Biotechnol. Prog. 2002, 18, 317−321

317

Modeling Pore Size Distribution in Cellulose Rolled Stationary Phases Craig Keim,†,| Chenghong Li,†,‡ Christine M. Ladisch,†,‡ and Michael Ladisch*,†,§,⊥ Laboratory of Renewable Resources Engineering, Textile Science, Department of Consumer Sciences and Retailing, Department of Agricultural and Biological Engineering, and Department of Biomedical Engineering, Purdue University, West Lafayette, Indiana 47907, and Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02420-9108

Rolled stationary phases are fabrics (i.e., nonparticulate phases) that rapidly separate proteins from salts on the basis of size exclusion. Pore size and pore size distributions in the stationary phase determine how different size molecules distribute between the stationary and mobile phases in liquid chromatography columns. The potential for size exclusion chromatography by fabrics is not initially obvious because their interlaced structures are atypical for size exclusion supports. A simple logistic model fits the pore size distribution of a rolled stationary phase when pore sizes were measured using PEG, Dextran, D2O, glucose, and NaCl probes. When the fabric is treated with cellulase enzymes, the water-accessible pores uniformly decrease and peak retention is lower. The logistic function model captures this result and enables comparison of pore size distribution curves between enzyme-treated and untreated fabrics in rolled stationary phase columns.

Introduction Cellulose-based chromatographic packing materials have been used for a wide variety of industrial applications with separations based on size exclusion, ion exchange, hydrophobic interaction, and affinity mechanisms (Gemeiner et al., 1998). The main engineering drawback to these materials is the high pressure drop associated with flow through packed beds of smalldiameter particles or small-pore membranes. An alternative cellulose-based separations media developed in our laboratory is the continuous rolled stationary phase. Cotton-based rolled stationary phases have been used to desalt proteins and to separate protein mixtures (Hamaker et al., 1996, 1998; Li, 2001). Because these columns have low pressure drops and a roughly constant plate height for a wide range of flow rates, rolled stationary phases are attractive alternatives to particleor membrane-based separations (Hamaker et al., 1998; Lin et al., 1987). While extensive modeling has been done on the effect of flow rate on pressure drop and plate height for these columns, relatively little information is available on the effect of different fabric treatments on column separation performance. This paper presents a simple model for evaluating pore size distribution in rolled stationary phase columns.

Modeling PEG Molecular Weights. The relation between radius and molecular weight of a poly(ethylene glycol) * To whom correspondence should be addressed. Ph: (765) 4947022. Fax: (765) 494-7023. Email: [email protected]. † Laboratory of Renewable Resources Engineering. ‡ Textile Science, Department of Consumer Sciences and Retailing. § Department of Agricultural and Biological Engineering. ⊥ Department of Biomedical Engineering. | Massachusetts Institute of Technology. 10.1021/bp010197e CCC: $22.00

Figure 1. Relationship between PEG molecular weight and PEG radius. Results from models are given by curves; data are indicated by figure legend. Equation 1, per Neuman and Walker (1992a), was used to fit the data represented by the squares in the graph above.

(PEG) molecule varies widely from one publication to the next. The main source of this variability is in the type of radius being measured. There is a hydraulic radius, a radius of gyration, a sedimentation-based Stokes radius, and an intrinsic-viscosity-based Stokes radius for any given molecule (Squire, 1981). For the remainder of our discussion, the term radius will refer to the intrinsicviscosity-based Stokes radius, rη. Figure 1 shows a graph of the different relationships between the molecular weight and radius of PEG molecules. Because PEG is a cylindrical molecule, the radius is approximately proportional to the square root of the molecular weight. Although most of the models shown in Figure 1 have similar exponential terms, the preexponential terms vary considerably between models. This variation most likely results from an incorrect assumption regarding the relationship between PEG diameter

© 2002 American Chemical Society and American Institute of Chemical Engineers Published on Web 02/01/2002

318

Biotechnol. Prog., 2002, Vol. 18, No. 2

and viscosity (Neuman and Walker, 1992a). As a result, for this paper, the data of Neuman and Walker (1992a,b) are used to relate molecular weight to the intrinsic viscosity radius. The equation used to calculate the radii of PEG probes is

rη ) 0.0286MW0.512

(1)

It should be noted that the data on which this equation is based are only for PEG molecules up to 8,000 daltons. Because the highest molecular weight PEG probe used in this study was 20,000 daltons, the equation has been extrapolated beyond the original data. The diameters of dextran probes used in this study were evaluated using eq 2 from Hagel et al., 1996:

rη ) 0.0271MW0.498

(2)

On the basis of the analysis of Nelson and Oliver (1971), the assumption was made that the pore diameter was three times the probe diameter (or six times the probe radius). Measuring Pore Sizes. There are several methods available to determine the pore size distribution of materials, including nitrogen adsorption, mercury intrusion, universal calibration theory (le Maire et al., 1989), inverse size-exclusion chromatography (Goto and McCoy, 2000; Ladisch et al., 1992), step solute exclusion chromatography (Grunwald et al., 1990; Neuman and Walker, 1992a), and batch contacting (Lin et al., 1987). Each of these methods has a unique mathematical model associated with it. For the inverse size-exclusion chromatography method alone, there are several simple models including a log-normal (Allan et al., 1991), a modified logistic model (Lin et al., 1987), a log-log model (Squire, 1981), and more sophisticated models that account for longitudinal dispersion, intraparticle and pore diffusion, and adsorption (Goto and McCoy, 2000; Neuman and Walker, 1992b). Because the stationary phase is continuous and does not have a defined particle size, parameter estimates such as diffusion and dispersion are complicated. As a result, we used simple curve fit models to describe the data. The logistic model represented the data with the least amount of error. This research involves at least two different disciplines: textile science and chromatography. Each discipline has unique terminology and characterization methods. In this paper, we relate the measured values from chromatographic analysis to the corresponding textile properties of interest to textile scientists. Lin et al. Model. Modified Logistic Function Four-Variable Model. One of the first models to estimate void fraction in rolled stationary phase columns is based on Lin et al. (1987). The model, which has four curve-fit parameters, is

I ) V t - Ve )

R 1 + e(β-γX)

(3)

where I is the inaccessible pore volume, Ve is the elution volume of the probe of interest, Vt is the total accessible pore volume, R, β, and γ are logistic curve fit parameters, and X is the log of the pore diameter, D. Both Vt and Ve are divided by the mass of the rolled stationary phase to normalize the data on a weight basis. Although the four-parameter logistic function fits the data fairly well, three of the parameters do not have any significant physical meaning and only two of the terms (Vt and R) can be estimated a priori. The curve-fitting

Table 1. Probes Used for Pore Size Characterization of Rolled Stationary Phase Columnsa probe D2O NaCl glucose

probe radius (rη, nm)

pore diameter (D, nm)

1.7 2.0 4.0

10.2 12.0 24.0

PEG Molecular Weights; Radii Calculated from eq 1 400 6.1 36.9 600 7.6 45.4 1,000 9.8 59.0 1,500 12.1 72.6 2,000 14.0 84.1 3,350 18.2 109.5 8,000 28.5 171.0 10,000 31.9 191.7 20,000 45.6 273.3 Dextran Molecular Weights; Radii Calculated from eq 2 66,300 68.2 409.5 506,000 187.8 1126.6 2,000,000 372.3 2233.7 a Although the pore diameter was assumed to be six times the probe radius, round-off error in displaying the probe radius in this table obscures this relationship.

procedure requires reasonable initial guesses for two parameters (β and γ) that cannot be easily estimated from the data. Thus, comparing the fit parameters from different rolled stationary phase columns does not provide much useful scientific information. Logistic Function Model. A simple logistic model that applies to rolled stationary phase columns is given by

Ve )

R 1 + β e-γD

(4)

Equation 4 differs from eq 3 because it is based on accessible void volume (instead of inaccessible void volume) and uses the pore diameter, D, in the exponential term in the denominator instead of log(D). The model also uses β as a pre-exponential term in the denominator instead of eβ in eq 3. For eq 4, R is approximately equal to the mass-normalized external void volume, V0, and β can be calculated from equation

()

β)-

V0 Vt

2

(5)

This logistic model has fewer curve-fit parameters than the model of Lin et al. (1987). Two of the three curve fit parameters can be easily estimated from the data.

Materials and Methods Molecular Probes. Molecular probes were deuterium oxide (D2O) from Cambridge Isotope Laboratories, Inc. (Andover, MA), sodium chloride (NaCl), D-glucose from Mallinckrodt (Paris, KY), a series of PEG probes, and Dextran 66,300 from Sigma (St. Louis, MO). The calculated probe radii and corresponding pore diameters are listed in Table 1. Enzyme Treatment of the Fabrics. The fabric used in all experiments was desized and bleached cotton print cloth style 400, obtained from Textile Innovators Corporation (Windsor, NC) with a fabric count of 78 × 76 (warp × filling) and a weight of 94.6 g/m2. For packing in chromatography columns, the fabric was cut into 60 cm × 21 cm swatches in the bias direction, each weighing approximately 12 g before treatment.

Biotechnol. Prog., 2002, Vol. 18, No. 2

319

Figure 4. Glucose on rolled stationary phase columns. Glucose concentration: 5 mg/mL. Mobile phase buffer: 50 mM pH 8.0 Tris. Sample size: 10 µL. Figure 2. A separation of BSA (elutes at 2.68 min) and NaCl (elutes at 3.64 min) by a cotton printcloth column 10 mm × 170 mm (i.d. × length). Flowrate: 2 mL/min. Mobile phase: 50 mM NaCl in 50 mM Tris buffer. Concentration: BSA 5 mg/mL, NaCl 5 mg/mL. Sample size: 50 µL.

Figure 5. Nondiluted D2O liquid on rolled stationary phase columns of cotton print cloth. Mobile phase buffer: 50 mM pH 8.0 Tris. Sample size: 10 µL.

Figure 3. Single molecule profile of PEG 20,000 on rolled stationary phase columns made of cotton print cloth. PEG concentration: 5 mg/mL. Mobile phase buffer: 50 mM pH 8.0 Tris. Sample size: 10 µL.

The fabric swatches were then scoured in a solution of sodium bicarbonate (2 g NaHCO3/100 g air-dried fabric) and AATCC standard detergent no. 124 without optical brightener (0.2 g detergent/100 g fabric) (American Association of Textile Chemists and Colorists, Research Triangle Park, NC) in deionized water. The liquid-tofabric weight ratio was 25:1. The fabric was boiled for 1 h in the scouring solution with occasional stirring and then thoroughly rinsed with deionized water. The cellulase enzyme Spezyme CP, secreted by Trichoderma longibrachiatum, formerly Trichoderma reesei, was from Genencor International, Inc. (Palo Alto, CA). The enzyme had an activity of 82 GCU/g as provided by the manufacturer and 59 IFPU/mL as determined by NREL Standard Procedure 006 (Adney and Baker, 1992). Enzyme treatment was conducted using a LaunderOmeter (Atlas Electric Devices Co., Chicago, IL) at two different concentrations, 0.82 GCU/g and 4.1 GCU/g, obtained by diluting the enzyme using 50 mM pH 5.0 citrate buffer to reach a liquid-to-fabric ratio of 50:1. Each fabric swatch was tumble agitated in a separate 1000mL stainless steel canister at 50 °C for 1 h; no steel beads were used. To denature the cellulase after enzyme treatment, the fabric was first rinsed thoroughly in deionized water and then boiled in 2 M NaCl solution for 5 min, followed by another thorough rinse with deionized water. Column Rolling and Packing. Each fabric was rolled into a column and inserted into a 10 mm (inner diameter) × 200 mm (length) Superformance glass tube (E. Merck, Darmstadt, Germany) to form a liquid chromatography column. For detailed procedures of column

rolling and packing, refer to Hamaker et al. (1998). A size exclusion separation is shown in Figure 2 where BSA is fractionated from NaCl with BSA eluting at 2.68 min and NaCl at 3.64 min. Liquid Chromatography System. The HPLC system used to characterize the performance of each column was the HPXL Solvent Delivery System from Rainin Instrument Company, Inc. (Woburn, MA). A programmable pump drew buffer from a reservoir and directed flow through a Model 7125 syringe-loading sample injector (Rheodyne, L. P., Rohnert Park, CA), then through the fabric column and finally through a Millipore Differential Refractometer no. 401 from Waters (Milford, MA). The mobile phase was 50 mM Tris buffer at pH 8.0, prepared using Trizma hydrochloride and Trizma base from Sigma (St. Louis, MO). The retention time of each probe was calculated by the software Dynamax HPXL Method Manager from Rainin Instrument Company, Inc. (Woburn, MA). Retention volume was obtained by multiplying the retention time by the volumetric flow rate. Five injections of each molecular probe at 5 mg/mL concentration were made at a flow rate of 4 mL/min with a sample size of 10 µL. Examples of typical elution profiles are given in Figures 3-5. Figure 3 shows an elution profile for PEG 20,000, an excluded molecule. The peak retention changes slightly, and the peaks are broader for enzyme-treated stationary phases. The smaller molecular probes are glucose (Figure 4) and D2O (Figure 5). The shift in retention volumes to a smaller value indicates that the larger pores are removed by enzyme treatment (Figure 6). Different columns are compared by plotting the elution profiles as a function of the fraction of retention volume to column volume.

Results and Discussion Table 2 shows the water-accessible pore volume for various cellulose-based materials. In traditional chroma-

320

Biotechnol. Prog., 2002, Vol. 18, No. 2

Figure 6. Effect of enzyme treatment on pore size distribution in cotton print cloth. Modeling data is calculated from the logistic model given in eq 4. The enzyme treatment shown in this figure was 4.1 GCU/g of Spezyme CP.

tography, the water-accessible pore volume is the total pore void volume available to water that is not available to large dye or protein molecules. It can be calculated by subtracting the external void volume, V0, from the total void volume, Vt. The total pore volume of the rolled stationary phases (0.30-0.35 mL/g) is lower than that for cellulose particles

(0.4-2.0 mL/g) (Gemeiner et al., 1998.) The most probable reason is that particles have a larger exposed surface area to volume ratio. As a result, more pores are available and accessible to the molecular probes in particulate cellulose compared to the rolled stationary phase. Similar results have been noted by Rowland et al. (1984) and Ladisch et al. (1992) where chopped fibers exhibited larger void volume than whole fibers. The simple logistic model fits all the data to within 3% of the measured value for all fabrics and probes tested. Table 3 shows a summary of the model parameters and the standard error, r. If γ is assumed to be ∼0.025, the model parameters (R,β,γ) can be predicted to within 8% of the fitted values, thus providing good initial estimates for a curve-fitting program. In actuality, R can be predicted with even higher accuracy (less than 3% from the fitted value) simply by measuring the excluded void volume of the column by injecting a highmolecular-weight probe (such as dextran). Table 4 summarizes the predicted and fitted values of R and β for the stationary phases tested in this paper. Experiments in our laboratory suggested that the rolled stationary phase columns have a negative surface charge in the running buffer at pH 8.0 (Li, 2001). The elution of NaCl in the rolled stationary phase is not driven solely by size exclusion; ion exclusion or attraction

Table 2. Summary of Water-Accessible Pore Volumes for Cellulose-Based Materials water-accessible volume (Vt - V0, mL/g)

reference this work Ladisch et al. (1992)

cotton fabrics: scoured enzyme-treated cotton fabric

same as Neuman and Walker (1992a) 0.35 0.30 0.26 (30 °C) 0.30 (60 °C) 0.092 (30 °C) 0.090 (60 °C) 0.38 0.36

ramie fabric Neuman and Walker (1992a)

Grunwald et al. (1990)

Lin et al. (1987) Rowland et al. (1984)

PEG curve fit

Solka Floc Avicel G. J. S.: 200-300 mesh 45-60 mesh cotton desized bleached mercerized finished viscose Solka Floc (BW300) purified cotton treated cotton NaOH NH3

same as Lin et al. (1987)

rη (nm) ) 0.0286MW0.512

0.40 0.36 0.26 0.31 0.38 0.30 0.47 1.6 0.25-0.30 0.45-0.50 0.35-0.40

rη (nm) ) 0.0424MW0.5061 same as Nelson and Oliver (1971)

Table 3. Fitted Parameters for Pore Size Distribution Using the Logistic Function Model Given in Equation 4a total pore volume (mL/g) cotton print cloth (CPC) no enzyme CPC with 4.1 GCU/g Spezyme CPC with 0.82 GCU/g Spezyme a

R

) V0

β

) -(V0/Vt)2

γ

r

predicted

measured

% error

0.6491 0.5643 0.5829 0.6395 0.6052

0.647 0.567 0.586 0.625 0.592

-0.4602 -0.4501 -0.4471 -0.4331 -0.4329

-0.424 -0.431 -0.442 -0.431 -0.425

0.0265 0.0249 0.0261 0.0270 0.0254

0.995 0.995 0.996 0.996 0.995

0.351 0.303 0.304 0.313 0.304

0.347 0.297 0.295 0.327 0.316

1.3 2.0 2.8 4.3 3.9

The predicted and measured water-accessible pore volume for each fabric is shown and labeled as total pore volume.

Table 4. Prediction of r and β for Equation 4 R

cotton print cloth (CPC) no enzyme CPC with 4.1 GCU/g Spezyme CPC with 0.82 GCU/g Spezyme

β

) V0

fit

% diff

) -(V0/Vt)2

fit

% diff

0.647 0.567 0.586 0.625 0.592

0.649 0.564 0.583 0.640 0.605

-0.4 0.4 0.6 -2.3 -2.2

-0.424 -0.431 -0.442 -0.431 -0.425

-0.460 -0.450 -0.447 -0.433 -0.433

7.9 4.3 1.1 0.5 1.8

Biotechnol. Prog., 2002, Vol. 18, No. 2

may play a significant role. Therefore, NaCl data were excluded from the curve fitting. This procedure is different from both Ladisch et al. (1992) and Rowland et al. (1984) where the data for D2O and glucose were excluded and data from NaCl was used. The apparent pore exclusion limit for the cotton rolled stationary phases studied is approximately 100 Å (10 nm). This value is consistent with exclusion limits between 20 and 500 Å (2 and 50 nm) for other cellulose-based materials (Gemeiner et al., 1998) and exclusion limits of 90-100 Å (9 and 10 nm) for cotton fibers (Rowland et al., 1984). When the fabric is treated with enzyme, the volume of all pores in the fabric decreases (Figure 6); the model fits this trend. Enzyme treatment of cotton print cloth decreases the water-accessible (total) pore volume by almost 20% (see Table 3). Because enzyme treatment significantly affects the number of charged groups that can be attached to the cellulose surface, enzyme treatment may affect separation resolution differently if the column is further derivatized with a charged group.

Conclusions A simple logistic model is able to fit the pore volume data within (3% for cotton print cloth, packed in liquid chromatography columns in a rolled form. Using molecular probes consisting of D2O, NaCl, glucose, highmolecular-weight dextrans, and PEG in molecular weight ranges of 400-20,000 Da, the water accessible pore volume was shown to decrease by 20% after treatment with cellulase enzyme, with this change affecting all of the pores in the fabric. Since the elution of NaCl from columns of the cotton rolled stationary phase appears to follow an ion exclusion mechanism, the enzyme treatment may affect the number of charged groups on the surface of the stationary phase. Consequently, enzyme treatment may affect resolution achieved for an underivatized column differently than for a cotton stationary phase derivatized with cation or anion exchange groups.

Acknowledgment This work was supported by the Purdue University Agricultural Experimental Station. Part of the project was supported by NSF Grant BES 9727096. We thank Nathan Mosier for helpful comments and suggestions during preparation of this manuscript.

References and Notes Adney, B.; Baker, J. Chemical Analysis and Testing Standard Procedure Number 006: Measurement of Cellulase Activities; National Renewable Energy Laboratory: Golden, CO, 1992.

321 Allan, G. G.; Ko, Y. C.; Ritzenthaler, P. The microporosity of pulp: The nature of the pore size distribution. Tappi J. 1991, 74, 205-212. Gemeiner, P.; Polakovic, M.; Mislovicova, D.; Stefuca. V. Cellulose as a (bio)affinity carrier: properties, design and applications. J. Chromatogr., B 1998, 715, 245-271. Goto, M.; McCoy, B. J. Inverse size-exclusion chromatography for distributed pore and solute sizes. Chem. Eng. Sci. 2000, 55, 723-732. Grunwald, M.; Burtscher, E.; Bobleter. O. HPLC determination of the pore distribution and chromatographic properties of cellulosic textile materials. J. App. Polym. Sci. 1990, 39, 301317. Hagel, L.; Ostberg, M.; Andersson, T. Apparent pore size distributions of chromatography media. J. Chromatogr., A 1996, 743, 33-42. Hamaker, K.; Liu, J.; Seely, R.; Ladisch, C.; Ladisch, M. Chromatography for rapid buffer exchange and refolding of secretory leukocyte protease inhibitor. Biotechnol. Prog. 1996, 12, 184-189. Hamaker, K.; Liu, J.; Ladisch, C.; Ladisch, M. Transport properties of rolled, continuous stationary phase columns. Biotechnol. Prog. 1998, 14, 21-30. Ladisch, C. M.; Yang, Y.; Velayudhan, A.; Ladisch, M. R. A new approach to the study of textile properties with liquid chromatography. Text. Res. J. 1992, 62, 361-369. le Maire, M.; Viel, A.; Moller, J. Size exclusion chromatography and universal calibration of gel columns. Anal. Biochem. 1989, 177, 50-56. Li, C. Rolled, continuous stationary phase columns from textile fabrics: Optimal packing and protein separation. Ph.D. Dissertation, Purdue University, West Lafayette, IN, May 2001. Lin, J. K.; Ladisch, M. R.; Patterson, J. A.; Noller, C. H. Determining pore size distribution in wet cellulose by measuring solute exclusion using a differential refractometer. Biotechnol. Bioeng. 1987, 29, 976-981. Nelson, R.; Oliver, D. W. Study of cellulose structure and its relation to reactivity. J. Polym. Sci., Part C 1971, 36, 305320. Neuman, R. P.; Walker, L. P. Solute exclusion from cellulose in packed columns: Experimental investigation and pore volume measurements. Biotechnol. Bioeng. 1992a, 40, 218-225. Neuman, R. P.; Walker, L. P. Solute exclusion from cellulose in packed columns: Process modeling and analysis. Biotechnol. Bioeng. 1992b, 40, 226-234. Rowland, S. P.; Wade, C. P.; Bertoniere, N. R. Pore structure analysis of purified, sodium hydroxide-treated and liquid ammonia-treated cotton celluloses. J. Appl. Polym. Sci. 1984, 29, 3349-3357. Squire, P. G. Calculation of hydrodynamic parameters of random coil polymers from size exclusion chromatography and comparison with parameters by conventional methods. J. Chromatogr. 1981, 210, 433-442.

Accepted for publication December 17, 2001. BP010197E