D₂O with 99.9% isotopic purity and (not crosslinked) pNIPAM with M _n = 40,000 g mol⁻¹ were purchased from Sigma Aldrich. D₂O was used as obtained, while pNIPAM was vacuum dried over night at 1.6 × 10⁻⁵ mbar before sample preparation. After drying, pNIPAM was quickly filled in NMR glass tubes and weighted before the solvent was added. For the sample used in the home-built spectrometers, 3.25 mg and 77.9 µL of dried polymer and D₂O, respectively, were used, resulting in a polymer concentration of 3.6 wt%, or, equivalently, a monomer concentration of 0.6 mol%. After the pNIPAM was dissolved (within a few minutes), the open end of the sample tube was flame-sealed while damage to the sample material was avoided by immersing the lower part in liquid nitrogen. The sample for the Bruker spectrometer contained 29.85 mg of dried polymer and 650 µL of D₂O. This sample was sealed with a pressure cap and sealing film. After preparation, the samples were repeatedly weighted over the course of several weeks to verify that they were leak-proof during all measurements.

Fixed-field ²H T ₁ and T ₂ measurements were conducted at several B ₀ fields produced by superconducting magnets. The corresponding ²H Larmor frequencies (ω _L/2π) amounted to 24.8 MHz, 46.1 MHz, and 153 MHz. Explicitly, we used two home-built spectrometers for the experiments at the two smaller Larmor frequencies and a Bruker 1 GHz-AEON spectrometer for the highest frequency. In these setups, the T ₁ times were measured using the inversion or saturation recovery pulse sequences. The waiting times between scans were 5T ₁ to ensure full equilibration of the magnetisation but at least 2 s to avoid unwanted sample heating. The T ₂ times were measured with the CPMG sequence (Carr and Purcell, 1954; Meiboom and Gill, 1958). To avoid sample heating also in these experiments, the number of pulses was limited to ∼30 per scan and the waiting time between scans was increased to 30 s. In order to nonetheless cover the entire decay of the transversal magnetisation, we combined measurements with various interpulse delays while taking care of sufficient overlap of the respective magnetisation decays. In doing so, we ensured that, even for longer interpulse delays, diffusion during these periods did not interfere with echo formation and, thus, did not impair the measured T ₂ times. Supplementary ¹⁷O T ₁ measurements were performed using the same methodology at a ¹⁷O Larmor frequency of 40.7 MHz.

A detailed description of the home-built field cycling relaxometer can be found elsewhere (Kresse et al., 2011). Briefly, an electromagnet is used to quickly switch the applied magnetic field B ₀ and, in this way, measure the T ₁ relaxation time in a broad range of Larmor frequencies ω _L. In particular, the field-cycling approach allows one to overcome the low signal-to-noise ratios inherent to T ₁ measurements at low magnetic fields. In total, our ²H field cycling experiments cover a range of 5 kHz ≤ ω _L/(2π) ≤ 4.6 MHz.

In the home-built fixed field setups, a cryostat operated by utilising liquid nitrogen as cooling agent was employed to set temperature. For the Bruker spectrometer and the field-cycling relaxometer, temperature was controlled using a tempered gas flow. In all setups, temperature accuracy was better than ±1 K and temperature stability better than ±0.5 K. The 90° pulse lengths were ∼3 µs in the home-built setups, including the field-cycling relaxometer, while they amounted to ∼200 µs in the 153 MHz setup. Further details about the home-built setups can be found in previous work (Schiller and Vogel, 2024).

To determine T ₁ relaxation times, we fit the experimental magnetization data M(t) with a modified stretched exponential function: M t = Δ M 1 − A ⁡ exp − t T 1 β + M 1 . (10) Here, A = 1 and A = 2 in saturation-recovery and inversion-recovery experiments, respectively, while the fit parameter M ₁ serves to adapt the equation to experimental imperfections or the situation in field-cycling measurements. The stretching parameter β in Eq. 10 allows for possible nonexponential ²H spin-lattice relaxation in disordered materials. However, the analysis revealed that the recovery occurs in a single exponential manner in the present measurements, i. e., β ≈ 1, see Supplementary Material. As aforementioned, this finding means that, provided slow and fast subensembles exist, rapid exchange between them occurs on the T ₁ time scale. With this in mind, we fit the CPMG data with single exponential decays to extract T ₂ times.

In Figure 1, we show ²H T ₁ and T ₂ relaxation times of D₂O in the pNIPAM mixture for a fixed Larmor frequency of ω _L = 2π ⋅46 MHz. Both T ₁ and T ₂ react to the LCST of pNIPAM with a rapid decrease. Similar changes across the LCST were observed in previous NMR works (Ohta et al., 1991b; Tanaka et al., 1998; Schönhoff et al., 2002; Kariyo et al., 2005; Sierra-Martin et al., 2005; Kametani et al., 2017). While T ₁ ≈ T ₂ below the LCST, as expected for fast liquid dynamics with ω _L τ ≪ 1, T ₂ is notably shorter than T ₁ above the coil-to-globule transition. Except near the LCST, both relaxation times increase when the temperature is increased, reflecting the corresponding speedup of water reorientation.

To remove this trivial effect and focus on the influence of pNIPAM, we renormalise T ₁ and T ₂ on their corresponding values in neat D₂O (Hindman et al., 2003) in Figure 2. The step-like decrease of T ₁ and T ₂ across the LCST is even more apparent on the basis of the renormalised relaxation times. The temperature of the coil-to-globule transition is in agreement with LCST values of 305 K in the literature (Halperin et al., 2015). Note that the LCST transition of pNIPAM was reported to be mildly broadened and shifted to higher temperatures when deuterated solvent is used (Shirota et al., 1999). Moreover, the renormalised data reveal that a heating-cooling hysteresis in the range from around 305 K–315 K is very small, consistent with previous results (Sierra-Martin et al., 2005; Rusu et al., 2006).

Naively one might assume that T ₁ and T ₂ increase rather than decrease when heating through the LCST because the accessible surface of collapsed pNIPAM is reduced (Vijayakumar et al., 2022) and polymer-water hydrogen bonds are broken so that less solvent molecules are slowed down by the interaction with the polymer. This could, however, be overcompensated if water molecules in contact with pNIPAM experience a particularly strong slowdown when the polymer is collapsed. The observation that T ₂ is shorter than T ₁ above the LCST is a first hint that such very slow water fraction emerges during the coil-to-globule transition. Specifically, because T ₂, unlike T ₁, depends on J ₂ (0), see Eqs 2, 3, this difference suggests that, above the LCST, some water molecules do not obey the limit of fast motion (ω _L τ ≪ 1) in the fixed-field measurements. Because detailed information about the dynamics of this slow water species is not available from conventional high-field T ₁ and T ₂ measurements at a single or at most very few Larmor frequencies, we will use ²H FCR for further quantification below.

Below the LCST, the T ₁ and T ₂ times of D₂O in the solution are smaller than those in the neat liquid and, hence, the renormalised values of the pNIPAM solutions are smaller than unity. Specifically, the ratio r of the relaxation times of the studied solution and the neat solvent amounts to r ≈ 0.8 well below the LCST. This finding, which again agrees with previous results (Sierra-Martin et al., 2005; Rusu et al., 2006), has several origins. First, it reflects the general increase in viscosity η when adding a solute, which, due to η ∝ τ ∝ T 1 − 1 in the limit of fast motion, leads to a shorter T ₁ time in the pNIPAM solution than in neat D₂O. In addition, a ratio r < 1 results because, even for pNIPAM’s coiled state, deuterons experiencing slower than bulk-like dynamics exist, e. g., deuterons in the hydration shell of the polymer, and lead to slower average dynamics and, hence, a reduced T ₁ time in the pNIPAM solution. Specifically, it is evident from Eqs 6, 9 that in the limit of fast motion, the ratio r of the spin relaxation times T _i of the neat solvent and the studied solution yields the inverse ratio of the respective mean correlation times ⟨τ⟩ and, thus, the average slowdown s of water reorientation due to the presence of pNIPAM molecules: 1 r = T i neat T i solution = 〈 τ solution 〉 〈 τ neat 〉 ≡ s . (11)

One might object that the observed drops of the ²H T ₁ and T ₂ times across the LCST do not reflect changes of water dynamics but result from altered relaxation behaviour of the small fraction of deuterons, which arrived at the amide groups of the polymer by chemical exchange. For example, one might argue that pNIPAM’s side group motion changes during the coil-to-globule transition such that the amide deuterons exhibit shorter T ₁ and T ₂ times above the LCST than below and, as a result, the measured exchange-averaged relaxation times decrease upon heating through this temperature. To dispel this objection, we performed supplementary ¹⁷O T ₁ measurements. In these experiments, chemical exchange with the polymer does not play a role and the results exclusively reflect water ( H 2 17 O) reorientation. We find that the drop of T ₁ across the LCST is similar for ²H and ¹⁷O, see the Supplementary Material, indicating that the effect clearly results from changes in water reorientation.

Thus, in agreement with previous studies (Ohta et al., 1991b; Tanaka et al., 1998; Schönhoff et al., 2002; Kariyo et al., 2005; Sierra-Martin et al., 2005; Kametani et al., 2017), our ²H NMR findings indicated that a slow water fraction emerges during the coil-to-globule transition of pNIPAM. This conclusion was confirmed by new ¹⁷O NMR results. However, such measurements at a single Larmor frequency do not allow one to independently determine the amount and the slowdown of the emerging bound water fraction.

Next, we apply ²H FCR to analyse the evolution of the spectral density of D₂O reorientation across pNIPAM’s coil-to-globule transition in more detail. In Figure 3, we see that the FCR approach yields T ₁ times over a frequency range of three orders of magnitude and by adding T ₁ data from measurements in superconducting magnets more than 4 decades are covered. In this figure, we do not show T ₁ (ω _L) but rather 1/T ₁ (ω _L), which is related more directly to the spectral density J ₂ (ω _L), see Eq. 2. In panel (A), the field-cycling and fixed-field data consistently show that, in the accessible frequency range, the 1/T ₁ rates of the D₂O-pNIPAM mixture do not exhibit a significant dependence on ω _L at T ≲300 K. Such an absence of 1/T ₁ dispersion is expected for the limit of fast motion, i. e., for Larmor frequencies in the range ω _L ≪ 1/τ, where the spectral density has a frequency-independent value, see Eq. 6. For the temperatures shown in panel (B) and also the higher temperatures shown in panel (A), we see that a frequency dependence of 1/T ₁ develops when heating through the LCST. Specifically, 1/T ₁ (ω _L) significantly increases when the Larmor frequency is decreased, indicating the emergence of a slow dynamical process. Thus, above the LCST, a minor fraction of D₂O, which shows slowed-down reorientation and adds a broad low-frequency dispersion, accompanies the major proportion of D₂O, which shows fast bulk-like reorientation outside the accessible frequency range and, hence, contributes with a frequency-independent 1/T ₁ plateau. In the following text, we refer to these fractions as bound (b) water and free (f) water, respectively.

To consider the existence of two D₂O species with distinguishable dynamics, we assume that the spectral density J ₂ (ω _L) is a weighted sum of two contributions: J 2 ω L = R J LG ω L + 1 − R J CD ω L (12) with 0 ≤ R ≤ 1 and J _CD and J _LG given by Eqs 4, 5, respectively. Thereby, the CD spectral density accounts for the faster free water species at sufficiently large distances from the pNIPAM molecules, which shows bulk-like reorientation, often characterised by such CD behaviour, whereas the LG spectral density describes the slower bound water species, which strongly interacts with the polymer and, hence, should experience a Gaussian energy landscape typical of disordered matrices. We note that the use of a CD form is not critical to our results but other spectral densities allowing for a constant value in the studied frequency range could have been employed as well. However, we determined that a LG spectral density better describes the observed increase of 1/T ₁ (ω _L) at small Larmor frequencies than several other functional forms, e.g., a CD form. Using this weighted superposition of J _CD (ω _L) and J _LG (ω _L) in Eq. 2, we fit the 1/T ₁ (ω _L) data of the D₂O-pNIPAM mixture, as will be described next.

Free fits suffer from the fact that the dynamics of free water is too fast to result in a 1/T ₁ (ω _L) dispersion in the accessible frequency range, interfering with a reliable determination of the parameters of J _CD. Explicitly, free water obeys ω _L ≪ 1/τ in the whole frequency window and, hence, yields a frequency-independent contribution to the spectral density, J _CD = ⟨τ _f⟩ = τ _CD γ _CD, see Eq. 7. The corresponding 1/T ₁ (ω _L) plateau is clearly observed when bound water is absent well below the LCST, see Figure 3A, but a flattening out of the 1/T ₁ dispersion at the highest of the studied Larmor frequencies implies that such plateau also exists above the LCST, see Figure 3B. Therefore, it is sufficient to use J _CD = ⟨τ _f⟩ in the fit analysis. Moreover, when we assume that the reorientation dynamics of free water molecules at sufficient distances from the pNIPAM molecules is not affected by the coil-to-globule transition, it is possible to predetermine this frequency-independent value at all studied temperatures based on existing knowledge. Specifically, using Eq. 11 and identifying ⟨τ _solution⟩ with ⟨τ _f⟩, the slowdown s of water dynamics in the solution can be obtained by comparison of the dispersion-free T ₁ times well below the LCST with the values for neat D₂O (Hindman et al., 2003), see Figure 3A. An average over the results for temperatures in the range 280–300 K yields a slowdown of s = 1.25, which is consistent with the above finding of r = 0.8 in the fixed-field measurements. Keeping this value of s fixed even above the LCST, yields ⟨τ _f⟩ from the results for neat D₂O (Hindman et al., 2003). Having obtained the CD spectral density at all temperatures in this manner, the remaining free fit parameters are the fraction R of bound water and the time constant τ _LG and standard deviation σ _LG of its LG distribution.

In Figure 3, we see that the fits with this two-species model, see Eq. 12, well describe the FCR data. In particular, the low-frequency process associated with the slow water fraction is well described by the LG spectral density J _LG at all temperatures T ≥ 306 K. As aforementioned, such a shape of the spectral density is not found in pure (viscous) liquids or polymer melts, where CD behaviour prevails, but it is often observed when a mobile component moves in a disordered matrix so that thermally activated motion is governed by a Gaussian distribution of energy barriers. Aside from the previously mentioned plasticizer molecules in polymer matrices (Jansen-Glaw et al., 1989), such a situation was also reported for mobile ions in disordered solid electrolytes (Haaks et al., 2017; Winter et al., 2020). Moreover, LG-like behaviours, explicitly, Cole-Cole spectral densities, were used to describe water dynamics in the hydration shells of proteins and polymers (Cerveny et al., 2004; 2008; Lusceac et al., 2011). Thus, the observed LG shape confirms the above suggestion that the low-frequency process can be assigned to a water fraction which strongly interacts with pNIPAM. Explicitly, we propose that the bound water species moves inside the dense polymer matrix formed by the collapsed pNIPAM globules and, in this way, shows rotational dynamics as they would result from a Gaussian distribution of energy barriers.

The resulting fit parameters are displayed in Figure 4. First, we focus on the findings at temperatures T ≥ 306 K. The time constant of the LG contribution, which specifies the peak position of the associated distribution of correlation times, amounts to τ _LG ≈ 10^–9 s near the LCST and decreases when the temperature is increased. The standard deviation σ _LG, which describes the width of the distribution, has a basically temperature-independent value of σ _LG ≈ 2.3. Thus, the LG distribution has a full width at half maximum of more than two orders of magnitude, indicating that very strong dynamical heterogeneity results from the interaction of bound water with the pNIPAM molecules in their collapsed state. To quantify the difference in the dynamics of free and bound water, it is important to characterize the respective distributed dynamics with the same type of average. Here, we utilize the mean correlation times ⟨τ _f⟩ and ⟨τ _b⟩ for this comparison, where the latter is available from τ _LG and σ _LG using Eq. 8. In Figure 4B, we see that ⟨τ _b⟩ is about 3 orders of magnitude longer than ⟨τ _f⟩ well above the LCST. Altogether, the ²H FCR analysis shows that the interaction with pNIPAM globules leads to strongly slowed down and much more heterogeneous water dynamics.

The bound water fraction is very small. It amounts to R = 0.002–0.003 above the LCST. To follow its evolution during the coil-to-globule transition, we extend the range of our fit analysis to lower temperatures, where less prominent 1/T ₁ (ω _L) dispersions lead to enhanced statistical uncertainty. Therefore, unlike in the above discussed fits at T ≥ 306 K, where σ _LG was treated as free parameter, we fix the standard deviation of the LG contribution at the average of the values at such higher temperatures, σ _LG = 2.3, when fitting data at lower temperatures. The results of fits with this constraint are shown as open symbols in Figure 4. We observe that R is negligibly small below 300 K and rapidly increases when heating across the LCST, confirming that the emergence of the slow water species is caused by pNIPAM’s coil-to-globule transition. The fit result of a significant temperature dependence of τ _LG near the LCST should be taken with great caution because of the marginal 1/T ₁ dispersion below 306 K, see Figure 3A.

Although only a very small water fraction strongly interacts with the polymer at a given instant, it should be noted that an exchange between bound and free water fractions occurs in the course of time. Moreover, we need to consider that a small value of R is a direct consequence of using a dilute solution. Specifically, considering the large molar fraction of water (99.4 mol%) in our sample, R = 0.002–0.003 still implies that 0.3–0.45 water molecules per NIPAM unit are slowed down. Currently available other estimates of the number of water molecules per NIPAM unit in the collapsed state of the polymer scatter significantly, e. g., values of 0.2–0.4 (Lele et al., 1997), 1.8 (Vorob’ev and Faleev, 2005), 4.5 (Balachandar et al., 2023), 6 (Philipp et al., 2014), and 8 (Heskins and Guillet, 1968) were reported. However, it should be mentioned in this context that these values may characterise metastable states because waiting-time dependent T ₂ measurements indicated that the captured water molecules are expelled from the pNIPAM globules on the time scale of ∼4 days (Starovoytova and Spěváček, 2006).

To check the results of our FCR analysis for consistency, we use the obtained fit parameters to calculate the evolution of the T ₁ and T ₂ times across the LCST for various fixed Larmor frequencies ω _L. In doing so, a running average is applied to mitigate the statistical fluctuations of the LG parameters and, thus, smoothen their temperature dependence. The resulting smoothed parameters are included in Figure 4. It can be seen in Figure 5 that the calculated T ₁ values well reproduce the temperature dependence of the experimental T ₁ times for all studied frequencies. In particular, the observation that the change across the LCST is much stronger for lower values of ω _L is well captured. This effect results from the finding, see Figure 3, that, above the LCST, the slow reorientation of the bound water influences the spectral density particularly at lower frequencies, whereas the fast dynamics of the free water continues to dominate J ₂ at higher frequencies. Likewise, we observe in Figure 6 that the J _LG and J _CD spectral densities obtained from the above T ₁ analysis even allow us to satisfactorily describe the variation of T ₂ across the LCST. Because T ₂, unlike T ₁, depends on J ₂ (0), see Eq. 3, the former relaxation time changes less than the latter when the Larmor frequency ω _L is varied in our case. Furthermore, the fact that the fits exclusively involved T ₁ data, which are independent of J ₂ (0), may rationalise the observation that the experimental T ₂ data, which strongly depend on this contribution, are less accurately described by the predictions calculated therefrom. Altogether, the determined spectral densities of the bound and free water fractions consistently describe the T ₁ and T ₂ relaxation times of the studied D₂O-pNIPAM mixture in broad temperature and frequency ranges. This is evidence that a small water fraction emerges during the collapse of the pNIPAM molecules, which shows much slower and more heterogeneous reorientation dynamics than bulk water.

To further illustrate our findings for bound water, we characterise the reorientation of this species by an NMR susceptibility χ _NMR (ω _L). For this purpose, we first determine the contribution of bound water to the 1/T ₁ (ω _L) dispersion by subtracting the contribution of free water from the experimental data, explicitly, R T 1 b ω L = 1 T 1 ω L − 1 − R T 1 f ω L . (13) In doing so, T 1 f ( ω L ) is calculated based on Eq. 6 from the mean correlation times ⟨τ _f⟩ used in the above analysis. Then, we exploit that an NMR susceptibility can be obtained when multiplying spin-lattice relaxation rates 1/T ₁ (ω _L) by the respective Larmor frequencies (Kruk et al., 2012; Becher et al., 2022), or in our case of bound water: χ NMR b ω L ≡ ω L R T 1 b ω L . (14)

Figure 7 shows the thus determined NMR susceptibilities of bound water. In this susceptibility representation of the results, it becomes particularly clear that the bound water shows a very broad susceptibility peak and, hence, very strong dynamical heterogeneity, which is well described by a LG distribution of correlation times. The susceptibility peak is even broader than the accessible frequency range. Specifically, information about its high-frequency flank is not available from the present ²H NMR relaxation study. Due to the prominent dynamical heterogeneity in combination with the small fraction of the bound water, the faster of these molecules do not cause a notable 1/T ₁ dispersion before the contribution of the major fraction of free water governs the experimental findings at sufficiently large Larmor frequencies ω _L.