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Pronounced Dielectric and Hydration/Dehydration Behaviors of Monopolar Poly(N‑alkylglycine)s in Aqueous Solution Kengo Arai,† Naoya Sagawa,‡ Toshiyuki Shikata,*,†,‡ Garrett L. Sternhagen,§ Xin Li,§ Li Guo,∥ Changwoo Do,⊥ and Donghui Zhang§ †

Division of Natural Resources and Eco-Materials, Graduate School of Agriculture and ‡Department of Symbiotic Science of Environment and Natural Resources, The United Graduate School of Agriculture, Tokyo University of Agriculture and Technology, 3-5-8 Saiwai-cho, Fuchu, Tokyo 183-8509, Japan § Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70873, United States ∥ The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ⊥ Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States S Supporting Information *

ABSTRACT: Poly(N-methylglycine) (NMGn) and poly(Nethylglycine) (NEGn) obtained by polymerization reactions initiated by benzylamine have no carboxy termini, such as those in normal polyamides, but have only amino termini, which exist primarily as cations in aqueous media at a pH value of ca. 9.5, observed in aqueous solutions without any buffer reagents. Therefore, polypeptoids, such as NMGn and NEGn, possessing a degree of polymerization (DP) higher than a certain value behave as cationic monopolar polymeric chain molecules in aqueous solution. It has not been clarified so far whether such a monopolar chain molecule exhibits dielectric relaxation (DR) behavior resulting from its molecular motions in aqueous media as dipolar chain molecules. DR measurements revealed that NMG19 and NEG17, possessing DPs of 19 and 17, respectively, dissolved in pure water clearly demonstrated pronounced DR behavior caused by fluctuating molecular motions of cationic termini at relaxation times of ca. 4 and 9 ns at 10 °C (283 K). The hydration numbers of NMG19 and NEG17 per monomeric residue (nm) in aqueous solution were also evaluated via DR data as functions of temperature, and the nm value of ca. 4.5 at 10 °C showed a remarkable reduction to ca. 2.0 around 40 °C (313 K) and 30 °C (303 K), depending on differences in the substituted group: methyl and ethyl groups. This temperature-dependent hydration/dehydration behavior found in NMG19 and NEG17 slightly influenced the sizes and molecular dynamics of the monopolar chain molecules in aqueous solution.

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INTRODUCTION Molecular motions of polymeric chain molecules dissolved in viscous liquid media have been well understood on the basis of a bead−spring model proposed by Rouse1 and modified by Zimm2 that takes into account the hydrodynamic interactions between the beads forming the chains.3,4 Viscoelastic measurements are a conventional method to probe the molecular motions of long polymeric chains, like macromolecular molecules in solution, in a frequency range lower than 102 s−1. When information on molecular motions in a frequency range higher than this value is necessary, dielectric relaxation (DR) experiments are useful for their precise investigation.4 Especially, polymeric chain molecules bearing monomeric dipole moments aligned parallelly along the polymer backbone, which are classified as type A chain molecules,5,6 demonstrate pronounced DR related to fluctuation motions of the chain termini systematically, depending on the degree of polymer© XXXX American Chemical Society

ization (DP), which are well described by a modified bead− spring model for type A chain molecules.4−35 When a monomeric dipole moment possesses a finite component perpendicular to the polymer backbone (such a polymer chain is classified as a type B chain), a DR process owing to the molecular dynamics of the monomers is also observed as segment or local motions in the polymeric chain irrespective of the value of DP.4 Many polymeric samples studied as type A chains have characteristics of both the type A and B chains.4,12,15,21,22 Polymeric chain molecules bearing dipolar, cationic, and anionic termini like the usual polypeptides and protein molecules with carboxy and amino termini also behave as a type A chain in aqueous solution because of the Received: May 28, 2016 Revised: August 24, 2016

A

DOI: 10.1021/acs.jpcb.6b05379 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B dissociation of both termini.5,6,36−38 Several years ago, DR measurements of an aqueous solution of collagen model synthetic polyamide (L-proline-L-prolylglycine)5 (PPG5), which bears carboxy and amino termini that dissociate into dipolar chain molecules in aqueous solution, in a frequency range higher than 109 s−1 revealed that molecular motions of PPG5 are quantitatively described by the modified bead−spring model.36−38 On the other hand, the modified bead−spring model predicts that monopolar chain molecules bearing only a cationic or anionic group as a chain terminus also demonstrate DR behavior due to molecular motions governed by the Rouse and Zimm dynamics.5,6 However, the predicted magnitude of DR strength for the slowest relaxation mode of the monopolar chain molecule is one-fourth that for a dipolar chain molecule with the same DP as that of the monopolar chain molecule. From a fundamental scientific point of view, whether such a monopolar polymeric chain molecule demonstrates profound DR behavior caused by fluctuating molecular motions of its monopolar terminus or not is a controversial open question, as there is no well-defined usual dipole moment responsible for the appearance of DR modes in the monopolar polymeric chain molecule. However, one should be aware that polypeptoid chains (poly(N-methylglycine) (NMGn) and poly(N-ethylglycine) (NEGn)), such as NMG19 and NEG17, always bear amide groups generated by the polymerization process, which possess finite dipolar components parallelly aligned to the polymer chain backbone like those in the type A chain, as depicted in Scheme 1.

case of monopolar polymeric chain molecules. The temperature dependencies of the hydration number per repeating residue, nm, were also determined for both NMG19 and NEG17 in aqueous solution. Moreover, the temperature dependency of molecular size was also discussed in relation to that of the hydration numbers for the polypeptoids.

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EXPERIMENTAL SECTION Materials. NMG19 and NEG17 and NEG18 were synthesized by ring-opening polymerization reactions of N-substituted Ncarboxyanhydride monomers: N-methyl N-carboxyanhydride and N-ethyl N-carboxyanhydride, respectively. The procedures of monomer synthesis and ring-opening polymerization have been reported in detail elsewhere.39,40 Highly deionized water possessing a specific electric resistance higher than 18 MΩ cm, obtained from a Direct-Q 3UV system (Millipore, Tokyo, Japan), was used as a solvent for sample preparation. The concentrations of NMG19 and NEG17 in the prepared aqueous solutions ranged from c = 0.42−1.0 to 0.1−0.41 M in monomeric residue units, respectively. Deuterium oxide (D2O, 99.9) was purchased from Sigma-Aldrich and used as a solvent for sample preparation for small-angle neutron scattering (SANS) measurements. The concentration of NEG18 in the prepared D2O solutions was c = 0.137 M (1% in weight) in monomeric residue units. Methods. Two systems were used to measure the DR behaviors of aqueous solutions of sample polymers over a frequency range from 1 MHz to 50 GHz. A dielectric probe kit, 8507E, equipped with a network analyzer, N5230C; an ECal module, N4693A; and a performance probe 05 (Agilent Technologies, Santa Clara), was used for DR measurements over a frequency range from 50 MHz to 50 GHz (3.14 × 108− 3.14 × 1011 s−1 in angular frequency (ω)). The probe, with a diameter of 9.7 mm, was inserted into a glass vial with an inner diameter of ca. 16 mm, and the distance from the probe edge to the bottom of the vial was kept longer than 3 mm. The volume of the tested liquid sample was ca. 2 mL. The real and imaginary parts (ε′ and ε″) of electric permittivity were automatically calculated from the reflection coefficients measured by the network analyzer via a program supplied by Agilent Technologies. A three-point calibration procedure using n-hexane, 3-pentanone, and water as the standard materials was performed before all of the DR measurements at each measuring temperature. Hexane has a low, constant ε′ of 1.89 (at 20 °C) and zero ε″, irrespective of the frequency, ω, whereas the polar liquid 3-pentanone demonstrates a middle ε′ value of 17.3 in a low ω side and a clear single DR process with a strength of 14.3 at a relaxation time of 7.0 ps (at 20 °C). Moreover, water shows a large ε′ value of 80.2 in the low ω side and a distinct single DR process with a strength of 75.0 at a relaxation time of 9.5 ps (at 20 °C). Employing the three liquids as the standard calibration materials for the network analyzer made precise DR measurements possible over the ω region described above for a wide range of ε′ values, from 2 to ca. 102.41 Details of the three-point calibration procedure used in this study have been described elsewhere.41 On the other hand, in the lower frequency range from 1 MHz to 3 GHz (ω = 6.28 × 106−1.88 × 1010 s−1), an RF LCR meter 4287A (Agilent) equipped with a homemade electrode cell with a vacant electric capacity of C0 = 0.23 pF was used, which consists of center and outer electrodes made of goldcovered brass insulated by poly(tetrafluoroethylene). The electrode cell had the same center and outer conductor

Scheme 1. Schematic Depiction Showing the Presence of Dipolar Components Parallel and Perpendicular (μm∥ and μm⊥) to the Polymer Backbone, Resulting from Monomeric Dipole Moments (μm) of Amide Groups Generated by the Polymerization Processa

a

The presence of a cationic electric charge likely induces a new terminus dipole moment, μterm, that disturbs the neighboring residual dipole moment, μm.

At present, it is not difficult to synthesize monopolar polymeric chain molecules. For example, a polymerization process for polypeptoid molecule synthesis initiated by benzylamine (BzAM) is able to generate monopolar polymeric chain molecules in aqueous solution, as BzAM has no ability to be an anionic chain terminus like the carboxy group.39,40 Then, using BzAM-initiated polypeptoid molecules dissolved in aqueous media as model molecules, one can investigate the DR behavior of the monopolar polymeric chain molecule. In this study, broadband DR measurements were carried out in aqueous solutions of NMG and NEG with DPs of 19 (NMG19) and 17 (NEG17) at several temperatures ranging from 10 to 70 °C to clarify whether the DR processes resulted from fluctuations in the molecular motions of chain termini in the B

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Figure 1. (a) Frequency (ω) dependence of the real and imaginary parts of the electric permittivity (ε′ and ε″) of aqueous NMG19 solution at c = 0.5 M and 10 °C as a typical example. Four constituent Debye-type relaxation functions necessary to reproduce the spectra as solid lines are shown as broken lines. (b) Results of subtraction of the two major relaxation components calculated, j = 1 (ε1′ and ε1″) and j = 4 (ε4′ and ε4″), from ε′ and ε″. The summation of two additional minor relaxation modes, ε2′ + ε3′ and ε2″ + ε3″, necessary to reproduce experimental ε′ and ε″ curves is also shown as solid lines.

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RESULTS AND DISCUSSION Dielectric Behavior. Figure 1a shows the frequency dependence of ε′ and ε″ of aqueous NMG19 at c = 0.5 M and 10 °C as a typical example. The large DR process found at ω = 8 × 1010 s−1 is easily assigned to the rotational relaxation mode of free water molecules because only a DR process is observed at the same frequency in pure water. A small but significant DR process was additionally observed around ω = 2 × 108 s−1, which is attributed to the DR process caused by fluctuating molecular motions of monopolar chain termini of NMG19 later. For quantitative relaxation analysis, the dielectric spectra seen in Figure 1a were decomposed into constituent fundamental Debye-type relaxation modes using the formula given by eq 1 below

diameters of electrodes (3.04 and 7.00 mm, respectively) as those of an impedance matching connector (APC7) of 50 Ω. A short (0 Ω) part of APC7 was used as a counter electrode against the center conductor electrode with a flat surface. The separation between the center and counter electrodes was 0.5 mm. Open (air), short (0Ω, a gold plate with a thickness of 0.5 mm), and load (water) calibration processes were performed before sample measurements at each measuring temperature. DR measurements were performed at temperatures ranging from T = 10 °C (283.2 K) to 70 °C (343.2 K) (accuracy of ±0.1 °C (K)), using a temperature controlling unit made of a Peltier device. The ε′ and ε″ values were obtained via the relationships ε′ = CC0−1 and ε″ = (G − GDC)(C0ω)−1, where C, G, and GDC represent the measured electric capacitance, conductance, and direct current conductance of a sample liquid, respectively. The contribution of GDC to the ε″ value was adequately removed in a low ω range. Density measurements for all of the aqueous sample solutions were carried out using a digital density meter, DMA4500 (Anton Paar, Graz), to determine the partial molar volumes of the solute molecules at the same temperatures used for the DR measurements. The mean radius of gyration, Rg, of NEG18 dissolved in aqueous (D2O) solution was obtained as a function of temperature, T, ranging from 10 to 70 °C, using the standard SANS techniques. The SANS experiments were performed at EQ-SANS SNS in Oak Ridge National Laboratory. The scattering profiles of NEG18 were measured at EQ-SANS using the wavelength band of 0.424 < λ < 0.771 nm at 1.3 m, with the Q range covering 0.1−7.0 nm−1. The sample polymer, NEG18, was directly dissolved in deuterated water at a concentration of 1.0 wt % at room temperature, and then, the solution sample was loaded into 2 mm thick banjo cells for measurements. Two sets of measurements were carried out: First run, the sample temperature was varied from 10 to 70 °C, with a step of 10 °C; second run, three measurements with doubled data acquisition times were performed at 10, 40, and 70 °C to obtain better statistics under these three conditions. The transmission of the NEG18 solution is higher than 0.9, indicating negligible multiscattering events. The scattering intensities were scaled to absolute values on the basis of standard sample (Porsil B) measurements.

ε′ =

∑ j

εj 1 + (ωτj)2

+ ε∞ , ε″ =

∑ j

εjωτj 1 + (ωτj)2

(1)

where εj, τj, and ε∞ represent the DR strength and time for mode j and the ω-independent electric permittivity, respectively.36−38,42 Four Debye-type relaxation modes were necessary to reproduce the spectral data seen in Figure 1a perfectly as the best fit curves described with solid lines, and the necessary constituent Debye-type relaxation modes, εj′ and εj″ (j = 1−4), are shown in the same figure as broken lines. Subtraction of the calculated εj′ and εj″ of two major DR modes: j = 1 and 4, which were easily determined first, from the experimental ε′ and ε″ curves allowed us to evaluate the dielectric parameters for two additional minor relaxation modes: j = 2 and 3. Figure 1b demonstrates reasonable agreement between ε′ − ε1′ − ε4′ and ε2′ + ε3′ and ε″ − ε1″ − ε4″ and ε2″ + ε3″, which reveals the validity of our analytical method using eq 1. In all of the aqueous samples prepared in this study, as well as in the aqueous NMG19 solution at c = 0.5 M seen in Figure 1, four Debye-type relaxation modes were necessary to reproduce the experimental dielectric spectra. Figure 2 shows a so called Cole−Cole plot42 of dielectric data, ε″ vs ε′, for the same aqueous NMG19 solution, with c = 0.5 M and 10 °C, as that used in Figure 1. A large semicircle, with a radius of 38, clearly represents the contribution of the major relaxation mode, j = 1 (and also of the minor mode, j = 2). A small but non-negligible shoulder is distinctively recognizable around ε′ = 80 (in a low ω side) in the Cole− C

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Figure S1. The pH values of aqueous NMG19 and NEG17 solutions without any buffer chemicals were 9.2−9.5. This observation suggests that the degree of protonation of the polypeptoid chain molecules in aqueous solution is higher than 0.9, as the typical pKa value of secondary amine termini is ∼11.43 Because the alternation of the electric charge condition of polypeptoid chain termini influenced the relaxation strength of mode j = 4, this mode corresponds to fluctuating molecular motions of polymer chains. Moreover, an aqueous solution of collagen model polypeptide PPG5, with a similar DP of 15 (in residue numbers), also demonstrates pronounced DR at a frequency close to that for the aqueous NMG19 solution: ω = 2 × 108 s−1 (cf. Figures 1a and 3a), which has been confirmed to be the fluctuating molecular motion of the dipolar termini of chain molecules, PPG5.36−38 This experimental fact strongly reveals that the DR process found as the relaxation model j = 4 results from the fluctuating molecular motion of monopolar polymeric chains of NMG19. Furthermore, the dependence of ε4 in proportion to c recognized in Figure 3b is consistent with the assignment. Two kinds of conceivable explanations are possible for the smallest relaxation process, observed as the relaxation mode j = 3, with a relaxation time of τ3 = 90 ps. The first possible assignment for this relaxation process is another fluctuating molecular motion of polymeric chain molecules, NMG19, that is slightly faster than mode j = 4. The second assignment is the molecular motion of monomeric residues, which possess an amide group, −N(−CH3)C(O)−, bearing a relatively large dipole moment, generated by the polymerization process. This molecular motion corresponds to the fastest dynamics occurring in the polymeric chain via rotation around chemical bonds and is related to the characteristics of the type B chain. In a later section, the second assignment will be accepted as an essential mechanism for the relaxation mode j = 3. In the case of an aqueous NEG17 system, similar DR spectra to those of the aqueous NMG19 system (cf. Figure 1) were observed. The same curve fit procedure was employed even in the aqueous NEG17 system to decompose the DR spectra into constituent Debye-type relaxation components as those used in the aqueous NMG19 system above. The dielectric parameters necessary to reproduce the obtained DR spectra for the aqueous NEG17 system at 10 °C are shown as functions of the concentration of NEG17, c, in Figure 4a,b. As the dependencies of the parameters for modes j = 1 and 2 on c in the aqueous NEG17 system agree well with those observed in the aqueous NMG19 system, the fundamental mechanisms for the modes, that is, rotational relaxation of free water molecules (j = 1) and

Figure 2. Cole−Cole plot of dielectric data, ε″ vs ε′, for the aqueous NMG19 solution at c = 0.5 M and 10 °C (cf. Figure 1).

Cole plot. This small shoulder reveals the presence of minor DR modes j = 3 and 4. The concentration, c, dependencies of τj and εj, determined via the curve fit procedure described above for an aqueous NMG19 system at 10 °C, are shown in Figure 3a,b. We numbered j = 1 from the fastest mode. In the case of mode j = 1, assignment was simply determined as a rotational relaxation mode of free water molecules in the aqueous NMG19 solution because the relaxation time of mode j = 1 was identical to that of pure water (cf. Figure 3a). All of the determined relaxation times possessed weak concentration dependences over the c range examined. This observation suggests that the relaxation time is not controlled by the macroscopic viscosity of the prepared solution but by an inner viscosity close to that of the solvent and water in the c range examined. Moreover, because the DP of NMG19 is low, the concentration range examined in this study was sufficiently lower than the overlap concentration of NMG19. The DR strength, ε1, which decreased almost proportionally to the concentration, c, as seen in Figure 3b, permitted one to determine the hydration number, nm, per monomeric residue, as described in the next section. The second fastest relaxation mode, j = 2, was assigned to the exchange mode of the hydrated water molecules because the relaxation strength, ε2, was proportional to c and was reasonably identical to a relaxation magnitude calculated from the hydration number, nm, determined from the ε1 value, assuming water molecules have the same DR strength irrespective of the formation of hydrogen bonds due to the hydration behavior. The fourth, longest relaxation mode, j = 4, was assigned to the fluctuating molecular motion of cationically charged termini, −N+(−CH3)H2, of chain-like NMG19 molecules because the addition of aqueous sodium hydroxide (NaOH) solution to promote the deprotonation of cationically charged termini substantially increased relaxation mode j = 4, as seen in

Figure 3. Concentration (c) dependencies of τj (a) and εj (b) determined via the curve fit procedure, using eq 1 described in the text, for an aqueous NMG19 system at 10 °C. D

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Figure 4. Concentration, c, dependencies of τj (a) and εj (b), determined via the curve fit procedure, for the aqueous NEG17 system at 10 °C.

Figure 5. Temperature (T) dependencies of hydration numbers per monomeric residue (nm) for aqueous NMG19 (a) and NEG17 (b) systems. Arrows indicate dehydration temperatures (Tdh; see text).

differs depending on the chemical species of monomeric residues, that is, Tdh ∼ 40 and 30 °C for NMG19 and NEG17, respectively, as seen in Figure 5a,b. The values nmL ∼ 4.5 and nmH ∼ 2 appear to be less dependent on the chemical species of the monomeric residue (cf. Figure 5a,b). It is worthy to note that for PPG5 nmL ∼ 9, nmH ∼ 3, and Tdh ∼ 27 °C;38 the asymptotic hydration number, nmL, for PPG5 is about twice as large as that for NMG19 and NEG17. These observations strongly suggest that the values of nmL and nmH essentially depend on the chemical species of the monomeric residue, whereas a difference between methyl and ethyl groups as substitute ones does not make a difference in the values of nmL and nmH. Monomeric amide groups probably possess two kinds of hydration sites or layers. Hydrated water molecules belonging to the first hydration layer directly hydrated to amide groups, and those belonging to the second hydration layer hydrated to water molecules forming the first hydration layer.45 The hydration water molecules in the second hydration layers would be easily dehydrated above Tdh.45 The hydration/dehydration behavior observed in aqueous NMG19 and NEG17 systems as a function of temperature very slightly influenced the sizes of the polymeric chains in aqueous solution. Figure 6 demonstrates the temperature, T, dependence of the mean radius of gyration, Rg, for NEG18 obtained from SANS measurements in aqueous (D2O) solution via the simplest analysis method proposed by Guinier.46 The dependencies of the logarithmic values of the macroscopic crosssection (scattering intensity, I(Q)) on the square of the magnitude of a scattering vector, Q2, for the aqueous NEG18 solution, determined at several temperatures ranging from 10 to 70 °C, were analyzed as described in the Supporting Information. The incoherent scattering component (Iinc) was determined from the data fitting procedure using a flexible

the exchange process of water molecules hydrated to NEG19 molecules (j = 2), are not so much influenced by a difference in the monomeric species of the polymeric chain molecules. Because the concentration dependence of DR time τ1, assigned to the rotational relaxation time for the free water molecules, shown in Figures 3a and 4a, is negligibly weak, the addition of polypeptoids does not influence the mobility of free water molecules. Then, we might conclude that both the polypeptoid samples, NEG17 and NMG19, do not behave as strong water structure forming, water structure breaking, or hydrophobic water structure forming solutes.44 On the other hand, although the c dependencies of ε3 and ε4 for the aqueous NEG17 system were similar to those for the aqueous NMG19 system, the τ4 value was almost twice as long as that for the aqueous NMG19 system. Then, one might conclude that the mechanism for mode j = 4 is highly influenced by the differences in the chemical species of monomers. Hydration Number. The dependencies of ε1 and the partial molar volume per monomeric residue (Vm) on c allow us to determine the hydration number, nm, using eq 2 given below36−38 ε1 1 − 10−3Vmc = − 10−3VWcnm εW 1 + 10−3Vmc /2

(2)

where VW represents the partial molar volume of water molecules. The temperature, T, dependence of nm for aqueous NMG19 and NEG17 systems are shown in Figure 5a,b, respectively. Pronounced dehydration, which means a decrease in the nm value with increasing T, was clearly recognized in both the aqueous systems. However, the dehydration temperature, Tdh, defined as a middle point between the asymptotic hydration numbers at low, nmL, and high, nmH, temperatures, E

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chain molecules possess nonzero qi and qf values. However, in the case of monopolar chain molecules, qi or qf should be zero. When one compares the magnitude of ⟨(μ1bs)2⟩ at the mode of p = 1 (corresponding to the mode j = 4 in the experimental results) for a monopolar chain molecule (qi = 1 and qf = 0) to that of a dipolar (qi = qf = 1) chain molecule bearing the same parameters, N, ζ, and b, the predicted value for the monopolar chain molecule is one-fourth of that for the dipolar one. It is noteworthy that even in the case of monopolar polymeric chain molecules without well-defined usual dipole moments finite nonzero ⟨(μ1bs)2⟩ values are predicted by the modified bead− spring model.5,6 As discussed above, there exist many water molecules hydrated to the polymer chains of NMGn and NEGn, and they are quickly exchanged by free water molecules in aqueous solution. As the presence of hydrated water molecules is not taken into account in the modified bead−spring model,5,6 any effect influencing the polymer chain dynamics and dielectric behavior due to the presence of hydration water does not appear explicitly in eqs 3 and 4. Although the presence of solvent water molecules including hydrating ones would result in the reduction of dipole moments of solute polymers, we do not consider such an effect for simple discussion in this study. Because the magnitude of DR strength is proportional to the quantity c⟨(μ1bs)2⟩(kBT)−1, from an experimental point of view, the concentration-reduced magnitude, ε4c−1, for the slowest mode, j = 4, should be compared between the monopolar and dipolar polymeric chains that are made from the same monomeric species and possess identical DP values. However, as we do not have dipolar NMG19 and NEG17 samples at present, such a quantitative comparison should be performed in the near future using systematically synthesized samples. The ε4c−1 data for monopolar NMG19 and NEG17 might be roughly compared to that for PPG5, possessing a similar τ4 value to that of NMG19 and NEG17, which means the size of PPG5 in aqueous solution is not so different from that of the NMG19 and NEG17. The temperature dependencies of the ε3c−1T and ε4c−1T values of NMG19 and NEG17 are shown in Figure 7. The ε4c−1T

Figure 6. T dependence of the mean radius of gyration, Rg, for NEG18 in aqueous (D2O) solution, resulting from SANS experiments via the simplest analysis method proposed by Guinier.46 Large and small symbols represent the first and second runs, respectively.

cylinder chain model47 involving an incoherent background component as a fit parameter. After subtraction of the incoherent background, Iinc, the coherent scattering can be analyzed using the Guinier plot to obtain Rg. In the procedure, the 5th to 25th data points in a range of Q < 1.0 nm−1 were used to precisely determine the initial slope between ln{I(Q) − Iinc} and Q2. Limited by the current instrument ability, the statistical error of Rg, as shown in Figure 6, is relatively large compared with the variation in the Rg values. Although the determined Rg data were highly scattered, the fact that the values of Rg for NEG18 molecules slightly increased with increasing T, or at least did not decrease with increasing T, as observed in Figure 6, reveals that the dehydration behavior in monomeric residues does not reduce the whole chain sizes in aqueous systems of NEG18. This weak T dependence of molecular sizes, induced by the dehydration process found in NEG17, is clearly opposite to that observed in the aqueous PPG5 system,38 in which the mean molecular sizes of PPG5 clearly decrease with increasing T. Significant differences observed in the asymptotic hydration numbers, nmL and nmH, between PPG5 (nmL ∼ 9 and nmH ∼ 3)38 and NEG17 would be a reason for the opposite T dependences of the sizes of the polymer chains. Because the average monomeric residue of PPG5 holds twice as many hydrated water molecules as that by NEG17, the amount of dehydrated water molecules is also twice as many. Then, the dehydration process of PPG5 in aqueous solution possibly induces a notable shrinkage in size. Dynamics of Polymeric Chains. According to a modified bead−spring model proposed by Stockmayer et al.,5,6 the mean square of the dipole moment, ⟨(μpbs)2⟩ , and the relaxation time, τpbs, for normal mode number p are given by eqs 3 and 4 ⟨(μpbs )2 ⟩ =

2(N − 1)b2e 2(q i ± q f )2 π 2p2 + , odd; − , even

τpbs =

Figure 7. T dependencies of the ε3c−1T and ε4c−1T values of NMG19 and NEG17 in aqueous solution.

(3)

b2 ζ 12kBT sin 2

( 2πNp )

value of NMG19 and NEG17 seems to be 1300 M−1 K at T = 20 °C and is about one-tenth of the value for PPG5 at the same temperature. As this observation obviously disagrees with the prediction from eq 3, that is, one-fourth, it is likely that the modified bead−spring model does predict an incorrect dipole moment value in the case of monopolar polymeric chain molecules. As no theoretical model, including the modified

(4)

where N, ζ, b, e, qi, and qf represent the number of beads in a chain molecule, the friction coefficient of a bead, the length of a spring, the elementary electric charge, the Boltzmann constant, the degree of ionization of the initial bead, and the degree of ionization of the final bead, respectively. Dipolar polymeric F

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Figure 8. Dependence of relaxation times τ2 and τ3 on T−1 for the aqueous NMG19 (a) and NEG17 (b) systems.

molecules to the peptoid molecules.48 Plots of τ3 versus T −1 seen in Figure 8a,b do show greater slopes than those of modes j = 1. This observation suggests that the dynamics of modes j = 3 is not controlled by the activation energy of free water molecules of 19 kJ mol−1 but by other T-dependent parameters related to the dynamics of apparent dipole moments, such as the effective rotational potential energy of monomeric amide units round the polymer backbone. In the case of mode j = 4, the obtained apparent activation energy, E4*, seems to be incidentally identical to E1* = 19 kJ mol−1 and markedly smaller than E3* in both the NMG19 and NEG17 aqueous systems, as seen in Figure 8a,b. If mode j = 3 is the overtone of mode j = 4, controlled by the same dynamics, the activation energies for the modes should be identical. This is another reason why mode j = 3 is assigned to molecular motion of monomeric residues and not to the overtone of mode j = 4. It is possible that the hydration/dehydration behavior seen in Figure 5a,b governs the T dependencies of the τ3 and τ4 values. As described above, the addition of NaOH to the aqueous NEG17 solution to reduce the degree of protonation of the amine termini substantially increased the ε4 value. The magnitude of mode j = 4 approached a certain value after a sufficient amount of NaOH was added (Figure S1). Then, one might conclude that the degree of protonation of the amine termini markedly influences the value of the apparent dipole moments corresponding to mode j = 4. As the result of the polymerization process, amide groups, −N(−CH3)C(O)− and −N(−CH2CH3)C(O)−, bearing relatively large monomeric dipole moments, μm, are generated in each polymeric chain molecule. Because the direction of μm for an amide group is not (perfectly) perpendicular to the polymer chain backbone, as depicted in Scheme 1, finite dipole components, parallel and perpendicular to the polymer backbone, μm∥ and μm⊥, result from μm in each monomeric residue. Because the parallel component, μm∥, for each monomer orients along the polymer backbone, both NMG19 and NEG17 are classified as monopolar type A chain molecules. Then, the summation of μm∥ over all of the constituent monomeric residues would be the intrinsic dipole moment for each polymer chain, which results in dielectric mode j = 4. Consequently, it is possible that the characteristics of a type A chain are the essential reason for the fluctuating molecular motions of polymer chain termini dielectrically observed as mode j = 4. On the other hand, time-dependent fluctuations of μm⊥ that resulted from monomeric local molecular motion, the rotation around chemical bonds, should be the essential origin for mode j = 3

bead−spring model, is able to predict the DR behavior of monopolar polymeric chain molecules correctly at present, a new model that holds well for both monopolar and dipolar molecules should be proposed in the near future. A slight increase observed in the ε4c−1T values of NMG19 and NEG17 with increasing T suggests a limited increase in their sizes, corresponding to the behavior found in Figure 6, whereas the ε4c−1T value of PPG5 markedly decreases with increasing temperature.38 This T-dependent change in the ε4c−1T value, which is correlated with the T dependencies of the sizes of NMG19 and NEG17 in aqueous solution, strongly reveals that the mode j = 4 corresponds to the fluctuating molecular motions of the chain termini of the monopolar polypeptoids. On the other hand, it seems that the ε3c−1T value, which should be proportional to the magnitude of the related dipole moments of the mode j = 3, is independent of temperature for aqueous systems of both NMG19 and NEG17. The distinct difference in the T dependencies of ε3c−1T and ε4c−1T seen in Figure 7 strongly suggests that the origins of DR modes j = 3 and 4 are not identical to each other. The assignment for experimental mode j = 3 from the viewpoint of dynamical behavior is not simple. If one accepts eqs 3 and 4 and substitutes qi = 0 as the constraint condition, an overtone of a theoretical bead−spring model chain designated by mode number p = 2 would be observed as experimental mode j = 3. In this case, the observable relaxation strength of mode j = 3 would be one-fourth that of mode j = 4 and is substantially smaller than the observed ratio of ε3ε4−1 ∼ 0.6 for both the NMG19 and NEG17 aqueous systems, as seen in Figures 3b and 4b. From these considerations, it is not likely that mode j = 3 is attributed to the theoretical mode designated by mode number p = 2. The fact that the T dependence of ε3c−1T is obviously different from that of ε4c−1T reveals that experimental mode j = 3 is not identical to theoretical mode p = 2. Consequently, mode j = 3 is assigned to the fundamental local molecular motion of monomeric residues bearing finite dipole moments as the type B chain molecule. The temperature, T, dependence of each relaxation time, τj, for the aqueous NMG19 and NEG17 systems are shown in Figure 8a,b. The slopes of the lines drawn in these figures represent the apparent activation energies for each DR mode observed. The activation energy of mode j = 1 simply represents that of the rotational relaxation mode of free water molecules: E1* = 19 kJ mol−1. The evaluated activation energy for mode j = 2, E2* = 23 kJ mol−1, which is slightly higher than the value of E1*, suggests the contribution of additional activation energy related to the hydration energy of water G

DOI: 10.1021/acs.jpcb.6b05379 J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B as the type B chain. It is likely that the presence of a protonated amino terminus bearing a cationic electric charge effectively disturbs a (fundamental) dipole moment, μ m , of the neighboring residue, as represented in Scheme 1, due to the appearance of an additional terminus dipole moment, μterm. The alternation of the degree of protonation, controlled by the addition of NaOH, possibly influences the magnitude of the total dipole moment corresponding to the DR strength for modes j = 3 and 4. NMR techniques to determine the longitudinal relaxation time (T1) are quite powerful in evaluating the rotation correlation time, which is related to the DR time for the mentioned chemical groups.49,50 Then, it is interesting to compare the values of DR time, τ3, for mode j = 3, which has been assigned to the rotational mode of monomeric amide groups, and the rotational correlation times of carbon and/or nitrogen atoms belonging to the amide groups. Additionally, DR measurements should be carried out in an aqueous solution of polypeptoid samples bearing different DPs in the near future to reconfirm the origin of mode j = 4 to be the fluctuation of chain termini.

ACKNOWLEDGMENTS

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REFERENCES

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CONCLUSIONS Dielectric behavior was examined for aqueous solution of NMGn at the DP = 19 (NMG19) and NEGn at DP = 17 (NEG17) possessing no carboxy terminus, but only an amino one, which exists as a cationic charged terminus in the aqueous condition without any buffer chemicals. It was newly discovered that such electrically monopolar polymeric chain molecules, possessing finite monomeric dipolar components provided by amide groups aligned parallel to the polymer chain backbone, obviously exhibit pronounced DR behavior, evidently resulting from their fluctuating molecular motions in aqueous media as the longest relaxation mode. On the other hand, dipolar components aligned perpendicular to the polymer chain backbone provided by monomeric amide groups demonstrate a DR mode as the second slowest relaxation mode, which is caused by local rotational molecular motions of monomeric amide groups around the polymer chain backbone. The obtained dielectric behaviors of the aqueous NMG19 and NEG17 systems also permitted us to determine the temperature dependence of the hydration numbers per monomeric residue in aqueous solution. A hydration number of ca. 4.5 determined at 10 °C remarkably decreased to ca. 2 around 40 and 30 °C, respectively, for NMG19 and NEG17. This temperaturedependent hydration/dehydration behavior slightly influences the sizes and molecular dynamics of the polymeric chain molecules in aqueous solution. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b05379. Effects of NaOH addition on the dielectric behavior and temperature dependence of SANS data (PDF)

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This work was partially supported by JSPS KAKENHI Grantin-Aid for Scientific Research (B) Number 26288055. The SANS studies are supported by the U.S. Department of Energy under EPSCoR Grant DESC0012432, with additional support from the Louisiana Board of Regents. The Research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: +81-42-367-5730. Notes

The authors declare no competing financial interest. H

DOI: 10.1021/acs.jpcb.6b05379 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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