Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Conformations of Ring Polystyrenes in Bulk Studied by SANS Takuro Iwamoto,† Yuya Doi,‡,† Keita Kinoshita,† Yutaka Ohta,† Atsushi Takano,*,† Yoshiaki Takahashi,§ Michihiro Nagao,∥,⊥ and Yushu Matsushita*,† †
Department of Molecular and Macromolecular Chemistry, Nagoya University, Nagoya, Aichi 464-8603, Japan Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan § Institute for Materials Chemistry and Engineering, Kyushu University, Kasuga, Fukuoka 816-8580, Japan ∥ NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6102, United States ⊥ Center for Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47408, United States ‡
S Supporting Information *
ABSTRACT: We prepared five pairs of hydrogenous and deuterated ring polystyrene samples over a wide range of molecular weights (10 kg/mol ≤ Mw ≤ 400 kg/mol) and investigated their chain conformations in bulk by small-angle neutron scattering (SANS) measurements. From the SANS profiles obtained, we estimated the radii of gyration Rg of the ring polymers by the Guinier approximation. Rg can be related to the degree of polymerization N as Rg ∼ N0.47. This scaling exponent ν = 0.47 ± 0.01 is evidently smaller than that for the Gaussian chains (ν = 0.50) but higher than previous experimental reports (ν = 0.42−0.43). Then our data were compared with various simulation and experimental data by introducing the entanglement degree of polymerization Ne for linear polymers as a normalized parameter. Rg of three smaller rings, i.e., R-10, R-30, and R-70, where the numbers denote molecular weights in kg/mol unit, are in good agreement with simulation results, while two larger rings, R-100 and R-400, exhibit higher Rg values than the simulations. Considering that the latter two higher molecular weight samples include maximum 3% of linear contamination, their effects on chain dimension were calculated. As a result, it has been confirmed that 3% of linear contaminations can overestimate Rg of rings as much as 6% for R-100 and 12% for R-400. Thus, Rg for pure large rings should be considerably lower than the present experimental values. We conclude Flory’s exponent v in Rg ∼ Nv for rings may not be constant but rather show molecular weight dependence due to their topological constraint. al.27 using by small-angle neutron scattering (SANS) measurements for hydrogenous and deuterated linear polymer blend samples in a wide molecular weight range, i.e., 104−106 kg/mol. In contrast, the conformational study on ring polymer melts is not as simple as linear ones because of their topological constraints, i.e., the noncrossability of intra-ring/inter-ring chains. When discussing conformations of ring polymers in melts, those in dilute solutions may give us some insights. In good solvents, Rg of ring chains is known to follow the dependency of N0.60,5,6,8 whose exponent is the same as linear chains. These results suggest that interactions between a polymer chain and a solvent molecule are dominant, and hence the topological constraints have little effect. In contrast, at θ solvent conditions, where the second virial coefficient A2 is zero for linear chains, ring polymer solutions exhibit distinctly positive A2 values.6,7,9 These experimental facts indicate that larger repulsive
1. INTRODUCTION Ring polymers with no chain ends have attracted considerable attention of researchers because the chain ends of polymers play important roles in physical properties of polymers. Theoretical studies on ring polymers were first performed more than half a century ago and predicted that the physical properties of ring polymers are definitely different from those of linear ones.1−4 In experimental aspects, various properties of ring polymers such as conformations in dilute solutions (under good and θ solvent conditions),5−9 those in bulk,10−15 and the dynamics in melt states16−23 were extensively investigated. Among them, the conformations of rings in bulk are one of the fundamental and still not clearly solved problems. For linear polymer melts, Flory24 and de Gennes25 theoretically predicted that the chains behave as Gaussian chains because the excluded volume effects are screened due to the balance between positive and negative interactions. Thus, they expected that the radii of gyration Rg and the degree of polymerization N of linear chains can be related as Rg ∼ Nν with the Flory exponent ν = 0.5. This prediction was experimentally confirmed by Cotton et al.26 and Kirste et © XXXX American Chemical Society
Received: November 4, 2017 Revised: January 11, 2018
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DOI: 10.1021/acs.macromol.7b02358 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
blend ring samples in bulk were performed. All ring samples were anionically synthesized and highly purified by the interaction chromatography (IC) methods. SANS data obtained were analyzed by the Guinier’s method to estimate the ring chain sizes, Rg, and those values were compared with the other experimental and simulation results. Moreover, the scattering profiles of the ring samples were analyzed by using particle scattering functions of ring polymers.
interaction is generated due to topological constraints which are naturally forced to have more compact conformation than linear chains at the θ temperature. Hence, apparent θ temperature depression occurs for ring chains. Concerning the conformations of ring polymer melts, various theoretical and simulation studies have been conducted up to date.28−42 Throughout the whole studies, ring chains are expected to possess more compact conformations than the Gaussian rings. This is mainly because the intermolecular penetration, which is not considered in dilute solution systems is hard to occur for ring chains. Cates et al.28 took into account the free energy balance between the intra- and interchain interactions and proposed that the ring chains have the exponent ν between the Gaussian (ν = 1/2) and collapsed (ν = 1/3) conformations. In particular, on the basis of the assumption of the Flory-type mean-field theory, they predicted ν = 2/5. Suzuki et al.34 and Vettorel et al.35 reported that the exponent ν approaches 1/3 for sufficiently long ring chains by simulations. Their explanation of these results was that the large rings possess denser conformations than small rings but still larger than collapsed globules, i.e., not completely segregated in molecular scales. Halverson et al.38 expected from molecular dynamics (MD) simulation that the exponent ν of ring polymer melts smoothly changes from the Gaussian (ν = 0.5), via a regime with ν = 2/5, to the crumpled globules (ν = 1/3) with increasing chain lengths. Sakaue also demonstrates the same crossover behavior for the exponent ν of ring melts through the mean-field theory by introducing the idea of the topological volume.39,40 Moreover, Halverson et al.41 summarized various simulation results32,34,35,37,38 by using the entanglement length, Ne, to normalize the length scales, and they proposed the universal behavior that all of the Rg data were aligned on one single smooth curve. Compared to the above numerous theoretical and computer simulation studies, experimental studies are few,10−15 mainly because there exists the difficulty in preparation of pure ring samples particularly with higher molecular weight than 100 kg/ mol. SANS is the most powerful technique to evaluate the conformations of polymer melts, though isotope-labeled samples are necessary in order to gain a strong scattering contrast. In recent years, a new chromatographic technique, liquid chromatography at the critical condition (LCCC) or interaction chromatography (IC), has been developed,43,44 and they are utilized to separate and purify ring samples. Arrighi et al.10,11 examined SANS of ring polydimethylsiloxane (PDMS) bulk samples with the molecular weights of 3−11 kg/mol and reported the relationship of Rg ∼ N0.42, which is consistent with the prediction by Cates et al.28 However, the molecular weight range adopted was too narrow to accurately determine the exponent ν. Moreover, they did not report the purities of the ring samples. Recently, Richter et al.12−15 performed SANS experiments for ring poly(ethylene oxide) (PEO) melt samples with M = 2, 5, 10, and 20 kg/mol, and they reported that the rings reveal the scaling exponents ν of 0.43−0.44 from the scattering profiles analyses, though the molecular weight range was still narrow. Therefore, to elucidate the whole picture on conformations of ring polymer melts, further experimental data in a wide molecular weight range, especially higher side, are required. Based on the above background, in this study, five pairs of hydrogenous (h) and deuterated (d) ring polystyrene samples covering a wide molecular weight range with Mw = 10−400 kg/ mol were prepared, and the SANS measurements for the h-/d-
2. EXPERIMENTAL SECTION 2.1. Materials. All polymer samples used in this study were prepared by anionic polymerizations in sealed glass apparatuses with break-seals under high-vacuum (∼1 × 10−3 Pa). Hydrogenous and deuterated telechelic linear polystyrenes, h-LPS and d-LPS, respectively, with 1,1-diphenylethylene (DPE) type vinyl groups on both ends were synthesized in the same manner as reported previously.45 In this study, five pairs of h-/d-LPS samples in a wide range of molecular weight M (10 kg/mol ≤ Mw ≤ 400 kg/mol) were synthesized, and their molecular characteristics are summarized in Table S1 of the Supporting Information. These telechelic samples were cyclized by using potassium naphthalenide (Naph-K) as a coupling agent in dilute THF solutions (ca. 0.1%).45 Cyclization products were purified by size exclusion chromatography (SEC) and interaction chromatography (IC) fractionations, by using preparative chromatography apparatuses. Concerning IC fractionations, a combination of bare silica gel columns (5SIL10E; Shodex) and a mixture eluent of THF/n-hexane (42/58 in volume) was adopted for the lower molecular weight samples (
