11527
J. Phys. Chem. 1994, 98, 11527-11532
Dynamics of Water in the Poly(ethy1ene oxide) Hydration Shell: A Quasi Elastic Neutron-Scattering Study A. C. Barnes,' T. W. N. Bieze,' J. E. Enderby,+and J. C. Leyte*r' H. H. Wills Physics Laboratory, Bristol University, Royal Fort, Tyndall Avenue, Bristol BS ITL, U.K., and Department of Physical and Macromolecular Chemistry, Gorlaeus Laboratories, P.O. Box 9502, 2300 RA Leiden, The Netherlands Received: March 29, 1994; In Final Form: July 21, 1994@
A quasi elastic neutron-scattering (QENS) experiment has been carried out to elucidate the nature of the dynamic hydration of perdeuterated poly(ethy1ene oxide) (PEO) in aqueous solution. A line-shape analysis of the QENS spectra clearly shows evidence for a hydration zone around the polymer, the dynamic properties of which are significantly different from those of the bulk. The data were analyzed in terms of a two-phase model assuming Fick diffusion for both phases and allowing for exchange between the populations. The mobility of the hydration water is on the order of IO-" m2 s-l. This value corresponds to the rate of diffusion of the polymer as determined by pulsed-field gradient NMR (PFG-NMR). The average residence time of water in the polymer's hydration shell is approximately lo-" s. Assuming the hydration water mimics the motion of the chain, a Zimm-type scattering law was fitted to the data. Although line shapes are well described, the mobility of bulk water is inconsistent with the literature value.
incoherent scattering from the solvent molecules. However, no detailed line-shape analysis was performed to confirm this In a previous paper,' results conceming the static aspects of model, and the study did not address the case of dilute solutions, the poly(ethy1ene oxide) (PEO) hydration structure were preis the focus of the present report. sented. The results indicate, contrary to prevailing o p i n i ~ n , ~ . ~ ,which ~ We report here on a study of the dynamic hydration of [2H4]that a model in which PEO is fitted into an unperturbed water PEO at cp = 2 monomolal. From a polymer-physics standpoint structure is not consistent with the experimentally observed the solution is concentrated; cp c**.* However, since the distribution of solvent around the PEO monomer. Approximonomedwater ratio is 1:25 and with nhyd 6, a significant mately six water molecules are positioned at the monomedwater number of water molecules are sufficiently remote from the interface; i.e., nhyd 6. polymer to allow them to be labeled as bulk. High-resolution In this paper we wish to extend the work reported in ref 1 to (1.O- 1.5 peV) quasi elastic neutron-scattering spectra were the dynamics of the hydration structure of PEO. Previous work in this field was carried out by Dahlborg and c o - ~ o r k e r sThe . ~ ~ ~ determined using a 30 peV energy window. Accordingly, the motions of the protons on the solvent are observed in a -500 quasi elastic neutron-scattering (QENS) spectra from ['h]PEO/ ps time window with 13 ps resolution. The principle of the H20 solutions were recorded in a broad concentration range (1 experiment is similar to that of the extensive work carried out 5 cp I15 monomolal). Molecular mobility was observed in a on aqueous ionic solutions previously. In these studies a model s time window. Since solute and solvent were both scattering law for the hydration of the aqua ion based on the hydrogenous, a composite line shape is observed. Linebroading Frank-Wen model is used.g Using this picture, the water resulting from polymer motion was determined independently in CCb and subtracted from the data. It was concluded that molecules at any instant in time are considered to be in one of there exists a strong concentration dependent interaction between the zones A or B. Figure 1 shows the Frank-Wen model the monomers and the surrounding water which affects both adapted for the case of a cylindrical solute, i.e. a polymer. Zone the translational and rotational motions of the water molecules.6 A corresponds to the water hydrating the polymer; zone B is However, in the same work, the authors show that polymer the normal bulk water. An intermediate region may be defined dynamics in D20 and CCl4 is qualitatively different. Since (second hydration shell). In practice, a two-state model was experiments were carried out at relatively high q values (0.75-3 found to be sufficient to explain dynamics in aqueous ionic kl) and with only a moderate energy resolution, no definite solutions. In this model, if the water is bound to the solute for conclusions could be drawn concerning the nature of the time scales greater than the characteristic time scale of the interaction. experiment (1O-ll to 5 x s), it will acquire a scattering Earlier experiments at lower q and higher resolution' revealed law characteristic of the scattering law of the solute to which it that, for PEO solutions (20 5 cp 5 55 monomolal) in which all is attached, the free water showing a characteristic diffusional water is in contact with the polymer surface, the line broadening (Fickian) scattering law representative of the bulk. The resulting showed a characteristic q3 dependence of the half width at half scattering law observed in the experiment is then simply a linear maximum, Le., similar to the q dependence expected for polymer combination of these two scattering laws. If the bound water dynamics when motions are influenced by hydrodynamic exchanges with the bulk phase on a time scale similar to or interactions. Perdeuterated polymer material was used in this faster than the experimental time scale, a composite scattering study.' The QENS signal is therefore dominated by the law results. In practice the difference between these slow, intermediate, and fast exchange regimes can be readily distinBristol University. guished by carefully fitting the appropriate line shape and * Gorlaeus Laboratories. intensities to the experimental data.l0 For example, it is clearly Abstract published in Advance ACS Abstracrs, October 1, 1994.
1. Introduction
-
-
@
0022-365419412098-11527$04.50/0
0 1994 American Chemical Society
-
Barnes et al.
11528 J. Phys. Chem., Vol. 98, No. 44, 1994 n
_____-.---_____--PEO __._.-----_..----
Figure 1. Frank-Wen picture of ionic hydration adapted for the case of a cylindrical solute, Le., a polymer; A, hydration water; B, bulk water. The model may be expanded to allow for water hydrating the polymer at intermediate distances, Le., second hydration shell between regions A and B (not shown), or hydration water at hydrophilic and hydrophobic interfaces.
observed that the six hydrating waters around Ni2+ reside in the primary hydration sphere for time scales longer than s, whereas in the case of K+ the typical binding time is considerably shorter. In this work we attempt to carry out a similar study for the case of an aqueous PEO solution. 2. Experimental Section [2H4]Poly(ethyleneoxide) was obtained from MSD (Quebec, Canada) with M w = 11 400 g mol-' and MwIMn = 1.4. Contamination of the polymer with 'H was ==0.25%. A 2 monomolal sample was prepared in natural water that had been distilled, deionized, and filtered with a Milli-Q water purification system (Millipore Corp.) fitted with a 0.22 p m filter. The samples were sealed, and ample time (3 days) was allowed for equilibration. After preparation, the solution was stored at 4 "C in the dark to minimize biological and (photo)chemical degradation. The QENS experiments were carried out using the IN10 backscattering high-resolution spectrometer at the ILL, Grenoble. The samples were held in a flat circular container with tantalum windows (0.1 mm thick), spaced 1.5 mm apart. A sample temperature of 25 ( f l ) "C was maintained throughout the experiment. The incident neutron beam (wavelength 6.275 A) was obtained from the 111 reflection of an unpolished silicon monochromator. Detectors at 6.3, 8.6, 10.9, 13.2, 15.66, and 17.8" wereused, giving q-values of 0.11,0.15,0.19,0.23,0.27, and 0.31 %.-I, respectively. The energy transfer range used was f 1 5 ,ueV with an energy resolution of 1.0-1.5 peV. The instrumental resolution function was determined by reference to a standard vanadium plate of 2 mm thickness. Corrections for the effects of absorption and multiple scattering were made to both the sample and the vanadium spectra using a modified version of the Monte-Carlo program DISCUSL1 as outlined by Hewish et a1.I2 and Sa1m0n.l~
where Dhyd and Dbuk are the diffusion constants of the bulk and hydration water, respectively, andfhyd = (1 - fbuk). The relationship between the hydrated water fraction fhyd and nhyd, the hydration number per monomer, is given by
where the monomer concentration cp is given in monomolal. The hydration number can sometimes be determined independently from appropriate neutron diffraction data.14 The scattering law above corresponds to two Lorentzians in which the half widths at half maximum are equal to hDhydq2 and wukq2, respectively. If, on the other hand, the water molecules are moving in and out of the hydration shell on a time scale shorter than -lo-" s, one speaks of fast exchange. The scattering law is then a single Lorentzian
(3) where D is a diffusion constant given by the weighted average of the two diffusion constants in the system (E =fhydDhyd fb,&&ullr). This corresponds to a single Lorentzian with a similar Dq2 dependent half width. Between these extremes is the so called intermediate exchange regime in which hydration water to 5 x exchanges with the bulk on a time scale s. In this case the scattering law is more complex and consists of a sum of two Lorentzians which have a q dependence such that
+
3. Results To interpret the quasi elastic spectra, a suitable model for the scattering law S(q,o) has to be constructed. For the case of aqueous ionic solutions previously studied, a two-state model based on the Frank-Wen picture is generally used. In all cases the motion of the solute itself is assumed to be Fickian. Provided the water molecules are bound to the solute for longer than 5 x 10-lo s, the water is deemed to be in slow exchange and the scattering law is characterized by two diffusion constants: that of the bulk water and that of the diffusion constant of the solute to which the hydration water is bound. In formula:
with c1 = (1 - 4. Here D1 and D2 do not reflect the actual solute and bulk diffusion constants but represent functions that depend on &yd, &,a.and the mean lifetime of a water molecule in the hydration shell, Thy& similarly, the fractional weights of the Lorentzians do not reflect the size of the populations but depend explicitly on the above parameters including the hydration number nhyd. The details of the theory and the methods employed in the data analysis are given in ref 10. Figure 2 shows the quasi elastic spectrum (after correction for multiple scattering and absorption) obtained for the PEO solution studied in this experiment. The best fit curve to a single
Poly(ethy1ene oxide) Hydration Shell
J. Phys. Chem., Vol. 98, No. 44, 1994 11529 3.00
n
i
1-
2.50 2.00 u)
E
I (II
0
1.50
r
x
n
Q=O. 11
Q.O.23
r"l, V
b
I1 ''
-
0.00 0.10
0.15
./--
1 eV
1eV
1.00
Figure 2. Single Lorentzian fit (full curve) and residue. Errors on data are indicated. Arbitary intensity units (ueV s-I) on y-axis.
0.25
0.20
q
[A-ll
T
0.00 0.10
4.0.23
0.15
1eV
1 eV
0.25
0.20
q
Figure 3. Double Lorentzian fit (full curve) and residue. Half width at half maximum (hwhm) and ratio of amplitudes of Lorentzians are free parameters. Errors on the data are indicated. Arbitary intensity units (uev s-l) on y-axis. Lorentzian at each q-value (after convolution with the instrumental resolution function) is shown, along with the corresponding residual. It is clear that this data cannot be satisfactorily described with a single Lorentzian. The small (0.1%) contribution to the incoherent scattering from the deuterated polymer is insufficient to explain the poor fit. Accordingly, the model assuming Fick diffusion and fast exchange is not valid for times 5 2 ns. Retaining Fick diffusion for the present time window (lo-" to 5 x s), this means that the hydration water and the bulk water do not exchange fully within 2 ns. An attempt was made to fit the data using two Lorentzians corresponding to two different diffusion rates for the water in the system. The diffusion constants (&y& &.,a and ) the ratio of bound and free water Cfhyd, fbuk) were freely varied for each q-value. The resulting fits are shown in Figure 3. The small residues show that two Lorentzians can give an adequate description of the data. In Figures 4 and 5 , the diffusion constants (Dhyd, &k) and the fraction of the amplitude corresponding to the broad Lorentzian component are plotted as a function of q, respectively. Errors on the fitted parameters are indicated. Data are collected in Table 1. Large errors occur if the line shape and the resolution function are similar. This is especially apparent at small q-values, i.e., at q = 0.11 A-1. In fact, a double-Lorentzian fit does not significantly improve the quality of the fit at the lowest momentum transfer value,
0.35
Figure 4. Diffusion coefficients corresponding to hwhm from doubleLorentzian fit. 1.00
Q = O . 11
0.30
0.35
0.30
IA-7
Figure 5. Fractional amplitude of broad Lorentzian component (&,ad) from double-Lorentzian fit. TABLE 1: Effective Diffusion Constants and Ratio of Amplitudes from a Two-Lorentzian Fit to Quasi Elastic Line Shapes from a 2 monomalal [z&]PEO Solution in HzO Q" (A-1) 0.11 0.15 0.19 0.23 0.27 0.31
D1
m2 s-l)
2.91 f 3.1 2.43 f 0.35 1.73 f 0.11 1.85 f 0.13 2.3 f 0.36 1.9 f 0.38
D2 (10-lo mz s-l) 5.70 f 7.6 3.30 f 0.34 2.00 f 0.26 2.51 f 0.26 2.95 f 0.25 3.13 f 0.35
q resolution is approximately 0.07
c2
0.089 f 0.15 0.45 f 0.07 0.72 f 0.09 0.77 f 0.10 0.79 f 0.12 0.81 f 0.16
,&-I.
and data from this detector will be discarded in the following discussion accordingly. The diffusion constants and the weighting of the amplitudes shown in Figures 4 and 5 are q dependent. Given a polymer concentration cp = 2 monomolal, Cbroad is calculated to be 0.79 (eq 2). From Figure 4 and Table 1 it is observed that only for the high q detectors is Cbrod consistent with a physically acceptable hydration number. This q dependence is inconsistent with slow exchange. We therefore refrain from identifying Cbmad with fb&. The third possibility using a two-phase model is that of intermediate exchange. Here the scattering law at each value of q remains a sum of two Lorentzians except that the effective diffusion constants and amplitudes become q dependent. The fractional amplitudes of the Lorentzians no longer directly reflect the hydrated and bulk populations. To illustrate the effect intermediate exchange would have on the effective diffusion constants (01,~)and the weighting of the amplitudes of the
11530 J. Phys. Chem., Vol. 98, No. 44, 1994
Barnes et al. TABLE 2: Translational Diffusion Coefficients for Water in a 2 monomolal [zHJPEO Solution Determined with Pulsed-Field Gradient NMR and Quasi Elastic Neutron Scattering
* \
2.50
'>,
QENSb
PFG-NMR"
Slow'
intermediated
0
3 x lo-" Dplyme/ (m2 s-l) D,,,, D (m2 s-l) 1.9 x Dbuk (m2 s-') Dhyd (m2s-') thyd (s)
1.94 x 10-9 1.9 x 10-9 2.6 x 8 x lo-" -10-10 (0.8-1.0) x 10-1'
Time scale s. Time scale lo-" to 5 x s. Discarding q = 0.11 and 0.15 A-1. dDiscarding q = 0.11 A-'. 'Taken from ref 0.10
0.15
0.20
0.25
0.30
0.35
16. hydration number was fixed at 6 water molecules per monomer. With each set of parameters the sum of the weighted squared deviations was recorded. A single minimum was recorded in the parameter space covered. This solution was obtained using Dhyd = 8 X lo-" m2 S-', D b u k = 1.9 X low9m2 S - ' , and Zhyd = 1 x lo-" s. The lines drawn in Figures 4 and 5 show the solutions corresponding to these parameters. It may be remarked that the experimental data in the 0.17 5 q 5 0.31 momentum transfer range are, within error, q independent and would permit a slow exchange interpretation. In view of the accuracy of the data and considering the effect of ?&yd on the line shape in the intermediate exchange regime, the smallest value for Zhyd consistent with this interpretation is -IO-1o s. Results from slow and intermediate exchange are collected in Table 2 .
0.80
0.60
0.40
4. Discussion 0.20
