Supramolecular Polymer Nanocomposites Derived from Plant Oils and

Article pubs.acs.org/Macromolecules

Supramolecular Polymer Nanocomposites Derived from Plant Oils and Cellulose Nanocrystals Lingzhi Song,† Zhongkai Wang,*,†,‡ Meghan E. Lamm,‡ Liang Yuan,‡ and Chuanbing Tang*,‡ †

School of Forestry and Landscape Architecture, Anhui Agriculture University, Hefei, Anhui 230036, China Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States

‡

ABSTRACT: Sustainable functional materials derived from renewable biomass provide momentum for the communities of polymer science. We report a supramolecular approach to the preparation of strong biobased polymer nanocomposites with stimuli-responsive behaviors using soybean oil (SO) and cellulose nanocrystals (CNCs). SO-derived polymers were modified with hydroxyl −OH and carboxyl −COOH groups via thiol−ene click chemistry, facilitating hydrogen-bonding interactions with CNCs to improve the overall compatibility in the nanocomposites. These nanocomposites exhibited high tensile strength and maintained high storage modulus up to 200 °C. Moreover, these nanocomposites showed a fast and reversible mechanical response to water, an external stimulus to tune intermolecular hydrogen bonding.

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INTRODUCTION Synthetic polymers from fossil oils have improved our living standards to an unparalleled level. However, it is increasingly alarming that fossil fuels are depleting at an unprecedented speed, and environmental concerns are affiliated with the consumption of fossil fuels. It is generally accepted to use biomass as sustainable resources for fuels, chemicals, and materials.1−7 Natural polymers, such as cellulose, lignin, and starch, have well served human beings before the discovery of fossil fuels.8,9 Development of polymer materials from biomass with comparable properties to those from fossil oils is one of the grand challenges facing the fields of chemistry, engineering, materials, etc.10−14 A wide range of biomass sources, such as sugars, terpenes, rosin acids, plant oils, lignin, and cellulose, have been explored to address the urgent challenge.1,13,15−18 Plant oils are one of the most abundant and low-cost biomass and have been widely used in chemical industry (i.e., surfactants, paper sizing agents).19−21 Thermoset materials have been widely achieved from plant oils for numerous applications (i.e., surface coatings, polyurethane foam, rubbers).22,23 For example, polyols were prepared from epoxidized vegetable oils and used for making thermosets.24−26 Recently, processable polymers prepared from plant oils were reported.27,28 A new trend is on the conversion of plant oils into monofunctional monomers for making reprocessable polymers. A vinyl ether monomer was prepared from the transesterification of 2-(vinyloxy)ethanol with soybean oil and polymerized by living cationic polymerization.29,30 We reported the preparation of a series of different (meth)acrylate monomers from soybean oil via facile amidation.31−35 Thermoplastic polymers with glass transition temperature in the range −54 to 60 °C were prepared after simple free radical © XXXX American Chemical Society

polymerizations of these monomers. However, the highest tensile strength from these polymers is only 3.0 MPa. Enhancing their mechanical strength is a prerequisite before serious consideration for valuable applications. Polymer nanocomposites incorporate various fillers such as silica nanoparticles, nanoclay, carbon nanotubes, and many other stiff nanomaterials for property enhancement of polymer matrix.36−40 Renewable cellulose nanocrystals (CNCs or nanowiskers), which have ultrahigh tensile stiffness (up to 150 GPa), are favored for making sustainable, mechanically reinforced polymer nanocomposites.41−44 For example, mechanical strength of low-density polyethylene, poly(ethylene oxide-co-epichlorohydrin), polyurethane, and epoxy resins was improved after CNCs were introduced to the polymer matrix.45−48 Thus, we hypothesized that biobased CNCs could improve the mechanical properties of soybean oil polymers, given that good compatibility is achieved between the matrix and nanofillers (Scheme 1A). On the other hand, installation of additional functionality onto these composites, such as response to external stimuli, could allow the formation of advanced materials for property-targeting applications. Herein we report a simple supramolecular approach to preparing high mechanical strength polymer nanocomposites using soybean oil and CNCs as renewable biomass materials (Scheme 1A). As the surfaces of CNCs are covered with hydroxyl groups, polymers that can facilitate the formation of hydrogen bonding with CNCs would be good candidates for enhancing compatibility between fillers and matrix. As shown in Received: August 4, 2017 Revised: September 14, 2017

A

DOI: 10.1021/acs.macromol.7b01691 Macromolecules XXXX, XXX, XXX−XXX

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Scheme 1. (A) Illustration of Supramolecular Nanocomposites from CNCs and Soy Polymers (with −COOH Groups as an Example); (B) Chemical Modification of Soy Polymers with −OH or −COOH Groups via Thiol−Ene Click Chemistry

were used as received. Azobis(isobutyronitrile) (AIBN, 98%, SigmaAldrich) was recrystallized before use. Modification of Soybean Oil Derived Polymers via Thiol− Ene Chemistry. Soybean oil based (meth)acrylate polymers (P1 and P2) were prepared according to our reported work.34 P1 and P2 were then modified via thiol−ene click reactions to introduce hydroxyl or carboxyl groups. A typical thiol−ene reaction procedure was given as follows: P1 (1.0 g, 2.5 mmol) was dissolved in dry THF (5 mL) in a 20 mL flask. 2-Mercaptoethanol (3.4 mL, 25 mmol) and AIBN (20 mg) were added to the flask. After complete dissolution of the polymer, the flask was sealed and purged with N2 for 15 min. The reaction was stirred at 65 °C for 12 h. The modified polymer was purified by precipitating from methanol for four times. Finally, P1-OH was dried under vacuum at room temperature for 24 h. P2-OH and P2-COOH were prepared in similar procedures. Preparation of Nanocomposites. Polymer/CNCs nanocomposites were prepared via a solution mixing method. CNCs powder (1.0 g) was mixed with DMF (20 mL) and sonicated for 2 h to obtain a gellike suspension. P1-OH (0.9 g) was dissolved in DMF (4 mL) before a suspension of CNCs/DMF (2 mL, 50 mg/mL) was added to the polymer solution. After sonication for 30 min, the mixture was transferred to a Teflon mold. The solution was dried at 50 °C on a hot plate for 24 h and then dried at 50 °C under vacuum for 12 h to obtain P1-OH/CNCs nanocomposites. Nanocomposites with different polymers and CNCs ratios were prepared by the same method. Dynamic Mechanical Analysis (DMA). The thermodynamic mechanical properties of nanocomposites were analyzed using a

Scheme 1B, two polymers (P1-OH and P2-OH) with hydroxyl groups and one polymer with carboxyl groups (P2-COOH) were prepared by thiol−ene chemistry with poly(soybean acrylate) (P1) and poly(soybean methacrylate) (P2).31 A homogeneous dispersion of CNCs in the modified polymers was observed by SEM. We also studied the effects of the polymer structure and the content of CNCs on the mechanical properties of polymer nanocomposites. Nanocomposite materials with tensile strength up to 23 MPa were obtained, and their storage modulus could be maintained up to 200 °C when the content of CNCs was higher than 10 wt %. With the presence of the hydrogen-bonding interactions, these nanocomposites exhibited a fast switching of modulus responding to water, which could reversibly trigger the disruption and reformation of supramolecular interactions between polymers and CNCs.

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EXPERIMENTAL SECTION

Materials. Plenish high oleic soybean oil (HOSO) was provided by DuPont. Poly(soybean acrylate) (P1) and poly(soybean methacrylate) (P2) were prepared from HOSO following previously reported methods.34 Cellulose nanocrystals (CNCs) were kindly supplied by Celluforce (Canada). 2-Mercaptoethanol (99%, Sigma-Aldrich), 3mercaptopropanoic acid (99%, Sigma-Aldrich), and all other reagents B


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Figure 1. 1H NMR spectra: (a) P1 and P1-OH; (b) P2, P2-OH, and P2-COOH. DSC curves: (c) P1 and P1-OH; (d) P2, P2-OH, and P2-COOH. Q5000 DMA (TA Instruments), operated on a tensile mode. Rectangular films with length (15 mm) and width (3 mm) were used. The DMA curves were obtained by scanning at a frequency of 1 Hz and a heating rate of 3 °C/min in a temperature range of −50 to 200 °C. All samples were dried under vacuum at 60 °C for 24 h prior to DMA tests. In order to characterize the kinetics of water-induced modulus change of nanocomposites, DMA experiments were conducted in a submersible clamp, where nanocomposites films were immersed in water at 25 °C during DMA measurements. Aqueous Swelling. The degree of water uptake for the nanocomposites was studied. Rectangular films with length (20 mm), width (5 mm), and thickness (0.3 mm) were dried under vacuum at 60 °C for 24 h and weighed using a four-digit balance. The nanocomposites were then immersed in deionized water. Every 24 h, the samples were taken out, the surfaces dried with filter papers, weighed, and immediately placed back in the deionized water. Swelling tests for nanocomposites were conducted for 7 days. The degree of swelling (Ds) was calculated according to eq 1

W − W0 Ds = t × 100% W0

microscopy (AFM) experiments were carried out using a Multimode Nanoscope V system (Veeco (now Bruker), Santa Barbara, CA). The measurements were performed using commercial Si cantilevers with a nominal spring constant and resonance frequency at 20−80 N/m and 230−410 kHz, respectively (TESP, Bruker AFM Probes, Santa Barbara, CA). The dispersion of CNCs in polymer matrix was characterized by field-emission scanning electron microscopy (FESEM, Zeiss UltraPlus). Thermogravimetric analysis (TGA) measurements were carried out on a TA Q5000IR thermogravimetric analyzer (TA Instruments). Samples of about 5 mg were heated from room temperature to 100 °C at a heating rate of 10 °C/min under a nitrogen atmosphere, held at this temperature for 30 min, and then cooled to 40 °C at a rate of 10 °C/min. Then the samples were heated from 40 to 600 °C at a heating rate of 10 °C/min. Tensile tests were carried out with an Instron 5543A instrument with a crosshead speed of 20 mm/ min.

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RESULTS AND DISCUSSION Modification of Soybean Oil Derived Polymers via Thiol−Ene Click Reactions. The polymer−CNCs interactions play an important role for CNCs dispersion in the polymer matrix. It is known that the surface of CNCs is covered with polar hydroxyl groups, while soybean oil derived polymers (P1, Mn = 36.2 kg/mol, and P2, Mn = 41.5 kg/mol) are highly hydrophobic and nonpolar and thus not suitable for direct blending with CNCs. Structurally, P1 and P2 contain unsaturated double bonds in the fatty side chains, which can be easily modified via thiol−ene click reactions to introduce polar groups. P1-OH (Mn = 33.4 kg/mol), P2-OH (Mn = 43.2 kg/mol), and P2-COOH with hydroxyl or carboxyl groups

(1)

where W0 and Wt are the sample mass of the nanocomposites before and after immersed in water for certain time (t). Characterization. 1H NMR spectra were recorded on a Bruker Avance III HD 300 MHz spectrometer with tetramethylsilane (TMS) as an internal reference. Glass transition temperatures (Tg) of soybean oil derived polymers were analyzed via differential scanning calorimetry (DSC) using a Q2000 instrument (TA Instruments). The sample was heated from room temperature to 150 °C and then cooled to −50 °C at a rate of 10 °C/min. A second heating and cooling cycle was repeated at a rate of 10 °C/min. The data were collected from the second heating scan. Tapping-mode atomic force C


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Figure 2. (a) AFM height image of CNCs. (b) SEM image of P2-COOH/CNCs nanocomposites with 20 wt % CNCs. (c) Photos of the mixture of CNCs and P2-COOH in DMF after shaking or standing for 10 min. (d) DSC curves of P2-COOH and P2-COOH/CNCs nanocomposite (20 wt % CNCs).

solution (P2-COOH in DMF). As shown in Figure 2c, the mixture of CNCs and P2-COOH in DMF formed a transparent gel, which implied that a physical network may form due to the hydrogen bonding between CNCs and P2-COOH. The gel can dynamically switch between sol and gel via strenuous shaking or standing for 10 min. This phenomenon further demonstrated the formation of physical network between CNCs and P2-COOH, even in the solution state. After removing the solvent, nanocomposites with CNCs well dispersed in P2-COOH were obtained. The microstructure of CNCs and nanocomposites were characterized via AFM and SEM. The size of pristine CNCs was in the range of 35 ± 8 nm in diameter and 310 ± 15 nm in length by AFM imaging (Figure 2a). The SEM image of P2-COOH/CNCs nanocomposites (20 wt % CNCs, Figure 2b) clearly showed that CNCs were well dispersed in the P2-COOH matrix. The DSC curve of P2-COOH/CNCs nanocomposites (20 wt % CNCs) is shown in Figure 2d, and the Tg value is about −8.1 °C. The DSC characterization demonstrated that the introduction of CNCs did not significantly affect the Tg value of P2-COOH polymer matrix (−8.6 °C). Mechanical Reinforcement of Soybean Oil Polymers with CNCs. A series of nanocomposites with different polymer matrix and CNCs weight contents were prepared (Table 1). The samples are labeled as “polymer-X”, where “polymer” is the name of the matrix polymer and “X” is the weight percentage of CNCs in the final nanocomposites. For example, P1-OH-30 represents a nanocomposite prepared from P1-OH with 30 wt % CNCs. The mechanical properties of nanocomposites were characterized by monotonic tensile tests. Three composites with 30

were prepared (Scheme 1B) to enhance their compatibility with CNCs. As shown in Figure 1a, 1H NMR spectra of P1 and P1-OH demonstrated the success of thiol−ene click reactions. The fatty chain double bond protons at 5.30 ppm from P1 nearly disappeared after the thiol−ene reaction, and protons at 2.50 ppm adjacent to the C−S bond were observed from P1-OH. New proton peaks at 2.62 and 3.64 ppm next to hydroxyl groups were also clearly identified. The degree of conversion was calculated to be 98.1%. 1H NMR spectra of P2, P2-OH, and P 2 -COOH are shown in Figure 1b, which also demonstrated the success of the thiol−ene reaction. The degree of conversion was calculated to be 99.3% for P2-OH and 94.6% for P2-COOH. Glass transition temperatures (Tg) of the polymer matrix are important to the mechanical properties of nanocomposites. As shown in Figures 1c and 1d, Tg values for P1 and P1-OH are −24.2 and −25.6 °C, respectively, while they are −7.2, −8.1, and −8.6 °C for P2, P2-OH, and P2COOH, respectively. The introduction of hydroxyl groups and carboxyl groups slightly decreased the Tg values of the precursor polymers. It is worth noting that polymers with varied Tg values (P1-OH, P2-OH, and P2-COOH) may influence mechanical properties of nanocomposites. Preparation of Nanocomposites Derived from CNCs and Soybean Oil. In order to prepare nanocomposites with CNCs well dispersed in a soybean oil polymer matrix, solution mixing is one of the most efficient methods. CNCs can be well dispersed in polar aprotic solvents such as DMF. The polargroup-containing polymers (P1-OH, P2-OH, and P2-COOH) are also well dissolved in DMF. As an initial test, CNCs were dispersed in DMF via sonication and mixed with polymers D


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dog-bone sample of P2-COOH-20, showing good toughness and flexibility of nanocomposites. It was understood that the CNCs provide high mechanical strength, while the relatively low Tg value of the polymer matrix endows the nanocomposite with flexibility. The thermodynamic mechanical properties of P2-COOH/ CNCs nanocomposites were characterized by DMA. Figure 4 shows the dependence of storage modulus (E′) and loss tangent (tan δ) as a function of temperature for P2-COOH/ CNCs nanocomposites with CNCs weight content in the range 5−30 wt %. The E′ vs temperature plots of all nanocomposites displayed three distinct stages: a glassy stage, a glass transition stage, and a rubbery stage. At temperature below Tg, the storage modulus increases gradually with the increase of CNCs weight content. In the glass transition range, the E′ showed dramatic decrease due to the higher segmental motion of the polymer matrix. However, the reduction of E′ of nanocomposites with higher CNCs content shows a decrease to a much less significant level, which implied that the introduction of CNCs may limit the motion of polymer segments of matrix. At temperatures higher than Tg, nearly all nanocomposites showed a rubbery plateau, demonstrating the formation of a network of CNCs. However, 5 wt % of CNCs in the composites was not sufficiently high to establish such a network, leading to the sudden drop of E′ of P2-COOH-5 at 120 °C. In comparison, other composites with CNCs higher than 10 wt % maintained the E′ even up to 200 °C. The storage modulus at room temperature is an important parameter representing the stiffness of materials. The storage modulus at room temperature for P2-COOH/CNCs nanocomposites is in the range 51.5−2786.7 MPa. With the increase of CNCs content from 5 to 30 wt %, the nanocomposites displayed a modulus increase of about 2 orders of magnitude, which can be attributed to the increase of physical cross-linking density formed via hydrogen bonding between CNCs and the polymer matrix. Figure 4b shows a depression of the loss tangent peak intensity, which further demonstrated that the chain mobility of polymer matrix is greatly limited by CNCs. Water-Induced Modulus Change of the Nanocomposites. In the case of our polymer nanocomposites, the hydrogen-bonding interactions are present not only within CNCs but also between CNCs and the polymer matrix. The introduction of water would weaken the hydrogen-bonding interactions and decrease the network density as well as the

Table 1. Compositions and Mechanical Properties of Nanocomposites sample code

CNCs content (wt %)

P1-OH-30 P2-OH-30 P2-COOH-30 P2-COOH-20 P2-COOH-15 P2-COOH-10 P2-COOH-5

30 30 30 20 15 10 5

failure strain (%) 7.6 12.0 3.9 8.2 21.6 35.2 80.4

± ± ± ± ± ± ±

0.3 0.7 0.4 0.3 0.5 0.5 1.3

failure stress (MPa) 6.4 9.2 19.9 23.0 10.1 6.9 1.0

± ± ± ± ± ± ±

0.2 0.4 0.9 0.6 0.4 0.4 0.2

wt % of CNCs and different polymer matrix (P1-OH-30, P2OH-30, and P2-COOH-30) were first prepared and their typical stress-strain curves were shown in Figure 3a to show the influence of polymer matrix on the composite properties. They all show typical plastic properties, and their mechanical properties are summarized in Table 1. The ultimate tensile strength is 6.4 ± 0.2, 9.2 ± 0.4, and 19.9 ± 0.9 MPa, the strain at break is 7.6 ± 0.3, 12.0 ± 0.7, and 3.9 ± 0.4%, the modulus is 715.3 ± 6.1, 783.2 ± 5.3, and 867.1 ± 4.6 MPa for P1-OH-30, P2-OH-30, and P2-COOH-30, respectively. From the results of P1-OH-30 and P2-OH-30, we can conclude that higher tensile strength can be obtained from the polymer matrix with a higher Tg value (P2-OH). The comparison between P2-OH-30 and P2-COOH-30 indicated that the modified polymer with carboxyl groups gave higher tensile strength, which is probably due to the stronger hydrogen-bonding interactions between polymer matrix and CNCs.49−51 The high values of modulus for these nanocomposites are mainly determined by the formation of CNCs networks. Using P2-COOH as a matrix, we also examined the effect of the weight content of CNCs on the nanocomposite properties. Five nanocomposites with the weight content of CNCs in the range of 5−30 wt % (Table 1) were prepared, and their representative stress−strain curves are shown in Figure 3b. For P2-COOH-5, P2-COOH-10, P2-COOH-15, and P2-COOH20, the mechanical strength increased from 1.0 ± 0.2 to 23.0 ± 0.6 MPa with the increase of CNCs (Table 1). P2-COOH-10 showed a 6.9 times increase of mechanical strength from P2COOH-5. However, P2-COOH-30 exhibited lower ultimate tensile strength and failure strain than those of P2-COOH-20. This might be related to the formation of CNC aggregates at higher weight content. The inset of Figure 3b is a photo of a

Figure 3. Typical stress−strain curves for (a) P1-OH-30, P2-OH-30, and P2-COOH-30 and (b) P2-COOH-30, P2-COOH-20, P2-COOH-15, P2COOH-10, and P2-COOH-5. Inset photo is a dog-bone sample of P2-COOH-20. E


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Figure 4. DMA curves of (a) storage modulus and (b) loss tangent, tan δ, as a function of temperature for P2-COOH/CNCs nanocomposites with the content of CNCs from 5 to 30 wt %.

Figure 5. (a) Evolution of water uptake in P2-COOH/CNCs nanocomposites with CNCs contents from 5 to 30 wt % as a function of time immersed in deionized water at room temperature. (b) Equilibrium water uptake of P2-COOH/CNCs nanocomposites as a function of CNCs content at room temperature.

between cellulose nanowhiskers. When in contact with water, water molecules would penetrate the surface of CNCs and form hydrogen bonding with CNCs, which could lead to the disengagement of the 3D network of nanowhiskers. Such altered 3D networks are suggested to be responsible for the significant decrease of mechanical strength. In our case, the strong hydrogen bonding interaction between soybean oil polymer matrix and CNCs suppresses the swelling of the polymer matrix. The effects of water presence on the mechanical properties of nanocomposites were studied by DMA with a submersible clamp. The measurements started immediately after adding water and conducted for 120 min at room temperature. Figure 6a−d shows the change of storage modulus as a function of time for P2-COOH-30, P2-COOH-20, P2-COOH-10, and P2COOH-5, respectively. The water-induced modulus decrease of nanocomposites was highly dependent on the CNCs content. E′ of P2-COOH-30 and P2-COOH-20 reduced dramatically from 1166 and 698 MPa to 123 and 85 MPa within 10 min, respectively, and then reached equilibrium within 30 min. In contrast, E′ of P2-COOH-5 continuously decreased even after 120 min. The percentage decreases of E′ that occurred in 120 min are 89.5, 87.8, 86.4, and 81.8% for P2-COOH-30, P2COOH-20, P2-COOH-10, and P2-COOH-5, respectively. The stress recovery for P2-COOH-30 as a function of time under air

storage modulus of nanocomposites. Experimental data for the water uptake of P2-COOH/CNCs nanocomposites with the content of CNCs from 5 to 30 wt % as a function of time of immersion in deionized water at room temperature are shown in Figure 5a. The plots clearly show that all P2-COOH/CNCs nanocomposites had distinct water uptake. The rate of water uptake decreased with the increase of CNCs content. For example, P2-COOH-30 absorbed 11.2 wt % water within 1 day and reached an equilibrium after 2 days, while P2-COOH-5 continuously absorbed water and swelled 30.7 wt % after 1 week. Figure 5b gives the equilibrium water uptake of P2COOH/CNCs nanocomposites as a function of CNCs content at room temperature, which is defined as weight ratio of water absorbed over dry weight of nanocomposites after immersion in water for 7 days. The results clearly showed that the equilibrium water uptake decreased with the increase of CNCs content. It is worth mentioning that the water uptake behavior of these nanocomposites was quite different from nanocomposites with hydrophobic polymer as matrix and cellulose nanowhiskers as nanofillers as reported by the groups of Rowan and Weder.46 They studied the water-triggered storage modulus change of nanocomposites using cellulose nanowhiskers as fillers.46,52 The mechanical reinforcement is primarily due to the formation of 3D network structures via hydrogen bonding F


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Figure 6. Water-induced storage modulus switching of (a) P2-COOH-30, (b) P2-COOH-20, (c) P2-COOH-10, and (d) P2-COOH-5. (e) Evolution of storage modulus as a function of time during air drying at room temperature for P2-COOH-30. (f) DMA experiments were performed using a submersible clamp.

materials. Polymers with pendent fatty chains, which originate from soybean oil, were prepared and modified with polar −OH and −COOH groups through thiol−ene click chemistry on the unsaturated side chains. A spectrum of nanocomposites with tunable mechanical properties were prepared by varying the polymer precursor structures and the content of CNCs filler. More importantly, the prepared nanocomposites exhibited a fast water-triggered modulus switching. Because of the sustainability, biocompatibility, and environmental friendliness, these biomass-derived nanocomposites could be used in various fields such as packaging and stimuli-responsive materials.

at room temperature was also characterized. As shown in Figure 6e, the stress of wet nanocomposites can be recovered gradually due to the evaporation of water molecules. Thus, the nanocomposites showed reversible water-induced mechanical switching. Moreover, higher contents of CNCs led to a faster response to water. Though the current study focuses on a proof of concept that moisture triggers would induce reversible stress change, these water-responsive composites may find applications in smart devices, such as moisture gradient-driven actuation systems.

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CONCLUSIONS In summary, a simple and effective strategy was demonstrated for the preparation of sustainable polymer nanocomposites using soybean oil and CNCs as the renewable starting

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (C.T.). G


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ORCID

Chuanbing Tang: 0000-0002-0242-8241 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Z. Wang thanks the National Science Foundation of China for financial support (Grants 51603002 and 51773001). Support from the National Science Foundation (DMR-1252611) is acknowledged.

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