Transport of liquid hydrocarbons in the polyurethane-based membranes

Journal of Membrane Science 302 (2007) 59–69

Transport of liquid hydrocarbons in the polyurethane-based membranes A. Woli´nska-Grabczyk ∗ Institute of Coal Chemistry, Polish Academy of Sciences, 44-121 Gliwice, Sowi´nskiego 5, Poland Received 22 December 2006; received in revised form 10 May 2007; accepted 12 June 2007 Available online 17 June 2007

Abstract The sorption and diffusion of liquid hydrocarbons have been studied in a series of polyurethanes (PU) based on poly(oxytetramethylene) diol (PTMO) extended with 2,4-tolylene diisocyanate (TDI) and 4,4 -bis (2-hydroxyethoxy) biphenyl (BHBP). The effects of the soft and hard segment length, and the penetrant structure, on the transport behaviour were investigated using immersion sorption method. The sorption rate curves were generally Fickian for all the PU/benzene systems. For n-hexane and cyclohexane as penetrants, various non-Fickian anomalies were observed for PUs with shorter soft segments (PTMO-1000, 650). The values of the diffusional exponent indicated that system was tending towards Fickian on decreasing the hard segment length or increasing the soft segment one, on decreasing the penetrant size or increasing its flexibility, and on increasing temperature. Diffusion coefficients (D) were determined from the initial slope of the sorption curves by the small-time method for the PU/benzene systems, and for the PTMO-2000-based PUs. The variation in D was found to depend strongly on the length of the PU hard and soft segments, and on the penetrant structure. The PU/penetrant interaction parameter (χ) was estimated from the results of solvent equilibrium uptake. The values of this parameter indicated that strong interaction existed for the PU/benzene and for all the PTMO-2000-based PU/solvent systems. The variations in sorption capability among PUs in those systems were found to be solely the effect of different ability of the hard domains to restrain membrane swelling. For other systems, no particular difference in normalised sorptivity among structurally different PUs was observed. The activation energy for diffusion, and the thermodynamic parameters were also calculated and discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: Polyurethanes; Sorption; Diffusion

1. Introduction Transport of small molecules through a polymer film occurs by an activated process, in which the permeant first dissolves in the polymer at the permeant/polymer interface, then diffuses through the film along a concentration gradient to the other side of the film, where it becomes desorbed. This is the physicochemical basis of the membrane based separation processes concerning gas and liquid mixtures, as well as of many other processes where polymer materials are exposed to various agents. It is known that composition and molecular structure of the polymer, and the molecular structure of the penetrant, both play a significant role in determining the permeability of a given material. When designing material for a particular application, it is necessary to have a prior knowledge about all ∗ Present address: Centre of Polymer and Carbon Materials, Polish Academy of Sciences, 41-819 Zabrze, M. Curie-Skłodowskiej 34, Poland. Tel.: +48 32 271 60 77; fax: +48 32 271 29 69. E-mail address: [email protected].

0376-7388/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2007.06.023

factors, which can affect the permeability values of a polymer. Although there are certain rules, which facilitate the selection of a polymer with desired transport properties, they lose effectiveness when more complex polymer systems are used or significant interactions between a polymer and a penetrant take place. On the other hand, the sensitivity of sorption and diffusion phenomena to subtle variations in polymer constitution or morphology, including those resulting from different processing conditions, limits the applicability of the transport data provided in literature for specific polymers or commercial materials to serve only as a guide for transport behaviour of a particular system. Therefore, further work needs to be done in this field to establish mechanisms and more general expressions relating sorption and diffusion with molecular properties and characteristics of polymer materials and permeants. The structure–transport properties relations of segmented polyurethanes have been the subject of our extensive investigations since some time [1–3]. These multiblock copolymers attract considerable attention as potential membrane materials, since they combine a variety of

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Table 1 Characteristics of PUs Sample code PU(X)-Mn

Composition TDI/BHBP/PTMO

Molecular mass

Mw /Mn

Soft segment content (wt%)

Tg of soft segments (◦ C)

ρPU (g/cm3 )

PU(3)-2000 PU(1)-2000 PU(3)-1000 PU(1)-650 PU(0.8)-650 PU(1.2)-650

4/3/1 2/1/1 4/3/1 2/1/1 5/2/3 5/3/2

44,100 37,300 46,200 38,900 40,500 41,200

2.1 1.5 2.7 2.7 2.1 1.7

57 76 40 51 63 43

−85 −85 −56 −31 −38 −25

1.091 1.053 1.197 1.161 1.143 1.182

Tg of the macrodiols: PTMO-2000: −85 ◦ C, PTMO-1000: −87 ◦ C, PTMO-650: −88 ◦ C

functional components into a single material, allowing thereby a simple and an effective modification of their structure. This in turn directly affects the physical and chemical properties of these polymers, including their permeation and separation ability. While the versatility of polyurethanes in obtaining membrane materials with tailor-made properties, or a body of structurally related polymers for fundamental transport studies is obvious, there is no doubts that the relationship of their transport properties to morphology is a complex one. This is mainly due to the fact that polyurethane segments may separate into more or less distinct microphases giving morphology whose detailed nature directly affects the polymer macroscopic properties. Moreover, strong interactions, which exist between microphases do not allow them to behave independently. Thus, these systems require a lot of attention in considering the nature, magnitude and distribution of the multiphases, or interphase effects, which tend to complicate the transport behaviour. To get a deeper insight into the transport phenomena in those materials, the more complete studies are therefore necessary, which should concern both permeation and sorption. The goal of this work was to examine a homologous series of the structurally different polyurethanes in their diffusion and sorption behaviour with respect to three different liquid hydrocarbons, i.e. n-hexane, cyclohexane and benzene. The materials studied comprise the similar set of poly(oxytetramethylene) (PTMO)-based polyurethanes used by us previously in pervaporation separation of benzene/cyclohexane mixtures [3]. For determining the transport characteristics, the gravimetric method has been chosen. This is one of the most convenient and straightforward

methods for estimating solubility and diffusion coefficients for various liquid/polymer systems, which is ideally suitable for the examination of the materials, which are not able to withstand the harsh conditions of the pervaporation experiments, e.g. PTMO-2000-based PUs exposed to benzene/cyclohexane mixtures. 2. Experimental 2.1. Materials The membrane materials studied constituted a series of segmented polyurethanes (PU) with varying both hard segment content and soft segment molar mass. The hard segments were composed of 2,4-tolylene diisocyanate (TDI, 95 wt.% of 2,4-isomer, Aldrich) and 4,4 -bis(2hydroxyethoxy)biphenyl (BHBP), whereas the soft segments were based on poly(oxytetramethylene) diol (PTMO, Mn = 650, 1000, 2000, BASF). The polymers were synthesised by a prepolymer two-step technique using dimethyl formamide (DMF) as a solvent. The method of the PU preparation as well as that of the BHBP synthesis has been described in details previously [1]. The composition of the materials and some of their physical properties related to the present studies are given in Table 1. The materials are designed as PU(X)-Mn , where X refers to the number of the TDI/BHBP repeat units in the hard segment, and Mn refers to the molar mass of the PTMO-based soft segment. The schematic representation of the PU structure is shown in Scheme 1.

Scheme 1. Molecular structure of PUs.

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Table 2 Properties of penetrants used in sorption experiments Penetrant

Molar mass

Density at 25 ◦ C (g/cm3 )

Solubility parameter ((4.1868 J/cm3 ))1/2 (cal/cm3 )1/2 )

Molar volume (cm3 /mol)

Kinetic radius ˚ ((10−10 m) (A))

Benzene Cyclohexane n-Hexane

78.11 84.16 86.17

0.874 0.779 0.655

9.2 8.2 7.3

89.4 108.8 131.6

3.346 3.351 2.604

Solubility parameter of PTMO: 36.42516 (J/cm3 )1/2 (8.7 (cal/cm3 )1/2 ).

2.2. Solvents DMF was purified by vacuum distillation. The solvents used for sorption experiments (i.e. benzene, cyclohexane and nhexane) were of an analytical grade and used without further purification. Some of the physical properties of the penetrants studied are shown in Table 2. 2.3. Polymer characterisation The obtained polymers were characterised by means of gel permeation chromatography (GPC) using a Knauer apparatus. DMF was used as a solvent at 80 ◦ C and the eluent flow rate was 1 ml/min. The MIXED-DPL gel columns and polystyrene standards were applied. A Rheometric Scientific DSC Plus differential scanning calorimeter was used for thermal behaviour investigations. The glass transition temperature (Tg ) measurements were performed at a 10◦ min−1 scanning rate according to the procedure given in ref. [1]. The mass densities of the polymers, used for the calculations of the polymer volume fraction in the swollen sample, were measured by using the buoyancy method in water. 2.4. Preparation of PU films Samples for sorption experiments were cut from films prepared by casting from a DMF solution (15 wt.%) and drying at 60 ◦ C in a nitrogen atmosphere for 72 h. The test samples were in a form of strips with dimensions of 2 cm × 0.8 cm and with the initial thickness ranging from 0.03 to 0.04 cm. The sample thickness was measured in several places with a micrometer calliper and averaged. The surface structure of the PU films was visualised by atomic force microscopy (AFM) using a Nanoscope E instrument (Digital Instruments, Santa Barbara, CA) working in contact mode, and by scanning electron microscopy (SEM) using a SEM BS 340 instrument (T), operated at 15 kV with magnifications between 200 and 1000.

ried out by exposing the samples directly to the air atmosphere in the controlled environment of the thermostated chamber containing activated carbon (Darco). Again, the weight changes as a function of time were recorded until equilibrium was reached. The polymer mass uptake or loss was then recalculated into moles of solvent sorbed or desorbed by 100 g of the polymer, and these data were used for obtaining sorption and desorption curves. The results of the measurements on as-prepared samples were found to be reproducible and the relative error of the weight changes determination was estimated as 6%. 3. Results and discussion 3.1. Structure of segmented polyurethanes Polyurethanes synthesised for the purpose of this study form a group of polymers of the same chemical constitution, which differ themselves in the length of the soft or hard segments due to the applied variations in the molar mass of a macrodiol, or in the molar ratio of reagents, respectively. Since the segment length is one of the key parameter determining the morphology and properties of polyurethanes [4], this allowed a homologues series of structurally different materials to be obtained. Generally, segmented polyurethanes might be microphase-separated to varying extents, covering the range from the microphase-mixed to the completely microphase-separated materials. Based on the DSC data shown in Table 1 and Fig. 1, and on the SAXS results presented earlier [5], and their compliance with the commonly accepted criteria for classifying a polyurethane as microphaseseparated [6], such as the presence of a low temperature Tg , and a peak in the SAXS curves, all the materials studied in this work may be regarded as being microphase-separated.

2.5. Sorption and desorption measurements Sorption was accomplished by immersing the samples in solvent contained tubes, which were placed in a thermostat. At appropriate time intervals, the samples were taken out, dried with a filter paper and weighed. The procedure was repeated until equilibrium weights were reached, i.e. no further weight gain was observed. After completion of sorption experiments, the procedure was reversed and the solvent desorption was car-

Fig. 1. DSC thermograms of PUs in the first heating run.

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The data summarised in Table 1 show the Tg values corresponding to the glass-to-rubber transition of the soft microphase determined for the PUs studied, as well as those corresponding to the macrodiols used as precursors of the soft segments. These values may be an indication of the extent of phase mixing of the hard segment units with the soft segment phase [7]. The Tg of the both PTMO-2000-based PUs is −85 ◦ C independently of the hard segment content. This is the same value as for the free PTMO, indicating that both polymers are completely phase-separated. This suggestion is also supported by the presence of the soft segments melting endotherm observed in the DSC scans of both PUs (Fig. 1), since if there had been phase mixing, crystallinity would have been destroyed. The Tg values of other PUs are much higher suggesting a lower degree of phase separation, and a presence of hard segments in the soft segment domains. However, there can be other factors as well that may cause the increase of the soft segment Tg values, like the restriction in the soft segment mobility introduced by the hard domains. Thus, in the PTMO-650-based series of PUs both phase mixing and decreased soft segment mobility may account for the increased Tg with increasing hard segment content. In Scheme 2, the simplified model is shown, which illustrates the both types of the soft segments domains, i.e. pure soft domains, B(1), proposed for both PTMO-2000-based PUs, and a solution of hard and soft segments, B(2), proposed for other PUs. The hard segment domains of the PUs studied, represented by the phase model designated as A in Scheme 2, have been found to display no crystallinity, as indicated by the wide-angle X-ray measurements. However, the DSC scans over the high temperature range for PUs with higher hard segment

Scheme 2. Schematical representation of domain structure in PUs: (A) hard segment domains, (B(1)) amorphous soft segment domains (PU-2000) and (B(2)) amorphous “solution” of hard and soft segments (PU-1000, PU-650).

content exhibit multiple endotherms associated with disordering processes, which occur in the semi-ordered hard domains. The detailed interpretation of these complex endotherms, with reference to the liquid crystalline behaviour in this type of polymers, has been presented earlier [8]. The results of our previous studies of the morphology in the polyetherurethanes, carried out using SAXS and AFM methods [5], have shown that large globular or circular structures of a few micron size, being presumably clusters of the hard segment lamellae, can develop in the BHBP-chain extended PUs having shorter soft segments. For PUs with the longest soft segments (PTMO-2000), the completely different surface morphology has been detected with distinct raised regions irregular in shape and size, and of various heights. The AFM images of the surface of PU(1)-650 and PU(3)-2000 representing both types of morphology are shown in Fig. 2, along with the respective SEM micrographs of both sam-

Fig. 2. SEM and AFM topographic images of the surface of PUs.

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Table 3 Sorption equilibrium constants (S, mol%) and Flory-Huggins interaction parameters (χ) for PU/penetrant systems at 25 ◦ C Polymer

PU(3)-2000 PU(1)-2000 PU(3)-1000 PU(1)-650 PU(0.8)-650 PU(1.2)-650

Benzene

Cyclohexane

n-Hexane

S

Scalc.

χB

S

Scalc

χC

S

Scalc.

χH

1.20 2.40 0.57 0.56 1.05 0.43

2.11 3.16 1.42 1.10 1.67 1.00

0.74 0.63 0.89 0.92 0.76 1.01

0.28 0.47 0.12 0.13 0.13 0.10

0.49 0.62 0.29 0.26 0.21 0.23

1.14 0.95 1.52 1.50 1.50 1.64

0.14 0.21 0.05 0.05 0.06 0.05

0.25 0.28 0.13 0.10 0.10 0.12

1.38 1.20 1.97 2.00 1.88 1.98

ples, where the presence of the similar structural features can be observed. 3.2. Sorption behaviour The sorption equilibrium constants (S) for the PUs studied are summarised in Table 3. They are expressed as mole percent units, i.e. as mole of solvent sorbed per 100 g of a sample. It has been shown, however, that incorporation of penetrant molecules into the hard segment domains of segmented polyurethanes should not be expected [9,10]. It is suggested that such domains can rather act similarly to impermeable crystallities in the partially crystalline polymers, where sorption is restricted to the amorphous regions of a polymer. Thus, according to such assumption, the solubilities in Table 3 have been normalised to the total soft segments content and expressed as Scalc . For sorption of aliphatic hydrocarbons in PUs with shorter soft segments (PTMO < 2000), it has been observed that the values obtained appear to conform to this assumption quite well, since the differences in Scalc among the polymers are very small. Moreover, the results suggest that in those systems sorption process involves all of the soft segments, and that it is not affected by the degree of microphase separation. The similarity of the Scalc values for PUs from the PU-650 and PU-1000 series is, however, in contrast with the much higher and different values obtained for the PTMO-2000-based PUs. For those polymers, the soft segment domains display ability of taking up more penetrant, probably as a result of the less effective cross-linking action of the hard segment domains. This in turn indicates that sorption ability of the PUs studied results not only from the presence of the impermeable regions but also from their power in restricting membrane swelling. The role of hard segments as tie units for the soft segment matrix is very well illustrated by the data concerning sorption ability of various PUs towards benzene. Table 3 shows that for both the PTMO-650 and PTMO-2000 series, the solubility is significantly higher for those series members, which possess shorter hard segments. However, there is no straightforward relationship between the length or amount of the hard segments, and the sorption capability of the polymer. The lack of such correlations can easily be explained by the fact that the ability to oppose swelling of the soft segment matrix is mainly linked with PU morphology. It was observed by us earlier [11] that PUs showing no signs of microphase separation or less developed morphology with structures on the size range of tens of nm exhibit higher benzene

solubility then those with distinct morphology on a macroscopic scale. Based on these data and the results presented, it can be found that generally the more developed is the morphology (e.g. PU(1)-650 versus PU(3)-2000) the greater is the reduction of the membrane sorption capacity. In all PUs investigated, the Scalc values decrease in the order benzene > cyclohexane > n-hexane. This dependence follows the similar sequence of the decreasing solubility parameters with the greatest difference in the solubility parameters between a permeant and a polymer for n-hexane (Table 3). According to the solubility parameter theory, the grater the difference in solubility parameters the less similar are the both chemical species, and the lower is their mutual solubility. In order to further examine the sorption phenomena, the Flory-Huggins theory has been used. In Table 3, the dimensionless Flory-Huggins interaction parameters, χ, are listed, which reflect the affinity between the particular PU and the penetrant. The χ parameter is defined by the following equation: lna1 = lnφ + (1 − φ) + χ(1 − φ)2

(1)

where a1 denotes the penetrant activity, and φ its volume fraction in a swollen polymer sample. This parameter is assumed to be constant over the entire activity range, and can be therefore determined from a single sorption experiment. For a liquid penetrant, a1 = 1, and χ is expressed as: χ = lnφ +

1−φ (1 − φ)2

(2)

The values of χ for the systems studied are found to be in the range of 0.63–2.00, and to depend on the kind of PU and the solvent. For all PUs, the χ values decrease in the order n-hexane, cyclohexane and benzene, and as expected, this is the order of increasing solvent power. The increased solvent power, demonstrated by the decreased χ values, can also be observed for the PTMO-2000-based PUs showing fully microphase-separated but less developed morphology, as well as for those PUs of the same soft segment length, which have a lower hard segment content. This is a general trend illustrating the variations in affinity between a penetrant and a polymer, which has been demonstrated by the sorption data, and which is thought to be the result of the swelling restrictions imposed by the hard segments domains. The another explanation that the presence of the hard segments dissolved in the soft matrix may account for the lower Flory-Huggins parameter values for PUs with a lower degree of microphase separation is less plausible, since the χ values do not

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Fig. 3. Sorption ( ) and desorption () curves of liquid hydrocarbons in PU(3)-2000: (a) benzene, (b) cyclohexane and (c) n-hexane.

follow the trend observed for the Tg variations. It is necessary to point out here that the validity of the Flory-Huggins theory over the entire activity range was assumed without experimental checks. Some literature data, concerning other PU/organic vapour systems for which deviation from the Flory-Huggins theory was observed [10,12], may suggest that this was too simplified approach. If so, the error resulting from this might have accounted for the less apparent differences within the series of PUs noticed for the PU/benzene systems in comparison to those with other two solvents. Thus, these results need further clarification by performing more detailed studies in a broader range of solvent activities. 3.3. Analysis of sorption and desorption curves The particular system can be regarded as Fickian [13] if both sorption and desorption curves of Mt /M∞ plotted as a function of the square root of reduced time t1/2 /d (where d is the thickness of a dry polymer film, Mt the weight gain at time t and M∞ is the equilibrium uptake) are linear in the initial stage (up to 60% of M∞ ), and then become concave to the abscise axis. Moreover, the reduced sorption curve should lie above the corresponding desorption one, if the diffusion coefficient D is an increasing function of permeant concentration, and respective curves for films of different thickness should superimpose each other. Figs. 3 and 4 show some representative examples of the reduced conjugate sorption and desorption curves for the systems studied. From the data obtained, it has appeared that only some of them exhibit sorption of a Fickian type. Basically, the processes of benzene sorption and desorption in all PUs (see Fig. 3), as well as those of other hydrocarbons in the PTMO2000-based PUs (see Fig. 4), seem to conform to the criteria set for Fickian sorption. However, it should be noted that even for those systems the results of sorption experiments with varying thickness of the film (not shown) only partially satisfy the

last criterion, i.e. some of the sorption curves coincide within the initial uptake range but differ in the way of approaching to equilibrium. As an example of the sorption data showing nonFickian behaviour, Fig. 4b and c present the curves for sorption and desorption of cyclohexane and n-hexane, respectively, in PU(3)-1000. The most important feature, which can be noted and which occurs in all those systems is a difference between solvent sorption and desorption. Sorption is characterised by an existence of a kind of an induction period, the duration of which is a strong function of the PU and the penetrant structure, which is then followed by the linear increase in sample weight up to the point where the sorption rate is again slowed down to reach the equilibrium. The appearance of the desorption curves is quite different. As shown in Fig. 4b and c, the initial weight loss, which is rapid and essentially linear with root-time, becomes successively slower during the later stages of the process. In general, this shape of the desorption curves has been found to be typical of many desorption runs despite the variations in the PU structure and type of solvent. Thus, the sorption process of aliphatic hydrocarbons in PUs with soft segment molar mass lower than 2000 exhibits various departures from the requirements of Fickian behaviour. There is another approach of qualifying the type of sorption process, which consists in the analysis of the sorption results, up to 50% of M∞ , by using the following empirical equation: ln

Mt = lnK + n lnt M∞

(3)

where n is the parameter indicating the type of sorption mechanism, K depends on the polymer ability to interact with penetrant molecules, and Mt and M∞ have the previous meanings [14]. According to this approach, the value of n = 0.5 suggests the Fickian type of sorption, whereas that of n = 1 the case II sorption. The values between both limiting types of sorption suggest more complex behaviour called “anomalous” sorption. The esti-

Fig. 4. Sorption ( ) and desorption () curves of liquid hydrocarbons in PU(3)-1000: (a) benzene, (b) cyclohexane and (c) n-hexane.

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Table 4 Kinetics analysis of penetrant transport in PUs at 25 ◦ C Polymer

Penetrant

Sorption

Desorption

n

K

(g/g sn )

n

K (g/g sn )

PU(3)-2000

Benzene Cyclohexane n-Hexane

0.49 0.51 0.51

0.217 0.102 0.152

0.53 0.54 0.50

0.103 0.093 0.146

PU(3)-1000

Benzene Cyclohexane n-Hexane

0.54 0.71 0.57

0.114 0.006 0.034

0.54 0.46 0.51

0.107 0.086 0.060

PU(1)-650

Benzene Cyclohexane

0.51 0.59

0.129 0.038

0.53 0.48

0.099 0.067

PU(0.8)-650

Benzene Cyclohexane

0.50 0.57

0.167 0.035

0.52 0.52

0.124 0.075

PU(1.2)-650

Benzene Cyclohexane

0.52 0.98

0.111 0.002

0.50 0.49

0.145 0.037

Fig. 5. Effect of temperature on sorption (a) and desorption (b) kinetics for PU(3)-1000/cyclohexane system; (c) sorption and desorption curves at 45 ◦ C.

mated values of n and K for the sorption and desorption processes are listed in Table 4. For the majority of cases, the values of n for the desorption experiments were in the range of 0.45–0.55 suggesting the type of process close to the Fickian one. The values of n around 0.5, indicating Fickian behaviour, have also been obtained for the sorption of all the liquid hydrocarbons in the PTMO-2000-based PUs, and generally for all the PU/benzene systems. However, in other cases the n values were higher than 0.5. For the PU-650 series and cyclohexane as a penetrant, the values of n were found to increase in the following order PU(0.8) < PU(1) < PU(1.2), which is in accordance with the increasing values of Tg , and the increasing amount of the hard segments in those PUs. Similarly, the very high value of n was observed for the sorption of cyclohexane in PU(3)-1000, another PU with the high hard segment content. The behaviour of the latter system at elevated temperatures is shown in Fig. 5. From Fig. 5a, it can be noticed that this system exhibits a strong anomalous feature of the sorption kinetics at ambient temperature, and tends toward Fickian dependence as the temperature is increased (Fig. 5c). The lower value of n at 45 ◦ C corresponds with this behaviour, however, for the investigated temperature range, these values are far from being close to 0.5 as expected for the Fickian type of sorption (Table 5). The values of the parameter K listed in Table 4 are higher for benzene as a penetrant, and increase with a rise in temperature (Table 5) suggesting increased penetrant/polymer interaction. Based on the data presented, it can be stated that PUs from the homologous series studied show a range of trans-

port behaviour depending on their molecular structure, type of solvent and temperature. The various behaviour of segmented polyurethanes has already been reported in literature. The immersion sorption behaviour of different solvents in commercial polyetherurethanes (Uralite, Vibrathane) was reported by Aminabhavi et al. [15–17]. For majority of solvents, they observed non-Fickian behaviour both in the slight sigmoidal shapes of the sorption curves, and in the estimated values of n, which varied from 0.51 to 0.68 for Uralite, and from 0.44 to 0.73 for Vibrathane, depending on the kind of solvent and temperature. Although no clear correlation between n and those factors was found, the decreasing of n with temperature was observed for some Vibrathane/n-alkane systems [17]. Various non-Fickian anomalies along with the behaviour reported as nominally FickTable 5 Kinetics analysis of cyclohexane transport in PUs at different temperatures Polymer

Temperature (◦ C)

Sorption

Desorption

n

K (g/g sn )

n

K (g/g sn )

PU(3)-1000

25 35 40 45

0.71 0.79 0.77 0.65

0.006 0.013 0.025 0.060

0.46 0.48 0.50 0.50

0.086 0.109 0.130 0.127

PU(1)-650

25 35 40 45

0.59 0.55 0.55 0.50

0.038 0.050 0.043 0.053

0.48 0.51 0.54 0.52

0.067 0.042 0.051 0.065

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ian were observed in the studies of solvent diffusion in Estane polyurethane (commercial polyurethane based on PTMO-1000) [18–20]. It was shown that the character of the sorption and desorption curves depends on the type of solvent, its concentration and the sample thickness. The effect of the amount of hard segments in the PTMO-2000-based polyurethanes has also been found [20]. In general, the pronounced anomalous sorption behaviour observed for many polyurethane/penetrant systems was often absent in the desorption runs, which remained Fickian in appearance at all penetrant activities [17–21]. This complex behaviour was discussed in terms of a Joshi-Astarita model of combined Fickian diffusion and relaxation process [22], according to which the changes in the relative rate between the polymer chain relaxation and the penetrant diffusion during the penetrant uptake cause the changes in transport kinetics. However, some specific effects observed by those authors remain unexplained, and more general relationship between structural parameters of the polyurethane and the permeant, and the type of transport process has not been established. The results of the present study concerning solvent transport in the homologous set of segmented polyurethanes have appeared to allow some parameters to be determined, which were found to affect transport kinetics. The results show a general rule, that decreasing the soft segment length, while keeping the length or amount of the hard segments constant, changes the transport kinetics from Fickian to anomalous one (PU(3)-2000 versus PU(3)-1000), or increases the severity of the anomalous behaviour for PUs with lower degree of microphase separation (PU(3)-1000 versus PU(1.2)-650). Similarly, the pronounced anomalous character of the sorption curves has been observed for PUs with phase-mixed morphology when the hard segment length was increased, whereas such effect was not observed for PTMO-2000-based PUs with fully phase-separated morphology. Moreover, decreasing the penetrant size (cyclohexane versus benzene), or its kinetic radius (cyclohexane versus nhexane), or increasing the temperature decreases the severity of the anomalous character of the sorption curves, leading at the extreme to the Fickian behaviour. These results can be explained based on the requirements for Fickian sorption to occur, which are associated with a high mobility of polymer segment units. Thus, the soft segments of the PTMO-2000-based PUs, exhibiting the lowest Tg values, seem to be sufficiently active to take up instantaneously the equilibrium conformation corresponding to the particular stage of the sorption process. Consequently, the stress applied by the unswollen part of the sample, e.g. by the hard segment domains, on the swollen one is immediately released by a rapid segment relaxation in those polymers. The increased mobility can also explain why the kinetics of sorption tends to transform to Fickian when the measurements are carried out at higher temperatures. On the other hand, the condition of a high mobility seem not to be obeyed for diffusion of liquid in PU with a lower degree of microphase-separation, where the free movement of the soft segments, according to their Tg values, is restricted and does not allow them for rapid rearrangement with the changes in the sorbed state. Thus, for those systems internal stress may influence process of diffusion leading to the time dependent effects.

Furthermore, the more pronounced non-Fickian behaviour for greater and non-flexible penetrant molecules in PUs with limited segment mobility may be explained by the fact that such molecules require large scale segmental rearrangements, less readily attainable in those polymers. The state of an enhanced segmental mobility seem to be realised, however, in case of benzene sorption due to the specific ability of its molecules to decrease the cohesive forces between neighbouring segments and to plasticise the system. 3.4. Structure-diffusivity correlations The sorption kinetics conforming to the criteria required for Fickian type of sorption can be described by the following equation [13]:   n=∞ 1 8  −D(2n + 1)2 π2 t Mt (4) =1− 2 exp M∞ π d2 (2n + 1)2 n=0 or by another form of this equation used for small time:  1/2 Dt 4 Mt = 1/2 M∞ π d2

(5)

where Mt , M∞ , D, t and d have the previous meanings, and n is an integer. The value of the diffusion coefficient, D, can be calculated from the initial slope, A, of the plot Mt /M∞ versus t1/2 /d by the relation: D=

πA2 16

(6)

For the polymer/solvent system, this relation gives a mean value for the diffusion coefficient, since D is usually concentration dependent. Table 6 shows the variation of diffusion coefficient with PU structure for the PU/benzene systems assumed to obey the basic conditions for Fickian sorption. Generally, the D values are found to decrease with the decrease in the soft segment length, or with the increase of the hard segment one. As can be seen from Table 6, the diffusivity of benzene during the sorption process decreases by a factor of 2.2 or 1.5 with the decrease of the soft segment molar mass from 2000 to 1000, or from 1000 to 650, respectively, and at the constant hard segment length or content. Similarly, more than two-fold decrease in the D values can be observed on increasing the hard segment length from x = 1 to 3 for the PTMO-2000-based PUs, or from x = 0.8 to 1.2 for the PTMO-650 based ones. Since diffusion of small molecules in polymer requires cooperative motion of the polymer segmental units, it seems obvious that penetrant diffusivity is lower in PUs with shorter soft segments, or in those with higher fraction of the constraining regions. The lower diffusivity in those polymers may also be attributed to the reduced effective crosssectional area available for transport, and to the longer diffusion path caused by the hard segment domains acting as impermeable islands. From the D values given in Table 6, it is seen that the effect of the both structural parameters becomes less apparent at the desorption process. This can be explained by the increased

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67

Table 6 Diffusion coefficient values, D(DI ) × 107 cm2 /s, for PU/benzene systems at 25 ◦ C Polymer

Benzene Sorption

PU(3)-2000 PU(1)-2000 PU(3)-1000 PU(1)-650 PU(0.8)-650 PU(1.2)-650

Desorption

D

DI

D

DI

2.16 4.75 0.97 1.29 1.53 0.65

7.85 33.99 2.14 2.77 5.15 1.21

0.81 0.91 0.68 0.70 0.78 0.65

2.94 6.51 1.50 1.50 2.62 1.21

solvent uptake associated with swelling that leads to the greater segmental mobility. On the other hand, the extensive swelling observed for PUs with a large soft segment fraction makes the assumption of the constant polymer dimensions to be no longer valid. Thus, another method has been applied, which enables the correction for polymer swelling to be made. By using the following expression [23]: DI = D(1 − φ)−5/3

(7)

where D is the mean diffusion coefficient obtained from the sorption (desorption) experiments and φ is the penetrant volume fraction, the intrinsic diffusion coefficient DI has been determined as a measure of a penetrant mobility. In Table 6, there is a comparison of the mean values of D with the results obtained following the correction for polymer swelling. As can be seen from these data the DI values are higher than the respective D ones, and they reflect the same trends already found for sorption of benzene in PUs studied. Moreover, due to the correction for penetrant volume fraction, the differences between membranes of the PU series have become even more pronounced; e.g. PU(1)-2000 versus PU(3)-2000, or PU(0.8)-650 versus PU(1.2)-650. It has also appeared that the results from desorption nearly coincide with those from sorption with respect to the polymer structure-penetrant mobility trends when DI values are considered. Variations in the diffusion coefficient with respect to the kind of penetrant diffusing through the PTMO-2000-based PUs are presented in Tables 6 and 7 for benzene, and for cyclohexane and n-hexane, respectively. For both PUs, there is a decrease in the D (DI ) values in the order benzene, n-hexane and cyclohexane. Comparing the molar volume of the penetrants given in Table 2, one can notice that smaller molecules diffuse faster

Fig. 6. Van’t Hoff plots of log S vs. 1/T for PU/penetrant systems: ( ) benzene, () cyclohexane, () n-hexane: (a) PU(3)-1000 and (b) PU(1)-650.

than the bigger ones (benzene versus cyclohexane). However, the molecular shape and flexibility are also very important in determining the diffusion coefficient, because larger n-hexane molecules but with smaller kinetic radius diffuse faster than the smaller cyclohexane molecules. 3.5. Activation energy and heat of sorption In experiments already discussed, the temperature has been found to influence the penetrant behaviour in PUs. To carry this analysis further, the attempts have been made to estimate the thermodynamic and kinetic parameters by using Van’t Hoff (7) and Arrhenius (8) equations: H S + (8) RT R Ea + lnA (9) lnD = − RT where H is enthalpy and S is entropy of sorption, Ea the activation energy, R the universal gas constant, T the absolute temperature and A is a constant (“frequency factor”). From the temperature dependence of equilibrium sorption constant, the heat of sorption can be evaluated, and from the temperature dependence of diffusion coefficient, the activation energy for diffusion can be determined. The sorption and diffusion results plotted in a form of logarithm of S or D against the reciprocal of the absolute temperature are shown in Figs. 6 and 7, respectively. As can be seen from the plots displayed, the linear relations of both constants over the investigated temperature range were obtained in all cases. Therefore, Eqs. (8) and (9) could be used to determine the H, S and Ea values. The results of these lnS = −

Table 7 Diffusion coefficient values, D(DI ) × 107 cm2 /s, for PU-2000/penetrant systems at 25 ◦ C Polymer

PU(3)-2000 PU(1)-2000

Cyclohexane

n-Hexane

Sorption

Desorption

Sorption

Desorption

D

D

D

D

DI

0.69 1.11 1.79 3.66

DI

0.66 1.06 0.76 1.55

DI

1.41 1.91 3.15 4.81

DI

1.18 1.60 1.20 1.83

Fig. 7. Arrhenius plots of log D vs. 1/T for PU/benzene systems; ( ) sorption, () desorption: (a) PU(3)-1000 and (b) PU(1)-650.

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A. Woli´nska-Grabczyk / Journal of Membrane Science 302 (2007) 59–69

Table 8 Van’t Hoff and Arrhenius parameters for PU/penetrant systems Polymer

Penetrant

HS (kJ/mol)

S (J/mol deg)

Ea (s) (kJ/mol)

Ea (d) (kJ/mol)

PU(3)-1000

Benzene Cyclohexane n-Hexane

8.00 18.47 21.98

22.20 43.96 48.67

39.24 – –

21.87 – –

PU(1)-650

Benzene Cyclohexane n-Hexane

7.66 14.27 20.60

20.82 30.83 44.57

31.85 – –

11.76 – –

calculations are summarised in Table 8. The values of H are positive, and fall in the similar range of 8–22 kJ/mol for both PUs studied, increasing in the order benzene, cyclohexane, nhexane. The results of S are also positive, and they are in the range of 21– 49 kJ/mol. The positive values of H suggest that sorption proceeds mainly by the Henry’s mode introducing the endothermic contribution to the process, which is concerned with the formation of a hole of a molecular size in the polymer matrix. According to the significantly higher H values for aliphatic hydrocarbons, it is shown that the probability of a hole formation is subsequently lower for those penetrants than for benzene. The activation energy for diffusion is the energy needed to enable the dissolved molecules to jump into another hole. Based on the data given in Table 8, it can be noted that for both PUs, this process requires the significant involvement of the polymer segments motion. The slightly higher Ea value for PU(3)-1000 does not comply with the lower Tg value of this polymer comparing to that of PU(1)-650, however, it may result from the greater tortuosity inside PU(3)-1000 of a higher hard segment content. On the other hand, the lower Ea values for the respective desorption processes seem to be largely accounted for by the higher fractional free volume of the swollen polymer. 4. Conclusions The transport behaviour of various liquid hydrocarbons through segmented PUs was studied by performing the immersion sorption experiments. The homologous series of PUs composed of the same PTMO-based soft segments and TDI/BHBP-based hard segments, but varying in the segment length was investigated. It has been shown that sorption and diffusion is a complex process. Depending on the molecular structure of the polyurethane and the kind of penetrant, the transport mechanism may change from nominally Fickian to the anomalous one. The sorption and desorption behaviour are both Fickian in appearance for all PU/benzene systems, whereas various non-Fickian anomalies can be observed for cyclohexane and n-hexane as penetrants. A general rule has been found for the latter systems that decreasing the soft segment length, while keeping the length or amount of the hard segments constant leads to the departure from the Fickian kinetics, or to the increased severity of the anomalous behaviour already existing. The similar effect has been observed for PUs with a lower degree of microphase separation as a result of the increased hard segment length. The variation in transport kinetics can be related to the differences in mobility of the soft segment units, and to the

degree of departure from a high mobility requirement for Fickian diffusion to occur. In the present experimental conditions, the state of enhanced segmental mobility seem to be realised in case of benzene sorption, due to its ability to plasticise the PU soft domains, and for PUs with the longest soft segments. It also appears that system tends to head towards Fickian behaviour on decreasing the hard segment length or increasing the soft segment one, on decreasing the penetrant size or increasing its flexibility, and on increasing the temperature. This is also the same trend of increasing penetrant diffusivity in the systems studied that can be attributed to the enhanced mobilities of both the polymer segment and the penetrant molecule, as well as to the diminished influence of the hard segment domains in creating an obstacle to diffusion. It has been shown that structure of the investigated PUs plays a significant role in determining the polymer sorption capability for these systems, which display a high polymer solvent interaction. The strong interaction, expressed by the low values of the Flory-Huggins interaction parameter (χ), has been observed for all PU/benzene systems, and for the PTMO-2000-based PUs exhibiting fully microphase separated and less developed morphology. The variation in sorptivity among PUs in those systems was found to be solely the effect of different ability of their hard segment domains to oppose soft segment matrix swelling. For other systems, showing weaker polymer solvent interaction, no particular difference in normalised sorption capability among the structurally different PUs has been observed. The similar heat of solution of a solvent into PUs with a lower degree of microphase separation and well-developed morphology is in agreement with those findings. In all PUs, the χ values were found to decrease in the order n-hexane, cyclohexane, benzene, which represents the order of increased solvent power. Acknowledgements This work was financed by the grant No. N 205 070 31/3205 given by the Ministry of Science and Higher Education of Poland from its means for scientific research for the years 2006–2008. The author gratefully acknowledges Mr. A. Jankowski for his assistance in this work. References [1] A. Woli´nska-Grabczyk, Relationships between permeation properties of the polyurethane-based pervaporation membranes and their structure studied by a spin probe method, Polymer 45 (2004) 4391–4402.

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