CN105388240B - The computational methods of chromatographic peak width available for the optimization of area of computer aided condition of gradient elution - Google Patents
The computational methods of chromatographic peak width available for the optimization of area of computer aided condition of gradient elution Download PDFInfo
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Abstract
According to non-linear solvent strength model and theoretical cam curve or according to the peak width variation model under non-linear solvent strength model and isocratic condition, the chromatographic peak width under different condition of gradient elution is calculated.Gained peak width is used for the calculating of separating degree, and is applied among the optimization of area of computer aided condition of gradient elution using separating degree as evaluation index.The invention has the advantages that：1. it is accurate to calculate.Non-linear solvent model can the retention behavior of accurate description sample on a column, so as to help to improve the precision of theoretical prediction.It is 2. applied widely.Calculating available for the chromatographic peak width under arbitrary shape gradient curve.3. good practice operability.At least 3 isocratic elution experiments is only needed to be achieved with the parameter value needed for theoretical calculation.This method is applied among the optimization of area of computer aided condition of gradient elution, can quickly search out the best condition of gradient elution for meeting and putting into practice separation demand.The invention discloses its methods.
Description
Technical field
The present invention relates to the computational methods for the chromatographic peak width that can be used for condition of gradient elution optimization in liquid chromatogram.Specifically
It says, is according to non-linear solvent strength model and theoretical cam curve or according to non-linear solvent strength model and isocratic elution
Under the conditions of peak width variation model, predict Arbitrary Gradient elution requirement under chromatographic peak width.Gained peak width can be used for separating degree
It calculates, and is applied among the optimization of area of computer aided condition of gradient elution using separating degree as evaluation index.
Background technology
Gradient elution is a kind of important operation pattern of liquid chromatogram.In this mode, what flowing phase composition can at any time
Change and change.The advantages of gradient elution is the time that can shorten analysis and the width for reducing chromatographic peak, therefore in reality
Have a wide range of applications (Chen X, Kong L, Su X, et al.J Chromatogr A, 2005,1089,87-100 in trampling；
Ma Yan, Zhang Wanjun, defend military camp, and Niu Ming waits chromatographies, 2011,29,205-211；Shen Danhong, Lu Xin, Chang Yuwei wait chromatographies,
2014,32,40-46)。
Compared with another operation mode isocratic elution of liquid chromatogram, the separating mechanism of gradient elution is complicated many.
This is because in gradient elution, solute bands of a spectrum will be by bands of a spectrum caused by condition of gradient elution " pinch effect " and mass transfer mistake
The joint effect of bands of a spectrum caused by journey " broadening effect ", and there is only the influences of bands of a spectrum " broadening effect " for isocratic elution.In gradient
In elution, the width of chromatographic peak (will be expressed as washing by force by solvent strength, i.e. sample retention factors (k) with flowing phase composition
Volume ratio of the desolventizing in mobile phase,) between relationship, the shape of gradient curve, height equivalent to a theoretical plate (H) is with mobile phase
The variation of composition and gradient delay time (tD) etc. factors influence.At present, about in the research of gradient elution, solvent is strong
Linearly, i.e., degree model is usually set to
Wherein lnk0With S be solvent strength parameter, subfixRepresent the flowing phase composition corresponding to it.Gradient simultaneously
Curve is set to single linear, i.e.,
WhereinFor initial flow phase composition, B is the slope of gradient, and t is the time, and Φ (t) is sets in transfusion system
Gradient program.Under the premise of it is assumed that H does not change with the change of flowing phase composition, Poppe proposes following mathematics
Formula, using calculate single linear gradient and solvent strength as linear bands of a spectrum compressibility factor (G) (Poppe H, Paanakker J,
Bronckhorst M.J.Chromatogr.1981,204:77-84)
The wherein calculation formula of p is
In above formulaThe retention factors for being sample in liquid phase.Under being substituted by the G values that (3) formula is calculated
Face (5) formula, can obtain the chromatographic peak width W under single linear condition of gradient elutionG(Zhu P L,Snyder LR,Dolan J W,et
al.J Chromatogr A,1996,756,21-39；Neue U D,Marchand D H；Snyder L R.J
Chromatogr A, 2006,1111,32-39),
N is theoretical cam curve in above formula, and J is empirical parameter, t0For the dead time of chromatographic column,Chromatographic column is flowed out for solute
When corresponding retention factors.
It may be noted that there are still comparable limitations in practical application for above-mentioned (1)-(5) formula.First, it is many to study
It is a kind of approximate description to sample chromatogram retention behavior to show linear solvent strength model.It is molten in many application examples
Agent intensity often show nonlinear feature (Nikitas P, Pappa-Louisi A.J Chromatogr A, 2009,
1216,1737-1755；Nikitas P,Pappa-Louisi A,Agrafiotou P,et al.J Chromatogr A,
2011,1218,5658-5663).It is a kind of non-linear solvent strength is typically described mathematical model be
WhereinIt is for flowing phase compositionWhen retention factors, lnk0、S1And S2For solvent strength parameter.Next, (1)-
(5) formula is only applicable to the calculating of chromatographic peak width under single linear gradient condition.And for any form of gradient combination, such as
Wherein i be gradient serial number, n be gradient number, tPFor the time coordinate value of node on gradient curve, (1)-(5) formula
Then no longer it is applicable in.In addition, many researchs also indicate that height equivalent to a theoretical plate (H) can also change with the change of flowing phase composition
Become (Poppe H, Paanakker J, Bronckhorst M.J Chromatogr, 1981,204,77-84；Gritti F,
Guiochon G.J Chromatogr A, 2009,1216,6124-6133), while gradient delay time (tD) to chromatographic peak width
Influence be also not included among (3) formula, these will all limit the application in practice of (1)-(5) formula.
By studying the mass transfer dynamics in gradient elution, inventors herein propose as follows suitable for any form of
Solvent strength model, gradient curve shape, height equivalent to a theoretical plate with flowing phase composition variation and consider gradient postpone when
Between the height equivalent to a theoretical plate equation (Hao W, Di B, Chen Q, the et al.J.Chromatogr.A, 2013,1295,67- that influence
81；Hao W,Di B,Chen Q,et al.Analyst,2014,139,1504-1511；Hao W,Di B,Yue B,et
al.J.Chromatogr.A,2014,1369:191-195),
Wherein HapFor the apparent height equivalent to a theoretical plate under condition of gradient elution, tRFor retention time, in symbol H and k under
It is designated as the flowing phase composition corresponding to it.On the basis of (8) formula, it can obtain
Wherein WIFor the chromatographic peak width measured under isocratic condition.(9) formula proposes that Arbitrary Gradient elutes item for the present invention
Good theoretical foundation has been established in the calculating of chromatographic peak width under part.In addition, inventor also proposed a kind of area of computer aided ladder
Spend the method (application for a patent for invention number 201510126615.3) of elution requirement optimization.By this method with it is proposed by the invention
The computational methods of chromatographic peak width are combined, and help to improve the precision of prediction, quickly search out the best ladder for meeting practice demand
Elution requirement is spent, so as to greatly shorten the time that separation condition is groped, improves the efficiency of work.
Invention content
The object of the present invention is to provide the calculating sides of the chromatographic peak width optimized available for area of computer aided condition of gradient elution
Method.This method is according to non-linear solvent strength model and theoretical cam curve or according to non-linear solvent strength model and isocratic
Peak width variation model under elution requirement, calculates the chromatographic peak width under different condition of gradient elution.This method have calculate it is accurate,
The features such as applied widely, easy to operate.This method is applied among the optimization of area of computer aided condition of gradient elution, had
Help quickly establish the condition of gradient elution for meeting and putting into practice separation demand.
The technical scheme is that：
The computational methods of chromatographic peak width available for the optimization of area of computer aided condition of gradient elution, include the following steps：
A. retention time and chromatographic peak width of the determination sample under different isocratic conditions, calculates corresponding retention factors
And theoretical cam curve；
B. according to isocratic elution experimental data, fitting obtains solvent strength mould of the description retention factors with flowing composition variation
The peak width variation model that chromatographic peak width changes with flowing phase composition under type ((6) formula) and description isocratic condition,
Wherein a, b, c are constant；
C. the chromatographic peak width under different condition of gradient elution, Huo Zhegen are calculated according to solvent strength model and theoretical cam curve
The chromatographic peak width under different condition of gradient elution is calculated according to the peak width variation model under solvent strength model and isocratic condition,
Obtained chromatographic peak width is used for the calculating of separating degree, and is applied to area of computer aided gradient strip by evaluation index of separating degree
Among the optimization of part.
The above-mentioned chromatographic peak width calculated according to solvent strength model and theoretical cam curve under different condition of gradient elution, it is special
Sign is, the chromatographic peak width (W under isocratic conditionI) relationship between k is described by following formula,
Wherein N is theoretical cam curve.(11) formula substitution (9) formula is obtained
With reference to solvent strength model (6) formula, so as to calculate the chromatographic peak width (W under different condition of gradient elutionG)。
The above-mentioned peak width variation model according under solvent strength model and isocratic condition calculates different gradient elution items
Chromatographic peak width under part, it is characterised in that (6) formula and (10) formula are substituted into (9) formula, so as to calculate under different condition of gradient elution
Chromatographic peak width (WG)。
The invention has the advantages that：
1. it is accurate to calculate.The present invention is with non-linear solvent strength model (i.e. (6) formula) description retention factors and mobile phase group
Relationship between, this more meets with practical situation, so as to help to improve the precision of theoretical prediction.Meanwhile chromatographic peak width
Calculation formula (i.e. (9) formula) in introduce gradient delay time (tD) influence, this also will be helpful to reduce theoretical value and reality
Test the error between value.
It is 2. applied widely.(9) formula is suitable for the calculating of the chromatographic peak width under arbitrary shape gradient curve, this is just breached
(1)-(5) formula may be only available for the limitation of single linear gradient.Method proposed by the invention is applied to area of computer aided ladder
It spends among the optimization of elution requirement, the shape of gradient curve can be optimized (such as (7) formula), so as to contribute to the maximum extent
Improve the efficiency that gradient elution detaches in practice.
3. good practice operability.At least 3 isocratic elution experiments is only needed to be achieved with theoretical calculation in practice to want
The parameter value (lnk i.e. in (6) formula0、S1And S2, the N in (12) formula and a, b and c in (10) formula), it is easy to operate easily
Row.In practice, the computational methods of two kinds of chromatographic peak widths proposed in the present invention can complement one another.When in isocratic elution experiment
It, can be according to the peak width variation model under solvent strength model and isocratic condition when there is good separating degree between chromatographic peak
The chromatographic peak width under condition of gradient elution is calculated, so as to obtain best precision of prediction.And when chromatographic peak in isocratic elution experiment
Between separating degree it is poor when, at this moment can be according to solvent strength model and reason since the coefficient in (10) formula is difficult to Accurate Determining
The chromatographic peak width under condition of gradient elution is calculated by the number of plates, so as to obtain good precision of prediction.
Description of the drawings
Table 1 is the coefficient value of the solvent strength model corresponding to the 12 kinds of compounds measured in embodiment 1.
Table 2 is the theoretical cam curve of the chromatographic column measured in embodiment 1 using 12 kinds of compounds as sample.
Table 3 is the coefficient value of the peak width variation model corresponding to the 12 kinds of compounds measured in embodiment 1.
Fig. 1 is the gradient curve employed in embodiment 2.
Fig. 2 is the experiment chromatogram (a) obtained in embodiment 2 and the comparison of theoretical chromatogram (b and c).B is schemed according to table 1
In non-linear solvent strength model and table 3 in isocratic condition under peak width variation model calculate condition of gradient elution under
Chromatographic peak width.Scheme non-linear solvent strength models and theoretical cam curve (be set as 10000) of the c in table 1 and calculate gradient
Chromatographic peak width under elution requirement.Compound corresponding to chromatographic peak：1st, P-hydroxybenzoic acid；2nd, parahydroxyben-zaldehyde；3rd, vanilla
Acid；4th, caffeic acid；5th, vanillic aldehyde；6th, syringic acid；7th, syringaldehyde；8th, p-Coumaric Acid；9th, Acetovanillone；10th, acetyl cloves
Ketone；11st, ferulic acid；12nd, sinapic acid.
Fig. 3 is the gradient curve employed in embodiment 3.
Fig. 4 is the experiment chromatogram (a) obtained in embodiment 3 and the comparison of theoretical chromatogram (b and c).Symbol description is same
Fig. 2.
Specific embodiment
With reference to example, the present invention will be further described.Example is only limitted to illustrate the present invention rather than to the present invention's
It limits.
Embodiment 1
12 kinds of compounds such as P-hydroxybenzoic acid are dissolved in 20% methanol aqueous solution, concentration is 50 μ g/mL.Using island
Tianjin Prominence liquid chromatographs detach this 12 kinds of compounds.Chromatographic condition：Chromatographic column, Welch Ultimate
XB-C18(4.6×150mm,5μm)；Mobile phase, 1% acetic acid aqueous solution (solvent A) and 1% acetic acid methanol solution (solvent B)
Mixed solution；Flow velocity, 0.8mL/min；Column temperature, 35 DEG C；Detection wavelength, 280nm；Sample size, 2 μ L.By solvent B in mobile phase
Volume ratio be set to 10%, 15%, 20%, 25% and 30% after carry out isocratic elution experiment, obtained solvent strength mould
Type, the theoretical cam curve of chromatographic column and peak width variation model are shown in Table 1-3.
Embodiment 2
Gradient curve as shown in Fig. 2, other experiment conditions with embodiment 1.Under the condition of gradient elution, test what is measured
The chromatogram of 12 kinds of compounds is shown in Fig. 2 a.According to the non-linear solvent strength model and isocratic condition obtained in embodiment 1
Under peak width variation model, calculate the chromatographic peak width under the condition of gradient elution, obtained theoretical chromatogram is shown in Fig. 2 b.According to reality
The non-linear solvent strength model obtained in example 1 and theoretical cam curve (being set as 10000) are applied, is calculated under the condition of gradient elution
Chromatographic peak width, obtained theoretical chromatogram is shown in Fig. 2 c.In Fig. 2 b and Fig. 2 c, the peak area of chromatographic peak is set as 1.
Embodiment 3
The method (application for a patent for invention number 201510126615.3) of appliance computer auxiliary condition of gradient elution optimization is right
Number of nodes is that the shape of 5 gradient curve optimizes.In optimization process, using separating degree as evaluation index, separating degree calculates
Non-linear solvent strength model and peak width variation model of the required peak width value in embodiment 1, which calculate, in the process obtains.
Other experiment parameters are the same as embodiment 1.The best gradient curve that the method for appliance computer auxiliary optimization obtains is shown in Fig. 3.In the ladder
It spends under elution requirement, tests the chromatogram of 12 kinds of compounds measured and see Fig. 4 a.According to non-linear solvent strength model and peak width
Variation model and according to real non-linear solvent strength model and theoretical cam curve (being set as 10000), calculates the gradient respectively
Chromatographic peak width under elution requirement, obtained theoretical chromatogram are shown in Fig. 4 b and 4c.
It can see by the result of embodiment 1, non-linear solvent strength model can be more preferable than linear solvent strength model
Ground description flowing phase composition changes the influence to sample chromatogram retention behavior.The obtained square value of related coefficient is fitted by the former
0.999 is all higher than, and the latter is then less than 0.999 mostly.Therefore, condition of gradient elution is calculated based on non-linear solvent strength model
Under chromatographic peak width, it will help reduce the error between theoretical value and experiment value.Table 2 the experimental results showed that, chromatographic column
Theoretical cam curve can occur to change to some extent with flowing phase composition and the change of sample type, and numerical value is on 10000 left sides
It is right.Table 3 the result shows that, using pass of (11) formula between the chromatographic peak width that is measured under isocratic condition and flowing phase composition
System's description, the square value of obtained related coefficient are all higher than 0.999.Therefore, which can be well to isocratic condition
Lower chromatographic peak width is described with the variation behavior of flowing phase composition.
Can see by the result of embodiment 2 and 3, using it is proposed by the invention according to non-linear solvent strength model and
Peak width variation model under isocratic condition calculates chromatographic peak width under condition of gradient elution and strong according to non-linear solvent
Model and theoretical cam curve computer chromatography peak width are spent, obtained theoretical value is coincide substantially with experiment value.Therefore, the present invention is carried
The two kinds of computational methods gone out are respectively provided with good precision of prediction.
In example 2, when being eluted using common single linear gradient, 5 and 6 separating degree of compound is poor.And
In embodiment 3, by the way that chromatographic peak width computational methods proposed by the invention are applied to area of computer aided condition of gradient elution
Optimization among, it can be achieved that the optimal separation of 12 kinds of compounds.It can be seen that by method and computer aided manufacturing proposed by the invention
Optimization method is helped to be combined, helps quickly to search out best condition of gradient elution, so as to greatly shorten lightning strip in practice
The time that part is groped improves the efficiency of work.
Claims (3)
1. the computational methods of the chromatographic peak width for the optimization of area of computer aided condition of gradient elution, include the following steps：
A. retention time and chromatographic peak width of the determination sample under different isocratic conditions, calculates corresponding retention factors and reason
By the number of plates；
B. according to isocratic elution experimental data, fitting obtains solvent strength model of the description retention factors with flowing composition variation,
And the peak width variation model that chromatographic peak width changes with flowing phase composition under description isocratic condition,
WhereinTo flow phase composition,It is for flowing phase compositionWhen retention factors, lnk0、S1、S2, a, b, c be constant,It is to flow phase composition under isocratic conditionWhen chromatographic peak width；
C. according to the chromatographic peak width under solvent strength model and the different condition of gradient elution of theoretical cam curve calculating or according to molten
Peak width variation model under agent strength model and isocratic condition calculates the chromatographic peak width under different condition of gradient elution, by institute
Obtained chromatographic peak width is used for the calculating of separating degree, and is applied to area of computer aided gradient condition by evaluation index of separating degree
Among optimization.
2. the computational methods of the chromatographic peak width optimized as described in claim 1 for area of computer aided condition of gradient elution,
It is characterized in that, the chromatographic peak width under different condition of gradient elution, chromatographic peak is calculated according to solvent strength model and theoretical cam curve
Width is by the way that (1) formula substitution following formula is calculated
Wherein WGFor the chromatographic peak width under condition of gradient elution, t0For the dead time, N is theoretical cam curve, tDWhen postponing for gradient
Between, tRFor retention time,For initial flow phase composition, Φ (t) be the flowing phase composition set in transfusion system at any time
The Gradient program of variation, kΦ(t)To flow retention factors when phase composition is Φ (t),It is solute in liquid phase
Retention factors,Corresponding retention factors during for solute outflow chromatographic column.
3. the computational methods of the chromatographic peak width optimized as described in claim 1 for area of computer aided condition of gradient elution,
It is characterized in that, is calculated under different condition of gradient elution according to the peak width variation model under solvent strength model and isocratic condition
Chromatographic peak width, chromatographic peak width is calculated by the way that (1) formula and (2) formula are substituted into following formula
Wherein WGFor the chromatographic peak width under condition of gradient elution, t0For dead time, tDFor gradient delay time, tRFor retention time,For initial flow phase composition, Φ (t) is the flowing phase composition time-varying gradient program set in transfusion system,
WI,Φ(t)To flow chromatographic peak width when phase composition is Φ (t) under isocratic condition,For mobile phase under isocratic condition
It forms and isWhen chromatographic peak width, kΦ(t)To flow retention factors when phase composition is Φ (t),It is solute in liquid phase
In retention factors,Corresponding retention factors during for solute outflow chromatographic column.
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