Lignin Molar Mass Estimation by Dispersion Analysis

Abstract

Lignin's complex and heterogeneous molecular structure poses significant challenges for accurate molar mass determination, which is important for its utilization in industrial applications, such as biochemicals, nanoparticles, biobased binders, and biofuels. This study evaluates the potential of Taylor Dispersion Analysis (TDA) for measuring lignin size and compares it with size‐exclusion chromatography (SEC) and diffusion‐ordered spectroscopy (DOSY) NMR. Using dual Gaussian fitting, flow‐induced dispersion analysis (FIDA), a TDA‐based method, successfully determined the average hydrodynamic radii of multiple species in solvent‐fractionated soda grass lignin samples, producing results consistent with DOSY. Molar mass calibration enabled comparisons between FIDA and SEC, revealing similar relative differences across lignin fractions. FIDA offers advantages such as rapid analysis and absence of stationary phase interactions, however its accuracy is limited by the variability of lignin fluorescence. Addressing these limitations will be critical for advancing FIDA as a method for lignin size estimation.

FIDA is employed to estimate the molar mass and the hydrodynamic radius of lignin samples. This innovative method showed results consistent with traditional techniques like SEC and DOSY NMR, demonstrating FIDA's potential for rapid lignin size analysis with minimal sample preparation and high reliability.

1. Introduction

Reliable knowledge of lignin's molar mass is essential for enhancing its valorization and application across a broad spectrum of bio‐based industries, including biofuels, aromatic chemicals, and biopolymers.^{[ 1} , ² , ³ , ^{4 ]}

Size‐Exclusion Chromatography (SEC) is the predominant method for estimating lignin size, but measurements often exhibit high variability due to a lack of standardization in calibration, sample preparation and data analysis.^{[ 5} , ⁶ , ⁷ , ^{8 ]} The International Energy Agency Round Robin study highlighted major interlaboratory variability in molar mass data across SEC‐equipped laboratories in seven countries.^{[ 7 ]} Subsequent work found that, while intralaboratory variations in number‐average molecular weight (M_n ) were within 15%, interlaboratory variations fluctuated up to fourfold in both tetrahydrofuran (THF)‐ and alkaline‐based systems.^{[ 6 ]} To address these challenges, Lange et al.^{[ 8 ]} demonstrated that standardizing calibration, sample preparation, and data interpretation, as well as incorporating lignin‐type correction factors from NMR data, can significantly reduce variability.^{[ 8 ]}

A viscometry detector enhances a UV/RI SEC setup by determining lignin size through intrinsic viscosity. This approach improves molar mass estimations but requires a comprehensive range of molar mass calibration standards for universal calibration or prior knowledge of the Mark‐Houwink‐Sakurada constants specific to the lignin.^{[ 9} , ^{10 ]} Unlike light‐scattering techniques, which introduce errors due to sample's light absorption and fluorescence, viscometry avoids these issues. However, this method remains highly sensitive to measurement conditions and prone to secondary column interactions, which can reduce accuracy.

Multi‐Angle Light Scattering (MALS) can improve the accuracy of lignin size measurements by providing an absolute molar mass estimation without the need for calibration.^{[ 11 ]} This method relies on the proportionality between light scattering and molar mass. However, applying MALS to lignin is challenging due to lignin's inherent fluorescence, which interferes with commonly used laser wavelengths (488 nm and 690 nm), leading to substantial overestimations of size.^{[ 12} , ^{13 ]} Researchers managed to reduce fluorescence interference by using bandwidth filters,^{[ 14 ]} equipping the detector with an alternative 785 nm near IR laser,^{[ 15 ]} or applying fluorescence interference correction factors.^{[ 16 ]} Despite these advances, implementing MALS is a costly task and requires extensive training for both operating and data analysis, limiting its widespread adoption.

Given the limitations of MALS, alternative methods are being explored to address the challenges of accurately determining lignin size. Asymmetric Flow Field‐Flow Fractionation (AF4) separates analytes by applying a cross‐flow perpendicular to a laminar flow, with larger molecules retained longer due to slower diffusion. Sulaeva et al.^{[ 17 ]} demonstrated for the first time how AF4 could be used to purify and determine the molar mass of lignosulfonates from industrial black liquors.^{[ 17 ]} However, AF4 is restricted to water‐soluble lignosulfonates, as its equipment is incompatible with commonly used lignin solvents such as THF, dimethyl sulfoxide (DMSO), or alkaline aqueous solutions. A recent study by Lu et al. (2021) compared alkaline SEC and analytical ultracentrifugation (AUC) for determining the size distribution of solvent‐fractionated PB1000 (soda) and Indulin (kraft) lignin.^{[ 2 ]} Although AUC offers valuable insights, its complex data analysis and the time‐consuming experiments (up to 24 h) limit its accessibility for routine use.

Diffusion‐Ordered Spectroscopy (DOSY) has also gained popularity as a technique for determining lignin size.^{[ 18} , ¹⁹ , ²⁰ , ²¹ , ^{22 ]} By applying pulsed field gradients in an NMR spectrometer, DOSY separates species based on their diffusion coefficients. Norgren & Lindström^{[ 22 ]} utilized this method to measure the hydrodynamic radius (R _h) of kraft lignin fractions, demonstrating a relationship between R _h and SEC‐based molar mass.^{[ 22 ]} Cornejo et al.^{[ 18 ]} further established a strong correlation between DOSY‐derived R _h and the molar mass measured by SEC for products from base‐catalyzed lignin depolymerization reactions.^{[ 18 ]} While DOSY provides valuable diffusion data and identifies individual chemical species, it requires advanced NMR instrumentation, substantial technical expertise, and considerable time, which limits high‐throughput capabilities.

The considerable effort invested in developing alternative methods for lignin size determination highlights the need for more reliable and accurate approaches. Flow‐Induced Dispersion Analysis (FIDA) represents a novel microfluidic method for determining R _h based on Taylor Dispersion Analysis (TDA), a concept originally introduced by Taylor in 1953.^{[ 23} , ²⁴ , ^{25 ]} TDA is an absolute technique that measures particle diffusion coefficients by analyzing the broadening of particle bands as they move through a silica‐based capillary under controlled laminar flow conditions. This approach, comprehensively reviewed by Moser & Baker,^{[ 26 ]} relies exclusively on fluid dynamics and eliminates the need for a stationary phase.^{[ 23} , ²⁴ , ^{26 ]} First detailed by Jensen & Østergaard in 2010, FIDA has primarily been applied to protein analysis, taking advantage of proteins’ inherent UV‐fluorescence characteristics, high purity, and monodispersity.^{[ 23} , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ^{31 ]}

The FIDA 1 instrument (Fida Biosystems, Denmark) uses TDA to determine particle diffusion coefficients under controlled hydrodynamic flow conditions to generate size‐dependent dispersion profiles (Figure 1 ). At the initial time (t ₀), the particles of interest are injected into the capillary as a plug uniformly distributed across its cross‐sectional area. When hydrodynamic pressure is applied (t ₁), the particle plug is carried forward by the flow, forming a parabolic velocity profile. Simultaneously, the particles undergo size‐dependent radial diffusion at the front and rear of the plug. At constant flow rate, the deformation of the plug profile at t ₂ depends solely on the radial diffusion of the particles. The resulting profile is detected over time at a cross‐section of the capillary, producing a Gaussian concentration curve. Smaller particles, with higher diffusion coefficients, experience greater radial diffusion, which generates a narrower and taller Gaussian distribution (Figure 1A). In contrast, larger particles diffuse more slowly, resulting in a broader Gaussian distribution profile (Figure 1B).

Figure 1.

Schematic representation of Taylor dispersion profiles in a capillary as utilized in the FIDA method. A) Dispersion profile of small particles. B) Dispersion profile of large particles. C) Dispersion profile of a sample with polydisperse particle size distributions.

A challenge arises when analyzing polydisperse size distributions, such as those found in most lignin samples. Unlike SEC, where retention time is size‐dependent, the retention time in FIDA is determined by the hydrodynamic pressure exerted by the instrument and the sample viscosity.^{[ 26 ]} As a result, only limited sample separation occurs with size‐dependent diffusion leading to overlapping dispersion profiles (Figure 1C).

Aragonès Pedrola et al.^{[ 32 ]} and Ray et al.^{[ 33 ]} demonstrated the applicability of FIDA in characterizing polydisperse protein samples, such as amyloid fibrils and α‐synuclein protein nanoclusters, respectively, by estimating their R _h and dispersity.^{[ 32} , ^{33 ]} For such polydisperse sample distributions it is advantageous to computationally divide the signal into multiple Taylorgrams.^{[ 34 ]} In a TDA‐based study of impure polysaccharides, Saetear et al.^{[ 35 ]} applied curve fitting with two or three Gaussian functions to detect multiple species within the samples.^{[ 35 ]} This multi‐Gaussian fitting approach not only enables the estimation of R _h for single species but also provides a more accurate averaged R _h (R _h,avg) weighting the calculated R _h according to their relative fluorescence intensities.

This method works particularly well for monomodal or bimodal distributions, effectively capturing the size variation within these ranges. However, for samples with multimodal distributions, this approach may lead to inaccuracies, as it struggles to fully represent the complexity of multiple distinct particle size populations. For such cases, pre‐analysis separation, such as solvent fractionation, are required to improve resolution.

In this study, we investigate the use of FIDA to assess the size‐distribution of alcohol fractionated lignin samples. FIDA is particularly appealing because lignin's inherent UV‐fluorescence and typical size range fall well within the detection limits of R _h between 0.5 and 500 nm.^{[ 36 ]} For reference, R _h of phenol is ≈0.3 nm.^{[ 37 ]} Compared to AUC, AF4 and DOSY, FIDA demands less technical expertise, and is well‐suited for high‐throughput analysis. The lack of a stationary phase and the use of a fused silica capillary make the method solvent‐flexible and mitigates errors related to secondary interactions.

While FIDA addresses significant limitations found in SEC and DOSY, it neither provides the high‐resolution molar mass distribution achievable by SEC nor the detailed chemical property insights of DOSY. Instead, FIDA serves as a complementary method for lignin size analysis. To explore this potential, measurements by FIDA were compared to DOSY NMR and SEC with molar mass calibration of both FIDA and SEC with Polystyrene Sulfonate (PSS) standards.

2. Results

2.1. FIDA versus SEC

The size distributions of PB1000's methanol and ethanol fractions were analyzed using FIDA and SEC methods. Initial comparisons were made between M_n from SEC and R _h determined by FIDA. Signal data from FIDA were fit to dual Gaussian functions (Figure 2A), enabling determination of the average R _h of both the larger and smaller lignin species within each fraction, achieving a high‐quality fit (R² = 0.98).

Figure 2.

A) Taylorgram of Protobind 1000 (black line) with a combined dual Gaussian fit (orange line). B) Lignin size comparison using SEC and FIDA. The FIDA‐based hydrodynamic radius (R _h) and SEC‐based number average molecular weight (M_n ) of PB1000 lignin and lignin fractions. The R _h of the smaller and larger species were determined by dual Gaussian fit.

PB1000, with an initial M_n of 1650 Da, was fractionated into methanol‐soluble (MeOH‐S, 52 wt.%) and ethanol‐soluble (EtOH‐S, 44 wt.%) fractions, with soluble lignin fractions exhibiting smaller M_n (1250 Da and 1400 Da, respectively) and insoluble fractions showing larger M_n (3400 Da and 3700 Da, respectively) (Figure 2B; see Figure S3, Supporting Information, for chromatograms). FIDA results revealed average R _h between 0.55 to 1.67 nm across all fractions. For the smaller lignin species, average R _h showed minimal variation, ranging from 0.55 to 0.62 nm, indicating that some smaller lignin molecules remained within the insoluble fraction after solvation, which is expected. This trend was also observed in SEC chromatograms, where smaller lignin molecules were detected at higher retention times in all samples (Figure S3, Supporting Information). Notably, the consistent presence of smaller species allowed the application of dual Gaussian fits to the EtOH‐S, where the size of the smaller species was fixed at an average R _h of 0.58 nm, as consistently observed across the other samples. This approach facilitated the identification of larger lignin molecules within the EtOH‐S fraction, characterized by an average R _h of 1.01 nm. However, the relatively small size difference between the smaller and larger species introduces some uncertainty into the computational separation of EtOH‐S.^{[ 38 ]}

The larger species showed greater variability, ranging from 1.01 to 1.67 nm. As with SEC, the largest species were identified in EtOH‐I and MeOH‐I, with average R _h of 1.61 nm and 1.67 nm, respectively. Furthermore, the species in MeOH‐S had slightly larger average R _h than the in EtOH‐S, indicating that methanol has the ability to dissolve slightly larger lignin molecules, in agreement with the SEC results (Figure 2B).

To evaluate how the two methods differ in assessing lignin dispersity, the ratio of the largest and smallest average R _h‐measured by FIDA was compared to the SEC‐derived dispersity (Ð = $\frac{M_w}{M_n}$). Both methods revealed a similar trend, with MeOH‐I showing the highest dispersity compared to PB1000 and EtOH‐I (Table 1 ). However, Ð determination based on TDA analysis requires further investigation in future studies.

Table 1.

Dispersity (Ð) calculated using FIDA and SEC methods. Detailed FIDA data can be found in Table S1 (Supporting Information).

Samples	Dispersity
	SEC	FIDA
PB1000	4.8	2.7
EtOH‐S	3	1.7
EtOH‐I	4.7	2.9
MeOH‐S	3.1	2.3
MeOH‐I	5	3.1

Both methods qualitatively indicated that the insoluble fractions predominantly contain larger lignin molecules, while soluble fractions contain smaller lignin molecules, consistent with literature.^{[ 39} , ^{40 ]} Additionally, both methods measured slightly larger lignin species in MeOH‐S compared to EtOH‐S, indicating that EtOH‐S exhibits lower dispersity. Although the relative trends in size distributions were consistent across samples, FIDA revealed less pronounced differences between soluble and insoluble fractions. To further assess the reliability of FIDA for lignin size determination, these results were compared with data obtained from DOSY.

2.2. FIDA versus DOSY

R _h were measured using DOSY and compared to those obtained by FIDA (Table 2 ). The DOSY spectra for all samples exhibited two distinct groups of signals corresponding to smaller and larger species, consistent with the separation observed in FIDA measurements.

Table 2.

Average hydrodynamic radii of lignin samples measured by FIDA and DOSY. DOSY results are based on the aromatic signals in the ¹ H dimension, related to the diffusion coefficient derived from dominant peaks.

Samples	FIDA		DOSY
	Small [nm]	Large [nm]	Peak 1 [nm]	Peak 2 [nm]
PB1000	0.60	1.56	1.00	1.90
EtOH‐S	0.58	1.01	0.59	1.10‐1.32
EtOH‐I	0.55	1.61	0.69	1.41
MeOH‐S	0.62	1.45	0.62	1.27‐1.47
MeOH‐I	0.55	1.67	1.19	2.04

For the unfractionated PB1000, DOSY revealed R _h values of 1.00 nm and 1.90 nm, compared to FIDA measurements of 0.60 nm and 1.56 nm for the smaller and larger species, respectively. This discrepancy could be attributed to the greater heterogeneity of PB1000, as the broader size distribution likely influences the precision of size estimations between the two methods.

In fractionated samples, the agreement between the methods was notably stronger. For smaller species, DOSY measured R _h values of 0.59 nm and 0.62 nm in EtOH‐S and MeOH‐S, respectively, which closely match the FIDA measurements of 0.58 nm for EtOH‐S and 0.62 nm for MeOH‐S. Larger species detected by DOSY in EtOH‐S and MeOH‐S had R _h values of 1.10‐1.32 nm in EtOH‐S and 1.27‐1.47 nm in MeOH‐S, respectively, which aligned well with the FIDA results of 1.01 nm and 1.45 nm (Figure S4, Supporting Information). For EtOH‐I and MeOH‐I, DOSY measured R _h values of 1.41 nm and 2.04 nm, respectively, compared to FIDA results of 1.61 nm and 1.67 nm. For smaller species, FIDA measured an average R _h of 0.55 nm in EtOH‐I, which corresponds to a strong peak at 0.69 nm in the DOSY spectrum of EtOH‐I.

The consistency between the two methods in differentiating larger and smaller lignin species demonstrates the effectiveness of the multi‐Gaussian fitting approach. Both methods showed strong agreement in hydrodynamic size estimations for the solvent fractionated lignin samples, consistently following the size order: EtOH‐S < MeOH‐S < EtOH‐I < MeOH‐I.

One of the key advantages of FIDA is its high‐throughput capability, enabling faster analysis compared to DOSY, which requires more complex data interpretation and longer measurement times. Additionally, FIDA's measures R _h without the need for extensive sample preparation or specialized NMR equipment, making it more accessible for routine laboratory use. However, while FIDA is effective in determining the relative sizes of lignin species, DOSY provides additional chemical information, which FIDA does not address.

To better compare SEC and FIDA and further evaluate FIDA's applicability, R _h was correlated with molar mass and the relative proportions of the smaller and larger species identified by FIDA were quantified.

2.3. Correlating Hydrodynamic Radius with Molar Mass

The accuracy of FIDA in estimating molar mass was evaluated by comparing the MW _avg obtained from FIDA with the M_n determined by SEC. For the unfractionated PB1000 sample, the FIDA derived MW _avg (1.54 kDa) closely aligned with the SEC‐based M_n (1.65 kDa) (Figure 3 ). Similarly, for EtOH‐S and MeOH‐S with M_n of 1.25 kDa and 1.40 kDa corresponded to MW _avg values of 1.11 kDa and 1.18 kDa from FIDA, respectively.

Figure 3.

Molar mass estimation of PB1000 and lignin fractions. The number average molecular weight measured by SEC (SEC M_n , red bars) is compared to the weighted average molecular weight (FIDA MW _avg, blue bars) measurements from FIDA 1.

Interestingly, while MeOH‐S fractions contained some larger lignin species with a FIDA derived R _h of 1.45 nm (corresponding to 3.42 kDa), this did not significantly shift the MW _avg compared to EtOH‐S due to the low abundance of these species.

For the insoluble fractions, the FIDA derived MW _avg values of EtOH‐I and MeOH‐I were nearly half the size of the SEC based M_n . This discrepancy may be attributed to the fluorescence behavior of lignin, on which the FIDA measurements depend.

Variations in factors such as molecular structure, molecular size distribution, and concentration across different lignin fractions can lead to discrepancies in fluorescence emission intensity,^{[ 15} , ^{41 ]} potentially leading to misinterpretation of the FIDA signal data. To investigate this, the relative fluorescence quantum yields of the samples were calculated using emission (λ_ex = 280 nm) and excitation spectra (λ_em = 425 nm) (Figure 4A; for spectra see Figure S5A,B, Supporting Information). The results suggest that the fractions and unfractionated lignin exhibit very similar quantum yields.

Figure 4.

A) Fluorescence quantum yields of PB1000 and fractions measured on FIDA 1. B) Excitation spectra recording emission at 425 nm, measured on FluoroMax‐4 spectrofluorometer.

Given that i) the intensity of the excitation source was constant and ii) all samples were equiconcentrated (1.0% (w/v)), the observed differences in FIDA measurements are likely attributable to variations in molar absorption coefficients. As shown in Figure 4B, the soluble fractions exhibit approximately double molar absorption coefficients of the insoluble fractions (cf. Figure S5B, Supporting Information). The intermediate fluorescence intensity observed for PB1000 aligns with this finding, reflecting the relative proportions of soluble and insoluble fractions in the unfractionated lignin (52% and 48% for methanol fractions, and 44% and 56% for ethanol fractions).

A similar trend was previously reported from size estimation using MALS, where larger lignin molecules exhibited lower fluorescence intensities compared to smaller molecular weight lignins.^{[ 15 ]} Nevertheless, the lack of comprehensive investigations on the size‐dependent fluorescence properties of lignin limits the understanding of this phenomenon. Consequently, suitable correction factors for accurately quantifying the average size of lignin using FIDA have not yet been developed. This underscores the broader knowledge gap in lignin fluorescence behavior, which future studies need to address.

While FIDA is currently limited to describing the average smallest and largest species in a lignin sample, solvent fractionation can increase its resolution for multimodal and polydisperse populations. For cases where solvent fractionation is unsuitable, SEC remains an invaluable method, offering detailed insights into size distribution despite its well‐documented limitations. Thus, while FIDA may not universally replace SEC, it has potential to be an effective complementary technique.

Accurate size determination of multimodal and polydisperse lignin populations by FIDA is currently hindered by insufficient understanding of lignin fluorescence properties, particularly the correlation between molecular size and fluorescence intensity. Nevertheless, FIDA provides a useful platform for future investigations into the fluorescence behavior of different lignin types across various solvent systems. Integrating complementary detection methods, such as UV detection, or coupling FIDA with pre‐SEC fractionation, could enable more comprehensive and accurate methodologies for analyzing lignin size distributions. Such advancements could open new research pathways to improve lignin utilization in biomaterials, biochemicals, and bioenergy applications.

3. Conclusions

By comparative size analysis of alcohol fractionated lignin using DOSY, SEC and FIDA, this study establishes FIDA as a robust, high‐throughput technique for estimating the R _h and molar mass while addressing key challenges associated with SEC. Although FIDA's reliance on fluorescence intensity requires careful interpretation to avoid potential size misestimations, its integration with solvent fractionation and dual Gaussian modeling effectively captures the size range of lignin species. FIDA offers an interesting foundation for further research into solvent‐lignin interactions and fluorescence properties of lignin. Its ability to provide rapid and reproducible size assessments makes FIDA valuable complementary method to SEC in lignin size analysis. However, further studies are needed to evaluate FIDA's applicability on a wider range of lignin samples and to develop corrections for size dependent fluorescence variability.

4. Experimental Section

Lignin Fractionation

Protobind 1000 (PB1000, PLT Innovations, Switzerland), a soda lignin obtained from agricultural fibrous feedstock, was used in the study. It contains over 90% sulfur‐free lignin, less than 3% hemicellulose and less than 2% minerals according to the producer.^{[ 42 ]} As previously described,^{[ 43 ]} PB1000 was fractionated using 96% ethanol or 100% methanol (VWR Chemicals) prepared in a 10:90 water:alcohol ratio (w/w) in 2 mL Eppendorf tubes in a solid to liquid ratio of 1:5 (w/w) based on lignin dry weight.^{[ 43 ]} The mixtures were stirred at 700 rpm for 1 h at ambient temperature and subsequently centrifuged at 1000 × g for 10 min. The pellets were defined as the insoluble fractions (EtOH‐I or MeOH‐I), and the supernatants were defined as the soluble fractions (EtOH‐S or MeOH‐S). Fractions were dried in vacuum oven at 40 °C until constant weight was reached. Fractionation yields were determined by calculating the ratio of dry weight between the soluble fraction and the unfractionated lignin, averaging over four replicates.

Flow Induced Dispersion Analysis (FIDA)

Lignin samples were measured with a solid concentration of 1.0% (w/v) in a 1:9 (v/v) ratio water:DMSO with 0.05 M LiBr. Solubilization was facilitated by 20‐minute ultrasound bath at 40 °C followed by mixing overnight at 700 rpm at 40 °C in a thermomixer. Lastly, samples were filtered using 0.45 µm pore size cellulose filters.

Measurements were performed in a FIDA 1 with a 280 nm (± 25 nm) excitation source.^{[ 44 ]} The photomultiplier tube fluorescence detector was equipped with a long wave pass filter for emissions above 300 nm and was run under reduced voltage (350 V) to manage high fluorescence intensity of samples. The temperature was maintained at 40 °C instead of ambient temperature, to reduce viscosity of the DMSO and shorten the retention time, avoiding higher temperatures to preserve lignin structure. This setup yielded an analysis time of 7‐minutes. With the sample tray set to 40 °C, the running method was initiated by cleaning and filling the 75 µm‐diameter fused silica capillary with 1:9 (v/v) water:DMSO with 0.05 M LiBr at 3500 mbar for 60 s. The sample was then injected into the capillary at 50 mbar for 20 s, and thereafter 1:9 (v/v) water:DMSO with 0.05 M LiBr was injected at 400 mbar for 400 s and fluorescence was measured. Multi‐Gaussian fitting and hydrodynamic radii were computed using the FIDA proprietary software. Replicates for lignin samples were n = 6.

Although our analysis suggested that a 1.0% (w/v) concentration may be near the fluorescence linearity threshold (Figure S2, Supporting Information), we decided to use this lignin concentration due to consistency across methods, given that the SEC UV‐detector requires considerable concentrations to achieve an acceptable signal‐to‐noise ratio.

The determination of sample diffusion is based by the Taylor‐Aris equation,^{[ 45 ]} where the diffusion coefficient D is defined by the retention time (t _R), width at half peak height (σ) and the radius of the capillary (𝑎):

$$D=\frac{a^2}{24{\sigma }^2}{t}_{\mathrm{R}}$$ (1)

The diffusion coefficient is then used to calculate R _h using the Stokes‐Einstein equation:

$$R_h=\frac{k_{B}T}{6\pi \eta D}$$ (2)

where k _B is the Boltzmann constant, T is the absolute temperature (in Kelvin) and $\eta$ is the dynamic viscosity (in Pa∙s).

To explore the usability of FIDA, the hydrodynamic volume was related to molar mass. Both FIDA and SEC systems were calibrated with the same PSS standards.

The molar masses of PSS standards used in the study are in the range 210 to 2.600.000 g mol⁻¹ (Merck KGaA). For both SEC and FIDA instruments, calibrations were based on a 3rd order polynomial fit between the peak molecular weight (M_p ) of PSS and the R _h for FIDA and retention time for SEC (Figure S1, Supporting Information).

As evident by Equation 2, there is an inverse proportionality between R _h and viscosity. Thus, a correction factor was used to adjust t _R related to the viscosity of DMSO by running Bovine Serum Albumin in water using the same method, which resulted in a t _R,H2O of 1.44 min. The correction was done using the viscosity correction tool in the FIDA 1 instrument software, which essentially divides R _h by the ratio of t _R,H2O to t _R,DMSO. Replicates for running calibration standards in FIDA 1 were n = 20.

The multi‐Gaussian fitting software feature in FIDA was used to determine the sizes of the larger and smaller lignin species within the samples. FIDA quantifies each species' relative abundance by measuring the fluorescence intensity associated with each fitted Gaussian concentration profile. On this basis, an average R _h (${R_{h,}}_{avg}$) and an average molar mass (MW_avg) were computed by weighting the R _h or molar mass of the fitted species with their relative fluorescence intensity:

$${R_{\mathrm{h},}}_{\mathrm{avg}}=\frac{F_1·R_{\mathrm{h}1}+F_2·R_{\mathrm{h}2}}{F_1+F_2}$$ (3)

(4)

where $F_1$ and $F_1$ are the relative fluorescence intensities, $R_{\mathrm{h}1}$ and $R_{\mathrm{h}2}$ are the average hydrodynamic radii, and $M{W}_1$ and $M{W}_2$ are the average molar mass of the smaller and larger species, respectively.

Size Exclusion Chromatography (SEC)

Lignin samples were dried in a vacuum oven at 45 °C for 48 h and then dissolved in HPLC‐grade DMSO (VWR Chemicals) at 1% (w/v). Their molar mass distribution was analyzed using a Shimadzu Prominence Liquid Chromatograph LC‐20‐AT, equipped with a DGU‐20A3 degasser and a heated Agilent PLgel 5 µm MiniMIX‐C column at 70 °C. The eluent was DMSO with 0.1% (w/v) LiCl at an isocratic flow rate of 0.2 mL min⁻¹. UV absorption at 280 nm was measured using a diode array detector SPD‐M20A. Lignin molar mass was determined using the same PSS calibration described for FIDA (Figure S1, Supporting Information).

Diffusion‐Ordered Spectroscopy Nuclear Magnetic Resonance (DOSY NMR)

Samples were prepared by dissolving ≈5 mg of lignin in a mixture of solvents composed of 450 µL of DMSO‐d6 and 50 µL of D₂O. Diffusion measurements were performed on a Bruker Avance III 400 MHz spectrometer in pseudo‐2D ‐mode with bipolar gradient pulses in the ledbpgp2s pulse sequence from the Bruker library. The gradient strength was linearly incremented in 16 steps from 2% to 95% of 48.6 G cm⁻¹, with a diffusion delay Δ = 200 ms and a gradient length δ/2 = 2 ms. For each sample, 16 scans were recorded per increment. The resulting diffusion coefficients were calculated from the aromatic signals in the ¹H dimension. The gradient constant was calibrated by using the residual signal of HDO in D₂O. All measurements were made at a temperature of 25 °C.

Spectrofluorometric Analysis

The fluorescence emission of a lignin population, as generally observed for other fluorophores, depends on i) the incident light intensity, ii) the luminescence quantum yield, and iii) the absorbance of each fluorescing species, influenced by the structure of the lignin molecules and their interactions.^{[ 41 ]} To investigate the fluorescence profiles of the lignin samples, a spectrofluorometric analysis was conducted using the FluoroMax‐4 (Jobin Yvon Horiba) spectrofluorometer. Samples were prepared at a concentration of 20 mg L⁻¹ in a solvent mixture of 1:9 (v/v) water:DMSO with 0.05 M LiBr. The analysis encompassed two measurements: 1) excitation spectrum: the excitation wavelengths were scanned from 200 to 400 nm, with a 2 nm slit width, to monitor emission at 425 nm; 2) emission spectrum: following the excitation at 280 nm – mirroring the conditions used in FIDA – with a 2 nm slit width, the emission spectra were captured from 300 to 520 nm to characterize the fluorescence profile of the samples.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Simonsen T. I., Djajadi D. T., Ponzecchi A., Crestini C., Gigli M., Sgarzi M., Thomsen S. T., Lignin Molar Mass Estimation by Dispersion Analysis. Macromol. Rapid Commun. 2025, 46, 2400751. 10.1002/marc.202400751

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.