Adsorption characteristics of surfactants on secondary wood fiber surface

Surfactant residues in recycled wood fiber from the deinking process can have impact on the subsequent bleaching and papermaking processes by increasing bleaching agents and disturbing papermaking wet-end chemistry. In this paper, the fundamental mechanism of surfactants adsorption characteristics on secondary fiber surface was studied. The adsorption isotherms and kinetics of an anionic surfactant, sodium dodecyl benzene sulfonate (SDBS) and a non-ionic surfactant, Triton X-100 (TX-100) on secondary fiber surface with or without the presence of electrolytes (Mg ions) were studied by using spectrophotometric methods. Results showed that the adsorption isotherm of SDBS could be subdivided into four regions, and the adsorption of SDBS was increased with the presence of Mg ions. While for TX-100, the adsorption isotherm showed typically Langmuir-type adsorption, and its adsorption was decreased with the presence of Mg ions. Kinetic analysis indicated that the adsorption processes both fit pseudo-second-order model well. The adsorption rate of both surfactants was affected by the initial surfactant concentration, electrolyte and temperature. The activation parameters confirmed that the adsorption processes of both surfactants were typically diffusion-controlled and endothermic at a temperature range commonly used for current flotation deinking processes. SDBS and TX-100 mainly adsorbed to the hydrophobic sites of secondary fibers surface, which decreased the fiber hydrophobicity and reduced the fiber loss in the flotation deinking process. The results suggested that the concentration of Mg ions should be maintained at a low level when SDBS was used in the flotation process.


INTRODUCTION
The current environmental awareness and legislation push people to maximize the recycling of waste paper.The utilization of secondary fiber from waste paper has been increasing over the past decades, and now over 65% of the paper products are made from secondary fibers in the world.Deinking is an important step in recycling waste paper and flotation is commonly used in this process.
In general, anionic and non-ionic surfactants have been widely used as deinking chemicals in current flotation operations to help in removing the ink particles from the pulp through reducing the surface tension of ink particles, wetting fibers and dispersing the ink binders, which improves the quality of secondary fiber ultimately. 1 Electrolytes, e.g., Ca 2+ and Mg 2+ ions, are capable of changing the colloid behaviors of dispersing system, the adsorption characteristics of surfactants on secondary fiber surface and the effect of adsorption on fiber loss in flotation process are seldom involved.
3][4][5] Some researchers believed that air bubbles routinely adhered to the hydrophobic parts of fibers during the flotation process, and the fiber loss was solely caused by hydrophobic interaction between air bubbles and fibers.Deng 6 reported that the hydrophobicity of fiber in an aqueous solution decreased as surfactant concentration increased, because the surfactant adsorbed to both water and fiber surface reduced the surface tension and interfacial energy between water and fibers.There would be no further increase in adsorption or decrease in contact angle when the surfactant concentration was higher than its critical micelle concentration (CMC).Beneventi et al. 7 found that fiber loss in flotation was concerned with adsorption of the surfactants which were added as process chemicals.
In general, the processes of washing and enrichment after flotation will reduce the amount of surfactant in water, but the residual surfactants on fiber surface may affect the subsequent processes of bleaching and papermaking.Some surfactants with unsaturated side chains played a complementary role in biological bleaching for being oxidized to produce organic peroxides which promoted the catalysis of manganese catalase. 8,9In conventional chemical bleaching systems, residual surfactants could improve the wettability of bleaching solution on fibers, accelerate the penetration and diffusion of bleaching solution, and thus enhance the bleaching effect.However, partial decomposition of bleaching chemicals such as H2O2 would be caused as a function of the excess of residual surfactants in the system. 10,11The excess of residual surfactants on fiber surface and in white water had a negative effect onretention system.Residual anionic surfactants could increase the content of anionic trash which may lead to the amount of cationic polyacrylamide increased.When polyethylene oxide/formaldehyde resin (PEO/PFR) was used as retention system, alkoxylated non-ionic surfactants typically formed insoluble complexes with PFR, seriously impairing the reaction between PEO and PFR. 12,13Fatehi et al. 14 reported that softness and dispersibility of fibers were improved by adsorbing surfactants, which might be responsible for the increased mechanical properties of paper.However, the excess of residual surfactants on fiber surface or in white water will cause bubbling on the wire part and destroy the fiber network, which eventually lead to the mechanical properties of paper decreased.
The adsorption of surfactants at the solid-liquid interface showed promise in many technological and industrial applications, such as deinking flotation, mineral flotation, corrosion inhibition, dispersion of solids, oil recovery and so on. 15Some factors, e.g., the nature of solid surface, type and structure of surfactant, electrolytes, pH and temperature,are vital in determining the adsorption of surfactants at the solid-liquid interface . 16On solid-liquid interface, aggregation of surfactant molecules tends to form associative structure called admicelle, which may be monolayer, bilayer, hemisphere or sphere.The geometry of admicelle is determined by the nature of surfactant and solid surface. 17,18he solid surfaces are either positively or negatively charged in the aqueous medium by ionization and dissociation of surface groups or by the adsorption of ions from solution onto a previously uncharged surface.Therefore, the electrical double layer at solid-liquid interface is usually an important phenomenon for the adsorption of ionic surfactants.Non-ionic surfactants are physically adsorbed rather than electrostatically or chemisorbed.Quite small changes in concentration, temperature, or molecular structure of the adsorbent have a large effect on the adsorption [19][20][21][22] .Adsorption kinetics on cotton, on filter paper and on active carbon have been studied [23][24][25][26] .Surfactants adsorbed increase rapidly in the beginning and become very slow in the end.Electrolytes (Mainly Ca 2+ ions and Mg 2+ ions) which commonly used in deinking flotation 27 , has a significant effect on adsorption of surfactants on secondary fiber surface.Sritapunya et al. 28 found that Ca 2+ ions enhanced the adsorption of sodium octanoate on negatively charged sits of secondary fiber surface.Denoyel and Rouquerol 29 found that the presence of NaCl shifted plateau position of TX-100 adsorbed on quartz towards lower equilibrium concentrations, which means that there was a decrease in the CMC.
In the present work, from a practical point of view, the adsorption characteristics of an anionic surfactant, SDBS and a non-ionic surfactant, Triton X-100 (TX-100) on secondary fiber surface were studied for the purpose of understanding the fundamental mechanism of flotation deinking process.Specifically, the experimental and model of adsorption isotherms and kinetics for these two surfactants were investigated, and the effects of initial surfactant concentration, electrolyte and temperature on adsorption rate were also studied.

Production of secondary fiber pulp
Secondary fiber pulp was prepared by pulping old newsprint with an alkaline condition (pH = 9.0 ± 0.5) at 10% consistency under 55 ºC for 20 min.The pulp was then filtered and washed with distilled water several times to remove all fillers, detached ink particles and extraneous ions.The washing step was repeated until the concentration of Mg 2+ ions and Ca 2+ ions in the filtrate was less than 0.1 ppm as determined by an atomic absorption spectrophotometer (Varian, SPA-220FSmodel).The secondary fiber was then pressed and dried at 50 ºC for 24 h prior to experiments.

Characterization and analysis
The CMC of SDBS and TX-100 at 45 ºC was determined from the break in the surface tension versus concentration plots using a drop shape analysis instrument (Krǜss, DSA-10MKZ model).BET surface areas (N2 adsorption) of the secondary fiber was 21.52 m 2 •g -1 , measured by a surface area analyzer (Quantachrome, NOVA2200 model).The surface of the secondary fiber has a zeta potential (approximates the electrical potential at the edge of the stern layer next to the surface) of -26.65 mV at pH 9, determined by using a zeta meter (BTG, SZP-10 model).The effective residual ink content (ERIC) of secondary fiber was 155.2 mg• kg -1 , analyzed by using an ERIC measurement (Metso, CPTC model).

Equilibrium isotherms studies
The adsorption experiments were performed in closed batch systems prepared in a series of 100 mL stoppered glass bottles.1.0 g prepared secondary fiber was added into 25 mL surfactant solution with different concentrations of SDBS or TX-100.The suspension pH was adjusted to 9 by adding NaOH.Subsequently, the experiment was performed in a thermostatic shaker shock for 24 h at 45 ºC .When the targeted time attained, the samples were centrifuged at 3000 rpm for 15 min.The obtained supernatants were further filtered by using 0.22 μm cellulose acetate filter membranes, and then analyzed with an UV/visible spectrophotometer (Varian, Cary-300model).
Both of the wavelengths selected of SDBS and TX-100 were 226 nm which was found available for SDBS and TX-100 in our previous work.The amount of adsorption at equilibrium, qe (mg• g -1 ), was calculated by the following equation： Where CO and Ce are the initial and equilibrium liquid-phase solute concentrations, respectively (mmol• L -1 ) and m is the dose of secondary fiber which always equals 1.0g.M is the molecular weight of the surfactant (g• mol -1 ).V is the volume of solution which always equals 25 mL.

Kinetic studies
The kinetics of the adsorption of SDBS and TX-100 were evaluated through the use of controlled experiments in a batch system.For each set of experiments, 1.0 g prepared secondary fiber was added into a 100 mL stoppered glass bottle, where 25 mL surfactant solution with known concentrations was added.The experiment was performed in a thermostatic shaker shock at a desired temperature.The suspension pH was adjusted to 9. Samples were taken at the pre-set time intervals.The amount of adsorption at time t (min), qt (mg• g -1 ), was calculated using the following equation: Where Ct is the liquid-phase solute concentration at time t (mmol• L -1 ).

CMC measurements
The CMC of surfactant at 45 ºC was defined by surface tension measurements.Specifically, the CMC of SDBS and TX-100 were 1.60 and 0.22 mmol• L -1 , respectively.Based on the surface tension data, the surface area occupied by a surfactant molecule at the air water interface was calculated by using Gibb's surface excess equations.For TX-100, the surface area calculated was 110.62 Å 2 per molecule, which compared well with the reported value (120 Å 2 per molecule). 30For SDBS, the surface area reached 57.43 Å 2 in absence of salt and 52.28 Å 2 in presence of 0.1g•L -1 MgCl2, apparently higher than the reported results (45 Å 2 per molecule).

Adsorption isotherms
Figures 1 and 2 show the equilibrium adsorption isotherms of SDBS and TX-100 onto secondary fiber surface at pH 9 and 45 ºC with or without the presence of Mg 2+ ions.It should be noted that the above pH and temperature condition had been commonly used for flotation deinking process. 31,32As shown in Fig. 1, the adsorption isotherm of SDBS was mainly divided into four regions.In Region I (low concentrations), as expected, SDBS molecules adsorbed curve generally obeyed Henry's Law in a linear fashion. 33In Region II, a decrease in slope appeared largely attributed to the repulsion between anionic head groups in the admicelles.In Region III, beyond a particular concentration, the adsorption was sharply increased.In Region IV, adsorption reached a maximum of 0.667 mg• g -1 at 1.76 mmol• L -1 near the CMC.Over the CMC, adsorption retained approximately constant because of the almost constant chemical potential of the surfactant, which region was known as the plateau adsorption region.It can be seen in Figure 2 that the equilibrium adsorption isotherm of TX-100 was in accordance with Langmuir-type.At low surfactant concentrations, TX-100 was adsorbed on a surface with limited molecules, fully obeying Henry's law.It was generally believed that the molecules were far away from each other, so the adsorbate-adsorbate interactions were negligible.Adsorption in this region occurred because www.Bioresources-Bioproducts.com 67 of Vander Waals interaction, therefore, it was mainly determined by the hydrophobic parts of the surfactant.As TX-100 concentration increased, it was accompanied by gradual decrease in the slope of the adsorption isotherm due to saturation of monolayer.At a concentration of 0.24 mmol• L -1 near the CMC, adsorption showed a maximum of 1.207 mg• g -1 .Above the CMC, adsorption was nearly constant.
From Fig. 1, in presence of Mg 2+ ions, the maximum adsorption of SDBS increased to 0.886 mg• g -1 , while CMC reduced to 1.56 mmol• L -1 .The surface of the secondary fiber had a zeta potential of -26.65 mV at pH 9. Mg 2+ ions enhanced the adsorption of SDBS on negatively charged sites of secondary fiber surface which acted like a bridge between the surface and negatively charged surfactant head groups.It could be concluded that the negative charge of the surfactant molecules was shielded by the Mg 2+ ions.In addition, the compressed electric double layer at the fiber surface shielded the surface charge.Consequently, the adsorption of SDBS molecules onto secondary fiber surface did not experience any inhibition arising from electrical repulsion, thereby resulting in the adsorption increased.
From Fig. 2, in presence of Mg 2+ ions, the maximum adsorption and the CMC of TX-100 decreased to 0.951 mg• g -1 and 0.21 mmol• L -1 , respectively.Mg 2+ ions shifted plateau position of TX-100 adsorbed on secondary fiber surface towards lower equilibrium concentrations, suggesting that there was a decrease in the CMC.The decreased adsorption was due to the strong adsorption of Mg 2+ ions on the polar surface and the resulting displacement of TX-100 molecules. 29 a typical approach, the two-parameter Langmuir and Freundlich models could be employed to fit the isotherms. 34Langmuir model suggested that adsorption occurs on a homogeneous surface without any lateral interaction between the adsorbed molecules.While the Freundlich model was widely used to describe adsorption on a surface having heterogeneous energy distribution, accompanied by interaction between the adsorbed molecules.Langmuir model was given as follows: Freundlich model was given as follows: Where KL is the Langmuir constant (L• mmol -1 ), qm is the amount of adsorption corresponding to complete coverage (mg• g -1 ), KF and n are the Freundlich constants.Langmuir and Freundlich models were fitted to the isotherm data for SDBS and TX-100, respectively, by a linear regression analysis.The fitting results were listed in Table 1.The detailed analysis of the R 2 values showed that the adsorption data of TX-100 was better fitted by the Langmuir model with or without the presence of Mg 2+ ions.On the other hand, neither Langmuir nor Freundlich models was suitable for the description of the isotherms of SDBS, because of the lower R 2 values.Paria et al. 25 and Sritapunya et al. 28 found that different anionic surfactants formed different types of admicelles such as monolayer or bilayer when adsorbed onto cellulosic surface.The observations relating to the adsorption of SDBS and TX-100 indicated the presence of both charged and hydrophobic sites on the secondary fiber surface.The electrical nature of the surface was manifested in the change in adsorption behavior in presence of electrolytes, while the hydrophobic nature was shown through the adsorption of TX-100.The non-ionic surfactants may also be adsorbed onto charged sites by hydrogen bonding but in this situation the extent of adsorption depended on the pH of the solution and electrolyte. 35,36Therefore, it could be hypothesized that the secondary fiber surface consisted of two kinds of sites for adsorption: electrically charged sites or polar and hydrophobic sites or non-polar sites.
SDBS and TX-100 were forming admicelles, but as the admicelle aggregation number was very low, calculation was carried out considering monolayer.The values for these effective areas were calculated using the following equation: www.Bioresources-Bioproducts.com Where S is the BET surface area of the secondary fiber (m 2 •g -1 ), asm is the area occupied per molecule (Å 2 ), NA is the Avogadro's constant.
Based on the observations presented earlier, secondary fiber surface consisting of negatively charged sites as well as neutral hydrophobic sites was assumed.Calculations had been conducted to determine the area occupied by surfactant molecules, and the results were presented in Table 2.It showed that the effective area occupied by a molecule of SDBS and a molecule of TX-100 was nearly the same in the absence of Mg 2+ ions.Such result indicated that SDBS and TX-100 were mainly adsorbed to the hydrophobic sites of the secondary fiber.In presence of Mg 2+ ions, SDBS adsorption was synergized due to Mg 2+ ions adsorption on negative surface sites and co-adsorption of the anionic surfactant on the positively charged cation.The calculated area occupied per molecule on the solid surface was more than the actual molecular area of TX-100 (120 Å 2 ) and SDBS (45 Å 2 ).This clearly showed that even at the maximum adsorption, multilayer adsorption did not occur.The possible adsorption sequences corresponding to the adsorption isotherms of SDBS and TX-100 on the secondary fiber surface with or without the presence of Mg 2+ ions were showed in Fig. 3. High level of fiber hydrophobicity contributes to the fiber loss in flotation deinking.SDBS and TX-100 were mainly adsorbed to the hydrophobic sites of the secondary fiber as a tail-down, head-out monolayer without the presence of Mg 2+ ions, which reduced the fiber loss by decreasing the fiber hydrophobicity.In the presence of Mg 2+ ions, there was no significant change in the adsorption sequence of TX-100, but for SDBS, surfactant molecules adsorbed to both charged and hydrophobic sites.At a high concentration of Mg 2+ ions, majority of SDBS molecules were adsorbed on the negative charged sites as a head-down, tail-out monolayer due to the bridging effect of Mg 2+ ions, which will increase the fiber hydrophobicity and enhance the fiber loss.Therefore, the concentration of electrolytes during flotation process should be maintained at a low level.Current industrial practice indicates that anionic surfactants generally will not be used alone due to the poor deinking selectivity and the disadvantage of excessive accumulation in circulating water system.Most paper mills are conducted using non-ionic surfactants for better deinking selectivity such as TX-100.

Adsorption Kinetics
Fig. 4 and 5 present the adsorption kinetics of SDBS and TX-100 onto secondary fiber surface at 45 o C. It was found that time variations on extent of adsorption could be divided into three different regimes, they were: (1) adsorption linear increase with time, (2) transition regime where the rate of adsorption decreased and (3) a plateau regime.The higher initial rate of surfactant adsorption may be explained by the large number of adsorption sites.The lower adsorption rate at the end was probably due to the saturation of active sites and attainment of equilibrium.The equilibrium adsorption of both surfactants increased with increase in the initial concentration.The result data showed that with increase in initial concentration from 0.2 to 0.4g• L -1 , the amount of SDBS and TX-100 adsorbed increased from 0.171 to 0.259 mg• g -1 and 1.005 to 1.164 mg• g -1 , respectively.This obviously indicated that for higher initial concentrations, efficient utilization of adsorption sites was expected due to a greater driving force by a higher concentration gradient pressure.Keeping surfactant concentration of 0.4 g• L -1 constant, Mg 2+ ions acted like a bridge between the negatively charged surface and negatively charged surfactant head groups, which increased the equilibrium adsorption of SDBS from 0.259 to 0.402 mg• g -1 , but for TX-100, there was a decrease from 1.164 to 0.887 mg• g -1 , because the strong adsorption of Mg 2+ ions on the polar surface can lead to displacement of TX-100 molecules.
Four simplified lumped kinetic models including the pseudo-first-ordermodel, pseudo-second-ordermodel, the Elovichmodel, and the intra-particle diffusion model were studied here.The pseudo-first-order model was given by 37 : e t e 1 ln(q -q ) = lnq -k t The pseudo-second-order model was given by 38 : The Elovich model was given by 39 : The intra-particle diffusion model originated from the Fick's second law was simply written as 40 : Where qe is the pseudo-equilibrium adsorption corresponding to the initial liquid concentration (mg• g -1 ).k1 is the pseudo-first-order rate constant (min -1 ).k2 is the pseudo-second-order rate constant (g• mg -1 • min -1 ).α and β are the initial adsorption rate (mg• g -1 • min -1 ) and desorption constant (g• mg -1 ) of Elovich model, respectively.kp and C are the rate constant of intra-particle diffusion (mg• g -1 •m in -1/2 ) and the constant related to thickness of the diffusion layer(mg• g -1 ) of intra-particle diffusion model, respectively.Table 3. Fitting results of pseudo-first-order and pseudo-second-order models for adsorption of SDBS and TX-100 onto secondary fiber surface Pseudo-first-order Pseudo-second-order qe,cal (mg• g -1) R 2 k1 (min -1 ) qe,cal (mg• g -1 ) R 2 k2 (g• mg -1 • min -1 ) SDBS (0.2g  3 shows the fitting results of pseudo-first-order and pseudo-second-order models for SDBS and TX-100.The parameters in the two models were determined from the linear plots of ln (qe-qt) versus t and t/qt versus t, respectively.It was observed that the adsorption of the both surfactants could not be followed by pseudo-first-order model in the presence or absence of Mg 2+ ions due to the low values of R 2 and the obvious difference between calculated and experimental equilibrium adsorption.Related studies reported that pseudo-first-order model can only describe the unsaturated process of adsorption 40 .However, it was observed that the adsorption of SDBS and TX-100 can be followed by the pseudo-second-order model with or without the presence of Mg 2+ ions due to the high R 2 values of 0.999.This suggested that the pseudo-second-order model basically included all steps of adsorption such as external film diffusion, adsorption, and internal particle diffusion.With the increase of the initial surfactant concentration, the adsorption rate (k2) were gradually decreased which was consistent with the previous studies 41 .This is because the collision between surfactant molecules was enhanced with the increase of the initial surfactant concentration which extended the time required for surfactant molecules adsorbing to the active points on secondary fiber surface.As a bridging role, Mg 2+ ions could accelerate the absorption of SDBS.But for TX-100, the values of k2 were decreased.
Table 4 shows the fitting results of Elovich and www.Bioresources-Bioproducts.com 70 intra-particle diffusion models for the adsorption of SDBS and TX-100 onto secondary fiber surface.The parameters in the two models were determined from the linear plots of qt versus lnt, and qt versus t 1/2 , respectively.It was observed that the adsorption of SDBS and TX-100 could not be followed by a forementioned two models in the presence or absence of Mg 2+ ions due to the low values of R 2 .The fitting results of intra-particle diffusion model indicated that the adsorption rate was not only controlled by intra-particle diffusion but also controlled by extra particle diffusion such as surface adsorption and liquid film diffusion. 40 42 .This was mainly because the rising temperature increased the solubility of SDBS in water which weaken the tendency of SDBS molecules escaping from water.Therefore, the trend of adsorption was declined.On the contrary, the equilibrium adsorption of TX-100 was increased from 1.019 to 1.220 mg• g -1 by rising temperatures.Such adsorption kinetics behavior had been reported by Partyka 43 and Corkill 44 .On the one hand, the solubility of TX-100 was gradually decreased with the temperature increasing within a certain range.Therefore, the hydration degree of polyoxyethylene chains was reduced which will lead to a promotion in hydrophobicity of TX-100 molecules.On the other hand, adsorption of solutes must be accompanied by desorption of water molecules.Increasing temperatures will decrease the adsorption of water molecules, and then enhance the adsorption of TX-100.Temperature had different effects on the physical and chemical properties of anionic and non-ionic surfactants such as solubility, CMC, molecular kinetic energy and so on, it also affected the swelling capacity of secondary fiber.Therefore, the above phenomenon of adsorption kinetics was the result of the combined effects of many factors.
According to the previous analysis of adsorption kinetics, adsorption of SDBS and TX-100 can be followed by the pseudo-second-order model.Fitting results of second-order model for adsorption of SDBS and TX-100 onto secondary fiber surface at different temperatures were presented in Table 5.It could be found that the adsorption of both surfactants followed the pseudo-second-order model well at different temperatures., the k2 values of both surfactants were gradually improved with the increase of temperature.This may be a result of increase in the mobility of surfactant molecules with higher temperature.Surfactant molecules may acquire sufficient energy to undergo an interaction with active sites at the surface.Such adsorption kinetics behavior had been reported earlier by Fava 23 and Meader 45 .

Activation Parameters
From the pseudo-second-order rate constant k2 in Table 5, the activation energy Ea(kJ• mol -1 ) for the adsorption of SDBS and TX-100 onto secondary fiber surface was determined using the Arrhenius equation 46,47 : Where A is Arrhenius constant, R is the molar gas constant (8.3145J• mol• K -1 ), T is the temperature of adsorption (K).By plotting lnk2 versus 1/T, and from the slope and the intercept, values of Ea can be obtained.
The Eyring equation 46 was used to calculate the standard enthalpy of activation (ΔH * , kJ• mol -1 ), entropy of activation (ΔS * , J• mol -  Where kB and h are the Boltzmann's constant and Planck's constant, respectively.The values of ΔH * and ΔS * were calculated from the slope and intercept of a plot of ln(k2/T) versus 1/T.
The free energy of activation (ΔG * , kJ• mol -1 ) was determined using the equation as follows 48 : * * * ΔG= ΔH -TΔS (12) Table 4. Fitting results of Elovich and intra-particle diffusion models for adsorption of SDBS and TX-100 onto secondary fiber surface R 2 SDBS (0.2g Table 6 shows the activation parameters for the adsorption of SDBS and TX-100 onto secondary fiber surface.It was observed that the values of Ea for the adsorption of SDBS and TX-100 were 20.89kJ• mol -1 and 21.83kJ• mol -1 , respectively.Low activation energies (5-40 kJ• mol -1 ) were characteristic for physisorption, while higher activation energies (40-800kJ• mol -1 ) suggested chemisorption 48 .Those low values of Ea suggested a diffusion controlled process, which was a physical step in the adsorption process.The positive value of ΔH * suggested that the adsorption of both surfactants was an endothermic process.The negative value of ΔS * indicated that molecules of SDBS and TX-100 at activated state on secondary fiber surface were always more organized than those in the bulk suspention phase.The positive values of ΔG * suggested the adsorption process require external energy to react, which could be achieved by shaking in the experiment and mechanical agitation in the industrial process.

CONCLUSIONS
The adsorption kinetics of SDBS and TX-100 fitted the pseudo-second-order model well.The effects of initial surfactant concentration, electrolyte and temperature on the adsorption rate were investigated.Results showed that the rate constants of both surfactants decreased with the increasing initial concentration and increased with the increasing temperature, respectively.The presence of Mg 2+ ions decreased the rate constant for SDBS but decreased that for TX-100.Equilibrium adsorption isotherms of SDBS onto secondary fiber surface could be subdivided into four regions.TX-100 exhibited a Langmuir-type equilibrium adsorption isotherm.In the presence of Mg 2+ ions, SDBS showed an increase in the maximum adsorption, while a decreased maximum absorption was observed for TX-100.Even at the maximum adsorption, multilayer adsorption did not occur in the presence or absence of Mg 2+ ions.
The fitting results indicated that the adsorption rate was not only controlled by intra-particle diffusion but also by extra particle diffusion.Activation parameters showed that the adsorption of SDBS and TX-100 onto secondary fiber surface was a typical diffusion-controlled process by an associative mechanism.The adsorption processes of both surfactants were endothermic in a temperature range commonly used in current flotation deinking processes.SDBS and TX-100 were mainly adsorbed onto the hydrophobic sites of the secondary fibers as a tail-down, head-out monolayer without the presence of Mg 2+ ions, which significantly decreased the fibers' hydrophobicity and reduced the fiber loss in the flotation deinking process.When using SDBS in the flotation process, the concentration of Mg 2+ ions should be maintained at a low level in order to prevent the rise in fiber hydrophobicity.

Table 2 .Fig. 3 .
Fig. 3. Possible adsorption sequences of SDBS and TX-100 on the secondary fiber surface

Fig. 6 Fig. 7
Fig. 6 Adsorption kinetics of SDBS onto secondary fiber surface at different temperatures

Table 1 .
Fitting results of adsorption isotherms of SDBS and TX-100 onto secondary fiber surface ① :practical qe got from experiment; qe,cal ② :qe calculated by formula 4 • K -1 ), It could be described as follows: www.Bioresources-Bioproducts.com 71

Table 5 .
Fitting results of second-order model for adsorption of SDBS and TX-100 onto secondary fiber surface at different temperatures

Table 6 .
Activation parameters for the adsorption of SDBS and TX-100 onto secondary fiber surface