Relationships between permeation properties of the polyurethane-based pervaporation membranes and their structure studied by a spin probe method

Polymer 45 (2004) 4391–4402 www.elsevier.com/locate/polymer

Relationships between permeation properties of the polyurethane-based pervaporation membranes and their structure studied by a spin probe method A. Wolin´ska-Grabczyk* Institute of Coal Chemistry, Polish Academy of Sciences, Sowin´skiego 5, 44-121 Gliwice, Poland Received 1 August 2003; received in revised form 9 April 2004; accepted 22 April 2004

Abstract The cyclohexane and water permeability properties as well as the structure of the polyurethane-based pervaporation membranes were investigated. The polyurethanes (PU) were synthesised from poly(oxytetramethylene) diols (PTMO) of various molar masses, 2,4-tolylene diisocyanate (2,4-TDI), and different chain extenders used in various molar ratios. The microstructure of the synthesised PU was investigated by means of the density measurements, DSC method, and ESR technique with a spin probe TEMPO incorporated into PU via diffusion. The results show that only the ESR method was sensitive to all structural modifications applied enabling the correlations between the PU molecular structure and the mobility of the spin probe to be established. The diffusion coefficients ðDÞ of cyclohexane and water were calculated based on the pervaporation results and the sorption data, and were correlated with the rotation correlation time ðtÞ of the spin probe as a measure of the microstructure of the permeable domains. The exponential and linear empirical equations were obtained for the PU/cyclohexane and PU/water systems, respectively, as a result of the fitting procedure applied. These correlations demonstrate that a spin probe method might be useful to characterise free volume, especially in case of complex membrane materials, and to predict the flux of permeant through the pervaporation membranes. q 2004 Elsevier Ltd. All rights reserved. Keywords: Polyurethanes; Pervaporation; Electron spin resonance (ESR)

1. Introduction Pervaporation as a membrane separation process has gained much importance in several areas of science and technology since it is expected to solve various environmental and energetic problems. In this process, a separated liquid mixture contacts one side of a membrane, whereas the permeate is continually removed from the other side as a vapour. A selective dense membrane is able to control the permeation of different species changing the vapour – liquid equilibrium established for a given separated mixture. According to the solution-diffusion model describing the transport of molecules through the pervaporation membranes [1], the permeation process consists of the three consecutive steps; (i) sorption from the liquid phase into the membrane which comprises the partitioning of the mixture * Tel.: þ48-32-238-07-84; fax: þ 48-32-231-28-31. E-mail address: [email protected] (A. Wolin´ skaGrabczyk). 0032-3861/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2004.04.039

components between the separated mixture and the swollen layer of the membrane, (ii) diffusion of the sorbed components through the membrane, and (iii) desorption from the polymer into the vapour phase at the permeate side of the membrane. The separation is realised because of the unequal permeability of the membrane for the solution components that depends on the both thermodynamic (sorption) and kinetic (diffusion) parameters. Therefore, the membrane material is a key factor for the successful separation of a particular liquid mixture by pervaporation. The growing demand for membrane materials with enhanced transport parameters, as well as for the convenient method of the prior selection of the materials most suited for achieving a desired separation, requires the correlations between the membrane permeability and permselectivity, and the polymer composition and structure to be well established. Segmented polyurethanes (PU)s seem to be versatile membrane materials for such studies. Typical PUs are condensation multiblock copolymers

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composed of alternating soft- and hard-segment sequences which can be described by (AB)n type of chain architecture. The soft segment is usually an oligomeric rubber at use temperature, whereas the hard segment is either of a glassy or semi-crystalline nature under these conditions. Thermodynamic incompatibility of both segments leads to their microphase separation and to the formation of an aggregated pseudo-two-phase structure, which play a dominant role in determining the PU properties. The nature and length of the segments and their relative composition constitute principal factors affecting morphology, and thereby the properties of PUs [2]. These parameters can be easily and widely modified at the synthesis step by changing each of the three reaction components, as well as the initial composition of the reaction mixture. In literature [3], transport of small molecules through segmented polyurethanes has been found to occur in an elastomeric phase formed by the soft segments. However, hard domains, which serve as virtual crosslinks by providing junction points for the soft segments, and as reinforcing filler at the same time, can influence the permeation process either by suppressing membrane swelling or by altering the path of the permeating molecules. Moreover, it has been demonstrated that the microphase separation is usually not complete and that appreciable hydrogen bonding takes place between hard and soft blocks. The presence of ‘dissolved’ hard-segment units in the soft microphase can modify its nature affecting thereby its transport properties. The extent of mixing within the hard microdomains can equally be important due to their role as swelling or diffusion path controlling factors. Thus, despite the versatility of segmented polyurethanes as membrane materials for structure – transport property studies, the construction of quantitative correlations is still a very complex task. Previous research performed by us with the aim of establishing of the structure – transport properties relationships was mainly concerned with the correlation between a molecular structure of the segmented polyurethanes and their permselectivity and permeability in the pervaporation separations of various organic/organic and organic/water mixtures [4 – 6]. From the experimental data obtained, it appeared that the modification of the polyurethane molecular structure comprising the variations of the chemical constitution and length of the PU segments had a tremendous effect on the transport properties of the resulting membrane materials. In order to explain the observed transport behaviour, some structural studies of the PUs [7 –10] along with the permeation investigations have been undertaken recently. However, such research requires multiple characterisations of the complex polymer materials to provide reliable information on their structure and properties. The aim of the present work was to study morphology of the polyurethane-based pervaporation membranes by using the ESR spin-probe technique and to correlate the results with permeation behaviour of the investigated membranes.

According to the ESR theory, the line shape of the ESR spectrum of a nitroxide radical is related to its rotational motion. When dispersed in a polymer matrix, the motion of such radical is sensitive to the polymeric environment and its ESR spectrum gives information on the dynamics of the polymer chain segments. There are some features of the spectra, which can be measured and used to parameterise the spectra. At the fast motion limit, it is customary to measure peak ratios, while at the slow motion limit, the extreme splitting is the usual parameter. The correlation time t characterising mobility of the nitroxide radical is then calculated, either by using the Kivelson’s expression [11] for fast isotropic rotation ð10211 s # t # 1029 sÞ; or the simplified expression proposed by Freed et al. [12] for isotropic rotation in the slow-motional region ð1029  s # t # 1026 sÞ: The information provided by the ESR technique reflect molecular dynamics and microstructure of polymer systems on the length scale of a few monomer units comparable to the size of a spin probe used. Therefore, it has been assumed it may aid in correlating the PU structure with its permeation behaviour, which also requires relatively local co-ordination of segmental motions. The permeation behaviour varies greatly depending upon the permeant type. Therefore, two distinct liquids, cyclohexane and water, have been chosen to study the permeation process through the investigated polyurethanes. Although a number of papers have been published relating to the application of nitroxyl radicals and the ESR technique in the motional and structural studies of polymers [13], including polyurethanes [14 – 16], there have been very limited ESR studies of a membrane structure and correlations between the spin probe mobility and diffusion of small molecules. Khulbe et al. [17] used the ESR technique to study the structure of the skin layer of asymmetric cellulose acetate membranes for reverse osmosis. TEMPO was used as a spin probe that was brought into the membranes either from feed solutions during the reverse osmosis experiments or from the casting solution at the membrane preparation stage. This method was also employed by these authors to investigate fouling of the ultrafiltration membranes [18]. Another application of the ESR spectroscopy in a study of a membrane structure, reported by the same authors, referred to the activated composite membranes which were characterised using the ESR data on the presence, dimension and distribution of pores in the membrane surface [19]. The structure of dense poly(phenylene oxide)-based membranes has also been studied by blending spin probes of different size in the casting solution of the membrane and by analysing the shape of the ESR signals of the doped membranes [20]. One of the scarce reports concerning the use of spin probe to study mass transport properties of polymers was presented by Yampolskii et al. [21]. These authors applied the ESR method for a group of high free volume glassy polymers, like PTMSP and other polyacetylenes, amorphous teflons, and polynorborenes, to study the role of free volume and

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local group mobility on spin probe parameters and gas transport properties. They observed reasonable correlations between the rotation frequency of TEMPO and gas permeability and diffusion coefficients for some polymers, and noticed some discrepancies between these parameters for polymers with side chains. In this work, the ESR technique was used in the investigations of the pervaporation membranes prepared from polymers which constitute a homologous series of the polyether-based segmented polyurethanes. The variability in the PU molecular structure, concerning the chemical constitution and length of the both hard and soft segments, were achieved at the synthesis stage by applying different reagents in various molar ratios. In order to study the membrane structure from the transport of small molecules standpoint, the spin probe TEMPO of the smallest size was introduced into the ready-prepared membranes via diffusion from the vapour phase. It has been expected that the comparison of the spin probe mobility with the parameters characterising diffusion of low molar mass liquids should help to understand better the mechanism of liquid transport through the pervaporation membranes.

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dropwise to the DMF solution of TDI at 60 8C. As the reaction proceeded, the temperature was raised to 80 8C and hold there for 24 h. A slight excess (0.5%) of TDI was used to compensate for side reactions involving isocyanate groups. Other polyurethanes were synthesised by a twostep polymerisation. In the first step of this reaction a prepolymer was prepared from appropriate amounts of PTMO and TDI according to the initial part of the former procedure. This was followed by the chain extension using BHBP, HQE or PP at adequate molar ratios (Table 1), dissolved in DMF and slowly added to the reaction mixture. The temperature of the second step of the reaction was raised to 80 8C in case of BHBP and HQE, or lowered to an ambient temperature for a chain extension with PP, and the reaction was allowed to proceed for 24 h. Nitrogen was kept flowing through the system continuously. If necessary, DMF was added to keep the solution viscosity low enough to allow stirring. A warm, viscous solution was poured into a cold MeOH/water mixture to precipitate the polymer. The polymers were filtered, washed and dried under vacuum for several hours at 100 8C. The structure of the investigated polyurethanes can be schematically expressed in Fig. 1.

2. Experimental 2.4. Membranes 2.1. Materials The poly(oxytetramethylene) diols (PTMO, Mn ¼ 2000; 1000, 650, BASF) were dried under vacuum for 24 h at 100 8C. 4,40 -Bis(2-hydroxyethoxy)biphenyl (BHBP) and hydroquinone bis(2-hydroxyethyl) ether (HQE, Aldrich) used as chain extenders (ChEt) were dried under vacuum for 48 h at 90 8C. Dimethylformamide (DMF) was purified by vacuum distillation. 2,4-Tolylene diisocyanate (TDI, 98 wt. % of 2,4-TDI, Aldrich), 4,40 -diaminodiphenylmethane (PP, POCh, Poland), and other starting materials were used as received.

The polyurethane-based membranes were prepared by casting a DMF solution of 15 wt% PU onto a glass plate and by evaporating the solvent at 60 8C in a dry nitrogen atmosphere for 72 h. The assumed thickness of the PU membranes was about 100 mm. The average thickness of an individual membrane was calculated based on the results of

2.2. 4,4 0 -Bis(2-hydroxyethoxy)biphenyl The BHBP diol was prepared following the procedure given in Ref. [22]. Sodium hydroxide (0.168 mol) and 4,40 dihydroxybiphenyl (0.042 mol) were stirred into 100 ml of ethanol. The mixture was heated under reflux, and a-chloroethanol (0.183 mol) was added dropwise. The reaction mixture was refluxed for 24 h and after that poured into water. The precipitated material was filtered and recrystallised from a 3:1 mixture of ethanol and DMF to give BHBP, mp 213 8C, yield 80%. 2.3. Polymers The polyurethanes PU-1, PU-5 and PU-10 were synthesised by the reaction of PTMO with equimolar amounts of TDI. The 15 wt% solution of PTMO in DMF was added

Fig. 1. Structures of the synthesised polyurethanes.

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Table 1 Composition and physical properties of polyurethanes Polymer

Molar composition

Soft segments content (wt%)

Density r (g/cm3)

Molar mass (g/mol)

Mw =Mn

Tg (8C)

PU-1 PU-2 PU-3 PU-4 PU-5 PU-6 PU-7 PU-8 PU-9 PU-10 PU-11 PU-12

PTMO-2000/TDI 1/1 PTMO-2000/TDI/PP 1/2/1 PTMO-2000/TDI/BHBP 1/4/3 PTMO-2000/TDI/PP 1/4/3 PTMO-1000/TDI 1/1 PTMO-1000/TDI/PP 1/2/1 PTMO-1000/TDI/BHBP 1/4/3 PTMO-1000/TDI/PP 1/4/3 PTMO-1000/TDI/HQE 1/4/3 PTMO-650/TDI 1/1 PTMO-650/TDI/BHBP 1/2/1 PTMO-650/TDI/PP 1/2/1

92 78 57 61 85 65 40 44 44 79 51 54

1.072 1.075 1.091 1.089 1.093 1.109 1.197 1.167 1.194 1.112 1.161 1.139

49,900 43,300 44,100 44,000 54,100 50,600 46,200 35,300 42,600 58,600 38,900 42,600

2.9 1.7 2.1 1.7 2.5 1.7 2.7 1.6 2.0 2.6 2.7 1.7

277 283 285 283 252 252 256 246 249 234 231 232

Tg of the macrodiols: PTMO-2000: 285 8C; PTMO-1000: 287 8C; PTMO-650: 288 8C.

several separate thickness measurements taken around the circumference of a membrane disc. 2.5. Polymer characterisation techniques Molar masses relative to polystyrene standards were determined by gel permeation chromatography (GPC) at 80 8C in DMF as eluent with a flow rate of 1 ml/min. The Knauer apparatus equipped with the MIXED-DPL gel columns was used. A Rheometric Scientific DSC plus differential scanning calorimeter was used to determine the glass transition temperature ðTg Þ: The dried, as-cast samples were heated to 60 8C and held at this temperature for 5 min. Then, they were cooled at 108/min. to 2 140 8C, kept at this temperature for about 5 min, and scanned at 108/min to room temperature. Measurements were repeated several times with fresh samples each time to establish the values of Tg : The Tg values reported were taken as the half-height of the change in the heat capacity. The mass densities of the polymers were measured by using the buoyancy method in water. 2.6. Preparation of spin-probed polyurethanes A stable nitroxyl radical, 2,2,6,6-tetramethylpiperidine1-oxyl (TEMPO, Aldrich) used as a spin probe was introduced into the polymer via diffusion from a vapour phase at room temperature. The PU sample, in a form of a ca. 3 mm wide strip cut from the PU membrane, and a solid TEMPO were kept in a closed vessel for 30 min. After that, the spin probed polymer sample was taken from the vessel, put into the ESR tube, and kept there at room temperature for 2 weeks to ensure a uniform distribution of the spin probe throughout the polymer. 2.7. ESR measurements ESR spectra were recorded in the temperature range of 21 – 180 8C with a CW X-band ESR-spectrometer

(Radiopan, Poland) operating at 9.2 GHz, using 100 kHz modulation. Since some of these spectra were found to reflect anisotropic rotation of the TEMPO spin probe, the unified approach was elaborated [23] enabling the comparison of PUs by means of the rotational correlation time t (s). In this approach, the correlation time is evaluated from the symmetric three line spectra representing the fast tumbling rate of the spin probe, attained above a certain temperature characteristic for a particular polymer. In this motional narrowing region, t is determined using the equation derived from the Kivelson’s theory [11]:

t ¼ 0:65 £ 1029 W0 ½ðh0 =h1 Þ1=2 þ ðh0 =h21 Þ1=2 2 2

ð1Þ

where W0 is the central line width ðGÞ; and h1 ; h0 and h21 are amplitudes of the ESR spectrum for low, central and high field lines, respectively. The apparent correlation time at a given reference temperature is then calculated from the Arrhenius relations of t vs. 1=T with the assumption that the Arrhenius behaviour prevails over a broader temperature range, within the adopted temperature limits. The upper temperature limit is determined by the thermal stability of the system and found to be approximately 180 8C, when the loss of signal intensity due to the decay of the TEMPO radicals is not severe yet. The exception are PUs with a high soft segment content showing the reduced upper temperature limit because of the deviation from the Arrheniuss relation at higher temperatures [23,24]. The lower temperature limit is determined by the transition temperature, at which the change in dynamics occurs. This temperature is defined by the crossover point of the extrapolated Arrheniuss relations corresponding to the fast and slow motional regimes, where t is expressed either by Eq. (1) or estimated from the outer peak splitting 2A0z ; respectively. This was found to be similar to the glass transition temperature measured by DSC [24]. The values of t reported in Table 2 were calculated at 25 8C. The relative error of t was estimated as 5%.

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Table 2 Mobility of TEMPO ðtÞ and permeability ðQÞ/diffusivity ðDÞ data for transport of cyclohexane and water molecules through polyurethanes of various molecular structure Polymer

PU-1 PU-2 PU-3 PU-4 PU-5 PU-6 PU-7 PU-8 PU-9 PU-10 PU-11 PU-12

TEMPO mobility

Cyclohexane

Water

t £ 109 (s)

Q £ 109 (mol m/m2 s)

C £ 1022 (mol/m3)

D £ 1012 (m2/s)

Q £ 108 (mol m/m2 s)

C £ 1022 (mol/m3)

D £ 1012 (m2/s)

Ea (kcal/mol)

0.78 0.70 0.74 0.98 1.31 1.79 5.67 6.84 5.90 2.81 3.67 4.23

42.70 37.07 32.10 33.10 27.8 3.60 0.40 0.20 0.23 2.32 0.33 0.23

41.75 38.79 23.66 30.12 31.35 20.00 11.49 13.93 14.31 19.87 12.96 13.65

10.2 9.56 13.6 11.0 8.7 1.80 0.35 0.14 0.16 1.17 0.26 0.17

4.83 4.16 1.42 3.00 3.02 1.85 1.08 0.74 0.77 1.40 0.86 0.88

48.79 37.33 15.84 35.66 39.07 24.16 17.89 39.73 20.45 27.26 15.79 21.88

9.90 11.14 8.96 8.41 7.73 7.66 6.04 1.86 3.77 5.14 5.45 4.02

3.41 – 5.64 10.85 10.95 7.99 15.71 16.99 18.01 13.68 8.71 14.15

2.8. Pervaporation measurements Permeation of cyclohexane and water through the PUbased membranes was investigated using the ordinary pervaporation technique. The set-up used for these experiments is shown in Fig. 2. The upper compartment of the pervaporation cell had a capacity of about 800 cm3, the membrane area in contact with the solvent was about 48 cm2. The feed solution in the upper compartment was stirred by a mechanical stirrer, and its temperature (25 8C) was controlled and measured using electronic temperature control system. The lower compart-

ment was evacuated to less than 1 mm Hg, and the permeate was condensed and frozen within one of the cold traps cooled with liquid nitrogen. Permeate was collected for a given time period, after which it was weighed. 2.8.1. Calculation of flux and diffusion coefficient The flux was determined at the steady state from the weight of the permeate, permeation time, and the effective membrane area, and recalculated for a standard membrane thickness to enable the membranes of various thickness to be compared. The specific flux Q was calculated as follows: Q¼

Ml At

ð2Þ

where M is an amount of permeate (mole), l is a membrane thickness (m), A is an effective membrane area (m2), and t is time (s). The relative error of Q was estimated as 7%. From the data of the specific flux, Q (mol m/m2 s], and the amount of solvent in a swollen membrane, C (mol/m3), determined according to the procedure given in Section 2.8.2, the apparent diffusion coefficient, D (m2/s), was obtained using the following equation: D¼

Q C

ð3Þ

A derivation of Eq. (3) based on a solution-diffusion model is presented in Appendix A.

Fig. 2. Pervaporation set-up.

2.8.2. Determination of the amount of solvent in membrane The dried PU films of thickness of about 300 mm were immersed into cyclohexane or water at 25 8C. The liquid uptake was monitored gravimetrically by weighing the PU samples at regular time intervals. After the sorption equilibrium was reached, a sample was taken out from solvent, wiped quickly with filter paper and weighed. The

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sorption equilibrium value Weq was calculated as: Weq ¼

Ws 2 Wd Wd

ð4Þ

where Ws ; Wd are the weights of a swollen and dry membrane, respectively. The relative error of Weq was estimated as 6%. The amount of solvent sorbed per unit volume of a swollen polymer was calculated from the relationship: C¼

p Weq

Weq 1 þ rs rPU

ð5Þ

p and Weq are the experimentally determined where Weq sorption equilibrium values in moles and grams per gram of the dry polymer, respectively, rs is solvent density (g/cm3) and rPU is experimentally determined polyurethane density (g/cm3). The relative error of rPU was estimated as 1%.

3. Results and discussion 3.1. Physical properties of polyurethanes In Table 1 molar compositions and some physical properties of the synthesised PUs are reported. Soft segments content was calculated on the basis of the PU general formula presented in Fig. 1 and of the amounts of the reagents used in the synthesis. The average molar masses and molar mass distributions of the PUs were obtained from GPC measurements in DMF. The Mw =Mn values are close to 2, expected for conventional condensation polymerisation. The relative molar masses based on polystyrene standards are comparable to those of conventional polyurethane elastomers and were sufficiently high to prepare the PU films with good and stable mechanical properties. As shown in Table 1, density of the synthesised PUs ranges from 1.072 g/cm3 for PU-1 of the highest soft segments weight fraction to 1.197 g/cm3 for PU-7 of the lowest soft segment content. A linear correlation has been found between the measured density value and the segment length expressed either by a molar mass of a soft segment, or a theoretical number of repeat units, x; for a hard segment. The observed decrease in density on the increase of the soft segment length, or on the decrease of the hard segment length, is in agreement with the additivity principle. The decrease in density can be correlated to the increase in free volume. On the other hand, it is known that the glass transition temperature, Tg ; decreases on increasing the free volume. For the homologous sets of PUs with the varying soft segment length and on the fixed hard segment structure and length (PU-1, PU-5, PU-10 or PU-2, PU-6, PU-12), when experimentally determined Tg values were plotted against the density values, straight lines were obtained. Increasing Tg on decreasing soft segment length results from

the presence of the highly polar urethane groups in the polymer chain, which can form interchain hydrogen bonds with similar groups or other electron donor groups like –O – groups from tetra(methylene)oxide units. The lower molar mass of the soft segment, the higher concentration of the TDI-based stiffening elements, and the higher Tg expressing the reduced free volume of the PU soft segments. As can be seen from the Tg values given in Table 1, the hard segment length is less important parameter influencing the free volume of the PU soft segment phase. Moreover, the correlations between the amount of urethane units per polymer chain and the Tg value, observed previously, have not been found for PUs with altering hard segment and fixed soft segment length. This can be attributed to the formation of microphase separated structures resulting from the incompatibility between both segments, the extent of which depends on the hard segments length and structure. 3.2. ESR results in correlation with PU molecular structure The ESR spectra for nitroxide spin-probed PUs varying in the soft and hard segment length recorded at room temperature are shown in Figs. 3– 5. The shapes of these spectra indicate that the nitroxide behaviour in the investigated PUs is strongly morphology dependent. The line-shape pattern changes from that of fairly narrow and symmetric three lines with the extreme separation of the two outer lines of 37 G (PU-1 or PU-2) to the broad and complex one, exhibiting two additional signals at a low and a high field with the splitting between them of ca. 67 G (PU-8). The intermediate ESR spectra with different amplitudes and width of the lines can also been observed for the PUs studied. Since each line shape can be associated with the spin-probe tumbling rate, it is obvious that these polymers create different environments where the motion of the probe can be either fast and isotropic or restricted with respect to the rates and orientations. From Fig. 3, it can be seen that ESR spectra of PUs composed of the longest soft segments (PU-1, PU-2 or PU-4) exhibit line shapes typical for fast isotropic rotation. However, as the soft segment length decreases, like for the representative

Fig. 3. ESR spectra for spin probe TEMPO in PTMO-2000 based PUs with variable hard segment length.

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Fig. 4. ESR spectra for spin probe TEMPO in PUs varying in the soft segment length.

series of PU-1, PU-5 and PU-10, the spectra depicted in Fig. 4 show gradual broading of their lines, and finally subsplitting of the outer signals when the molar mass of the soft segment reaches the value of 650 (PU-10). Additionally, the amplitude of the central line becomes much more than those of the both low and high field lines. The similar behaviour is demonstrated by the series of PUs with the increased hard segment length (PU-5, PU-6, and PU-8), as can be seen from the spectra in Fig. 5. The extensive studies of the temperature- and microwave powerdependent spectra, performed earlier [23] to resolve the complex spectral line shape observed for some PUs, revealed that the motion of the spin radicals is not isotropic in those systems. This was attributed to the slowed tumbling rate, which makes the averaging of all anisotropic effects in the g and hyperfine ðAÞ tensors incomplete. However, with increasing temperature the motional freedom increases and the initial slow-motion type of the spectrum transforms into the motionally-narrowed one [23,24]. For the purpose of comparing of all polymers, the motionally-narrowed spectra have been parameterised using Eq. (1), and the correlation

Fig. 5. ESR spectra for spin probe TEMPO in PTMO-1000 based PUs with variable hard segment length.

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times at 25 8C have been calculated according to the method presented in Section 2.7 and described in details in Ref. [23]. The obtained values of correlation time t have been summarised in Table 2. The effect of the soft segment length on the mobility of the nitroxide spin probe is illustrated by the rotation correlation time values for the series of polyurethanes with fixed hard segment length and structure. Like for the two representative series of polymers PU-1, PU-5, PU-10 and PU-2, PU-6, PU-12, decreasing the soft segment molar mass results in polyurethanes showing restricted mobility of the TEMPO spin probe by a factor of four or six, respectively. The rapid increase in t values is observed particularly with lowering of the soft segment molar mass below 1000. The results from Table 1 show that the density and Tg values vary linearly with the soft segment molar mass for the PU series with a fixed hard-segment length. On the other hand, the mobility of a spin probe should be sensitive to the size of free volume. However, the strong non-linear behaviour of t suggests that the rotational mobility of TEMPO in PUs with shorter soft segments is determined predominately by the local, smaller scale restriction in the chain mobility as compared to the segmental motions determining free volume. It can be seen from Table 2, that the effect of the hard segment on the mobility of a spin probe TEMPO is strongly dependent upon the length of the soft segment. The rotation correlation time values are very similar for PUs with the longest soft segment (PU-1 – PU-4), indicating that there is no significant difference in the nitroxide motion in PUs with a high degree of microphase separation. For PUs with shorter soft segments, a strong correlation between the hard segment length and the nitroxide mobility has been observed. The t value increases rapidly up to fivefold as the hard segment length increases from x ¼ 0 to x ¼ 3; like for the representative series of PU-5, PU-6, and PU-8. This effect may be attributed to the restraints being imposed on the soft segment matrix by the hard segment domains, as well as by the hard segments alone as a result of incomplete phase separation. The longer hard segments the higher driving force to microphase separation, which provides physical crosslinking sites for the soft microphase. On the other hand, a usually broad distribution of a hard segment sequence length, inherent from the polymerisation reaction, gives rise to the enhanced number of shorter segments in case of PUs with higher hard segment total amounts. These shorter hard segments, exhibiting a smaller tendency for microphase separation, can be expected to remain mixed within the soft microphase and, due to strong interactions with soft segments, to entail some restrictions on their movement. As no marked dependence of the hard segment length on the free volume of the soft segment matrix was observed from the DSC data, or at least such correlation was hardly manifested by the soft segment Tg values, there is a clear tendency for the reduced mobility of the spin probe

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with increasing hard segment length demonstrated by the ESR results. As can be seen from Table 2, the mobility of the nitroxide probe embedded in the soft segment matrix is also affected by the hard segment structure resulting from the structure of the chain extender used in the PU synthesis. A following set of PUs with different hard segments and other structural parameters constant, PUðPPÞ . PUðHQEÞ $ PUðBHBPÞ describes the increasing mobility of a spin probe TEMPO expressed by the decreasing t values. The major structural factor, which distinguishes the PPbased hard segments from the other ones, results from the presence of the urea groups formed in the reaction of diisocyanate with a diamine component. These groups increase the number of proton donors, and thereby, the extent of hydrogen bonding. Although the hydrogen bonding itself is not directly responsible for the mobility of polyurethane chains, it contributes to the creation of more dense arrangements of the hard segments. The greater number of smaller size domains anticipated as a result increases the effectiveness of the physical crosslinking of the soft matrix. Since, it is expected that in the vicinity of such domains segments of polymer chain are less free to undergo rotatory or other movement, the mobility of the spin probe TEMPO can be more restrained in the PP-based PUs than in the other PUs. 3.3. Pervaporation results in correlation with PU molecular structure In Table 2 are shown the results of the measurements of specific fluxes, Q; of pure liquids, cyclohexane and water, through the investigated PUs along with the sorption equilibrium amounts, C; determined for those systems from sorption kinetic measurements, and the diffusion coefficient values, D; calculated from Eq. (3). As shown in this table, variations in the PU molecular structure strongly affect transport parameters of the PU-based membranes. Generally, the flux, the diffusion coefficient, and the sorption equilibrium values decrease with reducing the soft segment length or increasing the hard segment length. The both structural changes are associated with the increase in the fraction of the hard segments, which act as impermeable barrier to permeating molecules reducing area available for transport. However, it has appeared that the effect on permeability of those structural parameters is more complex. For the series of homologous PUs with a fixed hard segment length and structure, like for the series of PU-1, PU-5, PU-10 or PU-2, PU-6, PU-12, the permeation rate of cyclohexane decreases by a factor of 18 or 160, respectively, and that of water by a factor of 3 or 5, respectively, with decreasing the soft segment molar mass from 2000 to 650. The soft segment length dependence of Q is non-linear

in character, particularly for cyclohexane, showing a significant drop in the Q values for shorter soft segments. The similar behaviour can be found for D plotted against the length of soft segment. The curvature of both the D and Q dependencies is more marked for the series with a shorter hard segment (PU-1, PU-5 and PU-10), comparing to that with a longer one (PU-2, PU-6, PU-12). The transport data obtained are in a good agreement with the results on the mobility of the nitroxide spin probe in the same sets of PUs, indicating that the reduction in the length of the polyurethane soft segment imposes the similar restrictions on the rotation of the TEMPO molecules as on the translational diffusion of liquid molecules. The temperature dependence data of Q obtained for water fitted the Arrhenius relations and gave the activation energy values, Ea ; which increase in a linear fashion from 3.4 kcal/mol for PU-1 to 13.7 kcal/mol for PU-10 as the soft segment length decreases, showing the same trend of transport restrictions. Although the character of the above mentioned correlations is common for both permeating liquids, there are significant differences in magnitude of the corresponding variations and in their background which result from the molecular size and nature of the liquid. The permeation rate of cyclohexane through PUs with the decreasing soft segment length, though governed by both the diffusivity and solubility, has been found to diminish as a consequence of the diffusion restrictions illustrated by the nine-fold or even 56-fold decrease of the D values from PU-1 to PU-10, or from PU-2 to PU-12 samples. On the other hand, for permeation of smaller water molecules, only 1.6 or 2.8 fold reduction in the D values has been observed for the same sets of PUs. This can be explained by the enhanced plasticization of the longer PU segments by cyclohexane that leads to the greater difference between extreme members of the PU homologous series, or, as for PU-1 and PU-5, can even invert the relation that the smaller permeate size the higher is the diffusion coefficient. The effect of the hard segment length and structure on the transport characteristics of the investigated PUs, like on the mobility of the nitroxide spin probe, varies according to the microphase separation degree of the PU sample, and additionally, according to the nature of the permeating liquid. For PUs with the longest soft segment ðMn ¼ 2000Þ; and hence the highest degree of microphase separation, the D values are independent of both the hard segment structure and length. Some variations in the permeation rate observed for those polymers are mainly due to the differences in their sorption capacity. These results are consistent with the data concerning the nitroxide probe motions in the studied PUs. The quite different types of behaviour have been found for PUs with shorter soft segments, i.e. the molar mass of which is lesser than 2000. Although all transport parameters have been shown to decrease with increasing hard segment length for both PU/cyclohexane and PU/water systems, the character of the respective relations, as well as the magnitude of the observed changes in the Q and D values,

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strongly depend on the kind of the permeating liquid. For the PU/cyclohexane system, Q and D decrease enormously (by 140 and 64 times, respectively) in a strong non-linear fashion on increasing the hard segment length from x ¼ 0 (PU-5) to x ¼ 3 (PU-8). On the other hand, there is only about a fourfold decrease in the Q and D values over the same increase of the hard segment length for the PU/water system. In addition, the straight line can approximate these data. The differences between both systems can be explained on the basis of the swelling effects. Contrary to the water molecules, which have no special plasticizing effect, the cyclohexane molecules can swell and plasticize the soft segment matrix, giving rise to the increased mobility of the polymer chain segments and to the increased permeation rate. The correspondence between the permeation behaviour observed for the PU/water system and the variation in the mobility of the TEMPO molecules as a function of the hard segment length confirms this explanation. For instance, the diffusivity of water and the mobility of the spin probe TEMPO decrease by a factor of four and five, respectively, as the hard segment length increases from x ¼ 0 (PU-5) to x ¼ 3 (PU-8). These results indicate that the permeation properties of PUs towards water, like the mobility of the spin probe molecules, are dominated by the soft segment mobility affected by the hard segments either separated into microdomains or mixed into the soft segment matrix. The elongation of the diffusion path caused by the hard segment domains can also play a role as a factor determining the transport behaviour. On the other hand, when analyse the diffusivity of both liquids as a function of x; the another performance of the hard segment domains can be seen. This is suppressing of the polyurethane swelling that makes diffusion more dependent on the size of the permeating molecules. Generally, decrease in the hard segment length is accompanied by an increased diffusion rate. However, this relation was found to be much more pronounced for cyclohexane than for water. As a result, the similar diffusivities of both liquids in PU with shorter hard segments (PU-5) have been observed, in contrast to a tenfold faster diffusion of water in PU with the longer hard segments. As it is shown in Table 2, transport properties of the PUs with shorter soft segments depend not only on the length of the hard segment but also on its chemical constitution. The dependence is not as profound as with the hard segment length, especially when the permeability is considered, however, it is clearly marked for both permeating liquids. The following set of the PUs with various hard segments resulting from the different chain extenders used in the PU synthesis, PUðPPÞ , PUðHQEÞ , PUðBHBPÞ describes the trend of the increasing diffusion rate, which coincides with the enhanced mobility of a spin probe TEMPO in those polymers.

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3.4. Structure – transport properties correlations As described in the previous section, the correlations established between the molecular structure of PU and its transport properties were associated with such structural variables as a length and structure of both the hard and soft segment. The extent of the microphase separation has been found to constitute a separate parameter strongly influencing the character of these correlations and making them rather complex ones. On the other hand, it has been observed that diffusivity of water and mobility of TEMPO molecules in the PU homologous series has several features in common. This has encouraged search for correlations between the diffusivity of a particular liquid, D; and the rotation correlation time of TEMPO, t; used as a quantitative parameter characterising morphology of the investigated PUs with a modified molecular structure. Based on the correlations obtained so far, the hypothesis that D is an exponential function of t in case of cyclohexane permeation, and D is a linear function of t in case of water have been verified using a least square method with errors in both co-ordinates. To measure how well the straight line model agrees with the experimental data, the coefficient of correlation, r; has been calculated. The values of r ¼ 0:952 and r ¼ 0:879; obtained for cyclohexane and water, respectively, gave the goodness-of-fit on the confidence level larger than 0.999 for cyclohexane and of 0.999 for water, indicating that fit is believable. In order to achieve the best-fit-parameters of the model with experimental errors being taken into account, the FIXEXY optimisation procedure has been used to find a minimum in the appropriate objective function [25]. The applied fitting routine returned the following parameters of the exponential (6) and linear (7) functions: DðtÞ ¼ expð224:433 2 10; 356 £ 105 tÞ

ð6Þ

DðtÞ ¼ 0:95661 £ 10211 2 0:10889 £ 1022 t

ð7Þ

which refer to the relationships for cyclohexane and water, respectively. The minimum values of x2 objective function were 150.70 and 39.814 for cyclohexane and water, respectively, with the following standard errors values for the coefficients a (intercept) and b (slope):

sa ¼ 0:05900

sb ¼ 32; 705 £ 103

sa ¼ 0:36332 £ 10212

sb ¼ 0:80935 £ 1024

assigned to the Eqs. (6) and (7), respectively. Although the determined errors of correlations can be acceptable, their values suggest that the experimental error values used in the calculations might have been underestimated. Nevertheless, the fitting and the experimental results given in Figs. 6 and 7 show that for both data sets the strong relationships between the PU structure characterised by the rotation correlation time and the rate of diffusion of liquid can be found.

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A. Wolin´ska-Grabczyk / Polymer 45 (2004) 4391–4402

Fig. 6. Correlation between diffusivity of cyclohexane and mobility of TEMPO (characterised by a rotation correlation time) in structurally different PUs; circles—experimental data, squares—regression results.

According to the free volume theory, used to predict solvent diffusion through polymers above Tg ; a relationship between D and free volume, f ; is expressed in terms of two system sensitive parameters A and B; by D ¼ Aexpð2B=f Þ

ð8Þ

Providing the reciprocal relation between a rotation correlation time and a free volume, the empirical equation obtained for the PU/cyclohexane system (Eq. (6)) seem to have the similar form, that reflects a concentration dependent diffusion. The results obtained for the PU/water system show a linear variation of D on t (Eq. (7)), however, with a somewhat worse result of the fittings. This different behaviour can only be attributed to the specific features of water molecules, which are their relatively small size and their ability to associate themselves or to interact with suitable groups of the polymer through hydrogen bond formation. Since the tendency for a particular type of interaction is related to the structure of polymer, the presence of the polar nucleation centres in the PUs studied may be expected to promote the clustering of water and its partial immobilisation. As a result, diffusion coefficients may not depend so strongly on concentration. One of the important consequences of the correlations found between PU structure characterised by the rotation

correlation time, t; and the diffusivities of liquids, D; is gaining additional information on transport behaviour in the pervaporation membrane. According to the solution-diffusion mechanism of this transport, when the steady-state in pervaporation is attained, the concentration of permeant across the membrane changes from that representing equilibrium saturation in the swollen feed side of the membrane to almost zero concentration at the non-swollen permeate side of the membrane. It has been found recently from the AFM [10] and SAXS [26] studies, that such anisotropic swelling can be accompanied by the microstructural transformations within the membrane occurring on different length scales. The results showed that more perfectly ordered morphology might be expected for the polyurethanes with already developed microstructure after treating with solvent of a high swelling power. Moreover, the monotonic change of the membrane structure expressed by the change of the lamellar repeat distance was observed in the depth of the operating membrane, from its swollen part to the dry side of the membrane [8]. Thus, for the strong concentration dependent systems, when the diffusive medium can also vary significantly, the diffusion process should be recognised as a complex phenomenon. On the other hand, when the steady state is reached, the permeant flux equals its flux through the dry layer of the

Fig. 7. Correlation between diffusivity of water and mobility of TEMPO (characterised by a rotation correlation time) in structurally different PUs; circles— experimental data, squares—regression results.

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membrane [27]:   0 p dC J ¼ 2D dx x¼l

ð9Þ

where Dp is intrinsic diffusivity of a given liquid, i.e. its diffusivity in the unswollen part of the membrane, l is a membrane thickness, and C is concentration of liquid. The correlations obtained in this work between D values calculated from the pervaporation flux using Eq. (3) and the t values determined for the studied PUs may suggest that the microstructure of the membrane layer responsible for the transport is not much different from that of the initial membrane material. For comparison, the mobility of the TEMPO spin probe in PUs at equilibrium saturation has been found to be the same within the whole homologues series of PUs, and similar to that in a pure liquid. The analogous behaviour can also be expected for the diffusion of permeants. On the other hand, some deviation from the empirical functions relating D and t can be expected, since the D values used for the correlation determination refer to the concentration averaged diffusion coefficients. Nevertheless, the results obtained suggest that the diffusion through the pervaporation membrane studied under the pervaporation conditions may be analysed on the basis of the free volume size. However, more work concerning other permeants as well as another method for the D determination is necessary for further detailed discussion, and it is now in progress.

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the PU/water system. Although the nature of the free volume represented by the rotation correlation time of the spin probe TEMPO and the diffusivity of liquid penetrant need to be more clarified, the obtained correlations show that the free volume theory can be used to predict the macroscopic flux of penetrant, especially organic solvent, through the pervaporation membranes. The procedure of an experimental assessment of the free volume using ESR technique with a spin probe incorporated into a membrane via diffusion can be particular useful in case of membranes prepared from materials of complex morphology, like microphase separated polymers or composite materials, for which the standard calculations of the free-volume cannot be performed. This method might also be very helpful to the design of new high-performance membrane materials with tailor-made properties, since it enables the correlations between the molecular architecture, morphology, and the permeation properties to be found and established.

Acknowledgements The author gratefully acknowledges the support for this work from the State Committee for Scientific Research of Poland through Grant No 3T09B07719. The author is also grateful to Mr A. Jankowski and to Dr J. Muszyn´ski for their assistance in this work and to Dr W. Bednarski for his assistance with the ESR measurements.

4. Conclusions Appendix A The investigations of the microstructure accountable for the permeation properties of the segmented PUs, performed by means of the density measurements, DSC method, or a spin probe technique, revealed that only the last method is sensitive to all the applied modifications concerning the macrochain architecture. The obtained correlations between the segment length or structure, and the mobility of the spin probe TEMPO reflect directly the changes in the microstructure of the permeable domains resulting from the variations of the PU molecular structure. This was achieved by incorporating the nitroxide probe into PU via diffusion from the vapour phase, so that it was placed throughout the part of a polymer available for transport. The similar relationships were found to exist between the molecular structure of PUs and their permeation properties. Thus, the correlation of the both data sets, representing the rate of diffusion of a particular liquid through PUs and the mobility of a spin probe, was proposed. The empirical equations relating diffusivity D and a rotation correlation time t; obtained as a result of the applied fitting procedure, differ one another with respect to the kind of the permeating liquid. The diffusivity data are adequately described by the exponential relation between D and free volume for the PU/cyclohexane system, and by the linear relation for

Based on the solution-diffusion mechanism, the permeation rate of a given component i through a pervaporation membrane can be described by Fick’s first law: dCi dx

ðA1Þ

C0i 2 C00i l

ðA2Þ

Ji ¼ 2Di or Ji ¼ Di where C 0i ¼ Si p0i

C 00i ¼ Si p00i

ðA3Þ

where Di is the diffusion coefficient, C0i and C00i are the concentrations, and p0i and p00i are the vapour pressures of the component i in the membrane on the feed side and permeate side, respectively, Si is the solubility coefficient, and l is the membrane thickness. Permeability Pi is defined as: Pi ¼ D i S i

ðA4Þ

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Thus, substitution of Eq. (A4) into Eq. (A2) gives: Ji ¼

Pi 0 ðp 2 p00i Þ l i

ðA5Þ

If the pressure on the permeate side is very low, that is a common situation in pervaporation, vapour pressure of component p00i can be assumed as equal 0; p0 q p00 ! 0; C 0 q C 00 ! 0: Assuming that the vapour pressure on the feed side is the saturated vapour pressure psat i ; Eqs. (A2) and (A5) reduce to: Ji ¼

Di Cisat l

ðA6Þ

Pi sat p l i

ðA7Þ

and Ji ¼

where Cisat is the saturation concentration of component i equal to the concentration of liquid in the membrane. By substituting Eqs. (A3) and (A7) into Eq. (A4), the diffusion coefficient, usually referred to as the apparent (or concentration averaged) diffusion coefficient, can be expressed in terms of specific flux and concentration of liquid in the membrane: Di ¼

Ji lpsat Q i ¼ i sat sat pi Ci Ci

ðA8Þ

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