Quantitative via a single marker

This article describes the development of a suitable Gel Permeation Chromatography method for cellulose nitrate plasticised with camphor (celluloid) found in cultural heritage. Current sample preparation and dissolution methods, apart from focusing on native, nonderivatised cellulose, require long preparation times, and often employ solvents that induce degradation. This study aims to develop a systematic method for sample preparation of cellulose nitrate that uses the least sample amount possible, is nondegrading, and can be applied on differ-ently aged samples. This is investigated through identification of a suitable solvent system and a statistically designed experiment testing the critical variables affecting the analysis, namely sample condition, sample, and salt concentration (lithium chloride) in N , N -dimethylacetamide. The use of 0.1% sample was inadequate for analysis because it did not fully dissolve in any salt concentration, while the 0.3% negatively impacted the analysis with its high molecular weight distributions. The 0.2% cellulose nitrate in a solution of 0.5% lithium chloride in N , N -dimethylacetamide offered the most consistent and repeatable molecular weight data. This method miniaturised the sample as much as possible and is suitable for museum objects in various ageing conditions.

and water. This, known as the nitration of cellulose, is a well-documented process [1,4]. Depending on the type or application of a product, the reaction can result in different levels of nitration, expressed as a percentage of nitrogen atoms per glucose residue in the molecule (i.e. [10][11].5% nitrogen content for three-dimensional objects and 11.5-12.3% for lacquer) [4].
Nitration is a reversible process, so over time, hydrolysis causes the emission of nitrogen oxides (NO x ) (denitration) and reversion of CN to cellulose. In a museum environment this means that with ageing, objects release acid volatile organic compounds, which, not only render them inherently unstable, but endanger other materials in their proximity too [5][6][7]. This acid release both occurs through and induces chain scission, resulting in molecular weight loss [4,7]. Τo propose effective conservation practices for the long-term preservation of CN, it is of utmost importance to elucidate the material's ageing mechanisms and degradation pathways [8].
Molecular weight distributions (MWD) of cellulose derivatives are commonly characterised with gel permeation chromatography (GPC), also known as SEC [9][10][11] that physically separates polymer molecules according to their size in solution [12]. Only a few studies have published relevant work addressing CN [13], which mostly derives from research in native cellulose [14,15], and uses polymer dissolution methods for highly nitrated cellulose (nitrogen > 12%) used in explosives (i.e. dynamites and gun propellants) [9,11,16,17]. The primary challenge of CN and its preparation for GPC analysis relates to solubility issues: (1) the intrinsic nitrogen content that results from CN production influences its solubility (reduced nitrogen levels lead to lower solubilities) [13,16]; (2) the ageing of CN results in a reduction of nitrogen content, which causes a further decrease in solubility [12].
To the knowledge of the authors, only publications [1] and [7] have adopted sample preparation methods for lownitrated cellulose (nitrogen < 12%) objects in museum collections; however, without investigating the most suitable amount of CN and solvent system (salt/solvent ratio) for sample preparation and analysis. While Quye et al. [1] have used tetrahydrofuran for cellulose derivatives, this GPC solvent was found unsuitable for CN, especially when severely aged [9,[16][17][18]. Similarly to other conventional GPC solvents (e.g. methylethylketone or dimethylsulfoxide), tetrahydrofuran may induce CN degradation [16,18,19]. To overcome this drawback, Mazurek et al. [7] along with other recent studies on cellulose and its derivatives [11,[19][20][21][22] have suggested the use of N,Ndimethylacetamide (DMAc) with lithium chloride (LiCl), as this solvent system is assumed to be nondegrading to CN. Mazurek et al. [7] used 0.5% LiCl for analysis of cellulose acetate and CN but mentioned that severely degraded samples may require a higher salt percentage (up to 8%) for dissolution to occur.
On one hand, the use of high salt concentrations may affect the sample's molecular size and increase the need for frequent system purification (column flushing) to avoid corrosion of the instrument, particularly at above ambient temperatures [13]. On the other hand, as earlier stated, degraded samples may require higher salt concentrations to fully dissolve. The risk with nonfully dissolved samples lies in the fact that they may form aggregates, mixtures of different molecular weight chains, which will offer inaccurate or false results, that is, higher molecular weight values [23,24]. For these reasons, there was a need for a balanced use between low enough LiCl concentration to avoid influencing the chromatographic separation or system contamination, and high enough for CN to dissolve [14].
This article aims to develop a systematic and suitable GPC method for sample preparation of CN, by using the least amount of sample possible and a nondegrading solvent system (LiCl/DMAc) with a salt/solvent ratio that can fully dissolve both fresh and severely aged material. The method development involves adapting and altering existing methods to render them suitable for an optimised application [9] with the use of design of experiments (DOE) [21]. DOE and its statistical analysis seek to understand where critical parameters lay in the analytical method, minimise or optimise their influence on precision, and identify the best parameter combination for optimisation of the GPC method [22]. The outcome intends to improve the analysis of CN objects in cultural heritage collections.

Dissolution of CN in LiCl/DMAc
Studies employing LiCl/DMAc have mostly focused on the analysis of native, derivatised cellulose; these include accounts of Patkar and Panzade [25] and Zhang et al. [26], who used 0.5% LiCl, and Strobin et al. [20], who used 8% LiCl. For dissolution of cellulose concentrations of up to 15-17%, McCormick et al. [27] and Strlič and Kolar [18], respectively indicated that LiCl of up to 9 and 11% may be required.
Based on the well-documented dissolution of nonderivatised cellulose [27,28], it was assumed that dissolution of CN takes place via scission of its intermolecular hydrogen bonding and of the Li-Cl ion parts, and the subsequent formation of strong hydrogen bonds between the CN hydroxyl protons and LiCl/DMAc chloride ions. Addition of other lithium salts, such as bromide, or similar organic solvents, such as N,N-dimethylformamide, has been ineffective in achieving a molecularly disperse cellulose solution [18,19]. It was speculated that since LiCl/DMAc constitutes a true, thermodynamically good, nondegrading solvent system for cellulose [14,23,25,27], it would behave similarly in contact with CN.

Experimental
In this research, sample preparation and analytical parameters were based on the method described by Mazurek et al. [7] with 0.5% LiCl/DMAc. Consultation with experts in the polymer testing industry also indicated the use of 0.5% LiCl (P. Montag, personal communication, July 2020). It was uncertain whether such a low salt concentration would be suitable for both the unaged and severely aged material. Therefore, increasing amounts of LiCl starting from 0.5 to 1 and 1.6% were tested. Previous work conducted by the authors used 0.3% sample concentration for characterising fresh and severely (naturally and artificially) aged CN [29]. Given the need to miniaturise the sample when analysing museum objects, it was decided to employ smaller amounts than the ones previously tested, starting from 0.3 to 0.2 and 0.1% CN. This intended to locate the least amount possible for preparation of samples without influencing dissolution or the chromatographic separation.
Regarding the presence of the plasticiser, camphor elutes very late in the chromatogram due to being a very small molecule, overlapping with a negative system peak. Its detection is best carried out with a different GPC system setup and solvent (P. Montag, personal communication, July 2020), and was not in the scope of this article. For a pioneer GPC study on camphor quantification in CN see [29].

Eluent preparation
Three different solutions were prepared by adding 5, 10, and 15 g LiCl (ACS 99%, Alfa Aesar) in 1 L DMAc (99.5% HPLC grade, Alfa Aesar) for preparing solvent systems (eluents) with 0.5, 1, and 1.6 wt% LiCl, respectively. Each solution was stirred on a magnetic stirrer for 2 h prior to be added in the GPC system for calibration and analysis.

Samples
The choice to study unaged and severely, naturally aged samples intended to represent museum objects in various ageing states, and assist in developing one method for all conditions including the extremes. Both types of materials were plasticised with camphor: a new, recently manufactured, and commercially obtained Incudo Clear  (Fig. 1). The latter was embrittled, cracked, crazed, crumbled, and yellowed. Sampling sites were obtained from the full thickness of the unaged sheet and as crumbled pieces fallen off the naturally aged sheet ( Fig. 1 in red).

Sample preparation
Three replicates of each sample in solution for both unaged and naturally aged CN were prepared in each of the three different eluents (see 2. 3): 0.1, 0.2, and 0.3 wt% CN corresponding to 1, 2, and 3 mg CN in 1 mL eluent.
Although CN was not expected to degrade in the LiCl/DMAc, it could display time-dependent degradation resulting from contact with residual acids from its nitration process [16]. To avoid this influencing the molecular weight and MWD of samples, while allowing enough time for complete dissolution, all samples were analysed 24 h after preparation. During this timeframe, the polymer chains were expected to form into balls of diameters corresponding to their molecular weight (https://www.agilent.com/cs/library/slidepresentation/ public/1-Conventional_GPC_-_Polymers_ans_ Molecular_Weight.pdf). Before analysis, sample solutions were manually agitated to separate potential aggregation of CN macromolecules that could influence the chromatographic separation, especially at such low LiCl concentrations [18]. Samples were filtered through a poly (tetrafluoroethylene) filter (PTFE, pore size 0.2 μm, diameter 25 mm, VWR) to remove any insoluble material and impurities.

Instrumentation
A SECcurity 2 -GPC system (PSS, Mainz, Germany) with a 1260 isocratic pump was used to achieve a LiCl/DMAc solution flow rate at 1 mL/min. A set of GRAM separation columns, one precolumn, one 30 Å and two 10 000 Å (PSS) were maintained at 60 • C. The columns were packed with polyester copolymer network particles. A SECcurity 2 GPC1260 Refractive Index detector (RID) was maintained at 40 • C and used at a range setting of 1.00-1.75 RI. Data acquisition was performed with WinGPC UniChrom Software (PSS).

Analysis
To measure molecular weight and its distribution of sizes, the weight average molecular weight (M w ) and the polydispersity index (PDI) were employed here. Calibration was carried out for each of the three LiCl/DMAc systems using ReadyCal-kit poly (methyl methacrylate) standards (PSS) of well-characterised peak M w (1 890 000; 936 000, and 592 000). Calibration data (maxima of all peaks for all three standards) used a fifth order polynomial fit function to generate a plot of M w versus elution volume, known as the calibration curve. The curve matched the M w of sample fractions (during analysis) to the M w of standards (during calibration) eluted at the same retention volume [16,23]. A sample solution of 100 μL was injected in the system. All chromatograms were processed and interpreted by the same operator to enhance repeatability of data.

Statistically designed experiments
A multilevel full-factorial experiment was designed and analysed in triplicate with the use of Minitab R 17 (n = 54 measurements). The factors considered critical for GPC analysis of CN were sample condition, sample concentration, and salt concentration with factorial levels: unaged and naturally aged, 0.1, 0.2, or 0.3% CN and 0.5, 1, or 1.6% LiCl, respectively. DOE allowed the simultaneous investigation of factors and their interactions, minimising the number of measurements [30] and, in turn, replicates needed for evaluation of results [31]. Analysis of Variance (ANOVA) of DOE was performed on the GPC numeric data (M w , PDI) and their standard deviations (StDev) to identify factors that influenced the analysis. A quantitative understanding of the factors was integral to applying DOE to method development and achieving optimal GPC results [24]. ANOVA paired all sample data, compared their mean values and used variation in their responses to determine their significance, set at P = 0.05 with a 95% confidence. If the P-value was less than the significance level (P < 0.05), it confirmed high probability of a statistical difference between factorial levels [32].
Once statistical difference was demonstrated, a Tukey's honestly significant difference (HSD) posthoc test was run to locate where the significant effect occurred. Tukey's HSD was selected for being sensitive to comparison of two levels at a time. It allowed simultaneous comparisons by examining random variation between any pair of means (standard error or HSD) and using it to compare all pairs against it. If a difference in means was greater than HSD then it was significant [32].

Averaged molecular weight values
Results of GPC measurements of CN replicates prepared in different sample and salt concentrations in DMAc are presented in Table 1. CN as a polydisperse substance, contains polymer chains of varying lengths, and thus, a wide range of molar masses [33]. Unaged samples -except for 0.1% CN-displayed averaged M w between ca. 230 000 and 280 000 g/mol, while naturally aged samples between ca. 14 000 and 17 000 g/mol. The unaged samples prepared with 0.1% CN showed very inconsistent M w values, almost double that of the rest. This is further discussed in Section 3.2. The decreased M w values of severely, naturally aged CN were attributed to scission of the glucosidic links that cause shortening of the main polymer chains [1,4,13,34]. M w values of unaged samples are in accordance with most commercial (low-nitrated) CN products, whose values range between 20 000 and 250 000 g/mol [35]. The naturally and severely aged samples displayed M w similar to a wide range of CN museum objects (14 000-82 000 g/mol) studied by [1] and [7]. The latter study favoured the use of degree of polymerisation, so, to enable data correlation here, the M w values were extrapolated from the relevant calculation available in that study. Figure 2 shows the chromatograms of all CN in different sample and salt concentrations, highlighting differences in molecular chain length due to their ageing state. This is visible as a change in retention time (RT) of the CN peak; shorter (degraded) chains eluted later at higher RT [36]. A shift is demonstrated in the peaks' position from around 18 min for unaged samples to 23 min for naturally aged samples. This was attributed to chain scission that occurred during natural ageing. This shift toward lower M w with ageing was consistent in all sample and salt concentrations. It was observed that higher CN concentrations led to higher absorbance (from ca. 0.0030 for 0.1% CN to ca. 0.0050 for 0.2% CN and 0.0065 for 0.3% CN).

Molecular weight distribution curves (chromatograms)
Replicates prepared with 0.1% CN displayed large variation in absorbance, shapes of curves, and RT of the CN peak ( Fig. 2A). More specifically, one of the unaged triplicates prepared in 0.5% LiCl formed a second peak at a lower M w , whereas all unaged and aged samples in 1.6% LiCl eluted at different times. A possible explanation for this data dispersion may be that the CN concentration was too small to allow bonding with the LiCl/DMAc ions (see Section 2.1), leading to the sample's insufficient dissolution and possibility of aggregate formation [14,37]. The exact reason for these additional peaks and inconsistencies in the chromatograms within triplicate sets was difficult to determine, but they indicated that the concentration of 0.1% was inadequate for sample preparation and could lead to false interpretations. The 0.1% CN was therefore disregarded but was kept throughout this investigation to enable the pairwise statistical interpretation of the other concentrations.

Broadness of molecular weight distribution (Polydispersity index)
The reduction of M w was accompanied by a change in the shape of curves (see Fig. 2), indicating a change in MWD with ageing. To illustrate this, the measure of the MWD broadness expressed as PDI [13] is depicted in Fig. 3. In ca. two of three aged samples, the PDI showed a small decrease, suggesting that MWD became narrower with ageing. The opposite tendency was observed for 0.2% CN in 0.5% LiCl, where the PDI slightly increased indicating that MWD became slightly broader with ageing. This could be attributed to an increase in the number of smaller M w chains [13].
The lower limiting value that PDI could achieve was 1, denoting uniformly monodisperse samples. PDI values close to 1 and below 2, observed in most samples in this study, represented a narrow distribution [14,24,25]. Naturally aged samples showed less consistency in distribution between replicates, evidenced by the larger StDev values.

Averaged molecular weight values
According to ANOVA of M w and its StDev, sample condition had a statistically significant impact on the analysis (M w P < 0.00; M w StDev P = 0.020), as evidenced by the large M w difference between unaged and naturally aged samples. Their statistical significance was confirmed by Tukey's HSD through comparison of their M w and StDev mean values; unaged and aged samples were allocated unique letters (A, B) denoting that their mean values were significantly different (Table 2).

Broadness of molecular weight distribution (Polydispersity index)
Results of ANOVA for PDI are presented in Fig. 4A, depicting the main effects of factors as lines connecting points. A main effect is the difference in the mean response  influence of CN% and LiCl% on the outcome, as well as on each other, was examined next (Fig. 4B). Points represented the PDI mean values of triplicates per factorial level and lines connecting them showed the difference in the mean response. According to Fig. 4B Tukey's HSD was powerful enough to find significant differences between PDI means of CN concentration levels, even though ANOVA showed no significance (P > 0.05). Comparing the means of different CN concentrations, Tukey's HSD allocated unique letters (A, B) to the significantly different samples with 0.1 and 0.3% CN ( Table 3). The next step was to examine if the effect of 0.3% CN was positive by comparing their mean PDI values from Fig. 4A. The 0.3% CN had an overall tendency of offering the highest PDI among concentrations (Fig. 4A), thus, negatively impacting the analysis. An exception to that was 0.3% CN in 1% LiCl, which presented among the lowest PDI (see Fig. 4B).
The 0.2% CN shared letters A and B with the other concentrations (Table 3), therefore, displaying no statistical significance. Similarly to the 0.3% CN, the lowest PDI for 0.2% CN was offered in 1% LiCl (see Fig. 4A). Given that the 0.2 and 0.3% CN displayed equally low PDI values when prepared in the same LiCl concentration, and the aim of this study was to miniaturise the sample amount as much as possible, the 0.3% was excluded and the 0.2% CN further scrutinised.

Selection of sample and salt concentrations
To determine the optimal LiCl% for preparation and analysis of 0.2% CN, emphasis was placed on the consistency of the M w and PDI values (StDev). In the chromatograms, the greatest consistency and repeatability of the 0.2% unaged and naturally aged triplicates was seen in 0.5% LiCl (Fig. 2B, solid line). This was confirmed by their M w StDev, which displayed the smallest values among the different LiCl concentrations ( Table 1). The PDI of 0.2% CN, although showing the lowest value in 1% LiCl, showed the greatest consistency in 0.5% LiCl for both unaged and aged material (see PDI StDev, Table 1). This result satisfied the requirements of this study to locate a salt concentration low enough to avoid influencing the chromatographic separation or contamination, and high enough to dissolve both unaged and aged CN. Therefore, 0.2% CN in 0.5% LiCl/DMAc was selected as the optimal parameter combination for offering the most consistent results.

Limitations and further research
Even though the method suggested in this study contributes to the optimisation of sample preparation of CN museum objects and therefore to the improvement of their analysis, further attention should be placed on developing analytical and data evaluation methods. Differences in the M w values documented by different research groups are attributed to variations in the experimental conditions (e.g., columns, calibration, sample concentration, eluent, temperature of columns, and RID), which influence the molecular conformation (i.e., the amount of unperturbed chains) [27,38]. GPC is not only a method, but a user-dependent technique, which reduces its reproducibility among different analysts/operators [14]. A study of nine laboratories using the same method to analyse CN showed that some of the reasons for their low data reproducibility were the lack of a definition of similar and "good" baselines and setting limits in the obtained raw chromatograms [11,14]. The number of available analytical GPC settings and processing conditions have limited the interpretation of data and rendered their discussion challenging. This often leads to the need of placing emphasis on the relative interpretation of data, rather than focusing on the absolute numeric values.
Further research should focus on developing standard operation and measurement protocols, as well as determining commonly accepted practices for data interpretation. It is hoped that more researchers will implement the sample preparation method suggested here in their protocols to render more studies comparable.

CONCLUDING REMARKS
This article presented the testing and statistical analysis of critical parameters to the GPC analysis of CN plasticised with camphor, leading to an optimised sample preparation method developed with the least amount of material possible and a nondegrading LiCl/DMAc solvent system with a suitable salt/solvent ratio for dissolving fresh and severely aged material. The results indicated that 0.1% CN was inadequate for sample preparation in all tested LiCl concentrations, evident from inconsistencies in the M w values, chromatograms, and the formation of additional peaks. The use of statistical DOE provided a data-driven method optimisation, reassured balanced results, avoided systematic and random errors, and rendered the suggested GPC method repeatable. Statistical analysis performed on M w , PDI, and their StDev, demonstrated that the 0.2 and 0.3% CN often behaved similarly by offering the lowest PDI values, but the latter negatively impacted the results by displaying the broadest MWD.
Given the aim of this study to miniaturise the sample (and salt) amounts, the 0.3% CN was discarded and the 0.2% further examined; in 0.5% LiCl/DMAc it offered the most consistent data for all samples. Therefore, these parameters are indicated as optimal for GPC analysis and are recommended for monitoring MWD changes. The newly developed method will support the characterisation of the ageing behaviour of celluloid objects in museum collections and the assessment of effectiveness of different storage conditions.

A C K N O W L E D G M E N T S
This research was carried out at the Conservation Science Department, Deutsches Museum as part of a three-year project on the cold storage of CN artefacts (Grant agreement No. 34790/01) (https://www. deutsches-museum.de/en/research/forschungsbereiche/ sammlungen/restaurierungsforsch/cold-storage-of-mus eum-objects), supported by the German Federal Environmental Foundation (Deutsche Bundesstiftung Umwelt). We would like to thank Christoph Heiner for kindly donating the naturally aged CN sheets and Dr Joy Mazurek at the Getty Conservation Institute for her advice. We appreciate the discussions with experts at PSS, in particular Dr Peter Montag for his valuable collaboration and technical support. Dr Kavda would like to thank the Deutsches Museum Research Institute for the opportunity to carry out this research and for financially supporting her through the Scholar-in-Residence programme.