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Article

Raman Spectroscopic Classification of Polyethylene Glycol Samples of Varying Molecular Weights Using Machine Learning

by
Thomas J. Tewes
,
Ciara N. Duismann
,
Udita Singh
,
Peter F. W. Simon
and
Dirk P. Bockmühl
*
Faculty of Life Sciences, Rhine-Waal University of Applied Sciences, Marie-Curie-Straße 1, 47533 Kleve, Germany
*
Author to whom correspondence should be addressed.
Molecules 2026, 31(5), 778; https://doi.org/10.3390/molecules31050778
Submission received: 2 February 2026 / Revised: 18 February 2026 / Accepted: 22 February 2026 / Published: 26 February 2026
(This article belongs to the Special Issue Recent Advances in Structural Characterization by Raman Spectroscopy)
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Abstract

Polyethylene glycol (PEG) is a widely used water-soluble polymer (WSP) whose properties such as crystallinity depend on molecular weight. This study explores whether Raman spectroscopy, combined with supervised machine learning, can differentiate PEG samples of defined molecular weights within the investigated molecular weight range. Eight PEG materials with molecular weights ranging from 1000 to 35,000 g/mol were analyzed by confocal Raman microscopy under standardized conditions. A Support Vector Machine (SVM) classifier achieved 93.4% accuracy in five-fold cross-validation and 72.6% on an independent test set, confirming that molecular-weight-dependent vibrational signatures are present in the Raman spectra. Principal component analysis followed by linear discriminant analysis (PCA–LDA) models supported these findings, revealing that discriminative information arises mainly from line-shape and shoulder regions rather than from peak centers, consistent with gradual increases in conformational order. Although sample morphology and drying behavior introduce variability, the results demonstrate that Raman spectroscopy provides a reproducible, non-destructive means of distinguishing between PEG samples of different molecular weights. The established workflow provides a foundation for future quantitative evaluations of spectral trends, cross-polymer generalization, and adaptation to variable measurement conditions to enhance applicability in analytical and industrial contexts.

1. Introduction

Polyethylene glycol (PEG) is a synthetic, water-soluble polymer (WSP) of high industrial and biomedical relevance [1]. Its biocompatibility [2], non-/low toxicity [3,4,5], and physicochemical versatility [3,6] have turned PEG into the gold standard in diverse fields ranging from pharmaceutical formulations [3] and surface functionalization [7] to tissue engineering [8] and diagnostics [9]. A central aspect governing PEG’s function and applicability is its molecular weight: low-molecular-weight PEGs (<1000 g/mol) are commonly used as solvents [10], dispersants [11], or excipients [12]. In contrast, medium- to high-molecular-weight PEGs (≈4000–20,000 g/mol) are used as viscosity modifiers [13,14], whereas higher variants (≥20,000 g/mol) can serve as macromolecular carriers [15] and are frequently involved in hydrogel formation [16]. The ability to control and verify the molecular weight of PEG is thus crucial for ensuring reproducibility, performance, and regulatory compliance in both research and production environments [1,11,17].
Molecular weight determination of PEG is traditionally performed using established techniques such as size exclusion chromatography (SEC) [18,19], viscometry [20], or mass spectrometry [21].
Raman spectroscopy offers a label-free, non-destructive analytical approach capable of probing molecular vibrations with high specificity [22,23]. Its sensitivity to subtle differences in molecular conformation, bond environments, and intermolecular interactions has led to its increasing use in polymer research, including material identification, crystallinity analysis, and degradation studies [24,25,26,27]. In the case of PEG, however, the ability of Raman spectroscopy to reflect systematic molecular-weight-dependent spectral trends has not been clearly established. Experimental studies demonstrate that Raman spectra of PEG samples with differing molecular weights exhibit discernible differences in peak intensities and positions, yet no consistent or broadly validated chemometric framework for molecular-weight-related discrimination is available. Authors emphasize the method’s potential but also highlight that the multitude of possible conformations, aggregation states, and the absence of standardized chemometric models complicate direct quantitative interpretation of Raman spectra in relation to molecular weight [23,28,29].
Raman spectral variations due to changes in chain length or molecular weight may be subtle and can overlap with physical factors such as film morphology, drying behavior, or water retention, especially for hygroscopic, low molecular weight PEGs. In recent years, low-frequency Raman (LFR) spectroscopy has been shown to provide direct access to longitudinal acoustic modes in polymers, which can be correlated with chain length and crystalline domain size [30,31,32]. Such approaches offer valuable structural insight into polymer architecture and have been successfully applied to molecular-weight-related investigations. However, LFR measurements require specialized instrumentation and optimized filtering close to the Rayleigh line, which is not universally implemented in standard confocal Raman microscopy systems [30,32].
The present study therefore does not aim to compete with or replace LFR methodologies. Instead, it evaluates whether molecular-weight-dependent information can be extracted from the conventional fingerprint region using widely accessible Raman configurations. In this spectral region, structural variations associated with chain length are expected to manifest as distributed and subtle changes across multiple vibrational modes rather than as a single diagnostic feature. Under such conditions, multivariate analysis becomes advantageous, as it allows the systematic integration of subtle spectral variations across different vibrational regions [33,34]. Within this context, if successful, a Raman-based chemometric model could provide a rapid, reagent-free, and potentially spatially resolved complement to established analytical techniques such as SEC or viscometry, particularly in scenarios such as quality control or materials screening.
The present study addresses this gap by investigating whether Raman spectral data, in combination with supervised machine learning models, can be used to reliably differentiate PEG samples of defined molecular weight. Support vector machines (SVM) were employed as a high-capacity model for nonlinear class separation, complemented by principal component analysis followed by linear discriminant analysis (PCA–LDA) to provide interpretable insights into the discriminative spectral regions. In the context of chemometric analysis, each molecular-weight sample was treated as a predefined “class”, following standard terminology in supervised machine learning. Both approaches have proven effective in spectroscopic pattern recognition and polymer analytics, allowing the evaluation of separability and spectral relevance across molecular weight classes. Eight PEG variants ranging from 1000 to 35,000 g/mol were prepared under standardized conditions and measured using confocal Raman microscopy. SEC analyses were performed separately to verify the nominal molecular-weight information provided by the manufacturer. Classification models were developed and validated on independent test sets, with a focus on evaluating their accuracy and robustness. In doing so, we aim to bridge molecular-level variation in PEG with its analytical detectability, providing a basis for practical, spectroscopy-driven polymer characterization.

2. Results and Discussion

2.1. Reference Analytics Using Size Exclusion Chromatography (SEC)

To verify the nominal molecular-weight information provided by the manufacturer, all PEG reference samples were analyzed by SEC (see Section 3). The obtained molar-mass averages (Mn, MW) and polydispersity (Đ = 1.06–1.21) confirmed the expected monotonic increase with sample designation (Table 1). The measured values closely matched the specified ranges, validating the reference quality of the materials used throughout this study. For the classification models described below, the nominal molecular-weight labels (PEG01–PEG35k) were retained, because the study design is based on predefined molecular weight classes (i.e., the categories used in the classification models) rather than numerical mass values. The SEC data therefore confirms the internal consistency of the set of polymer samples. The complete SEC molar mass distributions are provided in Supplementary Material S1.

2.2. Raman Spectra and Unsupervised Pattern Recognition

2.2.1. Overview of Acquired Raman Spectra

As described in detail in Section 3, PEG samples covering eight defined molecular weights were used for model training. The molecular weights (or classes) are abbreviated in this study with 01k, 02k, 04k, 06k, 08k, 12k, 20k, and 35k (see Table 1).
For each polymer, 512 Raman spectra were collected for model training and 256 spectra for validation. In total, 6144 spectra were acquired: 4096 spectra for training and 2048 spectra as a test set for external validation. This test set is an independent dataset collected in a separate batch. The mean Raman spectra for all polymers, with only z-score normalization applied, are shown in Figure 1a; the complete set of individual spectra is overlaid in gray. A distinct transition is visible from broader bands for PEG01k–PEG06k to sharper features at PEG08k and above. Figure 1b shows the same data after mathematical preprocessing (see Section 3 in this study), following Tewes et al., 2024 [35]. All spectra are plotted with vertical offsets to improve readability. For PEG01k–PEG06k, there is a slight trend of decreasing variance of the individual spectra (gray) with increasing molecular weight (Figure 1b). The apparent transition around 08k reflects a shift in spectral characteristics under the specific preparation and acquisition conditions of this study rather than a universal physical threshold.
The z-score normalized Raman spectra of PEG35k and 01k reveal distinct intensity patterns and band sharpness across the spectral range (Figure 2). PEG35k exhibits narrower and more intense peaks, particularly at 843, 1061, 1124–1139, 1229–1236, and 1468–1485 cm−1, which is consistent with the higher molecular order and crystallinity typically observed in high-molecular-weight polymers and with Raman-crystallinity relationships reported for other polymer systems [36,37]. A quantitative assessment of crystallinity would require complementary techniques such as wide-angle X-ray scattering (WAXS). In contrast, PEG01k shows broader bands with reduced peak intensities, reflecting increased molecular mobility and a more amorphous character. Despite these differences, the overall band positions remain largely consistent, suggesting that the observed spectral variations predominantly reflect molecular-weight-dependent structural organization, while the chemical composition remains unchanged. Interestingly, Kuzmin et al. (2020) reported Raman spectra of solid PEGs between approximately 1500 and 6000 g/mol exhibiting distinct and sharp peaks, consistent with a higher degree of conformational order and crystallinity [28]. In contrast, our droplet-based preparation likely produces less crystalline, more amorphous films in this molecular weight range.
The distinct spectral features observed in Figure 2 are consistent with the band assignments summarized in Table 2. Characteristic vibrations such as C–O–C stretching, CH2 twisting and wagging, and C–C skeletal modes appear at comparable positions for PEG35k yet differ in relative sharpness and intensity. These variations can reflect molecular-weight-dependent differences in chain conformation and crystallinity, which become evident in the relative prominence of the bands near 843 cm−1, 1061 cm−1, and 1468–1485 cm−1. The combination of the spectral overview (Figure 2) and the detailed assignments (Table 2) provide a coherent basis for the subsequent interpretation of the PEG structure and order across molecular weights.
The observed molecular-weight-dependent increase in band definition is consistent with literature reports describing systematic structural and conformational changes in PEG with increasing chain length [28,29]. With increasing PEG chain length, crystallization behavior and structural ordering are known to change, as longer chains can form more stable crystalline domains and extended conformations, facilitating more ordered packing [38,39,40]. Vibrational modes in the 800–900 cm−1 region, including CH2 rocking and backbone-related motions, are sensitive to conformational order and molecular packing (Table 2). The progressive sharpening and clearer separation of bands in this region are therefore plausibly associated with increased structural organization at higher molecular weights. In the present study, these observations are interpreted qualitatively and not as a quantitative measure of crystallinity.
Table 2. Observed Raman peaks of polyethylene glycol (PEG) with corresponding Raman shift ranges, vibrational mode assignments, and literature references. All peaks were experimentally observed in PEG35k and assigned based on peer-reviewed sources.
Table 2. Observed Raman peaks of polyethylene glycol (PEG) with corresponding Raman shift ranges, vibrational mode assignments, and literature references. All peaks were experimentally observed in PEG35k and assigned based on peer-reviewed sources.
Observed Peaks [cm−1]Reported Ranges [cm−1]Typical Vibrational ModeReferences
534525–550C–C–O/C–O–C backbone bending (out-of-plane and in-plane components)[41,42,43]
580582C–C–O/C–O–C backbone bending[44]
843842–844CH2 rocking + C–O–C stretching (crystallinity-/chain-conformation-sensitive)[41,45]
858859C–C stretch + C–O stretch + CH2 rocking (helical conformation, monoclinic crystalline phase)[46]
932932Backbone C–C stretching (skeletal), likely crystalline contribution[46]
10611059–1060C–C backbone stretching (crystalline domains; coupled with C–O stretch)[45,46,47]
11241123–1124C–O–C symmetric stretching (νs) + CH2 twisting; sensitive to chain conformation and crystallinity[45,46,47]
1139~1136C–O–C symmetric stretching (νs) coupled with CH2 twisting; associated with gauche/helical conformation and monoclinic crystalline phase[46,47,48]
1229/12361227–1239CH2 wagging (δ) coupled with C–C stretching; conformation-sensitive (trans/gauche segments)[28,42,46,49]
12791275–1280CH2 twisting/wagging (δ, τ) vibration coupled with C–C stretching; sensitive to chain conformation and crystallinity[42,46,48,50]
13601350–1370CH2 wagging (δ)/deformation coupled with C–C stretching[46,51]
13941391–1397ω(CH2) wagging[46,52]
14461447δ(CH2) scissoring[52]
1468/1477/14851468–1488CH2 scissoring (δ(CH2)) deformation; symmetric and asymmetric components, weakly conformation-dependent but sensitive to local crystalline order[28,41,42,46,53,54,55]
ν = stretching (valence vibration), δ = deformation (bending includes scissoring, rocking, wagging, and twisting), τ = twisting, ω = wagging, and s = symmetric.
To provide a numerical complement to this qualitative assessment, selected Raman bands were evaluated in terms of peak position and full width at half maximum (FWHM) using the mean spectra of the calibration samples (Supplementary Material S2). The evaluated regions were selected based on their visual prominence (Figure 1). Across molecular weights ≥ 08k, peak positions remained largely stable, with minor shifts observed in the 1120–1140 cm−1 and 1440–1470 cm−1 regions. Changes in FWHM were subtle and not uniformly directional across all bands; for example, the band near 842 cm−1 showed negligible variation, whereas bands in the higher-wavenumber regions exhibited modest fluctuations in width. These quantitative differences are small and are interpreted cautiously within the framework of the present analysis.

2.2.2. Principal Component Analysis (PCA)

Because molecular-weight effects in PEG spectra are expected to be subtle, we used PCA as an unsupervised, variance-oriented exploration rather than a classifier. An initial PCA on all samples shows substantial overlap between molecular weights (Figure 3a), consistent with small effect sizes relative to measurement variability. Visual inspection indicated a distributional shift ≥ 08k (see Figure 1), so we computed two separate PCAs: 01–06k and 08–35k. For 01–06k, variance is spread across PCs with modest explained variance per axis (PC1 ≈ 14%, PC2 ≈ 12%, and PC3 ≈ 8%). This distribution reflects the high spectral similarity within this molecular weight range, where differences are subtle and spread across many wavenumbers rather than dominated by a single structural feature. Molecular-weight groups remain largely intermixed. The symbol coding separates individual datasets (“droplets”, see Section 3), and their wide dispersion illustrates both batch-to-batch variation and sample position-dependent effects.
For 08–35k, the structure becomes more pronounced. PC1 captures the dominant trend (≈75% variance; Figure 3c,d), and a coarse gradient among 08k, 12k, 20k, and 35k emerges, although groups still overlap. The zoomed and rotated view in Figure 3d emphasizes that between-dataset spread remains large relative to the separations between molecular weights. Across all subplots in Figure 3, the breadth of data clouds demonstrates a systematic influence of sample presentation and instrumental conditions on the Raman spectra. These non-chemical factors could outweigh the molecular weight signal, especially below 08k. Consequently, robust modeling requires large, heterogeneous datasets and/or highly standardized measurement conditions that capture this “natural” variability in data, and any supervised analysis should be validated with independent datasets to avoid over-interpreting minor unsupervised data separations.

2.3. Model Selection Rationale

In this study, a supervised classification model was developed to assign Raman spectra of PEG samples to one of eight predefined molecular weight categories (1000, 2000, 4000, 6000, 8000, 12,000, 20,000, and 35,000 g/mol). The approach focuses on qualitative discrimination rather than quantitative prediction, aiming to evaluate whether spectra contain reproducible features that permit class-wise differentiation.
A regression strategy was initially considered but not pursued further, as the dataset comprises only eight discrete molecular weight levels; although these values are more evenly distributed on a logarithmic scale, the limited number of distinct levels restricts the robustness of a regression-based approach. Under these conditions, a regression model would inherently require interpolation and extrapolation beyond the observed range, for which no independent validation is available within the current experimental design.
The classification model, by contrast, corresponds directly to the categorical structure of the dataset and allows robust, interpretable assignments to defined molecular weight classes. It thus provides a suitable basis for assessing class separation and spectral distinctiveness under standardized conditions. Quantitative modeling is reserved for future work once more continuous molecular weight data become available.
SVMs were selected as the modeling approach, as they have consistently performed well with a similar data architecture and preprocessing strategy in our previous studies. In earlier work, this approach proved effective for identifying subtle spectral differences among microorganisms [56] and for predictive modeling of cleaning performance in complex multivariate datasets [57]. The established robustness and adaptability of SVMs therefore make them well suited for the present classification task. A model including all molecular weight classes was computed and is referred to hereafter as the “global model”. To enhance the detection of subtle differences among the lower molecular weight samples (01–06k), an additional model was trained comprising only these classes, referred to as the “low-molecular-weight model”.

2.4. SVM Model Training and Validation

The global SVM model, encompassing all eight molecular weights (classes), achieved an overall accuracy of 93.4% in five-fold cross-validation and 72.6% on the independent test dataset. All 1015 spectral variables of each spectrum contributed to the classification without prior PCA. The confusion matrices for both cross-validation and external testing are shown in Figure 4, illustrating the agreement between predicted and true classes as well as the true positive rate (TPR) and false negative rate (FNR) across all classes. As shown in Figure 4, the five-fold cross-validation (a) demonstrated consistently high correct classification rates, with true positive rates (TPR) above 90% for most classes and near-perfect prediction for 08k, 12k, 20k, and 35k.
In the independent test (b), overall performance decreased, and the reduction was not uniform across classes. Predictions for PEG01k, PEG08k, and PEG12k remained strong, with TPR values of approximately 93–99%, while mid-range molecular weights (PEG04k and PEG06k) showed the largest declines, with TPRs dropping to 33% and 48%, respectively. These classes also exhibited higher false negative rates (FNR > 50%), indicating increased overlap with neighboring molecular weight categories. The systematic reduction in test accuracy relative to cross-validation suggests that the model captures relevant discriminative features but remains sensitive to spectral variability among independently measured samples. The reduced performance on the independent test set likely reflects additional batch-related variability not fully represented in the training data. This gap underscores the importance of incorporating broader preparation-induced variation when aiming for application-oriented robustness. Despite this, the classification results confirm that Raman spectra provide sufficient information for the robust discrimination of several PEG molecular weight classes under standardized measurement conditions.
It is important to note that misclassifications among the independent test spectra predominantly occurred between neighboring molecular weights. For example, PEG04k and PEG06k, which differ only moderately in average molecular weight, were most frequently confused (false negative rates above 50%), or PEG20k was mainly misclassified as PEG12k and 35k but seldomly as PEG08k. This trend suggests that the Raman spectral features change gradually with increasing molecular weight, leading to higher separability at the extremes and partial ambiguity between adjacent samples.
Since the Raman spectra (see Figure 1) clearly show systematic differences between the lower molecular weights (01k, 02k, 04k, and 06k) and the higher ones (08k, 12k, 20k, and 35k), separate sub-models were trained. For the higher molecular weight range, the hyperparameters of the global SVM model were retained (so the outcome is the same, like in the global model shown in Figure 4), while for the lower molecular weights, a submodel including a preceding PCA was implemented, retaining 16 principal components. This adjustment slightly improved prediction accuracy for several classes, most notably for PEG06k, which increased from 48.4% to 82.8%. Minor improvements were observed for PEG01k (93.4% to 94.9%), while PEG02k decreased slightly from 84.4% to 79.7%. A pronounced decline occurred for PEG04k, whose true positive rate dropped from 33.2% to 24.6% (Figure 5). For the low-molecular-weight submodel, a similar pattern was observed like in the global model (Figure 4); misclassifications in the independent test set occurred mainly between neighboring classes, such as PEG02k and PEG04k, whereas the lowest (PEG01k) and highest (PEG06k) classes within this subset were predicted with higher reliability. This behavior supports the assumption that the spectral transitions between adjacent molecular weights are continuous rather than discrete, and that model uncertainty is primarily concentrated around these intermediate regions. When using the submodels instead of the global SVM model, the overall test accuracy increased from 72.6% to 75.5%. This improvement results from the dedicated low-molecular-weight model (70.5% test accuracy) in combination with the unchanged high-molecular-weight model (80.4%), whose parameters were identical to those of the global model. The moderate overall gain indicates that a tailored representation of the low-molecular-weight spectra provides slightly better generalization, whereas the global model already captured the essential variance structure across the higher molecular weight range.

2.5. PCA–LDA of Molecular Weight Classes

As described above, SVMs are powerful tools for modeling complex multivariate datasets and can yield highly reliable predictions [56,58,59]. However, they are not inherently interpretable, and despite the existence of techniques to visualize or approximate feature relevance [60,61], SVMs are generally considered black-box models [62]. In contrast, methods such as PCA combined with LDA (PCA–LDA) offer a more transparent representation of spectral variance and class separation. Although PCA–LDA is typically less flexible in capturing non-linear relationships than SVM-based approaches [63], it facilitates a direct and interpretable visualization of class separation in reduced-dimensional space [64]. By plotting sample scores along the linear discriminants (LDs) or canonical variables, the separation performance of the model can be visualized (see Figure 6).
PCA–LDA was applied exclusively for exploratory interpretation of discriminative spectral regions and not for performance evaluation. For this purpose, calibration and independent test spectra were combined to capture the full variability of the dataset and obtain stable loading structures. As described above, there is a jump from 01k–06k to 08k–35k, so two independent models have been calculated for the low and high molecular weights.
In the low-molecular-weight PCA–LDA model (Figure 6a), PEG01k was clearly separated from the other classes despite its high within-class variance, while PEG04k and PEG06k exhibited substantial overlap, reflecting limited discriminative potential in this range. This trend corresponds to the performance of the global SVM, which also showed partial confusion between these classes. In the high-molecular-weight PCA–LDA model (Figure 6b), class separation improved overall, with PEG12k and PEG20k forming distinct clusters and only minor overlap toward adjacent classes. PEG35k appeared as two subclusters, indicating batch- or presentation-related variability and emphasizing the importance of comprehensive datasets to ensure model robustness.
Furthermore, by back-projecting the discriminant loadings into the original spectral space, analogous to how PCA loadings indicate variables contributing most to total variance, it becomes possible to identify specific wavenumber/Raman shift regions that most strongly influence the class separation. This facilitates the interpretation of which spectral features are most characteristic for the differentiation between molecular weights.
The canonical loadings derived from the LDA models (Figure 7) identify the Raman features most responsible for class discrimination. For the low-molecular-weight model (a–c), LD1 shows distinct positive and negative contributions near 530, 787, 887, 1020, and 1435 cm−1, corresponding to characteristic C–O–C and C–C stretching as well as CH2 deformation vibrations of PEG. These bands coincide with minor spectral intensity variations among PEG01–06k, reflecting subtle differences in chain conformation or segmental order rather than changes in overall composition. LD2 highlights additional peaks at approximately 443, 779, 856, 1153, 1224, and 1458 cm−1, capturing weaker or overlapping contributions that account for residual intra-class variance. The signal near 443 cm−1 does not correspond to a distinct Raman band but rather reflects a baseline-related fluctuation, likely arising from the minor intensity rise at the lower edge of the spectral range. A comparable feature is unexpectedly visible in the first loading of the high-molecular-weight model (see Figure 7d), even though the corresponding reference spectra remains close to the baseline in this region (Figure 7e). This suggests that the effect is not physically meaningful but most likely results from statistical weighting during LDA optimization, where small baseline variations can be amplified when overall variance is low in adjacent regions, a phenomenon reminiscent of feature amplification occasionally observed in convolutional neural networks (CNNs) [65].
In the high-molecular-weight model, Figure 7d–f, the dominant LD1 features occur at 937, 1080, 1165, 1311, and 1449 cm−1, overlapping with major PEG backbone vibrations but appearing more sharply defined. This smoother loading profile indicates reduced experimental variability and a stronger, more systematic spectral response with increasing molecular weight. LD2 displays secondary features around 522–547, 582, 797, and 1281 cm−1, representing minor orthogonal contrasts likely associated with presentation- or batch-specific differences.
Overall, the comparison of the canonical loadings with the mean Raman spectra shows that the main discriminative contributions arise almost exclusively from shoulder and interpeak regions rather than from the peak maxima themselves (the dotted lines drawn in Figure 7 illustrate this). This applies to both models and is particularly evident in the spectral ranges around 780–900, 1040–1160, and 1260–1490 cm−1. Physically and analytically, this behavior is plausible: differences between molecular weight classes manifest mainly as subtle band shifts, changes in bandwidth and line shape, and variations in relative intensity ratios. These effects produce the steepest gradients along the band flanks, while the peak centers often co-vary across classes and therefore contribute little to discrimination. Because all spectra were processed using an identical workflow including z-score normalization, absolute intensity scaling was removed and subsequent interpretation focused on relative band positions and line-shape variations rather than on peak height differences. The potential influence of the pre-processing pipeline on peak appearance was evaluated separately (Supplementary Material S3). Consequently, the loadings exhibit locally derivative-like patterns, reflecting sensitivity to subtle line-shape variations such as shoulders and troughs between major bands.
For the low-molecular-weight model, this explains the pronounced overlap of PEG04k and PEG06k: their line shapes differ only slightly in the most discriminative flanks, even though their overall spectral maxima are similar. In the high-molecular-weight model, the loadings are smoother and more focused, consistent with the sharper and more systematic spectral response observed for higher molecular weights. Baseline-related contributions at the lower edge of the spectral range (around 443 cm−1) are not spectroscopic features but minor baseline effects; a similar small feature in LD1 of the high-molecular weight model likely results from statistical weighting in regions of low variance. Overall, the loadings confirm that class separation arises primarily from molecular-weight-dependent organization and modulation of line shapes rather than from the appearance of new Raman bands. The consistent occurrence of discriminative features near the main PEG backbone modes suggests that increasing molecular weight primarily modulates the relative contribution and sharpness of existing vibrations, in line with increasing segmental order and crystallinity.
The spectral trends underlying class discrimination are most plausibly attributed to differences in conformational order and crystallinity rather than to variations in terminal group concentration. End-group-related vibrations of PEG (e.g., O–H stretching) lie outside (approximately 2830 cm−1) the analyzed fingerprint region and are therefore expected to contribute only marginally to the observed variance, particularly at higher molecular weights where end-group concentration is low [29,41]. In contrast, the discriminative wavenumber ranges identified in the loadings, especially 780–900, 1040–1160, and 1260–1490 cm−1, coincide with modes known to be sensitive to trans/gauche segmental orientation, chain packing, and crystalline domain formation (see Table 1). Hence, the ability of the models to differentiate molecular weights arises primarily from molecular-weight-dependent modulation of conformational order and crystalline fraction, rather than from compositional or end-group differences.

2.6. Limitations and Outlook

While this study was designed for high reproducibility and controlled comparability between molecular weights, several limitations must be acknowledged that may affect both spectral interpretation and model generalizability.
A first limitation concerns the sample mass and drying behavior. Even small deviations in the applied droplet mass could induce disproportionate changes in crystallization kinetics and microstructure formation. Spectra derived from droplets of different mass are not directly comparable, since variations in solidification behavior can alter film morphology and, in particular, layer thickness, which is known to affect Raman spectra [66,67,68]. Although the droplet deposition was standardized, minor variations in ambient humidity or subtle surface irregularities of the polished stainless-steel slides could have influenced nucleation and drying patterns. Such factors may partly explain the spectral variability within the low-molecular-weight series (01k–06k) and should be considered when interpreting discriminative model features. In extreme cases, even partial crystallization of PEG06k or lower molecular weights cannot be entirely ruled out. However, controlled crystallization could in principle be exploited to obtain more standardized and well-defined spectral features.
A second potential limitation relates to laser-sample interaction during Raman acquisition. At the thin-film scale, low-molecular-weight PEGs (01k–06k) with our methodology formed semi-transparent, gel-like layers after drying. Under these conditions, partial displacement of material by the laser focus can occur, especially near the droplet periphery. Supplementary Material S4 depicts the edge region of a dried PEG06k droplet, where a series of small cavities at the lower margin indicate mechanical displacement of the material caused by local laser interaction. As neither darkened zones nor carbonized residues were observed by visual inspection, it is reasonable to assume that the polymer was not thermally degraded. Corresponding spectra in Supplementary Material S4, recorded under comparable conditions, demonstrate how the Raman signal intensity gradually diminishes and eventually converges to a weak baseline, while no graphitic D or G bands indicative of carbonization appear [69,70]. The spectra in Supplementary Material S4 are presented without any pre-processing or normalization. Taken together, these observations verify that the local interaction results in material relocation rather than combustion. When this effect appears, data can still be collected closer to the droplet center where the effect is reduced/disappears. In rare cases where local displacement of the gel-like PEG matrix by the laser focus was observed, the acquisition window was gradually shifted inward across the total width of the 8 × 8 mapping (see Section 3) area to ensure stable signal conditions. This adjustment followed a consistent procedure and was applied uniformly to all low-molecular-weight samples. The overall frequency of such occurrences was low, yet the measure is reported here for completeness. It should be emphasized that spectral classification performance did not rely on positional differences, as all datasets were collected under identical instrumental conditions.
Another consideration is the choice of sample morphology. The study deliberately avoided direct measurements of the original PEG flakes or solid chunks, as minor batch-specific differences in granule size, porosity, or residual moisture could introduce confounding spectral features unrelated to molecular weight. Prior work demonstrated that even morphologically similar polymer fragments can yield distinct scattering profiles, most likely due to surface texture and packing density [23]. The droplet-drying approach used here therefore represents a compromise between analytical standardization and physical realism. Nevertheless, future data expansion could explore Raman models based on the native solid forms of PEG (including flakes, powders, and compact chunks), provided that sufficient sample diversity is available to statistically disentangle morphology-induced features from molecular-weight effects.
Overall, these limitations emphasize that spectral differences among the predefined molecular weight classes may not solely originate from molecular weight variation, but also from complex interplays between deposition dynamics, crystallinity, and local measurement conditions. Addressing these aspects in future work, through systematic variation of environmental parameters, improved surface control, and high-throughput replicates, will further clarify the mechanistic basis of spectral separation. Such refinements could ultimately support more direct, preparation-free classification workflows for industrial or environmental polymer analyses, thereby extending the applicability of the presented framework beyond controlled laboratory settings.

3. Materials and Methods

3.1. Polymers and Size Exclusion Chromatography

The PEG samples examined are listed in Table 3. Size exclusion chromatography (SEC) measurements were performed at room temperature using 1,1,1,3,3,3-hexafluoropropan-2-ol (HFIP) (EVOCHEM Advanced Materials GmbH, Offenbach, Germany) with potassium trifluoroacetate (Sigma-Aldrich Chemie GmbH Taufkirchen, Germany) (c = 0.05 mol/L) at a flow rate of 0.5 mL/min (Agilent 1260 isopump) as the mobile phase. One PSS PFG linear M column (5 μ; 8·300 mm, PSS GmbH, Mainz, Germany) was employed as the stationary phase. Concentration detection was performed by an Agilent 1260 refractive index detector (Agilent Technologies, Santa Clara, CA, USA) (λ = 930 nm). Samples of a typical concentration of 0.6 mg/mL were injected employing an Agilent 1260 autosampler (Agilent Technologies, Santa Clara, CA, USA) (injection volume 40 µL). To compensate for flow-rate fluctuations, 20 ppm of 2,6-di-tert-butyl-hydroxytoluene (BHT) (Sigma-Aldrich Chemie GmbH Taufkirchen, Germany) was added as internal standard to each sample. Raw data were processed using the PSS WinGPC Unichrom software package (Version 8.30, Build 8251). Elugrams are flow-rate corrected; polyethylene glycol calibration was used to determine the molar mass, and the resulting SEC molar mass distributions are shown in Supplementary Material S1 together with the corresponding averages listed in Table 1.

3.2. Standardized Workflow for Sample Preparation and Raman Spectral Mapping

For each sample, 10.0 ± 0.5 mg of the respective polymer was weighed into a sterile 1.5 mL microcentrifuge tube (Eppendorf AG, Hamburg, Germany) (Figure 8a); the individual weighing values are provided in Supplementary Material S5. Contamination during handling was carefully avoided. The polymer was dissolved in 500 µL of sterile ultrapure water (Direct-Q 3UV Water Purification System, Merck KGaA, Darmstadt, Germany) and vortexed (Vortex-Genie 2, Scientific Industries, Bohemia, NY, USA) for at least one minute, or until complete dissolution was achieved. To ensure homogeneity, the solution was additionally swirled manually and visually inspected prior to use (Figure 8b).
A polished stainless-steel microscope slide (Renishaw, Pliezhausen, Germany) was placed on a preheated drying device (Trockenplatte 2540, miacom diagnostics GmbH, Düsseldorf, Germany) set to 52 °C. This substrate was selected due to its high reflectivity and the absence of detectable intrinsic Raman features under the applied measurement conditions, as previously verified in our earlier work [56]. Two droplets of 1 µL each were then pipetted from the polymer solution onto the preheated slide (Figure 8c), using a fresh pipette tip for each droplet. The droplets were positioned vertically aligned and allowed to dry for 1.5 min. Samples were dried at 52 °C to ensure reproducible solvent removal and defined film formation under controlled conditions. This temperature setting was dictated by the fixed operating point of the drying device and was chosen to standardize the preparation across all molecular weight classes rather than to apply a controlled thermal treatment (e.g., annealing). Temperature-dependent changes in PEG chain conformation and order are known to affect Raman bands in the fingerprint region [45]; however, a systematic thermal study was outside the scope of this work.
After drying, the slide was transferred to the stage of the confocal Raman microscope system (inVia, Renishaw, Gloucestershire, UK) (Figure 8d). Each droplet was analyzed using a 20× lens (numerical aperture: 0.40), and four distinct regions were selected for Raman mapping, approximately located in the northern, eastern, southern, and western zones of the dried droplet (Figure 8e). At each of these four positions, an 8 × 8 mapping grid was defined with a point-to-point spacing of 20 µm (Figure 8f).
Raman measurements were performed using a 633 nm excitation wavelength Helium–Neon (HeNe) laser and an 1800 L/mm grating. Spectral acquisition parameters were standardized across all measurements using the WiRE 4.4 software (Renishaw, Gloucestershire, UK):
  • Spectral center: 1050 cm−1, corresponding to a spectral window of approximately 440–1600 cm−1;
  • Exposure time: 2 s;
  • Laser power: 100% (approximately 10 mW on the sample);
  • Number of accumulations per spectrum: 5;
  • Cosmic ray removal: enabled.
The laser spot diameter on the sample surface was approximately 20 µm under the selected optical configuration (633 nm HeNe laser, 20× lens).
For each polymer, two droplets were prepared and measured as outlined in the experimental workflow (Figure 8), resulting in eight Raman mappings per polymer (four maps per droplet), corresponding to a total of 512 spectra. These data constituted the training set for the machine learning models (Figure 8f). To generate an independent test set, an additional droplet was prepared for each polymer and mapped in the same manner at four positions. The resulting 256 spectra per polymer were not used during model training and served exclusively for validation purposes (Figure 8f). In total, 4096 spectra were acquired for model training and 2048 spectra for independent testing, covering all eight molecular weight categories.

3.3. Raman Data Analysis and Model Developing

3.3.1. Data Pre-Processing

All Raman spectroscopic data were processed using MATLAB R2022b (MathWorks, Natick, MA, USA). Interpolation, baseline correction, smoothing, and z-score normalization was performed as in Tewes et al. 2024 [35]. The only difference lies in the smoothing. This was applied less strongly here: Instead of y = sgolayfilt(yOut, 3, 13), we used y = sgolayfilt(yOut, 2, 7), where the lower polynomial order (2) and shorter frame length (7) reduce smoothing intensity, preserving fine spectral details of higher-molecular-weight samples.
To evaluate the potential influence of baseline correction and smoothing on peak characteristics, a direct comparison between representative unprocessed and processed spectra in the 700–900 cm−1 region was performed. The corresponding results are provided in Supplementary Material S3. This assessment allows estimation of possible shifts or changes in band appearance introduced by the applied workflow.

3.3.2. Global Predictive Model

A Support Vector Machine (SVM) classifier was trained to discriminate between eight PEG molecular weight classes. The quadratic SVM model was trained with automatic kernel scaling and a box constraint level of 1 using MATLAB Classification Learner R2022b (MathWorks, Natick, MA, USA). A one-vs-one strategy was used for multiclass handling. Data standardization was disabled since data were already z-score-normalized. Feature selection was performed automatically, resulting in the inclusion of all 1015 variables from the full wavenumber range. Principal Component Analysis (PCA) was not applied prior to model training. Model performance was evaluated using five-fold cross-validation and subsequently validated with an independent test set.

3.3.3. Sub Model for Lower Molecular Weights

A separate SVM classifier was trained for the low-molecular-weight subset (PEG01k–06k) using the same parameter settings as above, except that PCA was applied prior to model training, retaining 16 PCs. The box constraint level was increased to 2, resulting in a stricter margin and slightly reduced tolerance for misclassification. This configuration emphasizes fine spectral distinctions within the narrower molecular weight range.

3.3.4. PCA–LDA for Interpretation

For interpretative analysis, combined datasets comprising all low (01k–06k) and high (08k–35k) PEG molecular weight classes (as defined in the chemometric models) were analyzed using the classification toolbox for MATLAB version 7.0 from Ballabio and Consonni [71]. Since no external validation was intended, all spectra were included to maximize class representation. PCA was used for dimensionality reduction, and the resulting scores were subjected to Linear Discriminant Analysis (LDA). Score plots were generated to visualize class separation, and canonical loading spectra (LD1 and LD2) were back-projected to the original wavenumber space to identify discriminative spectral regions. Back-projection reconstructs the canonical loadings (LD1, LD2) from LDA space into the original wavenumber domain, allowing direct interpretation of which spectral regions contribute most to class separation. The procedure preserves the linear PCA–LDA mapping and is therefore suitable for identifying discriminative Raman features while avoiding artifacts from dimensionality reduction. The MATLAB code used for the backprojection procedure following model creation with the classification toolbox 7.0 [71] is provided in Supplementary Material S6.

4. Conclusions

This study demonstrates that Raman spectroscopy, combined with supervised machine learning, can differentiate PEG samples across a typical range of molecular weights. Despite only subtle spectral differences, SVM classification achieved relatively high accuracy under standardized measurement conditions, indicating the presence of statistically exploitable spectral differences related to molecular weight, without implying a direct mechanistic assignment. Complementary PCA–LDA analyses revealed that discriminative information primarily arises from line-shape and shoulder regions rather than from major peak centers, consistent with gradual variations in conformational order and crystallinity.
While the approach remains sensitive to sample morphology and drying behavior, the findings establish a reproducible workflow that links polymer molecular structure with spectroscopic fingerprints. Further refinements such as annealing comparisons, controlled film-thickness variation, or mixed-PEG systems could help clarify how microstructure and sample preparation influence the observed spectral trends, and would represent valuable extensions for future methodological development. In addition to improved experimental control, systematically incorporating preparation-induced variability into model training may further enhance robustness and generalization across batches and conditions. The presented framework thus provides a foundation for the non-destructive classification of predefined molecular weight classes and could support future regression analyses of spectral trends once more continuous datasets become available. Future extensions could explore the transfer of the approach to other (water-soluble) polymers and the adaptation of models to varying experimental or environmental domains (varying measurement conditions and sample environments) to improve robustness in real-world applications.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/molecules31050778/s1. Supplementary Material S1: SEC molar mass distributions of PEG samples (1 k–35 k g/mol). Supplementary Material S2: Quantitative evaluation of selected Raman bands in PEG08k–PEG35k calibration mean spectra. Supplementary Material S3: Robustness of spectral pre-processing in the 700–900 cm−1 region for low-molecular-weight PEG samples. Supplementary Material S4: (a) Edge region of a dried PEG06k droplet showing small cavities formed by local laser-induced displacement. (b) Representative raw Raman spectra illustrating gradual signal loss (no pre-processing applied). Supplementary Material S5: Individual weighing values of PEG Samples. Supplementary Material S6: MATLAB script for PCA–LDA back-projection and canonical loading visualization.

Author Contributions

Conceptualization, T.J.T. and D.P.B.; methodology, T.J.T., P.F.W.S. and C.N.D.; software, T.J.T.; validation, T.J.T.; formal analysis, T.J.T. and P.F.W.S.; investigation, T.J.T., C.N.D. and U.S.; resources, D.P.B.; data curation, T.J.T.; writing—original draft preparation, T.J.T.; writing—review and editing, T.J.T., D.P.B. and P.F.W.S.; visualization, T.J.T.; supervision, D.P.B.; and project administration, D.P.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All normalized mean Raman spectra supporting the findings of this study are openly accessible at Zenodo (https://doi.org/10.5281/zenodo.18298725). Individual Raman spectra can be provided by the corresponding author upon reasonable request. Supplementary data are provided in the Supplementary Materials.

Acknowledgments

We would like to thank Felix Schacher for critical discussions, substantial suggestions for improvement, and constructive feedback on the manuscript, as well as Bianca White for weighing the SEC samples.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. All Raman spectra of polyethylene glycol (PEG) at eight molecular weights. (a) Mean spectra after z-score normalization; individual spectra are shown in gray. (b) Same data after preprocessing (see Section 3). Spectra are plotted with vertical offsets for clarity.
Figure 1. All Raman spectra of polyethylene glycol (PEG) at eight molecular weights. (a) Mean spectra after z-score normalization; individual spectra are shown in gray. (b) Same data after preprocessing (see Section 3). Spectra are plotted with vertical offsets for clarity.
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Figure 2. Untreated, but z-score-normalized, Raman spectra of polyethylene glycol (PEG) samples. All individual spectra are shown in grey, while the mean spectra of PEG35k and 01k are highlighted (vertical offset for clarity). Prominent Raman bands are annotated with their corresponding Raman shifts.
Figure 2. Untreated, but z-score-normalized, Raman spectra of polyethylene glycol (PEG) samples. All individual spectra are shown in grey, while the mean spectra of PEG35k and 01k are highlighted (vertical offset for clarity). Prominent Raman bands are annotated with their corresponding Raman shifts.
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Figure 3. Principal component analysis (PCA) of preprocessed Raman spectra of polyethylene glycol (PEG) samples with different molecular weights. (a) PCA of datasets 01–06k. (b) Zoomed view of 01–06k revealing minor grouping tendencies. (c) PCA of 08–35k with clearer variance distribution and partial ordering along PC1. (d) Zoomed view of (c) highlighting dataset-specific dispersion. Symbols represent individual datasets, and colors indicate molecular weights. The wide spread across PCs indicates that both instrumental and sample-presentation effects, as well as molecular-weight-related spectral variations, contribute to the overall variance, likely at comparable magnitudes.
Figure 3. Principal component analysis (PCA) of preprocessed Raman spectra of polyethylene glycol (PEG) samples with different molecular weights. (a) PCA of datasets 01–06k. (b) Zoomed view of 01–06k revealing minor grouping tendencies. (c) PCA of 08–35k with clearer variance distribution and partial ordering along PC1. (d) Zoomed view of (c) highlighting dataset-specific dispersion. Symbols represent individual datasets, and colors indicate molecular weights. The wide spread across PCs indicates that both instrumental and sample-presentation effects, as well as molecular-weight-related spectral variations, contribute to the overall variance, likely at comparable magnitudes.
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Figure 4. Confusion matrices of the global Support Vector Machine (SVM) classification model for all polyethylene glycol (PEG) molecular weight classes. (a) Five-fold cross-validation using the training dataset (overall accuracy cross-validation = 93.4%). (b) Independent test with unseen data (overall test accuracy = 72.6%). Diagonal cells indicate correct classifications, while off-diagonal cells represent misclassifications. TPR and FNR denote the true positive rate and false negative rate, respectively.
Figure 4. Confusion matrices of the global Support Vector Machine (SVM) classification model for all polyethylene glycol (PEG) molecular weight classes. (a) Five-fold cross-validation using the training dataset (overall accuracy cross-validation = 93.4%). (b) Independent test with unseen data (overall test accuracy = 72.6%). Diagonal cells indicate correct classifications, while off-diagonal cells represent misclassifications. TPR and FNR denote the true positive rate and false negative rate, respectively.
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Figure 5. Confusion matrices of the Support Vector Machine (SVM) sub-model for the lower molecular weight range of polyethylene glycol (PEG01k–PEG06k). (a) Five-fold cross-validation using the training dataset (overall accuracy cross-validation = 89.6%). (b) Independent test with unseen data (overall test accuracy = 70.5%). The sub-model included a preceding Principal Component Analysis (PCA) retaining 16 principal components. Diagonal cells indicate correct classifications, while off-diagonal cells represent misclassifications. TPR and FNR denote the true positive rate and false negative rate, respectively.
Figure 5. Confusion matrices of the Support Vector Machine (SVM) sub-model for the lower molecular weight range of polyethylene glycol (PEG01k–PEG06k). (a) Five-fold cross-validation using the training dataset (overall accuracy cross-validation = 89.6%). (b) Independent test with unseen data (overall test accuracy = 70.5%). The sub-model included a preceding Principal Component Analysis (PCA) retaining 16 principal components. Diagonal cells indicate correct classifications, while off-diagonal cells represent misclassifications. TPR and FNR denote the true positive rate and false negative rate, respectively.
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Figure 6. Linear discriminant analysis (LDA) score plots illustrating class separation among polyethylene glycol (PEG) samples of different molecular weights. (a) Low-molecular-weight model (PEG01–06k) and (b) high-molecular-weight model (PEG08–35k). Each point represents an individual Raman spectrum projected onto the first three linear discriminant functions (LD1–LD3). Colors correspond to molecular weight classes.
Figure 6. Linear discriminant analysis (LDA) score plots illustrating class separation among polyethylene glycol (PEG) samples of different molecular weights. (a) Low-molecular-weight model (PEG01–06k) and (b) high-molecular-weight model (PEG08–35k). Each point represents an individual Raman spectrum projected onto the first three linear discriminant functions (LD1–LD3). Colors correspond to molecular weight classes.
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Figure 7. Canonical loading spectra (LD1 and LD2) and corresponding mean Raman spectra for the low- (a–c) and high-molecular-weight (d–f) PEG PCA–LDA models. Gray spectra/background in (b,e) represent individual Raman spectra, while the black line indicates the mean spectrum of all spectra in each model. Dashed vertical lines mark Raman shift regions contributing strongly to class discrimination according to the canonical loadings. LD1 corresponds to the primary canonical direction of separation, while LD2 describes an orthogonal discriminative axis capturing additional spectral variance.
Figure 7. Canonical loading spectra (LD1 and LD2) and corresponding mean Raman spectra for the low- (a–c) and high-molecular-weight (d–f) PEG PCA–LDA models. Gray spectra/background in (b,e) represent individual Raman spectra, while the black line indicates the mean spectrum of all spectra in each model. Dashed vertical lines mark Raman shift regions contributing strongly to class discrimination according to the canonical loadings. LD1 corresponds to the primary canonical direction of separation, while LD2 describes an orthogonal discriminative axis capturing additional spectral variance.
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Figure 8. Workflow for polymer preparation, droplet deposition, Raman mapping, and dataset generation. (a) Weigh 10.0 ± 0.5 mg polymer into a sterile 1.5 mL tube. (b) Dissolve in 500 µL sterile ultrapure water, vortex ≥ 1 min, then swirl to homogenize. (c) Place a polished stainless-steel microscope slide on a 52 °C drying device. Pipette two 1 µL droplets per sample onto the preheated slide and dry for 1.5 min. (d) Transfer to the confocal Raman microscope system. (e) Per droplet, select four regions at approximately north, east, south, and west positions. At each region, acquire an 8 × 8 map with 20 µm spacing. For each polymer, two droplets were mapped for training and one additional droplet for independent testing, (f) yielding 512 spectra per molecular weight for training and 256 for testing. Blue arrows indicate the training (calibration) workflow, whereas green arrows denote the independent validation (test) workflow.
Figure 8. Workflow for polymer preparation, droplet deposition, Raman mapping, and dataset generation. (a) Weigh 10.0 ± 0.5 mg polymer into a sterile 1.5 mL tube. (b) Dissolve in 500 µL sterile ultrapure water, vortex ≥ 1 min, then swirl to homogenize. (c) Place a polished stainless-steel microscope slide on a 52 °C drying device. Pipette two 1 µL droplets per sample onto the preheated slide and dry for 1.5 min. (d) Transfer to the confocal Raman microscope system. (e) Per droplet, select four regions at approximately north, east, south, and west positions. At each region, acquire an 8 × 8 map with 20 µm spacing. For each polymer, two droplets were mapped for training and one additional droplet for independent testing, (f) yielding 512 spectra per molecular weight for training and 256 for testing. Blue arrows indicate the training (calibration) workflow, whereas green arrows denote the independent validation (test) workflow.
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Table 1. Molecular weight characteristics of polyethylene glycol (PEG) reference samples determined by size exclusion chromatography (SEC). Listed are the number-average molar mass (Mn), weight-average molar mass (MW), dispersity (Đ = MW/Mn), and peak molar mass (Mp). The results confirm the expected monotonic increase in molecular weight and the narrow distribution of all samples (Đ = 1.06–1.21).
Table 1. Molecular weight characteristics of polyethylene glycol (PEG) reference samples determined by size exclusion chromatography (SEC). Listed are the number-average molar mass (Mn), weight-average molar mass (MW), dispersity (Đ = MW/Mn), and peak molar mass (Mp). The results confirm the expected monotonic increase in molecular weight and the narrow distribution of all samples (Đ = 1.06–1.21).
AbbreviationMnMWĐMp
01k97010401.071070
02k205021701.062230
04k426045501.074750
06k633068501.087240
08k835090901.099750
12k15,04016,9101.1218,770
20k21,21024,6401.1627,140
35k34,78042,1001.2149,310
Table 3. Overview of the polyethylene glycol (PEG) samples investigated in this study, including nominal molecular weights, abbreviations, suppliers, article numbers, and lot/batch identifiers.
Table 3. Overview of the polyethylene glycol (PEG) samples investigated in this study, including nominal molecular weights, abbreviations, suppliers, article numbers, and lot/batch identifiers.
Supplier MW (Nominal)
[g/mol]		AbbreviationSupplierArticleLot/Batch
100001kCarl Roth (Karlsruhe, Germany)0150.1204350981
200002kCarl Roth0154.3275358179
400004kCarl Roth0156.3264356722
600006kCarl Roth0158.4304328008
800008kCarl Roth0263.1283334402
12,00012kSigma-Aldrich (St. Louis, MO, USA)81285BCCN6036
20,00020kCarl Roth0165.3463332128
35,00035kSigma-Aldrich94646-250G-FBCCD4303
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Tewes, T.J.; Duismann, C.N.; Singh, U.; Simon, P.F.W.; Bockmühl, D.P. Raman Spectroscopic Classification of Polyethylene Glycol Samples of Varying Molecular Weights Using Machine Learning. Molecules 2026, 31, 778. https://doi.org/10.3390/molecules31050778

AMA Style

Tewes TJ, Duismann CN, Singh U, Simon PFW, Bockmühl DP. Raman Spectroscopic Classification of Polyethylene Glycol Samples of Varying Molecular Weights Using Machine Learning. Molecules. 2026; 31(5):778. https://doi.org/10.3390/molecules31050778

Chicago/Turabian Style

Tewes, Thomas J., Ciara N. Duismann, Udita Singh, Peter F. W. Simon, and Dirk P. Bockmühl. 2026. "Raman Spectroscopic Classification of Polyethylene Glycol Samples of Varying Molecular Weights Using Machine Learning" Molecules 31, no. 5: 778. https://doi.org/10.3390/molecules31050778

APA Style

Tewes, T. J., Duismann, C. N., Singh, U., Simon, P. F. W., & Bockmühl, D. P. (2026). Raman Spectroscopic Classification of Polyethylene Glycol Samples of Varying Molecular Weights Using Machine Learning. Molecules, 31(5), 778. https://doi.org/10.3390/molecules31050778

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