Adsorption equilibrium and kinetic study of guaifenesin enantiomers on cellulose tris 3,5-dimethylphenylcarbamate packed column

Accepted Manuscript Adsorption equilibrium and kinetic study of guaifenesin enantiomers on cellulose tris 3,5-dimethylphenylcarbamate packed column Rujin Gong, Xiaojian Lin, Ping Li, Jianguo Yu, Alirio E. Rodrigues PII: DOI: Reference:

S1385-8947(14)00075-8 http://dx.doi.org/10.1016/j.cej.2014.01.050 CEJ 11692

To appear in:

Chemical Engineering Journal

Received Date: Revised Date: Accepted Date:

1 November 2013 16 January 2014 20 January 2014

Please cite this article as: R. Gong, X. Lin, P. Li, J. Yu, A.E. Rodrigues, Adsorption equilibrium and kinetic study of guaifenesin enantiomers on cellulose tris 3,5-dimethylphenylcarbamate packed column, Chemical Engineering Journal (2014), doi: http://dx.doi.org/10.1016/j.cej.2014.01.050

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1

Adsorption equilibrium and kinetic study of guaifenesin enantiomers on cellulose tris

2

3,5-dimethylphenylcarbamate packed column

3 4

Rujin Gong, Xiaojian Lin, Ping Li*, Jianguo Yu, Alirio E. Rodrigues

5 6

State Key Laboratory of Chemical Engineering, College of Chemical Engineering,

7

East China University of Science and Technology, Shanghai, 200237, China

8

E-mail: [email protected]

9

Phone/fax: +86-21-64250981

10 11

1

1

Abstract ： The chromatographic separation of guaifenesin enantiomers using

2

hexanes/ethanol mobile phase and cellulose tris 3,5-dimethylphenylcarbamate

3

stationary phase (Chiralcel OD) was investigated, where the column was packed with

4

particle size 20µm of chiral adsorbents. The adsorption equilibrium isotherms of

5

single enantiomer and racemic compounds of guaifenesin on Chiralcel OD stationary

6

phase were measured by the frontal analysis and the adsorption-desorption method,

7

respectively. Then, the experimental data were fitted with the Linear+Langmuir

8

isotherm model, and the relative model parameters for the competitive adsorption

9

equilibrium isotherm of guaifenesin enantiomers were obtained by the nonlinear

10

regression method. Both the elution and adsorption-desorption experiments for the

11

separation of guaifenesin enantiomers on the Chiralcel OD packed column were

12

carried out. The measured elution curves and adsorption-desorption profiles were

13

compared with the theoretical predictions by mathematical model, and adsorption

14

kinetics, separation efficiency, the effect of dead volume were discussed. According

15

to experiments and modeling, the competitive adsorption equilibrium and kinetics

16

information were acquired for the scale up and optimization of the separation of

17

guaifenesin enantiomers by both batch and continuous chromatographic system.

18

Keywords: Chiral separation; Equilibrium isotherm; Adsorption kinetics; Modeling;

19

Guaifenesin enantiomers; Chiralcel OD

20

2

1 2

1. Introduction Guaifenesin

(GUA),

(R,S)-3-(2-methoxyphenoxy)-propane-1,2-diol,

is

an

3

expectorant drug, and usually is taken orally to assist the bringing up of phlegm from

4

the airway in acute respiratory tract infections, which also can be used for sinusitis,

5

pharyngitis, and bronchitis [1-3]. Guaifenesin with a pair of enantiomers is

6

represented as R-(-)-GUA and S-(+)-GUA, respectively, as shown in Fig.1. Due to the

7

lack of research on the pharmacological properties of the individual enantiomers of

8

guaifenesin [4, 5], up to now, guaifenesin is used as an expectorant at the form of

9

racemate in cough remedy formulations. The development of chiral drugs as single

10

enantiomer is becoming a necessary trend in future. Therefore, the high efficient

11

technologies for the preparation of pure single guaifenesin enantiomer are becoming

12

more and more important.

13

With the rapid development of chiral separation for analysis and preparation,

14

chromatographic separation using chiral stationary phase has proven to be the most

15

popular technology [6-10]. Several kinds of stationary phases have been used

16

successfully for the separation of guaifenesin enantiomers, such as Chiralpak IA,

17

Chiralcel AD and Chiralcel OD. Miriam Zabkova group [11] separated the

18

guaifenesin racemate on the immobilized Chiralpak IA using n-heptane/ethanol as

19

mobile phase, where the adsorption equilibrium isotherm was described by Linear

20

model, and the lumped pore diffusion model (POR) was used to describe the dynamic

21

behavior of the fixed bed. Pedro Sa Gomes group [12] separated the racemic 3

1

guaifenesin on Chiralpak AD chromatographic column using n-heptane/ethanol

2

(85:15) as mobile phase, where the adsorption equilibrium isotherm was described by

3

Langmuir model, and the POR model was used to describe the dynamic behavior in

4

the packed column. Eric R. Francotte group [13, 14] used Chiralcel OD stationary

5

phase to separate guaifenesin enantiomers with heptane/ethanol (65:35) mobile phase,

6

where the competitive Langmuir adsorption isotherm model was determined, and the

7

feasibility of the separation process was validated. The knowledge of the adsorption

8

isotherms and kinetic information are acquired by these authors [11-14] are very

9

helpful for the design and optimization of the chromatographic separation process of

10

guaifenesin enantiomers [15-17].

11

Several reliable methods to determine the adsorption equilibrium isotherm,

12

including frontal analysis (FA), perturbation peak (PP), elution by characteristic

13

points (ECP), adsorption-desorption method, inverse method, have been used

14

frequently [18-20]. According to the experimental results, many adsorption isotherm

15

models have been proposed, such as Langmuir, Bi-Langmuir, Freundlich, Toth, etc.

16

Leonid Asnin [21] summarized a list of different isotherm models to describe the

17

dynamic equilibrium of solute between mobile phase and stationary phase in chiral

18

chromatography.

19

Various mathematical models have been developed to describe and predict the

20

adsorption behavior in chromatographic column [22-27], which is useful for both

21

analytical and preparative purposes. The general rate model (GR), is the most 4

1

complicated but accurate one, all the physicochemical phenomena involved in the

2

thermodynamics and kinetics of adsorption are considered in the separation process.

3

The GR model generally considers axial dispersion, film mass transfer resistance,

4

intraparticle diffusion, and the rate of adsorption-desorption. Because of its

5

complexity, it must take much more time to obtain the result of numerical solutions.

6

The lumped pore diffusion model (POR) is a simplification of the GR model for the

7

calculation of band profiles when the effective diffusion coefficient in the adsorbent is

8

sufficiently large. The POR model considers the mean value for the adsorbed

9

concentration of solute, not its actual distribution inside the pores, which makes the

10

numerical solution of POR much faster than that of the GR model. The equilibrium

11

dispersive model (ED) is the most popular when mass transfer resistances are small

12

and have a minor influence on the profiles. In many cases, the ED model is a good

13

approximation if the separation system has a high column efficiency. The work to

14

compare the GR, POR, ED models has been presented by Kaczmarski [28, 29]. In

15

addition, the extra-column dead volume is always larger in the industrial-scale

16

chromatographic separation process, so the effect of dead volume on the practical

17

operations cannot be negligible, otherwise, the high separation performance will not

18

be obtained [30-32]. In the case of the HPLC system, the transfer lines include two

19

parts: pump to the column (column head) and column to the detector (column tail). A

20

detail model is used to describe extra-column dead volume and evaluate its effect on

21

the separation performance. 5

1

In this work, adsorption isotherms of single and binary components of guaifenesin

2

enantiomers on cellulose tris 3,5-dimethylphenylcarbamate stationary phase

3

(Chiralcel OD) are determined, and the elution and adsorption-desorption experiments

4

for the separation of guaifenesin enantiomers are carried out and compared with the

5

theoretical predictions by the mathematical model. Based on the experimental and

6

theoretical research for the separation performance of guaifenesin enantiomers on

7

Chiralcel OD, the object is to acquire the competitive adsorption isotherm and kinetic

8

information.

9

2. Theoretical

10

2.1 Adsorption equilibrium isotherms

11

For the adsorption equilibrium isotherms of guaifenesin enantiomers on Chiralcel

12

OD stationary phase, there exists the concentration dependency of the selectivity.

13

Many models fail to account for the concentration dependency of the selectivity [33,

14

34]. It is found that the Linear+Langmuir model is suitable to describe this adsorption

15

behavior. The equation for pure compound is given as:

16

qi = H i ci +

17

Where, i is the number of components, qi (kg/m3) is the concentration of solute

18

adsorbed on the stationary phase, ci (kg/m3) is the concentration of solute in the

19

mobile phase, qs (kg/m3) is the saturation capacity on the enantioselective sites, Hi is

20

the equilibrium constant for the adsorption of enantiomers on the nonselective

qs bi ci 1 + bi ci

(1)

6

1

sites, bi (m3/kg) is the equilibrium constants on the enantioselective sites. qs , bi and

2

Hi are the model parameters determined by the experiments.

3

According to the adsorption equilibrium isotherm of single enantiomer with the

4

Linear+Langmuir model, the competitive adsorption equilibrium isotherm of two

5

enantiomers can be described as:

6

qi = H i ci +

7

Where, H1 , H 2 are the equilibrium constants of adsorption on the nonselective sites

8

for each enantiomer, b1 , b2 are the equilibrium constants on the enantioselective sites

9

for each component.

10

qs bi ci 1 + b1c1 + b2 c2

(2)

2.2 Mathematical model for chromatographic column

11

Mathematical model to describe the separation performance of guaifenesin

12

enantiomers in the chromatographic column is used with the consideration of the

13

extra-column dead volumes from transfer lines, as shown in Fig.2. In the case of the

14

HPLC system, the transfer lines include two parts: pump to the column (column head,

15

V1) and column to the detector (column tail, V2). The mass balances inside the

16

chromatographic column will be described using the general rate model (GR), the

17

lumped pore diffusion model (POR), and the equilibrium dispersive model (ED),

18

respectively. And the effect of the extra-column dead volume (V1, V2) caused by

19

transfer lines is described by the convection-diffusion model.

20

2.2.1 General rate model coupled with extra-column dead volume

7

1

The general rate model [35, 36] is the most general model of chromatography,

2

which consists of two differential mass transport equations, the partial differential

3

mass balance equations of the solute in the percolating mobile phase around the

4

particles and in the stagnant mobile phase inside the particles, as follows:

5

∂ci u ∂ci (1 − ε e ) 3 ∂ 2c + + k film,i [ci − c pi (r = rp )] = Dax ,i 2i ∂t ε e ∂x ∂x ε e rp

6

εp

7

Where ci (kg/m3) is the solute concentration in the mobile phase, c pi (kg/m3) is the

8

solute concentration in the stagnant fluid phase contained in the pores, qi (kg/m3) is

9

the solute concentrations in the solid phase in equilibrium with the stagnant fluid

∂c pi ∂t

+ (1 − ε p )

∂c pi ∂qi 1 ∂ 2 )] = 2 [r (ε p Deff ,i ∂t r ∂r ∂r

(3)

(4)

Deff ,i = Dm ,i ε p2 (1 − ε p ) 2 (m2/s) is the effective diffusion

10

phase at concentration c p i

11

coefficient (m2/s), k film,i = 1.09Dm,i (ε e d p )*(ε e vd p Dm,i )0.33 (m/s) is the external film

12

mass transfer coefficient, u (m/s) is the superficial velocity of mobile phase,

13

Dax,i (m2/s) is the axial dispersion coefficient, rp (m) is the equivalent particle radius,

14

external porosity ε e , internal porosity ε p , t (s) is the time, x (m) is the axial distance

15

along the column, and r (m) is the radial coordinate for particle.

16

Initial conditions are

17

t = 0, ci (t , x) = c pi (t , x, r ) = qi (t , x, r ) = 0

18

Boundary conditions for Eq.3 are:

19

∂ci = v(ci − c0 ) ∂x ∂c (t，x = L ) =0 x = L: i ∂x

20

,

(5)

x = 0 : Dax ,i

(6a) (6b) 8

1

Boundary conditions for Eq.4 are:

2

r = rp : k film ci − c pi ( t , x, rp )  = ε p Deff ,i

3

r = 0:

4

The convection-diffusion model [37] is used to describe the effect of the dead volume

5

in the connection tubes, as the following equation:

6

∂ci ∂c ∂ 2c + udead i = DL , dead 2i ∂t ∂x ∂x

∂c p i (t , x, 0) ∂r

=

2

∂c pi ( t , x, rp )

(6c)

∂r

∂qi (t , x, 0) =0 ∂r

2

(6d)

(7)

7

Where DL,dead = u d

8

udead (m/s) is the velocity of the mobile phase through the tube. Ldead (m) is the length

9

of the tubes.

2 192 Dm (m /s) is the axial dispersion coefficient in the pipes,

10

The initial and boundary conditions for Eq.7 are as follows:

11

t = 0, ci = 0

12

x = 0 : DL , dead

(9a)

13

x = Ldead

(9b)

14

2.2.2 Lumped pore diffusion model

(8)

∂ci = udead (ci − c0 ) ∂x ∂c (t , x = Ldead ) : i =0 ∂x

15

The lumped pore diffusion model (POR) is a simplification of GR model, which

16

considers a mean value for the adsorbed concentration, not its actual distribution

17

inside the pores [38, 39]. When the effective diffusion coefficient in an adsorbent

18

material is not too low, for example, Pe > 100

19

used to substitute the GR model [28, 29]. Here, Pe = uL ( Daxε e ) is the Peclet number,

20

St = kext a p Lε e u is the Stanton number, Bi = kext d p Lε e 2 Deff is the Biot number.

21

a p = 3 rp (m2/m3) is the surface area per unit volume of the adsorbent particles. 9

St Bi > 5 , the POR model can be

1

In POR model, the mass balances of the component in the mobile phase and solid

2

phase are written as follows:

3

∂ c pi ∂ci u ∂ci (1 − ε e ) ∂q ∂ 2c + + [ε p − (1 − ε p ) i ] = Dax,i 2i ∂t ε e ∂x ∂t ∂t ∂x εe

4

εp

5

Where ci (kg/m3) is the solute concentration in the mobile phase, c pi (kg/m3) is the

6

average concentration of the solute in the stagnant fluid phase contained in the pores,

7

qi (kg/m3) is the average concentrations of the solute in the solid phase in equilibrium

8

with the stagnant fluid phase at concentration c pi , keff ,i = 1 k film,i + 1 kint,i  is the

9

effective mass transfer coefficient (m/s), and kint,i = 10 Deff ,i d p is the internal mass

∂c pi ∂t

− (1 − ε p )

(10)

∂qi 3 = keff ,i (ci − c pi ) ∂t rp

(11)

−1

10

transfer coefficients (m/s).

11

2.2.3 Equilibrium dispersive model

12

The equilibrium dispersive model (ED) is another simplification of GR model,

13

easily derived from the POR model, where the contribution of band broadening due to

14

finite mass-transfer limitation and axial dispersion are lumped into an apparent axial

15

dispersion coefficient. The ED model is numerically equivalent to the POR model

16

when [28, 29] 500 > Pe > 100

17

St > 2000 or Pe > 500 1 + Bi / 5

St > 4000 . 1 + Bi / 5

In ED model, the mass balances of the component in the mobile phase and solid

18

phase are written as follows:

19

∂ci* u ∂ci* (1-εT ) ∂qi* ∂ 2 c* + + = Dax ,i 2i ∂t εT ∂x ∂x ε T ∂t

(12)

10

1

∂qi* 3 * * = k L ,i ( qeq , i − qi ) ∂t rp

(13)

2

* Where ci* (kg/m3) is the solute concentration in the mobile phase, qi (kg/m3) is the

3

* solute concentration adsorbed on the stationary phase, qeq ,i (kg/m3) is the adsorbed

4

phase concentration in equilibrium with the mobile phase at concentration ci* , total

5

-1 * porosity ε T , and k L ,i = keff ,i [ε p + (1 − ε p )(dqeq ,i dci )] (s ) is the overall mass transfer

6

coefficient.

7

Based on Samuelsson et al work [32], it is not possible to accurately account for

8

extra-column dispersion by the

9

2D-convection-diffusion model must be used, in particular for modern analytical

10

systems using short and narrow columns. In many practical separation problem [12,

11

30, 31], the preparative column with longer column length and larger inner diameter,

12

1D-convection-diffusion model is available to evaluate the effect of extra-column

13

dead volume on the separation performance with an acceptable accuracy. For

14

simplification, 1D-convection-diffusion model is used to evaluate the effect of the

15

extra-column dead volume in this work.

16

2.3 Numerical solution of the mathematical models

1D-convection-diffusion model,

instead

a

17

The mathematical models mentioned previously are solved using the software of

18

gPROMS 3.2 (PSE Enterprise, Ltd., London), which is a process modeling system

19

with proven capabilities for the simulation, optimization and parameter estimation of

20

highly complex processes. The partial differential equations are discretized into a set

21

of ordinary differential-algebraic equations through the discretization of the axial

22

domain. In this work, the discretization method of orthogonal collocation on finite 11

1

elements method (OCFEM) over a uniform grid of 30 intervals is used for the general

2

rate, equilibrium-dispersive, lumped pore diffusion models. Then, the set of ordinary

3

differential-algebraic equations are integrated by the DASOLV solver with the

4

absolute and relative tolerances of 10-5.

5

3. Experimental

6

3.1 Materials and apparatus

7

Guaifenesin (GUA, purity>98.0) are purchased from Tokyo Chemical Industry

8

Ltd., Japan, pure R-(-)-GUA and S-(+)-GUA enantiomer are prepared by the

9

simulated moving bed separation methods in our laboratory. The mobile phase is a

10

mixture of n-hexane/ethanol (70/30) solution, which are purchased from Sinopharm

11

Chemical Reagent Co. Ltd., Shanghai. Two kinds of chromatographic columns

12

packed with Chiralcel OD stationary phase are used, one is the preparative column

13

(150×10mm) with 20µm particle size, and another is the analytical column (150×

14

4.6mm) with 5µm particle size.

15

Dionex Ultimate 3000 HPLC system (Dionex Corporation, now Thermo Fisher

16

Scientific) is used for the experiments, which is equipped with a Dual gradient pump,

17

automatic injector, column compartment, UV detector. The experimental data are

18

obtained through the software of Chromeleon 6.80. Experimental temperature is

19

controlled by the column compartment at the constant temperature of 25.0℃ with

20

±0.1℃ accuracy. At the wavelength of 270nm, the wavelength is stable and the

21

absorbency is higher. 270 nm is considered as an optimal wavelength for the detection 12

1

of the guaifenesin enantiomers. The detector calibration curve is performed on an

2

analytical column (4.6×150mm) over the concentration range of 0-4.0 mg/ml with a

3

linear behavior. The samples collected during the experiments with the concentration

4

more than 4.0mg/ml should be diluted before analyzing by the analytical HPLC

5

system.

6

3.2 Measurement of adsorption equilibrium isotherms

7

The measurement of the adsorption isotherm is performed on a preparative column

8

(10×150mm). Adsorption equilibrium isotherm for each enantiomer is measured by

9

the multiple frontal analysis [40]. The pure guaifenesin sample is continuously fed

10

into the preparative column by increasing the concentration of enantiomer step by step,

11

and the samples from the packed column are collected and detected by the analytical

12

HPLC system. The amount of each enantiomer adsorbed on Chiralcel OD stationary

13

phase can be calculated by the following equation:

14

qi , j =

15

Where qi , j , qi , j −1 are the solute concentrations in the stationary phase after jth and

(Vi , Rj − Vm )(ci , j − ci , j −1 )

Va

+ qi , j −1

(14)

16

j − 1th step, ci , j

17

Vi ,Rj , Vm are the retention volume of the jth breakthrough curve and dead volume of

18

the column, respectively. Va is the volume of adsorbent (Chiralcel OD) packed

19

inside the preparative column.

,

ci, j −1 are the solute concentrations in mobile phase, respectively.

20

Adsorption-desorption method [41] is used to measure the competitive adsorption

21

isotherms of guaifenesin enantiomers. The concentration of guaifenesin racemate is at 13

1

the range of 0 to 7.80 mg/ml. The preparative column is saturated with a known

2

concentration of feed solution until the adsorption equilibrium is reached. Then, the

3

column is regenerated completely with the fresh mobile phase. During the

4

experiments, the samples from the packed column are collected and detected by the

5

analytical HPLC system. The quantity of the component in the column is calculated

6

by the following equation:

7

Q ∫ (Ci ,0 − Ci )dt = (1 − ε T )Vc qi + ε T VcCi ,0

t

(15)

0

8

Where Q (m3/s) is flow rate of the mobile phase, Vc (m3) is the column volume,

9

ci,0 (kg/m3) is the feed concentration of each enantiomer in the mobile phase.

10

3.3 Elution profile and adsorption-desorption experiments

11

Elution profile and adsorption-desorption curves are measured to evaluate the

12

separation performance of guaifenesin enantiomers on the Chiralcel OD preparative

13

column. The elution experiments of guaifenesin enantiomers are carried out with

14

different concentration of guaifenesin racemate and different injection period. The

15

adsorption-desorption experiments for pure guaifensin enantiomer and racemic

16

mixture are carried out with different feed concentration. The experimental

17

procedures are the same as the previous work [42]. During the experiments, the

18

samples from the packed column are collected and detected by the analytical HPLC

19

system, and experimental curves are obtained.

20

4. Result and discussion

21

4.1 Competitive adsorption isotherm 14

1

4.1.1 Adsorption isotherm of single guaifenesin enantiomer

2

The adsorption isotherm of pure guaifenesin enantiomer is measured by the frontal

3

analysis method on Chiralcel OD preparative column at 3.0 ml/min flow rate and

4

25.0℃. The adsorption equilibrium isotherms of the weaker adsorption enantiomer

5

(R-(-)-GUA) and the stronger adsorption enantiomer (S-(+)-GUA) are shown in Fig.3,

6

where the points represent the experimental data and the lines represent the predicted

7

results by the Linear+Langmuir model (Eq.16a and Eq.16b). According to the

8

experimental data, the model parameters are obtained by the nonlinear regression

9

method. There exists a good agreement between experimental data and the predicted

10

results using the Linear+Langmuir model, as shown in Fig.3.

11

qR −GUA = 1.2cR−GUA +

31.0 × 0.028cR−GUA 1 + 0.028cR −GUA

(16a)

12

qS −GUA = 2.2cS −GUA +

31.0 × 0.098cs −GUA 1 + 0.098cS −GUA

(16b)

13

4.1.2 Binary competitive adsorption isotherm

14

Usually, the competitive adsorption equilibrium isotherms of R-(-)-GUA and

15

S-(+)-GUA on Chiralcel OD stationary phase can be predicted by Eq.17a and Eq.17b,

16

which are derived based on the adsorption isotherm of pure enantiomer measured

17

previously. In this work, the binary competitive adsorption equilibrium data also are

18

measured by the adsorption-desorption method, as shown in Fig.4. It is found that the

19

predicted results by Eq.17a and Eq.17b fit the experimental data with the acceptable

20

accuracy. 15

1

qR −GUA = 1.2cR−GUA +

31.0 × 0.028cR −GUA 1 + 0.028cR−GUA + 0.098cS −GUA

(17a)

2

qS −GUA = 2.2cS −GUA +

31.0 × 0.098cS −GUA 1 + 0.028cR−GUA + 0.098cS −GUA

(17b)

3

4.2 Experiments and modeling for elution profiles and adsorption-desorption curves

4

4.2.1 Model parameters

5

Before predicting the separation performance of guaifenesin racemate on the

6

Chiralcel OD preparative column by the mathematical model, some important model

7

parameters, such as diffusion coefficient, mass transfer resistance coefficient et al.,

8

should be measured or estimated previously by the appropriate method.

9

The total porosity in the preparative column is measured by the pulse experiment

10

with TTBB (1.5mg/ml, 20µl injection amount) tracer, a non-retained compound on

11

Chiralcel OD stationary phase. The total porosity is obtained as ε T = 0.69 , the external

12

porosity is estimated as ε e = 0.44 , the porosity of the particles is estimated as

13

ε p = 0.45 , the experimental procedure can be found elsewhere [42].

14

The axial dispersion coefficient Dax ,i is measured based on Van Deemter equation

15

[43]. The theoretical plate number in the preparative column is measured with the

16

pulse experiments of guaifenesin enantiomers. According to the theoretical plates of

17

guaifenesin enantiomers under different flow rates, the values of dispersion

18

coefficients are estimated as shown in Table 1 and are almost constants at the range of

19

experimental concentrations, the detailed calculation method can be found elsewhere

20

[42]. 16

1

The mass transfer resistance coefficients are estimated by comparing the

2

adsorption-desorption experimental data of pure enantiomer with the predicted results

3

by three models, respectively. Here, the adsorption-desorption curves for single

4

enantiomer are measured under the conditions: CR-GUA=0.53mg/ml, feeding time

5

8.0min; CS-GUA=0.46mg/ml, feeding time 10.0min, and the results are shown in Fig.5a

6

and Fig.5b. The points represent the experimental data and the lines represent the

7

predicted results by three models (Dash dot line: ED model; Solid line: POR model;

8

Dash line: GR model). The mass transfer coefficients are estimated initially from

9

empire equations, and the best values are obtained by fitting the experimental data

10

with the numerical results. The effective diffusion coefficient, Deff ,i in the GR

11

model is estimated using the same method. The estimated parameters for three

12

mathematical models are summarized in Table 1.

13

4.2.2 Elution profiles

14

Pulse experiments with different concentrations of guaifenesin enantiomers and

15

different injection times are carried out, and the elution curves of R-(-)-GUA

16

enantiomer and S-(+)-GUA enantiomer on Chiralcel OD preparative column are

17

measured, as shown in Fig.6a-c, where the experimental conditions are listed in Table

18

2. Fig.6a and Fig.6b show that R-(-)-GUA enantiomer and S-(+)-GUA enantiomer

19

can be separated by the Chiralcel OD preparative column when the pulse time of feed

20

is set 1.0 min. With the increase of the pulse time, such as 4.0 min, R-(-)-GUA

17

1

enantiomer and S-(+)-GUA enantiomer cannot be separated completely, as shown in

2

Fig.6c.

3

The measured elution curves are compared with the theoretical predictions by the

4

general rate (GR), equilibrium-dispersive (ED), lumped pore diffusion（POR）models

5

coupled with extra-column dead volume, respectively, as shown in Fig.6a-c. The

6

theoretical predictions by three models fit the experimental data with an acceptable

7

accuracy, although there are the obvious difference among the predicted results of

8

peak height by three models. The POR model can be used to substitute the GR model

9

since the ratio of St and Bi is more than 160. Comparing ED model with POR model,

10

there is a little difference because of the value of St (1 + Bi) as 752 less than the

11

criterion. The CPU running times of computer for solving three models are presented

12

in Table 2, it is found that GR model with a high accuracy requires a longer

13

computing time, almost 40 times than that of ED and POR model.

14

Pulse chromatograms under different feed concentrations are compared by

15

simulation, as shown in Fig.7. The effect of nonlinearity on the profiles is observed

16

with the increase of the feed concentration. Under the concentration of 7.8 mg/ml for

17

each enantiomer, the chromatographic peak represents the tail and becomes

18

asymmetry. On the other hand, the retention time of S-(+)-GUA decreases slightly

19

with the increase of the feed concentration.

20

4.2.3 Adsorption-desorption curves

18

1

Adsorption-desorption curves of guaifenesin enantiomers on Chiralcel OD

2

preparative column are measured with the different concentrations of feed at

3

3.0ml/min flow rate, where the experimental conditions are listed in Table 2. At the

4

lower concentration of feed, for example CR-GUA=1.00mg/ml, CS-GUA=1.00mg/ml, the

5

experimental data and the predicted results by ED, GR, POR models, present a good

6

agreement in Fig.8a. At the higher concentration of feed, for example

7

CR-GUA=7.80mg/ml, CS-GUA=7.80mg/ml, there is a roll up for the R-(-)-GUA

8

breakthrough curve due to the competitive adsorption between R-(-)-GUA and

9

S-(+)-GUA enantiomers under nonlinear condition. The predicted results given by ED,

10

POR and GR models are almost the same. In Fig.8b, the small discrepancies between

11

experimental data and calculation can be found for the stronger adsorption component

12

(S-(+)-GUA) at the period when S-(+)-GUA eluted out of the column.

13

4.3 Influence of extra-column dead volume on separation performance

14

In the above mentioned theoretical prediction for the elution curves and

15

adsorption-desorption profiles, the GR, ED and POR models are coupled with the

16

extra-column dead volume in order to improve the accuracy of the modeling. Fig.9

17

and Fig.10 show the effect of the extra-column dead volume in the experimental

18

system on the separation performance of guaifenesin enantiomers in the Chiralcel OD

19

preparative column, where the theoretical prediction is done using the ED model

20

coupled with or without the dead volume. In the HPLC system, the connection tubes

21

include two parts: pump to the column (column head, V1) and column to the detector 19

1

(column tail, V2), and the lengths of the connection tube lines are measured and listed

2

in Table 3. Here, two cases are discussed, Case 1 dealing with 1/16〞connection tubes

3

in the experimental system, and Case 2 dealing with 1/8〞connection tubes (assumed

4

condition).

5

According to the simulated results with 1/16〞connection tubes, it is found that the

6

profiles delay 15 seconds approximately. If the length of the tubes is kept the same

7

and the connection tubes of 1/16〞is replaced with 1/8〞×ID 1.75mm tubes, the

8

simulated results are presented at the same condition of flow rate and concentration,

9

as shown in Dash dot lines in Fig.9-10. The longer delay time about 50 seconds is

10

observed, which can be explained by the decreasing of linear velocity through tube

11

with the increasing of the diameter of tube. In the work of Samuelsson et al [32], it

12

was also observed that the injection profiles became more eroded as the increase of

13

flow rate, and the effect of the flow rate is not as dramatic under the experimental

14

injection volume of 200µl. By comparison, more than fifteen times volume of the

15

guaifenesin solution were injected in our work, the effect of different flow rate would

16

be slight. Moreover, the effect of dead volume obtained by 1-D-concection-diffusion

17

indicates that the elution curve becomes more eroded with the increasing of the inner

18

diameter of the tube, as shown in Fig.9 and Fig.10. The result is in an agreement with

19

Samuelsson’s work that the injection profiles become more eroded with increasing

20

inner diameter of the loop capillary.

20

1

The dead volume existing in system means when collecting the corresponding

2

pure components in single column chromatography, the delay time caused by

3

extra-column dead volume should be taken into consideration. Otherwise, high purity

4

and high recovery performance of the target component can’t be obtained. Certainly,

5

the influence of extra-column dead volume can be minimized by reducing the length

6

of connection tube or increasing the flow rate of feed appropriately.

7

5. Conclusion

8

According to the experimental and simulated results, guaifenesin (GUA)

9

enantiomers can be separated on Chiralcel OD preparative column, where S-(+)-GUA

10

enantiomer is the more retained component, and R-(-)-GUA enantiomer is the less

11

retained component. The competitive adsorption equilibrium isotherms of guaifenesin

12

enantiomers on Chiralcel OD stationary phase can be described using the

13

Linear+Langmuir model (Eq.17a and Eq.17b) with an acceptable accuracy.

14

The elution curves and adsorption-desorption curves of guaifenesin enantiomers

15

from Chiralcel OD preparative column are measured using Dionex Ultimate 3000

16

HPLC system. The experimental data are compared with the predicted results by

17

general rate (GR) model, equilibrium dispersive (ED) model, lumped pore diffusion

18

(POR) model, with the consideration of extra-column dead volume effect,

19

respectively. It is found that the developed mathematical models coupled with the

20

measured competitive adsorption isotherms, can predict the separation process with

21

an acceptable accuracy. Based on the experimental and theoretical research for the

22

separation performance of guaifenesin enantiomers on Chiralcel OD packed column,

23

the kinetic information, such as dispersion coefficient and mass transfer resistance

24

coefficient are obtained (listed in Table 1), that will be useful for the scale up and 21

1

optimization of both batch and continuous chromatographic separation of guaifenesin

2

enantiomers.

3

Acknowledgements

4 5

This study is financially supported by the National Natural Science Foundation of China (Grant No. 21276080).

22

1

References

2

[1] L. Kagan, E. Lavy, A. Hoffman, Effect of mode of administration on guaifenesin

3

pharmacokinetics and expectorant action in the rat model, Pulm. Pharnacol. Ther. 22

4

(2009) 260-265.

5

[2] P.V. Dicpinigaitis, Y.E. Gale, Effect of guaifenesin on cough reflex sensitivity,

6

CHEST 124 (2003) 2178-2181.

7

[3] M. Hatami, K. Farhadi, A. Abdollahpour, Using dispersive liquid-liquid

8

microextraction and liquid chromatography for determination of guaifenesin

9

enantiomers in human urine, J. Sep. Sci. 34 (2011) 2933-2939.

10

[4] W. P. Shum, H. Mazurek, J. Chen, Process for producing enantiomerically

11

enriched guaifenesin, EP Patent EP0704420 A1, April 3, 1996.

12

[5] I. Demian, High-Performance Liquid Chromatography (HPLC) Chiral Separations

13

of Guaifnesin, Methocarbamol and Racemorphan, Chirality 5 (1993) 238-240.

14

[6] M. Schulte, J. Strube, Preparative enantioseparation by simulated moving bed

15

chromatography, J. Chromatogr. A 906 (2001) 399-416.

16

[7] A. Rajendran, G. Paredes, M. Mazzotti, Simulated moving bed chromatography

17

for the separation of enantiomers, J. Chromatogr. A 1216 (2009) 709-738.

18

[8] L. Asnin, G. Guichon, Chromatographic separation of phenylpropanol

19

enantiomers on a quinidine carbamate-type chiral stationary phase, J. Chromatogr. A ,

20

1091 (2005) 11-20.

23

1

[9] L. Asnin, K. Kaczmarski, G, Guiochon, The adsorption of Naproxen enantiomers

2

on the chiral stationary phase Whelk-O1 under revered-phase conditions: The effect

3

of buffer composition, J. Chromatogr. A 1217 (2010) 7055-7064.

4

[10] K. Mihlbachler, K. Kaczmarski, A. Seidel-Morgenstern, G. Guiochon,

5

Measurement and modeling of the equilibrium behavior of the Trö ger's base

6

enantiomers on an amylase-based chiral stationary phase, J. Chromatogr. A 955 (2002)

7

35-52.

8

[11] M. Zabkova, M. Zabka, A.E. Rodrigues, Separation of Racemic Chiral Durgs

9

Using Immobilized CHIEALPAK IA: Methodology for Preparative Scale

10

Deveopment, Sep. Sci. Technol. 44 (2009) 275-303.

11

[12] P.S. Gomes, M. Zabkova, M. Zabka, M. Minceva, A.E. Rodrigues, Separation of

12

Chiral Mixtures in Real SMB Units: The FlexSMB-LSRE, AIChE J. 56 (2010)

13

125-142.

14

[13] E. Francotte, P. Richert, M. Mazzotti, M. Morbidelli, Simulated moving bed

15

chromatographic resolution of a chiral antitussive, J. Chromatogr. A 796 (1998)

16

239-248.

17

[14] E. Francotte, P. Richert, Application of simulated moving bed chromatography to

18

the separation of the enantiomers of chiral drugs, J. Chromatogr. A 769 (1997)

19

101-107.

24

1

[15] G. Duan, C.B. Ching, S. Swarup, Kinetic and equilibrium study of the separation

2

of propranolol enantiomers by high performance liquid chromatography on a chiral

3

adsorbent, Chem. Eng. J. 69 (1998) 111-117.

4

[16] C.V. Gonalves, M.J.S. Carpes, C.R.D. Correa, C.C. Santana, Determination of

5

the kinetic and equilibrium parameters of the n-boc-rolipram enantiomers on a chiral

6

stationary phase by high performance liquid chromatography, Chem. Eng. J. 133

7

(2007) 151-156.

8

[17] C.V. Goncalves, M.J.S Carpes, C.R.D. Correa, C.C. Santana, Purification of

9

n-boc-Rolipram racemate on Chiral stationary phase using simulated moving bed

10

chromatography under linear conditions, Biochem. Eng. J. 48 (2008) 526-536.

11

[18] T. Fornstedt, Characterization of adsorption processes in analytical liquid-solid

12

chromatography, J. Chromatogr. A 1217 (2010) 1217, 792-812.

13

[19] J. Samuelsson, R. Arnell, T. Fornstedt, Potential of adsorption isotherm

14

measurements for closer elucidating of binding in chiral liquid chromatographic phase

15

systems, J. Sep. Sci. 32 (2009) 1491-1506.

16

[20] A. Seidel-Morgenstern, Experimental determination of single solute and

17

competitive adsorption isotherms, J. Chromatogr. A 1037 (2004) 255-272.

18

[21] L. Asnin, Adsorption model in chiral chromatography, J. Chromatogr. A 1269

19

(2012) 3-25.

25

1

[22] A. Cavazzini, G. Bardin, K. Kaczmarski, P. Szabelski, M. Al-Bokari, G.

2

Guiochon, Adsorption equilibria of butyl- and amylbenzene on monolithic

3

silica-based columns, J. Chromatogr. A 957 (2002) 111-126.

4

[23] K. Miyabe, G. Guiochon, Kinetic study of the mass transfer of bovine serum

5

albumin in anion-exchange chromatography, J. Chromatogr. A 866 (2000) 147-171.

6

[24] G. Guiochon, Preparative liquid chromatography, J. Chromatogr. A 965 (2002)

7

129-161.

8

[25] C. Shene, A. Lucero, B.A. Andrews, J.A. Asenjo, Mathematical modeling of

9

Elution Curves for a Protein Mixture in Ion Exchange Chromatography and for the

10

Optimal Selection of Operational Conditions, Biotechnol. Bioeng. 95 (2006) 704-713.

11

[26] C.A. Orellana, C. Shene, J.A. Asenjo, Mathematical Modeling o Elution Curves

12

for a Protein Mixture in Ion Exchange Chromatography Applied to High Protein

13

Concentration, Biotechnol. Bioeng. 104 (2009) 572-581.

14

[27] C. Migliorini, M. Mazzotti, G. Zenoni, M.P. Pedeferri, M. Morbidelli,

15

Modeling Chromatographic Chiral Separations under Nonlinear Competitive

16

Conditions, AIChE J. 46 (2000) 1530-1540.

17

[28] K. Kaczmarski, D. Antos, Modified Rouchon and Rouchon-like algorithms for

18

solving different models of multicomponent preparative chromatography, J.

19

Chromatogr. A 756 (1996) 73-87.

26

1

[29] K. Kaczmarski, D. Antos, H. Saionz, P. Sajonz, G. Guiochon, Comparative

2

modeling of breakthrough curves of bovine serum albumin in anion-exchange

3

chromatography, J. Chromatogr. A 925 (2001) 1-17.

4

[30] Y.-II. Lim, S.K. Bhatia, Effect of dead volume on performance of simulated

5

moving bed process, Adsprorption 17 (2011) 109-120.

6

[31] C. Migliorini, M. Mazzotti, M. Morbidelli, Simulated Moving-Bed Units with

7

Extra-Column Dead Volume, AIChE J. 45 (1999) 1411-1421.

8

[32] J. Samuelsson, L. Edstrom, P. Forssen, T. Fornstedt. Injection profiles in liquid

9

chromatography. I. A fundamental investigation, J. Chromatogr A 1217 (2010)

10

4306-4312.

11

[33] R.M. Nicoud, A. Sedel-Morgenstern, Adsorption isotherm ： Experimental

12

determination and application to preparative chromatography, Isol. & Purif. 2 (1996)

13

165-200.

14

[34] M. Zabka, A.E. Rodrigues, Thermodynamic and Kinetic Study of Adsorption of

15

R,S-α-Tetralol Enantiomers on the Chiral Adsorbent CHIRALPAK AD, Sep. Sci.

16

Technol. 42 (2007) 739-768.

17

[35] X.L. Du, Q.P. Yuan, Y. Li, Mathematical Analysis of Solanesol Adsorption on

18

Macroporous Resins Using the General Rate Model, Chem. Eng. Technol. 31 (2008)

19

1310-1318.

27

1

[36] K. Kaczmarski, M. Gubernak, D.M. Zhou, G. Guiochon, Application of the

2

general rate model with the Maxweill-stefan equations for the prediction of the band

3

profile of the 1-indanol enantiomers, Chem. Eng. Sci. 58 (2003) 2325-2338.

4

[37] S. Katsuo, C. Langel, P. Schanen, M. Mazzotti, Extra-column dead volume in

5

simulated moving bed separations: Theory and experiments, J. Chromatogr. A 1216

6

(2009) 1084-1093.[38] D.M. Zhou, D.E. Cherrak, K. Kaczmarski, A. Cavazzini, G.

7

Guiochon, Prediction of the band profiles of the mixtures of the 1-indanol

8

enantiomers from data acquired with the single racemic mixture, Chem. Eng. Sci. 58

9

(2003) 3257-3272.

10

[39] A. Cavazzini, K. Kaczmarski, P. Szabelski, D.M. Zhou, X. Liu, G. Guiochon,

11

Modeling of the separation of the enantiomers of 1-phenyl-1-propanol on Cellulose

12

Tribenzoate, Anal. Chem. 73 (2001) 5704-5715.[40] P. Sajonz, G.M. Zhong, G.

13

Guiochon, Influence of the concentration dependence of the mass transfer properties

14

on chromatographic band profiles: II. Accuracy of the determination of isotherm data

15

by frontal analysis, J. Chromatogr. A 731 (1996) 1-25.

16

[41] A.E. Ribeiro, N.S. Graca, L.S. Pais, A.E. Rodrigues, Preparative separation of

17

ketoprofen enantiomers: Choice of mobile phase composition and measurement of

18

competitive adsorption isotherms, Sep. Purif. Technol. 61 (2008) 375-383.

19

[42] R.J. Gong, P. Li, J.G. Yu, Experiment and modeling for the separation of

20

trans-stilbene oxide enantiomers on Chiralcel OD preparative column, J. Chromatogr.

21

A 1286 (2013) 119-126. 28

1

[43] G. Guiochon, S.G. Shirazi, A.M. Katti, Fundamentals of Preparative and

2

Nonlinear Chromatography; Academic Press: Boston, 2006.

3

29

1

Figure Captions

2

Fig.1 Chemical structure of guaifenesin enantiomers

3

Fig.2 Schematic diagram for the module of chromatographic column and the

4

extra-column dead volume

5

Fig.3 Adsorption equilibrium isotherms for R-(-)-guaifenesin and S-(+)-guaifenesin

6

on Chiralcel OD stationary phase at 25.0℃. Symbol: experimental data, line:

7

Linear+Langmuir model, Eq.16a and Eq.16b

8

Fig.4 Binary competitive adsorption isotherm for guaifenesin racemate on Chiralcel

9

OD stationary phase at 25.0 ℃ . Symbol: experimental data, Line:

10

Linear+Langmuir model, Eq.17a and Eq.17b

11

Fig.5 Adsorption-desorption curve of pure R-GUA enantiomer and S-GUA

12

enantiomer on Chiralcel OD at 25.0℃. Points: experimental data. Dash dot

13

line: ED model; Solid line: POR model; Dash line: GR model

14

(a) CR-GUA=0.53mg/ml, feeding time 8.0min

15

(b) CS-GUA=0.46mg/ml, feeding time 10.0min

16

Fig.6 Elution curves of guaifenesin enantiomers on from the Chiralcel OD at 25.0℃.

17

Points: experimental data. Dash dot line: ED model; Solid line: POR model;

18

Dash line: GR model

19

(a) CR-GUA=2.21mg/ml, CS-GUA=2.21mg/ml, pulse time 1.0min

20

(b) CR-GUA=4.21mg/ml, CS-GUA=4.23mg/ml, pulse time 1.0min

21

(c) CR-GUA=2.21mg/ml, CS-GUA=2.21mg/ml, pulse time 4.0min

22

30

1

Fig.7 Elution curves of guaifenesin enantiomers on Chiralcel OD packed column

2

under different feed concentration at 25.0℃.

3

Solid line: CR-GUA=2.21mg/ml, CS-GUA=2.21mg/ml, pulse time 1.0min

4

Dash dot line: CR-GUA=4.21mg/ml, CS-GUA=4.23mg/ml, pulse time 1.0min

5

Dash line: CR-GUA=7.80 mg/ml, CS-GUA=7.80mg/ml, pulse time 1.0min

6

Fig.8 Adsorption-desorption curves of guaifenesin enantiomers on Chiralcel OD at

7

25.0℃. Points: experimental data. Dash dot line: ED model; Solid line: POR

8

model; Dash line: GR model

9

(a) CR-GUA=1.00mg/ml, CS-GUA=1.00mg/ml

10

(b) CR-GUA=7.80mg/ml, CS-GUA=7.80mg/ml

11

Fig.9 Elution curve of guaifenesin enantiomers on Chiralcel OD calculated by ED

12

model with or without the effect of extra-column dead volume (experimental

13

conditions same as Fig.6a). Points: experimental data. Solid line: ED model,

14

Dash line: ED model with dead volume of 1/16" tube. Dash dot line: ED model

15

with dead volume of 1/8" tube

16

Fig.10 Adsorption-desorption curves of guaifenesin enantiomers on Chiralcel OD

17

calculated by ED model with or without the effect of extra-column dead volume

18

(experimental conditions same as Fig.7a). Points: experimental data. Solid line:

19

ED model, Dash line: ED model with dead volume of 1/16" tube. Dash dot line:

20

ED model with dead volume of 1/8" tube

21

31

1 2

Fig.1

32

1 2

Fig.2

3

33

1 2

Fig.3

3

34

1 2

Fig.4

3

35

1

2 3

Fig.5

4

36

1 2

3

4 5

Fig.6

37

1 2

Fig.7

3

38

1

2

3 4

Fig.8

5

39

1 2

Fig.9

3

40

1 2

Fig.10

3

41

1 2

Table Captions

Table 1 Parameters used in the mathematical models

3

Table 2 Experimental conditions and Computation time for the separation of

4

guaifenesin enantiomers on the Chiralcel OD preparative column

5

Table 3 The information of extra-column dead volume in HPLC system

6

42

1

Table 1 Parameters L×d (mm) dp (um) εT εe εp kfilm (s-1) kL,R-GUA (s-1) kL,S-GUA (s-1) keff,R-GUA (s-1) keff,S-GUA (s-1) DL,dead (cm2/s) Dax,R-GUA (cm2/s) 2 Dax,S-GUA (cm2/s) Deff,S-GUA (cm2/s) 2 Deff,S-GUA (cm2/s)

LDF 150×10 20 0.69 0.44 0.45

POR 150×10 20 0.69 0.44 0.45

GR 150×10 20 0.69 0.44 0.45 0.0403

0.00014 0.00025

2.25×102 3.69×10-4 2.75×10-4

Method

Experimental measurement

Empire equation Numerical fitting

0.00034 0.00096 2.25×102 2.25×102 3.69×10-4 3.69×10-4 2.75×10-4 2.75×10-4 1.73×10-7 5.13×10-7

2

2 3

43

Numerical fitting

Empire equation Experimental measurement Numerical fitting

1

Table 2 Run

1 2 3 4

1 2 1 2

Pulse time CR-GUA CS-GUA Computation time (min) (mg/ml) (mg/ml) (s) Pulse experiments GR POR ED 1.0 2.21 2.21 Fig.6a 11983 252 223 1.0 4.21 4.23 Fig.6b 11246 242 213 4.0 2.21 2.21 Fig.6c 12764 248 225 7.80 7.80 4.21 4.23 1.0 Fig.7 2.21 2.21 Adsorption-desorption experiments 15.0 1.00 1.00 Fig.8a 13392 331 301 15.0 7.80 7.80 Fig.8b 13825 335 284 Extra-dead volume analysis (calculated by ED model) 1.0 2.21 2.21 Fig.9 15.0 1.00 1.00 Fig.10

2 3

44

1

Table 3 Extra dead volume Pipe range(cm) Pipe diameter(cm) Case 1 Column head (V1) 87.8 OD 1/16〞×ID 0.75 Column tail (V2) 72.0 OD 1/16〞×ID 0.75 Case 2 Column head (V1) 87.8 OD 1/8〞×ID 1.75 Column tail (V2) 72.0 OD 1/8〞×ID 1.75

2 3

45

1

Highlights

2

(1) Adsorption isotherm of racemic guaifenesin on Chiralcel OD was measured.

3

(2) Adsorption kinetic of racemic guaifenesin on Chiralcel OD was studied.

4

(3) Separation process of racemic guaifenesin was predicted by chromatographic

5 6 7

model. (4) Chromatographic model included the column model and extra column dead

volume.

8

46