Dissolution of viscose rayon multifilament yarn in the ionic liquid 1-ethyl-3-methylimidazolium acetate studied using time–temperature superposition

Wide-angle X-ray diffraction (WAXS) and mechanical testing techniques are used to track the dissolution of a viscose rayon multifilament yarn in the ionic liquid 1-ethyl-3-methyl-imidazolium acetate [C2mim]+ [OAc]− for different times and temperatures. In the dissolution process, the oriented cellulose II crystals in the regenerated cellulose fibres dissolve and then reform into randomly oriented crystals to form a matrix phase, and this change in orientation enables us to follow the dissolution process using WAXS, and hence determine the dissolved matrix volume fraction vm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{m}$$\end{document}. The change in the average molecular orientation P2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P}_{2}$$\end{document} determined from an azimuthal (α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha$$\end{document}) X-ray scan, allows the growth of the matrix volume fraction vm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{m}$$\end{document} to be calculated with time and temperature. The growth of vm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{m}$$\end{document} was found to follow time temperature superposition, with an Arrhenius behaviour, giving a value for the activation energy of Ea = 149 ± 4 kJ/mol. Young’s modulus was measured on all the resulting processed composites. The fall of Young’s modulus with dissolution time and temperature was also found to follow time–temperature superposition, with an Arrhenius behaviour giving a value for Ea = 198 ± 29 kJ/mol. The Young’s Modulus results plotted against vm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{m}$$\end{document} determined from the WAXS measurements fitted well to the Voigt upper bound parallel Rule of Mixtures .\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$.$$\end{document}


Introduction
Cellulose offers the possibility to be a renewable material source with nontoxicity and biodegradability (Kalia et al. 2011).Cellulose fibres can be found as both natural fibres and as man-made fibre: the man-made fibres are known as regenerated cellulose.Regenerated cellulose fibres can be made by dissolving natural cellulose (a mixture of cellulose I crystals and amorphous cellulose), which after dissolution and coagulation results in a mixture of cellulose II crystals and amorphous cellulose (Zugenmaier 2001;Jiang et al. 2020).
Regenerated cellulose fibres, which can be used to produce textile materials, are produced on the industrial scale via the viscose and lyocell processes (Meredith et al. 2013;Shen et al. 2010).Cross and Bevan first discovered the viscous process in 1893 as discussed in papers of (Woodings 2001;Nevell Vol:.( 1234567890) et al. 1985).The viscous process is based on dissolving wood pulp in sodium hydroxide and using carbon disulphide (CS2) to produce cellulose xanthate (Einsiedel et al. 2010).The cellulose xanthate is subsequently injected into a bath containing sulfuric acid and zinc sulphate (Hermanutz et al. 2019).The lyocell process is based on dissolving wood pulp directly in methylmorpholine-N-oxide (NMMO) monohydrate to get a homogenous solution.The homogenous solution is then spun and stretched in the air gap in the filament form.After that, the fibres are regenerated by coagulating in a mixture of a water/NMMO spin bath, and then washed and dried discussed in papers of (Sayyed et al. 2019;Woodings 2001).
Viscose rayon multifilament yarn is a regenerated cellulose man-made fibre, which can be obtained from wood pulp using the viscous process.Viscose rayon multifilament yarn is considered to be an ecoenvironmental material.Viscose rayon multifilament yarn was first produced by Glanzstoffwerke in 1938.Viscose rayon multifilament yarn has excellent mechanical properties, which include high temperature resistance and the ability to take high stresses.Therefore, Viscose rayon multifilament yarn have been used in a variety of commercial applications including car tyres, automotive brake hoses and rubber goods (Cordenka 2022).
To dissolve and regenerate cellulose fibres, different solvent systems have been used.The solvent systems such as N, N-dimethylacetamide with Lithium chloride (DMAc/LiCl), and sodium hydroxide with urea (NaOH/urea) have been employed in the dissolution of cellulose (Seydibeyoğlu et al. 2008;Sescousse et al. 2010).However, it has been found that these solvents systems were unable to dissolve high concentrations of cellulose directly (Sescousse et al. 2010;Zhao et al. 2009).For this reason, ionic liquids have found increasing popularity as good solvents to dissolve cellulose.Walden first defined an ionic liquid in 1914 (Pinkert et al. 2009;Walden 1914); an ionic liquid (IL) is a salt which has a melting point below 100 • C (Pinkert et al. 2009;Hall et al. 2012).An organic ionic liquid has attractive properties, in general nontoxic, potential recyclability, thermal stability, and low vapor pressure (Zavrel et al. 2009;Pinkert et al. 2009;Sescousse et al. 2010;Seydibeyoğlu et al. 2008).Ionic liquids can be used in various applications such as electro-elastic materials, heat storage, energy, and chemical analysis (Gupta et al. 2015).
In 2002, Swatloski discovered that the ionic liquid 1-butyl-3-methylimidazolium chloride [BIMIM] [Cl].could directly dissolve cellulose, and can dissolve a high cellulose concentration (Swatloski et al. 2002).It is worth noting that the purity of the IL (95% in our case) could also affect the dissolution due to additional side reactions or derivatizing reactions; (Liebner et al. 2010) caution that additional side reactions with cellulose can occur if the IL contains significant impurities.Furthermore, (Zweckmair et al. 2015) describe how acetylation reactions can occur with cellulose for aged ILs (they studied 1,3-dialkylimidazolium acetate) with resultant impurities.They propose that pure ILs do not show this reaction.
Ionic liquid systems based on the imidazolium ring have excellent properties, such as low viscosity and high thermal stability (Ghandi 2014).A common ionic liquid based on the imidazolium ring such as 1-ethyl-3-methylimidazolium acetate [C2mim] + [OAc]-has been extensively utilized to dissolve cellulose (Zavrel et al. 2009;Liu et al. 2012).This is due to excellent properties of the IL [C2mim] + [OAc]-such as low melting point and being biodegradable (Sun et al. 2009).This ionic liquid has the ability to dissolve a high concentration (~ 20 wt.%) of cellulose (Köhler et al. 2007).
The structure of regenerated cellulose fibres is often comprised of oriented cellulose II crystals and a randomly oriented amorphous phase (Shen et al. 2010).As the regenerated cellulose fibres dissolves, the oriented cellulose II crystals are transformed into randomly oriented cellulose crystals after coagulation.By analysing the decrease of the cellulose II crystalline orientation (specified by the Herman's Orientation Factor P 2 ) then the rate of dissolution can be followed with time and temperature.This paper aims to understand the dissolution mechanism of a Viscose rayon multifilament yarn in the Ionic liquid-1-ethyl-3-methyl-imidazolium acetate [C2mim] + [OAc].This was achieved and compared using two methods, by following the change in both the average crystal orientation using an azimuthal ( ) X-ray scan to measuring the 2nd Legendre polynomial function ( P 2 ) , and the change in the Young's modulus of dis- solved and regenerated 'composites' with time and temperature.The reduction in both parameters were found to follow time-temperature superposition (Cotts et al. 1969), allowing the activation energy of dissolution to be calculated independently by these two methods.In addition, the two measurements were combined to show that the modulus of the partially dissolved regenerated 'composite' multifilament yarn followed closely to the rule of mixtures.The ultimate aim of the research will be to manufacture all cellulose composites from regenerated cellulose fibres, although this is not reported in this current paper, where the focus is to understanding the physics of the dissolution process and how to use this in the future, to control and tailor properties of composites.
The unprocessed viscose rayon multifilament yarn (which were untwisted) were wound around a frame, as shown in Fig. 1.Three samples were made for measuring x-ray diffraction and three samples for mechanical measurements.A PTFE dish containing the IL [C2mim] + [OAc] − was preheated in a vacuum oven at 1 h for each processing temperature (30, 35, 40, and 45 • C ).After this preheating step the samples were put into the dish of IL [C 2 mim] + [OAc] − and then left in the vacuum oven at the same temperature for set times.The last step was to wash (and coagulate) the processed partially dissolved composites, while still on the frames to remove all the ionic liquid by soaking in water for 24 h, followed by a final drying process on a hot plate at 120 °C for 1 h.

Preparation of film sample
For preparing a fully dissolved sample (which is proposed as representative of the matrix phase of the partially dissolved multifilament), the viscose rayon multifilament yarn was cut into small pieces and then submerged into [C2mim] + [OAc]-with a magnetic stirrer at a speed of 90 rpm, for 48 h at 90 • C on a hot plate, as shown in Fig. 2a.The solution had a total concentration of 19:1 IL [C2mim] + [OAc]-to regenerated cellulose multifilament.The IL was then spread evenly into a 5 cm × 5 cm polystyrene petri dish and left for 30 min in a vacuum oven at 90 • C , to remove any bubbles from the film.This petri dish with solution was put on an upside-down beaker, and then put it in a larger beaker filled with water and sealed, heated at 90 ℃ using a hot plate, for 24 h as shown in Fig. 2b.The water was evaporated slowly inside the beaker to slowly coagulate the film.The resultant film was then washed with water for 24 h, to remove any residual ionic liquid.We are making the assumption that after washing the residual IL is at a significantly low enough fraction to not affect mechanical properties, giving a resultant film with light yellow colour as shown in Fig. 2c, and finally this film was dried at 120 ℃ for one hour, using a hot press machine under a minimal contact pressure.This film is considered to be similar to the matrix phase within the viscose rayon composite multifilament yarn.

Wide angle x-ray diffraction
The degree of orientation within the unprocessed multifilament yarn, the film and the processed composite samples was determined using Wide-Angle X-ray Diffraction (WAXD) with Cu Kα radiation (λ = 1.54 Å) at 40 kV and 30 mA (DRONEK 4-AXES, Huber Diffractions Technik GmbH & Co. KG, Germany).Qualitative measurements of the change in crystalline structure and orientation were obtained by capturing a 2D image of each sample.This was done by passing x-rays through the sample and capturing the resulting pattern on an x-ray sensitive film placed 5 cm away.The exposure time was 3 h.
Quantitative measurements of crystal structure and orientation were carried out using a Huber goniometer and x-ray detector.The 2 equatorial scans from 5° to 40° were carried out with a counting time of 40 s per step (0.1°) with the processed composites located in the vertical direction.This allowed the crystalline structure to be confirmed and then enabled the choice of the most appropriate Bragg peak for the circumferential scans.The orientation degree of the crystals was then determined by setting the 2 angle at 20.3°, which is the position with the maximum count rate and so has the best signal/noise ratio.Circumferential scans were carried out at increments of 5° with an interval time of 30 s per step, with azimuthal angles from −90° to + 90°.For the circumferential scan, a number of processed composite filaments were placed side by side in the WAXS sample holder to increase the signal to noise ratio.
The crystal structure of the viscose rayon multifilament yarn is transformed from an aligned crystalline structure to randomly oriented crystals in the coagulated phase.Experimentally, the azimuthal scan is used to measure the orientation of the crystal structure of the processed composites.Once the intensity distribution is measured, then we can determine an average orientation of the crystal's fibre < cos 2  > by using: where I( ) indicates the intensity distribution and is the angle formed by the fibre axis and reference direction.The average orientation of the processed composites can then be further quantified using the second-order coefficient of Legendre polynomial P 2 (cos ).
Equation 2 is known as Herman's orientation factor function ( f ) of the crystalline material (Ellison  et al. 2008; Zhu et al. 2016).When f = 1 this indi- cates that crystallites have a perfect alignment, and when f = 0.25 the crystallites are completely ran- domly oriented in a 2D plane, and in the case of f = −0.5 molecules crystallites are oriented perpendicular to the axis of the sample (Rusznák et al. 1975).

Young's modulus measurements
The Young's modulus of the processed composite samples was measured using an electromechanical tensile machine Instron 5564 with the Bluehill™ (1) Fig. 2 The preparation of viscose rayon film version software employed.The load cell was 2000 N and a crosshead speed of 10 mm/min was used.The cross-section area ( m 2 ) of each processed composites was determined using a gravimetric technique measured by equation: where l is the length of fibre and is the density of cellulose, which has been recorded as 1400 kg∕m 3 (Mwaikambo et al. 2001;Sun 2005), and m is the mass of fibre.End tabs to give good load transfer were formed using paper and superglue.The sample to be tested was then fixed between two clamps with sandpaper, after measuring the gauge length.Young modulus measurements were repeated three times for each set of processing temperature and processing time to reduce human error and sample to sample variability.
Experimentally, an Instron tensile test machine was used to determine the force-displacement of each sample, and then calculate the Young's Modulus from the relationship between measured stress and strain of the sample displacements (Gu et al. 2014).

Two-dimension x-ray diffraction pattern
Cellulose II has three Bragg peaks located at 20.16° and 21.76° and with small peak at 12° (Ohira et al. 2012).A two-dimensional diffraction pattern was captured to determine qualitatively the crystalline structure of the unprocessed multifilament yarn using x-ray sensitive photographic films.Quantitative measurement of the crystal orientation was obtained from an circumferential scan setting in two dimensions (2D) from −90° to 90° at 2θ = 20.3°.The results of 2D x-ray image showing the positions and reflection peaks are showed in Fig. 3, where the dark arcs correspond to Bragg beaks.There were peaks with reflections 1 − 10 , 110, 020 which are positioned at 12.4°, 20.2°, 21.8° of 2 angles respectively for cellu- lose II.There is another reflection peak which appears in cellulose, which is due to the 012 planes, and can be seen in the 2D x-ray scattering at a circumferential angle of ~ ± 60° (see also Fig. 4) and a 2θ value of 20.3° as described in ref (Nam et al. 2016).As this 012-reflection plane has a very similar value of 2θ to the chosen equatorial position with maximum signal intensity (20.3°), then this reflection will appear in a circumferential α scan (as shown schematically in Fig. 4).We have proposed to include both these reflections in the determination of P 2 from a numeri- cal integration between -90 and + 90.Our hypothesis is that following the change of any appropriate parameter with time and temperature, allows us to investigate time-temperature superposition and determine an activation energy for dissolution.The measurements of 2θ scan of Viscose rayon multifilament yarn examined the changes of crystal structure during the dissolution and subsequent coagulation process.Experimentally, it was found that the 2θ line scan for the three materials (unprocessed multifilament, processed composites and a film) were not significantly different, as shown in Fig. SI1, and so could not be used to follow change in crystal structure during the dissolution/coagulation process as we have done before in our previously published work on the dissolution of cotton filaments (Liang et al. 2021), which is predominantly cellulose I. Therefore, an alternative method is proposed to calculate the volume fraction of dissolving Viscose rayon multifilament yarn, which was to use the azimuthal scan to follow the change of crystal orientation with time and temperature.This technique has worked successfully for silk fibres, as has been demonstrated in a previous publication from our research group (Zhang et al. 2021).
The x-ray technique for the azimuthal α scan was carried out from -90° to 90° at a fixed angle 2θ of 20.3° as mentioned above.The measurement of the azimuthal scan allowed a measurement of the degree of molecular orientation in the various samples.As described above in Fig. 3, and as seen in Fig. 4, such a circumferential scan picks up both the equatorial peak reflection (α = 0°) (which is actually a combination of the 110 and 020 Bragg peaks) and then outer peaks from the 012 reflections as shown in this ref (Nam et al. 2016).It can be seen that the dissolution of the processed composites influenced the intensity of the crystalline reflections.As the oriented crystals (associated with the unprocessed multifilament yarn) dissolved and then they reformed as random crystals, leading to an increase of the background level.For the film sample, a constant intensity was seen at all angles, indicating random orientation of the crystal structure.
The overall average of P 2 for all processed compos- ites, from processing at different times and temperatures, was calculated by using Eq. 2. The results of the change in the average value of P 2 with temperature and time are shown Fig. 5.The reduction in the average P 2 value for processed composites is due to the increasing in the random molecular orientation component due to the dissolved and coagulated matrix fraction.From Fig. 5, It can be seen that the P 2 of the processed com- posites has reduced with increased time and temperature.The reduction of the average value of P 2 of the processed composites at various times and temperatures appears broadly linear, although with an increasing slope as the processing temperature increases.This indicates increased effectiveness of [C 2 mim] + [OAc] − to dissolve the viscose rayon multifilament yarn with increasing time and temperature.
The P 2 data can be formed into a master curve using the concept of time-temperature superposition.This method was previously reported in the study of the dissolution of cotton and silk fibres in [C 2 mim] + [OAc] − by our research group (Liang et al. 2021;Zhang et al. 2021).Based on this previous work the data of P 2 values are first plotted as function of the logarithm of time and the different temperature curves are then superposed in (ln time) using Eq. 4 at a chosen reference temperature.
where T 1 is the temperature, T R is reference temperature, t 1 is the time value before scaling, t R is the time value after scaling/shifting, and ln a T is the shift factor (Zhang et al. 2021).Figure 6a explains the steps used to find the best shift factors so that all the points overlap on one master curve.Firstly, the orange line at a processing temperature of 35 • C was chosen as the reference temperature (T R ) on the ln time axis t R = t 1 a T (4) ln t R = ln t 1 + ln a T Fig. 5 The calculated P 2 and different dissolution times and temperatures for processed composites (Fig. 6a).Then all the other temperature curves were shifted horizontally by an initial shift factor (ln a T ) to the data at 35 • C curve along the ln time, x-axis.Next, a polynomial function was introduced as a guide around this preliminary shifted data.Then the individual shift factors were changed to get the best fit between the polynomial function and the shifted points by maximizing the value of R 2 .The final master curve between the average P 2 and the shifted data at a reference temperature of 35 • C , is shown in Fig. 6b.
From the relation between the shifted average P 2 values (at a reference temperature of 35 °C) with linear dissolution time, as shown in Fig. 6c, it can be estimated that complete dissolution of the Viscose rayon multifilament yarn would be achieved after 14 h dissolution time at 35 °C, as the P 2 value of completely dissolved Viscose rayon multifilament yarn extrapolates to 0.25.
Figure 7 shows that plotting the ln of the shift factors versus the inverse temperature gives a linear relationship, indicating that the dissolution of the Viscose rayon multifilament yarn follows an Arrhenius behaviour.We can therefore use Eq. 5 to calculate an activation energy for this dissolution through the Arrhenius equation, as follows: where a T is the simple multiplicative factor, E a is the activation energy, R is the universal gas constant and T is temperature (K) (Ries et al. 2014;Laidler 1984).
Figure 7 shows the best fit line to this data (using the LINEST function in Excel) resulting in an activation energy value of 151 ± 3 kJ/mol.This value quantifies the temperature dependence of dissolution, which is a useful parameter in controlling the fraction of matrix formed when creating an all-cellulose composite to obtain the optimum balance of mechanical properties.
Dissolved and coagulated matrix fraction v m from wide angle x-ray diffraction By applying a rule of mixtures to the experimental data of P 2 , from the azimuthal scan measurements, the volume fraction v m of the dissolving fraction of the original composite multifilament could then be calculated.This dissolved and coagulated fraction ( v m ) now indicates the amount of 'matrix' phase resulting in the processed composites combined with the unprocessed multifilament yarn.This procedure was done by calculating the points between the orientation of the unprocessed multifilament yarn with ( v m ) = 0% dissolved and the completely dissolved matrix with ( v m ) = 100%, by assuming a linear mixing rule as given by: assuming v m + v f = 1 .Here p 2c indicates the P 2 value of the processed composites, p 2f is the P 2 value of the unprocessed multifilament (measured as = 0.57) and p 2m is the P 2 value of the completely dissolved matrix (film) with 0.25 (randomly oriented crystals). ( Figure 8a presented the relationship between the calculated v m value and the dissolution time and tem- perature.The volume fraction of dissolved viscose rayon multifilament yarn increases with increasing time and temperature.As carried out above, the data of v m is likewise shifted with time and temperature, using the temperature of 35 °C as the reference temperature.Once again, this data was found to collapse to a single master curve, as would be expected as it is mathematically based on the P 2 data.The vol- ume fraction as function of time temperature after superposition is shown in Fig. 8b.From the relation between the volume fraction of v m with linear dissolu- tion time, as shown in Fig. 8c, it can be seen that the complete dissolution of the Viscose rayon multifilament yarn would be achieved after 14 h dissolution time at 35 °C, as the V m value of completely dissolved Viscose rayon multifilament yarn extrapolates to 1, as shown in Fig. 6c. Figure 8d shows that plotting lna T against the inverse of temperature gives a linear relationship and from this the activation energy value was calculated by applying the Arrhenius (Eq.5).
The value obtained was 149 ± 4 kJ/mol, which is very close to that found from the time temperature superposition of the average P 2 values, as expected, nev- ertheless it is a confirmation of our time temperature superposition approach since the two data sets were analysed independently.

Mechanical measurements
The measured Young's modulus of the processed composites as a function of time at various temperatures is shown in Fig. 9a and typical stress-strain curves are shown in Fig. SI2.It can be seen that the pattern of the decrease of the measured Young's modulus values, with time and temperature, is very similar to that shown on Fig. 5 for the measured average P 2 values, as both are a measure of the remaining fraction of the unprocessed filaments.The data of the measured Young's modulus is next shifted with time and temperature, using the temperature of 35 °C as the reference temperature using the same procedure as explained above.Figure 9b, shows the result of the final master curve after shifting the data, plotted against Ln (time).The relationship between the shifting factors and the inverse temperature was again used to calculate an activation energy (as they showed a linear dependence) using the Arrhenius Eq. 5, see Fig. 10.This gave an activation energy value of 198 ± 29 kJ/ mol.
By comparing these three methods, the values of the activation energies of P 2 and the activation ener- gies of volume fraction V m are similar and lower than the activation energy from analysing the measured Young's modulus data, as shown in Table 1.It is seen that there is a much larger uncertainty in the calculated activation energy based on the Young's modulus measurements.
The relation between the Young's modulus with linear dissolution time in the ionic liquid [C2mim] + [OAc]-, is presented in Fig. 11 for a reference temperature of 35 °C.At short times, the Young's modulus is seen to first fall rapidly, and then, the Young's modulus decreases at a slower, but linear, rate with time.We propose that this is because at early dissolution times, when the individual viscose rayon multifilament yarn are not connected (being untwisted as described earlier), the ionic liquid can penetrate more easily between each individual multifilament, enabling the surrounding outer layer of each multifilament to be dissolved to form the matrix.Once the inner space between the individual multifilament yarn is filled with a dissolved cellulose/[C2mim] + [OAc]-gel, we propose that this forms a barrier to the ionic liquid and therefore dissolution proceeds more slowly by now only dissolving the multifilament yarn on the outside of the fibre bundles and so proceeding at a slower rate.
To obtain a value of the modulus of the unprocessed multifilament yarn the data for the early times (the first four points shown in more detail in Fig. 12) are used to extrapolate the modulus to zero time.From the correlation between the Young's modulus data and the linear dissolution time at 30 °C, and using a second order polynomial function, the best fit gave a value of 14.8 GPa for the unprocessed multifilament bundle (limit t tends to zero).Fig. 11 Master curve between Young's modulus and dissolution time using 35 °C Fig. 12 The extrapolation method to determine the modulus for unprocessed multifilament yarn from Young's modulus master curve at 30 °C Experimentally, the azimuthal α scan technique has been used to calculate the volume fraction of processed composites of the partially dissolved multifilament.The measured Young's modulus data could then be plotted against these calculated volume fraction values from the azimuthal α scan measurements to evaluate the possibility of applying rule of mixtures to our processed composites, and to specify the effect of changing the volume fraction on the behaviour of the Young's modulus results.The upper-bound (Voigt series), which is also called the parallel rule of mixture and the lowerbound (Reuss series) are used to estimate the effective stiffness of the two phases, fibre and matrix.The Voigt series assumes that the two composite phases have the same strain, while Reuss series assume two phases of composite have the same stress (Lakes et al. 2002;Luo 2021).
The result of plotting the measured Young's modulus and the calculated volume fraction (from the α scan) with the two mixing rules is shown in Fig. 13.Based on the extrapolated fibre value of E f =14.8 GPa with using v m = 0% dissolved and the completely dissolved matrix v m = 100%, with value of E m =1.5 GPa (from measuring the film), the upper-bound and lower-bound are calculated by the following equations respectively: where E C indicates the young modulus of processed composites in the fibre direction, E f is the young modulus of 100% multifilament yarn and E m of a completely dissolved 'matrix' multifilament yarn, assuming v m + v f = 1 .The data points of Young's modulus versus v m have excellent agreement with the upper-bound (Voigt series), confirming excellent adhesion between the unprocessed multifilament yarn and the dissolved and coagulated matrix fraction.This is an important finding for future work on all cellulose composites made from regenerated cellulose fibres as it demonstrates good bonding can be achieved.

Conclusion
Wide-angle X-ray diffraction and mechanical test techniques have been used in this research to follow quantitatively the physics of the dissolution, and the resulting mechanical properties of multifilament yarn of Viscose rayon.This was done by dissolving the viscose rayon multifilament yarn in an ionic liquid of 1-ethyl-3-methylimidazolium acetate [C2mim] + [OAc]-for different times and temperatures.An azimuthal α scan was employed to determine the dissolution mechanism of the viscose rayon multifilament yarn.The azimuthal α scan at an angle 2 =20.3 • (position of maximum equatorial intensity) was used to follow the change in the crystal orientation with time and temperature of dissolution and hence calculate the volume fraction of the dissolved fraction.The P 2 value of the unprocessed multifila- ment yarn was found to be 0.57 while the P 2 value of film was measured to be 0.25, which is the expected value for a perfectly random crystalline orientation in a 2D plane.The measured value of P 2 for the partially dissolved composites was found to decrease as time and temperature increased, indicating an increase in the random orientated crystal fraction associated with the dissolved and coagulated matrix fraction.The rule of mixtures was applied to the measured P 2 values to calculate the volume fraction v m of viscose rayon multifilament yarn dissolving, using the data from the azimuthal scan for processed composite samples.The Young's modulus values of the processed composites were also measured for different processing times and temperatures.The time-temperature superposition method was applied to the experimental data of the average P 2 values, the cal- culated matrix volume fraction v m and the processed composites Young's modulus values.Each data set transformed used time-temperature superposition to form a master curve and then the activation energy was calculated by using an Arrhenius equation (all three measured followed Arrhenius behaviour).The activation energies for the three measures, P 2 , vol- ume fraction v m and Young's modulus were found to be 151 ± 3 kJ/mol, 149 ± 4 kJ/mol, and 198 ± 29 kJ/ mol, respectively.The activation energies measured from different methods gave similar values, which indicates they could all be used to follow the dissolution behaviour of the Viscose rayon multifilament yarn.By extrapolating the Young's modulus of the processed composites at low temperatures and early times, the modulus of the unprocessed multifilament yarn was measured to be E f =14.8 GPa, which can often in practice be a difficult parameter to measure.Combining this with the modulus of a completely dissolved and coagulated film, allowed the Young's moduli of the processed composites to be tested against the rules of mixture.The correlation between volume fraction (from the P 2 , meas- urements) and the Young's modulus agreed very well with the predicted parallel rule of mixtures.

Fig. 3
Fig. 3 2D X-ray scattering pattern from unprocessed multifilament yarn showing the circumferential scan setting in two dimensions (2D) from -90° to 90° (red dashed line) at 2θ = 20.3° and how this includes the 012 reflection

Fig. 6 a
Fig. 6 a Logarithm of time (ln a T ) with P 2 , all data of time and temperature shifted at reference 35 • C. b the master curve of relation between P 2 and shifting time at various tempera-

Fig. 7 Fig. 8 a
Fig. 7 lna T plotted against the inverse of temperature, dotted line is Arrhenius equation

Fig. 10
Fig. 10 Activation energy determined from TTS

Fig. 13
Fig. 13 Relation between volume fraction v m and Young's modulus from α scan with prediction of rule of mixtures, Voigt and Reuss series

Table 1
The comparison between the values of E P 2 and E V m and the E E