Introduction

Cellulose derivatives are biobased polymers in which some or all the hydroxyl groups are replaced with other functional groups; thus, their solubility in solvents and thermal properties can be controlled to suit various applications [1]. Modification of the hydroxyl groups can yield cellulose ethers or esters, depending on the substituent [1]. Ethylcellulose (denoted ECx, where x is the degree of substitution based on the number of hydroxyl groups in a repeating unit and varies from 0 to 3) is a cellulose ether (Fig. 1) prepared by substituting ethoxy groups at the hydroxyl positions. For x = 0.8–1.7, EC is soluble in water, whereas for x > 1.7, it dissolves only in organic solvents [1].

Fig. 1
figure 1

Chemical structure of ECx (x = 3.0 and 2.5)

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ECx has broad applications, for example, in cosmetics and as adhesives, binders, coating agents, thickeners, film-forming agents, plasticizers, and excipients [1]. Furthermore, owing to its solubility in organic solvents, it is used in pharmaceuticals, inks, paints, adhesives, plastics, textile finishing agents, and electronic materials [1]. Most commercial ECs have x = 2.5 and thus dissolve in various organic solvents. EC2.5 is frequently used as a rheology control agent and binder for inorganic particle dispersions [2,3,4,5,6,7,8,9,10,11,12]; a primary application is the preparation of nickel paste for multilayer ceramic capacitors (MLCCs), which are essential electronic components in modern society. The main component consists of submicron-sized nickel particles (50 wt%) and barium titanate particles (5–15 wt%), the latter serving as a sintering inhibitor. The paste also contains binder resins, EC2.5, solvents such as α-terpineol and dihydroterpineol, and additives, including dispersants and plasticizers [4, 11]. Recently, demand has increased for smaller nickel particles, which enhance performance (e.g., increased capacitance) and enable the miniaturization of MLCCs. However, as the particle size decreases, the rheological properties of the paste change significantly [11]. Furthermore, the effects of each component, as well as the mechanisms underlying these effects, remain unclear, making it challenging to design a nickel paste that meets all the requirements.

A key material governing the rheological properties of the nickel paste is EC2.5. It has been reported that a transient network structure forms in the paste through the cross-linking (bridging) of particles by EC2.5 molecules [2, 3]. However, the mechanism by which EC2.5 and the particles interact to form a network structure remains unclear. EC2.5 has also been reported to aggregate in solvents such as α-terpineol and other organic solvents [13], suggesting that this may be the mechanism underlying network formation (note that the network is also loosened by shearing). Given that the internal structure of nickel paste is poorly understood, nickel-paste-based products are developed through trial and error. Therefore, understanding the conformational properties of isolated EC2.5 chains in solvents and determining the molecular parameters characteristic of EC2.5 would aid in elucidating its effects on rheological properties, including the state of nickel paste under shear and aggregate dissociation, and contribute to the design of next-generation nickel pastes.

To date, there have been few reports on the molecular characterization of isolated EC2.5 chains in solution. For example, Moore and Brown [14] and Scherer et al.[15] reported the dilute solution properties of EC2.5 with molar masses ranging from 1 × 104 to 2 × 105 g mol–1, as determined by viscosity measurements in ethyl acetate and chloroform. Meyerhoff and Sütterlin [16] also reported the dilute solution properties of EC2.7 with molar masses ranging from 1 × 104 to 1.4 × 105 g mol–1, as determined by light-scattering measurements in ethyl acetate. Furthermore, Hua et al.[13] demonstrated that EC2.5 molecules aggregate in dilute organic solvents, yielding nearly monodisperse 200–300-nm-sized colloidal particles without isolated chains. However, because significant heterogeneity in molar mass (Mw/Mn > 2.3, where Mw and Mn are the weight- and number-averaged molar masses, respectively) and x in the samples was not fully considered, the molecular characterization of isolated EC2.5 chains in solution remains incomplete. Furthermore, the effect of x on the molecular conformation of the EC chain remains poorly understood.

In this study, we focused on fully substituted EC (EC3.0) with a uniform degree of substitution to eliminate ambiguity and determined its conformational properties in tetrahydrofuran (THF) at 25 °C. The EC3.0 sample was prepared by reacting commercially available EC2.5 with ethyl iodide at 55 °C in the presence of sodium hydride. The synthesized EC3.0 sample was further fractionated by recycling preparative size exclusion chromatography (SEC) into 11 components with narrow molar mass distributions (Mw/Mn < 1.22) and a molar mass range of 7.05 × 103 to 1.87 × 105 g mol–1. These samples were analyzed by SEC fitted with a multiangle light scattering (MALS) detector and a viscosity (Vis) detector in THF at 25 °C. Additionally, small-angle X-ray scattering (SAXS) measurements were conducted on the lower-molar-mass sample. The z-averaged root-mean-squared radius of gyration (< S2 > z1/2) and intrinsic viscosity ([η]) of EC3.0 were measured and rationalized as functions of Mw. Furthermore, the experimental data were analyzed using cylindrical wormlike chain and wormlike touched-bead models to determine the molecular parameters characteristic of the EC3.0 chain. In addition, similar fractionation, measurements, and analyses were performed on EC2.5, and the molecular conformational properties of an isolated EC2.5 chain in THF were clarified by comparison with those of EC3.0.

Experimental section

Materials

Three EC2.5 samples (STD-4, 45, and 300) were purchased from Dow Chemical Co., USA, and used after they were vacuum dried at 60 °C for more than 24 h. THF (> 99.5%) was used as the solvent and was purchased from Kanto Kagaku Co., Ltd., Tokyo, Japan, and distilled over sodium. Ethyl iodide and chloroform-d (99.8%) were purchased from Kanto Kagaku Co., Ltd., Tokyo, Japan, and used without further purification. Chloroform (99.0%, Junsei Chemical Co., Ltd., Tokyo, Japan) was used as received. Spectroscopic-grade THF, which was used for SAXS, differential refractive index increment, and partial specific volume measurements, was purchased from Kanto Kagaku Co., Ltd., Tokyo, Japan, and used as received.

The ethylation of EC2.5 (STD-4, 45, and 300) was performed according to the method reported by Budgell [17]. Briefly, the reaction was carried out in THF at 55 °C for 5 h, using eight equivalents of ethyl iodide relative to the remaining hydroxyl groups, in the presence of sodium hydride under a nitrogen atmosphere. The reaction mixture was reprecipitated in deionized water, centrifuged, and vacuum-dried. The dried sample was redissolved in THF, reprecipitated, centrifuged, vacuum-dried, and subsequently redissolved as described above. This process was repeated five times for purification. In the first and second precipitation steps, sodium thiosulfate was added to deionized water at a 2:1000 weight ratio to prevent the formation of free iodine. By modifying EC2.5, fully ethylated EC3.0 samples were prepared with 0.13 × 104 g mol–1 < Mn < 5.3 × 104 g mol–1 relative to a polystyrene (PS) SEC calibration. These samples were further fractionated using recycling preparative SEC (NEXT, Japan Analytical Industry (JAI) Co., Ltd., Japan) at 22–26 °C. The experimental conditions were as follows: chloroform eluent, 7–14 cm3 min–1 flow rate, 3H-40 and 4H-40 (JAI Co., Ltd., Japan) columns, 5–10 cm3 injection volume, and 1–5 wt% concentration. Finally, eleven EC3.0 samples with Mw/Mn < 1.22 and Mw values ranging from 7.05 × 103 to 1.87 × 105 g mol–1 were prepared (Table 1). The fractionation of unmodified EC2.5 (STD-4, 45, and 300) was also conducted in the same manner, and eight EC2.5 samples with Mw/Mn < 1.19 and Mw values ranging from 6.32 × 103 to 2.50 × 105 g mol–1 were collected (Table 2).

Table 1 Molecular characteristics of EC3.0 in THF at 25 °C, determined by SEC‒MALS‒Vis measurements
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Table 2 Molecular characteristics of EC2.5 in THF at 25 °C, determined by SEC-MALS-Vis measurements
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Measurements

1H NMR measurements were carried out in chloroform-d using a JEOL JNM-ECX 400 MHz apparatus; the degree of substitution (x) was estimated as x = 3(7b/(9a–6b)), in which b is the integrated intensity of the signal from CH3 in the ethyl groups and a is that from CH and CH2 in the glucose unit and ethyl group (Fig. S1). The partial specific volume (vsp) of the EC3.0-6 and EC2.5-4 samples in THF was measured at 25 °C using a DMA 4500 M densimeter (Anton Paar GmbH, Austria) as the EC mass concentration C (g cm-3) was varied from 4.0 to 10.0 mg cm−3. The differential refractive index increments (dn/dc) for EC3.0-6 and EC2.5-3 were determined in THF at 25 °C using a differential refractometer (Otsuka Electronics DRM-1021, wavelength λ = 632.8 nm) as C was varied from 2.5 to 6.0 mg cm–3.

The Mw, <S2 > z1/2, and [η] for a series of EC3.0 and EC2.5 samples were measured by SEC fitted with a MALS detector (Wyatt Technology Corporation DAWN HELEOS, λ = 658 nm), a refractive index detector (RI: Wyatt Technology Corporation Optilab T-rEX, λ = 658 nm), and a viscometer (Vis; Viscotek Technology Co. T-60A Dual Detector) at 25 °C. The SEC measurements were carried out at a column temperature of 25 °C using THF as the eluent at a flow rate of 1.0 cm3 min−1, with a DG-2080-53 degasser (Jasco Corp.), a 1100 Series isocratic pump (Agilent Corp.), a CO-2060 Plus column oven (Jasco Corp.), and three Tosoh TSKgel GMHHR-H (S) columns.

Notably, EC2.5 aggregates in most organic solvents [13], thereby making studies of isolated chains extremely difficult. Through trial and error, we discovered that isolated EC2.5 chains can be studied using the following solution preparation method. All sample solutions for vsp, dn/dc, SAXS, and SEC-MALS-Vis measurements were prepared by dissolving EC3.0 and EC2.5 in THF at 50 °C, and the temperature was maintained at 50 °C until immediately before measurement. The calibration of the MALS and Vis devices and the MALS analysis were performed according to previously reported methods [18, 19].

With respect to the SEC-MALS measurements, SEC column cleaning is crucial. Many commercially available columns contain impurities within their micro- and nanopores, resulting in a low signal-to-noise ratio in light-scattering intensities, even when the RI and MALS signals are stable enough for the measurements. Thus, thorough column cleaning is required to achieve accurate determinations of the molar mass and radius of gyration, particularly for polymers with low Mw and dn/dc values [20]. Furthermore, the delay volume between the RI and MALS detectors can be determined accurately using the new method we have developed [20]. By considering these points, it is possible to reliably evaluate the molar mass and molar mass distribution using SEC-MALS.

SAXS measurements were performed in THF at 25 °C on a NANO-Viewer (Rigaku Co.) with a Pilatus 100 K detector (DECTRIS Co.), an X-ray wavelength (λ) of 0.15418 nm, and a camera length of 630 mm [19]. The scattering vector (q) is defined as q = 4πsinθ/λ at the scattering angle (2θ). The excess scattering intensity [ΔI(q)] was obtained from the scattering intensity difference corrected by the X-ray transmittance for the solution and solvent at the same q. SAXS measurements were carried out at four different concentrations, and [C/ΔI(q)]1/2 was plotted against C, yielding \({\left[C/\Delta I\left(q\right)\right]}_{C\to 0}^{1/2}\) at infinite dilution by extrapolating the data points at each q to zero concentration using least squares [21]. Notably, when EC2.5 was dissolved in THF at room temperature, significant scattering was observed in the low-q region, which was attributed to aggregate formation. However, after dissolving EC2.5 in THF at 50 °C and maintaining it at that temperature until immediately before measurement, this aggregate scattering completely disappeared within at least 1.5 h, and normal scattering profiles from isolated EC2.5 chains were obtained.

Results and discussion

Fully ethylated EC3.0 with x = 3.0 was prepared, as confirmed by 1H-NMR measurements (Fig. S1). Figure 2 shows the SEC traces (THF as the eluent) of the eleven EC3.0 and eight EC2.5 samples fractioned by recycling preparative SEC using CHCl3 as the eluent. The Mw, <S2 > z1/2, and [η], determined from the SEC-MALS-Vis measurements, are also plotted against the retention volume (RV). The Mw, <S2 > z1/2, and [η] reasonably decrease as the RV increases, indicating that the SEC separation conditions are appropriate for EC3.0 and EC2.5. Crucially, our solution preparation method enables measurements of isolated EC2.5 chains. The Mw and Mw/Mn values for EC3.0 and EC2.5, averaged over the entire eluted substance, were estimated from the absolute calibration curves constructed with EC3.0 and EC2.5 as standards, along with ethylbenzene (not shown). These values are listed in Tables 1 and 2, along with those obtained from the conventional calibration curve using PS standards, for comparison. The apparent Mw values from the PS calibration curve are approximately two- to threefold greater because of the differences in the molecular structure of the repeating unit and the conformation between PS and EC. The Mw/Mn values determined from the PS calibration are also higher than those from the absolute calibration, implying that the EC3.0 and EC2.5 chains are considerably stiffer than the flexible PS chains. The Mw and Mw/Mn values determined by SEC-MALS are also listed in Tables 1 and 2, and the Mw values are very close to those determined by absolute calibration within experimental error. In contrast, the Mw/Mn values obtained by SEC-MALS are significantly lower than those obtained by absolute calibration, likely because of band broadening in the latter method [20]. Considering that SEC-MALS measurements for polymers with narrow molar mass distributions may contain errors in the high-RV region of the chromatogram, resulting in an underestimation of Mw/Mn [20], the actual Mw/Mn value may lie between the two values. Since the Mw, <S2 > z1/2, and [η] values at the peak top of the RI signal (RVp) in the SEC-MALS-Vis chromatogram are most reliable, they were used to study the following dimensional properties (Tables 1 and 2). For the high-molar-mass samples EC3.0-11, EC2.5-7, and EC2.5-8, the highly reliable values for components eluted before RVp were also used. When using <S2 > z1/2 obtained from SAXS measurements, the Mw value derived from the absolute calibration curve was employed.

Fig. 2
figure 2

SEC chromatograms of the a EC3.0 (left) and b EC2.5 (right) samples used in this study; the Mw, <S2 > z, and [η] determined by SEC-MALS-Vis are also shown

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First, the partial specific volume (vsp), which may be related to the conformational properties, state (aggregated or not), and polymer–solvent interactions, is described. Figure 3(a) shows the plots of (ρs – ρ0) versus C for EC3.0-6 and EC2.5-4 in THF at 25 °C. Here, vsp was determined using Eq. 1.

$${\rho }_{s}={\rho }_{0}+(1-{v}_{sp}{\rho }_{0})C$$
(1)

Here, ρ0 and ρs are the densities of the solvent and solution, respectively. The vsp values determined from the slope and ρ0 are listed in Table 3. Almost identical values of 0.787 and 0.809 cm3 g−1 for EC3.0 and EC2.5, respectively, are obtained; these values are smaller than that (0.905 cm3 g−1) of flexible PS in THF [22] and that (0.95 cm3 g−1) of semiflexible poly(n-hexyl isocyanate) in hexane [23] and slightly larger than that (0.714–0.724 cm3 g−1) of amylose tris(phenylcarbamate) in 1,4-dioxane at 25 °C [24]. Measurements were also performed on the THF solution of EC2.5 prepared at 25 °C, as indicated by the blue circles in Fig. 3(a). A significantly larger value (0.854 cm3 g−1) than that for the EC2.5 solution prepared at 50 °C is obtained, although it is very close to the range (≈0.84–0.90 cm3 g−1) reported at 25 °C in various solvents [16]. The difference in vsp arises from differences in sample preparation methods, although both solutions are transparent and homogeneous. It is possible that EC2.5 is aggregated at 25 °C, yielding a colloidal dispersion [13]. This aggregate cannot be unraveled in THF at 25 °C. Assuming that the aggregates are rigid bodies and impermeable to the solvent, vsp may be equal to the reciprocal of the solute density. As the density of solid EC2.5 is 1.14 cm3 g−1 at 25 °C, vsp is calculated to be 0.877 cm3 g−1, which is close to the observed and literature values. Therefore, EC3.0 molecularly dissolves in THF, regardless of the sample preparation temperature, but EC2.5 forms colloidal aggregated particles in THF at 25 °C. Crucially, the EC2.5 aggregates in THF dissociate upon heating to 50 °C, enabling the study of the dilute-solution properties of isolated EC2.5 chains. Figure 3(b) shows the excess refractive index Δn plotted against C. The dn/dc values were determined from the slopes (Table 3). Slight differences in dn/dc can be interpreted as resulting from differences in the chemical composition with respect to x.

Fig. 3
figure 3

a Plots of [ρ – ρ0] versus C for EC3.0-6 and EC2.5-4 in THF at 25 °C. Data (blue circles) for the EC2.5−4 solution prepared at 25 °C are also shown. b Plots of Δn vs. C for EC3.0-6 and EC2.5−4 in THF at 25 °C

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Table 3 dn/dc, vsp, and the cylindrical wormlike chain and wormlike touched-bead model parameters characteristic of isolated EC3.0 and EC2.5 chains in THF at 25 °C
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The root plots of \({\left[C/\Delta I\left(q\right)\right]}_{C\to 0}^{1/2}\) versus q2 obtained from SAXS measurements for the EC3.0-1, EC3.0-2, EC2.5-1, and EC2.5-2 samples with low Mw in THF at 25 °C are shown in Fig. 4. Normal root plots without any increase in the scattering intensities in the low-q region are observed, indicating the absence of EC2.5 aggregates in THF. The experimental profiles show some variation because of the small difference in electron density, but the <S2 > z1/2 value can be determined from the initial slope and intercept of the straight line (solid red lines in Fig. 4) with sufficiently high reliability using Eq. 2, and the results are listed in Table 1 and 2.

$${\left(\frac{C}{\Delta I(q)}\right)}_{C\to 0}^{1/2}={\left(\frac{C}{\Delta I(0)}\right)}_{C\to 0}^{1/2}+\frac{1}{6}{\left(\frac{C}{\Delta I(0)}\right)}_{C\to 0}^{1/2}{\langle {S}^{2}\rangle }_{z}{q}^{2} + \cdots \cdots$$
(2)
Fig. 4
figure 4

Root plots of \({\left[C/\triangle I(q)\right]}_{C\to 0}^{1/2}\) vs. q2 for the EC3.0 and EC2.5 samples in THF at 25 °C. The vertical axis is plotted by adding a factor, α, for clarity. The solid lines show the initial slope within the Guinier region

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Figure 5(a) shows a double logarithmic plot of <S2 > z1/2 versus Mw for EC3.0 and EC2.5, as obtained by SAXS and SEC-MALS measurements. Figure 5(b) shows the results plotted against the degree of polymerization, Nw, as the molar mass of the repeating unit changes between EC3.0 and EC2.5. These figures indicate that both EC3.0 and EC2.5 exhibit the typical Mw- and Nw-dependent behavioral characteristics of semiflexible linear polymers, where in the low-Mw region, the slope is greater than 0.6 but decreases with increasing Mw. The relationships between <S2 > z1/2 and Mw for EC3.0 and EC2.5 isolated chains in THF at 25 °C are given in Eq. 3.

$${{{{\rm{EC}}}}}_{3.0}: < {S}^{2}{{ > }_{z}}^{\frac{1}{2}}\left({{{\rm{nm}}}}\right) = 3.6\times {10}^{-3}{{M}_{w}}^{0.79} [7.05 \times {10}^{3} < {M}_{w} < 2.47 \times {10}^{4}] < {S}^{2}{{ > }_{z}}^{1/2}({{{\rm{nm}}}}) = 2.6\times {10}^{-2}{{M}_{w}}^{0.60}[3.05 \times {10}^{4} < {M}_{w} < 2.68\times {10}^{5}] \\ {{{{\rm{EC}}}}}_{2.5}: < {S}^{2}{{ > }_{z}}^{1/2}({{{\rm{nm}}}}) = 3.1\times {10}^{-3}{{M}_{w}}^{0.80}[9.94 \times {10}^{3} < {M}_{w} < 1.83\times {10}^{4}] < {S}^{2}{{ > }_{z}}^{1/2}({{{\rm{nm}}}}) = 3.6\times {10}^{-2}{{M}_{w}}^{0.56} [5.29 \times {10}^{4} < {M}_{w} < 3.83\times {10}^{5}]$$
(3)
Fig. 5
figure 5

a Mw dependence of <S2 > z1/2 for EC3.0 and EC2.5 in THF at 25 °C and b their Nw dependencies. The solid lines represent the theoretical curves for the perturbed cylindrical wormlike chain model using the parameters in Table 3

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The <S2 > z1/2 value of EC2.5 is always smaller than that of EC3.0, with the corresponding Nw, implying that the chains may be markedly different. In addition, the difference in slope in the high-Mw region suggests that THF is a good solvent for EC3.0 but not a very good solvent for EC2.5. Considering that EC2.5 aggregates in THF at 25 °C [13] and that the slope appears to decrease further with increasing Mw, THF might be close to the θ-solvent. Notably, for EC2.5, compositional heterogeneity persists (x ranges from 2.43 to 2.62 in Table 2); thus, the results are subject to some uncertainty. However, a comparison with the EC3.0 results and the slight difference in the dn/dc values between them allows the study of the molecular chain conformation of EC2.5 with considerable confidence.

The molecular parameters characterizing isolated EC3.0 and EC2.5 chains were evaluated by comparing the experimental data with those obtained using the cylindrical wormlike chain model. The <S2> for an unperturbed wormlike cylinder may be expressed as the sum of the mean-square cross-sectional radius of gyration, <Sc2 > , and the radius of gyration of the main chain contour, <SM2 > [25]. The value of <Sc2> was first estimated by comparing the experimental and theoretical scattering form factors, P(q). When the Kuhn segment number (nK = λL) is close to 1, the polymer chain is considered a cylinder with contour length L and diameter d, where λ−1 is the stiffness parameter, which will be determined later. P(q) for the cylinder is given by Eq. 4 [19].

$$P(q)=2\int _{0}^{\pi }{\left\{{j}_{0}\left[\left(\frac{qL}{2}\right)cos\theta \right]\right\}}^{2}{\left\{\frac{{J}_{1}\left[\left(\frac{qd}{2}\right)cos\theta \right]}{\left(\frac{qd}{2}\right)cos\theta }\right\}}^{2}sin\theta {{{\rm{d}}}}\theta$$
(4)

Here, j0(x) and J1(x) are the 0th-order spherical and 1st-order Bessel functions, respectively. Figure 6 compares the experimental and theoretical P(q) in a Kratky plot.

Fig. 6
figure 6

Kratky plot for EC3.0-1 (black circles) and EC2.5-1 (red circles) in THF at 25  °C. The black and red curves are the theoretical values calculated from the cylinder model with d = 0.60 nm and the indicated L values

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The experimental P(q) for EC3.0 and EC2.5 was quantitatively described using a cylinder with d = 0.60 nm, yielding an <Sc2 > 1/2 value of 0.21 nm, assuming the relationship <Sc2 > = (1/8)d2. The contribution of <Sc2> to the observed <S2 > z in Tables 1 and 2 is less than 0.1% but was nevertheless considered in the subsequent analysis.

The radius of gyration of the main chain, <SM2 > = < S2 > z-<Sc2 > , is expressed by the Kratky–Porod (KP) chain (< S2 > KP) with L and λ–1, as given by Eq. 5 [26].

$${\langle {S}^{2}\rangle }_{{{\rm{KP}}}}=\frac{L}{6\lambda }-\frac{1}{4{\lambda }^{2}}+\frac{1}{4{\lambda }^{3}L}-\frac{1}{8{\lambda }^{4}{L}^{2}} \left[1-\exp(-2\lambda L)\right]$$
(5)

L is related to the molecular structure of the polymer according to Eq. 6.

$$L=\frac{M}{{M}_{L}}$$
(6)

Here, M is the molar mass of the polymer, and ML is the molar mass per unit contour length. Equation 5 can be approximated as Eq. 7 [27].

$${\left(\frac{M}{\langle {S}_{M}^{2}\rangle }\right)}^{1/2}={(6\lambda {M}_{L})}^{1/2}\left[1+\frac{3{M}_{L}}{4\lambda }\frac{1}{M}\right]$$
(7)

Here, the maximum error from the exact value is 1.5% for nK > 2. The plots of (Mw/<SM2 > )1/2 against Mw–1 for EC3.0 and EC2.5 are shown in Fig. 7. As indicated, the linear relationship holds in the region 13 > nK > 2. Two molecular parameters characterizing the isolated EC chains, λ–1 and ML, can be estimated from the intercept and slope of the straight line: 23.1 nm and 491 g mol−1 nm−1 for EC3.0 and 16.5 nm and 467 g mol−1 nm−1 for EC2.5, respectively (Table 3).

Fig. 7
figure 7

Plots of [Mw/<SM2 > ]1/2 vs. Mw−1 for EC3.0 (black circles)) and EC2.5 (red circles). The solid lines represent linear regions

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In the high-Mw region shown in Fig. 7, a downward deviation of the experimental values from the straight line is observed. The deviation is due to excluded-volume effects, which were accounted for using the radius expansion factor (αS) based on the quasi-two-parameter (QTP) theory [28,29,30,31], as given by Eqs. S1–S4 in the SI. The solid lines in Fig. 5(a), (b) show the theoretical curves calculated from the perturbed cylindrical wormlike chain model using the parameters listed in Table 3, where B is the excluded-volume strength and is estimated to be 2.3 nm for EC3.0 and 0.83 nm for EC2.5 in THF at 25 °C. The significant change in the B value with increasing x is likely due to the polar hydroxyl groups present in EC2.5, which substantially increase the intra- and intermolecular attractive interactions between the segments in THF. As shown in Fig. 5, the wormlike chain model quantitatively describes the experimental Mw dependence of <S2 > z1/2 for EC3.0 and EC2.5 over the entire Mw range.

The double logarithmic plots of [η] with respect to Mw (a) and Nw (b) for EC3.0 and EC2.5 in THF at 25 °C are shown in Fig. 8. The Mw dependence of [η] for EC3.0 and EC2.5 shows typical semiflexible polymer behavior, with a power law exponent greater than 0.8. In addition, the [η] value for EC3.0 is always greater than that for EC2.5 at the same Nw, as in the Nw dependence of <S2 > z1/2. The Mark–Houwink–Sakurada equations are given in Eq. 8.

$$E{C}_{3.0}: \quad [\eta ](c{m}^{3}/g) = 1.7 \times {10}^{-3}{{M}_{w}}^{1.08} \, [8.00 \times {10}^{3} < {M}_{w} < 3.05 \times {10}^{4}] [\eta ](c{m}^{3}/g)= 9.6 \times {10}^{-3}{{M}_{w}}^{0.92} \, [5.45 \times {10}^{4} < {M}_{w} < 2.68 \times {10}^{5}] \\ E{C}_{2.5}: \quad [\eta ](c{m}^{3}/g) = 9.5 \times {10}^{-4}{{M}_{w}}^{1.11} \, [6.34 \times {10}^{3} < {M}_{w} < 1.83 \times {10}^{4}] [\eta ](c{m}^{3}/g)=1.5 \times {10}^{-2}{{M}_{w}}^{0.85} \, [5.29 \times {10}^{4} < {M}_{w} < 3.83\times {10}^{5}]$$
(8)
Fig. 8
figure 8

a Mw dependence of [η] for EC3.0 (black circles) and EC2.5 (red circles) in THF at 25 °C and b their Nw dependencies. The solid lines represent the theoretical curves for the perturbed KP touched-bead chain model with the parameters listed in Table 3

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The Mw dependencies of [η] can be analyzed using the wormlike touched-bead model [32,33,34], as described in the SI. The solid lines in Fig. 8(a), (b) are the theoretical values calculated from the perturbed touched-bead model (Eqs. S5–S11) using molecular parameters determined from the Mw dependence of <S2 > z1/2 and the bead diameters (dB = 1.8 nm for EC3.0 and 1.1 nm for EC2.5) as an additional parameter. The theory consistently reproduces the experimental [η] across the examined Mw range. The estimated dB values are much larger than those obtained from SAXS (d = 0.6 nm), likely because SAXS ultimately measures the electron density difference between the polymer chain swollen by solvent and the surrounding solvent, thereby underestimating it. Furthermore, the dB value for EC2.5 is 1.6 times smaller than that for EC3.0, indicating that EC2.5 behaves as a hydrodynamically thinner polymer than EC3.0 in THF at 25 °C, most likely because of desolvation around the remaining polar hydroxyl groups.

Next, the local conformation is described. The monomer contour length (lM), which is related to the helical pitch and local conformation, is given by Eq. 9.

$${l}_{{{{\rm{M}}}}}=\frac{{M}_{0}}{{M}_{{{{\rm{L}}}}}}$$
(9)

Here, M0 is the molar mass of the repeating unit, as listed in Table 3. The lM value was estimated to be 0.50 ± 0.03 nm for both EC3.0 and EC2.5, suggesting that the local conformation of the EC chain remains largely unaffected by x from 2.5 to 3.0. The lM value obtained is almost equal to that (0.51–0.52 nm) of crystalline cellulose [35] and that (0.45–0.51 nm) of cellulose tris(alkyl carbamate) in THF [36] but considerably greater than that (0.13–0.19 nm) of cellulose in 1-butyl-3-methylimidazolium chloride ionic liquid [37] and that (0.33 nm) of α-1,4-linked amylose derivative [38], which assumes a gradual helical structure in solution.

Finally, the λ−1 value is discussed. The value increased from 16.5 to 23.1 nm as x increased from 2.5 to 3.0, likely due to increased steric hindrance from the greater number of ethyl groups. The λ−1 value for EC3.0 obtained in this study is comparable to those of cellulose tris(phenylcarbamate) in THF (21 nm) [38] and 1-methyl-2-pyrrolidone (16 nm) [39], cellulose myristate (21 nm) [40], (cyanoethyl)(hydroxypropyl)cellulose (29 nm) [41], cellulose tris(ethylcarbamate) (17 nm) in THF [36], cellulose tris(n-butylcarbamate) (25 nm) in THF [36], and cellulose tris(n-octadecylcarbamate) (24 nm) in THF [36] but much greater than those of methylcellulose (11.6 nm) in water [42] and cellulose acetate (10 nm) in THF [43]. Compared with methylcellulose and cellulose acetate, which have substituents of similar size, EC3.0 has considerably greater chain rigidity.

Conclusions

Molecular characterization of isolated ethylcellulose chains (EC3.0 and EC2.5) has been reported. The dimensional properties of ethylcellulose with a weight-averaged molar mass (Mw) ranging from 6.32 × 103 to 3.83 × 105 g mol−1 and a relatively narrow molar mass distribution (Mw/Mn < 1.22) were studied in THF at 25 °C using static light and small-angle X-ray scattering and the intrinsic viscosity. The z-averaged root-mean-squared radius of gyration and intrinsic viscosity for the isolated EC3.0 and EC2.5 chains were rationalized as functions of Mw, and their Mw dependencies were analyzed in terms of cylindrical wormlike chain and wormlike touched-bead models. The chain stiffness parameter (the Kuhn segment length, λ−1), molar mass per unit contour length (ML), and hydrodynamic bead diameter (dB) were 23.1 nm, 491 g mol−1 nm−1, and 1.8 nm for EC3.0 and 16.5 nm, 467 g mol−1 nm−1, and 1.1 nm for EC2.5, respectively. Thus, EC3.0 and EC2.5 in THF at 25 °C behave as semiflexible chains with considerable stiffness. The monomer counter length (lM) was estimated to be 0.50 nm for both EC3.0 and EC2.5, suggesting that the local conformation of the EC chain remains largely unaffected by x. The lM value was almost equal to that of crystalline cellulose (0.51–0.52 nm) but considerably greater than that of α-1,4-linked amylose derivatives (0.33 nm). In contrast, the λ−1 and dB values were significantly influenced by x, most likely due to increased steric hindrance along the cellulose backbone and the desolvation of residual polar hydroxyl groups.