An experimental study on distinguishing gel pen ink stains using desorption electrospray ionization mass spectroscopy combined with the K-means algorithm

Abstract

In the realm of document examination, the identification of suspicious alterations to handwritten documents is an important factor in case characterization. Investigating the differences in gel pen ink compositions has significant implications. In this study, we used desorption electrospray ionization mass spectrometry (DESI-MS) to analyze the ink compositions of gel pens. The methodology involved the following steps. (i) Sample selection: a total of 227 gel pens available in the market were procured for the study. (ii) Pre-experimental parameter exploration: preliminary experiments were performed to optimize the experimental parameters. (iii) Analytical technique: DESI-MS was used to collect compositional data from the gel pen ink samples, without requiring pre-treatment of the samples. (iv) Data analysis: the obtained data were analyzed using the Davies–Bouldin index, Calinski–Harabasz index, and K-means algorithm for ink sample classification. The experimental findings indicated that DESI-MS is a viable method for examining the ink compositions of gel pens. Notably, the testing process is minimally destructive and does not necessitate pre-treatment of the samples. Furthermore, variations in the ink compositions were observed among different models of gel pens within the same brand, and the extent of the variation in the composition varied across brands. Additionally, there were instances in which the ink compositions of different brands of gel pens exhibited similarities.

Introduction

The addition to and alteration of handwritten documents are ubiquitous tactics in document forgery, and they are frequently observed in instances of contract fraud, the falsification of financial negotiable instruments, and tampering of files. In this context, determining whether suspicious handwritten documents have been subjected to addition or alteration is a challenging task in forensic science. Common writing pens include fountain pens, water pens, and ballpoint pens, and gel pens are a type of ballpoint pen [1]. The popularity of gel pens can be attributed to a number of advantages, including portability, smooth writing mechanics, lightfastness, and waterproof properties [2], making them internationally favoured writing tools. The composition of the ink of gel pens includes a blend of solvents, colourants, surfactants, lubricants, emulsifiers, and assorted additives. Critically, these formulations exhibit variations across different brands. Such nuances in the composition are crucially important for discerning the presence of alterations within suspicious documents [3].

Conventional methods for the analysis of ink predominantly rely on infrared light detection, fluorescence detection, ultraviolet light detection, and other optical detection techniques. While these methods provide rapid and nondestructive evaluation, their ability is restricted to distinguishing between organic-dye ink and carbon-pigment ink.

There is a burgeoning body of research using thin-layer chromatography [4], ultraviolet–visible spectrometry [5], liquid chromatography mass spectrometry [6], Raman spectrometry [7], time-of-flight mass spectrometry direct analysis [8], and laser resolving mass spectrometry [9] for the analysis of additive handwriting. However, these methodologies often require cumbersome operational procedures or intricate pretreatment protocols, and they are infrequently used in practical identification scenarios.

Desorption electrospray ionization mass spectrometry (DESI-MS) [10] has emerged as a prominent in situ open mass spectrometry technique in recent years. This method obviates the need for elaborate pretreatment processes and enables the direct analysis of the ink composition on a substrate in an open environment (Figure 1). Notably, the consumption of the analyte during the testing process is minimal, typically on the order of micrograms. Owing to its attributes of in situ analysis, expeditiousness, high molecular specificity, and near nondestructiveness, DESI-MS has significant advantages in forensic applications [10]. There have been numerous reports on the use of mass spectrometry for the examination of writing ink stains, but most of these studies have focused on ballpoint pen ink. There has not been a comprehensive comparative analysis of gel pen ink stains with a large sample size.

In this study, we investigated the applicability of DESI-MS to the ink analysis of gel pens. Experiments of a comprehensive selection of gel pens comprising 227 models from 23 prevalent brands of gel pens available in the market were performed. The objective of this study was to perform an in-depth analysis of gel pen ink using DESI-MS technology and to classify the ink compositions of different brands and models through the K-means algorithm. This research aims to provide an effective tool to detect additions to and alterations of documents for forensic document examination. By combining advanced mass spectrometry techniques with unsupervised learning algorithms, this study provides a novel approach for gel pen ink analysis, which boasts higher specificity than traditional optical detection methods and is nondestructive.

Materials and methods

Sample preparation and examination

Before beginning the specific experiments, we first performed the selection and preparation of samples to ensure the representativeness of the data and the reproducibility of the experiments. A comprehensive set of 227 models of black gel pens from 23 distinct brands was assembled. The details are given in Table 1. Subsequently, three specimens of each model were procured for experimentation.

A rectangular ink mark measuring approximately 0.7 × 2.0 cm was inscribed on APP brand SANXIN Topgun A4 paper (Yalong Paper Products, Co., Ltd., Kunshan, China) with a grammage of 70 g/m², using the gel pen. The paper specimens bearing the ink marks were then stored in a ventilated, cool, and dry environment for a duration of 7 days.

To facilitate subsequent classification, we first performed a preliminary classification of the samples using a document examiner (Foster + Freeman VSC8000). Infrared light examination of the samples was performed using infrared light with wavelengths of 830 and 850 nm. The analysis revealed the distinct characteristics of the ink compositions of the examined gel pens.

Of the 227 gel pen models evaluated, 179 contained carbon-pigment-based colourants, showing pronounced absorption of infrared light, 39 models were identified to contain feature-dye-based colourants, exhibiting diminished absorption of infrared light, and 9 models contained a blend of pigment-based and dye-based colourants, demonstrating attenuated absorption of infrared light [11].

Notably, the gel pens characterized as carbon-pigment-based or mixed-colourant-based exhibited an augmented absorption rate of infrared light, concomitant with high carbon content in the ink composition. Accordingly, the gel pens can be classified into three main categories: mixed-colourant type, dye-colourant type, and pigment-colourant type.

Instruments and reagents

The main analytical instrument used in this study was a Thermo Fisher Exactive Plus mass spectrometer (Thermo Scientific, San Jose, CA, USA).

A custom-built DESI ion source was used, comprising a spray capillary, an electrically controlled platform, a platform control unit, an injection needle, and a peristaltic pump. This ion source was seamlessly integrated with the inlet port of the mass spectrometer.

High-purity methanol (99.999%, HPLC grade; Honeywell, Charlotte, UC, USA) and formic acid (98%, HPLC grade; Sigma-Aldrich, St. Louis, MO, USA) were used as solvents. All of the chemicals were used without prior purification.

Instrument working conditions

The mass spectrometer parameters were as follows: positive ion mode sampling and mass resolution of 70 000. The capillary temperature was maintained at 275°C, with a microscan of 1 and a maximum ion injection time of 270 ms. The ions within the mass-to-charge (m/z) range of 40–900 were sampled.

The nebulizing solvent used was a methanol solution containing 0.01 mmol/L formic acid [12]. For the external auxiliary gas, nitrogen (N₂) was used, with the air pressure set to 0.6 MPa. Notably, the distance between the paper surface to be analyzed and the tip of the spray capillary was maintained at 1.6 mm. The distance between the spray capillary and the extension tube of the mass spectrometer inlet were set to 4 mm, ensuring alignment within the same vertical plane. The spray impingement angle was fixed to 50°, with a spray voltage of 4.5 kV.

After preparing the samples, we optimized the parameters of the mass spectrometer to ensure consistent and comparable data across the different types of gel pen ink. The atomization gas flow rate in the DESI ion source significantly influenced the ink blotting during testing. An insufficient flow rate could result in larger droplet volumes, decreasing the solvent charge per unit volume and reducing the desorption efficacy. Conversely, an excessively high flow rate could exacerbate the ink blotting. While previous studies on DESI ion source application for ink blotting have mainly focused on ballpoint pen ink, with atomization gas flow rates ranging from 1 to 10 μL/min [13], this study aimed to explore the optimal flow rate for testing gel pen ink blotting. One-way variable experiments were performed with various flow rates within the above range. Considering the differences in the blotting resistance among mixed-colourant-based, dye-colourant-based, and pigment-colourant-based inks, ink samples from each type were subjected to atomized gas flow rates of 10, 7, 5, 4, 3, 2, and 1 μL/min. Ultimately, a flow rate of 5 μL/min gave the optimal ionization effects while mitigating the ink blotting.

Inspection process

The sample was positioned flat on the electrically controlled platform, ensuring its uniformity and stability. Subsequently, the electric control platform was manoeuvred to position the handwriting sample directly beneath the spray capillary tip. Upon activation of the spray and high voltage, the designated area for handwriting inspection was selected.

The electric control platform was then set to traverse horizontally, proceeding line by line at a constant rate of 2.4 cm/min. Each sample underwent a purging process for 1 min, facilitating the optimal conditions for analysis.

Data processing

The large number of samples and extensive data captured for each sample present challenges in effectively classifying the gel pen ink samples solely based on their mass spectra. Consequently, a process of data normalization and dimensionality reduction were performed to distil the most pertinent features. Subsequently, unsupervised classification and recognition algorithms were used to reveal the potential relationships among the different gel pen ink components. The K-means algorithm, an unsupervised machine learning technique, was used for clustering the ink composition data. This algorithm partitions the dataset into distinct clusters by minimizing the variance within each cluster, making it an ideal choice for classifying the diverse ink types based on their DESI-MS profiles.

The initial step involved randomly selecting numerous scanning points from the mass spectrometry data of the ink samples for each grade, forming a comprehensive dataset. Subsequently, the signals corresponding to blank paper were subtracted to eliminate any interference arising from the paper substrate. Data normalization was performed using the mapminmax algorithm to standardize the ink intensity values, minimizing the biases during classification. Dimensionality reduction was performed using principal component analysis to extract the most significant features from the mass spectrometry data. The Davies–Bouldin index (DBI) and Calinski–Harabasz index (CHI) were chosen as evaluation metrics because of their ability to assess the compactness and separation of clusters, ensuring the robustness of the K-means clustering process. The entire analytical process was performed using MATLAB software (https://www.mathworks.com/), leveraging common methods for analyzing the mass spectrometry data readily available within MATLAB’s function library.

Results and discussion

Gel pen categorization

Cluster analysis of the sample data encompassing mixed colourant, dye colourant, and pigment-colourant types of gel pens was performed. Initially, the optimal parameters for the cluster analysis were determined by evaluating the DBI and CHI. The DBI achieves maximum cluster analysis validity at its minimum value, while the CHI attains maximum validity at its maximum value. Following a comparative assessment, the optimal parameters were selected and used for clustering. The specific grades within each gel pen type are enumerated and tabulated in Table 2.

Given spatial constraints, a representative mass spectrum for each gel pen sample type is shown in Figure 2.

Comparative analysis of the ink compositions among different brands

From statistical analysis (Figure 3), the Pilot brand exhibited the most significant internal differences and largest numbers of categories. The Pilot brand includes 16 models of gel pens, encompassing dye-based types 1 and 2, as well as pigmented types 1, 3, 5, 9, 11, 12, 14, and 15. Conversely, the DELI gel pens were categorized as dye-based type 2 and pigmented types 1, 2, 3, 7, 8, 11, 12, and 15. In contrast, the KOKUYO, BEIFA and Faber-castell gel pens showed the fewest internal differences and categories. The KOKUYO gel pens were exclusively categorized as pigment-based type 3 and 9, the BEIFA gel pens were solely categorized as dye-based type 2 and pigment type 13, while the Faber-castell gel pens were categorized as dye-based type 2 and pigment type 9.

To analyze the compositional differences within each brand, a stacked bar chart was generated, representing all of the gel pen models categorized by ink composition type (Figure 3). In Figure 3, the brand name is the horizontal axis, the number of models is the vertical axis and the distinct colour stratifications on the bars indicate the various ink composition categories.

From statistical analysis, the dye type 2 category showed the highest representation among the brands, comprising gel pens from 13 distinct manufacturers: AIHAO, DELI, Truecolor, BAOKE, UNI, PILOT, SIMBALION, Sakura, Premec, Faber-castell, BEIFA, and Comix. Conversely, several categories contained only a single brand, such as mixed type 2 (GENVANA), mixed type 3 (Zebra), and pigment type 6 (Truecolor).

To further assess the compositional similarities across the different brands, stacked bar charts were generated for all gel pens based on their classification, as seen in Figure 3. Each chart features the ink composition category on the horizontal axis and the number of models on the vertical axis. The distinct colour stratifications within the columns denote the presence of different brands.

These classification results indicate that the combination of DESI-MS technology and the K-means algorithm can effectively differentiate the ink compositions of different models and brands of gel pens, validating the hypothesis proposed in the Introduction section. It is noteworthy that the Pilot brand exhibited the most significant internal differences and largest numbers of categories. Although the PILOT, AIHAO and COMIX brand gel pens could be all divided into 10 categories, the PILOT brand contained the minimum number of models These findings support our assessment of the potential of DESI-MS technology in ink analysis.

Conclusion

In this study, we investigated the applicability of DESI-MS for analyzing ink samples from gel pens. Without any sample pretreatment, ink composition data were collected from 227 grades of gel pens using DESI-MS. We identified the ion peak m/z values from the ink samples and classified the gel pens using the DBI and CHI metrics, along with the K-means algorithm.

Ultimately, we classified the nine mixed-colourant-type gel pens into three categories, the 39 dye-colourant-type gel pens into five categories, and the 179 pigment-colourant-type gel pens into 15 categories, demonstrating the efficacy of DESI-MS in classifying the ink stains from gel pens. Furthermore, visual inspection revealed no observable diminishment or blotting phenomena in the ink samples following DESI-MS analysis, indicating minimal damage by the technique.

Our analysis of ink samples from 23 brands of gel pens revealed variations in the ink compositions among different models within the same brand. Moreover, while there were differences in the ink compositions among different brands, there were also instances of similar compositions among different gel pen brands.

In conclusion, through the extensive analysis of 227 gel pen ink samples, we have validated the potential of combining DESI-MS with the K-means algorithm for differentiating gel pen inks. Future research could increase the sample size and explore the application of this technology to other writing instruments.

Acknowledgements

The authors extended their gratitude to the Anhui Public Security Department and the Institute of Forensic Science, Ministry of Public Security, China, for their funding and support that facilitated this research. Additionally, the authors would like to express thanks to Ms. Ying Chen, a PhD. candidate, and Guangming Huang from the Department of Chemistry at the University of Science and Technology of China, for their guidance throughout the data analysis process and for their contributions to the preparation of this manuscript.

Authors' contributions

Yiting Yuan conceived the study, conducted the experiments, analyzed the data, and drafted the initial manuscript; Yu Tao provided significant assistance in revising the manuscript; and Da Qin designed the research framework and contributed to the drafting of the manuscript. All authors contributed to the final text and approved it.

Compliance with ethical standards

This article does not contain any studies with human participants or animals performed by any of the authors.

Disclosure statement

No potential competing interest was reported by the authors.

Funding

This work was supported by the Anhui Provincial Key Research and Development Project [grant number 202104d07020007] and the Fundamental Research Funds of Institute of Forensic Science, MPS [grant number 2023JB014].

References