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1H nuclear magnetic resonance (NMR) cryoporometry as a tool to determine the pore size distribution of ultrafiltration membranes
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Journal of Membrane Science 309 (2008) 233–238
1
H nuclear magnetic resonance (NMR) cryoporometry as a tool to determine the pore size distribution of ultrafiltration membranes Jae-Deok Jeon, Soo Jung Kim, Seung-Yeop Kwak ∗
Hyperstructured Organic Materials Research Center (HOMRC), and Department of Materials Science and Engineering, Seoul National University, 599 Gwanangno, Gwanak-gu, Seoul 151–744, South Korea Received 16 July 2007; received in revised form 22 October 2007; accepted 24 October 2007 Available online 30 October 2007
Abstract The pore size distribution (PSD) of an ultrafiltration (UF) membrane is of great importance as it governs liquid permeability, filtration ability, and the interaction between molecules and the membrane matrix. Two series of UF membranes were studied: commercial regenerated cellulose (PL) membranes and polyethersulfone (PB) membranes, each with molecular weight cutoff (MWCO) values of 5, 10, and 30 kDa. This study was conducted to determine the PSDs of UF membranes using 1 H nuclear magnetic resonance (NMR) cryoporometry. NMR cryoporometry is based on the theory of the melting point depressions (MPDs) of liquid confined within a pore, which are dependent on the pore diameter. The MPDs were determined by analyzing the variation of the NMR signal intensity with temperature. From spin-echo intensity versus temperature curves, it was found that for each series of UF membranes the maximum MPDs of cyclohexane confined within the membrane pores were inversely proportional to the MWCO. For the same MWCO, the MPDs of the PL membrane were larger than that of the PB membrane, implying that the pores in the PL membranes were smaller than those in the PB membranes, consistent with their water and solute flux performances reported by the manufacturers. These findings indicate that NMR cryoporometry is a very effective method for determining the PSDs of UF membranes with asymmetric pore structures. © 2007 Elsevier B.V. All rights reserved. Keywords: Ultrafiltration membrane; NMR cryoporometry; Pore size distribution; Melting point depression; Cyclohexane
1. Introduction Ultrafiltration (UF) membranes have been widely applied in molecular separation technologies such as those used in low concentration effluent treatment, water purification, and virus removal [1,2]. UF membranes with pore sizes in the range of 1–100 nm are classified by molecular weight cutoff (MWCO), which is typically defined as the molecular weight of a solute that has a rejection coefficient of 90% or greater. The pore geometry of UF membranes consists of an interconnected threedimensional network of channels of non-uniform size and shape. A prominent feature of UF membranes is their thin skin layer on the surface, which is usually 0.1–1 m in thickness. This skin layer permits high hydraulic permeability while the more
∗
Corresponding author. Tel.: +82 2 880 8365; fax: +82 2 885 1748. E-mail address: [email protected] (S.-Y. Kwak).
0376-7388/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2007.10.034
open/porous sublayer (typically 125 m in thickness) provides good mechanical support; additional strength is sometimes provided by casting the membrane on a spun-bonded polyethylene or polypropylene backing [3]. Therefore, the small pores in the thin and dense skin layer are mainly responsible for the separation characteristics of the membrane and the open sublayer does not usually influence the membrane performance. Thus, when developing a UF membrane for a particular molecular separation process, it is of prime importance to determine the size and distribution of the pores of the membrane, as accurately as possible [3,4]. Various methods have been employed to determine the pore size distribution (PSD) of porous membranes, including the microscopic observation method [5,6], bubble pressure method [7], mercury intrusion porosimetry [8], permporometry [9], gas adsorption–desorption [10], and differential scanning calorimetry (DSC) thermoporometry [11–13]. These methods vary widely in applicability, sensitivity, and information that
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they yield. However, some methods have their specific disadvantages such as irreversible damage of the samples and time consuming, which limited their applications for porous materials having the small pores. In the case of mercury intrusion porosimetry and gas adsorption–desorption, it is necessary to suppose a structural model for the pores, making the interpretation of the results quite complex. DSC thermoporometry observes heat transfer in a measurement consisting of dynamic and isothermal steps, from which the amount of liquid molten within given temperature ranges can be calculated with the help of the known enthalpy of fusion. However, DSC thermoporometry is somewhat limited in the pore size range detectable, implying that it is difficult to obtain detailed information about the pore size distribution with a few nanometer sizes in UF membranes. Several approaches have been developed for characterizing the PSD of porous materials by means of 1 H nuclear magnetic resonance (NMR) [14–18]. These approaches exploit differences between the NMR characteristics of a material trapped within a porous network depending on whether it is in the liquid or solid state. Several studies have examined the phase transition of liquid confined within the pores of a porous material by using the longitudinal (spin-lattice, T1 ) and transverse (spin–spin, T2 ) relaxation times of hydrogen nuclei. These studies were based on the well-established method for 1 H NMR relaxation time measurement known as relaxometry. However, to accurately estimate the PSD, relaxometry requires knowledge of the surface layer parameter determined by the nitrogen adsorption method. Another NMR method has been adopted by Strange and Rahman [19], Strange et al. [20] and Hansen et al. [21,22] to determine the PSD of porous materials. This method, known as cryoporometry, utilizes the melting point depression (MPD), Tm , of a material confined within pores of porous materials. The theoretical basis of cryoporometry is the Gibbs-Thomson equation [11]. From this equation, it was found that the difference between the bulk and the depressed melting temperature was inversely proportional to a linear dimension of the liquid confined within the pores. Strange and Rahman [19] and Strange et al. [20] determined the PSD of a variety of porous silicas using cyclohexane as a probe molecule. They found that the sensitivity of cyclohexane was approximately three times greater than that of water. However, when cyclohexane was used as a probe molecule, the PSD of the porous materials could not be accurately determined due to differences in the magnetic susceptibility effects between the matrix and liquid as a function of temperature. Allen et al. [23,24] determined the PSD of cyclohexane confined within porous materials using a spinecho pulse sequence (90◦ –τ–180◦ –τ–echo). They found that pore susceptibility differences could be ignored when a spinecho pulse sequence was used. At a pulse separation time, τ, of approximately 10 ms, the signal intensity, I, from the liquid phase of cyclohexane confined within the pores was obtained as a function of temperature. The cyclohexane outside of the sample behaves as bulk cyclohexane, and provides a reference point for the change in melting temperature arising from the confinement. Based on these considerations, cryoporometry has been successfully applied to various porous materials, including
uniform and nanoporous materials such as glasses, silica gels, and sandstones. To our knowledge, however, no previous study has directly and precisely characterized the PSDs of UF membranes with non-uniform and asymmetric pore structures. Therefore, in the present work we investigated the PSDs of such UF membranes using 1 H NMR cryoporometry. The UF membranes used were two different series of commercial regenerated cellulose (PL) and polyethersulfone (PB) membranes, where each series had MWCOs of 5, 10, and 30 kiloDalton (kDa). 2. Experimental 2.1. Materials The UF membranes used in this study were a series of three PL membranes (MWCO = 5, 10, and 30 kDa) and a series of three PB membranes (MWCO = 5, 10, and 30 kDa); all of these membranes were obtained from Millipore corp. (Bedford, MA, USA). These membranes are asymmetric UF flat sheet PL and PB membranes that have been commercialized under the filter brand names Ultracel and Biomax, respectively. The probe molecule, cyclohexane (C6 H12 ; 99%, Aldrich Chemicals), has a melting point of 280 K and a surface energy at the liquid–solid interface of 4.6 erg/cm2 . In this study, PLxK and PBxK denote the PL and PB series of membranes with an MWCO of x kDa, respectively. 2.2. Sample preparation The membranes were submerged in water and then peeled off the supporting backing layer using tweezers. All samples were dried completely for 24 h or more at room temperature in a vacuum oven. The dried membranes were immersed in high purity cyclohexane for a week at room temperature. Excess cyclohexane remaining on the top and bottom surfaces of each sample was then removed by pressing the sample with a soft rubber roller and by wiping the sample with a filter paper, respectively. The samples were packed into 10 mm outer diameter NMR tubes and sealed. The sample height was restricted to approximately 15 mm to ensure that all of the sample was located within the transmitter/receiver coil, and thus was homogenously irradiated. All procedures were carried out in a drying room. 2.3. Characterization 1H
NMR cryoporometry measurements were carried out on a Bruker mq20 spectrometer at 0.47 Tesla and 19.95 MHz resonance frequency. Each sample test was performed over a temperature range of 200–280 K with an interval of 1 K using a Bruker BVT-3000 temperature control unit. During an experiment, the monitored temperature usually remained within ±0.1 K of the target temperature. A 90◦ pulse length of 2 s was applied with a recycle delay of T > 5T1 . To prevent complications associated with supercooling or hysteresis, all measurements were recorded with increasing the temperature from a low initial temperature. Specifically, the sample was initially quenched
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to 200 K in liquid nitrogen until all the liquid was frozen, after which it was warmed slowly, while continuously measuring the NMR signal intensities from the liquid phase, until all of the crystalline cyclohexane had melted. At each new temperature, the sample was allowed to equilibrate for at least 10 min before any measurements were performed. All measurements were performed using a spin-echo pulse sequence (90◦ –τ–180◦ –τ–echo). In this study, the spin-echo amplitude was measured with a pulse separation time, τ, of 10 ms to ensure that the signal was entirely from the liquid phase. The signal intensity was corrected for temperature by implementing Curie’s law; that is, the observed signal intensity was multiplied by the factor T/Tm , where Tm = 280 K and T is the actual temperature.
From this equation, it is found that the difference between the normal and depressed melting temperatures is inversely proportional to a linear dimension of the liquid confined within the pores. The spin-echo signal intensity, V, provides a measure of the amount of cyclohexane confined within the pores that is in the liquid phase at a particular temperature, T, and thus the volume of the pores that have a linear dimension equal to the pore diameter, D, in Eq. (1). The volume of the pores with pore diameters between D and D + D is (dV/dD)D. If the pores are filled with liquid, the PSD (dV/dD) is determined from the derivative of the intensity-temperature (IT) curves given by
3. Results and discussion
From Eq. (1), dTm (D)/dD = K/D2 , and hence Eq. (2) can be rewritten as
Cyclohexane used as a probe molecule in this study is an organic compound that comprises a ring molecule with a sixfold symmetrical structure. It is liquid at room temperature but nucleates at ca. 280 K to form a plastic crystal phase that consists of a rotationally disordered fcc lattice based on random orientation of the molecules [25]. The spin–spin relaxation time, T2 of liquid for cyclohexane is easily distinguishable from that of solid, because liquid has characteristically long T2 , ranging from milliseconds to seconds, whereas solid usually has very short T2 in the order of microseconds. NMR cryoporometry measurements are performed using a spin-echo pulse sequence (90◦ –τ–180◦ –τ–echo). The 90◦ x pulse shifts the spins onto the y-axis where they start to recover but dephase during the time of the experiment. After a time τ, they have dephased in the x–y plane. Applying an 180◦ y pulse rotates the spins about the y-axis, causing them to rephase. Then, a maximum signal will be measured at 2τ. This is known as a spin-echo and the height of the echo is directly dependent on the volume of liquid in the sample. In this study, the spin-echo amplitude is measured with a time interval τ of 10 ms (shorter than T2 of liquid and longer than that of solid for cyclohexane) to ensure that the signal is entirely from the liquid present. Therefore, this signal amplitude is measured as a function of temperature and should be proportional to the volume of liquid confined within pores of the membranes. The theoretical basis for cryoporometry is the GibbsThomson equation [11], which expresses the MPD of liquid confined within a small pore, Tm (D), as follows: Tm (D) = Tm − Tm (D) =
4σsl Tm K = DHf ρs D
dV dV dTm (D) dI = = dD dD dTm (D) dD
dV K dV = 2 dD D dTm (D)
(2)
(3)
Thus, provided K is known for the liquid used, the PSD function can be determined from measurements of dV/dTm (D). Fig. 1 shows the measured spin-echo intensity as a function of temperature and the first derivative of the intensity with respect to temperature for bulk cyclohexane. The signal intensity increases abruptly at ca. 280 K, at which dI/dT exhibits a maximum. From these results, the transition temperature from the solid to the liquid state of bulk cyclohexane was set to Tm = 280 K, which is in very good agreement with the reference value of ca. 280 K. Fig. 2 shows the 1 H spin-echo signals of cyclohexane confined within the PL10K membrane at four temperatures, 200, 240, 270, and 280 K. Comparison of these signals reveals that the spin-echo height from the liquid phase of cyclohexane confined within the pores increases gradually as the temperature is increased. At the lowest temperature, 200 K, the intensity is 0%, consistent with all of the cyclohexane being in the solid phase. At 280 K, which corresponds to the melting point of bulk cyclohexane, the spin-echo signal intensity from the liquid phase is approximately 100%. Below the bulk melting temperature, only the membrane, trapped between the solid matrix of the absorbent and the frozen liquid inside the pores, contributed to
(1)
where σ sl is the surface energy at the liquid–solid interface, Tm is the normal (bulk) melting point of the bulk material, Tm (D) is the melting point of the confined solid of dimension D, Hf is the bulk enthalpy of fusion, ρs is the mass density of the crystalline solid, and K is a constant depending solely on the physical properties of the liquid confined within the porous materials. Provided K is known, the PSD can be estimated from measurements of the amount of liquid confined within the pores as a function of temperature. In this study, cyclohexane was used as the probe liquid, for which K is approximately 178 K nm [26].
Fig. 1. NMR data of bulk cyclohexane: the spin-echo intensity () and the derivative () of the intensity with respect to temperature as a function of temperature.
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Fig. 2. Spin-echo signals of cyclohexane confined within pores of a PL10K membrane at 200, 240, 270, and 280 K.
the NMR signal. In fact, this spin-echo signal is observable down to approximately 220 K in the smallest pore systems. This observation indicates that normal colligative freezing of the surface layer does not take place in these systems. Under the present experimental conditions, however, the nuclei at the wall surface will only contribute to the signal in a more limited temperature region owing to the relatively short decay. In the melting region, the molecules of the melted liquid will be in fast exchange with the molecules at the pore walls, giving rise to an averaged signal. It has been reported [25] that the excess bulk liquid on the outside of the porous material behaves like bulk cyclohexane, and thus provides a calibration point for the melting curves of the liquid within the pores. Therefore, we determined the signal intensity at the highest temperature (i.e., 280 K), and normalized the IT curves by this intensity. Fig. 3a and b show plots of the spin-echo signal intensity versus temperature for cyclohexane confined within the pores of the PL and PB series of membranes, respectively. These IT curves show that for both membrane types, the signal intensity increases smoothly as the temperature is increased from 200 to 280 K, consistent with the gradual melting of the frozen cyclohexane confined within the pores of the membranes. These curves clearly show the marked difference between the signal intensities of the solid and liquid phases, with the pure solid and liquid phases having relative signal intensities of 0 and 1, respectively. The IT curves additionally confirm that the minimum
Fig. 3. Relative signal intensity vs. temperature curves (IT curves) for cyclohexane confined within pores of (a) PL and (b) PB series of membranes with 5 (), 10 (), and 30 kDa ().
melting points of cyclohexane confined within the membrane pores shift to lower temperatures with decreasing the MWCO. Further, it was found that the MPD of cyclohexane confined within the pores of both series of membranes decreased with increasing the MWCO and that the MPDs of the PL membranes were larger than those of the corresponding PB membranes. The MPDs were determined from plots of dI/dT or dV/dT as a function of temperature, which were generated from the IT curves. Based on these functions, the maximum MPDs for each system were estimated from the difference between the minimum and normal melting points of cyclohexane confined within the membrane pores and are listed in Table 1. The maximum
Table 1 Characteristics of the PL and PB series of UF membranes used in this study Sample
MWCOa (kDa)
Maximum melting point depression (K)
Pore size distribution (nm)
Average pore size (nm)
Water/solute flux b (ml/min/cm2 )
PL5K PL10K PL30K PB5K PB10K PB30K
5 10 30 5 10 30
76 45 39 65 39 32
2.2–15.0 3.7–25.0 4.5–30.0 2.7–30.0 4.0–35.0 5.0–50.0
2.8 4.9 6.1 4.4 5.9 7.6
0.09/0.09 –/0.13 1.41–1.44/0.17 0.6–0.7/0.13 2.1–2.4/0.15 3.2–4.0/0.16
a b
Molecular weight cutoff. Data provided by the manufacturers (Millipore corp.).
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Fig. 5. Average pore size vs. MWCO for the PL and PB series of membranes.
the Stokes Einstein equation. Also, this tendency was in good agreement with water and solute (i.e., sucrose and albumin) flux performances provided by the manufacturers (Millipore corp.). These findings indicate that 1 H NMR cryoporometry is a very effective method for characterizing the PSD of UF membranes with asymmetric pore structures, and that the PSDs of the membranes studied correlated strongly with the flux performances. 4. Conclusions 1H
Fig. 4. Pore size distribution (PSD) curves of (a) PL and (b) PB series of membranes with 5 (), 10 (), and 30 kDa ().
MPDs for both series of membranes were inversely proportional to the MWCO. Also, the maximum MPDs of the PL membranes were larger than those of the PB membranes with the same MWCO. These results indicate that the pores in the PB membranes were larger than those in the PL membranes. Eq. (1) indicates that the MPDs of cyclohexane confined within the pores of UF membranes are inversely proportional to a linear dimension of the pore diameter. The PSDs of the PL and PB series of membranes are shown in Fig. 4a and b, respectively. Comparison of the two series reveals that the PSDs of the PB membranes are broader than those of the PL membranes with the same MWCO. Within each series of membranes, the PSDs increase with increasing the MWCO (i.e., in the sequence 5K < 10K < 30K) in the range of 2–50 nm for both series of membranes. Fig. 5 shows the average pore sizes of the PL and PB series of membranes with different MWCOs, and these data are listed in Table 1. The average pore sizes of the PB membranes (ca. 4–8 nm) were larger than those of the corresponding PL membranes (ca. 3–6 nm) with the same MWCO. Sch¨afer et al. [27] reported pore size values for a series of PL membranes of 3.7, 5.2, and 9.6 nm for PL5K, 10K, and 30K, respectively, which are very similar to those obtained in the present study. They calculated pore diameters using an equation determined by Worch and
NMR cryoporometry was used to characterize the pore size distribution and average pore size of PL and PB series of UF membranes. This method utilized the NMR signal intensities, I, directly proportional to the only non-frozen volume fraction of the liquid measured as a function of temperature, T, using a spin-echo pulse sequence (90◦ –τ–180◦ –τ–echo). From these IT curves, the maximum MPDs of the cyclohexane confined within the pores of two different series of membranes were observed to be inversely proportional to MWCO. Also, it was found that the maximum MPDs of PL membranes were larger than those of PB membranes with the same MWCO. On the basis of the Gibbs-Thomson equation, the PSDs of both series of membranes saturated with cyclohexane were derived from 1 H NMR IT-curves of the confined cyclohexane. From the results, the PSDs of PB membranes were observed to be larger than those of PL membranes with the same MWCO. In addition, in the case of the same series of membranes, their PSDs were increased with increasing the MWCO (i.e., in the sequence 5K < 10K < 30K) in the range of 2–50 nm, which was in good agreement with water and solute flux performances provided by the manufacturers. In conclusion, 1 H NMR cryoporometry was found to be a very effective method for characterizing the PSDs of UF membranes, which are strongly correlated with their flux performances. Acknowledgments The authors are grateful to the Korea Science and Engineering Foundation (KOSEF) for support of this study through the Hyperstructured Organic Materials Research Center (HOMRC).
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The corresponding author, S.-Y. Kwak, gratefully acknowledges Professor Colin A. Fyfe at the Department of Chemistry, University of British Columbia (UBC), for his valuable suggestions and comments regarding the NMR results.
Nomenclature D Hf I K T1 T2 T Tm Tm (D)
pore diameter (m) bulk enthalpy of fusion (J/mol) intensity constant associated with the liquid (K m) longitudinal (spin-lattice) relaxation time (min) transverse (spin–spin) relaxation time (min) temperature (K) normal (bulk) melting point (K) melting point of the confined solid of pore diameter D (K) Tm (D) melting point depression (K) of a confined liquid to the pore diameter D (K) V volume (m3 ) Greek letters τ pulse separation time (min) σ sl surface energy at the liquid–solid interface (J/m2 ) ρs mass density of the crystalline solid (g/m3 )
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Journal of Membrane Science 309 (2008) 233–238
1
H nuclear magnetic resonance (NMR) cryoporometry as a tool to determine the pore size distribution of ultrafiltration membranes Jae-Deok Jeon, Soo Jung Kim, Seung-Yeop Kwak ∗
Hyperstructured Organic Materials Research Center (HOMRC), and Department of Materials Science and Engineering, Seoul National University, 599 Gwanangno, Gwanak-gu, Seoul 151–744, South Korea Received 16 July 2007; received in revised form 22 October 2007; accepted 24 October 2007 Available online 30 October 2007
Abstract The pore size distribution (PSD) of an ultrafiltration (UF) membrane is of great importance as it governs liquid permeability, filtration ability, and the interaction between molecules and the membrane matrix. Two series of UF membranes were studied: commercial regenerated cellulose (PL) membranes and polyethersulfone (PB) membranes, each with molecular weight cutoff (MWCO) values of 5, 10, and 30 kDa. This study was conducted to determine the PSDs of UF membranes using 1 H nuclear magnetic resonance (NMR) cryoporometry. NMR cryoporometry is based on the theory of the melting point depressions (MPDs) of liquid confined within a pore, which are dependent on the pore diameter. The MPDs were determined by analyzing the variation of the NMR signal intensity with temperature. From spin-echo intensity versus temperature curves, it was found that for each series of UF membranes the maximum MPDs of cyclohexane confined within the membrane pores were inversely proportional to the MWCO. For the same MWCO, the MPDs of the PL membrane were larger than that of the PB membrane, implying that the pores in the PL membranes were smaller than those in the PB membranes, consistent with their water and solute flux performances reported by the manufacturers. These findings indicate that NMR cryoporometry is a very effective method for determining the PSDs of UF membranes with asymmetric pore structures. © 2007 Elsevier B.V. All rights reserved. Keywords: Ultrafiltration membrane; NMR cryoporometry; Pore size distribution; Melting point depression; Cyclohexane
1. Introduction Ultrafiltration (UF) membranes have been widely applied in molecular separation technologies such as those used in low concentration effluent treatment, water purification, and virus removal [1,2]. UF membranes with pore sizes in the range of 1–100 nm are classified by molecular weight cutoff (MWCO), which is typically defined as the molecular weight of a solute that has a rejection coefficient of 90% or greater. The pore geometry of UF membranes consists of an interconnected threedimensional network of channels of non-uniform size and shape. A prominent feature of UF membranes is their thin skin layer on the surface, which is usually 0.1–1 m in thickness. This skin layer permits high hydraulic permeability while the more
∗
Corresponding author. Tel.: +82 2 880 8365; fax: +82 2 885 1748. E-mail address: [email protected] (S.-Y. Kwak).
0376-7388/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2007.10.034
open/porous sublayer (typically 125 m in thickness) provides good mechanical support; additional strength is sometimes provided by casting the membrane on a spun-bonded polyethylene or polypropylene backing [3]. Therefore, the small pores in the thin and dense skin layer are mainly responsible for the separation characteristics of the membrane and the open sublayer does not usually influence the membrane performance. Thus, when developing a UF membrane for a particular molecular separation process, it is of prime importance to determine the size and distribution of the pores of the membrane, as accurately as possible [3,4]. Various methods have been employed to determine the pore size distribution (PSD) of porous membranes, including the microscopic observation method [5,6], bubble pressure method [7], mercury intrusion porosimetry [8], permporometry [9], gas adsorption–desorption [10], and differential scanning calorimetry (DSC) thermoporometry [11–13]. These methods vary widely in applicability, sensitivity, and information that
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they yield. However, some methods have their specific disadvantages such as irreversible damage of the samples and time consuming, which limited their applications for porous materials having the small pores. In the case of mercury intrusion porosimetry and gas adsorption–desorption, it is necessary to suppose a structural model for the pores, making the interpretation of the results quite complex. DSC thermoporometry observes heat transfer in a measurement consisting of dynamic and isothermal steps, from which the amount of liquid molten within given temperature ranges can be calculated with the help of the known enthalpy of fusion. However, DSC thermoporometry is somewhat limited in the pore size range detectable, implying that it is difficult to obtain detailed information about the pore size distribution with a few nanometer sizes in UF membranes. Several approaches have been developed for characterizing the PSD of porous materials by means of 1 H nuclear magnetic resonance (NMR) [14–18]. These approaches exploit differences between the NMR characteristics of a material trapped within a porous network depending on whether it is in the liquid or solid state. Several studies have examined the phase transition of liquid confined within the pores of a porous material by using the longitudinal (spin-lattice, T1 ) and transverse (spin–spin, T2 ) relaxation times of hydrogen nuclei. These studies were based on the well-established method for 1 H NMR relaxation time measurement known as relaxometry. However, to accurately estimate the PSD, relaxometry requires knowledge of the surface layer parameter determined by the nitrogen adsorption method. Another NMR method has been adopted by Strange and Rahman [19], Strange et al. [20] and Hansen et al. [21,22] to determine the PSD of porous materials. This method, known as cryoporometry, utilizes the melting point depression (MPD), Tm , of a material confined within pores of porous materials. The theoretical basis of cryoporometry is the Gibbs-Thomson equation [11]. From this equation, it was found that the difference between the bulk and the depressed melting temperature was inversely proportional to a linear dimension of the liquid confined within the pores. Strange and Rahman [19] and Strange et al. [20] determined the PSD of a variety of porous silicas using cyclohexane as a probe molecule. They found that the sensitivity of cyclohexane was approximately three times greater than that of water. However, when cyclohexane was used as a probe molecule, the PSD of the porous materials could not be accurately determined due to differences in the magnetic susceptibility effects between the matrix and liquid as a function of temperature. Allen et al. [23,24] determined the PSD of cyclohexane confined within porous materials using a spinecho pulse sequence (90◦ –τ–180◦ –τ–echo). They found that pore susceptibility differences could be ignored when a spinecho pulse sequence was used. At a pulse separation time, τ, of approximately 10 ms, the signal intensity, I, from the liquid phase of cyclohexane confined within the pores was obtained as a function of temperature. The cyclohexane outside of the sample behaves as bulk cyclohexane, and provides a reference point for the change in melting temperature arising from the confinement. Based on these considerations, cryoporometry has been successfully applied to various porous materials, including
uniform and nanoporous materials such as glasses, silica gels, and sandstones. To our knowledge, however, no previous study has directly and precisely characterized the PSDs of UF membranes with non-uniform and asymmetric pore structures. Therefore, in the present work we investigated the PSDs of such UF membranes using 1 H NMR cryoporometry. The UF membranes used were two different series of commercial regenerated cellulose (PL) and polyethersulfone (PB) membranes, where each series had MWCOs of 5, 10, and 30 kiloDalton (kDa). 2. Experimental 2.1. Materials The UF membranes used in this study were a series of three PL membranes (MWCO = 5, 10, and 30 kDa) and a series of three PB membranes (MWCO = 5, 10, and 30 kDa); all of these membranes were obtained from Millipore corp. (Bedford, MA, USA). These membranes are asymmetric UF flat sheet PL and PB membranes that have been commercialized under the filter brand names Ultracel and Biomax, respectively. The probe molecule, cyclohexane (C6 H12 ; 99%, Aldrich Chemicals), has a melting point of 280 K and a surface energy at the liquid–solid interface of 4.6 erg/cm2 . In this study, PLxK and PBxK denote the PL and PB series of membranes with an MWCO of x kDa, respectively. 2.2. Sample preparation The membranes were submerged in water and then peeled off the supporting backing layer using tweezers. All samples were dried completely for 24 h or more at room temperature in a vacuum oven. The dried membranes were immersed in high purity cyclohexane for a week at room temperature. Excess cyclohexane remaining on the top and bottom surfaces of each sample was then removed by pressing the sample with a soft rubber roller and by wiping the sample with a filter paper, respectively. The samples were packed into 10 mm outer diameter NMR tubes and sealed. The sample height was restricted to approximately 15 mm to ensure that all of the sample was located within the transmitter/receiver coil, and thus was homogenously irradiated. All procedures were carried out in a drying room. 2.3. Characterization 1H
NMR cryoporometry measurements were carried out on a Bruker mq20 spectrometer at 0.47 Tesla and 19.95 MHz resonance frequency. Each sample test was performed over a temperature range of 200–280 K with an interval of 1 K using a Bruker BVT-3000 temperature control unit. During an experiment, the monitored temperature usually remained within ±0.1 K of the target temperature. A 90◦ pulse length of 2 s was applied with a recycle delay of T > 5T1 . To prevent complications associated with supercooling or hysteresis, all measurements were recorded with increasing the temperature from a low initial temperature. Specifically, the sample was initially quenched
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to 200 K in liquid nitrogen until all the liquid was frozen, after which it was warmed slowly, while continuously measuring the NMR signal intensities from the liquid phase, until all of the crystalline cyclohexane had melted. At each new temperature, the sample was allowed to equilibrate for at least 10 min before any measurements were performed. All measurements were performed using a spin-echo pulse sequence (90◦ –τ–180◦ –τ–echo). In this study, the spin-echo amplitude was measured with a pulse separation time, τ, of 10 ms to ensure that the signal was entirely from the liquid phase. The signal intensity was corrected for temperature by implementing Curie’s law; that is, the observed signal intensity was multiplied by the factor T/Tm , where Tm = 280 K and T is the actual temperature.
From this equation, it is found that the difference between the normal and depressed melting temperatures is inversely proportional to a linear dimension of the liquid confined within the pores. The spin-echo signal intensity, V, provides a measure of the amount of cyclohexane confined within the pores that is in the liquid phase at a particular temperature, T, and thus the volume of the pores that have a linear dimension equal to the pore diameter, D, in Eq. (1). The volume of the pores with pore diameters between D and D + D is (dV/dD)D. If the pores are filled with liquid, the PSD (dV/dD) is determined from the derivative of the intensity-temperature (IT) curves given by
3. Results and discussion
From Eq. (1), dTm (D)/dD = K/D2 , and hence Eq. (2) can be rewritten as
Cyclohexane used as a probe molecule in this study is an organic compound that comprises a ring molecule with a sixfold symmetrical structure. It is liquid at room temperature but nucleates at ca. 280 K to form a plastic crystal phase that consists of a rotationally disordered fcc lattice based on random orientation of the molecules [25]. The spin–spin relaxation time, T2 of liquid for cyclohexane is easily distinguishable from that of solid, because liquid has characteristically long T2 , ranging from milliseconds to seconds, whereas solid usually has very short T2 in the order of microseconds. NMR cryoporometry measurements are performed using a spin-echo pulse sequence (90◦ –τ–180◦ –τ–echo). The 90◦ x pulse shifts the spins onto the y-axis where they start to recover but dephase during the time of the experiment. After a time τ, they have dephased in the x–y plane. Applying an 180◦ y pulse rotates the spins about the y-axis, causing them to rephase. Then, a maximum signal will be measured at 2τ. This is known as a spin-echo and the height of the echo is directly dependent on the volume of liquid in the sample. In this study, the spin-echo amplitude is measured with a time interval τ of 10 ms (shorter than T2 of liquid and longer than that of solid for cyclohexane) to ensure that the signal is entirely from the liquid present. Therefore, this signal amplitude is measured as a function of temperature and should be proportional to the volume of liquid confined within pores of the membranes. The theoretical basis for cryoporometry is the GibbsThomson equation [11], which expresses the MPD of liquid confined within a small pore, Tm (D), as follows: Tm (D) = Tm − Tm (D) =
4σsl Tm K = DHf ρs D
dV dV dTm (D) dI = = dD dD dTm (D) dD
dV K dV = 2 dD D dTm (D)
(2)
(3)
Thus, provided K is known for the liquid used, the PSD function can be determined from measurements of dV/dTm (D). Fig. 1 shows the measured spin-echo intensity as a function of temperature and the first derivative of the intensity with respect to temperature for bulk cyclohexane. The signal intensity increases abruptly at ca. 280 K, at which dI/dT exhibits a maximum. From these results, the transition temperature from the solid to the liquid state of bulk cyclohexane was set to Tm = 280 K, which is in very good agreement with the reference value of ca. 280 K. Fig. 2 shows the 1 H spin-echo signals of cyclohexane confined within the PL10K membrane at four temperatures, 200, 240, 270, and 280 K. Comparison of these signals reveals that the spin-echo height from the liquid phase of cyclohexane confined within the pores increases gradually as the temperature is increased. At the lowest temperature, 200 K, the intensity is 0%, consistent with all of the cyclohexane being in the solid phase. At 280 K, which corresponds to the melting point of bulk cyclohexane, the spin-echo signal intensity from the liquid phase is approximately 100%. Below the bulk melting temperature, only the membrane, trapped between the solid matrix of the absorbent and the frozen liquid inside the pores, contributed to
(1)
where σ sl is the surface energy at the liquid–solid interface, Tm is the normal (bulk) melting point of the bulk material, Tm (D) is the melting point of the confined solid of dimension D, Hf is the bulk enthalpy of fusion, ρs is the mass density of the crystalline solid, and K is a constant depending solely on the physical properties of the liquid confined within the porous materials. Provided K is known, the PSD can be estimated from measurements of the amount of liquid confined within the pores as a function of temperature. In this study, cyclohexane was used as the probe liquid, for which K is approximately 178 K nm [26].
Fig. 1. NMR data of bulk cyclohexane: the spin-echo intensity () and the derivative () of the intensity with respect to temperature as a function of temperature.
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Fig. 2. Spin-echo signals of cyclohexane confined within pores of a PL10K membrane at 200, 240, 270, and 280 K.
the NMR signal. In fact, this spin-echo signal is observable down to approximately 220 K in the smallest pore systems. This observation indicates that normal colligative freezing of the surface layer does not take place in these systems. Under the present experimental conditions, however, the nuclei at the wall surface will only contribute to the signal in a more limited temperature region owing to the relatively short decay. In the melting region, the molecules of the melted liquid will be in fast exchange with the molecules at the pore walls, giving rise to an averaged signal. It has been reported [25] that the excess bulk liquid on the outside of the porous material behaves like bulk cyclohexane, and thus provides a calibration point for the melting curves of the liquid within the pores. Therefore, we determined the signal intensity at the highest temperature (i.e., 280 K), and normalized the IT curves by this intensity. Fig. 3a and b show plots of the spin-echo signal intensity versus temperature for cyclohexane confined within the pores of the PL and PB series of membranes, respectively. These IT curves show that for both membrane types, the signal intensity increases smoothly as the temperature is increased from 200 to 280 K, consistent with the gradual melting of the frozen cyclohexane confined within the pores of the membranes. These curves clearly show the marked difference between the signal intensities of the solid and liquid phases, with the pure solid and liquid phases having relative signal intensities of 0 and 1, respectively. The IT curves additionally confirm that the minimum
Fig. 3. Relative signal intensity vs. temperature curves (IT curves) for cyclohexane confined within pores of (a) PL and (b) PB series of membranes with 5 (), 10 (), and 30 kDa ().
melting points of cyclohexane confined within the membrane pores shift to lower temperatures with decreasing the MWCO. Further, it was found that the MPD of cyclohexane confined within the pores of both series of membranes decreased with increasing the MWCO and that the MPDs of the PL membranes were larger than those of the corresponding PB membranes. The MPDs were determined from plots of dI/dT or dV/dT as a function of temperature, which were generated from the IT curves. Based on these functions, the maximum MPDs for each system were estimated from the difference between the minimum and normal melting points of cyclohexane confined within the membrane pores and are listed in Table 1. The maximum
Table 1 Characteristics of the PL and PB series of UF membranes used in this study Sample
MWCOa (kDa)
Maximum melting point depression (K)
Pore size distribution (nm)
Average pore size (nm)
Water/solute flux b (ml/min/cm2 )
PL5K PL10K PL30K PB5K PB10K PB30K
5 10 30 5 10 30
76 45 39 65 39 32
2.2–15.0 3.7–25.0 4.5–30.0 2.7–30.0 4.0–35.0 5.0–50.0
2.8 4.9 6.1 4.4 5.9 7.6
0.09/0.09 –/0.13 1.41–1.44/0.17 0.6–0.7/0.13 2.1–2.4/0.15 3.2–4.0/0.16
a b
Molecular weight cutoff. Data provided by the manufacturers (Millipore corp.).
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Fig. 5. Average pore size vs. MWCO for the PL and PB series of membranes.
the Stokes Einstein equation. Also, this tendency was in good agreement with water and solute (i.e., sucrose and albumin) flux performances provided by the manufacturers (Millipore corp.). These findings indicate that 1 H NMR cryoporometry is a very effective method for characterizing the PSD of UF membranes with asymmetric pore structures, and that the PSDs of the membranes studied correlated strongly with the flux performances. 4. Conclusions 1H
Fig. 4. Pore size distribution (PSD) curves of (a) PL and (b) PB series of membranes with 5 (), 10 (), and 30 kDa ().
MPDs for both series of membranes were inversely proportional to the MWCO. Also, the maximum MPDs of the PL membranes were larger than those of the PB membranes with the same MWCO. These results indicate that the pores in the PB membranes were larger than those in the PL membranes. Eq. (1) indicates that the MPDs of cyclohexane confined within the pores of UF membranes are inversely proportional to a linear dimension of the pore diameter. The PSDs of the PL and PB series of membranes are shown in Fig. 4a and b, respectively. Comparison of the two series reveals that the PSDs of the PB membranes are broader than those of the PL membranes with the same MWCO. Within each series of membranes, the PSDs increase with increasing the MWCO (i.e., in the sequence 5K < 10K < 30K) in the range of 2–50 nm for both series of membranes. Fig. 5 shows the average pore sizes of the PL and PB series of membranes with different MWCOs, and these data are listed in Table 1. The average pore sizes of the PB membranes (ca. 4–8 nm) were larger than those of the corresponding PL membranes (ca. 3–6 nm) with the same MWCO. Sch¨afer et al. [27] reported pore size values for a series of PL membranes of 3.7, 5.2, and 9.6 nm for PL5K, 10K, and 30K, respectively, which are very similar to those obtained in the present study. They calculated pore diameters using an equation determined by Worch and
NMR cryoporometry was used to characterize the pore size distribution and average pore size of PL and PB series of UF membranes. This method utilized the NMR signal intensities, I, directly proportional to the only non-frozen volume fraction of the liquid measured as a function of temperature, T, using a spin-echo pulse sequence (90◦ –τ–180◦ –τ–echo). From these IT curves, the maximum MPDs of the cyclohexane confined within the pores of two different series of membranes were observed to be inversely proportional to MWCO. Also, it was found that the maximum MPDs of PL membranes were larger than those of PB membranes with the same MWCO. On the basis of the Gibbs-Thomson equation, the PSDs of both series of membranes saturated with cyclohexane were derived from 1 H NMR IT-curves of the confined cyclohexane. From the results, the PSDs of PB membranes were observed to be larger than those of PL membranes with the same MWCO. In addition, in the case of the same series of membranes, their PSDs were increased with increasing the MWCO (i.e., in the sequence 5K < 10K < 30K) in the range of 2–50 nm, which was in good agreement with water and solute flux performances provided by the manufacturers. In conclusion, 1 H NMR cryoporometry was found to be a very effective method for characterizing the PSDs of UF membranes, which are strongly correlated with their flux performances. Acknowledgments The authors are grateful to the Korea Science and Engineering Foundation (KOSEF) for support of this study through the Hyperstructured Organic Materials Research Center (HOMRC).
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The corresponding author, S.-Y. Kwak, gratefully acknowledges Professor Colin A. Fyfe at the Department of Chemistry, University of British Columbia (UBC), for his valuable suggestions and comments regarding the NMR results.
Nomenclature D Hf I K T1 T2 T Tm Tm (D)
pore diameter (m) bulk enthalpy of fusion (J/mol) intensity constant associated with the liquid (K m) longitudinal (spin-lattice) relaxation time (min) transverse (spin–spin) relaxation time (min) temperature (K) normal (bulk) melting point (K) melting point of the confined solid of pore diameter D (K) Tm (D) melting point depression (K) of a confined liquid to the pore diameter D (K) V volume (m3 ) Greek letters τ pulse separation time (min) σ sl surface energy at the liquid–solid interface (J/m2 ) ρs mass density of the crystalline solid (g/m3 )
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