Molecular-scale descriptions and experimental characterizations of nitrocellulose soaked in pure liquid ethanol or diethyl ether respectively at room temperature

First-principle calculations in this study refer to the Quantum Mechanism-based Density Functional Theory (DFT) method. It was said that the DFT method has already been an influential researching approach for microstructure and phase interfaces [26]. Meanwhile, the catalytic properties of new matters could be predicted, as well [27]. Thanks to the developer team of CASTEP [28], our DFT calculations were performed by their package. In its computing code, the plane-wave pseudopotential method is applied to process Kohn–Sham equations with one-electron, and ab initio pseudopotentials define the electron-ion potential while under calculations [29]. Both norm-conserving and ultrasoft formulations are alternative in CASTEP [29]. As the pre-work for MD simulations, first-principle calculations in this study focused on the minimization of total energy, so that the bonding and atomic information of each model could be summarized. We drew the initial chemical structure of NC, ethanol and diethyl ether according to their molecular formula. Molecular formulas of ethanol (C₂H₅OH) and diethyl ether (C₄H₁₀O) have been well recognised, so we won't cover this again. Take the only macromolecule, NC, as an example. The polymerisation degree of NC chain was designed to be 8, and the degree of its substitution was 2. Therefore, there were 48 carbon (C) atoms, 66 hydrogen (H) atoms, 16 N atoms and 73 oxygen (O) atoms in this NC chain. Those three organic models were optimized under Generalized Gradient Approximations (GGA)-Perdew–Burke–Ernzerhof (PBE) style exchange-correlation effects. The cut-off energy of the plane wave basis was set as 350 eV [30], and the size of the standard grid was about 2.8. Next, a Monkhorst-Pack mesh of 4 × 4 × 4 k-points was applied for this DFT study. As for the convergence tolerance for geometry optimization, the acceptable ionic force ought to be less than 0.03 eV Å⁻¹, while the standard for total energy was 0.2E-4 eV/atom. Finally, all models were placed at the centre of a 40 × 40 × 40 ų cubic cell.

If we need to take further requirements, like complexity and trajectory, into account, first-principle calculations would be incapable in this situation. Therefore, we performed Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [31] based MD simulations to study the large organic mixture system. There were three molecular models with four types of elements in this study. To deal with the potential break or formation of chemical bonds, we selected the ReaxFF force field to describe atomic interactions. ReaxFF potential was first induced by professor Adri van Duin [32] to enable reactions in MD simulations, while in this study, the specified ReaxFF potential file was a combined potential, as those parameters were provided by two references. Firstly, parameters for C, H and O elements were reported by K Chenoweth et al [33]. Secondly, N and boron atoms were studied by M R Weismiller et al [34]. Both of those original potential files were developed according to quantum mechanical results. Based on those implementation data, the bond-order functions were solved to judge bonding effects and energies.

The computational model for MD simulations was initially provided by DFT calculations. Those stabilized organic molecules were packed into a specific area by PACKMOL [35] program. Due to the consideration of computing cost, we designed a medium-sized computational box about 40 × 40 × 40 ų. At the same time, periodical boundaries were set on three dimensions. The box was vertically divided into two equal regions. The lower region was for 5 NC chains, while the other one was for the ethanol or diethyl ether system. According to their real densities, the total amount of diethyl ether molecules was 185, and the amount of ethanol was about 330. Because this is a comparative study, diethyl ether and ethanol systems were placed in two individual computational models. In the following sections, all snapshots of computational models were rendered by OVITO and VESTA programs [35, 36].

As the electronegativity equalisation method is implemented in ReaxFF potential to process charge distribution [37], the atomic style of both LAMMPS datafiles was defined as 'charge'. The creation and export of data files were accomplished by Visual Molecular Dynamics (VMD) [38]. In this part of the investigation, the Nose [39]/Hoover [40] algorithm was performed for temperature control, and entire systems were under isothermal–isobaric (NPT) ensemble. From beginning to the end, the temperature was fixed around room temperature (300 K), and the external pressure was about 1 atmosphere. The total integration term of each computational system ended at 1 ns, and each time step was about 0.5 fs.

Despite those numerical simulations, we also performed experimental characterizations in this study. Above all, the physical properties of dried NC were characterized before mixing operations. The morphology of dried NC was presented via an optical microscope, and the functional groups of NC were tested by FTIR (Nicolet Avatar 370, Thermo Nicolet Corporation, USA). Both tests were operated in the Harbin Engineering University, China. Because NC is a typical polymer material, we measured its averaged molecular weights by GPC (Agilent 1100, Agilent Technologies Inc., USA, tested in Harbin University of Science and Technology, China) and capillary viscosimeter (purchased from Shanghai Baoshan Qihang Glass Instrument Factory, China) respectively. The conversion formula of viscosity averaged molecular weight will be discussed in section 3.3. The last characterization for NC itself was the titration of N at about 10 °C. The reaction mechanism for titration is presented as equations (1)–(3) below. In which, x represents the degree of substitution. We calculated the mass percentage of N in NC through the volume of consumed FeSO₄ solution (0.5 mol l⁻¹). The titration ended while the crimson complex: [Fe(NO)]SO₄ appeared.

$$\begin{eqnarray}&&{{\rm{C}}}_{6}{{\rm{H}}}_{7}{{\rm{O}}}_{2}{\left({\rm{OH}}\right)}_{3-{\rm{x}}}{\left({{\rm{ONO}}}_{2}\right)}_{{\rm{x}}}+{{\rm{xH}}}_{2}{{\rm{SO}}}_{4}\leftrightarrows {{\rm{C}}}_{6}{{\rm{H}}}_{7}{{\rm{O}}}_{2}{\left({\rm{OH}}\right)}_{3-{\rm{x}}}{\left({{\rm{HSO}}}_{4}\right)}_{{\rm{x}}}+{{\rm{xHNO}}}_{3}.\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&3{{\rm{Fe}}}^{2+}+{{{\rm{NO}}}_{3}}^{-}+4{{\rm{H}}}^{+}=3{{\rm{Fe}}}^{3+}+{\rm{NO}}+2{{\rm{H}}}_{2}{\rm{O}}{\rm{.}}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{{\rm{FeSO}}}_{4}+{\rm{NO}}\leftrightarrows \left[{\rm{Fe}}\left({\rm{NO}}\right)\right]{{\rm{SO}}}_{4}.\end{eqnarray} \tag{ 3 }$$

Next, the characterized NC specimen was soaked in liquid ethanol or diethyl ether, respectively. We mixed 0.1 g NC with 100 ml liquid ethanol or diethyl ether, then each mixture was stirred for 3 h at least. We tested the viscosity of the filtered solution and made comparisons with pure ethanol and diethyl ether. Finally, the mass of NC addition was increased to 19 g. The penetration and volatilisation of organic mixtures were recorded as a function of time. The producer of penetrometer was Beijing Zhongke Lanhang Test Instrument Co., Ltd, China, and the penetrating time was 15 s.

In this study, some raw materials or reagents, such as dried NC, pure ethanol, diethyl ether, acetone, potassium bromide and concentrated sulfuric acid, were supplied by Harbin Engineering University, China. The solvent for capillary viscosimeter test was acetone, and the tablet for FTIR was the mixture of NC and potassium bromide. Additionally, solid FeSO₄ powder was purchased from Sinopharm Chemical Reagent Co., Ltd, China.

As mentioned before, our NC consisted of 8 identical glycosyl residues, and each glycosyl residue has three substitution sites. In this model, two of those three sites were connected with nitrate ester groups, therefore, its degree of substitution was 2. Conversion formulas between substitution degree (x), the mass percentage of N (M%) and nitrification degree (NO) are listed as equations (4)–(6) below [6]:

$$\begin{eqnarray}&&x=\displaystyle \frac{162\times M}{1400-45M}\approx \displaystyle \frac{3.6\times M}{31.11-M}.\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&M \% =\displaystyle \frac{14x}{162+45x}\times 100 \% .\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&NO({\rm{ml}}\,{{\rm{g}}}^{-1})=\displaystyle \frac{1000\times 22.39\times M}{14\times 100}\approx 15.99M.\end{eqnarray} \tag{ 6 }$$

Consequently, the mass percentage of N of this model was about 11.1%, and the nitrification degree was 177.489 ml g⁻¹. Figure 1 is the snapshot of the NC model after geometry optimisations. In which, all atoms were rendered by atomic types. Along the X-axis, the entire chain was presented as an arch structure with 114.54°. From one edge O atom to the other side, the NC chain was as long as 37.392 Å. Between each couple of glycosyl residues, there was a connecting ether group (R–O–R'). The angle of C–O–C bonds was around 116°(±1°). As our NC chain was a repetitive structure, it may be prolix to state all bonding information. Therefore, we only focus on middle glycosyl residue (figure 2). The studied glycosyl residue was about 7.87 Å high and 5.25 Å wide. Different from figures 1, 2 was rendered without lighting and perspective effects. Due to the limitation of VASTA, all types of bonds are presented as a single stick in figure 2. Bonding details of figure 2 are listed in table 1 below. It is shown that the bonding geometry of R–O–NO₂ was not affected by its substitution site, because they had similar approximation values of bond length and angle. This consequence was also validated by other glycosyl residues in NC chain. Besides, the C–C bond length value of substitution sites was about 0.02–0.04 Å higher than other C–C bonds.

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As the second stage of this study, we performed a set of comparisons based on MD simulations. Figure 3 shows the initial configurations of both ethanol and diethyl ether systems. In which, purple clusters represent NC chains, next, green and red groups are ethanol and diethyl ether molecules respectively. Due to the minimization algorithm for each mixture system, the placement of each molecule was not as same as pre-designed. In this study, pre-treatment of minimization was performed by Conjugate Gradient (CG) algorithm. The ending criteria of energy (unitless) and force (Kcal mol⁻¹ Å⁻¹) were both about 1.0E-10. It was recorded that the total energy of ethanol and diethyl ether systems was minimised for about 9212.39 and 11 690.91 Kcal mol⁻¹ respectively. Because the mixing process was a vertical transition in this study, we plotted the content distribution of ethanol and diethyl ether atoms along the Z-axis in figure 4. Initially, the vacuum lower than 20 Å represented the NC layer, and the peak on 2.5 Å resulted from periodical boundaries. According to those points at 500 ps, it seems that the mixing effect for both systems was quite unsatisfactory. Although parts of ethanol or diethyl ether molecules were moved into the NC layer, the final distribution of those molecules was still not uniform in the computational box, and those NC chains were keeping undissolved.

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The change of potential energies was presented by scattering points in figure 5 to make a clear comparison of transition processes. It is shown that the rapid transition process for both systems happened in the first 50 ps. Then the decline of potential energies trended to be flat and stable in the following 450 ps. The major difference between the two systems was on the deviation of potential energies. For the ethanol mixture system, the potential energy was declined for about 2142.67 Kcal mol⁻¹ after 500 ps. At the same interval, the value for diethyl ether mixture system was only 1039.14 Kcal mol⁻¹. It is reasonable to deduce that interactions from ethanol molecules were stronger than diethyl ether, although both of them had shown little solubility. Figure 6 is the Mean Square Displacement (MSD) of NC itself and two overall systems. From which, the diffusion coefficient of each object could be obtained. The formula for this transition has been introduced in our previous report [41]. In this study, the obtained diffusion coefficient for diethyl ether system was only 0.397E-6 cm² s⁻¹, while the data for ethanol system was about 0.644E-6 cm² s⁻¹, which means that dynamic movements of ethanol system were stronger than the ether system. Meanwhile, the same consequence was also proved by the diffusion state of NC chains, because the diffusion coefficient of NC in ethanol system was about 0.0696E-6 cm² s⁻¹ higher than those in diethyl ether system.

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Overlapping fibres of NC are visible in the optical microscope images (figure 7). It is indicated that those curly fibres were originally twined together, and the edge of fibres was narrow. As assisted by the ruler at micrometres, the diameter of their cross-sections was measured in the range from 24.41 to 28.59 μm. Therefore, those dried NC varied in length and had uneven thickness. To obtain the information of the functional group, the dried NC specimen was tested by FTIR. As the spectrum in figure 8 shows, six downward peaks were detected from NC specimen. Despite the appearance of nitrate ester groups and other regular bonds, the most critical peak was about hydroxy (–OH). It is known that the NC was produced by exothermic esterification reactions on hydroxy groups [5]. Which means that the degree of esterification (substitution) could be various in industry. Our FTIR results indicated that the esterification reaction was not thorough, and a large number of hydroxy groups were still kept in NC. Next, the mass percentage of N was obtained by titration of Fe(SO₄). While after ten parallel experiments, it was confirmed that each 0.2 g (m) NC needed 8.05 ml (V) Fe(SO₄). According to equation (7) below, the mass percentage of N (M%) was around 9.39%. As transformed by equations (4)–(6), the substitution degree of the specimen was 1.556, and its nitrification degree was 150.146 ml g⁻¹.

$$\begin{eqnarray}&&M \% =\displaystyle \frac{V\times 0.002333}{{\rm{m}}}\times 100 \% .\end{eqnarray} \tag{ 7 }$$

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As a typical macromolecule, the molecular weight of NC is always averaged by its number (Mn), weight (Mw), Z value (Mz) and viscosity (Mv). In this study, those properties of NC were obtained by GPC tests. The selected eluent for NC was THF, and the concentration was about 1 g l⁻¹. The GPC test was carried out around 30 °C, and the flow rate was about 1 ml min⁻¹. Those obtained results from GPC have been listed in table 2. Additionally, the Mv of NC was validated by capillary viscosimeter. The provided constant of viscosimeter was 0.0635 mm² s⁻². Equations (8)–(11) [42, 43] are formulas for viscosity, where η: viscosity of NC solution; η₀: viscosity of acetone; η_r: relative viscosity; η_sp: specific viscosity; c: concentration of NC solution; [η]: intrinsic viscosity of NC; K' and α are empirical constants. Table 3 has summarised all viscosity results from four acetone solutions with different concentrations of NC. Those acetone/NC solutions were labelled as solutions 1#, 2#, 3# and 4# with same concentration difference. Therefore, the intrinsic viscosity of this NC specimen was about 2.606. In this study, the K' and α were 2.53E-4 and 0.795, respectively [43], so the Mv obtained from capillary viscosimeter was 1.12E5. This value was close to the GPC result.

$$\begin{eqnarray}&&{\eta }_{{\rm{r}}}=\displaystyle \frac{\eta }{{\eta }_{0}}.\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{\eta }_{sp}={\eta }_{r}-1.\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&\left[\eta \right]=\mathop{\mathrm{lim}}\limits_{c\to 0}\displaystyle \frac{{\eta }_{sp}}{c}.\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&\left[\eta \right]=K^{\prime} {M}_{r}^{\alpha }.\end{eqnarray} \tag{ 11 }$$

Once the characterization of NC specimen itself was finished, the next stage of this section was focused on the mixture of NC and two liquid organics. Due to the poor solubility of both ethanol and diethyl ether, we could not prepare much NC solution with a certain concentration. Therefore, we had to test the filtered NC solution to make comparisons on their saturated state. In table 4, specimen 1* and 3* are pure liquid ethanol and diethyl ether respectively, while specimen 2* and 4* are their saturated solutions with NC. It seems that the dissolving effects on ethanol solution were higher than that on diethyl ether solution because the viscosity of diethyl ether was hardly changed after the addition and filtering of NC. However, the viscosity of ethanol solution was increased for about 52%. Comparing with the ether solution, its deviation was much higher. In other words, the solubility of diethyl ether was even lower than ethanol, and this result was in good agreement with MD simulations above.

If the excess weight of NC was soaked under ethanol or diethyl ether solutions, the consistency of mixture could then be represented by penetration degree. The penetration degree of NC mixtures is demonstrated by histograms in figure 9. Meanwhile, the mass of each specimen is also plotted as a function of time. Generally, the ether-soaked NC specimen showed stronger volatility than ethanol-soaked one. As the model of volatilisation was a tablet, the exposure of diethyl ether-NC tablet under atmosphere resulted in the rapid loss of weight. On the contrast, the linear volatilisation of the ethanol-NC specimen was much slower than the former one. As for the penetration data, the standard penetration container is much larger and deeper than the tablet, so the strong volatilisation of diethyl ether delayed the decline of penetration degree. It seems that the substantial volatility of diethyl ether could keep the soaking effect on the mixture surface shortly because the inner diethyl ether volatilized efficiently up to surface.

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