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. 2023 Oct 9;3(10):2826–2834. doi: 10.1021/jacsau.3c00384

Correlating Surface Chemistry to Surface Relaxivity via TD-NMR Studies of Polymer Particle Suspensions

Murilo T Suekuni 1, Alan M Allgeier 1,*
PMCID: PMC10598564  PMID: 37885588

Abstract

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This study elucidates the impact of surface chemistry on solvent spin relaxation rates via time-domain nuclear magnetic resonance (TD-NMR). Suspensions of polymer particles of known surface chemistry were prepared in water and n-decane. Trends in solvent transverse relaxation rates demonstrated that surface polar functional groups induce stronger interactions with water with the opposite effect for n-decane. NMR surface relaxivities (ρ2) calculated for the solid–fluid pairs ranged from 0.4 to 8.0 μm s–1 and 0.3 to 5.4 μm s–1 for water and n-decane, respectively. The values of ρ2 for water displayed an inverse relationship to contact angle measurements on surfaces of similar composition, supporting the correlation of the TD-NMR output with polymer wettability. Surface composition, i.e., H/C ratios and heteroatom content, mainly contributed to the observed surface relaxivities compared to polymer % crystallinity and mean particle sizes via multiple linear regression. Ultimately, these findings emphasize the significance of surface chemistry in TD-NMR measurements and provide a quantitative foundation for future research involving TD-NMR investigations of wetted surface area and fluid-surface interactions. A comprehensive understanding of the factors influencing solvent relaxation in porous media can aid the optimization of industrial processes and the design of materials with enhanced performance.

Keywords: TD-NMR, polymer science, surface–solvent interactions, adsorption energy, particle suspensions, surface relaxivity, solvent relaxation

1. Introduction

Time-domain nuclear magnetic resonance (TD-NMR) is a convenient and nondestructive method to study porous media.1 Compared to commonly used surface area characterization techniques, such as gas physisorption and mercury intrusion, it avoids time-consuming data collection and the structural damage of soft matter induced by aggressive outgassing or high-pressure analyses.2,3 In TD-NMR studies, the enhanced relaxation rates of NMR-active nuclei, e.g., 1H, characterize confinement effects and solid–fluid affinity of pore-entrapped molecules.4,5 Although TD-NMR does not readily replace conventional techniques, characterizing pore fluid relaxation may allow scientists to rapidly characterize novel materials and study complex mass transport phenomena.6,7

In NMR analyses, the magnetic properties of specific atomic nuclei with nonzero spin prompt their parallel or antiparallel orientation with an externally applied magnetic field (B0).1 Upon reaching equilibrium, radiofrequency (RF) pulses, e.g., 90 or 180°, disrupt the acquired nuclei orientation. As B0 is held constant, atomic re-equilibration occurs, characterized by specific time periods, namely, the spin–lattice (T1) and spin–spin (T2) relaxation times.1,8 Compared to spectroscopy, which typically uses deuterated solvents and studies the chemical properties of the solute, time-domain, or solvent relaxation, experiments provide insights into fluid dynamics based on the solvent response.5,9,10 Bulk liquids are highly mobile, and their relaxation times, usually on the order of seconds, are correlated with transport properties like self-diffusion coefficient and viscosity.11 Inside porous media, fluid molecules will experience the influence of relaxation centers, e.g., paramagnetic or surface adsorption sites, resulting in reduced relaxation times.4,12 In such systems, the surface relaxivity (ρi, i = 1 or 2) parameter can be determined experimentally and used as a criterion for the extent of solvent relaxation enhancement.1 In paramagnetic-induced relaxation, electron–proton interactions dominate, and information on adsorption strength and material porosity is mostly limited.13−15 In contrast, in the absence of paramagnetism, fluid relaxation rates may reflect dipolar couplings from inter- and intramolecular interactions of surface-adsorbed molecules, and ρi may indicate solid–fluid interaction strength.16 Surface chemistry is an important component in the design and performance of several industrially relevant processes, which can be optimized by leveraging the benefits of TD-NMR analyses.17−19

Substantial work has been done comprising TD-NMR studies of porous media, including particle suspensions,20−23 catalysis,24−27 zeolites7,28,29 construction products,30,31 and bioengineering.32−36 Additionally, in the petroleum field, NMR logging allows the evaluation of the porosity and permeability of reservoir rocks and shales upon calibration via laboratory measurements.37−40 The impact of surface chemistry on solvent relaxation measurements has been acknowledged in several studies. For instance, Schlumberger et al. showed that Stöber silicas may have a wetting preference for water compared to ethanol and tetrahydrofuran using T1 and T2 measurements.21 The authors hypothesized that access to ultramicropores was limited by the kinetic diameter of the probe fluid, resulting in higher specific surface areas estimated from TD-NMR data of water-saturated samples compared to their ethanol counterparts and the argon physisorption benchmark.21 Cosgrove et al. compared multiple silica samples and showed that without proper calibration, the differences in their surface composition, e.g., the density of silanol and siloxane groups, can lead to overestimated surface areas from T2 data.18 In tests with carbonaceous materials, Marchesini et al. correlated increased relaxation rates of protic and aprotic solvents to graphite surface heteroatom (O, N) content for samples modified via plasma functionalization.41 Sharma et al. recently promoted solvent relaxation as an alternative method to estimate the Hansen solubility parameters for dispersions of carbon black samples.22 It is clear that the solid–fluid interaction strength impacts solvent relaxation data. However, a molecular-level understanding of the influence of surface functional groups remains underexplored and limits the elaboration and predictive power of TD-NMR characterization techniques. This gap is surprising given its relevance to fundamental and practical studies and the significant body of work correlating the hydration numbers of molecules to system physicochemical properties.42−46

In this study, synthetic copolymers with varying well-defined surface chemistries were suspended in a polar (water) and a nonpolar (n-decane) solvent to elucidate qualitative and quantitative correlations between surface chemistry and NMR surface relaxivity. The insights enable progress toward the long-term goals of providing a molecular-level understanding of TD-NMR characterization techniques and allowing the prediction of surface relaxivity. The reported ρ2 values help elucidate the importance of surface chemistry in TD-NMR methods and may serve as a reference for future studies of complex systems with similar chemical traits. It is notable that polymer particle suspensions are widely used in pharmaceuticals,47 printing technologies,48 composite manufacturing,15,49 and coatings.50 With such diverse applications, the systems under study serve not only as control samples but also represent commercial applications governed by fluid–surface interactions.

2. Experimental Section

2.1. Materials

Polystyrene (PS), poly(acrylic acid) (PAA), poly(ethylene-co-acrylic acid) (PE-AA), poly(4-vinylpyridine-co-styrene) (P4VP-S), poly(vinyl alcohol-co-ethylene) (PVOH-EE), poly(styrene-co-allyl alcohol) (PS-AAL), and Nylon-6 were purchased from Sigma-Aldrich. Table 1 provides the molar compositions of the tested copolymers, as provided by the supplier. Poly(ethylene terephthalate) (PET) was obtained from Goodfellow Materials. Kevlar pulp 1F538 was provided by DuPont Safety & Construction (Richmond, VA). ChromAR-grade water was purchased from Macron Fine Chemicals, and n-decane (≥99%) was obtained from Fisher Scientific.

Table 1. Molar Composition of Tested Copolymers as Reported by the Supplier.

copolymer molar composition (mol %)
poly(ethylene-co-acrylic acid) 95% ethylene, 5% acrylic acid
poly(4-vinylpyridine-co-styrene) 90% 4-vinylpyridine, 10% styrene
poly(vinyl alcohol-co-ethylene) 68% vinyl alcohol, 32% ethylene
poly(styrene-co-allyl alcohol) 60% styrene, 40% allyl alcohol
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Figure 1 presents the chemical structures of the polymers studied here.

Figure 1.

Figure 1

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Chemical structures of the polymers used in this study.

2.2. Particle Size Reduction

Fine polymer powders were obtained via cryogenic milling using an SPEX 6770 SamplePrep Freezer Mill. Approximately 2 g of polymer samples were loaded into polycarbonate vials and ground at liquid N2 temperature (−196 °C). The milling procedure comprised 10 or 20 min of precooling, 4 cycles of 1 min grinding at 10 CPS (counts per second), and 1 min cool time between runs. Kevlar pulp 1F538 and poly(acrylic acid) were used without grinding.

2.3. Laser Diffraction

The particle size distributions of the copolymers were obtained via laser diffraction (LD) using a Beckman Coulter LS 13 320 Particle Size Analyzer. Approximately 0.5 g of each polymer was dispersed in 5 mL of sodium hexametaphosphate solution at 5 wt %. Deionized water was added until the total volume reached 45 mL. Before data collection, a background scan was carried out for pure deionized water. The particle size distributions are presented in Figure S1, and the average particle sizes (d50) are compiled in Table S1.

2.4. N2 Physisorption

The specific surface areas (SSA) were characterized using the Brunauer–Emmett–Teller (BET) method via N2 physisorption in a Micromeritics ASAP2020 Surface Area and Porosity Analyzer.51 The reported values were calculated from the P/P0 range between 0.01 to 0.25. Polymer samples were degassed at 60 °C for 12 h at less than 5 μm Hg before data collection. The specific surface areas are presented in Table S1.

2.5. X-ray Diffraction

Powder X-ray diffraction (XRD) data were collected using a Bruker D2 Phaser Diffractometer with Co Kα (λ = 1.7890 Å), operated at 30 kV and 10 mA. Diffractograms were obtained at room temperature (295 K) with 2θ values ranging from 5 to 90° with a step size of 0.02° and rate of 0.3 s/step. For comparison with the literature, the XRD diffractograms were converted to 2θ values equivalent to those obtained using Cu Kα radiation (λ = 1.5406 Å). The %crystallinity (%C) values were estimated via curve fitting. See Supporting Information.52

2.6. Helium Pycnometry

The skeletal densities were determined via He pycnometry using a Micromeritics AccuPyc II 1340 Gas Pycnometer. The reported volumes and densities characterize the average value of 10 repeated cycles. The total uncertainty was propagated from the random and systematic uncertainties found from 10 different sample preparations and 7 consecutive polyethylene analyses. Most polymers were vacuum-dried at 60 °C for 12 h before data collection. Kevlar was vacuum-dried at 120 °C for 12 h. The skeletal densities are presented in Table S1.

2.7. Time-Domain Nuclear Magnetic Resonance (TD-NMR)

Transverse relaxation time data were collected using the Carr–Purcell–Meiboom–Gill pulse sequence using a Bruker Minispec mq-20 (0.47 T, 20 MHz) maintained at 20 °C using a Julabo CP-200F circulator bath.53,54 Each magnetization decay curve comprised 30,000 echoes, collected with a 90–180° pulse time spacing (τ) of 0.2 ms and a recycle delay of 4.5 s (n-decane) or 10 s (water). Particle suspensions with polymer concentrations varying from 1.3 to 10.0 wt % solid were prepared in 8 × 40 mm2 glass vials. Homogeneous dispersion was promoted by vigorous stirring using an IKA Minishaker. Samples were vacuum-dried (<77 Torr) at 60 °C for 12 h using a VWR Vacuum Oven before suspension in liquids. Measurements were performed in triplicate.

The observed solvent transverse relaxation rates were assessed based on their correlation to the surface chemistry and system porosity, eq 1.

2.7. 1

T2b represents the transverse relaxation time of the bulk fluid (2.3 s for water and 1.3 s for n-decane at 20 °C), ρ2 represents the transverse surface relaxivity, S the total particle surface area interacting with the fluid, and V the fluid volume. The values of T2b were determined separately for the pure liquid samples. Effects of relaxation induced by molecular diffusion and magnetic field gradient in the observed T2 are eliminated by the use of low-intensity magnetic fields and short echo-spacing separation.38,55,56 Because of their hindered translational motion, solids possess small T2 values, in the order of μs, and are undetectable in the tested conditions.57 The uncertainties in T2 and ρ2 were assessed based on the random and systematic uncertainties in sample preparation, the relaxation time of the bulk fluid, and the specific surface area of the polymers, see Supporting Information.

2.8. Interparticle Spacing Calculations

Interparticle spacing (IPS) calculations were performed using the model proposed by Hao and Riman, assuming homogeneous dispersion of spherical particles surrounded by a liquid cell, eq 2.58

2.8. 2

where rPol represents the polymer particle radius, estimated using laser diffraction analysis; ϕ the polymer volume fraction; and ϕm the maximum packing fraction density, taken as 0.59 for random loose packing.58 Here, ϕ was determined based on the polymer and liquid masses and the densities obtained from He pycnometry (Table S1).

3. Results and Discussion

3.1. Characterization of Polymer Wettability via TD-NMR

Solvent relaxometry is a convenient analytical method for porous media and particle suspensions as it allows sample characterization under their conditions of use.18,59 In TD-NMR experiments, the observed solvent relaxation rates provide insights into the material wetted surface area and solid–fluid affinity. Intermolecular interactions may induce faster relaxation of surface-adsorbed molecules compared to their “undisturbed” state.12 In particle suspensions, the observed T2 will depend on the frequency and strength of surface-fluid interactions as a reflection of the relative populations of surface-bound and free fluid molecules.60 Accordingly, the solid concentration and 1/T2 are expected to be positively correlated. Following these principles, Figure 2 displays the transverse relaxation rate data of the tested polymer particle suspensions in water and n-decane versus the respective surface-to-volume ratios. The data for PAA in water are not shown because it dissolved at the tested conditions; see Figures S3 and S4. The data for Kevlar in water are taken from Suekuni et al.15 The intercepts were set as the 1/T2b of deionized water (0.44 s–1) and n-decane (0.80 s–1) at 20 °C. The plotted error bars represent a rigorous uncertainty assessment within a 95% confidence interval, see Supporting Information.

Figure 2.

Figure 2

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1/T2 data for polymer particle suspensions.

Traditionally, materials are identified by whether they get wet by (philic) or repel (phobic) liquids, with water (hydrophilic/hydrophobic) and hydrocarbons (oleophilic/oleophobic) as common probing fluids.61 This fluid–surface compatibility is generally explained by fundamental concepts such as the “like-dissolve-like” rule, where polar moieties are expected to facilitate interactions with polar liquids.62 The trends in 1/T2 were notably regulated by polymer surface chemistry with a general opposite behavior for water and n-decane for most of the tested samples. Accordingly, the slopes of polymers with a high affinity for water were steeper than their response to n-decane and vice versa. Certain functional groups can induce preferential attraction or repulsion of fluids, regulating the wetting properties of surfaces. Figure 3 presents the transverse surface relaxivities linearly regressed by using eq 1 ordered by the observed affinity to water. Here, bar charts are used to clarify the trends and help elucidate their correlation to the expected wetting nature of the tested polymers. The reported values were regressed under the assumption that relaxation occurred in the fast-diffusion regime limit, where surface-bound and bulk fluid molecules are assumed to be diffusionally averaged throughout the experimental time.38,63 Here, a dimensionless parameter (k) was used to assess the validity of this assumption, as shown in eq 3.

3.1. 3

where α represents half of the interparticle spacing (see Section 2) and D is the liquid self-diffusion coefficient. At 20 °C, Dwater ∼ 2.0 × 10–5 cm2 s–1 and Ddecane ∼ 1.4 × 10–5 cm2 s–1.64,65 Based on the theory, systems with k ≪ 1.0 correspond to the fast-diffusion regime limit and the observed relaxation rates are directly associated with the pore surface chemistry and surface-to-volume ratio.38,63,66 In this study, k (water or n-decane) < 0.05, validating the assumption that the fast-diffusion regime criterion was met, Table S6. These values were calculated from the most diluted conditions tested, i.e., ∼1.3 wt % polymer, representing the largest interparticle spacing in suspension.

Figure 3.

Figure 3

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Transverse surface relaxivities of polymer–water and polymer-decane pairs. Kevlar (water) was obtained from Suekuni et al.15

PVOH-EE and P4VP-S yielded the highest surface relaxivities for water of the tested sample set, reflecting their mostly polar compositions (Table 1). Notably, the regressed ρ2 values for n-decane of these polymers are 4–11 times lower, indicating the preference for interactions with polar liquids. The regressed ρ2 values for Nylon-6 and PET were slightly lower than those of the first two copolymers. Such values can be associated with the contributions from the oxygen- and nitrogen-bearing moieties. Ono and Shikata showed that amide groups present high hydration numbers, i.e., 5–6 water molecules per group, supporting the high surface relaxivity of Nylon.67 Additionally, this value is in good quantitative agreement with the study by Fieremans et al., who reported a ρ2 of 4.6 μm s–1 for Nylon-6,12.68 For the case of PET, although ester groups have been recently classified as hydroneutral in dielectric relaxation studies, they can serve as H-bond acceptors in interactions with water and possess a similar dipole moment compared with the hydroxyl group.44 Furthermore, previous studies have shown that PET possesses a hygroscopic behavior, absorbing moisture from its surroundings.69 PET is the only polymer tested with a high surface relaxivity for both liquids, suggesting an amphiphilic behavior with a slight preference for water.

PE and PS, which are traditionally known for their hydrophobic nature, displayed ρ2 < 1.0 μm s–1, in good quantitative agreement with previous work. Fieremans et al. reported a ρ2 of 0.1 μm s–1 for ultrahigh molecular weight PE in water and Hansen et al., a ρ2 of 0.4 μm s–1 for poly(styrene) beads cross-linked with divinylbenzene.68,70 The relatively small concentration of acrylic acid of PE-AA did not result in a higher affinity for water, and its ρ2 is similar to PE. In fact, their (PE, PE-AA) response to n-decane is almost the same within the estimated uncertainty. Besides, the ρ2 values of PE and PE-AA for n-decane are larger than the one regressed for PS, reflecting the preferred interactions with alkane chains and the contributions of the higher proton density at the surface, favoring intermolecular proton–proton relaxation. Kevlar is known for its rigid polymeric structure, reflecting the low mobility of phenyl rings and the strong intermolecular hydrogen bonding between amide groups.71 These characteristics grant Kevlar its high tensile strength and low solubility, which might reflect the low surface relaxivities observed here.72 Surprisingly, PS-AAL also showed low surface relaxivity values for both liquids. Jeong et al. recently discussed the dominance of dispersive over polar forces in PS-AAL (40% AAL) surfaces, reporting contact angles of ∼73 and ∼32° for water and diiodomethane, respectively.73 These values agree with the past studies by Lee et al., who reported values of ∼81° (water) and ∼30° (diiodomethane) for PS-AAL (5.4–6.0% AAL).74 Comparison of these two works suggests that the allyl alcohol concentration does not significantly enhance the water wettability of PS-AAL regardless of the noticeable difference in the alcohol content. The dominance of dispersive surface forces, as reported in both studies, may contribute to the observed water-repelling nature of PS-AAL and the similar ρ2 of PS-AAL (0.5 ± 0.1 μm s–1) and PS (0.4 ± 0.2 μm s–1) for water. However, the low ρ2 of PS-AAL for n-decane requires further investigation.

3.2. Comparison of ρ2 and Water Contact Angles

The results of other surface-sensitive methods can help qualitatively assess the observed trends. Hence, ρ2 was compared with water contact angles (WCA) on polymers of equivalent composition from the literature, Figure 4.73,75−80 Here, two red dashed lines were used to mark the contact angle of 90°, traditionally known as the limit between hydrophilic and hydrophobic materials and ρ2 = 1.0 μm s–1. The comparison was restricted to water because finite contact angles for low surface tension liquids, such as normal alkanes, are rarely achievable under atmospheric conditions and require special features, e.g., fluorination and engineered topography.81,82 Further information about the contact angles used is provided in Table S4.

Figure 4.

Figure 4

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Comparison of the regressed surface relaxivities with contact angle measurements of equivalent polymers from the literature.

A general inverse relationship between ρ2 and water contact angles was observed, supporting the relationship between the polymer hydrophilicity and the surface relaxivity value for water. A linear regression, represented by the dotted blue line, showed a R2 = 0.64. Remarkably, the absence or the negligible heteroatom content contributed to a subpopulation of hydrophobic polymers by both techniques, i.e., PE, PE-AA, and PS, suggesting a useful correlation for practical applications. Kevlar and PS-AAL were outliers in the trend, with ρ2 < 1.0 μm s–1 and WCA < 90°. The influence of several aspects that may contribute to polymer ρ2 is evaluated in the following section.

3.3. Evaluating Contributing Factors to ρ2

A quantitative assessment of contributing factors to polymer surface relaxivity was implemented through multiple linear regression analysis, considering the unique contributions of predictor variables (xj) and their respective slopes (βj), eq 4.83

3.3. 4

where Y and β0 are the mean dependent variables and the regressed intercept, respectively. Here, the heteroatom content (hc), the hydrogen-to-carbon ratios (H/C), the %C, and d50 of the copolymers were considered predictors of ρ2. The value of hc was taken as the oxygen-to-carbon ratio for all polymers except P4VP, where the nitrogen-to-carbon ratio was used, calculated based on the molar compositions from Table 1, along with H/C ratios. The multiple linear regression analyses were conducted using the Minitab Statistical Software.

From the calculations, the polymer chemical composition (hc and H/C) was the most relevant predictor for ρ2 toward water and n-decane, with values 2–3 orders of magnitude greater than %C and d50, eqs 5 and 6. The p-values of each contributor are presented in Table S7. For the current data set, only hc (water) showed a p-value ≤ 0.05. No interactions between variables were observed for the considered predictors. Future studies that expand this database may support more statistically significant values.

3.3. 5
3.3. 6

As expected, while hc has a positive relationship with ρ2,water, it has the opposite behavior for ρ2,decane, in agreement with the “like-dissolve-like rule.” The hydrogen-to-carbon ratios showed positive correlations in both cases. However, the concentration of heteroatoms played a more significant role, indicating that hydrogen bonding has a stronger effect on solvent relaxation than homonuclear dipolar coupling. The correlation to heteroatom content may not capture the diverse properties of moieties, considering, for example, the different hydration numbers of oxygen- and nitrogen-bearing groups.43,44 Further investigation comparing such characteristics may yield more accurate predictors of ρ2 from the polymer composition and physical attributes. Highly crystalline polymers possess low surface free energy and are more resistant to surface treatments compared to their amorphous counterparts, given the strong intermolecular bonding between the chains.84,85 However, polymer crystallinity only weakly reduced the surface relaxivities, showing that surface chemistry is the most important contributor. These results agree with water wettability studies by Borcia et al., who did not observe strong correlations between the wettability and crystallinity of a series of polymers.86 The equally weak correlation to the average particle size indicates that small particles of high surface areas did not bias the observed values.

4. Conclusions

Time-domain NMR is a convenient and noninvasive method to study porous media under in situ conditions. Herein, trends in the transverse relaxation rates of polymer particles suspended in water and n-decane were used to probe the impact of surface chemistry upon solvent relaxation. The regressed ρ2 for polymer–water and polymer-n-decane pairs reflected their expected chemical affinity, ranging from 0.4 to 8.0 μm s–1 (water) and 0.3 to 5.4 μm s–1 (n-decane). The correlation between ρ2 and the polymer wetting properties was further supported by comparison with the water contact angle data from the literature. Polymer heteroatom (O, N) content, H/C ratios, %crystallinity, and average particle sizes were considered as predictor variables for ρ2 in multiple linear regression analyses. The obtained trends showed that surface chemistry (hc and H/C) has a superior influence upon ρ2 compared with crystallinity and particle size, with the content of heteroatoms as the most influential. Kevlar and PS-AAL were outliers in the assessed trends and may be the objectives of future investigations. Developing a database of surface relaxivities is important to decouple the effects from composition to material porosity, supporting the development and accuracy of TD-NMR methods. Furthermore, well-defined surface chemistries may provide a benchmark for understanding fluid relaxation in pores of naturally occurring materials.

Acknowledgments

The authors acknowledge the financial support from the American Chemical Society-Petroleum Research Funds (ACS-PRF) grant (61103-ND10); DuPont Safety and Construction for the generous donation of the Kevlar sample; and Spencer Kiessling from the Kansas Geological Survey for his assistance with the laser diffraction analysis.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.3c00384.

  • Polymer particle size distributions, specific surface areas, skeletal densities, uncertainty assessment for T2 and ρ2, X-ray diffraction data, polymer solubility assessment, and regressed contributors and p-values (PDF)

The authors declare no competing financial interest.

Supplementary Material

au3c00384_si_001.pdf (1.5MB, pdf)

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