Role of Thermodynamic and Kinetic Interaction of Poly(Vinylidene Fluoride) With Various Solvents for Tuning Phase Inversion Membranes.
INTRODUCTIONApplication of membrane-based processes for treatment of ground water, surface water and industrial waste water is increasing rapidly. Suitability of a particular membrane depends mainly on its macromolecular properties such as porosity, morphology, hydrophilicity, and surface roughness. Thermodynamics govern the final composition of polymer rich phase, thereby dictating the porosity and morphology. Kinetics of phase inversion influences the surface hydrophilicity and roughness, thereby impacting the fouling of the membrane. Therefore, understanding and fine tuning of thermodynamics and kinetic stability during phase inversion would result into tailor-made membranes for various applications.
Experimental and theoretical studies of thermodynamics based on Flory-Huggins theory have been undertaken extensively for cellulose acetate and its derivatives [1-4], polysulfone [5, 6], polyethersulfone [5-8], and poly aery lonitrile [9]. Data derived from thermodynamic model are used to predict the kinetic pathway during phase inversion [9]. Poly(vinylidene fluoride) (PVDF) is an attractive starting polymer for membrane preparation due to its excellent chemical resistance, mechanical, and thermal properties [10-12]. PVDF is semicrystalline in nature and the properties of PVDF membranes depend on several additional factors including percentage crystallinity and morphology of crystals. Hence, it is difficult to predict the characteristics of PVDF-based membranes. Literature on thermodynamic modeling of PVDF during phase inversion is scant. Wang et al., modeled the phase diagram for PVDF-DMAc (N,N-dimethyl acetamide)-water system [13]. However, the values of parameters and algorithm of calculation were not divulged. Matsuyama et al., studied the thermodynamics of PVDF-DMF (N,N-dimethyl formamide)-water system [14] but the validation experiments were conducted by vapor induced phase separation. Moreover, the study was done for a single-solvent system. Thermodynamics of PVDF with various solvent systems was studied experimentally in fair details using cloud point data by Bottino et al. [15] and Fadaei et al. [16], but no theoretical understanding was developed.
Kinetic study of phase separation of PVDF is scantly reported. Sun et al. [17] have reported experimental study on the thermodynamics and kinetics for different grades of PVDF with N-methyl pyrrolidone (NMP) as solvent and water as non-solvent and observed the relative location of binodal curve on phase diagram and the difference in rate of solvent leaching for varying grades of PVDF. However, the study was attempted for single-solvent system (NMP) and to the best of our knowledge, similar data for other solvents are not available in literature.
The present work focuses on the study of thermodynamics and kinetics of phase inversion of PVDF-solvent-water system for four different solvents. Theoretical observations are validated by experimental determination of cloud points and comprehensive membrane characterization on a comparative scale. The solvents are selected based on solubility of PVDF, spanning a wide range on the phase diagram. The cast membranes are characterized in terms of morphology, porosity, permeability, molecular weight cut-off, and contact angle. PVDF being semicrystalline polymer, the crystallinity of the membranes is also monitored. We demonstrate in this work how the location of binodal curve on phase diagram dictates the morphology, porosity, and permeation characteristics of the final cast membrane.
Theory
The non-solvent-induced phase separation by immersion method is by far the most used membrane preparation technique. Thermodynamics of phase separation of ternary systems is described based on Flory-Huggins theory [18] for free energy of mixing extended for three components by Tompa [19]. According to this theory, the Gibb's free energy of mixing ([DELTA][G.sub.m]) for a ternary system is given as
[DELTA][G.sub.m]/[R.sub.g]T = [n.sub.1]ln[[phi].sub.1] + [n.sub.2]ln[[phi].sub.2] + [n.sub.3]ln[[phi].sub.3] + [g.sub.12]([u.sub.2]) [n.sub.1] [[phi].sub.2] + [g.sub.13]([[phi].sub.3]) [n.sub.1] [[phi].sub.3] + [g.sub.23]([[phi].sub.3]) [n.sub.2] [[phi].sub.3] (1)
where subscripts 1, 2, and 3 refer to nonsolvent (NS), solvent (S), and polymer (P), respectively. [n.sub.i] and [[phi].sub.i] are the number of moles and volume fraction of ith component, [R.sub.g] is the universal gas constant, and T is the absolute temperature. [g.sub.12] is the non-solvent-solvent interaction parameter which is a strong function of the concentration term ([u.sub.2]). This term is defined as [u.sub.2]=[[phi].sub.2]/ ([[phi].sub.1] + [[phi].sub.2]). [g.sub.13] is the nonsolvent-polymer interaction parameter and is practically constant for a pair of components. [g.sub.23] is the solvent-polymer interaction parameter, which is a weak function of solvent concentration and the literature available on the concentration dependency of g23 is also very scant. And hence, several researches have considered it as independent of polymer concentration [5, 14]. Chemical potential of ith component ([DELTA][[mu].sub.i]) is defined as
[mathematical expression not reproducible] (2)
where, [DELTA][G.sub.m] is the Gibbs free energy of mixing. From Eqs 1 and 2, the expressions for chemical potentials for all three components are obtained in terms of their volume fraction.
[DELTA][[mu].sub.1]/[R.sub.g]T = ln [[phi].sub.1] + 1 - [[phi].sub.1] [v.sub.1]/[v.sub.2] [[phi].sub.2] - [v.sub.1]/[v.sub.3] [[phi].sub.3] + [[g.sub.12]([u.sub.2])[[phi].sub.2] + [g.sub.13][[phi].sub.3]]([[phi].sub.2]/ [[phi].sub.3]) - [v.sub.1]/[v.sub.2] [g.sub.23] [[phi].sub.2] [[phi].sub.3] - [[phi].sub.2][u.sub.2] (1 - [u.sub.2])d[g.sub.12]/d[u.sub.2] (3)
[DELTA][[mu].sub.2]/[R.sub.g]T = ln [[phi].sub.2] + 1 - [[phi].sub.2] [v.sub.2]/[v.sub.1] [[phi].sub.1] - [v.sub.2]/[v.sub.3] [[phi].sub.3] + [[v.sub.2]/[v.sub.1][g.sub.12]([u.sub.2]) [[phi].sub.1] + [g.sub.23] [[phi].sub.3]] x([[phi].sub.1] + [[phi].sub.3]) - [v.sub.2]/[v.sub.1][g.sub.13][[phi].sub.1][[phi].sub.3] + [v.sub.2]/[v.sub.1] [[phi].sub.1][u.sub.2](1 - [u.sub.2]) d[g.sub.12]/d[u.sub.2] (4)
[DELTA][u.sub.3]/[R.sub.g]T = ln [[phi].sub.3] + 1 - [[phi].sub.3] [v.sub.3]/[v.sub.1] [[phi].sub.1] - [v.sub.3]/[v.sub.2] [[phi].sub.2] + [[v.sub.3]/[v.sub.1][g.sub.13][[phi].sub.1] + [v.sub.3]/[v.sub.2][g.sub.23] [[phi].sub.2]] ([[phi].sub.1] + [[phi].sub.2]) - [v.sub.3]/[v.sub.1][g.sub.12]([u.sub.2]) [[phi].sub.1] [[phi].sub.2] (5)
where, [v.sub.1], [v.sub.2], [v.sub.3] represent the molar volume of pure nonsolvent, solvent, and polymer, respectively. At chemical equilibrium, the chemical potential of each species is same in coexisting polymer-rich (r) and polymer-lean (l) phases, which can be represented as
[DELTA][[mu].sup.r.sub.i] = [DELTA][[mu].sup.l.sub.i] i = 1, 2, 3 (6)
Binodal is the limit of stability (or homogeneity) of solutions, defined as the condition at which two phases coexist. Eq. 6 represents the binodal for a nonsolvent-solvent-polymer (NS-S-P) system. The region toward the left of binodal is the single phase region. Any point in this region represents a homogeneous solution. The region toward the right of binodal is the metastable region. Any small perturbation in composition in this region leads to instability and the solution gets separated into two phases. The limit of this metastable region is represented by the spinodal curve. The region toward the right of spinodal represents completely immiscible system compositions. The limit of this stability is given by the locus of all the points where the second derivative of Gibb's free energy is zero [4, 19]. Spinodal curve can thus be evaluated from the following equation:
[G.sub.22][G.sub.33] = [([G.sub.23]).sup.2] (7)
Where [G.sub.ij] = ([[partial derivative].sup.2] [bar.[DELTA][G.sub.m]]/[partial derivative][[phi].sub.i][partial derivative] [[phi].sub.j]])[v.sub.ref]: [v.sub.ref] is the molar volume of the reference component ([v.sub.1] in our case) and i,j = 2,3. The plait point is the point where both binodal and spinodal curves coincide and is identified by the Eq. 4:
[G.sub.222][G.sub.33.sup.2]-3[G.sub.223][G.sub.23][G.sub.33] + 3[G.sub.233][G.sub.23.sup.2] -[G.sub.22][G.sub.23][G.sub.333] = 0 (8)
where [G.sub.ijk] = [[partial derivative].sup.3] [bar.[DELTA][G.sub.m]]/[partial derivative][[phi].sub.i][partial derivative][[phi].sub.j] [v.sub.ref] and i, j, k = 2, 3.
Method of Calculation
Calculation of binodal curve needs six variables ([[phi].sub.i], i = 1-3 in each phase) to be solved simultaneously. Out of this, one variable ([[phi].sup.r.sub.2] in our case as the polymer rich phase covers a wide region in the phase space) is selected as independent variable. Thus, the problem is reduced to solution of the following five set of equations for remaining 5 variables.
[DELTA][[mu].sup.r.sub.1] - [DELTA][[mu].sup.1.sub.1] = 0 (9a)
[DELTA][[mu].sup.r.sub.2] - [DELTA][[mu].sup.1.sub.2] (9b)
[DELTA][[mu].sup.r.sub.3] - [DELTA][[mu].sup.1.sub.3] = 0 (9c)
[3.summation over (i=1)] [[phi].sup.r.sub.i] = 1 (9d)
[3.summation over (i=1)] [[phi].sup.l.sub.i] = 1 (9e)
It may be noted that solution of above set of nonlinear equations result in trivial solution where the two phases will have equal composition. Therefore, to obtain the binodal curve, above five equations are solved as a constrained optimization problem, to minimize the objective function:
Z = [[([DELTA][[mu].sup.r.sub.1] - [[mu].sup.1.sub.1])].sup.2] + [[([DELTA][[mu].sup.r.sub.2] - [[mu].sup.1.sub.2])([v.sub.1]/[v.sub.2])].sup.2] + [[([DELTA][[mu].sup.r.sub.3] - [DELTA][[mu].sup.1.sub.3])([v.sub.1]/[v.sub.3])].sup.2] (10)
subject to the constraints expressed by Eq. 9d and e. This procedure is repeated for every values of [[phi].sup.r.sub.2] from 0.1 to 0.9 to get the binodal curve.
As spinodal does not represent the phase equilibrium, calculation of it requires evaluation of 3 variables, in polymer rich phase (r). This is performed by taking one of the components ([[phi].sup.r.sub.2] in our case) as independent variable and solving the following set of equations simultaneously to obtain the remaining two variables.
[G.sub.22][G.sub.33] = [([G.sub.23]).sup.2] (11a)
[3.summation over (i=1)] [[phi].sup.r.sub.i] = 1 (11b)
Solving Eq. 8 along with Eq. 11a and b, the location of the plait point is identified.
Interaction Parameters
The interaction parameters, namely [g.sub.12], [g.sub.23] and [g.sub.13] are used to describe the mutual interaction among various components. The functional form of [g.sub.12] for various solvents are widely reported in literature [1, 5, 15]. The parameters [g.sub.23] and [g.sub.13] are calculated based on Hansen solubility parameters [5, 15, 20], using the following equation 5 for a pair of components (i, j):
[g.sub.ij] = [v.sub.i][/.sub.Rg]T {[([[delta].sub.iD] - [[delta].sub.jD]).sup.2] + 0.25 [([[delta].sub.iP] - [[delta].sub.jP]).sup.2]} (12)
where, [v.sub.i] is the molar volume of component [R.sub.g] is the universal gas constant, T is the absolute temperature, [[delta].sub.iD], [[delta].sub.iP], and [[delta].sub.iH] are the corresponding energy from dispersion forces, dipolar intermolecular forces, and hydrogen bonding between molecules, respectively. The solubility parameters and molar volume data used for the calculations are listed in Table 1. The reported (g12) and calculated values of interaction parameters ([g.sub.23], [g.sub.13]) for NS-S-PVDF systems are shown in Table 2. Variation of [g.sub.12] with concentration is plotted for all four solvents in Fig. la. Smaller the value of the interaction parameter, higher will be the interaction and more will be the miscibility of the two components. Therefore, from the trend in Fig. la, it is concluded that solubility of PVDF follows the trend: acetone < NMP < DMF < DMAc. The interaction of various solvents with water, as shown in Fig. lb, follows exactly the same trend.
EXPERIMENTAL
Materials
Poly(vinylidene fluoride) (PVDF) polymer with weight-averaged molecular weight 500 kDa was procured from Solvay India, Mumbai. DMAc, DMF, NMP, acetone, and polyethylene glycol (molecular weight 35, 100, and 200 kDa) were procured from Merck (India) Ltd., Mumbai and dextran (molecular weight 70 kDa) was obtained from Sigma Chemicals, USA. Nonwoven polyester fabric (product number TNW006013) was purchased from Hollytex Inc., USA.
METHODS
Membrane Preparation
Casting solution was prepared by preheating the solvent at 60[degrees]C and then adding PVDF slowly under continuous stirring. The mixture was thoroughly stirred for 6 h to obtain a homogeneous solution and was allowed to cool for 1 h under closed conditions. Polyester fabric was placed on the glass plate and fixed by tape on all four corners. Casting solution was poured on the fabric on one side and drawn manually with a casting knife at a speed of 20 mm [s.sup.-1] with gap of 200 [micro]m. The glass plate with casting solution was immersed in the nonsolvent bath after 30 s and left undisturbed for 24 h to complete the phase inversion process. After this, the membranes were labeled and transferred to fresh water bath.
Solvent Leaching Kinetics
The rate of solvent-nonsolvent transport determines the rate of phase inversion. This is estimated by measuring the concentration of solvent in the precipitation bath. To determine this, membrane was cast with a known quantity of polymer solution (15 g of casting solution) and concentration of solvent in the precipitation bath (2 1 of distilled water) was determined by measuring total organic carbon (TOC) using a TOC analyzer (model: TOC-L CPN 638-91110-58 manufactured by Shimadzu corporation, Japan and supplied by Swan Environmental Pvt. Ltd., India).
Cloud Point Determination
Cloud points were measured by usual titration precipitation method. To determine cloud points, homogeneous polymer solution of different concentrations (1-10%) was prepared for all polymer solvent combinations. To perform titration, 10 g of this solution was taken in a preweighed beaker and water was added dropwise using a microsyringe under continuous stirring. At the onset of turbidity, addition of water was stopped and stirring was continued for another 30 min. If the turbidity disappears on stirring, water was further added slowly and the same process was repeated. If the turbidity persists, it is noted as cloud point. The quantity of water was measured and the weight fraction of each component was located on the phase diagram to indicate the cloud point.
MEMBRANE CHARACTERIZATION: MORPHOLOGY
Field Emission Scanning Electron Microscope (FESEM) Analysis
Membrane surface and cross-section morphology were studied using FESEM (Model: JSM 7610, Make: JEOL, Japan). For cross-sectional analysis, membranes were frozen in liquid nitrogen and fractured. Sampling surface was coated with platinum using a sputtering machine. Membrane and skin thickness were measured using image analysis software in FESEM.
Contact Angle
Contact angle was measured for different membranes by sessile drop method using Goniometer (model number: 200-F4, manufactured by Rame-Hart Instrument Co., New Jersey, USA).
Atomic Force Microscope (AFM)
Surface roughness of membranes was measured on scan size of 10 X 10 ([micro]m in tapping mode using AFM (Model: 5500 AFM, by Agilent Technologies, USA).
Pore Size and Surface Area
Porosity of membranes was analyzed by Brunauer--Emmett--Teller (BET) analysis (model: AUTOSORB-1, supplied by Quantachrome Instruments, Florida, USA).
Fourier Transform Infrared (FTIR) Spectroscopy
To determine the presence of different crystal phases FTIR (model: Spectrum 100 supplied by Perkin Elmer, USA), spectroscopy was performed and spectra were recorded at 4 [cm.sup.-1] resolution. The absorbance/transmittance peaks of specific functional groups were identified at corresponding wave number.
X-ray Diffraction
Crystal structure of membranes was determined using X-ray diffractometer (Model: Xpert Pro supplied by PANalytical, The Netherlands using Cu [K.sub.[alpha]] radiations). Intensity of radiation was increased by a step size of 0.05[degrees] in the range 10[degrees]< 2[theta] <60[degrees]. Characteristics diffraction peaks corresponding to the specific phase were identified, and area under the curve and width at maximum intensity were identified from the graph for analysis.
MEMBRANE CHARACTERIZATION: PROPERTIES
Permeability
Pure water flux through the membrane was calculated by measuring the permeate flow rate using distilled water at different transmembrane pressure (TMP) using the equation:
[J.sub.w] = Q/A[DELTA]t (13)
where [J.sub.w] is the pure water flux, Q is the differential volume of permeate collected in the time interval [DELTA]t, and A is the effective membrane surface area. The permeate flux at different TMP resulted in a straight line through origin and membrane permeability was determined from the slope.
Molecular Weight cut-off (MWCO)
Dilute solution of neutral solutes (concentration 100 ppm) of different molecular weights is filtered by the membrane at a TMP of 70 kPa and at a stirrer speed of 2000 rpm. Concentration of solute in feed ([C.sub.f]) and permeate ([C.sub.p]) were determined by refractive index measurements against calibration with a known solute concentration (digital refractometer model: 300034 from SPER scientific supplied by Cole-Parmer, Kolkata, India). Percentage rejection of solute (R) was obtained using the equation:
R = (1 - [C.sub.p]/[C.sub.f])x 100% (14)
Molecular weight corresponding to 90% rejection gave the MWCO for the given sample.
Mechanical Strength
Mechanical properties of the samples were analyzed by measuring Tensile strength at yield and at break using Universal Testing Machine (UTM) (model: H50KS from Tinius Olsen Ltd., Redhill, England).
Differential Scanning Calorimeter (DSC)
All membrane variants were subjected to DSC (DSC Model: Q20 manufactured by TA Instruments, Texas, US) analysis by gradually annealing the polymer at a temperature gradient of 10[degrees]C/min within a temperature range of 60[degrees]C-200[degrees]C and the quantity of heat flow with respect to the reference pan was plotted against temperature.
RESULTS AND DISCUSSION
Ternary phase diagram (binodal and spinodal curves) of PVDF-solvent-water system is calculated using the extended Flory-Huggins theory as explained previously, for 4 different solvents and are plotted on a ternary plot, as shown in Fig. 2a and b. To validate the model, experimental cloud points are determined for DMAc, DMF, and NMP systems and plotted along with the modeled binodal curve. As observed in Fig. 2a, the cloud points are in close agreement with the theoretical binodal curves. Owing to high volatility of acetone, the cloud points could not be determined for this system. The modeled phase curves for PVDF-NMP/DMF/DMAc-Water system are also in close agreement with the experimental cloud point data available in literature [15-17].
The binodal curve divides the phase diagram into two domains, a homogeneous single phase region toward the polymer-solvent axis and a heterogeneous two phase region toward the polymer nonsolvent axis. Phase transition takes place across the binodal from homogeneous to heterogeneous region. Depending on the solvent-nonsolvent exchange rate, the concentration of nonsolvent in the mixture during phase inversion may vary. For a faster exchange, the composition of the mixture crosses binodal and spinodal curves quickly and is known as spinodal demixing, resulting into an asymmetric porous membrane. On the other hand, if the rate of solvent-nonsolvent exchange is slow, the composition changes gradually, spanning the metastable region between binodal and spinodal before reaching the final composition to the right of spinodal curve. This mode of demixing is by nucleation and growth and leads to the formation of a symmetric dense membrane [21, 22]. An increase in the affinity of the solvent toward water leads to a more unstable system. Even a small disturbance across binodal curve in terms of change in composition of nonsolvent leads to immediate phase separation [23]. As we move from right to left on the nonsolvent axis, thermodynamics predicts a porous membrane structure. The location of binodal is dictated by the combined effect of three interaction parameters. The system under study has same polymer (PVDF) and nonsolvent (water) for all four solvents. Thus, [g.sub.13] is the same for all. Smaller be the value of [g.sub.12], higher will be the miscibility of the solvent-nonsolvent leading to a faster demixing of solvent from the polymer phase. This will result in the formation of a more porous membrane with macrovoids. At lower [g.sub.12], lesser quantity of water will be required to precipitate the polymer resulting in shifting of the binodal curve toward the solvent axis.
Similarly, a smaller value of [g.sub.23] implies higher miscibility of solvent and polymer. This will make the demixing of solvent from polymer matrix delayed, leading to a denser membrane. Also, more water will be required to precipitate the polymer causing the binodal to shift toward right. Therefore, theoretically, a small value of [g.sub.12] and a large value of [g.sub.23] favor the formation of a porous membrane. In the present system, the magnitude of [g.sub.12] follows the order: DMAc < DMF < NMP < acetone, shown in Fig. la, for all concentrations. Variation in [g.sub.23] also follows the same trend but from Fig. 1b, it is observed that the magnitude of [g.sub.23] is very less compared to [g.sub.12] for all solvents. Thus, the effect of [g.sub.12] is expected to be more prominent compared to [g.sub.23]. Therefore, the location of binodal curve for DMAc is on extreme left and that for acetone is on the extreme right on the solvent-nonsolvent axis. Thus, DMAc results in the most porous membrane and acetone leads to the densest one.
Spinodal curve indicates the limit of instability of polymer solution and the region enclosed by this curve to the right of phase diagram represents two phase region forming the final membrane matrix. Spinodal curves corresponding to four solvents are presented in Fig. 2b. It can be noted that spinodal curves are always located to the right of the binodal curves and they meet at the plait point. Filled circles in Fig. 2b indicate the plait points. The exact coordinates of plait point in the phase diagram are given in Table 3. Therefore, computation of spinodal curves and plait points confirm the accuracy of location of binodal curves in the phase diagram (Fig. 2a).
The membranes made with 4 different solvents, namely, DMAc, DMF, NMP, and acetone, are identified hereafter as Ml, M2, M3, and M4, respectively. By analyzing the FESEM micrographs in Fig. 3, it is observed that the membranes (Ml, M2, and M3) have an asymmetric structure having dense skin layer at the top followed by a porous sub layer (Fig. 3a-c). On the other hand, Fig. 3d indicates that M4 is having a uniform dense cross section with fine pores. This clearly indicates that the phase separation is by spinodal demixing for M1-M3, whereas for M4, it is by nucleation and growth. An examination of morphology of top surface in Fig. 4 reveals that the surface porosity also follows the same trend, that is, gradually decreasing from Ml to M4. These observations are in accordance with the theoretical predictions of membrane porosity based on thermodynamic considerations. This observation is in corroboration with the fact that the effect of [g.sub.12] is more prominent than [g.sub.23] and hence, the relative magnitude of variation of interaction parameters is a key factor to be considered while selecting a solvent to have a desired porosity of a tailor-made membrane.
Kinetics of phase inversion is a combined effect of several factors including physical properties of different components and interaction among them. To compare the kinetics of phase inversion, relative concentration of solvent in the precipitation bath ([C.sub.t]/[C.sub.[infinity]]) was plotted with time in Fig. 5a. [C.sub.[infinity]] is the concentration of solvent in precipitation bath at infinite time (i.e., at steady state). The figure shows a steep rise initially due to high rate of diffusion of solvent during polymer precipitation. As solvent leaches out of polymer matrix, its concentration gradient between water and polymer phase is reduced, thereby decreasing the driving force for solvent transport. At the same time, the precipitated polymer causes enhanced resistance for solvent movement [17], leading to a slower transport of solvent into precipitation bath. Therefore, the slope of the curve gradually decreases and finally reaches saturation value at [C.sub.[infinity]]. For all membranes, the steady state is reached within 10 min. Initial period of fast exchange of solvent-nonsolvent is considered as diffusion controlled and a simplified equation for solvent concentration is used to fit the experimental data [17, 23].
[C.sub.t]/[C.sub.[infinity]] = m([t.sup.0.5] - [t.sup.0.5.sub.0]) (15)
where m depends on the diffusion coefficient of solvent, nonsolvent, volume of fluid taken, area of the membrane cast, and compaction factor. A plot of[ .sub.Ct]/[C.sub.[infinity]] against [t.sup.0.5] gives a straight line with m as the slope. Higher the value of m, faster will be the rate of leaching of solvent indicating faster kinetics. The values of m for four solvents under study are shown in Fig. 5b, which clearly shows that the rate of phase inversion is almost comparable for Ml, M2, and M3. However, for M4, it is quite slow. This is in accordance to the argument that the phase separation for Ml, M2, and M3 is by spinodal decomposition and hence, very fast leading to an asymmetric structure. Whereas for M4, it is by nucleation and growth and the kinetics is relatively slower compared to DMAc, NMP, and DMF. The modeling and experimental results of our present study for M2 are in close agreement with the results of Sun et al. [17].
Rejection analysis of various membrane variants as explained in previous sections is shown in Fig. 6, with molecular weight interpolated at 90% rejection indicating the MWCO of the membrane. The skin and membrane thickness were measured from FESEM micrographs (magnified images in Fig. 3) and plotted for various membranes in Fig. 7a. The skin thickness is gradually increasing from M1 to M4. The results are following the same trend as predicted by the kinetic data. The pore volume data as obtained from BET results, as shown in Fig. 7b, are also in accordance with the pore dimensions as observed in FESEM micrographs. These results are in line with the location of binodal for different solvents as predicted by the phase diagram. The membrane permeability and MWCO, as shown in Fig. 7c and, reflect the combined effect of membrane skin thickness and pore structure. M1 is having the highest permeability and MWCO, followed by M2 and M3. M4 is found to be impermeable to water when tested at TMP of 690 kPa. The mechanical strength of membranes was analyzed by measuring the yield strength and the ultimate strength. The results in Fig. 7d show that both yield and ultimate strength gradually increase from Ml to M4 due to the corresponding reduction in permeability and pore volume of the membranes.
To account the steep increase in ultimate strength for M4, further investigations were carried out. It is well established that PVDF is a semicrystalline polymer and occurs in 5 crystalline forms ([alpha], [beta], [gamma], [delta], and [epsilon]) [24]. Among these, [alpha] and [beta] conformations are predominantly reported in membranes [25]. The nonpolar [alpha] phase has trans-gauche ([TG.sup.+][TG.sup.-]) configuration and thermodynamically more stable, whereas the polar [beta] phase has trans (TTT) configuration and metastable [25]. Percentage crystallinity of PVDF membranes is determined by estimating the enthalpy change during melting in DSC. The thermograph obtained in DSC (Fig. 8) shows single peak at ~143[degrees]C for all four membranes. Peaks with varying area but identical peak temperature clearly indicate that the membranes differ only in crystallinity but the phase composition of all membranes is identical. Larger the area under the peak, higher is the crystallinity, indicating that M4 is having the highest crystallinity followed by M2, M1, and M3. To know the presence of particular crystal form, FTIR was performed. Figure 9 represents the infrared absorption spectra of membrane surface, which clearly signifies that the membranes do not differ in the phase composition. The absorption peaks at 769, 890, 1062, 1189, and 1412 [cm.sup.-1] correspond to [alpha] phase and a single peak at 840 [cm.sup.-1] corresponding to [beta] phase are present in all four membranes [24, 25]. Presence of particular morphology is confirmed by X-ray diffraction analysis of membranes shown in Fig. 10a. There is a distinct single characteristic peak at 18.7[degrees] which is assigned to the reflective surface (020) correspond to [alpha] phase [24, 25]. The area of the peak at 18.7[degrees] is the highest and relatively very high compared to other zones. Characteristic peaks corresponding to [beta] phase were not detected. FTIR indicates the presence of phases on the surface only, whereas XRD analyses the entire membrane cross-section. From this, it can be concluded that [alpha] is the predominant crystal structure in all membranes, whereas a small quantity of [beta] phase can be detected at the surface. The percentage crystallinity was estimated by dividing the area under the peak by the total area under the curve. Full width at half maximum height also gives an indication about the crystallinity. Smaller the width, narrower is the peak and more is the crystallinity. The data obtained from XRD are exactly matching with the results of DSC and percentage crystallinity follows the trend M4 > M2 > M1 > M3 plotted in Fig. 10b. However, it is the general assumption based on kinetics that the slower is the rate of phase inversion, more will be the time required for the polymer molecules to align into the lamellar structure, and more will be the crystallinity. Based on this, the trend of crystallinity should be M4>M3 >M2 > M1 which is different from the XRD observations. This discrepancy among Ml, M2, and M3 can be explained if we closely look at the properties of the solvents. All solvents are polar and aprotic solvents with varying molecular weight, boiling point, and viscosity (Table 4). Among these, NMP is the most viscous and high boiling solvent followed by DMAC, DMF, and acetone. We here propose that the crystallinity of the polymer phase, precipitated from concentrated solutions using nonsolvent-induced phase separation (NIPS), is determined during the solvation step, where the polymer chain uncoils and rearranges in the lamellar form. Highly viscous solvent hinders the rearrangement of polymer molecules into lamellae leading to much less orderly arrangement in polymer solution. The process of phase inversion for PVDF using water is very fast and the polymer molecules do not get sufficient time to rearrange themselves during precipitation. So, the arrangement achieved during solution preparation prevails or acts as nucleus for precipitation. However, in case of acetone, the kinetics is relatively slow providing provision to the polymer molecules to further rearrange, thereby leading to larger volume of crystalline lamellae and hence highest crystallinity. This also explains the sharp jump in the tensile strength of M4 membrane as presented in Fig. 7d.
The surface roughness of membranes, which depends on membrane porosity and surface smoothness, was estimated using atomic force microscopy. The AFM images, as shown in Fig. 11a-d, are in accordance with the porosity as predicted by the binodal curve on the phase diagram. The plateaus of high feature height observed on M3 membrane surface indicate the presence of amorphous clusters of polymer molecules, resulting into high surface roughness. Whereas smooth surface of M4 justifies the observed values of highest crystallinity and lowest porosity. These observations are further confirmed by contact angle measurement, shown in Fig. 10e, which correlates very well with the surface roughness.
CONCLUSIONS
Ternary phase diagram of PVDF with four different solvents and water as nonsolvent was established and used to predict membrane characteristics. Relative magnitude of interaction parameter was a key factor to be considered while selecting a solvent. The range of solvent-nonsolvent interaction parameter ([g.sub.12]) for four solvents varied from 0.6 to 1.96, whereas the same for polymer-solvent interaction parameter ([g.sub.23]) was from 0.005 to 0.165. The importance of [g.sub.12] was more significant than [g.sub.23] to control the location of binodal curve on phase diagram, thereby dictating the membrane morphology. The binodal curve for DMAc was located closest to the polymer--solvent axis and the same for DMF, NMP, and acetone were situated progressively toward the polymer-nonsolvent axis in that order. This made the membrane with DMAc most porous and that with acetone the densest. Accuracy of calculation of binodal curves was justified by computation of spinodal curve and plait points. Both thermodynamic and kinetic calculations confirmed that phase separation by DMAc, DMF, and NMP was by spinodal decomposition (relatively porous and asymmetric membrane morphology) and that for acetone was by nucleation and growth (relatively symmetric and denser membrane morphology). Various properties of the membranes supported this observation. MWCO values for M1, M2, and M3 were observed as 120, 99, and 92 kDa, respectively. Skin thickness measured from FESEM micrographs for Ml, M2, M3, and M4 were 3.51, 5.42, 6.36, and 7.37 |im, respectively. PVDF being a semicrystalline polymer, choice of solvent had significant effect on percentage crystallinity of final cast membranes. As against the general belief that kinetics of phase inversion determines the percentage of crystallinity, it is established here that arrangement of polymer chains was determined during solution preparation stage rather than during phase inversion and viscosity of the solvent played a key factor in affecting the rearrangement of polymer lamellae. Solvent properties altered the arrangement of polymer chains giving rise to a variation in percentage crystallinity from 15% to 31%. This also reflected in reduction of surface roughness by an order of magnitude, from 251 to 25 [micro]m. The effect of solvent was clearly evident by an increase in yield strength from 1.429 to 4.67 N [mm.sup.-2] and ultimate strength from 2.2 to 11.5 N [mm.sup.-2].
Krishnasri V. Kurada, Sirshendu De (iD)
Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India
DOI 10.1002/pen.24666
ACKNOWLEDGMENT
Any opinions, findings, and conclusions expressed in this article are those of the authors.
NOMENCLATURE
A Effective membrane surface area, [m.sup.2]
[C.sub.f] Concentration of solute in feed, kg [m.sup.-3]
[C.sub.[infinity] Concentration of solvent in precipitation bath
at infinite time, kg [m.sup.-3]
[C.sub.p] Concentration of solute in permeate,
kg [m.sup.-3]
[C.sub.t] Concentration of solvent in precipitation bath
at any time instant, kg [m.sup.-3]
[DELTA][G.sub.m] Gibb's free energy of mixing, J
[DELTA]t Time interval, s
[g.sub.ij] Interaction parameter for pair of components
i and j
[G.sub.ij] Second derivative of Gibb's free energy of
mixing with respect to volume fraction of ith
and jth component, J
[G.sub.ijk] Third derivative of Gibb's free energy of
mixing with respect to volume fraction of ith,
jth, and Ath component, J
[J.sub.w] Pure water flux, m [Pa.sup.-1] [s.sup.-1]
l Polymer lean phase
m Slope of kinetic curve represented by Eq.
15, [s.sup.-1/2]
[M.sub.i] Membrane variant i
[n.sub.i] No. of moles of ith component
Q Differential volume of permeate, [m.sup.3]
r Polymer-rich phase
R Percentage rejection of solute, %
[R.sub.g] Universal gas constant, J/mol K
t Time, s
T Absolute temperature, K
T/G Trans/Gauche configuration
[u.sub.2] Concentration function
[V.sub.i] Molar volume of pure component,
[m.sup.3]/mol
Z Minimization objective function
Greek letters
[alpha], [beta],
[gamma], [delta], Different crystalline forms of PVDF
[epsilon]
[[delta].sub.iD] Energy from dispersion forces [Mpa.sup.1/2]
[[delta].sub.iP] Energy from dipolar forces [Mpa.sup.1/2]
[[delta].sub.iH] Energy from intermolecular forces,
[MPa.sup.1/2]
[DELTA][[mu].sub.i] Chemical potential of ith component J/kg
[[phi].sub.i] Volume fraction of ith component
[[phi].sup.l.sub.i] Volume fraction of ith component if 1 phase
[[phi].sup.4.sub.i] Volume fraction of ith component if r phase
2[theta] Twice the angle of diffraction ([degrees])
ABBREVIATIONS
AFM Atomic force microscopy
BET Brunauer-Emmett-Teller
DMAc N, N-dimethyl acetamide
DMF N, N-dimethyl formamide
DSC Differential scanning calorimeter
FESEM Field-emission scanning electron microscope
FTIR Fourier-transform infrared
MWCO Molecular weight cut-off
NIPS Non-solvent-induced phase separation
NMP N-methyl pyrrolidone
NS Nonsolvent
P Polymer
PVDF Poly(vinylidene fluoride)
S Solvent
TOC Total organic carbon
TMP Transmembrane pressure
UTM Universal testing machine
REFERENCES
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Correspondence to: S. De; e-mail: [email protected]
Contract grant sponsor: SRIC, IIT Kharagpur; contract grant number: IIT/ SRIC/CHE/SMU/2014-15/40; contract grant sponsor: INAE Chair Professorship.
Caption: FIG. 1. Variation of (a) [g.sub.12] with concentration (b) [g.sub.12] and [g.sub.23] for different solvents.
Caption: FIG. 2. (a) Binodal and (b) spinodal curves for PVDF-solvent-water system for 4 different solvents.
Caption: FIG. 3. FESEM micrographs of cross-section of membrane: (a) M1, (b) M2, (c) M3, and (d) M4. [Color figure can be viewed at wileyonlinelibrary.com]
Caption: FIG. 4. FESEM micrographs of top surface of membrane: (a) M1, (b) M2, (c) M3, and (d) M4.
Caption: FIG. 5. Variation of (a) relative concentration of solvent in precipitation bath against time and (b) slope of Eq. 15 (m) of kinetic curve for various solvent systems.
Caption: FIG. 6. Determination of MWCO.
Caption: FIG. 7. Variation of (a) membrane and skin thickness, (b) pore volume distribution, (c) permeability and MWCO, and (d) tensile strength of various membranes.
Caption: FIG. 8. DSC thermograph of different membranes.
Caption: FIG. 9. FTIR absorption spectra of different membrane surfaces.
Caption: FIG. 10. (a) X-ray diffraction pattern, (b) Variation of percentage crystallinity for various membranes. [Color figure can be viewed at wileyonlinelibrary.com]
Caption: FIG. 11. Atomic force micrographs of top surface of (a) M1, (b) M2, (c) M3, and (d) M4. (e) Variation of contact angle and roughness of various membranes. [Color figure can be viewed at wileyonlinelibrary.com]
TABLE 1. Solubility parameter and molar volume for various components.
Parameter
Hansen parameter ([square root of Mpa])
Component [[delta].sub.iD] [[delta].sub.iP]
DMAc 16.8 11.5
DMF 17.4 13.7
NMP 18.0 12.3
Acetone 15.5 10.4
PVDF 17.2 12.5
Water 15.5 16.0
Parameter
Molar volume
(v) (cc [mol
Component [[delta].sub.iH] .sup.-1])
DMAc 10.2 92.5
DMF 11.3 77
NMP 7.2 96.5
Acetone 7.0 74.05
PVDF 9.2 123000
Water 42.3 18
TABLE 2. Interaction parameters.
Parameter
[g.sub.12][g.sub.12] = [a.sub.0] + [a.sub.1]x +
[a.sub.2] [x.sup.2] + [a.sub.3][x.sup.3] +
[a.sub.4] [x.sup.4]]
Component [a.sub.0] [a.sub.1] [a.sub.2] [a.sub.3]
DMAc 0.4672 0.1126 0.0404 0.0012
DMF 0.4727 0.1496 0.1245 -0.0936
NMP 0.5483 -0.092 2.0522 -3.9428
Acetone 1.10 -0.42 4.09 -6.7
Parameter
[g.sub.12][g.sub.12] =
[a.sub.0] + [a.sub.1]x +
[a.sub.2] [x.sup.2] +
[a.sub.3][x.sup.3] +
[a.sub.4] [x.sup.4]]
Component [a.sub.4] [g.sub.23] [g.sub.13]
DMAc 0.0159 0.0246 2.045
DMF 0.1248 0.0467 2.045
NMP 2.6792 0.0643 2.045
Acetone 4.28 0.1555 2.045
TABLE 3. Coordinates of plait point for various solvent systems.
Volume fraction of component
Solvent system Water Polymer Solvent
DMAc 0.063 0.019 0.918
DMF 0.088 0.014 0.898
NMP 0.118 0.010 0.872
Acetone 0.238 0.012 0.750
TABLE 4. Physical properties of solvents.
Molar mass Boiling point Viscosity (cP) at
Solvent (g mol l) ([degreegs]C) 25[degrees]C
DMAc 87.12 165-166 0.945
DMF 73.10 152-154 0.92
NMP 99.13 202-204 1.65
Acetone 58.08 56-57 0.295
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| Author: | Kurada, Krishnasri V.; De, Sirshendu |
|---|---|
| Publication: | Polymer Engineering and Science |
| Article Type: | Report |
| Date: | Jul 1, 2018 |
| Words: | 7163 |
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