number of linkers/constraint segments. The findings are discussed in terms of the entropy theory and the free volume theory of glass formation.
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EXPERIMENTAL SECTION
Materials. The following chemicals were analytical grade and used as received unless otherwise stated: alumina, activated basic (Aldrich: Brockmann I, standard grade, ∼150 mesh, 58 Å), Dowex ion-exchange resin (Sigma-Aldrich, 50WX8-200), magnesium sulfate, anhydrous (MgSO4: Scharlau, extra pure) potassium carbonate (K2CO3: AnalaR, 99.9%), silica gel 60 (230−400 mesh ATM (SDS)), pyridine (99%, Univar reagent), 1,1,1-triisopropylsilyl chloride (TIPS-Cl: Aldrich, 99%), phosphorus tribromide (Aldrich, 99%), tetrabutylammonium fluoride (TBAF: Aldrich, 1.0 M in THF), ethylmagnesium bromide solution (Aldrich, 3.0 M in diethyl ether), triethylamine (TEA: Fluka, 98%), 2-bromopropionyl bromide (BPB: Aldrich, 98%), 2-bromoisobutyryl bromide (BIB: Aldrich, 98%), propargyl bromide solution (80 wt % in xylene, Aldrich), 1,1,1-(trihydroxymethyl)ethane (Aldrich, 96%), sodium hydride (60% dispersion in mineral oil), sodium azide (NaN 3 : Aldrich, 99.5%), TLC plates (silica gel 60 F254), N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA: Aldrich, 99%), copper(II) bromide (Cu(II)Br2: Aldrich, 99%). Copper(I) bromide and Cu(II)Br2/PMDETA complex were synthesized in our group. Styrene (STY: Aldrich, >99%) was deinhibited before use by passing through a basic alumina column. The following linkers were B
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules rate was maintained at 10 mL min−1, and HPLC grade tetrahydrofuran was used as the eluent. Separations were achieved using a PL Gel 10 μm 10 × 103 Å, 300 × 25 mm preparative SEC column at 25 °C. The dried crude polymer was dissolved in THF at 100 mg mL−1 and filtered through a 0.45 μm PTFE syringe filter prior to injection. Fractions were collected manually, and the composition of each was determined using the Polymer Laboratories GPC50 Plus equipped with triple detection as described above. 1 H Nuclear Magnetic Resonance (NMR) Spectroscopy. All NMR spectra were recorded on a Bruker DRX 500 MHz spectrometer using an external lock (CDCl3) and referenced to the residual nondeuterated solvent (CHCl3). A DOSY experiment was run to acquire spectra presented herein by using the gradient strength (gpz6) from 85 to 90% and gradient pulse length (p30, little delta, δ = p30 × 2) from 1.6 to 2 ms with 256−512 scans. The molecular characteristics of the linear and multicyclic polymers are depicted in Table 1, and the different PS topologies are shownin a schematic wayin Scheme 1.
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 a sapphire standard. In addition to normal DSC, we employed temperature-modulated DSC (TM-DSC).20,21 In TM-DSC a low-frequency sinusoidal perturbation ranging from 0.001 to 0.1 Hz (1000−10 s period) is overlaid on the baseline profile.21 TM-DSC was made with an amplitude of 1 K and for periods in the range from 20 to 200 s with corresponding heating rates from 10 to 1 K/min (T = T0 + βt + AT sin(ωt), where β is the rate, t the time, AT the amplitude, and ω the frequency). More specifically, the linear heating rate for each period of modulation was determined from β = (ΔT/nP)60 s/min, where ΔT is the temperature width of glass “transition” (between the “onset” and “end” temperature), n is the number of modulation cycles, and P is the period of modulation.22 We have used six modulation cycles and seven periods of modulation (200, 150, 100, 80, 40, and 20 s). Dielectric Spectroscopy (DS). DS measurements were made with a Novocontrol Alpha frequency analyzer. Measurements were performed at different temperatures in the range from 173 to 438 K in steps of 5 K for frequencies in the frequency range from 10−3 to 107 Hz. The complex dielectric permittivity ε* = ε′ − iε″, where ε′ is the real and ε″ is the imaginary part, was obtained as a function of frequency, ω, and temperature T, i.e., ε*(T,ω).23,24 The analysis was made using the empirical equation of Havriliak and Negami (HN):25
Scheme 1. Linear Polystyrene (8d), Cyclic Polystyrene (9d), and Complex Topologies from Multicyclic Polystyrenes
* (ω , T ) = ε∞(T ) + εHN
σ (T ) Δε(T ) + 0 [1 + (iωτHN(T ))m ]n iεf ω
(1)
where ε∞(T) is the high-frequency permittivity, τHN(T) is the characteristic relaxation time in this equation, Δε(T) = ε0(T) − ε∞(T) is the relaxation strength, m and n (with limits 0 < m, mn ≤ 1) describe respectively the symmetrical and asymmetrical broadening of the distribution of relaxation times, σ0 is the dc conductivity, and εf is the permittivity of free space. From τHN, the relaxation time at maximum loss, τmax, was obtained analytically following
⎛ πm ⎞ 1/ m⎛ πmn ⎞ τmax = τHN sin−1/ m⎜ ⎟ ⎟ sin ⎜ ⎝ 2(1 + n) ⎠ ⎝ 2(1 + n) ⎠
(2)
At low temperatures a single β-process appears within the experimental window that conforms to a single HN function with low- and high-frequency slopes of m = 0.25, mn = 1, and effective dielectric strength of TΔε ∼ 10 K (values are for the tricyclic polystyrene, 33). At higher temperatures, the dielectric response of the linear and multicyclic polystyrenes could be fitted by a single Havriliak−Negami function together with the conductivity contribution. For the monocyclic polystyrene (9d), instead, an additional slower process was included in the fitting procedure (with shape parameters m = 0.8, mn = 0.2, and T-corrected dielectric strength of TΔε ∼ 20 K). The fitting procedure was made with OriginPro 8.5. Typically, the maximum number of iterations was set to 400 and tolerance to 10−15.
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RESULTS AND DISCUSSION Comparison of Linear and Monocyclic Polystyrenes. The segmental dynamics of the linear (8d) and monocyclic (9d) polystyrenes was investigated by DS. Dielectric loss curves of the two compounds are compared in Figure 1. For the linear polymer a single HN function together with the ionic conductivity at lower frequencies provided adequate description to the dielectric loss curves. For the monocyclic polystyrene, however, in addition to the main process a slower process with a reduced dielectric strength was included in the fitting procedure. The segmental relaxation times of the two polystyrenes are depicted in Figure 2 in the usual activation diagram. The main process conforms to a Vogel−Fulcher−Tammann (VFT) dependence as
Differential Scanning Calorimetry (DSC). The thermal properties were investigated with a Q2000 (TA Instruments) differential scanning calorimeter (DSC). Thermograms were obtained during the second cooling and heating runs with a rate of 10 K/min within the temperature range from 323 to 433 K. The DSC traces from the second heating scan are shown in Figure 4. 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 C
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
located below the conventional glass temperature (here taken at τ = 100 s). Values of these parameters for all compounds are summarized in Table 2. Tg values for the two samples are practically the same (TgL = 376.8 ± 0.3 K; TgR = 377.1 ± 0.4 K). The slower process in the monocyclic polymer with approximately half the dielectric strength of the main process seems to follow a VFT dependence and to freeze at the same “ideal” glass temperature with the main segmental process. Yet, the origin of the process is unclear at present. It may contain contributions from additional polar groups present in the cyclic polymer as linkers (Figure S1, Supporting Information). At this point we compare literature glass temperatures for cyclic and linear polystyrenes with the ones from the present investigation. The result of this comparison is shown in Figure 3 as a function of molecular weight. The figure comprises Tg Figure 1. Dielectric loss curves of linear (blue, 8d) and cyclic (yellow, 9d) polystyrenes compared at the same temperature (393.15 K). Solid lines represent fits to a summation of one (linear) and two (cyclic) HN functions together with the conductivity contribution. Dashed lines and shadowed areas (9d) indicate simulations of the individual processes.
Figure 3. Glass temperature as a function of molecular weight for linear (squares) and cyclic (circles, triangles) polystyrenes. Blue squares and the blue circle are from ref 12 (DSC, rate 10 K/min). Magenta square and magenta circle are from ref 13 (DSC). Green triangles are from ref 14 (DSC). Orange symbols are from the present study (DS, Tg defined at τ = 100 s). Red symbols are also results from the present study but from samples of a different origin (DS, Tg defined at τ = 100 s).27 The dash-dotted line gives the glass temperature for polystyrenes of very high molecular weight.
Figure 2. Relaxation map of the segmental dynamics for linear (blue, 8d) and cyclic (red, 9d) polystyrenes. The slower process in cyclic polystyrene is shown with solid symbols. Solid lines are fits to the VFT equation.
⎛ B ⎞ τ = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠
data obtained with DSC and DS studies. Linear PS exhibit a strong reduction in Tg below about Mw ∼ 18K. Parenthetically, the entanglement molecular weight for PS is also in the same range (Me ∼ 17K).26 Cyclic polystyrenes, on the other hand, exhibit also a reduction in Tg but to a much smaller extent. The glass temperature for the smallest cyclic PS (Figure 3) is at 368 K, i.e., some 40 K higher than the corresponding linear PS.
(3)
Here, τ0 is the relaxation time at very high temperatures, B is the activation parameter, and T0 is the “ideal” glass temperature
Table 2. Vogel−Fulcher−Tammann (VFT) Parameters, “Ideal” Glass Temperature, Conventional Glass Temperature, and Fragility or Steepness Index for the Different PS Topologies
a
sample code
log(τmax/s)a
8d 9d 31 32 33 34 35 36
−12 −12 −12 −12 −12 −12 −12 −12
B (K) 1518 1535 1564 1563 1575 1613 1593 1592
± ± ± ± ± ± ± ±
7 8 3 4 6 10 6 7
Tg (K)b
T0 (K) 326.1 325.8 326.1 329.4 327.5 327.5 325.6 331.2
± ± ± ± ± ± ± ±
0.3 0.4 0.2 0.2 0.3 0.4 0.2 0.3
376.8 377.1 378.3 381.7 380.1 381.4 378.8 384.4
± ± ± ± ± ± ± ±
0.3 0.4 0.2 0.2 0.3 0.4 0.2 0.3
Tg (K)c 373.2 373.4 374.5 377.9 376.4 377.5 375.0 380.6
± ± ± ± ± ± ± ±
0.3 0.4 0.2 0.2 0.3 0.4 0.2 0.3
m*b 97 96 94 95 94 92 93 94
± ± ± ± ± ± ± ±
m*c 2 2 1 1 2 2 1 2
111 110 109 109 108 106 106 108
± ± ± ± ± ± ± ±
2 3 1 1 2 2 1 2
Value held fixed. bAt τ = 10 s. cAt τ = 100 s. D
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules The glass temperature of cyclic polymers has been the subject of the Gibbs−Di Marzio lattice model of glass formation.28,29 According to the model, the glass “transition” occurs when the configurational entropy reaches a critically small value. The model further predicts a second-order transition (Ehrenfest) at a finite temperature where the configurational entropy is zero. Because the number of configurations of cyclics is reduced with respect to linear polymers, the model predicts invariably an increasing Tg with decreasing molecular weight. To a first approximation, the configurational entropy between cyclic and linear chains on a per monomer basis is SLinear − SCyclic ∼ 3(ln(2πx/3))/(3x), where x is the number of segments per chain.28,29 In the limit of infinite molecular weight, the model predicts identical glass temperatures for linear and cyclics, whereas for finite molecular weights a significantly higher Tg is predicted for the latter. However, experiment (Figure 3) is not consistent with the predictions of the model as even the smallest cyclic PS present reduced glass temperatures with respect to the Tg∞ value. Note that for the same argumentation the Tg in thin films would invariable increase with confinement because confinement reduces the configurational entropy, which is also in contradiction to the experimental results. Thermal Properties. The DSC traces for the different multicyclic polystyrenes of Table 1 are depicted in Figure 4.
Figure 5. Heat capacity step at Tg as a function of (a) glass temperature (defined at τ = 10 s) as obtained from dielectric spectroscopy and (b) number of constrained segments calculated from the chemical structure of each compound. The dashed-dotted line is the value for linear PS.20
provides two time scales to the measurement of Tg; a fast one given by the modulation period and a slower one given by the average heating or cooling rate. Some representative results for compound 34 are provided in Figure 6. The figure depicts the
Figure 6. (a) Temperature dependence of the reversing heat capacity for penta-cyclic polystyrene (34), obtained from TM-DSC at different periods of modulation as indicated. Vertical arrows indicate the respective glass temperatures. (b) Absolute value of the derivative of heat capacity with respect to temperature plotted as a function of temperature for different periods of modulation.
Figure 4. DSC traces of the different PS topologies obtained during heating with a rate of 10 K/min. Vertical dashed line indicates the glass temperature of linear polystyrene (8d). Curves are shifted vertically for clarity.
Consistent with the DS study, the DSC Tg values for 8d and 9d are practically the same. An earlier investigation12 on cyclic PS of lower molecular weight (nominal molecular weight ∼4 kg/ mol) have shown a Tg value (371.3 K) lower than that of the corresponding linear PS (nominal molecular weight 5.4 kg/ mol, Tg = 360.9 K) being comparable to linear PS of higher molecular weight. The reason for the apparent discrepancy is the lower molecular weight of the cyclic PS. Furthermore, traces display varying glass temperatures by about 10 K with 8d and 36 having the lowest and highest Tg values, respectively. The heat capacity step at Tg, Δcp, measured by temperature modulated DSC is plotted in Figure 5 as a function of Tg (and as a function of the number of constrained segments, to be defined below). Wunderlich’s rule30 of a constant heat capacity step at Tg (for linear PS, Δcp ∼ 0.3 J/(g K)) is obeyed for the multicyclic polystyrenes as well (Δcp ∼ 0.30 ± 0.02 J/(g K)). Subsequently we employed TM-DSC to investigate the segmental dynamics in the multicyclic polystyrenes. TM-DSC
reversing cp signal for different modulation periods. Invariably glass temperature increases with decreasing modulation period and this is more evident in the absolute derivative of cp with respect to temperature. These dynamic Tg data are compared below with the results from the DS investigation. Effect of Ring Topology on Segmental Dynamics. As the investigation of the thermal properties revealed differences in glass temperatures by about 10 K, we investigate subsequently the segmental dynamics by DS. Typical dielectric loss curves for the tricyclic PS (33) are shown in Figure 7. The figure depicts a fast process (with an Arrhenius temperature dependence) of low dielectric strength and with a broad distribution of relaxation times (m ∼ 0.25, mn ∼ 1) characteristic of processes in the glassy state. This process is usually discussed as the β-process.31 We will return to this point after examining the segmental dynamics. At higher temperE
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
frequency-scale shift factor, aT, and a single (much smaller) loss-scale shift factor, bT, allow superposition of all dielectric data at temperature T with the data at the reference temperature Tref according to ε*(ω,T) = bTε*(aTω;Tref). The resulted “master curves” for all compounds can be discussed in terms of the superposition of the individual master curves with respect to Figure 9 (i.e., the superposition of the super-
Figure 7. Dielectric loss curves of tricyclic polystyrene (33) at some selected temperatures as indicated. Solid lines represent fits to the αand β-process using the HN function and the conductivity contribution. Dashed and dotted lines are simulations of the HN function and conductivity contribution, respectively. Note the higher values of dielectric loss as compared to the linear polymer (Figure 1).
atures, the segmental process is the dominant mode of relaxation with a contribution from ionic conductivity at lower frequencies. For all multicyclic polystyrenes a single segmental process suffices to describe the dielectric loss spectra at T > Tg. Dielectric loss spectra of the multicyclic polystyrenes are compared at the same temperature in Figure 8. The figure
Figure 9. Superposition of individual master curves for each compound. Sample 33 was used as the reference, and the reference temperature in all cases was at Tref = 408.15 K.
positions). This representation is more informative than discussing individual master curves; it shows that tTs is only valid in a small frequency range around the peak. This effect is not new for linear polymers, especially when studied by DS in the vicinity of the glass temperature. It further reveals a narrowing in the distribution of relaxation times especially from the higher frequency side for the cyclic structures bearing the higher functionality. Evidently, multicyclic PS topology suppresses some high-frequency modes. This is better depicted in Figure 10 where the low- and high-frequency slopes of the dielectric loss curves of the segmental process are compared.
Figure 8. Dielectric loss curves for the investigated compounds at 403.15 K.
depicts loss curves that vary by about 1 decade with respect to the peak frequency and by another decade with respect to the magnitude of dielectric loss. Although the former was anticipated by the difference in the glass temperature found in DSC, the latter raises questions on the chemical composition of the compounds. To this end, the linkers in the case of the multicyclic PSs contain triazole units that contribute significantly to the dielectric loss (Figure S1, Supporting Information). Before we discuss the contribution of the polar triazole units, we first discuss the shape of loss curves and its possible relation to thermorheological simplicity/complexity. We employ the principle of time−temperature superposition (tTs) that allows the frequency ω dependence of the complex ε* at any temperature T to be determined from a master curve at a reference temperature. At each temperature T, a single
Figure 10. Havriliak−Negami parameters for the low-frequency (open symbols) and high-frequency (filled symbols) HN shape parameters for all polystyrene topologies (8d, blue circles; 9d, red squares; 31, magenta up-triangles; 32, green down-triangles; 33, orange lefttriangles; 34, wine rhombi; 35, cyan right triangles; 36, olive hexagons) plotted as a function of inverse temperature. F
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Compound 36 with the more complex multicyclic topology has the narrower distribution from the high-frequency side. The effective dielectric strength for the different compounds is discussed with respect to Figure 11. It reveals an increasing
Figure 12. Activation plot of the segmental dynamics for the different PS topologies (8d, blue circles; 9d, red squares; 31, magenta uptriangles; 32, green down-triangles; 33, orange left-triangles; 34, wine rhombi; 35, cyan right triangles; 36, olive hexagons). Solid lines represent fits to the VFT equation. Tg is operationally defined at τ = 10 s. Filled rhombi are from TM-DSC for the pentacyclic polystyrene (34).
Figure 11. Dielectric relaxation strength, Δε, corrected for the temperature dependence, plotted for the segmental dynamics of multicyclic polystyrenes (filled symbols; same as in Figure 10). The corresponding strength for the slower process in cyclic polystyrene (9d) is also shown with the open circles.
segments in the vicinity of linkers. Hence, in the monocyclic PS with the single triazole unit there are two constraint segments; in the dicyclic there are four constraint segments, etc. The heptacyclic PS (compound 36) bearing the highest number of triazole units will contain the highest number of constraint segments. Figure 13 gives the dependence of Tg on
dielectric strength that increases with the number of triazole units. Of course, triazoles are not the only polar units used as coupling agents by they certainly carry most of the dipole moment. Perhaps more informative is a representation where the dielectric strength is normalized by the number of triazole units (Figure S3, Supporting Information). Under the premise that the contribution of triazole units is much higher from the remaining dipolar units, the figure suggests that there exist destructive interactions among the dipoles that reduce the normalized intensity in multicyclic polystyrenes. An additional concern is the remaining temperature dependence of TΔε for some multicyclic polystyrenes. According to theory,23,24 Δε is inversely proportional to temperature; hence, the product TΔε, in the absence of interactions, should remain constant. However, as Figure 11 and Figure S3 reveal, the heptacyclic (36) and pentacyclic (34) polystyrenes display increasing TΔε with temperature. The additional dependence can be attributed to an increased cooperativity associated with the smaller and hence more constrained loops, in the heptacyclic (36) and pentacyclic (34) as compared to the tetracyclic (35) and tricyclic (33) polystyrenes, respectively. The influence of chain topology on the segmental dynamics can be discussed with respect to the usual activation plot in Figure 12. A VFT dependence adequately describes the τ(T) for all compounds within the investigated temperature/ frequency range. In addition, the results from TM-DSC on the structural relaxation of pentacyclic polystyrene (compound 34) are in excellent agreement with the results from the DS study. The VFT parameters are summarized in Table 2. These results on the segmental dynamics can be discussed in terms of the multicyclic topology. Relaxation of polystyrene segments in multicyclic compounds naturally is affected by the polar units used as “linkers”. Thus, changes in the segmental dynamics and the concomitant changes in Tg can be discussed in terms of the number of triazole linkers. In a more detailed view, the segmental dynamics will be affected for those
Figure 13. Glass temperature obtained from dielectric spectroscopy (defined at τ = 10 s) as a function of (a) the number of constrained segments and (b) the number of triazole units.
the number of constraint segments and the number of polar triazole units at the linker positions. A near linear relationship is found in both with compounds 32 and 35 having a higher and a lower Tg, respectively. An alternative way of discussing changes in Tg is by examining the effect of the molecular weight of the formed cycles. This comparison is shown in Figure 14 where the glass temperatures are now plotted as a function of the average molecular weight per loop. This representation has, however, two shortcomings. First, the latter quantity cannot be defined unambiguously especially for compounds 34, 35, and 36 because loops are not uniform in molecular weight. In this case an average molecular weight was used. Second, and more important, it suggests that the increased Tg associates with the G
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increasing function of Tg. The former gives a fractional free volume at Tg of 3.34% for all compounds, whereas the latter a decreasing thermal expansion coefficient of the free volume with increasing number of rings/linkers (Figure 15c). We mention here that an earlier study on linear and cyclic alkanes reported13 different (lower) thermal expansion coefficient and specific volume for cyclic compounds. The two approaches discussed here, the first emphasizing the role of intramolecular constraints through the number of linkers and the second emphasizing intermolecular contributions by differences in free volume, are inherently very different. Pressure-dependent dielectric experiments on linear PS revealed that the origin of the slowing down of segmental dynamics on approaching Tg results by contributions of both freezing of intramolecular degrees of freedom by reduced thermal energy and by increased density.32−34 The relative contribution of the two mechanisms was discussed in terms of the ratio, R, of the apparent activation energy at constant volume, Qv(T,V), to that at constant pressure, QP(T,P).34 For PS,35 R = 0.64 at T = Tg, suggesting that the reduced thermal energy with respect to the intramolecular barriers plays a more significant role in determining Tg than increasing density. Hence, a definite answer to the origin of the dynamic slowing down at Tg in cyclic PS requires pressure-dependent measurements of the segmental dynamics and of the thermodynamics (e.g., the equation of state). Experiments in this direction are currently in progress in our laboratory (UoI). A closer look to the τ(T) dependence of multicyclic polystyrenes reveals an additional weak dependence of segmental times in a Tg-scaled plot (Figure S2, Supporting Information). To quantify this effect, we employ the most widely accepted metric of the steepness for the temperature dependence of the segmental relaxation times in the vicinity of the glass temperature, i.e., the fragility parameter or the steepness index, m, defined as ϑ log τ/ϑ(Tg/T)|T=Tg, which is equivalent to the slope in the “fragility” plot of log τ vs Tg/T.36 The steepness index can readily be calculated as
Figure 14. Glass temperature obtained from dielectric spectroscopy (defined at τ = 10 s) as a function of the average molecular weight per loop.
smaller molecular weight of loops. The latter conclusion is erroneous as a monocyclic PS with the same (small) molecular weight would have a much lower Tg than the one shown in Figure 14 (Figure 3). In essence, this representation ignores the effect of linkers that in multicyclic polymers plays a crucial role. The discussion above emphasized intramolecular constraints through the “linkers” as mainly affecting Tg. Alternatively, these results can be discussed in terms of classical free volume theories.26 The frequency-scale shift factors, aT, used in tTs through the Williams−Landel−Ferry (WLF) coefficients c1g and c2g log aT = −
c1g(T − Tg) c 2g + (T − Tg)
(4)
contain information on the fractional free volume at Tg ( f(Tg) = 1/2.303c1g) and the thermal expansion coefficient of free volume (αf = f(Tg)/c2g). The WLF coefficients and the respective fractional free volume and thermal expansion coefficients are shown in Figure 15. The figure depicts a c1g = 13.00 ± 0.01 independent of topology and a c2g value that is an
Figure 15. (a) WLF coefficients plotted as a function of the glass temperature, the latter obtained from dielectric spectroscopy (defined at τ = 10 s). Lines are guides for the eye. (b) Fractional free volume at Tg and (c) thermal expansion coefficient of free volume plotted as a function of the number of constraints. H
DOI: 10.1021/acs.macromol.7b02579 Macromolecules XXXX, XXX, XXX−XXX
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BTg 2
2.303(Tg − T0)
can be contrasted with the dynamics of a polar polymer in a densely cross-linked network where the cross-linker is less polar. This was case for example when poly(methylphenylsiloxane) networks were formed by the less polar cross-linker tetrakis(dimethylsiloxy)siloxane and their segmental dynamics where investigated by DS.38 In this case, both the shape of the segmental relaxation and fragility were insensitive to cross-linking. The results suggest that the relative dipole moment of the polymer segments to the linker plays an important role in determining the characteristics (distribution, fragility) of the segmental dynamics. Given that complex cyclic topologies exist both in the synthetic and in the biological world, this work emphasizes that the details of the coupling agents cannot be ignored especially when studying dynamic properties.
(5)
Values of the steepness index are shown in Table 2 and further plotted in Figure 16 as a function of the number of constraint segments and as a function of loop molecular weight.
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CONCLUSION The segmental dynamics and the corresponding glass temperature were investigated in a monocyclic and the corresponding linear polystyrene as well as in a series of multicyclic polystyrenes, all with the same total molecular weight, with dielectric spectroscopy and DSC. The latter can be considered as having a special topology comprising multibranched structures without chain ends. The comparison of the monocyclic with the linear polystyrene as well as with literature data for other cyclic polystyrenes revealed a strong reduction of Tg with decreasing molecular weight for linear chains but only a moderate reduction for cyclic chains and this below a certain molecular weight. The critical molecular weight below which differences between linear and cyclic chains become important is Mn ∼ 18 000 g/mol, i.e., in the vicinity of the entanglement molecular weight for polystyrene. These data contradict the Gibbs−Di Marzio lattice model predicting an increasing glass temperature with decreasing molecular weight of cyclic polymers. In the case of multicyclic polystyrenes the value of glass temperature is not governed by the total molecular weight. Instead, glass temperature is affected by the number of polar linkers and concomitantly, by the number of constraint segments in their vicinity. A nearly linear increase of Tg was evidenced with increasing number of linkers/constraint segments. This approach emphasizes intramolecular contributions to Tg. An alternative approach that is based on the concept of free volume emphasizes intermolecular contributions and predicts the same amount of fractional free volume for multicyclic polystyrenes at their respective glass temperature (3.3%) but differences in the thermal expansion coefficient of free volume. Cyclic topology affects high-frequency modes in the spectrum of segmental relaxation. We found similar fragilities for the linear and the respective monocyclic polystyrene both with a molecular weight of ∼18K. However, multicyclic topology affects fragility that decreases with increasing number of constrained segments.
Figure 16. Fragility or steepness index calculated as a function of (a) the number of constrained segments and (b) the average molecular weight per loop.
Fragility values are the same within experimental accuracy for the linear and monocyclic PS. This is not surprising given the (high) molecular weights employed herein. In an earlier study12 the fragility of a cyclic PS of lower molecular weight (Mw = 4700 g/mol) was found to be higher than the corresponding linear PS being comparable to that of high molecular weight linear polystyrenes. This is understandable as the lack of chain ends in the shorter cyclic polymer induces additional constraints on the segmental dynamics. However, for the higher molecular weights employed here this effect will diminish. Returning to the multicyclic PS, there is a decreasing fragility with increasing number of linkers and hence of constrained segments. In addition, there is a decreasing fragility with decreasing loop molecular weight, a property found also in linear polymers.37 Overall, chain topology affects fragility in the case of multicyclic topologies. In addition to the segmental processes we investigate the effect of topology on the secondary process. By comparing the dielectric spectra at low temperatures (Figure S3), we find a splitting of the secondary process to a dual process (β1 and β2). Furthermore, both processes are somewhat faster in the cyclic polystyrene as compared to the linear polystyrene with corresponding activation energies of 44 ± 0.2 and 52 ± 0.5 kJ/mol (Figure S4). In the case of the multifunctional polystyrene 33 both processes have higher dielectric strength revealing that the polar units also contribute to the local relaxations. The results presented here emphasize the role of coupling agents/linkers on determining practically all features of segmental dynamics and sub-Tg processes in multicyclic polystyrenes; from the exact temperature dependence of relaxation times, to the dielectric strength, the distribution of relaxation times, and finally the fragility. They further show that total molecular weight is an irrelevant parameter in discussing their dynamics. These results on the segmental dynamics of the nonpolar polymer (PS) restricted by a polar linker (triazole)
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b02579. Chemical structures indicating the polar units and dielectric results on the segmental and secondary processes (PDF) I
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AUTHOR INFORMATION
Corresponding Author
*E-mail: gfl
[email protected] (G.F.). ORCID
Michael J. Monteiro: 0000-0001-5624-7115 George Floudas: 0000-0003-4629-3817 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Jack Douglas for comments on the manuscript. The current work was also 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).
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