Note pubs.acs.org/Macromolecules
Diffusivity of Water Molecules in Amorphous Phase of Nylon‑6 Fibers V. M. Litvinov* DSM Resolve, P.O. Box 18, 6160 MD Geleen, The Netherlands S Supporting Information *
1. INTRODUCTION Transport of small molecules through polymers is one of the fundamental phenomena of large importance for many application areas of polymeric materials.1−3 The self-diffusion coefficient of small molecules in single-phase materials is traditionally obtained from analysis of permeability and gravimetric data.4 Several other methods are often used too, such as pulsed-field gradient NMR (PFG-NMR), fluorescence spectroscopy, radiative tracers, quasi-elastic neutron scattering, IR spectroscopy and microscopy, and MRI.5−8 The selfdiffusion of molecules in polymers is affected by several factors like mobility and orientation of chain segments, specific interactions between the absorbed molecules and the polymer matrix, and size and shape of the penetrant molecules.1,2,9,10 In addition to these factors, the diffusivity of small molecules through semicrystalline and multiphase polymers is also affected by crystallinity, crystal size and crystal aspect ratio, crystal orientation, and the type of semicrystalline morphology.1,9 Also in such multiphase systems the absorption of small molecules and their molecular mobility may differ between different permeable domains, leading to local diffusivities. Knowledge of intrinsic diffusivity of small molecules in the permeable phase is desired for understanding underlying molecular mechanisms of diffusion in multiphase polymers. However, different methods, which are used for determining the self-diffusion coefficient of molecules in polymers, measure the one-dimensional root-mean-square displacement of the molecules in the time window related to the method used, i.e., an apparent self-diffusion coefficient, possibly averaged over diffusion in different domains. Since the apparent self-diffusion coefficient is affected by several factors, its knowledge does not help in understanding the role of processing conditions and thermal history on permeability in semicrystalline polymers. Also, methods that are used for determining apparent selfdiffusion coefficient suffer from several artifacts. PFG-NMR is one of the most powerful methods for studying selfdiffusion.11−13 Possible complications related to this technique are caused by (1) direct spin exchange via dipolar coupling between nuclear spins of the solvent molecules and polymer chains (spin-diffusion) which affects the apparent self-diffusion coefficient14,15 and (2) changes of the magnetic susceptibility at internal interfaces.16 The permanent magnetic field of NMR magnet will generate internal field gradients which cause a variation in the magnetic susceptibility inside the sample at crystal−amorphous interfaces and/or at the sample−air interface. The last effect can be especially large in the case of semicrystalline polymeric fibers but can be partially reduced by the NMR experiments performed using low-field NMR equipment. © XXXX American Chemical Society
Semicrystalline polyamides and polyesters are widely used for food packaging due to their low permeability to water and oxygen molecules. Small molecules are mainly absorbed in soft fraction of the amorphous phase in nylons17,18 and therefore diffuse through this fraction. The amount of soft fraction of the amorphous phase and chain mobility in this fraction largely depend on processing conditions and thermal history of semicrystalline polymers.9,17,19 A fair comparison between selfdiffusion of small molecules in the amorphous phase of semicrystalline polymers which are prepared at different conditions is thus complicated. This also explains very large difference in apparent self-diffusion coefficient of water in nylon-6 processed at different conditions, as will be shown below. Thus, understanding the role of amorphous phase in transport properties of semicrystalline polymers is of a large practical importance for improving barrier properties of this class of polymers. The aim of this study is to assess the feasibility of using a NMR spin-diffusion method to measure indirectly the relative dif ference in self-diffusion of small molecules in the soft fraction of the amorphous phase of semicrystalline polymers. It is expected that the motion of the absorbed molecules affects the spin-diffusion between the amorphous and crystalline domains in the polymer. The spin-diffusion method is commonly used for determining the size of crystalline and amorphous domains. This method avoids the use of externally applied magnetic field gradients and therefore is less sensitive to sample internal susceptibility variations. It is expected that self-diffusion of small molecules followed by spin cross-relaxation at the border between crystalline and amorphous phases will affect the results of the spin-diffusion experiment. The cross-relaxation of water in hydrated polymers and its effect on water magnetization in Goldman−Shen experiments were studied in the past.20−22 To our knowledge, the effect of cross-relaxation between water spins and polymer spins on the magnetization transfer between hard and soft domains was not studied before. Because nylons absorb significant amounts of water, nylon-6 fibers that are processed at different conditions17 are a good model system for such study.
2. EXPERIMENTAL SECTION 2.1. Samples. Three nylon-6 fibers, differing in wind-up speed and draw ratio used for the fiber spinning, were used for this study, i.e., (1) as-spun fiber, winding speed = 500 m/min; (2) as-spun fiber: winding speed = 4800 m/min; (3) drawn fiber: winding speed = 500 m/min and draw ratio = 4.4. The samples are identified by a code such as F/ Received: March 17, 2015 Revised: June 19, 2015
A
DOI: 10.1021/acs.macromol.5b00570 Macromolecules XXXX, XXX, XXX−XXX
Note
Macromolecules 500/4.4 which indicates winding speed of 500 m/min and draw ratio of 4.4. The NMR experiments were performed for dried samples and those saturated with H2O. The amount of water absorbed by fibers was approximately 6 wt %. Detailed characterization of samples and their preparation for NMR experiments were provided previously.17 2.2. NMR Measurements and Data Analysis. Proton NMR T2 relaxation experiments were performed on a Bruker Minispec MQ-20 spectrometer. This spectrometer operates at a proton resonance frequency of 20 MHz. A BVT-3000 temperature controller was used for temperature regulation with an accuracy of ±0.1 °C. The experiments were performed at 40 and 120 °C for fibers saturated with H2O and dried samples, respectively. Absorbed water plasticizes the amorphous phase, causing a decrease in glass transition temperature (Tg) from ∼54 °C for dried nylon-6 to approximately −25 °C after saturation with water.23 Thus, for all samples, dried and saturated with water, the NMR experiments were performed at temperature ∼65 °C above Tg, i.e., at 120 °C for dried fibers (Tg ≈ 54 °C) and at 40 °C for fibers saturated with H2O (Tg ≈ −25 °C). To determine the proton spin-diffusion between the crystalline and amorphous domains, the 1H NMR Goldman−Shen experiment was used in this study.24−26 The experiment consists of three time periods: (1) magnetization filter used for selecting the magnetization of the amorphous phase and possibly absorbed water, (2) a mixing time tm (spin-diffusion period) during which the magnetization is allowed to be transferred between crystalline and amorphous phases via spin flips, and (3) a detection period for determining the degree of the magnetization transfer. Solid echo pulses with tse of 9 μs were used in both the preparation and the detection phases of the experiment: 90°x−tse−90°y−(tse + tr)−90°−x−tm−90°x−tse−90°y−[acquisition of the amplitude A(t) of the transverse magnetization relaxation as a function of timefree induction decay (FID)]. The point at the time from the beginning of the first pulse t = (2tse + t90) was taken as zero, where t90 was the duration of the 90° pulse. A delay time tr of 35.5 μs between the maximum of the first solid echo and 90°−x pulse was used to turn the magnetization of the soft fraction of the amorphous phase back to the equilibrium. Since the rate of T2 decay for the crystalline phase is hardly affected by water uptake, the same tr value was used for dried fibers and those saturated with water. It should be noted that the Goldman−Shen filter suffers from high selectivity due to rather small difference in the rate of T2 relaxation for different phases in nylon-6. A fraction of the magnetization of soft fraction of the amorphous phase and crystal−amorphous interface is not selected for dried fibers (see Supporting Information). However, it should not significantly affects results to be presented below since only change in the magnetization of the crystalline phase upon increasing tm is used for characterization of relative difference in self-diffusion of water in the amorphous phase. The filter selectivity is higher for fibers saturated with water due to plasticization of the amorphous phase, causing longer T2 of the amorphous phase. The filter selects in this case the magnetization of soft fraction of the amorphous phase and water. Water is mainly absorbed in this fraction,17,18 and its T2 relaxation is comparable to that of the soft fraction of the amorphous phase.17 The shortest mixing time tm was 0.1 ms. The signal at shorter mixing times is affected by the zero and double quantum coherences.27,28 The recycle delay time was 0.9 s. The number of scans for recording each FID was 32. A linear combination of Gaussian and two exponential functions was used for analysis of the FID17
for dried nylon-6, i.e., phase composition in weight percent. The analysis of FID provides the amount of low mobile chain segments, % Ts2, which is close to NMR crystallinity for dried fibers at ∼120 °C.17 For the fibers saturated with water, the slow decaying part of the FID (Tl2 relaxation) is due to soft fraction of the amorphous phase and absorbed water.17 No significant annealing of fibers occurs at 120 °C as was shown previously by experiments at 140 °C.17 FID’s recorded at different mixing times were analyzed with a leastsquares software program developed in our laboratory. The program is not only capable of fitting a single FID but can be also used to obtain a best fit of an array of FID’s measured at different mixing times, tm (global fit). The global fit provides one Tindex value for each relaxation 2 component of FID which fits the best all FID’s in the array. It was values were not significantly found by a separate fit of FID’s that Tindex 2 affected by the mixing time. The important improvement of the global fit, as compared with a separate fit of each FID, is the high reliability of the best fit values of the relative fractions of the relaxation . The use of the relative intensities, %Tindex , components, %Tindex 2 2 instead of the absolute amplitude of each relaxation component, A(0)index, largely compensates for a decrease in signal amplitude due to the T1 relaxation process. 2.3. Spin-Diffusion Experiments for Domain Size Determination. Applications of solid-state NMR for the analysis of domain sizes in heterogeneous polymers have been described previously for various polymers29−32 and nylon-6 fibers.33,34 Usually, the method yields information on domain sizes over length scales of approximately 0.5−200 nm. More precisely speaking, the NMR method probes the shortest distance across domains and “weight-average” domain sizes in the case of a distribution of domain sizes. It has to be noted that spindiffusion is not due to molecular diffusion but is due to transfer of the spin magnetization over a distance among coupled spins via consecutive mutual flips of neighboring nuclei spins. The time scale of spin-diffusion depends on the strength of the dipolar interactions between neighboring spins. For the magnetization transfer between two neighboring spins, the inverse of the dipolar interaction roughly is between 10 and 1000 μs, depending of the local chain mobility. The spin-diffusion process, like any diffusion process, is driven by a concentration gradientin this case by the spatial gradient in the nuclear magnetization. After many spin flips, the magnetization can be transferred over relatively long distances until the spin system in different phases reaches an internal equilibrium. The time which is required for the equilibration depends on domain sizes, morphology, and the efficiency of spin-diffusion as defined by a spin-diffusion coefficient. Two type of filters are used in NMR spin-diffusion experiments, i.e., DQ33,34 and Goldman−Shen filters.23 The DQ filter is highly selective for glassy and crystalline phases. Despite high selectivity of the DQ filter, the intensity of signal selected from soft phases is low with this filter.35 The Goldman−Shen filter is advantageous in this case, although it can suffers from lower selectivity to different phases as in the samples with small difference in T2 value for rigid and soft domains. Domain sizes are obtained by a fit of the entire spin-diffusion curve33,34 or by using the initial slope of the spindiffusion curve.36
3. RESULTS AND DISCUSSION 3.1. Effect of Water on Spin-Diffusion Data. The result of 1H spin-diffusion experiments using the Goldman−Shen dipolar filter for dried nylon-6 fiber F/500/4.4 is shown in Figure 1. In this experiment, the filter selects the magnetization of protons in soft amorphous domains and a fraction of the crystal−amorphous interface as shown in the Supporting Information. The selected magnetization is the source. The magnetization is then transferred to the crystalline phasethe sink. With increasing mixing time tm, this process results in an increase in the signal intensity of the crystalline phase at the expense of the signal of the source. The signal intensity for the crystalline phase is close to zero at short mixing time tm, showing the efficiency of the dipolar filter. This, however, is not
A(t ) = A(0)s exp[− (t /T2s)]2 + A(0)i exp[− (t /T2i )] + A(0)l exp[− (t /T2l )]
(1)
, is related to molecular where the characteristic decay time, Tindex 2 mobility in different phases: (i) α- and γ- crystalline phases: Ts2; (ii) crystal−amorphous interface: T2i ; and (iii) soft fraction of the amorphous phase: Tl2. Indexes “s”, “i”, and “l” stand for short, intermediate, and long decay time, respectively. The shorter the relaxation time, the lower the frequency and/or amplitude of the molecular motions is. The fraction of the relaxation components, as = {A(0)index/[A(0)s + A(0)i + A(0)l]} designated in the text by %Tindex 2 × 100%, represents the percentage of hydrogen atoms in these phases B
DOI: 10.1021/acs.macromol.5b00570 Macromolecules XXXX, XXX, XXX−XXX
Note
Macromolecules
ments for heterogeneous materials with absorbed small molecules (Figure 3). These are (1) self-diffusion of the
Figure 1. Spin-diffusion buildup curve of the magnetization of the crystalline phase and decay curves for the crystal−amorphous interface and soft fraction of the amorphous phase of the dry nylon-6 fiber F/ 500/4.4 at 120 °C. The initial slope of the curve for the crystalline phase is shown by the dotted line. The linear dependence in the initial spin-diffusion time regime leads to the intercept t00.5 at reaching the equilibrium amount of crystalline phase. Intercept value is used for determining domain sizes.36 The larger the intercept value, the larger the domain size is.
Figure 3. Schematic drawing of different phenomena which affect NMR relaxation behavior and the magnetization transfer in NMR spin-diffusion experiments in nylons with absorbed water: (1) selfdiffusion of water in the amorphous phase; (2) chemical exchange between hydrogen atoms of water and amide groups; (3) the magnetization transfer between crystalline and amorphous phases by spin-diffusion via flip-flops proton nuclear spins of polymer; and (4) spin-diffusion through cross-relaxation between polymer spins and those of water molecules which diffuse in the amorphous phase.
the case for fibers saturated with H2O (Figure 2). Here the signal intensity of the crystalline phase is already relatively large
small molecules, (2) chemical exchange if exchangeable hydrogen atoms are present, (3) spin-diffusion due to flipflop of polymer proton nuclear spins, and (4) spin-diffusion through cross-relaxation of polymer protons and protons of small molecules those position within sample changes due to molecular diffusion. It should be noted that the term crossrelaxation is generally used to describe the coupling between the spin−lattice relaxation of distinctly different nuclei, in particular in the presence of motions.20 However, the term spin-diffusion is used almost exclusively to describe the quantum-mechanical process by which nuclear spins can flip in a rigid solid lattice. A combination of two-dimensional 1H−1H NOESY and ROESY experiments can provide information on the rate of cross-relaxation and chemical exchange.40 The relative contribution of these two processes to the magnetization transfer depends on molecular mobility. The rate of cross-relaxation is higher for slower molecular motions, whereas the rate of chemical exchange decreases.14,40 Theoretical modeling of cross-relaxation, spin-diffusion, and self-diffusion of small molecules together with the fit of experimental data can be used for determining the contribution of each of these processes to the magnetization transfer in the Goldman− Shen experiment.14,20,21 Comprehensive analysis of all these phenomena in nylon-6 fibers with absorbed water is out of the scope of the present study. Qualitative comparison of the rate of water self-diffusion with the rate of cross-relaxation and chemical exchange is provided below. Chemical exchange between water protons and especially the polymer NH groups masks the true NMR relaxation behavior in nylons with absorbed water. The relations between true and apparent T1 and T2 relaxation times and exchange rate were established in the past.41,42 Fast proton exchange occurs between water and amide group of nylon chains.17,19 Since the majority of water is absorbed in the soft fraction of the amorphous phase,17,18 the exchange occurs in this fraction and
Figure 2. Buildup curve of the magnetization of the crystalline phase of water-saturated nylon-6 fibers F/500/1, F4800/1, and F/500/4.4 at 40 °C. Since crystallinity of fibers differs, the intensity of signal Mr(tm) at different mixing time tm is normalized to its value at the equilibrium Mreq. The normalization makes it easier to compare the relative difference in the spin-diffusion rates in these fibers. The dotted line shows the slope of the steepest part of the spin-diffusion curve for fiber F/500/4.4. The linear dependence provides the intercept t00.5 which is approximately the same as for the dried fiber at 120 °C.
at short mixing times and differs significantly for these three fibers studied. In order to understand the origin of such behavior, the role of water in this experiment should be considered in detail. 3.2. Self-Diffusion of Water and Its Effect on the SpinDiffusion Data. Interpretation of NMR relaxation data in polymers with absorbed water is impaired by numerous complicating factors.14,37−39 An exchange of nuclear spin magnetization between protons of a polymer and protons of small molecules largely depends on (i) hydrogen chemical exchange and the strength of hydrogen bonds, if exchangeable hydrogens are present, and (ii) molecular mobility of polymer segments and of the small molecules.14,40 Several phenomena affect the magnetization transfer rate in spin-diffusion experiC
DOI: 10.1021/acs.macromol.5b00570 Macromolecules XXXX, XXX, XXX−XXX
Note
Macromolecules
diffusion, no large signal intensity of the crystalline phase will be observed at short mixing times (Figure 2). The role of absorbed water is especially large for these studied fibers since the amount of hydrogens in the soft fraction of the amorphous phase, where water molecules mainly resides, is small (Table 3).17 Thus, relative amount of water hydrogens in soft fraction of the amorphous phase is high.
will not affect the magnetization of the crystalline phase. The molecular mobility of absorbed water molecules is largely restricted as compared to pure water due to hydrogen bonds with amide groups and surrounding polymer chains which hinder the translational motion of water molecules.19 Selfdiffusion of water in the amorphous phase of nylons should be also suppressed due to the same reasons. Two processes are competing in the magnetization transfer from protons in the amorphous domains to protons in the crystalline phase during the variable mixing time tm in the Goldman−Shen experiment, i.e., (1) the magnetization transfer which is caused by self-diffusion of water molecules within the amorphous phase followed by cross-relaxation at the border between amorphous and crystalline domains in combination with hydrogen exchange, and (2) the spin-diffusion process, i.e., the magnetization transfer by flip-flops of polymer nuclear spins. The self-diffusion coefficient of water in nylon-6 was determined by several authors from permeability data. The spin-diffusion coefficients for direct transfer of the magnetization from amorphous to crystalline domains for the same fibers were determined previously.34 The rates of these two processes of completely different origin are compared in Tables 1 and 2. First, different authors report largely different values of
Table 3. Phase Composition (in wt %) and Molecular Mobility in Dried Nylon-6 Fibers at 140 °C17 a F/500/1 phase composition crystalline phases 51.9 crystal−amorphous interface 31.9 soft fraction of the amorphous phase 16.2 chain mobility by T2 values crystalline phases 19.0 crystal−amorphous interface 50.1 soft fraction of the amorphous phase 198
D, cm2/s
reference
5 23 40 20 25 25
0.5 × 10−10 1.4 × 10−10 2.4 × 10−10 40 × 10−10 (46 ± 11) × 10−10 5.3 × 10−7
43 43 43 44 45 46
soft fraction of the amorphous phase semirigid crystal−amorphous interface crystalline phases
57.3 34.7 8.0
60.5 35.7 3.8
18.3 44.9 178
18.2 33.8 130
The rate of the magnetization transfer to the crystalline phase by self-diffusion of water decreases in the following order for nylon-6 fibers: F/500/1 > F/4800/1 > F/500/4.4. This is concluded from the signal intensity of the crystalline phase at short mixing times (Figure 2). In order to relate this difference to the phase composition, domains sizes, and molecular mobility in the amorphous phase of nylon-6, results of previous spin-diffusion experiments33,34 and a 1H NMR T2 relaxation study17 of the same fibers are summarized. Increase in winding speed and draw ratio causes a large decrease in the amount of soft fraction of the amorphous phase (Table 3). This means that the size of amorphous domains parallel and perpendicular to the fiber axis decreases with increasing winding speed and draw ratio.33,34 It should be noted that soft amorphous domains in nylons are “channels” for diffusion of small molecules.9 If the size of soft amorphous domains would be the key parameter determining the rate of the magnetization transfer from amorphous to crystalline domains at short tm values, the intercept value at tm = 0 should be the largest for fiber F/500/ 4.4 (Figure 2). However, the opposite is observed. This means that the main reason for the slower water diffusion in soft fraction of the amorphous phase is due to decrease in chain mobility in this fraction upon increase in winding speed and draw ratio that are used for fiber spinning (Table 3)17 and possibly higher chain orientation in the amorphous phase. The effect of local orientation of polymer chains on diffusivity of small molecules was shown by molecular dynamic simulations.47 It should be noted that the order parameter for the amorphous phase of nylon-6 fibers is larger for fibers processed with higher winding speed and draw ratio.48,49 Thus, the results reported above allow us making the following conclusion. The Goldman−Shen experiment can be used for determining relative dif ference in the rate of self-diffusion of water in amorphous phase of nylons if samples were processed at comparable conditions and have similar thermal history. The spin-diffusion method might be possibly used for estimating the size of crystalline domains in nylons with absorbed water. The magnetization transfer by self-diffusion of water followed by cross-relaxation at the crystal−amorphous
Table 2. Range of Spin-Diffusion Coefficients at Room Temperature in Different Phases of Nylon-6 Fibers Spun with Different Winding Speeds and Draw Ratios33,34 a physical phase
F/500/4.4
a Molecular mobility in different phases is defined by T2 value (μs); i.e., the shorter the T2 relaxation time, the lower molecular mobility and/or motional amplitude is.
Table 1. Apparent Self-Diffusion Coefficient of Water in Nylon-6 Which Was Determined by Analysis of Absorption Isotherms at Different Temperatures temperature, °C
F/4800/1
range of spin-diffusion coefficients (cm2/s) (5.1−8.5) × 10−13 (1.4−2.1) × 10−12 (2.1−2.5) × 10−12
The same fibers are used for the present study. In these previous studies,33,34 spin-diffusion coefficients were determined for fibers swollen in D2O. Therefore, the values of spin-diffusion coefficients were not affected by the presence of H2O protons. a
the apparent self-diffusion coefficient of water near ambient temperatures. This highlights the complexity of the analysis of absorption isotherms in the relation to intrinsic diffusivity of water molecules in amorphous phase of nylon-6. Despite the large difference in the provided values, it is clear that the apparent self-diffusion coefficient of water is at least 2 orders in the magnitude larger than the spin-diffusion coefficients in crystalline and amorphous phases of nylon-6. Therefore, the self-diffusion of water which is followed by cross-relaxation between polymer and water protons is the dominant factor in the transfer of the magnetization between the amorphous and the crystalline phases at the short mixing time. If the rate of cross-relaxation would be comparable with the rate of spinD
DOI: 10.1021/acs.macromol.5b00570 Macromolecules XXXX, XXX, XXX−XXX
Note
Macromolecules interface is much faster than spin-diffusion process. Therefore, this mechanism reaches a steady state already at short mixing time tm in the Goldman−Shen experiment. At longer tm, spindiffusion should play a major role as can be concluded by comparison of the data for fiber F/500/4.4 in Figures 1 and 2. The slope of the dependence and the intercept value t00.5 are approximately the same for dried fiber at 120 °C and for the same fiber with absorbed water at 40 °C.
Notes
4. CONCLUSIONS Transport of small molecules through polymers is one of fundamental phenomena of large importance for many application areas of polymeric materials. Self-diffusion of small molecules through semicrystalline polymers is affected by many factors. Different methods measure the one-dimensional root-mean-square displacement of small molecules in a time window given by the method used and not self-diffusion coefficient in amorphous phase which is a “channel” for diffusion of small molecules. The amount of soft fraction of the amorphous phase, chain mobility in this fraction, phase dimensions, and orientation which affect the tortuosity factor largely depend on processing conditions and thermal history of polymer. Therefore, knowledge of the apparent self-diffusion coefficient does not help in understanding the role of the various factors influencing the permeability in semicrystalline polymers. The present low-resolution 1H NMR study demonstrates that relative dif ference in the rate of self-diffusion of small molecules in the soft fraction of the amorphous phase of semicrystalline polymers can be inderectly determined by using the Goldman−Shen spin-diffusion method. The applicability of the method is illustrated for nylon-6 fibers with absorbed water. Although results of this method are influenced by several factors, i.e., water self-diffusion, chemical exchange between water and NH hydrogens of nylon, spin-diffusion, and cross-relaxation, these processes are effective at largely different time scales. Self-diffusion of water is the dominant factor in the transfer of the magnetization from the amorphous to crystalline phases of nylons at short mixing time values in the Goldman− Shen experiment, whereas spin-diffusion is efficient at longer tm. It is shown that self-diffusion of water in amorphous phase of nylon-6 fibers is lower for fibers spun with higher winding speed and higher draw ratio. The main reason for the decrease is more hindered chain mobility in the amorphous phase at more extensive fiber spinning conditions. Thus, the Goldman− Shen experiment can be used for determining the effect of processing conditions and thermal history of nylons on relative dif ference in the rate of self-diffusion of water in the amorphous phase. The method can be also applied for other heterogeneous polymers. This study demonstrates significant role of small molecules in the magnetization transfer in spin-diffusion experiments. Therefore, great care should be taken in sample preparation for spin-diffusion experiments used for determining domain sizes.
(1) Weinkauf, D. H.; Paul, D. R. Barrier Polymers and Structures; Koros, W. J., Ed.; ACS Symposium Series 423; American Chemical Society: Washington, DC, 1990. (2) Kärger, J., Haberlandt, R., Heitjans, R., Eds.; Diffusion in Condensed Matter; Vieweg: Wiesbaden, 1998. (3) Pitt, C. G. Int. J. Pharm. 1990, 59, 173. (4) Masaro, L.; Zhu, X. X. Prog. Polym. Sci. 1999, 24, 731. (5) Kärger, J.; Freude, D. Chem. Eng. Technol. 2002, 25, 769. (6) Osaka, N.; Shibayama, M.; Kikuchi, T.; Yamamuro, O. J. Phys. Chem. B 2009, 113, 12870. (7) Adriaensens, P.; Pollaris, A.; Carleer, R.; Vanderzande, D.; Gelan, J.; Litvinov, V. M.; Tijssen, J. Polymer 2001, 42, 7943. (8) Reuvers, N. J. W.; Huinink, H. P.; Adan, O. C. G. Polymer 2015, 63, 127. (9) Litvinov, V. M.; Persyn, O.; Miri, V.; Lefebvre, J. M. Macromolecules 2010, 43, 7668. (10) Tomić, K.; Veeman, W. S.; Boerakker, M.; Litvinov, V. M.; Dias, A. A. J. Pharm. Sci. 2008, 97, 3245. (11) Kimmich, R. NMR Tomography, Diffusometry, Relaxometry; Springer: New York, 1997. (12) Callaghan, P. T. Translational Dynamics and Magnetic Resonance. Principles of Pulsed Gradient Spin Echo NMR; Oxford University Press: Oxford, 2011. (13) Walderhaug, H.; Söderman, O.; Topgaard, D. Prog. Nucl. Magn. Reson. Spectrosc. 2010, 56, 406. (14) Peschier, L. J. C.; Bouwstra, J. A.; de Bleyser, J.; Junginger, H. E.; Leyte, J. C. J. Magn. Res., Ser. B 1996, 110, 150. (15) Horstmann, M.; Urbani, M.; Veeman, V. S. Macromolecules 2003, 36, 6797. (16) Sørland, G. H.; Aksnes, D. Magn. Reson. Chem. 2002, 40, S139. (17) Litvinov, V. M.; Penning, J. P. Macromol. Chem. Phys. 2004, 205, 1721. (18) Reuvers, N.; Huinink, H.; Adan, O. Macromol. Rapid Commun. 2013, 34, 949. (19) Litvinov, V. M.; Koning, C. E.; Tijssen, J. Polymer 2015, 56, 406. (20) Edzes, H. T.; Samulski, E. T. J. Magn. Reson. 1978, 31, 207. (21) Topgaard, D.; Söderman, O. Langmuir 2001, 17, 2694. (22) Wende, C.; Schönhoff, M. Langmuir 2010, 26, 8352. (23) Dlubek, G.; Redmann, F.; Krause-Rehberg, R. J. Appl. Polym. Sci. 2002, 84, 244. (24) Goldman, M.; Shen, L. Phys. Rev. 1966, 144, 321. (25) Kenwright, A. M.; Packer, K. J. Chem. Phys. Lett. 1990, 173, 471. (26) Mellinger, F.; Wilhelm, M.; Belik, P.; Schwind, H.; Spiess, H. W. Macromol. Chem. Phys. 1999, 200, 2454. (27) Packer, K. J.; Pope, J. M. J. Magn. Reson. 1983, 55, 378. (28) Kenwright, A. M.; Say, B. J. Solid Stae Nuclear Magn. Res. 1996, 7, 85. (29) Demco, D. E.; Johansson, A.; Tegenfeldt, J. Solid State Nucl. Magn. Reson. 1995, 4, 13. (30) Mellinger, F.; Wilhelm, M.; Spiess, H. W. Macromolecules 1999, 32, 4686. (31) Litvinov, V. M.; Braam, A. W. M.; van der Ploeg, A. F. M. J. Macromolecules 2001, 34, 489. (32) Wouters, M. E. L.; Litvinov, V. M.; Binsbergen, F. L.; Goossens, J. G. P.; van Duin, M.; Dikland, H. G. Macromolecules 2003, 36, 1147. (33) Buda, A.; Demco, D. E.; Bertmer, M.; Blümich, B.; Litvinov, V. M.; Penning, J. P. J. Phys. Chem. B 2003, 107, 5357. (34) Buda, A.; Demco, D. E.; Blümich, B.; Litvinov, V. M.; Penning, J. P. ChemPhysChem 2004, 5, 876. (35) Litvinov, V. M. Macromolecules 2006, 39, 8727.
■
The authors declare no competing financial interest.
■ ■
ACKNOWLEDGMENTS The author is thankful to D. E. Demco and W. S. Veeman for comments on the manuscript.
ASSOCIATED CONTENT
S Supporting Information *
Figure 1S. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.macromol.5b00570.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. E
REFERENCES
DOI: 10.1021/acs.macromol.5b00570 Macromolecules XXXX, XXX, XXX−XXX
Note
Macromolecules (36) Litvinov, V. M.; Xu, J.; Melian, C.; Demco, D. E.; Möller, M.; Simmelink, J. Macromolecules 2011, 44, 9254. (37) Smyth, G.; Quinn, F. X.; McBrierty, V. J. Macromolecules 1988, 21, 3191. (38) Quinn, F. X.; Kampff, E.; Smith, G.; McBrierty, V. J. Macromolecules 1988, 21, 3198. (39) Overloop, K.; Vangerven, L. J. Magn. Reson. 1993, 101, 147. (40) Rajamohanan, P. R.; Ganapathy, S.; Ray, S. S.; Badiger, M. V.; Mashelkar, R. A. Macromolecules 1995, 28, 2533. (41) Zimmerman, J. R.; Brittin, W. E. J. Phys. Chem. 1957, 61, 1328. (42) Woessner, D. E.; Zimmerman, J. R. J. Phys. Chem. 1963, 67, 1590. (43) Hernandez, R. J.; Gavara, R. J. Polym. Sci., Part B: Polym. Phys. 1994, 32, 2367. (44) Brandup, J.; Immergut, E. H. Polymer Handbook; John Wiley & Sons: New York, 1989; p V-115. (45) Monson, L.; Braunwarth, M.; Extrand, C. W. J. Appl. Polym. Sci. 2008, 107, 355. (46) Kojima, Y.; Usuki, A.; Kawasumi, M.; Okada, A.; Kurauchi, T.; Kamigaito, O. J. Appl. Polym. Sci. 1993, 49, 1259. (47) Chassapis, C. S.; Petrou, J. K.; Petropoulos, J. H.; Theodorou, D. N. Macromolecules 1996, 29, 3615. (48) Penning, J. P.; van Ruiten, J.; Brouwer, R.; Gabriëlse, W. Polymer 2003, 44, 5869. (49) Schreiber, R.; Veeman, W. S.; Gabriëlse, W.; Arnauts, J. Macromolecules 1999, 32, 4647.
F
DOI: 10.1021/acs.macromol.5b00570 Macromolecules XXXX, XXX, XXX−XXX
