Network Young Membrains (NYM14) Permeation through NF and UF membranes Patrizia Marchetti/ Lonza Ltd/ Imperial College London (UK), 20-22 September 2012
Transport mechanisms through membranes no pores pore dimension RO NF UF MF NF mechanism Convection / Sieving Electrostatic interactions (in H 2 O) (Diffusion) Surface interactions: hydrophilicity / hydrophobicity, polarity,... UF mechanism Convection / Sieving Electrostatic interactions (in H 2 O) sieving surface interactions slide 2
Outline 1. Solvent permeation solvent membrane interactions improved phenomenological model 2. Solute permeation additional interactions: solute solvent + solute membrane industrial case study: peptide in ACN / water by Design of Experiments (DoE) solute solvent membrane solvent membrane slide 3
Solvent permeation (1) Membrane MWCO [Da] d p [nm] Inopor Nano 450 450 0.9 Inopor Nano 750 750 1 Sulzer 1000 2.5 Inopor Ultra 2000 2000 3 Hagen-Poiseuille model (viscous flow) L = P K HP µ good for UF failed for NF slide 4
Solvent permeation (2) Non-purely viscous flow for the solvent in NF: viscosity as main mechanism experimental points scattered around the viscous behaviour scatter (+ or -) given by surface interactions slide 5
Model development 1 μ as main influencing parameter K HP L P = 1+ µ Hagen-Poiseuille-type constant ( f ) C f C as correction factor (function of interaction parameters) Laplace term Dipole term Steric term f C = C 1 2 γ LV cosθθ + r p C 2 2 from Washburn equation r for capillary rise in s nanotubes δ k + pol C3 r p model parameters θ θ J v > flux < flux > flux < flux 1 Marchetti P., Buttè A., Livingston A.G., An improved phenomenological model for solvent permeation through NF and UF membranes, J.Membr. Sci., 415-416 (2012) 444-458 slide 6 J v
Prediction of pure solvent permeability Lp [l m -2.h -1.bar -1 ] 120 80 40 0 Inopor Nano 750 Da experimental proposed model K µ HP L P = 1+ ( f ) L p linear vs. (1 + f C ) μ -1 C water ACN ethanol DMF regressed toluene methanol solvent NMP isopropanol acetone THF predicted DMSO Model parameters (K HP, C 1, C 2 and C 3 ) regressed on data for permeation of five solvents Predictive capability tested on data for six further solvents Good regression & prediction for both NF and UF slide 7
Prediction of solvent mixture permeability μ again the most influencing factor K ( f ) HP L P, MIX = 1+ C, MIX µ MIX f C dependent on the composition ( xi ) fc j f C, MIX = xi fc, i + 1, good predictions for both aqueous and organic mixtures in the NF range singular exception of ACN / water slide 8
ACN/water mixture: the steric term micro-heterogeneity region formation of some complexes between ACN and water 1 : CH 3 CN 2 H 2 O 2 CH 3 CN 3 H 2 O modification of r s = r s (%m ACN) CH 3 CN H 2 O 2 CH 3 CN H 2 O f C = C 1 2 γ LV cosθ + C r p 2 δ k pol + C negligible variation in the UF range 3 r r ( unmodified steric term; modified steric term) s p 2 significant improvement in the NF range ( unmodified steric term; modified steric term) 1 Kinart C.M., Kinart W.J., Kolasinski A., Acetonitryle water binary mixtures and their assumed internal structures, Phys. Chem. Liq. 35 (1997) 201-208 slide 9
Organic Solvent NF / UF in peptide industry Peptides: Therapeutic Active Pharmaceutical Ingredients (APIs) Synthesis and intermediate + final purifications in organic solvents / solvent mixtures Ceramic NF and UF: Concentration, purification, salt / solvent exchange (diafiltration) Understanding / modelling peptide rejection: Fundamental modelling: transport mechanism has to be known Statistical modelling: practical tool for efficient lab screening + qualitative insight into the process slide 10
Statistical modelling: Design of Experiments (DoE) planned approach for determining cause and effect relationships 1 Main features: simultaneous variation of all potential influencing factors randomization, replication reduction or minimization of the total number of trials (compared to one factor-at-a-time) information compactness (low number of graphs and tables) polynomial degree, approximation quality 1 Z. R. Lazic, Design of Experiments in Chemical Engineering, (2004) WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim slide 11
Case study by DoE DoE experimental set (Fractional Factorial Design FRFE): PEP 1 ~ 3000 Da, 20 amino acids, pi = 3.7 / + + concentration + solvent exchange in ACN / water Inopor Nano 750 Da, TiO 2 / Al 2 O 3, d p = 1 nm + + + + PEP 1 Name High level High level C peptide [g/l] 1 5 %v TFA 0.02 0.1 %v ACN 0 30 Pressure [bar] 2 10 Pump frequency [Hz] (linear velocity [m/s]) 25 (2) 45 (4) only 19 experiments required to study the effect of 5 operating parameters! slide 12
Responses: solvent flux and peptide rejection regression and correlation analysis - by Analysis Of Variance (ANOVA), Design Expert 7.0.3 Solvent flux (4 to 55 l m -2 h -1 ) Rejection (83 to 99.8%) single effects interaction effects single effects interaction effects normalized effect: regression coefficient of polynomial models for coded factors (upper level = +1; lower level = -1) slide 13
Physical interpretation of statistical models (1) Single effects Interaction effects Flux Rejection C p (-) C p (+) P (+) P (n.s.) Pump freq. (+) Pump freq. (+,n.s.) %v TFA (+) %v TFA (+) %v ACN (+) %v ACN (+) C p %v TFA (+) C p %v TFA (-) C p - %v ACN (+) C p - %v ACN (-) %v TFA - %v ACN(-) P Pump freq. (+) 1) solute membrane: direct effect on solute passage 2) solvent solute membrane: solvent effect on solute passage solvent n.s. = non significant solute membrane slide 14
Physical interpretation of statistical models (2) 1) Solute membrane interactions: C p has negative effect on flux and positive on rej.: adsorption / accumulation ads. layer Single effects Interaction effects Flux Rejection C p (-) C p (+) P (+) n.s. = non significant Pump freq. (+) P (n.s.) Pump freq. (+,n.s.) %v TFA (+) %v TFA (+) %v ACN (+) %v ACN (+) C p %v TFA (+) C p %v TFA (-) C p - %v ACN (+) C p - %v ACN (-) %v TFA - %v ACN(-) P Pump freq. (+) J v J v d p d p P has a positive effect on flux and no significant effect on rej. Pump freq. ( u B ) has positive effect on flux and rej. ads. layer d p d p fast u B slow u B slide 15
Physical interpretation of statistical models (3) 2) Solvent solute membrane interactions: Single effects Interaction effects Flux Rejection C p (-) C p (+) P (+) P (n.s.) Pump freq. (+) Pump freq. (+,n.s.) %v TFA (+) %v TFA (+) %v ACN (+) %v ACN (+) C p %v TFA (+) C p %v TFA (-) C p - %v ACN (+) C p - %v ACN (-) %v TFA - %v ACN(-) P Pump freq. (+) %v TFA and %v ACN have positive effect on both flux and rej.: increase molecular size and hydrophobicity TFA TFA TFA TFA TFA TFA TFA TFA > friction J s < friction < flux J v > flux J s J v n.s. = non significant J s = solute flux; J v = solvent flux slide 16
Summary of ternary interactions μ, γ LV, δ s, r solvent peptide case-study described by statistical model (DoE) physical interpretation of statistical model solvent permeation of pure solvent and solvent mixture through ceramic NF and UF membranes described by phenomenological model solute r solute, pi, hydrophilicity C solute, P, Hz (u solvent ) membrane γ SV, k pol, r p, pi slide 17
Acknowledgements Dr. Alessandro Butté, Lonza Ltd (Visp, CH) Prof. Andrew G. Livingston, Imperial College London (London, UK) NEMOPUR project, Marie Curie ITN, FP7 slide 18
Thank You Questions slide 19
ACN/water mixture 1: water-rich region 3: ACN-rich region (Graph from Kinart et al. 2 ) Hypothesis: parabolic distribution of r s in function of the composition region 2 region 1 region 3 2: micro-heterogeneity region 1 formation of some complexes between ACN and water 2 : CH 3 CN 2 H 2 O 2 CH 3 CN 3 H 2 O CH 3 CN H 2 O 2 CH 3 CN H 2 O f C = C 1 2 γ LV cosθ + C r p 2 δ k pol + C 3 r r s p 2 1 Moreau C., Douhéret G., Thermodynamic behavior of water-acetonitrile mixtures, Thermochimica Acta 13 (1975) 385-392 2 Kinart C.M., Kinart W.J., Kolasinski A., Acetonitryle water binary mixtures and their assumed internal structures, Physics and Chemistry of Liquids 35 (1997) 201-208 slide 20
k pol = 2 γ γ p SV p LV cosθ = 2 γ d SV + k pol γ γ p LV d LV γ γ d LV LV 1 slide 21
Meaning of interaction effects the combined change in two factors that produces an effect greater (or less) than the additive effect expected from the factors alone No interaction: z = x + y 0 1 2 3 z 40 30 20 10 0 0 1 2 3 4 50 1 2 3 4 5 x y 30-40 20-30 10-20 0-10 Antagonistic interaction: z = x + y - x y x 30 20 10 0-10 4 50 1 2 3 4 5 y Synergistic interaction: z = x + y + x y z 40 30 20 10 40 z 30-40 20-30 10-20 0-10 -10-0 30-40 20-30 10-20 0-10 0 0 1 2 3 4 50 1 2 3 4 5 x y slide 22
Outline Introduction Transport mechanism through NF and UF membranes Solvent permeation solvent solvent membrane interactions improved phenomenological model Solute permeation additional interactions: solute solvent + solute membrane industrial case study: peptide in ACN / water by DoE membrane solvent Conclusions solute membrane slide 23
Conclusions An improved model was proposed to: describe permeation of pure solvent and solvent mixture through ceramic NF and UF membranes describe solvent-membrane interactions The permeation of one case-study peptide was: studied by DoE, as reliable investigation strategy at lab scale described by physical interpretation of statistical models Classification and identification of ternary interactions: can help fundamental modelling for complicated molecules, like peptides slide 24
DoE: Factorial designs First-order mathematical model: Yˆ = b0 + k i b i X i + k i b ij X i X j response value estimated constants for single effects estimated constants for interaction effects independent parameters Design experiment of type 2k: 2 = number of levels; k = number of parameters Orthogonal matrix For k = 3: slide 25
DoE: Response Surface Model (RSM) Second-order mathematical model: Yˆ = b0 k + b i i X i k + a i i X 2 i + k b ij i X i X j response value estimated constants for firstorder single effects estimated constants for secondorder single effects estimated constants for interaction effects independent parameters Computer aided design (D-optimal design) with the best subset of all possible experiments Non orthogonal matrix of design points slide 26
DoE: data collection and analysis For 5 factors: FRFE: 16 experiments + 4 center points linear model 2FI (factorial) model D-Optimal: 28 experiments + with 6 center points linear model 2FI (factorial) model quadratic model (FUFE: 3 5 = 243 experiments) Factor A B C D E Name C peptide [g/l] ph Pressure (P) [bar] Pump frequency [Hz] %v ACN slide 27