Structure and mobility in water plasticized poly(ethylene oxide)

Polymer 48 (2007) 3294e3305 www.elsevier.com/locate/polymer

Structure and mobility in water plasticized poly(ethylene oxide) Charlotte Trotzig a, Susanna Abrahmse´n-Alami b, Frans H.J. Maurer a,* a

Department of Polymer and Materials Chemistry, Lund Institute of Technology, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden b AstraZeneca R&D, SE-431 83 Mo¨lndal, Sweden Received 10 September 2006; received in revised form 13 March 2007; accepted 16 March 2007 Available online 21 March 2007

Abstract The change in structure and mobility of poly(ethylene oxide) (PEO) containing 2 wt% of fumed silica and the water self-diffusion coefficient in concentrated PEOewater systems have been investigated at room temperature in the water weight fraction, ww, range 0e0.50 w/w. Pulsed field gradient nuclear magnetic resonance was used to measure the self-diffusion coefficients. Structure and mobility properties of PEO were measured with differential scanning calorimetry as well as with positron annihilation lifetime spectroscopy. The largest reduction of the degree of crystallinity of PEO was observed when ww was increased from 0.13 w/w to 0.50 w/w. Moreover, water induced relaxation of the PEO segments in the amorphous phase, which seemed to have been strained by the crystals during compression molding. The water self-diffusion coefficient increased logarithmically with increased water content below water weight fractions in the amorphous phase of 0.30 w/w and the water molecules were obstructed by the crystalline phase. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Self-diffusion coefficient; Degree of crystallinity; Free volume

1. Introduction Poly(ethylene oxide) (PEO) is a thermoplastic watersoluble polymer that, among other fields, is used in the pharmaceutical industry [1] to formulate tablets with extended drug release. In the pharmaceutical industry, fumed silica is usually added to PEO in order to improve its powder flow properties. When exposed to water, the structure and mobility of the semi-crystalline PEO are altered. Incorporation of water in low molecular weight PEO has previously been shown to decrease the degree of crystallinity [2e7] and increase the mobility [3] of the PEO. For semi-crystalline polymerewater systems the free volume hole size, Vh, has been shown to both decrease and increase as a function of the water content [8e10]. The structural changes of PEO affect the mobility of water in PEOewater systems. One way of characterizing the mobility of the water molecules is by measuring the self-diffusion * Corresponding author. Tel./fax: þ46 46 222 40 12. E-mail address: [email protected] (F.H.J. Maurer). 0032-3861/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2007.03.047

coefficient, Dself, which is a measure of the translational motion in an equilibrated system, using pulsed field gradient nuclear magnetic resonance (PFG NMR). The self-diffusion of water has previously been measured in PEOewater systems, where PEO had a molar mass of at most 14,000 g/mol and the water weight fractions were above 0.4 w/w [11,12]. As the water content was relatively high in these samples, the degree of crystallinity of PEO was assumed to be negligible. In contrast, at low water contents the degree of crystallinity has to be taken into consideration since the self-diffusion is regarded to take place only in the amorphous phase [13]. When regarding the crystallites as impermeable, the lengthening of the diffusive pathway caused by the crystallites [14] must be taken into account when interpreting Dself obtained by PFG NMR. Another aspect to consider when performing PFG NMR experiments with the stimulated echo (STE) pulse program in systems where the mobility of the system components is low [15] is the possibility of proton spin exchange between the water proton spins and the ethylene oxide (EO) proton spins [16].

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

A semi-crystalline polymer may contain a rigid amorphous (ra) phase, positioned at the interphase between the crystalline (c) and the undisturbed amorphous (a) phases [17]. The rigid amorphous phase does not give rise to any melting point, and in contrast to the undisturbed amorphous phase, the rigid amorphous phase exhibits a glass transition that is much broader and occurs at higher temperatures [18]. Thus, the rigid amorphous phase does not contribute to the change in heat capacity, DCp, at the glass transition temperature, Tg, of the undisturbed amorphous phase [18]. By plotting the DCp obtained at the Tg of the undisturbed amorphous phase for samples of varying degrees of crystallinity vs. the heat of fusion, DHf, of the same samples, the presence of a rigid amorphous phase can be proven if the plot displays a negative deviation from a straight line [17]. Water in polymers can be classified thermally as being either freezing or non-freezing and is termed bound if it melts below the melting temperature of free (bulk) water. The term ‘‘bound’’ originates from that the water molecules reside close to the polymer and consequently are strongly affected by its presence. Non-freezing water is always considered bound to the polymer, whereas freezing water may be bound both to the polymer and to the surrounding water molecules. Water, that melts at the same temperature as free (bulk) water experiences only its surrounding water molecules and is termed freezing water. In contrast, water that melts at lower temperatures than free water and hence resides close to the polymer is termed freezing bound water. The term non-freezing bound water is used for water that does not show any thermal transition when measured with DSC [19]. It has previously been shown that only non-freezing bound water exists in PEOe water systems below water weight fractions of 0.09 w/w [7]. The aim of the reported research was to investigate the change in structure and mobility of PEO as well as the variation of the water self-diffusion coefficient as a function of water content. Furthermore, the water absorption in PEO as a function of the relative humidity and the thermal properties of water in the system were investigated by using thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC), respectively. Dself was determined with PFG NMR. Structural and mobility properties of PEO such as the degree of crystallinity, xc, the melting temperature interval, the glass transition temperature, Tg, and the heat capacity change, DCp at Tg were measured with DSC, whereas the free volume hole size, Vh, was quantified by means of positron annihilation lifetime spectroscopy (PALS). 2. Experimental section 2.1. Materials The semi-crystalline poly(ethylene oxide) POLYOX RESIN WSR N-10 was produced by Dow Chemical Company and contained 2 wt% of fumed silica as determined by TGA according to Section 2.3 given below. Its weight average molar mass, Mw, was 1.08  105 g/mol as determined by size exclusion chromatography with water as the mobile phase.

3295

2.2. Sample preparation PEO, in the form of powder, was melted in a DSM corotating twin screw midi-extruder at 120  C and 50 rpm during a residence time of 8 min. The extruded PEO was then dried under vacuum at 44  C for 15 h, after which the extrudate was compression molded at 120  C to 1 mm thick films. These films were cooled between two metal plates of approximately 20  C to room temperature and finally dried for 24 h at room temperature. By putting the samples in desiccators containing various salt solutions providing relative humidities ranging from 0% to 98%, a variety of water weight fractions, ww, in the samples could be obtained. The films were equilibrated for at least 10 days at each respective relative humidity in desiccators stored at room temperature in a dark environment. 2.3. TGA The water uptake in dried 1 mm thick PEO films that had been cut to 1 cm squares and weighed around 0.15 g was measured gravimetrically every third day until a constant water weight fraction (0.5 wt%) was reached (approximately 8 weeks at the highest relative humidity). The final water uptake in films after complete absorption as well as the water content of the samples probed with DSC, NMR and PALS was measured with a TA instruments TGA Q500 by heating the samples at 10  C/min until a constant weight was reached (around 150  C). Moreover, the amount of fumed silica in the PEO films was determined by heating at 50  C/min to 1000  C. 2.4. DSC The thermal properties of both PEO and water in the PEOe water system were measured with a TA Instruments DSC Q1000. Sealed hermetic aluminum pans containing 2e5 mg of sample were cooled, held isothermally and finally reheated. The cooling and heating rates were optimized for the property intended to be measured. The samples were cooled at 1  C/min from 25  C to 5  C, where the samples were held isothermally for several hours, cooled to 20  C at 1  C/min and finally cooled to 90  C at 20  C/min, where they were kept isothermally for 3 min. The slow cooling was performed in order to give the PEO time to further crystallize. After 3 min at 90  C, Tg of PEO was determined by running the samples at a heating rate of 20  C/min to 20  C. Thereafter, melting of PEO was measured with a heating rate of 10  C/min from 20  C to 100  C. The state of the water in the samples was measured by cooling the samples at 1  C/min from 25  C to 90  C, where they were kept isothermally for 15 min prior to heating to 25  C at 1  C/min. 2.5. PALS The ortho-positronium (o-Ps) lifetime, to-Ps, and intensity, Io-Ps, were measured by means of PALS. The measured mean to-Ps value, in nanoseconds, can be used in the

3296

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

semi-empirical TaoeEldrup equation [20,21] in order to obtain the representative radius of a free volume cavity, R, ˚: with its units in A   1 R 1 2pR sin to-Ps ¼ 0:5 1  þ R0 2p R0

ð1Þ

Here, R0 is the radius of a spherical potential well with an electron layer of thickness DR ¼ R0  R. DR has been cali˚ previously, by obtaining the best fit of Eq. brated to 1.66 A (1) to experimental data of various molecular solids [22]. The free volume hole size, Vh is defined through Eq. (2): 4pR3 ð2Þ 3 The PALS equipment used in this study has been described in detail elsewhere [23]. The 22Na source had an activity of approximately 1.2 MBq and was deposited between two 8 mm thick Kapton foils. The source gave a count rate of approximately 700 counts per second. Thus, three spectra, of which each contained 2.5 million counts, could be collected within 3 h. The experiments were performed at 1 atm pressure and 23  C. The spectra were evaluated with the program POSITRONFIT [24] into three mean lifetimes, tp-Ps, tfree positron, and to-Ps, which correspond to para-positronium, direct annihilation of positrons and ortho-positronium with intensities Ip-Ps, Ifree positron, and Io-Ps, respectively. No source correction was used and tp-Ps was fixed at 0.125 ns during the evaluation procedure. The reported values of to-Ps are average values of the mean o-Ps lifetimes in the three spectra. The 22Na source was inserted between two identical polymer samples that were circular with a diameter of approximately 15 mm and a thickness of about 1 mm. Each wet sample was separated from the source by inserting an 8 mm thick sheet of Kapton foil between the source and the sample. The sample holder was sealed in order to prevent moisture loss throughout the experiment. Vh ¼

2.6. NMR PFG NMR was used to measure the mean square molecular displacement of the water molecules using both stimulated echo (STE) (a) and spin echo (SE) (b) pulse programs [25], as described in the sequences below: (a) 90 e t1 e 90 e t2 e 90 e t1 e echo (b) 90 e t e 180 e t e echo In the programs, radio frequency (rf) pulses that turn the magnetization signal 90 or 180 are applied on the sample at millisecond time intervals of t1, t2 and t. An echo is created at time 2t1 þ t2 in the STE pulse program and at time 2t in the SE pulse program. Two gradients that tag or read the positions of the proton spins are applied on the samples short after the first and the last rf pulse and are separated by a time interval, D. The gradients were of amplitude G and duration d. G was varied between 0.1 T/m and 10 T/m. When running the

samples with water contents below 0.50 w/w with the STE pulse program, D was 40 ms or 200 ms, d was 3 ms and t1 was 4 ms and with the SE pulse program, D was 20 ms and d was 1 ms. The sample with a water content of 0.50 w/w was run with the SE pulse program with D set to 50 ms and d to 1 ms. The repetition time between consecutive scans was set to at least 5 times the longitudinal relaxation time, T1. The experiments were carried out at 20  0.5  C with a Bruker DMX spectrometer and a Bruker Wide Bore spectrometer, the latter equipped with a diffusion probe head (DIFF 30), operating at a 1H resonance frequency of 200 MHz and 400 MHz, respectively. The NMR samples with water weight fractions below 0.50 w/w were rectangular films and approximately 2 mm wide, 35 mm long and 1 mm thick, whereas the NMR sample with a water weight fraction of 0.50 w/w was a thick solution. All samples were inserted into 5 mm NMR tubes that were sealed by melting. Dself was determined through the StejskaleTanner relation [26] below for the STE (Eq. (3a)) and the SE (Eq. (3b)) pulse programs, respectively:


ð3aÞ I 2t1 þ t2 ¼ I 0 exp  kDself


I 2t ¼ I 0 exp  kDself 2

k ¼ ðgH GdÞ D  d=3




ð3bÞ ð4Þ

Here I(2t1 þ t2) and I(2t) represent the signal amplitude or integrated peak area in the presence of a gradient and I(0) the signal amplitude or integrated peak area in the absence of a gradient. gH is the gyromagnetic ratio of hydrogen. I(0) can be described according to Eqs. (5a) and (5b) for the STE and SE pulse programs, respectively [27,28]:   2t1 t2 Ið0Þ ¼ I0 0:5 exp   ð5aÞ T2 T1 

2t Ið0Þ ¼ I0 exp  T2

 ð5bÞ

I0 is the transverse magnetization directly after a 90 pulse has been applied on the sample. Only half of I0 is stored in the longitudinal direction in the stimulated echo experiment. T2 and T1 are the transverse and longitudinal relaxation times of the water protons in the sample, respectively. 3. Results and discussion 3.1. Melting of PEO The water weight fraction (the weight of the water divided by the total weight) of the PEOewater system, ww, as a function of the relative humidity (RH) is shown in Fig. 1. As can be seen, there was a large increase in the absorbed amount of water above a RH of 90%. This drastic absorption increase has been observed previously for chloroform absorption in PEO and was most likely accompanied by a reduction of the

C. Trotzig et al. / Polymer 48 (2007) 3294e3305 0.7 0.6 0.5

ww

0.4 0.3 0.2 0.1 0.0 0

20

40

60

80

100

RH (%) Fig. 1. The weight of water divided by the total sample weight, mwater/ mPEOþwater, ww, as a function of the relative humidity (RH).

crystalline phase and reconstructions and increase in size of the remaining spherulites [29]. This increased amount of amorphous phase can be expected to be associated with an enlargement of the amorphous inter-lamellar distances [30] and hence enables room for water molecules between the crystalline lamellas [13]. In Fig. 2 the heat of fusion, DHf, and degree of crystallinity, xc, of PEO are shown as a function of the water weight fraction, ww. The measured DHf was not only corrected for the fraction of water in the sample, but also for a fraction of 2 wt% of fumed silica that had been added to the pure PEO by the producers. The degree of crystallinity was based on a reference heat of fusion value for a PEO crystal of 203 J/g [31] and was calculated as: xc ¼

DHf 203

ð6Þ

3297

the crystalline material in the PEO melted when exposed to water. This melting seemed to continuously increase in magnitude as the water weight fraction increased and the remaining crystallinity at 0.50 w/w was only 0.004. Such depletion of the crystalline structure above a ww of 0.50 w/w has previously been seen in PEGs of varying molar masses [4e6]. Fig. 3 displays the start and end melting temperatures for PEO as functions of ww. The end melting temperature decreased from 74  C to 24  C whereas the start melting temperature decreased from 37  C to 16  C. Thus, the melting temperature interval (i.e. the difference between the start and end melting temperature) decreased from around 35  C at ww values of 0e0.13 w/w to 8  C at a ww of 0.50 w/w. The melting temperature interval moved toward lower temperatures, but did not decrease during the beginning of the water absorption (0e0.13 w/w). This indicates that both small and large crystals in the PEO spherulites were affected when water was absorbed and that the slow cooling prior to the heating of these samples did not result in any further crystallization. The more or less constant melting temperature interval in the water content region 0e0.13 w/w was in agreement with previous measurements on PEOewater systems [2]. At a water weight fraction of 0.50 w/w, the melting temperature interval had decreased significantly, indicating a narrower crystal size distribution than in the low water content region and reconstruction of crystals [29]. Moreover, the melting temperature interval at 0.50 w/w, i.e. 16e24  C, combined with the low degree of crystallinity at this ww, indicated that almost no spherulites were present at room temperature. The water weight fraction in the amorphous phase, ww(amorphous phase), was calculated by using xc together with the corresponding ww of each sample. In Fig. 4, ww is plotted vs. ww(amorphous phase). The solid line in Fig. 4 corresponds to a completely amorphous sample. As can be seen, ww and ww(amorphous phase) approached each other as the water content increased above a ww of 0.13 w/w. In Fig. 5, xc vs.

According to the calculations, xc in the dry sample was 0.74. As can be seen, xc decreased as ww increased, indicating that 160

0.8

140

0.7

120

0.6

100

0.5

80

0.4

60

0.3

40

0.2

20

0.1

20

0.0

10

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

ww Fig. 2. The heat of fusion, DHf, and the degree of crystallinity, xc, of PEO as a function of the water weight fraction, ww.

Melting temperature (ºC)

70

xc

ΔHf (J/g PEO)

80

60 50 40 30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

ww Fig. 3. The start (:) and end (C) melting temperature as a function of the water weight fraction, ww.

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

3298 0.6

ww(amorphous phase)

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

ww Fig. 4. The water weight fraction in the amorphous phase, ww(amorphous as a function of the total water weight fraction, ww.

phase),

ww(amorphous phase) is illustrated. The decrease in crystallinity was continuously increasing in magnitude as ww(amorphous phase) increased. If this trend remained throughout the melting, a steep drop in xc would eventually be obtained resulting in ww(amorphous phase) being more or less constant during the melting of most of the crystals. This behavior would be in agreement with the behavior previously observed for PEOe chloroform systems [29]. For the PEOewater system, it can be concluded that the decrease in crystallinity was lower during the melting of the last crystals than during the melting of most of the crystals, rendering some crystallinity left at ww(amorphous phase) of 0.51 w/w. 3.2. Thermal properties of water in the PEOewater system

slow cooling can be seen in Fig. 6. No crystallization of the water was observed for the sample containing 0.30 w/w of water during cooling as opposed to the sample containing 0.51 w/w of water. However, upon heating, after cooling, the water cold-crystallized in the 0.30 w/w sample in the same temperature interval as the crystallization during cooling of the 0.51 w/w sample. The water in the 0.51 w/w sample melted at higher temperatures than the water in the 0.30 w/w sample. The cold-crystallization and consecutive melting of the 0.30 w/w sample are indicated with arrows and also shown as a magnification in Fig. 6. No endotherms corresponding to the melting of water were observed for samples with lower water contents than 0.30 w/w. Melting of PEOewater eutectics with water contents of 0.45 w/w has previously been observed in the same melt temperature interval as that of the sample with a water content of 0.51 w/w [2]. Thus, it is possible that the melting peak for the sample with a ww(amorphous phase) of 0.51 w/w corresponds to an overlay of a water melting peak and a eutectic melting peak. Furthermore, the melting temperature interval of the water in both samples indicated that the water could be classified as freezing bound water in the water weight fraction range 0.30e0.51 w/w, whereas the absence of water melting endotherms at 0.23 w/w denoted the presence of only non-freezing bound water, at least below 0.23 w/w. Water has previously been observed to start freezing in PEOewater systems of similar molar mass in the water weight fraction range 0.09e 0.17 w/w over the total sample weight (ww) [7]. This ww range includes 0.13 w/w, which is the ww in the sample that corresponds to a ww(amorphous phase) of 0.30 w/w. The amount of water per EO unit in the amorphous phase is 0.7 mol and 1.1 mol for the samples containing 0.23 w/w and 0.30 w/w of water, respectively. Hence, it appears as if the water in the PEOewater system started to freeze in the water content region where the amount of water molecules exceeded the amount of EO units.

Thermograms corresponding to the heating of PEOewater samples with ww(amorphous phase) of 0.30 w/w and 0.51 w/w after 1.0

0.0

Heat Flow (mW/g)

0.8

xc

0.6

0.4

-0.2 0.08

-0.4

0.06 -60

-40

-20

0.2 -0.6 0.0

-100 0.0

0.1

0.2

0.3

0.4

0.5

0.6

ww(amorphous phase) Fig. 5. The degree of crystallinity, xc, of PEO as a function of the water weight fraction in the amorphous phase, ww(amorphous phase).

-80

-60

-40

-20

0

20

40

Temperature (°C) Fig. 6. Melting of freezing bound water in samples of two water weight fractions in the amorphous phase: 0.30 w/w (upper curve) and 0.51 w/w (lower curve). The inset shows a magnification of the upper curve (0.30 w/w).

C. Trotzig et al. / Polymer 48 (2007) 3294e3305 1.0

3.3. Heat capacity change at the glass transition of PEO

In the glass transition temperature interval of PEO, DCp of water [33] is small in comparison to DCp of PEO. Thus, DCp (water) was considered negligible when calculating DCp (PEO). When DCp per gram of PEO was calculated, both the water weight fraction and the 2 wt% of fumed silica that had been added to the pure PEO by the producers were taken into account. In Fig. 8, DCp (PEO) is plotted vs. DHf (PEO). The solid line in the figure connects the theoretical values of DCp (a) (0.86 J/g/ C) [34] and DHf (c) (203 J/g) [31] for 100% amorphous and 100% crystalline PEO, respectively. As can be seen, experimental data displayed a negative deviation from the theoretical data, but approached the theoretical data as the water content increased. According to Pyda and Wunderlich negative deviations indicate the existence of a rigid amorphous phase in the polymer [17]. The amount of rigid amorphous phase, xra, can be calculated by the following equation [18]: DHf ðscÞ DCp ðscÞ  DHf ðcÞ DCp ðaÞ

ð8Þ

Here DHf (sc) and DCp (sc) are the heat of fusion and heat capacity change, respectively, for a semi-crystalline sample. Fig. 9 shows xra vs. ww(amorphous phase). As can be seen, the rigid amorphous phase was almost completely depleted above water weight fractions in the amorphous phase of 0.30 w/w.

0.8

ΔCp (J/g PEO/°C)

The change in heat capacity, DCp, at the Tg of each PEOe water sample was measured in the water weight fraction range 0e0.13 w/w. No Tg was detected at a ww of 0.50 w/w. Fig. 7 illustrates DCp per gram of the total sample as well as per gram of PEO in the sample as a function of ww(amorphous phase). The DCp of PEO can be calculated by assuming the following relation [32]:


DCp sample ¼ xPEO DCp PEO þ xwater DCp water ð7Þ

xra ¼ 1 

3299

0.6

0.4

0.2

0.0 0

50

100

150

200

ΔHf (J/g PEO) Fig. 8. The heat capacity change, DCp, per gram of PEO, as a function of the heat of fusion, DHf, per gram of PEO.

Another way of interpreting the change in DCp at Tg, without involving any rigid amorphous phase, is by taking into account that changes in the interactions between the PEO and water upon altering the water weight fraction, render a change in the contributions from different conformational heat capacities to the overall heat capacity [35]. 3.4. Glass transition temperature of the PEOewater system Fig. 10 displays the glass transition temperature, Tg, of the PEOewater system (determined as the midpoint of the heat capacity change, DCp) as a function of ww(amorphous phase) in the range 0e0.30 w/w. As a comparison, the Tg of PEG 5700 containing 0 w/w and approximately 0.3 w/w of water [3] is also included in the figure. Moreover, the prediction of the Tg with the Fox equation [36] as well as a fit of the GordoneTaylor (GT) [37] equation to experimental data can

0.35 0.16 0.30

0.14 0.12

0.20

0.10

0.15

0.08

xra

ΔCp (J/g /°C)

0.25

0.06

0.10

0.04

0.05

0.02 0.00 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

ww(amorphous phase) Fig. 7. The heat capacity change, DCp, per gram of sample (-) and per gram of PEO (C) as a function of the water weight fraction in the amorphous phase, ww(amorphous phase).

0.00 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

ww(amorphous phase) Fig. 9. The degree of rigid amorphous phase, xra, of PEO as a function of the water weight fraction in the amorphous phase, ww(amorphous phase).

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

3300 -40

phase might have obstructed the separation of the PEO segments in the amorphous phase to some extent.

-50

Tg ( ºC)

3.5. Free volume properties of the PEOewater system -60

-70

-80

-90

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

ww(amorphous phase) Fig. 10. The glass transition temperature, Tg, in the studied PEOewater system (C) and in PEG 5700 (:) [3] as a function of the water content in the amorphous phase, ww(amorphous phase). (e e) is the fitting of the GordoneTaylor equation to the Tg in the studied PEOewater system and (ee) is the calculation of Tg according to the Fox equation.

The ortho-positronium (o-Ps) lifetime, to-Ps, and intensity, Io-Ps, were measured on films with water weight fractions in the amorphous phase, ww(amorphous phase), in the range 0e 0.30 w/w. The spectra were evaluated with POSITRONFIT with a maximum variance of fit of 1.4 and a standard deviation for to-Ps and Io-Ps of at most  0.03 ns and  0.2%, respectively. In Fig. 11a and b the variation in to-Ps and Io-Ps vs. ww(amorphous phase) can be seen. It was observed that to-Ps decreased from 2.08 ns in dry PEO to 2.02 ns at ww(amorphous phase) 0.23 w/w, after which it increased to 2.03 ns at ww(amorphous phase) 0.30 w/w (Fig. 11a). The to-Ps value of dry PEO is in agreement with previous measurements [40,41]. In pure water to-Ps is 1.86 ns as measured by Eldrup

A

be seen in the figure. Eqs. (9) and (10) describe the Fox and GT equations, respectively.

1 Tgblend

¼

wPEO þ kwH2 O wPEO TgPEO þ kwH2 O TgH2 O

ð9Þ

2.05

τo-Ps (ns)

1 wPEO wH2 O ¼ þ Tgblend TgPEO TgH2 O

2.10

2.00

1.95

ð10Þ 1.90

1.85

0.0

0.2

0.4

0.6

0.8

1.0

0.8

1.0

ww(amorphous phase)

B

28 26 24

Io-Ps (%)

Here Tgblend and Tgwater are the glass transition temperatures of the PEOewater system and pure water, respectively. Tgwater has been reported to be 135 K [33]. The Tg of dry PEO (TgPEO) in the present study was slightly higher than the previously measured Tg of PEO with a molar mass of 200,000 g/mol [38]. The decrease in Tg in our system agreed with the decrease in Tg of PEG 5700 as a function of the water content in spite of the fact that PEG 5700 had crystallized in the presence of water. In contrast to the Tgs calculated with the Fox equation, exhibiting a fairly constant slope at all water contents in the intermediate and high water content regions, a slightly negative deviation from the linear decline of the experimental Tgs at intermediate and high water contents was observed for the sample with a ww(amorphous phase) of 0.30 w/w. The Fox equation predicted much lower Tg values than the experimentally determined data. Furthermore, the fit of the GT equation to the experimental data was poor with a k-value above 1 (1.10), which is an indication of a high miscibility between PEO and water [32]. The strong positive deviation from the Fox equation as well as the k-value of 1.10 may have been due to water molecules interacting simultaneously with two PEO ether oxygens on different PEO segments [39] and consequently hindering separation of the PEO segments. In addition, strained conformations in the rigid amorphous phase surrounding the undisturbed amorphous

22 20 18 16 14

0.0

0.2

0.4

0.6

ww(amorphous phase) Fig. 11. (a) The ortho-positronium lifetime, to-Ps, as a function of the water weight fraction in the amorphous phase, ww(amorphous phase). (b) The orthopositronium intensity, Io-Ps, as a function of the water weight fraction in the amorphous phase, ww(amorphous phase).

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

et al. [42]. The decrease of to-Ps indicates that the free volume hole size, Vh, in the PEOewater system decreased when the amount of water increased. The densification of the PEOe water system might have been due to certain water molecules interacting simultaneously with two ether oxygens on different PEO segments, causing them to come closer together. Densification of nylons, through the formation of hydrogen bonds between water and carbonyl and amide groups on the polymer backbone has previously been shown [8,9]. However, this densification has been ascribed to the release of strained conformations, induced by the hydrogen bonding between the polymer backbone groups [9]. Consequently, another explanation might be that stress, created in the sample due to PEO crystal formation during the cooling after compression molding, was released as the plasticizing water molecules entered the PEO matrix and caused the polymer segments to relax and come closer together. As ww(amorphous phase) reached 0.23e0.30 w/w, the decrease diminished and a slight increase in to-Ps was seen. An increase should be due to an enlargement of Vh, owing to increased distances between polymer segments, caused by the incorporation of water molecules [10]. In semi-crystalline poly(vinylalcohol) (PVA) it has been shown that water absorbed after preparation of the PVA increased the free volume hole size slightly even at low water weight fractions [10]. Moreover, in PEO plasticized by dioctyl phthalate, an increase of the free volume hole size has been shown to accompany a decrease in Tg [41]. These PEO films were, however, prepared in the presence of the plasticizer. This fact distinguished these samples from those in the present PEOewater system. The intensity, Io-Ps, which is a measure of the probability of o-Ps formation, was found to decrease from 18.4% in dry PEO to 14.9% at ww(amorphous phase) 0.10 w/w, after which it remained more or less constant (Fig. 11b). In pure water, Io-Ps has been measured as 26.9% by Eldrup et al. [42]. The reduction of Io-Ps as the water content increased was probably a result of the incorporation of the small and plasticizing water molecules that increased the polarity of the system. Polar water molecules decrease the probability of o-Ps formation due to shielding of the electrons and free positrons [43]. From Fig. 11b it can be estimated that Io-Ps stayed rather constant in the range 0.10e0.23 w/w in the amorphous phase after which Io-Ps increased slightly. This slight increase of Io-Ps at ww(amorphous phase) 0.30 w/w indicated that a weighted average of Io-Ps in the waterePEO system and in water clusters was measured. This is due to that the probability of o-Ps formation in pure water is higher than in the plasticized PEO. Thus, Io-Ps would probably increase further to the value of pure water with an increased water weight fraction. 3.6. Self-diffusion coefficient of water in the PEOewater system The self-diffusion coefficient of water was measured for water weight fractions in the amorphous phase of 0.04e0.51 w/w. The spectra obtained from samples of ww(amorphous phase) 0.10e0.30 w/w measured with a D of 40 ms are shown in

3301

Fig. 12. The large peak, corresponding to water protons can be clearly seen in each spectra. Its shift increased from around 4.0 ppm to around 4.4 ppm with increasing water content approaching the shift of pure water, 4.8 ppm. This indicated that the magnetic field experienced by the water protons was affected by the increasing amount of water in the PEOewater system, altering the environment in the proximity of the water molecules. In the spectrum for the sample with the highest water weight fraction a small peak is seen at 3.6 ppm. This peak corresponds to the protons of the EO units and was totally invisible in the spectrum corresponding to a sample of ww(amorphous phase) 0.10 w/w at the lowest gradient strength. However, the latter spectrum at high gradient strength (magnified 30 times and seen on top of the bottom-line spectrum in Fig. 12) revealed the presence of a small EO proton peak, which, in spite of the low water weight fraction in the sample, was still quite narrow. The change in position of the maximum height of the water peak to lower shifts upon increasing the gradient strength indicated that loosely bound water contributed much less than tightly bound water to the signal at the high gradient. Moreover, the width of the water peak at half maximum height, u1/2, at high gradient was much larger than u1/2 at low gradient, indicating a relatively higher anisotropy among the water molecules probed at high gradient, which primarily were the most slowly diffusing water molecules in the PEOewater system. In the spectra of the lowest gradient, u1/2 changed from 102 Hz at a ww(amorphous phase) of 0.04 w/w to 32 Hz at a ww(amorphous phase) of 0.30 w/w. Consequently, the degree of anisotropy among the water molecules decreased with the water weight fraction. The experimental signal decay of water in a PEOewater sample of ww(amorphous phase) 0.10 w/w measured with the SE and STE pulse sequence at various diffusion times can be seen in Fig. 13. The non-linear appearance of the signal decay

6

5

4

3

2

δ(ppm) Fig. 12. Low gradient spectra in samples with four water weight fractions in the amorphous phase 0.10 w/w, 0.16 w/w, 0.23 w/w and 0.30 w/w, where the water content increases from bottom to top (black lines) and high gradient spectra (magnified 30 times) in a sample with a water content of 0.10 w/w in the amorphous phase (grey line). The peak corresponding to EO protons is indicated with an arrow.

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

3302 1

I/I0

0.1

0.01

0.001

0

500

1000

1500

2000

k/109 (s/m2) Fig. 13. The decay of the normalized integrated peak area, I/I0, as a function of k in a sample with a water weight fraction in the amorphous phase of 0.10 w/w as measured with the STE pulse sequence with D set to 40 ms (C) and 200 ms (B) as well as measured with the SE pulse sequence with D set to 20 ms (6).

was observed in all samples except for the sample with the highest water weight fraction, i.e. 0.51 w/w, and rendered a sum of three exponentials necessary to use in order to fit experimental data to the StejskaleTanner equation (Eq. (3)) in the samples of ww(amorphous phase) 0.10e0.30 w/w. For the sample with the lowest water weight fraction in the amorphous phase, i.e. 0.04 w/w, a sum of two exponentials was enough to fit the signal decay. In the samples where three exponentials were used, two of the three self-diffusion coefficients obtained differed from each other with less than one order of magnitude, rendering them indistinguishable. The lowest selfdiffusion coefficient, on the other hand, differed more from the other two and probably originated from the EO proton peak due to overlapping of the water proton peak and the EO proton peak, as seen in Fig. 12. It is unlikely that the anisotropy of the closest environment in which the measured water molecules were situated, as shown by the difference in shift and u1/2 for the water peak at low and high gradients, was the origin of the multi-exponential decay since the time scales of the diffusion experiments should correspond to several exchanges of water molecules. There are, however, other reasons for the multi-exponential decays of the water molecules in this system. The diffusion of water molecules was probably obstructed by the small thickness (about 10 nm [44]) of the amorphous phase between the crystals to diffuse in directions perpendicular to the crystals. This implies that another model than the StejskaleTanner model would be more suitable when calculating the Dself. A means of overcoming the directional effect of the small thickness of the amorphous phase was to treat the PEOewater system as a two-dimensional system with lateral dimensions of several microns [45]. Due to the spherulitic crystalline structure, the stacks of two-dimensional amorphous lamellas are randomly oriented in three dimensions at various angles to the gradient direction [25]. However, this two-dimensional model is based on the assumption that the crystals remain impermeable, not

letting any water to diffuse through and might consequently not be valid in the PEOewater system since water acted as a melting agent on the crystalline structure. Trials with this model resulted in the use of a sum of three exponentials with the largest and second largest Dself being of the same order of magnitude and the lowest Dself differing at least one order of magnitude from the others. The largest Dself obtained with the two-dimensional model was around 30% smaller than the largest Dself obtained with the StejskaleTanner model. Both models did, however, indicate that Dself of water in PEO seemed to be best described by a distribution. Lognormal distributions of the StejskaleTanner model have previously been used [46] and have been shown to give orientation averaged self-diffusion coefficients similar to those obtained with physically correct models in semi-crystalline cellulose [47]. Consequently, a log-normal distribution of diffusing water molecules together with a single component, corresponding to the integrated EO proton peak, was chosen. The results of the fittings to the log-normal distribution are shown in Table 1. The Dself corresponding to the first part of the decay, Dself(mean), can be determined with the highest accuracy and is the Dself at which 50% of the distribution is covered. The variation of the diffusion time gave a hint of possible obstruction of the water molecules by the crystals. Dself(mean) was between 10% and 30% higher at the short D, i.e. 40 ms, than at the long D, i.e. 200 ms, with the largest difference at the lowest water content. This relative decrease in Dself(mean) at higher diffusion times might show that the crystalline phase obstructed the water molecules to a certain extent. The mean square displacement, i.e. hr2i, of the water molecule during the diffusion time, t ¼ D  d/3, can be calculated by means of Eq. (11), if the diffusant is considered as freely diffusing [48],

2 ð11Þ r ¼ 6Dself t Here, the brackets denote time averaging. The root mean square displacement (hr2i)0.5 gives a measure of the lengthscale measured. As mentioned above, the water molecules might have been somewhat obstructed by the crystals and thus not able to diffuse freely. However, calculations were still considered useful in order to get an insight into which length scales that had been probed. When using Dself(mean), the measured length scale ranged from 2.5 mm to 4.2 mm at D ¼ 40 ms and from 5.1 mm to 9.0 mm at D ¼ 200 ms. The spherulites seemed to have diameters of less than 10 mm when examined in an optical microscope. Furthermore, molten PEO quenched Table 1 Results of the fittings to the log-normal distribution ww(amorphous

0.10 0.16 0.23 0.30

phase)

(w/w)

Dself(mean) (1011 m2/s) D ¼ 40 ms

D ¼ 200 ms

2.69 3.52 5.37 7.48

2.13 3.00 4.86 6.77

Dself(mean) is the self-diffusion coefficient of water as determined by PFG NMR.

C. Trotzig et al. / Polymer 48 (2007) 3294e3305 1e-8

Dself (mean) (m2/s)

to room temperature has previously been shown to exhibit spherulitic structures of 3e5 mm with individual lamellar crystals having lengths of 0.2e0.4 mm [45]. Thus, the calculated length scales were at least 10 times longer than the length scale of a single lamellar crystal in a dry PEO spherulite [45] and might also have been longer than the diameters of the spherulites. Thus, the water molecules must have passed through several crystals independent of the D used. However, it might be conceivable that only the water molecules probed with a D of 200 ms passed over the spherulite boundary, which seemed to have caused a slight obstruction to the water molecules. No such obstruction was found when the self-diffusion of alkanes in poly(ethylene) was measured [49]. Cross-relaxation (CR) is a phenomenon that may result in lower self-diffusion coefficients and/or multi-exponential decays of water in the PEOewater system, if exchange of the proton spins between the water and the PEO is possible. According to a previously proposed model [15,16], CR would imply that a water molecule that interacts closely with an ether oxygen for a long enough period of time will exchange one of its proton spins with an EO proton spin. This spin exchange will result in an increase in the EO proton echo signal decay as well as a decrease of the water proton echo signal decay in measurements run with the STE pulse program. However, as CR only affects the longitudinal magnetization, no effects should be seen when running the SE pulse program [25]. To check if CR was present in the system, the samples containing the lowest water weight fraction with multi-exponential decays, i.e. 0.10 w/w and 0.16 w/w, were run with PFG SE NMR. Fig. 13 displays the echo signal decay obtained with the SE sequence in a sample containing 0.10 w/w of water in the amorphous phase. The exponential decays obtained at both water contents were double exponential, which might have been due to the echo signal not being decreased as much as when the STE pulse program was used. The selfdiffusion coefficients obtained with the SE program were about the same as the Dself(mean) of the samples run with the STE program. With the lack of difference between the magnitude of the self-diffusion coefficients obtained with the SE and STE experiments as a basis, it was concluded that no or only minor CR effects existed in the system. Another way to determine the presence of CR is to differentiate the slopes of the echo signal decays at high k-values in the STE experiments, corresponding to the Dself of the PEO, measured at short and long diffusion times. In the presence of CR the slope should be higher at long diffusion times [15]. As can be seen in Fig. 13, the slope seemed to be slightly higher at the long diffusion time for the PEOewater system. The appearance of CR effects, when exploring the polymer part of the sample, as opposed to when investigating the water part with the SE experiment, might have been due to a larger portion of the mobile segments in the PEO, as compared to the probed water molecules, experiencing spin exchange. Hence, CR effects became more pronounced for the part of the PEO that was included in the echo signal decay. Fig. 14 shows the increase of the Dself(mean) of water in the PEOewater samples as a function of ww(amorphous phase), with samples run both with the STE and

3303

1e-9

1e-10

1e-11

0.0

0.1

0.2

0.3

0.4

0.5

0.6

ww(amorphous phase) Fig. 14. Dself as obtained with the STE sequence with D set to 40 ms (C) and 200 ms (B) and with the SE sequence with D set to 20 ms (,) and 50 ms (:) as a function of the water weight fraction in the amorphous phase, ww(amorphous phase).

the SE pulse programs. The standard deviation of the data in the figure was at most 5%. As can be seen, the relative increase in Dself(mean) between samples with 0.30 w/w and 0.51 w/w of water was slightly larger than for samples with water weight fractions below 0.30 w/w. This probably originated from less pronounced obstruction effects by the crystals due to the melting of a relatively large number of them in this water content region. The self-diffusion coefficients of the EO segments were poorly defined in all samples as the EO peak signals could not be decreased sufficiently when using optimal settings for the water diffusion. However, one measurement with the SE pulse program was performed with the most optimal settings for PEO diffusion in the sample of water content 0.30 w/w in order to check the validity of the value obtained when fitting the water measurements of the same sample to the log-normal distribution plus a single exponential. Unfortunately, the value of the integrated EO peak could at most be decreased to around 40% of its initial value. Thus, the value obtained was not completely reliable but merely gave a hint of the log-normal plus single exponential fitting, delivering a value of the same order of magnitude (1013 m2/s) as the optimal measurement for EO diffusion, at least in the sample with a water content in the amorphous phase of 0.30 w/w. This order of magnitude must have corresponded to a PEO of much lower molar mass than the Mw of the sample in the present study [50,51]. 4. Concluding remarks The present work has shown that water absorption reduces the degree of crystallinity of PEO and that PEO is almost completely molten at room temperature at a water weight fraction of 0.50 w/w. Dry PEO was found to be partly constituted of a rigid amorphous phase that was situated between the undisturbed amorphous and the crystalline phases. The amount of this phase seemed to decrease as water was incorporated in

3304

C. Trotzig et al. / Polymer 48 (2007) 3294e3305

the PEO, leading to essentially no rigid amorphous phase remaining at a water weight fraction of 0.13 w/w. This value corresponded to a water weight fraction in the amorphous phase of 0.30 w/w. The rigid amorphous phase seemed to be depleted just before the absorption of water in the PEO started to increase drastically. This, in turn, rendered an accelerating decrease in crystallinity and probably also a reorganization of the crystalline structure. The decrease in glass transition temperature of PEO in the presence of water indicated the relaxation of the PEO segments in the amorphous phase as the water was absorbed. Moreover, the positive deviations of the experimental glass transition temperatures from those predicted by the Fox equation and the poor fit of the Gordone Taylor equation to the experimental data indicated that some water molecules might have interacted simultaneously with ether oxygens on different PEO segments and consequently counteracted the relaxation effect of the introduced water molecules. In accordance with this observation, a reduction in the ortho-positronium lifetime was seen after incorporation of water and indicated relaxation of the PEO segments, initially strained by the presence of the crystals that were formed during compression molding. The decrease of the ortho-positronium lifetime changed to a slight increase at a water weight fraction in the amorphous phase of 0.30 w/w. At this water content the decrease in glass transition temperature experienced a drop in its slope. An explanation to this observation might be that a large part of the strained conformations in the amorphous phase, induced by the crystalline structure in the PEO, had been released at this water weight fraction. The water in the PEO was shown to be freezing bound above water weight fractions in the amorphous phase of 0.30 w/w, corresponding to more than one water molecule being bound to every ethylene oxide group in the amorphous phase. NMR spectra of the water in the PEO below water weight fractions in the amorphous phase of 0.30 w/w showed that the environment surrounding the water molecules changed as the water content increased and that the relative number of water protons probed at higher gradient strengths was more tightly bound to the PEO than the relative number of water protons probed at lower gradient strengths. The mean self-diffusion coefficient of water, as obtained from a log-normal distribution increased approximately logarithmically at water weight fractions in the amorphous phase below 0.30 w/w. At water weight fractions in the amorphous phase between 0.30 w/w and 0.51 w/w, the relative increase of the mean self-diffusion coefficient seemed to be slightly higher than below 0.30 w/w of water. This was explained as being due to an accelerated melting of PEO crystals in this region, as shown by DSC, reducing the obstruction effects of the crystals. No unique relation between the self-diffusion coefficient and the free volume hole size was observed. Acknowledgements This work was financed by the VINNOVA and Industry sponsored Centre for Amphiphilic Polymers (CAP), Lund University, Lund, Sweden. The authors are very grateful to

Prof. Olle So¨derman and Dr. Daniel Topgaard (Lund University) for fruitful discussions and generous sharing of evaluation programs. Many thanks are also expressed to Geraldine Lafitte and Markus Nilsson (Lund University) for guidance in the use of the NMR equipment. References [1] The Dow Chemical Company. Polyoxewater soluble resins; 2002. [2] Bogdanov B, Mihailov M. J Polym Sci Part B Polym Phys 1985;23(10): 2149e58. [3] Graham NB, Zulfiqar M, Nwachuku NE, Rashid A. Polymer 1989;30(3): 528e33. [4] Hager SL, Macrury TB. J Appl Polym Sci 1980;25:1559e71. [5] Hey MJ, Ilett SM. J Chem Soc Faraday Trans 1991;87(22):3671e5. [6] Svensson A, Neves C, Cabane B. Int J Pharm 2004;281(1e2):107e18. [7] Takei T, Kurosaki K, Nishimoto Y, Sugitani Y. Anal Sci 2002;18(6): 681e4. [8] Welander M, Maurer FHJ. Mater Sci Forum 1992;105e110:1815e8. [9] Dlubek G, Redmann F, Krause-Rehberg R. J Appl Polym Sci 2002;84(2): 244e55. [10] Hodge RM, Bastow TJ, Edward GH, Simon GP, Hill AJ. Macromolecules 1996;29(25):8137e43. [11] Abrahmse´n-Alami S, Stilbs P, Alami E. J Phys Chem 1996;100(16): 6691e7. [12] Foster KR, Cheever E, Leonard JB, Blum FD. Biophys J 1984; 45(5):975e84. [13] Crank J, Park GS. Diffusion in polymers. 1st ed. London: Academic Press Inc.; 1968 [chapter 6]. [14] Hedenqvist M, Gedde UW. Prog Polym Sci 1996;21(2):299e333. [15] Horstmann M, Urbani M, Veeman WS. Macromolecules 2003;36(18): 6797e806. [16] Otting G. Prog Nucl Magn Reson Spectrosc 1997;31:259e85. [17] Pyda M, Wunderlich B. Heat capacities of high polymers. In: Brandrup J, Immergut EH, Grulke EA, editors. Polymer handbook. 4th ed. New York: Wiley-Interscience; 1999. p. VI/484. [18] Cheng SZD, Wu ZQ, Wunderlich B. Macromolecules 1987;20(11): 2802e10. [19] Hatakeyama H, Hatakeyama T. Thermochim Acta 1998;308(1e2):3e22. [20] Tao SJ. J Chem Phys 1972;56(11):5499e510. [21] Eldrup M, Lightbody D, Sherwood JN. Chem Phys 1981;63(1e2): 51e8. [22] Nakanishi H, Yean YC. Positron and positronium chemistry. Amsterdam: Elsevier; 1988 [chapter 5]. [23] Wastlund C, Maurer FHJ. Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 1996;117(4):467e73. [24] Risoe National Laboratory. PATFIT-88. Denmark; 1988. [25] Callaghan PT. Principles of nuclear magnetic resonance microscopy. 1st ed. Oxford: Oxford University Press; 1991 [chapters 2 and 6]. [26] Stejskal EO, Tanner JE. J Chem Phys 1965;42(1):288e92. [27] Topgaard D. Ph.D. thesis. Lund University, Lund; 2003. [28] Stilbs P. Prog Nucl Magn Reson Spectrosc 1987;19:1e45. [29] Khasanova AY, Wolf BA. Macromolecules 2003;36(17):6645e52. [30] Ellul MD. Rubber Chem Technol 1988;71(2):244e76. [31] Wunderlich B. Macromolecular physics. 1st ed. New York: Academic Press; 1980 [chapter 8]. [32] Schut JA. Ph.D. thesis. INSA, Lyon; 2003. [33] Sugisaki M, Suga H, Seki S. Bull Chem Soc Jpn 1968;41(11):2591e9. [34] Bicerano J. Prediction of polymer properties. 3rd ed. New York: Marcel Dekker; 2002 [chapter 4]. [35] Pyda M. Macromolecules 2002;35(10):4009e16. [36] Fox TG. Bull Am Phys Soc 1956;1:123. [37] Gordon M, Taylor JS. J Appl Chem 1952;2(9):493e500. [38] Schmidt M. Ph.D. thesis. Chalmers University of Technology, Go¨teborg; 2000. [39] Lusse S, Arnold K. Macromolecules 1996;29(12):4251e7.

C. Trotzig et al. / Polymer 48 (2007) 3294e3305 [40] Wastlund C, Maurer FHJ. Macromolecules 1997;30(19):5870e6. [41] Queiroz SM, Machado JC, Porto AO, Silva GG. Polymer 2001;42(7): 3095e101. [42] Eldrup M, Mogensen O, Trumpy G. J Chem Phys 1972;57(1): 495e504. [43] Mogensen O. Positron annihilation in chemistry. 1st ed. Berlin: Springer Verlag; 1995 [chapter 10]. [44] Sperling LH. Introduction to physical polymer science. 3rd ed. New York: Wiley-Interscience; 2001 [chapter 6].

3305

[45] Cheng SZD, Barley JS, Von Meerwall ED. J Polym Sci Part B Polym Phys 1991;29(5):515e25. [46] Topgaard D, Soderman O. Langmuir 2001;17(9):2694e702. [47] Topgaard D, Soderman O. J Phys Chem B 2002;106(46):11887e92. [48] Einstein A. Ann Phys 1905;17:549e60. [49] Fleischer G. Polymer Bull 1982;7:423e9. [50] Brown W. Polymer 1984;25(5):680e5. [51] Griffiths PC, Stilbs P, Yu GE, Booth C. J Phys Chem 1995;99(45): 16752e6.