^{1}

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In order to explore internal factors for adsorption kinetic effect of miglitol by D001 resin, a batch adsorption operation for miglitol kinetic adsorption at different concentrations, temperatures and vibrating rates was investigated in oscillator (SHZ-A), respectively. The different kinetic mathematical model, Webber-Morris kinetic equation, film diffusion coefficient equation and kinetic boundary model were all applied to discuss the adsorption process. The results showed that Type 1 pseudo-second order kinetic equation can be all used to describe miglitol adsorbed by D001 resin at different concentrations, temperatures and vibrating rates. Moreover, the total activation energy (Ea) can be calculated and its value is 9.7 kJ/mol, and then calculated values of the process film diffusion coefficient and pore diffusion coefficient, it may be inferred from these gotten values that the ion exchange process is all mainly controlled by film diffusion. Therefore, the results also suggest that the external adsorption factors such as solute concentration, temperature and vibrating rate for effect of mass transfer diffusion process control of miglitol onto D001 resin are relatively weak.

Miglitol ((2R, 3R, 4R, 5S)-1-(2-hydroxyethyl)-2-(hydroxymethyl) piperidine- 3,4,5-triol, CAS No.7 2432-03-2 ) is a desoxynojirimycin derivative, also competitively inhibits glucoamylase and sucrase but has weak effects on pancreatic α-amylase, it is the first pseudomonosaccharide α-glucosidase inhibitor, smooths postprandial peak plasma glucose levels and thus can improve glycaemic control, Miglitol is generally well tolerated and is not associated with bodyweight gain or hypoglycaemia as monotherapy. Meanwhile, the drug is also systemically absorbed and not metabolised, also is rapidly excreted via the kidneys [

As known that adsorption of cation ion exchange resin is a suitable technology for the separation of N-substituted-1-desoxynojirimycin and miglitol [

The D001 resin (Na^{+} form) was purchased from Sunresin Technol. Ltd., Xi’an, China. The chemical and physical properties of the resin are similar to those of Amberlite IR200 resins [_{4} and NaOH were used to aid the content determination of miglitol, and all other reagents in the experiment were of analytical grade. The constant temperature bath oscillator (SHZ-A) was used for adsorption process studies, The content of miglitol was determined at 610 nm by the double-beam UV-Vis spectrophotometer (TU-1900) [

Fixed 200 mg resin into the different conical flasks (250 mL), miglitol was diluted by the distilled water and formed experimental set concentration solution. The adsorption process factors of different concentrations (4 mmol/L, 6 mmol/L, 8 mmol/L), different temperatures (30˚C, 40˚C, 50˚C) and different vibrating rates (80 rmp, 120 rmp, 160 rmp) were investigated in batch adsorption experiment, respectively. The adsorbed solutions were taken 1 mL by pipette at different time intervals and were measured by spectrophotometer at 610 nm. The process adsorption capacity at time t by D001 resins was as follows:

q t = C 0 V 0 − [ C n V n + ∑ i = 1 n − 1 C i V i ] W (1)

where q_{t} (mmol/g) is the adsorption capacity of resin at time t, C_{0} (mmol/L) and V_{0} (L) are the initial concentration and volume of miglitol solution, C_{n} (mmol/L) and V_{n} (L) are the concentration and volume of remaining miglitol solution at time n, C_{i} (mmol/L) and V_{i} (L) correspond with the substance concentration and volume of the taken solution sample at time i, W is the weight of resin.

The pseudo-first order equation for solid-liquid adsorption system was firstly proposed by Lagergren in 1989 [

d q t d t = k 1 ( q e − q t ) (2)

where q e (mmol/g) is the amount of adsorbate adsorbed at equilibrium, q t (mmol/g) is the amount of adsorbate adsorbed at time t. k 1 (g/mmol・h) is rate constant for the Lagergren equation. Integrating Equation (2) with the following boundary condition:

1) t = 0 , q t = 0

2) t = t , q t = q t

The linear equation is obtained:

log ( q e − q t ) = log q e − k 1 t 2.303 (3)

If t → 0 , the initial rate (h1) is [

h 1 = k 1 q e (4)

As k 1 ( q e − q t ) cannot stand for total active site of adsorbent, and at the same time log q e in Equation (3) is the adjustable parameter and often finds that its value is not equal to intercept value by linear regression with log ( q e − q t ) and t. The values of log q e must be intercept value if the equation is the first-order kinetic equation. Therefore, in order to distinguish the first-order equation, and the above Lagergren equation is also called the pseudo-first order equation. The pseudo-first order equation can only be used for estimating rate constant k 1 and not estimate q e value.

The pseudo-second order equation was firstly proposed by Ho and McKay [

d q t d t = k 2 ( q e − q t ) 2 (5)

where k 2 (g^{2}/mmol^{2}・h) is rate constant for the pseudo-second order equation.

Integrating Equation (5) with the following boundary condition:

1) t = 0 , q t = 0

2) t = t , q t = q t

The following equation can be gotten:

t q t = 1 k 2 q e 2 + t q e (6)

If t → 0, the initial rate (h_{2}) is

h 2 = k 2 q e 2 (7)

The Equation (7) is substituted into Equation (6) and obtains Type 1 pseudo-second order equation, the equation can be written as:

t q t = 1 h 2 + t q e (8)

By means of linear fitting with t q t and t, the gotten results may use for

calculating values of q e and k 2 , respectively.

In addition, the above pseudo-second order equation can also transform other four types of pseudo-second order equation by a series of transformation. These equations are separately as follows:

The Type 2 pseudo-second order equation is:

1 q t = 1 h 2 t + 1 q e (9)

The Type 3 pseudo-second order equation is:

1 t = h 2 q t − h 2 q e (10)

The Type 4 pseudo-second order equation is:

q t t = h 2 − h 2 q e q t (11)

The Type 5 pseudo-second order equation is:

1 ( q e − q t ) = 1 q e + k 2 t (12)

The Elovish equation was generally applied to chemisorption kinetic analysis [

d q t d t = α exp ( − β q t ) (13)

where α (mmol/g・h) is initial adsorption rate, β (g/mmol) is desorption constant. As far as chemical adsorption is concerned, the β value is relate to adsorption activation energy and covering content of adsorbate onto adsorbent surface.

By assuming α β t ≫ 1 , and Integrating Equation (13) with the following boundary condition:

1) t = 0 , q t = 0

2) t = t , q t = q t

The above Equation (13) can be transformed into the following equation:

q t = 1 β ln ( α β ) + 1 β ln t (14)

The kinetic constant values of α and β can be estimated by linear fitting with q_{t} and t.

As far as ion exchange adsorption process is concerned, it is very important to understand transfer direction and transfer rate of adsorbate for exploring mass transfer mechanism during adsorption process. The kinetic boundary model is widely applied to judge control step of mass transfer rate [

Film diffusion: ln ( 1 − F ) = − k t (15)

Particle pore diffusion: 1 − 3 ( 1 − F ) 2 / 3 + 2 ( 1 − F ) = k t (16)

Chemical reaction: 1 − ( 1 − F ) 1 / 3 = k t (17)

There into, k is mass transfer rate constant, F is called ion exchange degree, the corresponding equation is written as:

F = C 0 − C t C 0 − C e (18)

The established relationship between F and t from the kinetic boundary model may be used to judge main mass transfer process by correlation coefficient (R^{2}) during ion exchange. The main mass transfer process corresponds with the slowest diffusion, and its process means the largest mass transfer resistance.

Meanwhile, there are different mass transfer rate constants with at different experimental temperatures. The corresponding activation energy (E_{a}) can be calculated by Arrhenius equation [

k = A exp ( − E a / R T ) (19)

where R is a ideal gas constant, A is a constant. Equation (19) can be rewritten to a linear form from which the activation energy can be calculated from the slope, the equation expression is:

ln k = − E a R T + ln A (20)

The calculated value of E_{a} can also be used to determine ion exchange control step [_{a} < 16.0 kJ/mol. It is for particle pore diffusion at 21.0 kJ/mol < E_{a} < 38.0 kJ/mol, and at E_{a} > 50.0 kJ/mol, it belongs to chemical reaction control.

In addition, the activation entropy change value ( Δ S * ) can be estimated by the following equation and the calculated value A by the above Arrhenius equation. The equation is defined as [

A = ( 2.72 d 2 K T h ) exp ( Δ S * R ) (21)

where K (1.38 × 10^{−23} J/K) is Boltzmann constant, h (6.62 × 10^{−34}) is Plank constant. d is for the average distance of the ion exchange active site, and its value is generally taken as 5 × 10^{−10} m, T is absolute zero degree , its value is set to 273 K.

The ion exchange process at different initial concentrations of miglitol solution onto resin D001 resin was investigated and was analysized by the kinetic adsorption mathematical models, and the results are shown in Figures 1-3. At the same time, the parameters are got by kinetic equation fitting and are given in _{1} and h_{1} increase with enhancing the initial concentration solution of miglitol, and their change trends are closely related to the value of initial solution concentration and concentration difference between solution adsorbate and absorbent surface. Meanwhile, _{e}_{,exp}) is not equal to the theoretical adsorption capacity(q_{e}_{,exp}) gotten from pseudo-first order kinetic equation. The result further proves the ion exchange process is not adapted to first-order kinetic equation. In addition, the

parameter values of k_{2} and h_{2} were calculated by Type 1 pseudo-second order kinetic equation vary with the same change trend for values of k_{1} and h_{1} in _{e}_{,cal} and q_{e}_{,exp} is showed from

On the other hand, the ion exchange behavior is discussed at different initial concentrations for miglitol solution onto D001 resin by Webber-Morris particle pore diffusion model [

q t = k i d t 0.5 + C (22)

where k i d (mmol/g・min^{0.5}) is internal diffusion rate constant. C is an intercept of the equation, its value is related to the boundary layer thickness of particle, the external mass transfer resistance is directly proportional to the size of the value.

Supposing substance diffusion process is only controlled by particle internal pore diffusion, at this time, the relationship between q t and t 0.5 can present

Kinetic models | Parameters | C_{0} (mmol/L) | ||
---|---|---|---|---|

4 | 6 | 8 | ||

Pseudo-first order: log ( q e − q t ) = log q e − k 1 t 2.303 | q_{e}_{,exp} (mmol/g) | 1.86 | 2.68 | 2.76 |

q_{e}_{,cal} (mmol/g) | 1.29 | 1.69 | 2.13 | |

k_{1} (g/mmol・h) | 1.28 | 2.42 | 2.95 | |

h_{1} (1/h) | 1.64 | 4.09 | 6.28 | |

R^{2} | 0.9980 | 0.9925 | 0.9967 | |

Type-1 pseudo-second-order: t q t = 1 h 2 + t q e | q_{e}_{,exp} (mmol/g) | 1.86 | 2.68 | 2.76 |

q_{e}_{,cal} (mmol/g) | 1.90 | 2.70 | 2.78 | |

k_{2} (g^{2}/mmol^{2}・h) | 2.48 | 5.49 | 7.05 | |

h_{2} (1/h) | 8.97 | 40.00 | 54.50 | |

R^{2} | 0.9998 | 0.9999 | 0.9999 | |

Type 2 pseudo-second-order: 1 q t = 1 h 2 t + 1 q e | q_{e}_{,exp} (mmol/g) | 1.86 | 2.68 | 2.76 |

q_{e}_{,cal} (mmol/g) | 2.00 | 2.94 | 2.94 | |

k_{2} (g^{2}/mmol^{2}・h) | 1.67 | 1.66 | 2.36 | |

h_{2} (1/h) | 6.67 | 14.32 | 20.45 | |

R^{2} | 0.9974 | 0.9606 | 0.9778 | |

Type 3 pseudo-second-order: 1 t = h 2 q t − h 2 q e | q_{e}_{,exp} (mmol/g) | 1.86 | 2.68 | 2.76 |

q_{e}_{,cal} (mmol/g) | 1.97 | 2.95 | 2.92 | |

k_{2} (g^{2}/mmol^{2}・h) | 1.68 | 1.49 | 2.28 | |

h_{2} (1/h) | 6.53 | 12.97 | 19.45 | |

R^{2} | 0.9974 | 0.9606 | 0.9778 | |

Type 4 pseudo-second-order: q t t = h 2 − h 2 q e q t | q_{e}_{,exp} (mmol/g) | 1.86 | 2.68 | 2.76 |

q_{e}_{,cal} (mmol/g) | 1.97 | 2.90 | 2.92 | |

k_{2} (g^{2}/mmol^{2}・h) | 1.67 | 1.68 | 2.36 | |

h_{2} (1/h) | 6.52 | 14.13 | 20.12 | |

R^{2} | 0.9961 | 0.9488 | 0.9901 | |

Type 5 pseudo-second-order: 1 ( q e − q t ) = 1 q e + k 2 t | q_{e}_{,exp} (mmol/g) | 0.86 | 2.68 | 2.76 |

k_{2} (g^{2}/mmol^{2}・h) | 11.79 | 73.72 | 53.03 | |

h_{2} (1/h) | 40.57 | 529.02 | 403.73 | |

R^{2} | 0.8639 | 0.8459 | 0.8092 | |

q_{e}_{,exp} (mmol/g) | 1.86 | 2.68 | 2.76 | |

Elovich q t = 1 β ln ( α β ) + 1 β ln t | q_{e}_{,cal} (mmol/g) | 2.03 | 2.93 | 2.84 |

α (mmol/g・h) | 16.68 | 71.32 | 96.25 | |

β (g/mmol) | 2.50 | 2.08 | 2.00 | |

R^{2} | 0.9959 | 0.9277 | 0.9747 |

the straight line through the origin, and C is equal to zero. Meanwhile, the corresponding pore diffusion coefficient ( D p , cm^{2}/min) can be calculated, the calculating equation expression is:

k i d = 6 q e r 0 D p π (23)

where r_{0} is the radius of particle, and the value is generally set to 0.05 cm.

The graph between q t and t 0.5 at different initial concentrations about miglitol solution was plotted before reaching adsorption equilibrium. The results are shown in

C 0 (mmol/L) | k i d (mmol/g・min^{0.5}) | r 0 (cm) | D p × 1 0 6 (cm^{2}/min) | C (mmol/g) | R^{2 } |
---|---|---|---|---|---|

4 | 0.09 | 0.05 | 0.50 | 0.700 | 0.9546 |

6 | 0.12 | 0.05 | 0.43 | 1.428 | 0.8545 |

8 | 0.14 | 0.05 | 0.50 | 1.434 | 0.9333 |

However, the calculating value D p in

Furthermore, the film diffusion coefficient can be calculated by film diffusion coefficient equation during ion exchange [

D f = 0.23 r 0 δ t 1 / 2 C ¯ C 0 (24)

where D f (cm^{2}/min) is film diffusion coefficient, δ (cm) is a film thickness, the δ value is set to 10^{−3} cm for the spherical particle adsorbent. t 1 / 2 (min) is the corresponding time for reaching halfway of adsorption capacity in the total ion exchange process. C ¯ is the solute quantity adsorbed by adsorbent particles. C_{0} is an initial concentration for miglitol solution.

The experimental ion exchange was discussed by Type 1 pseudo-second order kinetic equation and film diffusion coefficient, the related parameters results are shown in ^{−6} cm^{2}/min to 10^{−8} cm^{2}/min, the ion exchange process is regarded as pore diffusion control at D p value from 10^{−11} cm^{2}/min to 10^{−13} cm^{2}/min [^{−6} to 10^{−8} cm^{2}/min in

The ion exchange process at different temperatures was investigated and the adsorption data gotten at the above experimental condition was analysed by the kinetic boundary model. The fitting result was obtained and the corresponding correlation coefficients were presented in

C 0 (mmol/L) | C ¯ (mmol/L) | r 0 (cm) | t 1 / 2 (min) | D f × 1 0 6 (cm^{2}/min) |
---|---|---|---|---|

4 | 3.71 | 0.05 | 12.6 | 0.8 |

6 | 5.36 | 0.05 | 4.05 | 2.53 |

8 | 5.52 | 0.05 | 3.06 | 2.59 |

Temperature | Correlation coefficient (R^{2}) | ||
---|---|---|---|

− ln ( 1 − F ) | 1 − 3 ( 1 − F ) 2 / 3 + 2 ( 1 − F ) | 1 − ( 1 − F ) 1 / 3 | |

30˚C | 0.986 | 0.93 | 0.89 |

40˚C | 0.97 | 0.92 | 0.898 |

50˚C | 0.97 | 0.97 | 0.94 |

for film diffusion and particle pore diffusion gradually come close each other with the increase experimental temperature. It can be concluded with increasing temperature that the mass transfer mechanism in ion exchange process is transferred gradually from film diffusion control to particle pore diffusion control. The main reason is that the mutual collision probability for solute molecules in particle pore and repulsion role of molecules each other all increase with the adding temperature, and hinders the external solute molecules to pass into the pore particle. The mass transfer resistance increases and leads to decrease for diffusion rate of solute molecules in particle pore. Therefore, the phenomenon in the whole ion exchange process emerges from film diffusion to the common control with particle pore diffusion and film diffusion.

In addition, the rate constant at different temperatures were obtained by the linear slope in

Moreover, the ion exchange process is analysed further by Type 1 pseudo-second order kinetic Equation (8) and the gotten drawing and the corresponding parameters are shown in _{t} and t is displayed the gradual increasing slope and has higher fitting degree by Equation (8) with the increase temperature. Their correlation coefficients reach over 0.99, and it finds that the difference between the theory adsorption capacity for D001 resins (q_{e}_{,cal}) and the gotten experimental value (q_{e}_{,exp}) is very small. This indicates that the Type 1 pseudo-second order kinetic equation can be used to describe the ion exchange process for miglitol onto D001 resin at different temperatures, and it is the same to the gotten results at different concentrations. The initial rate and the rate constant are all influenced obviously by experimental temperature. The initial rate h_{2} declines apparently with the increase temperature and the rate constant reaches maximum at 40˚C. Meanwhile, the film diffusion constant is calculated by Equation (24) and shown in ^{−6} to 10^{−8} cm^{2}/min, and the ion exchange process is regarded as the film diffusion control, its inference is consistent with the gotten conclusion by the kinetic boundary model.

The adsorption process at different vibrating rate was discussed and analysed by

Temperature (˚C) | q_{e}_{,cal} (mmol/g) | k_{2} (g^{2}/mmol^{2}・h) | h_{2} (1/h) | R^{2} | q_{e}_{,exp} (mmol/g) |
---|---|---|---|---|---|

30 | 2.70 | 5.49 | 40.00 | 0.9999 | 2.68 |

40 | 1.65 | 9.69 | 26.30 | 0.9999 | 1.64 |

50 | 1.52 | 2.80 | 6.49 | 0.9983 | 1.48 |

Temperature (˚C) | C 0 (mmol/L) | C ¯ (mmol/L) | r 0 (cm) | t 1 / 2 (min) | D f × 10 6 ^{}(cm^{2}/min) |
---|---|---|---|---|---|

30 | 6 | 5.36 | 0.05 | 4.05 | 2.53 |

40 | 6 | 3.28 | 0.05 | 3.76 | 1.68 |

50 | 6 | 2.96 | 0.05 | 14.00 | 0.40 |

Type 1 pseudo-second order kinetic equation, the gotten process parameters were shown in _{2} and rate constant k_{2} all gradually increase with the boosting vibrating rate, and also affects mass transfer distinctly.

The film diffusion coefficient Equation (24) was used to calculate film diffusion coefficients in the experimental conditions, and was presented in _{2} and h_{2}. At the same time, the calculated film diffusion coefficients is also existed in 10^{−6} and 10^{−8} cm^{2}/min, and the ion exchange process at different vibrating rates are regarded as film diffusion control too. The main reason is due to the selected adsorption resin D001 that belongs to a macroporous resin, and there is relatively weak adsorption resistance into the macroporous resin, ion exchange rate appears very fast and leads to complete the ion exchange very quickly within a very short time. The above a series of analysis can be concluded that the external adsorption factors such as solute concentration, temperature and vibrating rate for effect of mass transfer diffusion process control of miglitol onto D001 resin is relatively weak.

In the present work, a batch adsorption operation at the different influence factors for concentrations, temperatures and vibrating rate in the constant temperature bath oscillator (SHZ-A) has been performed for miglitol adsorption by resin D001. The experimental results showed that Type 1 pseudo-second order kinetic equation can be all used to describe miglitol adsorbed by D001 resin at different concentrations, temperatures and vibrating rates. Moreover, Webber-Morris kinetic equation, film diffusion coefficient equation and kinetic boundary model were also applied to discuss the adsorption process, and then calculated values of the process film diffusion coefficient and pore diffusion coefficient, the total activation energy (E_{a}) can be calculated and its value is 9.7 kJ/mol. The ion exchange process is all mainly controlled by film diffusion. The external adsorption factors such as solute concentration, temperature and vibrating rate for effect of mass

Vibrating rate (rmp) | q_{e}_{,cal}_{ } (mmol/g) | k_{2} (g^{2}/mmol^{2}・h) | h_{2} (1/h) | R^{2} | q_{e}_{,exp} (mmol/g) |
---|---|---|---|---|---|

80 | 2.94 | 0.39 | 3.4 | 0.9963 | 2.68 |

120 | 2.70 | 5.49 | 40.0 | 0.9999 | 2.68 |

160 | 2.70 | 5.97 | 43.5 | 0.9999 | 2.68 |

Vibrating rate (rmp) | C 0 (mmol/L) | C ¯ (mol/L) | r 0 (cm) | t 1 / 2 (min) | D f × 10 6 ^{}(cm^{2}/min) |
---|---|---|---|---|---|

80 | 6 | 5.36 | 0.05 | 51.16 | 0.20 |

120 | 6 | 5.36 | 0.05 | 4.05 | 2.53 |

160 | 6 | 5.36 | 0.05 | 3.73 | 2.74 |

transfer diffusion process control of miglitol onto D001 resin is relatively weak.

We acknowledge the financial supports from the special fund of education department of Shaanxi province (16JK1510) and the nurturing fund projects of Xi’an University of Science and Technology (2014022) in China.

Zhang, J.B., Ren, X.B., Wang, G.H. and Zhang, X.L. (2017) Ion Exchange Adsorption Kinetics of Miglitol by D001 Resins. Advances in Chemical Engineering and Science, 7, 420-438. https://doi.org/10.4236/aces.2017.74030