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Charging and aggregation behavior of cellulose nanofiber in aqueous solution Yusuke Sato, Yasuyuki Kusaka, and Motoyoshi Kobayashi Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02742 • Publication Date (Web): 10 Oct 2017 Downloaded from http://pubs.acs.org on October 11, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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Charging and aggregation behavior of cellulose nanofiber in aqueous solution
Yusuke Sato1, Yasuyuki Kusaka2, Motoyoshi Kobayashi3*
1
Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki
305-8572, Japan 2
Flexible Electronics Research Center, National Institute of Advanced Industrial Study and Technology, 1-1-1 Higashi,
Tsukuba, Ibaraki 305-8565, Japan 3
Faculty of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8572, Japan
AUTHOR INFORMATION *Corresponding author E-mail address: [email protected] Tel.: +81 29 853 5721; Fax: +81 29 853 4861
1
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ABSTRACT: To understand the charging and aggregation of cellulose nanofiber (CNF), we performed the following experimental and theoretical studies. The charging behavior of CNF was characterized by potentiometric acid-base titration measuring the density of deprotonated carboxyl groups at different KCl concentrations. The charging behavior from the titration was quantitatively described by the 1-pK Poisson-Boltzmann (PB) model for a cylinder. The electrophoretic mobility of CNF was measured as a function of pH by electrophoretic light scattering. The mobility was analyzed with the equation for an infinitely long cylinder considering the relaxation of electric double layer. Good agreement between experimental mobilities and theoretical calculation was obtained by assuming the reasonable distance from the surface to the slipping plane. The result demonstrated that the negative charge of CNF originates from the deprotonation of β(1-4)-D-glucuronan on the surface. The aggregation behavior of CNF was studied by measuring the hydrodynamic diameter of CNF at different pH and KCl concentrations. Also, we calculated the capture efficiencies of aggregation, using interaction energies of perpendicularly and parallelly oriented cylinders. The interaction energies between cylinders in both the orientations were obtained by Derjaguin, Landau, Verwey, and Overbeek theory, where the electrostatic repulsion was calculated from the surface potential obtained by the 1-pK PB model. From the comparison of the theoretical capture efficiency with the measured hydrodynamic diameter, we suggest that CNFs can be aggregated in perpendicular orientation at low pH and low salt concentration, and the fast aggregation regime of CNF is realized by the reduction of electric repulsion for both perpendicularly and parallelly interacting CNFs. Meanwhile, the application of Smoluchowski’s equation to the mobility of CNF results in the underestimation of the zeta potential.
Key words: Nano rod Relaxation effect Surface potential DLVO theory
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INTRODUCTION Organic nanofibers play significant roles in many fields such as environmental engineering, industrial application, water purification and so on. The possibility of transportation of uranium (IV) by the complex of colloidal iron oxides and organic nanofibers in enviro is pointed out.1,2 There are a lot of products containing nanofibers; for example ink, medicine, foods and plastics. Sorption of toxic heavy metal species by nano-celluloses is reported.3,4 The transport property of nanofibers and the quality of products containing nanofibers depend on the dispersion and aggregation of nanofibers.5,6 The aggregation and dispersion are controlled by the surface charging characteristics. The sorption of heavy metal species are also affected by the surface charging characteristics. Therefore, the understanding of charging and aggregation of nanofibers is important for environmental engineering, industrial applications and water purification. Cellulose nanofiber (CNF) is an attractive material in industry because of its unique property and sustainability. For example, elastic modulus of CNF is five times higher than that of iron.7 CNF suspension is colorless and transparent and shows outstanding shear thinning.8 Films containing CNF reduce the penetration of oxygen.9 The wide application of CNF is expected to composite material of polymer, cosmetic, food and medicine in industry as a reinforce agent, rheological modifier, film and so on. Also, CNF can be a model of natural organic nanofibers. CNF is obtained by breaking up pulps which are bundles of cellulose microfibrils. The cellulose microfibril is a crystal consisting of 30~40 cellulose molecules and its width is ~3 nm for higher plants.10 C6 hydroxyls on the surface of cellulose microfibrils are oxidized to carboxyl groups by 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO).11 The surface negative charge originated from the dissociated carboxyl groups make it easier to disperse the pulps in aqueous solutions to thin fibers with a few nanometers in diameter. Thus, the TEMPO-oxidized CNFs show pH-dependent negative charge and colloidal stability.12 The dispersion and aggregation of colloidal particles are dominated by the interaction energy between particles. According to Derjaguin, Landau, Verwey and Overbeek (DLVO) theory, the inter-particle interaction energy is expressed as the sum of repulsive electrostatic interaction energy affected by charging behavior and attractive van der Waals energy. The pH and salt dependency of aggregation rate of well-characterized spherical particles such as silica and carboxyl latex particles is quantitatively described by the DLVO theory with the theoretical model of electric charging as well as the measurements of surface charge density and surface potential by potentiometric titration and electrophoresis.13,14 These studies point out the importance of taking account of the relaxation of electric double layer during electrophoresis and the necessity of obtaining both the surface charge and the surface potential. The aggregation and dispersion of CNF are expected to be affected by solution chemistry due to the sensitivity of charging behavior of CNF on pH and ionic strength. However, systematic studies on the aggregation behavior of CNF with the characterization of charging behavior are insufficient. While Wågberg calculated the surface potential and the DLVO interaction energy of carboxymethylated celluloses that have a similar form with CNF, the calculated surface 3
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potential did not quantitatively agree with the zeta potential calculated from electrophoretic mobility.15 Also, the used equation connecting the zeta potential and the electrophoretic mobility was unclear. Isogai showed experimentally that the critical coagulation concentrations (CCCs) of CNF follow the Shultze-Hardy rule.16 Furthermore, the CCCs calculated by the DLVO theory was in good agreement with experimental values. However, the electrostatic interaction energy of CNF did not seem to be evaluated properly, because the zeta potential, which is thought to be calculated by the Smoluchowski equation, was used instead of the surface potential. The Smoluchowski equation can be applied for large particles compared with the thickness of electric double layer. The diameter of CNFs is as thin as 3 nm. Therefore, it is doubtful to apply the Smoluchowski equation to obtain the zeta potential of CNF from the electrophoretic mobility. It is known that the Smoluchowski equation can be inaccurate even for large spherical particles at low salt concentration because of the relaxation of electric double layer.17,18 At this moment, however, no attempt has been reported for the influence of the relaxation of double layer on the electrophoresis of thin nanofibers. In this paper, we report results of experimental and theoretical study on the aggregation and charging of CNF. In the theoretical model, CNF is regarded as a cylindrical particle. The diameter and length of cylinder were determined by measuring the dimension with atomic force microscopy. The surface charge density of CNF was characterized by comparing the measured amount of deprotonated carboxyl groups and the calculation by 1-pK Poisson-Boltzmann model for a thin cylinder. Furthermore, the measurement of electrophoretic mobility of CNF and the theoretical analysis by the equation taking account of the relaxation of electric double layer were conducted to evaluate the surface electric potential. The aggregation behavior of CNF detected by the increase of size was investigated by dynamic light scattering. The capture efficiency of aggregation is compared with the measured hydrodynamic diameter as a function of pH at different salt concentrations. Aggregation behavior of CNF is examined by the capture efficiency obtained from the classical Fuch’s expression for spherical particles with DLVO theory for cylinders.
EXPERIMENTAL METHODS Material. Cellulose nanofiber suspension (RHEOCRYSTA I-2SP) was kindly provided from DKS Co. Ltd. The suspension was treated as follows. First, the pH of suspension was adjusted to 2.2 with HCl to protonate the surface. Second, the suspension was extensively dialyzed against deionized water until the electric conductivity became below 1 µS/cm. Ionic strength and pH of the suspension were adjusted with KCl, HCl and KOH (JIS special grade, Wako Pure Chemical Industries). KCl and HCl solutions were filtrated with 0.2 µm pore filter (25HP020AN, Toyo Roshi Kaisha, Ltd.) to exclude particulate contaminants. Carbonate free KOH solution was prepared by diluting filtrated supernatant of ~10 M KOH containing 0.2 g/L CaO with degassed water prepared under vacuum.19 Mechanical dispersion processes were conducted to prepare stock suspension except for potentiometric titration. That 4
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is, 0.1 wt% CNF suspension with 2 mM KOH was sheared by a homogenizer (AHG-160A, As one) for 30 seconds at the scale of 80 and followed by the sonication by an ultrasonic homogenizer (THU-80, As one) for 30 seconds at the scale of MIN. The suspension and solutions were degassed under vacuum before experiments.
Atomic Force Microscopy (AFM). The thickness and length of CNFs deposited on a mica substrate were measured by using an AFM (LSP 5600, Agilent) in a tapping mode with a cantilever (OMCL-AC160TS-C2, Olympus). The spring constant of the cantilever was 42 N/m and the tip radius was less than 10 nm. To prepare the CNF-deposited substrate for AFM, 5 µL of 0.001 wt% CNF suspension was dropped on a cleaved mica surface and dried in air. The height of surface on the substrate can be measured with the AFM. The thickness was determined by the subtraction of the height between a higher part of CNF and the neighboring lower part. The length of CNF was determined by the length of the sequence of higher parts on AFM images. Preparation of the substrate and measurement of the height of CNF were carried out at room temperature. Average values of measured thickness and length of CNF are used as the diameter and length of a cylinder in the present theoretical model.
Potentiometric Titration. The amount of deprotonated carboxyl groups was measured by potentiometric acid-base titration. The titration was carried out by using a pH meter integrated with a burette (Easy pH, Mettler Toledo). Blank solution at ionic strength of 10 mM was prepared by mixing 25 mL of 10 mM KCl and 10 mL of 10 mM HCl in a beaker. The blank solution was continuously stirred and bubbled with CO2-free moist Ar gas to avoid CO2. ~10 mM KOH was set to the burette and titration was carried out with easy pH. Equilibrium pH and the volume of titrant were recorded. Equilibrium pH was determined when the change in pH became within 0.01 for 8 seconds. ~10 mL of ~0.3 wt% CNF suspension with 10 mM HCl was added to the beaker and bubbled Ar gas again. The titration of the CNF suspension was started with easy pH. Equilibrium pH and the volume of titrant were recorded again. The precise concentration of KOH and parameter of electrode were obtained from the blank titration with Gran’s plot. pH was calibrated by these values. The amount of deprotonated carboxyl groups was calculated by the subtraction of added HCl−KOH (mol) between the blank titration curve and the titration curve of CNF suspension at the same pH. The surface density of deprotonated carboxyl groups was obtained by dividing the amount of deprotonated carboxyl groups by the total surface area of CNF. The total surface area can be obtained by multiplying the total mass of CNFs contained in the suspension and the specific surface area, which is calculated from the density, 1.6 Mg/m3,20,21 and the cylindrical shape of the CNF. The measurement was also done at the ionic strength of 50 mM. The titration experiments were carried out duplicate at each KCl concentration at 20°C.
Electrophoresis. The electrophoretic mobility of CNF was measured by an electrophoretic light scattering instrument 5
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(Zeta sizer nano ZSP, Malvern). The measurement was carried out for 0.01 wt% CNF suspension as a function of pH at different ionic strengths (10 and 50 mM KCl). pH of the suspension was measured by a pH meter (HM-30R, TOADKK). To prevent contamination with CO2, pH measurement was carried out in the condition sealed with parafilm. All the measurements of the mobility were carried out at 20°C.
Dynamic Light Scattering (DLS). The hydrodynamic diameter of CNF was measured by a dynamic light scattering instrument (Zeta sizer nano ZSP, Malvern) as a function of pH at different KCl concentrations. The increased hydrodynamic diameter due to aggregation after a certain constant period from the preparation of the suspensions is considered to reflect the rate of aggregation even for large aggregates. When the capture efficiency is high, most of colliding particles aggregate and the aggregates are thought to grow up rapidly. And when the capture efficiency is low, the collision can hardly result in aggregation and the growth of aggregates is slow. Therefore, we consider the size of large aggregates after a certain constant period also reflects the capture efficiency. The CNF suspensions were prepared by mixing KCl solution, HCl or KOH solution, and CNF suspension in a cleaned polystyrene cuvette. Then, 1 mL of 0.001 wt% CNF suspensions with different pH and KCl concentration were obtained. The DLS measurement was carried out at 112, 164 and 216 seconds after mixing the suspension. The detection of temporal increase of the hydrodynamic diameter in the initial stage was difficult because of weak scattering intensity at low CNF concentration. The hydrodynamic diameter is calculated in following method. Measured scattering light intensity is fluctuated in short time scale due to Brownian motion. The degree of decrease in the autocorrelation function of scattering intensity with the progress of time reflects the diffusion coefficient, because the reduction of correlation between particles is fast when Brownian motion is intense. Intensity-averaged diffusion coefficient can be obtained by the cumulant expansion of the autocorrelation function. The proportional coefficient of time in the expansion reflects the degree of decrease in the autocorrelation function and thus intensity-averaged diffusion coefficient. The diffusion coefficient and the hydrodynamic diameter is related by the Einstein-Stokes equation. After the DLS measurement, the pH of the suspension in the cuvette was measured in the sealed condition. All the DLS experiments were performed at 20°C.
THEORETICAL METHODS 1-pK Poisson-Boltzmann (PB) model. 1-pK PB model is used to evaluate the charging behavior of CNF. The deprotonation of surface carboxyl groups is expressed as −COOH ⇄ −COO + H
(1)
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The dissociation-association of K＋ is also taken into account as 22 −COOK ⇄ −COO + K
(2)
The dissociation constants of the above reactions are defined as −COO −COOH −COO p = − log = − log −COOK
p = − log = − log
(3) (4)
where is the surface concentration (mol/m2), is the surface activity of H＋ (mol/L) and is the surface activity of K＋. The surface activity is given by the Boltzmann distribution. = × exp − = × exp −
! /#$
! /#$
%
%
(5) (6)
where and are the bulk concentration of H＋ and K＋ respectively, is the quantum of electricity,
!
is the
surface potential, # is the Boltzmann constant and $ is the absolute temperature. The density of total carboxyl groups &'(' is the sum of the density of －COOH, －COO－ and －COOK. That is
&'(' = )* −COOH + −COO + −COOK % = &+,, + &+,,- + &+,,
(7)
where )* is the Avogadro number and & is the surface number density (m-2). －COO－ contributes to the surface
negative charge of CNF. Thus the surface charge density of CNF is given by . = − &+,,- = − &'(' ⁄ 1 + ⁄ + ⁄ %
(8)
Solving the Poisson-Boltzmann equation in the cylindrical coordinate, the relationship between the surface charge density and the surface potential of a cylinder in a 1-1 electrolyte solution is obtained approximately by 23 ⁄? 223 2 4#$ : 1 1 .= sinh 9 ; cosh? : /4%
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(9)
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with
2)* ? D ? 4= , 23 2 #$
(10)
, #$ 4% >= 4% : =
(11) (12)
where 23 is the relative permittivity of the solution, 2 is the permittivity of a vacuum, D is the ionic strength, F G%
is the modified Bessel function of the second kind of order H and is the radius of a cylinder. By solving Eqs. (3)－
(9) simultaneously, one can obtain the density of deprotonated carboxyl groups, the surface charge and the surface
potential. The free parameters are p , p and &'(' . CNF is a crystal of cellulose molecules combined by van der Waals attractive force and hydrogen bonds,24 so we neglect the penetration of ions in CNF in the modeling.
The zeta potential is an electric potential at a slipping plane. Hence, one can obtain the zeta potential from the potential distribution. The electric Potential distribution around a cylinder in a 1-1 electrolyte solution is approximately given by 23 1−> 1 + KI% =1 + KI@ 2#$ 1+> I% = ln J L 1−> 1 − KI% =1 − KI@ 1+>
(13)
with 4M% , 4% : 1+> K = tanh 9 ; < C. 4 1 + Q1 − 1 − >? %tanh? : ⁄4R/? I=
(14) (15)
The zeta potential can be calculated by substituting M = + G into Eq. (13) where G is the distance from the surface of a cylinder to an assumed slipping plane. In this case, the surface potential can be given by 1-pK PB model.
Electrophoretic Mobility. Electrophoretic mobilities are calculated from the zeta potential by using the Smoluchowski equation, the equation considering the curvature of a cylinder and the equation considering the relaxation of electric double layer for infinitely a long cylinder. By comparing them, the electrophoretic behavior of nanofiber is examined. 8
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Firstly, the widely used Smoluchowski equation is expressed as T=
23 2 U V
(16)
where T is the electrophoretic mobility and U is the zeta potential and V is the viscosity of the solution. The
Smoluchowski equation is applied in the condition where the radius of a particle is much larger than the thickness of electric double layer and the zeta potential is low. The radius of CNF is said to be a few nanometer. Hence, the Smoluchowski equation is applicable at high ionic strength. An average electrophoretic mobility of a cylinder orientated randomly to the electric field is given by 25 TWX =
T∥ + 2TZ 3
(17)
where T∥ and TZ are the electrophoretic mobility of cylinders oriented parallelly and perpendicularly to the electric
field, respectively. Bakker et al. observed the orientation-dependent mobility of silica rods during electrophoresis under a microscope and did not address the alignment of cylinder to applied electric field. This is probably due to significant rotational diffusion in their case; the viscosity is 1.5675 mPa·s and the average length of rods is 2290 nm and the diameter is 600 nm.25 In the present experiment, the dimension of particles is small and the viscosity of solution is low, thus the rotational diffusion of CNF seems to be sufficient for assuming the random orientation of CNF. Also, the
concentration of CNF is adjusted to as low as 0.01 wt% so as not to align to a particular direction. Therefore we think Eq.(17) can be applied in our study. For the parallel orientation, the electric field around the infinitely long cylinder is parallel to the surface and thus the Smoluchowski equation is applicable.27,28 T∥ =
23 2 U V
(18)
Secondly, the equation taking account of the surface curvature is introduced. We call this equation the
Ohshima-Henry equation. For cylinders oriented perpendicularly with low zeta potential, the mobility TZ\ is expressed as 27
TZ\ =
23 2 U 1
Article
Charging and aggregation behavior of cellulose nanofiber in aqueous solution Yusuke Sato, Yasuyuki Kusaka, and Motoyoshi Kobayashi Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02742 • Publication Date (Web): 10 Oct 2017 Downloaded from http://pubs.acs.org on October 11, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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Charging and aggregation behavior of cellulose nanofiber in aqueous solution
Yusuke Sato1, Yasuyuki Kusaka2, Motoyoshi Kobayashi3*
1
Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki
305-8572, Japan 2
Flexible Electronics Research Center, National Institute of Advanced Industrial Study and Technology, 1-1-1 Higashi,
Tsukuba, Ibaraki 305-8565, Japan 3
Faculty of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8572, Japan
AUTHOR INFORMATION *Corresponding author E-mail address: [email protected] Tel.: +81 29 853 5721; Fax: +81 29 853 4861
1
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ABSTRACT: To understand the charging and aggregation of cellulose nanofiber (CNF), we performed the following experimental and theoretical studies. The charging behavior of CNF was characterized by potentiometric acid-base titration measuring the density of deprotonated carboxyl groups at different KCl concentrations. The charging behavior from the titration was quantitatively described by the 1-pK Poisson-Boltzmann (PB) model for a cylinder. The electrophoretic mobility of CNF was measured as a function of pH by electrophoretic light scattering. The mobility was analyzed with the equation for an infinitely long cylinder considering the relaxation of electric double layer. Good agreement between experimental mobilities and theoretical calculation was obtained by assuming the reasonable distance from the surface to the slipping plane. The result demonstrated that the negative charge of CNF originates from the deprotonation of β(1-4)-D-glucuronan on the surface. The aggregation behavior of CNF was studied by measuring the hydrodynamic diameter of CNF at different pH and KCl concentrations. Also, we calculated the capture efficiencies of aggregation, using interaction energies of perpendicularly and parallelly oriented cylinders. The interaction energies between cylinders in both the orientations were obtained by Derjaguin, Landau, Verwey, and Overbeek theory, where the electrostatic repulsion was calculated from the surface potential obtained by the 1-pK PB model. From the comparison of the theoretical capture efficiency with the measured hydrodynamic diameter, we suggest that CNFs can be aggregated in perpendicular orientation at low pH and low salt concentration, and the fast aggregation regime of CNF is realized by the reduction of electric repulsion for both perpendicularly and parallelly interacting CNFs. Meanwhile, the application of Smoluchowski’s equation to the mobility of CNF results in the underestimation of the zeta potential.
Key words: Nano rod Relaxation effect Surface potential DLVO theory
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INTRODUCTION Organic nanofibers play significant roles in many fields such as environmental engineering, industrial application, water purification and so on. The possibility of transportation of uranium (IV) by the complex of colloidal iron oxides and organic nanofibers in enviro is pointed out.1,2 There are a lot of products containing nanofibers; for example ink, medicine, foods and plastics. Sorption of toxic heavy metal species by nano-celluloses is reported.3,4 The transport property of nanofibers and the quality of products containing nanofibers depend on the dispersion and aggregation of nanofibers.5,6 The aggregation and dispersion are controlled by the surface charging characteristics. The sorption of heavy metal species are also affected by the surface charging characteristics. Therefore, the understanding of charging and aggregation of nanofibers is important for environmental engineering, industrial applications and water purification. Cellulose nanofiber (CNF) is an attractive material in industry because of its unique property and sustainability. For example, elastic modulus of CNF is five times higher than that of iron.7 CNF suspension is colorless and transparent and shows outstanding shear thinning.8 Films containing CNF reduce the penetration of oxygen.9 The wide application of CNF is expected to composite material of polymer, cosmetic, food and medicine in industry as a reinforce agent, rheological modifier, film and so on. Also, CNF can be a model of natural organic nanofibers. CNF is obtained by breaking up pulps which are bundles of cellulose microfibrils. The cellulose microfibril is a crystal consisting of 30~40 cellulose molecules and its width is ~3 nm for higher plants.10 C6 hydroxyls on the surface of cellulose microfibrils are oxidized to carboxyl groups by 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO).11 The surface negative charge originated from the dissociated carboxyl groups make it easier to disperse the pulps in aqueous solutions to thin fibers with a few nanometers in diameter. Thus, the TEMPO-oxidized CNFs show pH-dependent negative charge and colloidal stability.12 The dispersion and aggregation of colloidal particles are dominated by the interaction energy between particles. According to Derjaguin, Landau, Verwey and Overbeek (DLVO) theory, the inter-particle interaction energy is expressed as the sum of repulsive electrostatic interaction energy affected by charging behavior and attractive van der Waals energy. The pH and salt dependency of aggregation rate of well-characterized spherical particles such as silica and carboxyl latex particles is quantitatively described by the DLVO theory with the theoretical model of electric charging as well as the measurements of surface charge density and surface potential by potentiometric titration and electrophoresis.13,14 These studies point out the importance of taking account of the relaxation of electric double layer during electrophoresis and the necessity of obtaining both the surface charge and the surface potential. The aggregation and dispersion of CNF are expected to be affected by solution chemistry due to the sensitivity of charging behavior of CNF on pH and ionic strength. However, systematic studies on the aggregation behavior of CNF with the characterization of charging behavior are insufficient. While Wågberg calculated the surface potential and the DLVO interaction energy of carboxymethylated celluloses that have a similar form with CNF, the calculated surface 3
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potential did not quantitatively agree with the zeta potential calculated from electrophoretic mobility.15 Also, the used equation connecting the zeta potential and the electrophoretic mobility was unclear. Isogai showed experimentally that the critical coagulation concentrations (CCCs) of CNF follow the Shultze-Hardy rule.16 Furthermore, the CCCs calculated by the DLVO theory was in good agreement with experimental values. However, the electrostatic interaction energy of CNF did not seem to be evaluated properly, because the zeta potential, which is thought to be calculated by the Smoluchowski equation, was used instead of the surface potential. The Smoluchowski equation can be applied for large particles compared with the thickness of electric double layer. The diameter of CNFs is as thin as 3 nm. Therefore, it is doubtful to apply the Smoluchowski equation to obtain the zeta potential of CNF from the electrophoretic mobility. It is known that the Smoluchowski equation can be inaccurate even for large spherical particles at low salt concentration because of the relaxation of electric double layer.17,18 At this moment, however, no attempt has been reported for the influence of the relaxation of double layer on the electrophoresis of thin nanofibers. In this paper, we report results of experimental and theoretical study on the aggregation and charging of CNF. In the theoretical model, CNF is regarded as a cylindrical particle. The diameter and length of cylinder were determined by measuring the dimension with atomic force microscopy. The surface charge density of CNF was characterized by comparing the measured amount of deprotonated carboxyl groups and the calculation by 1-pK Poisson-Boltzmann model for a thin cylinder. Furthermore, the measurement of electrophoretic mobility of CNF and the theoretical analysis by the equation taking account of the relaxation of electric double layer were conducted to evaluate the surface electric potential. The aggregation behavior of CNF detected by the increase of size was investigated by dynamic light scattering. The capture efficiency of aggregation is compared with the measured hydrodynamic diameter as a function of pH at different salt concentrations. Aggregation behavior of CNF is examined by the capture efficiency obtained from the classical Fuch’s expression for spherical particles with DLVO theory for cylinders.
EXPERIMENTAL METHODS Material. Cellulose nanofiber suspension (RHEOCRYSTA I-2SP) was kindly provided from DKS Co. Ltd. The suspension was treated as follows. First, the pH of suspension was adjusted to 2.2 with HCl to protonate the surface. Second, the suspension was extensively dialyzed against deionized water until the electric conductivity became below 1 µS/cm. Ionic strength and pH of the suspension were adjusted with KCl, HCl and KOH (JIS special grade, Wako Pure Chemical Industries). KCl and HCl solutions were filtrated with 0.2 µm pore filter (25HP020AN, Toyo Roshi Kaisha, Ltd.) to exclude particulate contaminants. Carbonate free KOH solution was prepared by diluting filtrated supernatant of ~10 M KOH containing 0.2 g/L CaO with degassed water prepared under vacuum.19 Mechanical dispersion processes were conducted to prepare stock suspension except for potentiometric titration. That 4
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is, 0.1 wt% CNF suspension with 2 mM KOH was sheared by a homogenizer (AHG-160A, As one) for 30 seconds at the scale of 80 and followed by the sonication by an ultrasonic homogenizer (THU-80, As one) for 30 seconds at the scale of MIN. The suspension and solutions were degassed under vacuum before experiments.
Atomic Force Microscopy (AFM). The thickness and length of CNFs deposited on a mica substrate were measured by using an AFM (LSP 5600, Agilent) in a tapping mode with a cantilever (OMCL-AC160TS-C2, Olympus). The spring constant of the cantilever was 42 N/m and the tip radius was less than 10 nm. To prepare the CNF-deposited substrate for AFM, 5 µL of 0.001 wt% CNF suspension was dropped on a cleaved mica surface and dried in air. The height of surface on the substrate can be measured with the AFM. The thickness was determined by the subtraction of the height between a higher part of CNF and the neighboring lower part. The length of CNF was determined by the length of the sequence of higher parts on AFM images. Preparation of the substrate and measurement of the height of CNF were carried out at room temperature. Average values of measured thickness and length of CNF are used as the diameter and length of a cylinder in the present theoretical model.
Potentiometric Titration. The amount of deprotonated carboxyl groups was measured by potentiometric acid-base titration. The titration was carried out by using a pH meter integrated with a burette (Easy pH, Mettler Toledo). Blank solution at ionic strength of 10 mM was prepared by mixing 25 mL of 10 mM KCl and 10 mL of 10 mM HCl in a beaker. The blank solution was continuously stirred and bubbled with CO2-free moist Ar gas to avoid CO2. ~10 mM KOH was set to the burette and titration was carried out with easy pH. Equilibrium pH and the volume of titrant were recorded. Equilibrium pH was determined when the change in pH became within 0.01 for 8 seconds. ~10 mL of ~0.3 wt% CNF suspension with 10 mM HCl was added to the beaker and bubbled Ar gas again. The titration of the CNF suspension was started with easy pH. Equilibrium pH and the volume of titrant were recorded again. The precise concentration of KOH and parameter of electrode were obtained from the blank titration with Gran’s plot. pH was calibrated by these values. The amount of deprotonated carboxyl groups was calculated by the subtraction of added HCl−KOH (mol) between the blank titration curve and the titration curve of CNF suspension at the same pH. The surface density of deprotonated carboxyl groups was obtained by dividing the amount of deprotonated carboxyl groups by the total surface area of CNF. The total surface area can be obtained by multiplying the total mass of CNFs contained in the suspension and the specific surface area, which is calculated from the density, 1.6 Mg/m3,20,21 and the cylindrical shape of the CNF. The measurement was also done at the ionic strength of 50 mM. The titration experiments were carried out duplicate at each KCl concentration at 20°C.
Electrophoresis. The electrophoretic mobility of CNF was measured by an electrophoretic light scattering instrument 5
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(Zeta sizer nano ZSP, Malvern). The measurement was carried out for 0.01 wt% CNF suspension as a function of pH at different ionic strengths (10 and 50 mM KCl). pH of the suspension was measured by a pH meter (HM-30R, TOADKK). To prevent contamination with CO2, pH measurement was carried out in the condition sealed with parafilm. All the measurements of the mobility were carried out at 20°C.
Dynamic Light Scattering (DLS). The hydrodynamic diameter of CNF was measured by a dynamic light scattering instrument (Zeta sizer nano ZSP, Malvern) as a function of pH at different KCl concentrations. The increased hydrodynamic diameter due to aggregation after a certain constant period from the preparation of the suspensions is considered to reflect the rate of aggregation even for large aggregates. When the capture efficiency is high, most of colliding particles aggregate and the aggregates are thought to grow up rapidly. And when the capture efficiency is low, the collision can hardly result in aggregation and the growth of aggregates is slow. Therefore, we consider the size of large aggregates after a certain constant period also reflects the capture efficiency. The CNF suspensions were prepared by mixing KCl solution, HCl or KOH solution, and CNF suspension in a cleaned polystyrene cuvette. Then, 1 mL of 0.001 wt% CNF suspensions with different pH and KCl concentration were obtained. The DLS measurement was carried out at 112, 164 and 216 seconds after mixing the suspension. The detection of temporal increase of the hydrodynamic diameter in the initial stage was difficult because of weak scattering intensity at low CNF concentration. The hydrodynamic diameter is calculated in following method. Measured scattering light intensity is fluctuated in short time scale due to Brownian motion. The degree of decrease in the autocorrelation function of scattering intensity with the progress of time reflects the diffusion coefficient, because the reduction of correlation between particles is fast when Brownian motion is intense. Intensity-averaged diffusion coefficient can be obtained by the cumulant expansion of the autocorrelation function. The proportional coefficient of time in the expansion reflects the degree of decrease in the autocorrelation function and thus intensity-averaged diffusion coefficient. The diffusion coefficient and the hydrodynamic diameter is related by the Einstein-Stokes equation. After the DLS measurement, the pH of the suspension in the cuvette was measured in the sealed condition. All the DLS experiments were performed at 20°C.
THEORETICAL METHODS 1-pK Poisson-Boltzmann (PB) model. 1-pK PB model is used to evaluate the charging behavior of CNF. The deprotonation of surface carboxyl groups is expressed as −COOH ⇄ −COO + H
(1)
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The dissociation-association of K＋ is also taken into account as 22 −COOK ⇄ −COO + K
(2)
The dissociation constants of the above reactions are defined as −COO −COOH −COO p = − log = − log −COOK
p = − log = − log
(3) (4)
where is the surface concentration (mol/m2), is the surface activity of H＋ (mol/L) and is the surface activity of K＋. The surface activity is given by the Boltzmann distribution. = × exp − = × exp −
! /#$
! /#$
%
%
(5) (6)
where and are the bulk concentration of H＋ and K＋ respectively, is the quantum of electricity,
!
is the
surface potential, # is the Boltzmann constant and $ is the absolute temperature. The density of total carboxyl groups &'(' is the sum of the density of －COOH, －COO－ and －COOK. That is
&'(' = )* −COOH + −COO + −COOK % = &+,, + &+,,- + &+,,
(7)
where )* is the Avogadro number and & is the surface number density (m-2). －COO－ contributes to the surface
negative charge of CNF. Thus the surface charge density of CNF is given by . = − &+,,- = − &'(' ⁄ 1 + ⁄ + ⁄ %
(8)
Solving the Poisson-Boltzmann equation in the cylindrical coordinate, the relationship between the surface charge density and the surface potential of a cylinder in a 1-1 electrolyte solution is obtained approximately by 23 ⁄? 223 2 4#$ : 1 1 .= sinh 9 ; cosh? : /4%
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(9)
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with
2)* ? D ? 4= , 23 2 #$
(10)
, #$ 4% >= 4% : =
(11) (12)
where 23 is the relative permittivity of the solution, 2 is the permittivity of a vacuum, D is the ionic strength, F G%
is the modified Bessel function of the second kind of order H and is the radius of a cylinder. By solving Eqs. (3)－
(9) simultaneously, one can obtain the density of deprotonated carboxyl groups, the surface charge and the surface
potential. The free parameters are p , p and &'(' . CNF is a crystal of cellulose molecules combined by van der Waals attractive force and hydrogen bonds,24 so we neglect the penetration of ions in CNF in the modeling.
The zeta potential is an electric potential at a slipping plane. Hence, one can obtain the zeta potential from the potential distribution. The electric Potential distribution around a cylinder in a 1-1 electrolyte solution is approximately given by 23 1−> 1 + KI% =1 + KI@ 2#$ 1+> I% = ln J L 1−> 1 − KI% =1 − KI@ 1+>
(13)
with 4M% , 4% : 1+> K = tanh 9 ; < C. 4 1 + Q1 − 1 − >? %tanh? : ⁄4R/? I=
(14) (15)
The zeta potential can be calculated by substituting M = + G into Eq. (13) where G is the distance from the surface of a cylinder to an assumed slipping plane. In this case, the surface potential can be given by 1-pK PB model.
Electrophoretic Mobility. Electrophoretic mobilities are calculated from the zeta potential by using the Smoluchowski equation, the equation considering the curvature of a cylinder and the equation considering the relaxation of electric double layer for infinitely a long cylinder. By comparing them, the electrophoretic behavior of nanofiber is examined. 8
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Firstly, the widely used Smoluchowski equation is expressed as T=
23 2 U V
(16)
where T is the electrophoretic mobility and U is the zeta potential and V is the viscosity of the solution. The
Smoluchowski equation is applied in the condition where the radius of a particle is much larger than the thickness of electric double layer and the zeta potential is low. The radius of CNF is said to be a few nanometer. Hence, the Smoluchowski equation is applicable at high ionic strength. An average electrophoretic mobility of a cylinder orientated randomly to the electric field is given by 25 TWX =
T∥ + 2TZ 3
(17)
where T∥ and TZ are the electrophoretic mobility of cylinders oriented parallelly and perpendicularly to the electric
field, respectively. Bakker et al. observed the orientation-dependent mobility of silica rods during electrophoresis under a microscope and did not address the alignment of cylinder to applied electric field. This is probably due to significant rotational diffusion in their case; the viscosity is 1.5675 mPa·s and the average length of rods is 2290 nm and the diameter is 600 nm.25 In the present experiment, the dimension of particles is small and the viscosity of solution is low, thus the rotational diffusion of CNF seems to be sufficient for assuming the random orientation of CNF. Also, the
concentration of CNF is adjusted to as low as 0.01 wt% so as not to align to a particular direction. Therefore we think Eq.(17) can be applied in our study. For the parallel orientation, the electric field around the infinitely long cylinder is parallel to the surface and thus the Smoluchowski equation is applicable.27,28 T∥ =
23 2 U V
(18)
Secondly, the equation taking account of the surface curvature is introduced. We call this equation the
Ohshima-Henry equation. For cylinders oriented perpendicularly with low zeta potential, the mobility TZ\ is expressed as 27
TZ\ =
23 2 U 1
